Finite Group Databasebeta

← #10974354

Subgroups — #10974354

Order 768.

2802 conjugacy classes of subgroups.

The subgroup lattice has 1714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#520C211yesmaximal, characteristic, complemented
2C2×#5547C211yesmaximal, characteristic, complemented
3#84096C211yesmaximal, characteristic, complemented
4#84091C211yesmaximal, characteristic, complemented
5#82502C211yesmaximal, characteristic, complemented
6#82501C211yesmaximal, characteristic, complemented
7#82498C211yesmaximal, characteristic, complemented
8#82497C211yesmaximal, characteristic, complemented
9#82419C211yesmaximal, characteristic, complemented
10#82410C211yesmaximal, characteristic, complemented
11#82407C211yesmaximal, characteristic, complemented
12#82404C211yesmaximal, characteristic, complemented
13#82402C211yesmaximal, characteristic, complemented
14C4×#937C211yesmaximal, characteristic, complemented
15#82364C211yesmaximal, characteristic, complemented
16#82360C211yesmaximal, characteristic, complemented
17#82356C211yesmaximal, characteristic, complemented
18#82327C211yesmaximal, characteristic, complemented
19#82324C211yesmaximal, characteristic, complemented
20#82285C211yesmaximal, characteristic, complemented
21#82284C211yesmaximal, characteristic, complemented
22#82280C211yesmaximal, characteristic, complemented
23#82278C211yesmaximal, characteristic, complemented
24#82275C211yesmaximal, characteristic, complemented
25#82247C211yesmaximal, characteristic, complemented
26#82198C211yesmaximal, characteristic, complemented
27#82195C211yesmaximal, characteristic, complemented
28#82192C211yesmaximal, characteristic, complemented
29C2×#4989C211yesmaximal, characteristic, complemented
30#82173C211yesmaximal, characteristic, complemented
31#82158C211yesmaximal, characteristic, complemented
32#35353—31nomaximal, Sylow
33C22×C3×#41C2211yescharacteristic
34C22×#235C2211yescharacteristic
35C23×C4×D3C2211yescharacteristic
36C3×#520—28no—
37C2×C3×C4×Q8C2211yescharacteristic, complemented
38C2×C3×C4×Q8C2211yescharacteristic, complemented
39C2×C3×C4×D4C2211yescharacteristic
40C2×C3×C4×D4C2211yescharacteristic
41C2×C3×C4×D4C2211yescharacteristic
42C2×C3×C4×D4C2211yescharacteristic
43C2×C3×C4×D4C2211yescharacteristic, complemented
44C2×C3×C4×D4C2211yescharacteristic, complemented
45C2×C3×#117C2211yescharacteristic
46C2×C3×#117C2211yescharacteristic, complemented
47C2×C3×#117C2211yescharacteristic, complemented
48C22×C3×C4⋊C4C2211yescharacteristic
49C22×C3×C4⋊C4C2211yescharacteristic, complemented
50C22×C3×C4⋊C4C2211yescharacteristic, complemented
51C2×#939C2211yescharacteristic
52C2×#939C2211yescharacteristic
53C2×#937C2211yescharacteristic
54C2×#937C2211yescharacteristic
55C2×#930C2211yescharacteristic
56C2×#929C2211yescharacteristic
57C2×#929C2211yescharacteristic
58C2×#929C2211yescharacteristic, complemented
59C2×C4×#67C2211yescharacteristic
60C2×C4×#67C2211yescharacteristic
61C2×C4×#67C2211yescharacteristic
62C2×C4×#67C2211yescharacteristic
63C22×(C2×D3)⋊C4C2211yescharacteristic
64C22×(C2×D3)⋊C4C2211yescharacteristic
65C2×#924C2211yescharacteristic, complemented
66C22×Dic3⋊C4C2211yescharacteristic
67#5547—28no—
68C2×#896C2211yescharacteristic
69C2×#894C2211yescharacteristic
70C2×#884C2211yescharacteristic
71C2×#883C2211yescharacteristic
72C2×#882C2211yescharacteristic
73C2×#878C2211yescharacteristic
74C2×C4×D12C2211yescharacteristic
75C2×#872C2211yescharacteristic
76#5231C2211yescharacteristic
77#5231C2211yescharacteristic
78#5231C2211yescharacteristic, complemented
79#5230C2211yescharacteristic, complemented
80#5223C2211yescharacteristic
81#5223C2211yescharacteristic
82#5223C2211yescharacteristic, complemented
83#5222C2211yescharacteristic, complemented
84#5220C2211yescharacteristic
85#5220C2211yescharacteristic
86#5220C2211yescharacteristic
87#5220C2211yescharacteristic
88#5213C2211yescharacteristic
89#5213C2211yescharacteristic
90#5213C2211yescharacteristic
91#5213C2211yescharacteristic
92#5213C2211yescharacteristic
93#5213C2211yescharacteristic
94#5213C2211yescharacteristic
95#5213C2211yescharacteristic, complemented
96#5213C2211yescharacteristic, complemented
97#5213C2211yescharacteristic, complemented
98#5212C2211yescharacteristic, complemented
99#5211C2211yescharacteristic
100#5211C2211yescharacteristic, complemented
101#5210C2211yescharacteristic
102#5210C2211yescharacteristic, complemented
103#5210C2211yescharacteristic, complemented
104#5210C2211yescharacteristic, complemented
105#5210C2211yescharacteristic, complemented
106#5210C2211yescharacteristic, complemented
107C4×#217C2211yescharacteristic
108C2×C3⋊#95C2211yescharacteristic
109C2×C3⋊#95C2211yescharacteristic
110#4994C2211yescharacteristic
111#4994C2211yescharacteristic
112#4994C2211yescharacteristic
113#4993C2211yescharacteristic
114#4993C2211yescharacteristic, complemented
115#4992C2211yescharacteristic
116#4991C2211yescharacteristic
117#4991C2211yescharacteristic
118#4991C2211yescharacteristic
119#4990C2211yescharacteristic, complemented
120#4990C2211yescharacteristic, complemented
121#4989C2211yescharacteristic
122#4989C2211yescharacteristic
123#4989C2211yescharacteristic
124#4989C2211yescharacteristic
125#4989C2211yescharacteristic
126#4989C2211yescharacteristic
127#4989C2211yescharacteristic
128#4989C2211yescharacteristic
129#4989C2211yescharacteristic
130#4989C2211yescharacteristic
131#4989C2211yescharacteristic, complemented
132#4989C2211yescharacteristic, complemented
133#4989C2211yescharacteristic, complemented
134#4986C2211yescharacteristic, complemented
135#4983C2211yescharacteristic, complemented
136#4982C2211yescharacteristic, complemented
137#4982C2211yescharacteristic, complemented
138#4982C2211yescharacteristic, complemented
139#4980C2211yescharacteristic, complemented
140#4980C2211yescharacteristic, complemented
141#4979C2211yescharacteristic, complemented
142#4979C2211yescharacteristic, complemented
143#4978C2211yescharacteristic, complemented
144#4978C2211yescharacteristic, complemented
145#4978C2211yescharacteristic, complemented
146#4976C2211yescharacteristic, complemented
147#4976C2211yescharacteristic, complemented
148#4961C2211yescharacteristic
149#4960C2211yescharacteristic
150#4959C2211yescharacteristic
151#4959C2211yescharacteristic
152#4959C2211yescharacteristic, complemented
153#4958C2211yescharacteristic
154#4956C2211yescharacteristic
155#4956C2211yescharacteristic
156#4956C2211yescharacteristic, complemented
157#4955C2211yescharacteristic
158#4952C2211yescharacteristic, complemented
159#4951C2211yescharacteristic, complemented
160#4951C2211yescharacteristic, complemented
161#4950C2211yescharacteristic
162#4950C2211yescharacteristic
163#4949C2211yescharacteristic, complemented
164#4948C2211yescharacteristic, complemented
165#4946C2211yescharacteristic
166#4944C2211yescharacteristic, complemented
167#4942C2211yescharacteristic
168#4940C2211yescharacteristic
169#4940C2211yescharacteristic
170#4940C2211yescharacteristic
171#4940C2211yescharacteristic
172#4940C2211yescharacteristic
173#4940C2211yescharacteristic, complemented
174#4940C2211yescharacteristic, complemented
175#4939C2211yescharacteristic
176#4939C2211yescharacteristic
177#4939C2211yescharacteristic
178C4×(C2×D3)⋊C4C2211yescharacteristic
179C4×(C2×D3)⋊C4C2211yescharacteristic
180#4937C2211yescharacteristic, complemented
181#4936C2211yescharacteristic, complemented
182#4933C2211yescharacteristic, complemented
183#4933C2211yescharacteristic, complemented
184#4933C2211yescharacteristic, complemented
185#4933C2211yescharacteristic, complemented
186#4933C2211yescharacteristic, complemented
187#4929C2211yescharacteristic, complemented
188#4928C2211yescharacteristic, complemented
189#4928C2211yescharacteristic, complemented
190C2×#525—31no—
191C2×#520D311yescharacteristic, complemented
192#2609—31no—
193#2600—31no—
194#2599—31no—
195#2598—31no—
196#2580—31no—
197#2579—31no—
198#2476—31no—
199#2470—31no—
200#2465—31no—
201#2458—31no—
202#2456—31no—
203#2455—31no—
204#2449—31no—
205#2449—31no—
206#2443—31no—
207#2443—31no—
208#2438—31no—
209#2430—31no—
210#2424—31no—
211#2418—31no—
212#2411—31no—
213#2407—31no—
214#2406—31no—
215#2404—31no—
216#2325—31no—
217#2322—31no—
218#2318—31no—
219C4×#120—31no—
220C2×#385—31no—
221C24×D3C2311yescharacteristic
222C2×C3×#41—24no—
223C2×C3×#41—24no—
224C2×C3×#41—24no—
225C22×C3×Q8C2311yescharacteristic
226C22×C3×D4C2311yescharacteristic
227C22×C3×D4C2311yescharacteristic
228C22×C3×D4C2311yescharacteristic
229C23×C3×C4C2311yescharacteristic
230C23×C3×C4C2311yescharacteristic
231C23×C3×C4C2311yescharacteristic
232C23×C3×C4C2311yescharacteristic
233C23×C3×C4C2311yescharacteristic
234C23×C3×C4C2311yescharacteristic
235C23×C3×C4C2311yescharacteristic
236C23×C3×C4C2311yescharacteristic
237C23×C3×C4C2311yescharacteristic
238C22×#67C2311yescharacteristic
239C22×#67C2311yescharacteristic
240C22×#67C2311yescharacteristic
241C22×#67C2311yescharacteristic
242C22×#67C2311yescharacteristic
243C22×#67C2311yescharacteristic
244C22×#67C2311yescharacteristic
245C23×Dic3C2311yescharacteristic
246C23×Dic3C2311yescharacteristic
247C23×Dic3C2311yescharacteristic
248C2×#235—24no—
249C2×#235—42no—
250C2×#235—42no—
251C22×D12C2311yescharacteristic
252C22×D12C2311yescharacteristic
253C22×C4×D3—24no—
254C22×C4×D3—42no—
255C22×C4×D3—42no—
256C22×C4×D3C2311yescharacteristic
257C22×C4×D3C2311yescharacteristic
258C22×C4×D3C2311yescharacteristic
259C22×C4×D3C2311yescharacteristic
260C22×C4×D3C2311yescharacteristic
261C22×Dic6C2311yescharacteristic
262C3×C4×Q8—24no—
263C3×C4×Q8—24no—
264C3×C4×D4—24no—
265C3×C4×D4—24no—
266C3×C4×D4—24no—
267C3×C4×D4—24no—
268C3×C4×D4—24no—
269C3×C4×D4D418yescomplemented
270C3×#117—24no—
271C3×#117—24no—
272C3×#117—24no—
273C2×C3×C4⋊C4—24no—
274C2×C3×C4⋊C4—24no—
275C2×C3×C4⋊C4—24no—
276C2×C3×C4⋊C4C2311yescharacteristic
277C2×C3×C4⋊C4C2311yescharacteristic
278C2×C3×C4⋊C4C2311yescharacteristic
279C2×C3×C4⋊C4C2311yescharacteristic
280C2×C3×C4⋊C4C2311yescharacteristic
281C2×C3×C4⋊C4C2311yescharacteristic
282C2×C3×C4⋊C4C2311yescharacteristic
283C2×C3×C4⋊C4C2311yescharacteristic
284C2×C3×C4⋊C4C2311yescharacteristic
285C2×C3×C4⋊C4C2311yescharacteristic
286C2×C3×C22⋊C4C2311yescharacteristic
287C2×C3×C22⋊C4C2311yescharacteristic
288C2×C3×C22⋊C4C2311yescharacteristic
289C2×C3×C22⋊C4C2311yescharacteristic
290C2×C3×C22⋊C4C2311yescharacteristic
291C2×C3×C22⋊C4C2311yescharacteristic
292C2×C3×C42C2311yescharacteristic
293C2×C3×C42C2311yescharacteristic
294C2×C3×C42C2311yescharacteristic
295C2×C3×C42C2311yescharacteristic
296C2×C3×C42C2311yescharacteristic
297C2×C3×C42C2311yescharacteristic
298C2×#217C2311yescharacteristic
299C2×#217C2311yescharacteristic
300C2×#217C2311yescharacteristic
301C2×#217C2311yescharacteristic
302C2×#217C2311yescharacteristic
303C2×#217C2311yescharacteristic
304C2×#217C2311yescharacteristic
305C2×#217C2311yescharacteristic
306C2×#217C2311yescharacteristic
307C2×#217C2311yescharacteristic
308C2×#217C2311yescharacteristic
309C2×#217C2311yescharacteristic
310C2×#217C2311yescharacteristic
311#939—24no—
312#939—24no—
313#937—24no—
314#937—24no—
315#930—42no—
316#929—24no—
317#929—42no—
318#929—42no—
319C4×#67—24no—
320C4×#67—24no—
321C4×#67—42no—
322C4×#67—42no—
323C2×(C2×D3)⋊C4—24no—
324C2×(C2×D3)⋊C4—42no—
325C2×(C2×D3)⋊C4C2311yescharacteristic
326C2×(C2×D3)⋊C4C2311yescharacteristic
327C2×(C2×D3)⋊C4C2311yescharacteristic
328C2×(C2×D3)⋊C4C2311yescharacteristic
329C2×(C2×D3)⋊C4C2311yescharacteristic
330C2×(C2×D3)⋊C4C2311yescharacteristic
331C2×(C2×D3)⋊C4C2311yescharacteristic
332C2×(C2×D3)⋊C4C2311yescharacteristic
333C2×(C2×D3)⋊C4C2311yescharacteristic
334C2×(C2×D3)⋊C4C2311yescharacteristic
335C2×(C2×D3)⋊C4C2311yescharacteristic
336C2×(C2×D3)⋊C4C2311yescharacteristic
337C2×(C2×D3)⋊C4C2311yescharacteristic
338C2×(C2×D3)⋊C4C2311yescharacteristic
339C2×(C2×D3)⋊C4C2311yescharacteristic
340C2×(C2×D3)⋊C4C2311yescharacteristic
341C2×(C2×D3)⋊C4C2311yescharacteristic
342C2×(C2×D3)⋊C4C2311yescharacteristic
343C2×(C2×D3)⋊C4C2311yescharacteristic
344C2×(C2×D3)⋊C4C2311yescharacteristic
345C2×(C2×D3)⋊C4C2311yescharacteristic
346C2×(C2×D3)⋊C4C2311yescharacteristic
347C2×(C2×D3)⋊C4C2311yescharacteristic
348C2×(C2×D3)⋊C4C2311yescharacteristic
349C2×(C2×D3)⋊C4C2311yescharacteristic
350C2×(C2×D3)⋊C4C2311yescharacteristic
351C2×(C2×D3)⋊C4C2311yescharacteristic
352C2×C4⋊Dic3C2311yescharacteristic
353C2×C4⋊Dic3C2311yescharacteristic
354C2×C4⋊Dic3C2311yescharacteristic
355C2×C4⋊Dic3C2311yescharacteristic
356C2×C4⋊Dic3C2311yescharacteristic
357#924—42no—
358C2×Dic3⋊C4—42no—
359C2×Dic3⋊C4C2311yescharacteristic
360C2×Dic3⋊C4C2311yescharacteristic
361C2×Dic3⋊C4C2311yescharacteristic
362C2×Dic3⋊C4C2311yescharacteristic
363C2×Dic3⋊C4C2311yescharacteristic
364C2×Dic3⋊C4C2311yescharacteristic
365C2×Dic3⋊C4C2311yescharacteristic
366C2×Dic3⋊C4C2311yescharacteristic
367C2×Dic3⋊C4C2311yescharacteristic
368C2×Dic3⋊C4C2311yescharacteristic
369C2×Dic3⋊C4C2311yescharacteristic
370C2×Dic3⋊C4C2311yescharacteristic
371C2×Dic3⋊C4C2311yescharacteristic
372C2×Dic3⋊C4C2311yescharacteristic
373C2×Dic3⋊C4C2311yescharacteristic
374C2×Dic3⋊C4C2311yescharacteristic
375C2×Dic3⋊C4C2311yescharacteristic
376C2×C4×Dic3C2311yescharacteristic
377C2×C4×Dic3C2311yescharacteristic
378C2×C4×Dic3C2311yescharacteristic
379#896—24no—
380#894—24no—
381#884—24no—
382#883—24no—
383#882—24no—
384#878—24no—
385C4×D12—24no—
386#872—24no—
387C3⋊#95C2311yescharacteristic
388C3⋊#95C2311yescharacteristic
389C3⋊#95C2311yescharacteristic
390C3⋊#95C2311yescharacteristic
391C3⋊#95C2311yescharacteristic
392C3⋊#95C2311yescharacteristic
393C3⋊#95C2311yescharacteristic
394C3⋊#95C2311yescharacteristic
395C3⋊#95C2311yescharacteristic
396C3⋊#95C2311yescharacteristic
397C3⋊#95C2311yescharacteristic
398C3⋊#95C2311yescharacteristic
399C3⋊#95C2311yescharacteristic
400C3⋊#95C2311yescharacteristic
401C3⋊#95C2311yescharacteristic
402C3⋊#95C2311yescharacteristic
403C3⋊#95C2311yescharacteristic
404C3⋊#95C2311yescharacteristic
405C3⋊#95C2311yescharacteristic
406C3⋊#95C2311yescharacteristic
407C3⋊#95C2311yescharacteristic
408C3⋊#95C2311yescharacteristic
409C3⋊#95C2311yescharacteristic
410C3⋊#95C2311yescharacteristic
411C3⋊#95C2311yescharacteristic
412C3⋊#95C2311yescharacteristic
413C3⋊#95C2311yescharacteristic
414C3⋊#95C2311yescharacteristic
415C3⋊#95C2311yescharacteristic
416C3⋊#95C2311yescharacteristic
417C3⋊#95C2311yescharacteristic
418C3⋊#95C2311yescharacteristic
419C3⋊#95C2311yescharacteristic
420C3⋊#95C2311yescharacteristic
421C3⋊#95C2311yescharacteristic
422C3⋊#95C2311yescharacteristic
423C22×#41—31no—
424C22×#41C2×D311yescharacteristic
425C24×C4—31no—
426#525—68no—
427C2×#123—31no—
428C2×#123—31no—
429C2×#123—31no—
430C2×#123—31no—
431C2×#123—31no—
432C2×C22⋊Q8—31no—
433C2×C22⋊Q8—31no—
434C2×C22⋊Q8—31no—
435C2×#121—31no—
436C2×#121—31no—
437C2×#121—31no—
438C2×#121—31no—
439C2×#120—31no—
440C2×#120—31no—
441C2×#120—31no—
442#520—28no—
443C2×C4×Q8C2×D311yescharacteristic, complemented
444C2×C4×Q8C2×D311yescharacteristic, complemented
445C2×C4×D4—31no—
446C2×C4×D4—31no—
447C2×C4×D4—31no—
448C2×C4×D4—31no—
449C2×C4×D4—31no—
450C2×C4×D4C2×D311yescharacteristic
451C2×C4×D4C2×D311yescharacteristic
452C2×C4×D4C2×D311yescharacteristic
453C2×C4×D4C2×D311yescharacteristic
454C2×C4×D4C2×D311yescharacteristic, complemented
455C2×C4×D4C2×D311yescharacteristic, complemented
456C2×#117—31no—
457C2×#117C2×D311yescharacteristic
458C2×#117C2×D311yescharacteristic, complemented
459C2×#117C2×D311yescharacteristic, complemented
460C22×C4⋊C4—31no—
461C22×C4⋊C4C2×D311yescharacteristic
462C22×C4⋊C4C2×D311yescharacteristic, complemented
463C22×C4⋊C4C2×D311yescharacteristic, complemented
464C22×C22⋊C4—31no—
465C22×C22⋊C4—31no—
466#400—31no—
467#399—31no—
468#399—31no—
469#399—31no—
470#398—31no—
471#398—31no—
472#398—31no—
473#398—31no—
474#397—31no—
475#397—31no—
476#396—31no—
477#396—31no—
478#396—31no—
479#396—31no—
480#395—31no—
481#395—31no—
482#395—31no—
483#394—31no—
484#394—31no—
485#394—31no—
486#394—31no—
487#394—31no—
488#394—31no—
489#394—31no—
490#394—31no—
491#393—31no—
492#393—31no—
493#393—31no—
494#392—31no—
495#392—31no—
496#392—31no—
497#392—31no—
498#391—31no—
499#390—31no—
500#390—31no—
501#390—31no—
502#389—31no—
503#389—31no—
504#389—31no—
505#389—31no—
506#388—31no—
507#388—31no—
508#388—31no—
509#388—31no—
510#388—31no—
511#388—31no—
512#388—31no—
513#388—31no—
514#388—31no—
515#388—31no—
516#388—31no—
517#388—31no—
518#387—31no—
519#387—31no—
520#387—31no—
521#387—31no—
522#387—31no—
523#387—31no—
524#387—31no—
525#387—31no—
526#387—31no—
527#387—31no—
528#386—31no—
529#386—31no—
530#386—31no—
531#386—31no—
532#386—31no—
533#386—31no—
534#386—31no—
535#386—31no—
536#386—31no—
537#386—31no—
538#386—31no—
539#386—31no—
540#386—31no—
541#386—31no—
542#386—31no—
543#386—31no—
544#386—31no—
545#386—31no—
546#385—31no—
547#385—31no—
548#385—31no—
549#385—31no—
550#385—31no—
551#385—31no—
552#385—31no—
553#385—31no—
554#385—31no—
555#385—31no—
556#385—31no—
557#385—31no—
558#385—31no—
559#385—31no—
560#385—31no—
561#385—31no—
562#385—31no—
563#385—31no—
564#385—31no—
565#385—31no—
566#385—31no—
567#385—31no—
568#383—31no—
569#382—31no—
570#381—31no—
571#381—31no—
572#380—31no—
573#380—31no—
574#379—31no—
575C4×C22⋊C4—31no—
576C4×C22⋊C4—31no—
577C4×C22⋊C4—31no—
578C2×#95—31no—
579C2×#95—31no—
580C24×C3C2411yescharacteristic
581C24×C3C2411yescharacteristic
582C24×C3C2411yescharacteristic
583C23×D3—22no—
584C23×D3—22no—
585C23×D3—22no—
586C23×D3—22no—
587C23×D3—22no—
588C23×D3—41no—
589C23×D3—41no—
590C23×D3C2411yescharacteristic
591C23×D3C2411yescharacteristic
592C23×D3C2411yescharacteristic
593C3×#41—232no—
594C2×C3×Q8—22no—
595C2×C3×Q8—22no—
596C2×C3×Q8—22no—
597C2×C3×D4—22no—
598C2×C3×D4—22no—
599C2×C3×D4—22no—
600C2×C3×D4—22no—
601C2×C3×D4—22no—
602C2×C3×D4—22no—
603C2×C3×D4—22no—
604C2×C3×D4C2×D414yes—
605C2×C3×D4#4114yescomplemented
606C22×C3×C4—22no—
607C22×C3×C4—22no—
608C22×C3×C4—22no—
609C22×C3×C4—22no—
610C22×C3×C4—22no—
611C22×C3×C4—22no—
612C22×C3×C4—22no—
613C22×C3×C4—22no—
614C22×C3×C4—22no—
615C22×C3×C4—22no—
616C22×C3×C4—22no—
617C22×C3×C4—22no—
618C22×C3×C4—41no—
619C22×C3×C4—41no—
620C22×C3×C4—41no—
621C22×C3×C4—41no—
622C22×C3×C4—41no—
623C22×C3×C4—41no—
624C22×C3×C4—41no—
625C22×C3×C4—41no—
626C22×C3×C4—41no—
627C22×C3×C4—41no—
628C22×C3×C4—41no—
629C22×C3×C4—41no—
630C22×C3×C4C2×D414yes—
631C22×C3×C4C2×D414yes—
632C22×C3×C4#4114yescomplemented
633C22×C3×C4C2411yescharacteristic
634C22×C3×C4C2411yescharacteristic
635C22×C3×C4C2411yescharacteristic
636C22×C3×C4C2411yescharacteristic
637C22×C3×C4C2411yescharacteristic
638C22×C3×C4C2411yescharacteristic
639C22×C3×C4C2411yescharacteristic
640C22×C3×C4C2411yescharacteristic
641C22×C3×C4C2411yescharacteristic
642C22×C3×C4C2411yescharacteristic
643C22×C3×C4C2411yescharacteristic
644C22×C3×C4C2411yescharacteristic
645C2×#67—22no—
646C2×#67—22no—
647C2×#67—22no—
648C2×#67—22no—
649C2×#67—22no—
650C2×#67—22no—
651C2×#67—22no—
652C2×#67—22no—
653C2×#67—22no—
654C2×#67—22no—
655C2×#67—22no—
656C2×#67—22no—
657C2×#67—22no—
658C2×#67—22no—
659C2×#67—41no—
660C2×#67—41no—
661C2×#67—41no—
662C2×#67—41no—
663C2×#67—41no—
664C2×#67—41no—
665C2×#67—41no—
666C22×Dic3—22no—
667C22×Dic3—22no—
668C22×Dic3—22no—
669C22×Dic3—22no—
670C22×Dic3—41no—
671C22×Dic3—41no—
672C22×Dic3—41no—
673C22×Dic3—41no—
674C22×Dic3—41no—
675C22×Dic3C2411yescharacteristic
676C22×Dic3C2411yescharacteristic
677C22×Dic3C2411yescharacteristic
678C22×Dic3C2411yescharacteristic
679C22×Dic3C2411yescharacteristic
680C22×Dic3C2411yescharacteristic
681C22×Dic3C2411yescharacteristic
682C22×Dic3C2411yescharacteristic
683C22×Dic3C2411yescharacteristic
684C22×Dic3C2411yescharacteristic
685C22×Dic3C2411yescharacteristic
686C22×Dic3C2411yescharacteristic
687C22×Dic3C2411yescharacteristic
688#235—416no—
689C2×D12—22no—
690C2×D12—22no—
691C2×D12—22no—
692C2×D12—22no—
693C2×D12—41no—
694C2×D12—41no—
695C2×C4×D3—22no—
696C2×C4×D3—22no—
697C2×C4×D3—22no—
698C2×C4×D3—22no—
699C2×C4×D3—22no—
700C2×C4×D3—22no—
701C2×C4×D3—22no—
702C2×C4×D3—22no—
703C2×C4×D3—22no—
704C2×C4×D3—416no—
705C2×C4×D3—41no—
706C2×C4×D3—41no—
707C2×C4×D3—41no—
708C2×C4×D3—41no—
709C2×C4×D3—41no—
710C2×C4×D3—41no—
711C2×Dic6—22no—
712C2×Dic6—22no—
713C2×Dic6—41no—
714C3×C4⋊C4—22no—
715C3×C4⋊C4—22no—
716C3×C4⋊C4—22no—
717C3×C4⋊C4—22no—
718C3×C4⋊C4—22no—
719C3×C4⋊C4—22no—
720C3×C4⋊C4—22no—
721C3×C4⋊C4—22no—
722C3×C4⋊C4—22no—
723C3×C4⋊C4C2×D414yes—
724C3×C22⋊C4—22no—
725C3×C22⋊C4—22no—
726C3×C22⋊C4—22no—
727C3×C22⋊C4—22no—
728C3×C22⋊C4C2×D414yes—
729C3×C22⋊C4C2×D414yes—
730C3×C42—22no—
731C3×C42—22no—
732C3×C42—22no—
733C3×C42—22no—
734C3×C42—22no—
735C3×C42C2×D414yes—
736#217—22no—
737#217—22no—
738#217—22no—
739#217—22no—
740#217—22no—
741#217—22no—
742#217—41no—
743#217—41no—
744#217—41no—
745#217—41no—
746#217—41no—
747#217—41no—
748#217—41no—
749(C2×D3)⋊C4—22no—
750(C2×D3)⋊C4—22no—
751(C2×D3)⋊C4—22no—
752(C2×D3)⋊C4—22no—
753(C2×D3)⋊C4—22no—
754(C2×D3)⋊C4—22no—
755(C2×D3)⋊C4—22no—
756(C2×D3)⋊C4—22no—
757(C2×D3)⋊C4—22no—
758(C2×D3)⋊C4—22no—
759(C2×D3)⋊C4—22no—
760(C2×D3)⋊C4—22no—
761(C2×D3)⋊C4—22no—
762(C2×D3)⋊C4—22no—
763(C2×D3)⋊C4—22no—
764(C2×D3)⋊C4—22no—
765(C2×D3)⋊C4—22no—
766(C2×D3)⋊C4—22no—
767(C2×D3)⋊C4—22no—
768(C2×D3)⋊C4—41no—
769(C2×D3)⋊C4—41no—
770(C2×D3)⋊C4—41no—
771(C2×D3)⋊C4—41no—
772(C2×D3)⋊C4—41no—
773(C2×D3)⋊C4—41no—
774(C2×D3)⋊C4—41no—
775(C2×D3)⋊C4—41no—
776C4⋊Dic3—22no—
777C4⋊Dic3—41no—
778C4⋊Dic3—41no—
779C4⋊Dic3—41no—
780C4⋊Dic3—41no—
781Dic3⋊C4—22no—
782Dic3⋊C4—22no—
783Dic3⋊C4—22no—
784Dic3⋊C4—22no—
785Dic3⋊C4—22no—
786Dic3⋊C4—22no—
787Dic3⋊C4—22no—
788Dic3⋊C4—22no—
789Dic3⋊C4—22no—
790Dic3⋊C4—22no—
791Dic3⋊C4—41no—
792Dic3⋊C4—41no—
793Dic3⋊C4—41no—
794Dic3⋊C4—41no—
795Dic3⋊C4—41no—
796Dic3⋊C4—41no—
797Dic3⋊C4—41no—
798C4×Dic3—22no—
799C4×Dic3—41no—
800C4×Dic3—41no—
801C25—31no—
802C2×#41—24no—
803C2×#41—24no—
804C2×#41—24no—
805C2×#41—64no—
806C2×#41—122no—
807C2×#41—122no—
808C22×Q8—31no—
809C22×Q8C22×D311yescharacteristic
810C22×D4—31no—
811C22×D4—31no—
812C22×D4—31no—
813C22×D4—31no—
814C22×D4—31no—
815C22×D4—31no—
816C22×D4—31no—
817C22×D4—31no—
818C22×D4—31no—
819C22×D4C22×D311yescharacteristic
820C22×D4C22×D311yescharacteristic
821C22×D4C22×D311yescharacteristic
822C23×C4—31no—
823C23×C4—31no—
824C23×C4—31no—
825C23×C4—31no—
826C23×C4—31no—
827C23×C4—31no—
828C23×C4—31no—
829C23×C4—31no—
830C23×C4—64no—
831C23×C4—122no—
832C23×C4—122no—
833C23×C4C22×D311yescharacteristic
834C23×C4C22×D311yescharacteristic
835C23×C4C22×D311yescharacteristic
836C23×C4C22×D311yescharacteristic
837C23×C4C22×D311yescharacteristic
838C23×C4C22×D311yescharacteristic
839C23×C4C22×D311yescharacteristic
840C23×C4C22×D311yescharacteristic
841C23×C4C22×D311yescharacteristic
842#123—64no—
843#123—64no—
844#123—64no—
845#123—122no—
846#123—122no—
847C22⋊Q8—64no—
848C22⋊Q8—64no—
849C22⋊Q8—122no—
850#121—64no—
851#121—64no—
852#121—64no—
853#121—122no—
854#120—64no—
855#120—64no—
856#120—64no—
857C4×Q8—24no—
858C4×Q8—24no—
859C4×D4—24no—
860C4×D4—24no—
861C4×D4—24no—
862C4×D4—24no—
863C4×D4—24no—
864C4×D4—64no—
865C4×D4—64no—
866C4×D4—64no—
867C4×D4—122no—
868C4×D4—122no—
869C4×D4#6718yescomplemented
870#117—24no—
871#117—24no—
872#117—24no—
873#117—64no—
874C2×C4⋊C4—24no—
875C2×C4⋊C4—24no—
876C2×C4⋊C4—24no—
877C2×C4⋊C4—31no—
878C2×C4⋊C4—31no—
879C2×C4⋊C4—31no—
880C2×C4⋊C4—31no—
881C2×C4⋊C4—31no—
882C2×C4⋊C4—31no—
883C2×C4⋊C4—31no—
884C2×C4⋊C4—31no—
885C2×C4⋊C4—31no—
886C2×C4⋊C4—31no—
887C2×C4⋊C4—31no—
888C2×C4⋊C4—31no—
889C2×C4⋊C4—31no—
890C2×C4⋊C4—31no—
891C2×C4⋊C4—31no—
892C2×C4⋊C4—31no—
893C2×C4⋊C4—31no—
894C2×C4⋊C4—31no—
895C2×C4⋊C4—31no—
896C2×C4⋊C4—31no—
897C2×C4⋊C4—31no—
898C2×C4⋊C4—31no—
899C2×C4⋊C4—122no—
900C2×C4⋊C4C22×D311yescharacteristic
901C2×C4⋊C4C22×D311yescharacteristic
902C2×C4⋊C4C22×D311yescharacteristic
903C2×C4⋊C4C22×D311yescharacteristic
904C2×C4⋊C4C22×D311yescharacteristic
905C2×C4⋊C4C22×D311yescharacteristic
906C2×C4⋊C4C22×D311yescharacteristic
907C2×C4⋊C4C22×D311yescharacteristic
908C2×C4⋊C4C22×D311yescharacteristic
909C2×C4⋊C4C22×D311yescharacteristic
910C2×C22⋊C4—31no—
911C2×C22⋊C4—31no—
912C2×C22⋊C4—31no—
913C2×C22⋊C4—31no—
914C2×C22⋊C4—31no—
915C2×C22⋊C4—31no—
916C2×C22⋊C4—31no—
917C2×C22⋊C4—31no—
918C2×C22⋊C4—31no—
919C2×C22⋊C4—31no—
920C2×C22⋊C4—31no—
921C2×C22⋊C4—31no—
922C2×C22⋊C4—31no—
923C2×C22⋊C4—31no—
924C2×C22⋊C4—31no—
925C2×C22⋊C4—31no—
926C2×C22⋊C4—31no—
927C2×C22⋊C4—31no—
928C2×C22⋊C4—31no—
929C2×C22⋊C4—31no—
930C2×C22⋊C4—31no—
931C2×C22⋊C4—31no—
932C2×C22⋊C4—31no—
933C2×C22⋊C4—31no—
934C2×C22⋊C4—31no—
935C2×C22⋊C4—31no—
936C2×C22⋊C4—31no—
937C2×C22⋊C4—31no—
938C2×C22⋊C4—31no—
939C2×C22⋊C4—31no—
940C2×C22⋊C4—31no—
941C2×C22⋊C4—31no—
942C2×C22⋊C4—31no—
943C2×C22⋊C4—31no—
944C2×C22⋊C4—31no—
945C2×C22⋊C4—31no—
946C2×C22⋊C4—31no—
947C2×C22⋊C4—31no—
948C2×C22⋊C4—31no—
949C2×C22⋊C4—31no—
950C2×C22⋊C4—64no—
951C2×C22⋊C4—122no—
952C2×C22⋊C4C22×D311yescharacteristic
953C2×C22⋊C4C22×D311yescharacteristic
954C2×C22⋊C4C22×D311yescharacteristic
955C2×C22⋊C4C22×D311yescharacteristic
956C2×C22⋊C4C22×D311yescharacteristic
957C2×C22⋊C4C22×D311yescharacteristic
958C2×C42—31no—
959C2×C42—31no—
960C2×C42—31no—
961C2×C42C22×D311yescharacteristic
962C2×C42C22×D311yescharacteristic
963C2×C42C22×D311yescharacteristic
964C2×C42C22×D311yescharacteristic
965C2×C42C22×D311yescharacteristic
966C2×C42C22×D311yescharacteristic
967#95—31no—
968#95—31no—
969#95—31no—
970#95—31no—
971#95—31no—
972#95—31no—
973#95—31no—
974#95—31no—
975#95—31no—
976#95—31no—
977#95—31no—
978#95—31no—
979#95—31no—
980#95—31no—
981#95—31no—
982#95—31no—
983#95—31no—
984#95—31no—
985#95—31no—
986#95—31no—
987#95—31no—
988#95—31no—
989#95—31no—
990#95—31no—
991#95—31no—
992#95—31no—
993#95—31no—
994#95—31no—
995#95—31no—
996#95—31no—
997#95—31no—
998#95—31no—
999#95—31no—
1000#95—31no—
1001#95—31no—
1002#95—31no—
1003C23×C3—21no—
1004C23×C3—21no—
1005C23×C3—21no—
1006C23×C3—21no—
1007C23×C3—21no—
1008C23×C3—21no—
1009C23×C3—21no—
1010C23×C3—21no—
1011C23×C3—21no—
1012C23×C3—21no—
1013C23×C3—21no—
1014C23×C3—21no—
1015C23×C3—21no—
1016C23×C3—21no—
1017C23×C3—21no—
1018C23×C3—21no—
1019C23×C3C22×D412yes—
1020C23×C3C22×D412yes—
1021C23×C3C2×#4112yes—
1022C23×C3C2×#4112yes—
1023C23×C3C2×#4112yes—
1024C23×C3C2511yescharacteristic
1025C22×D3—28no—
1026C22×D3—21no—
1027C22×D3—21no—
1028C22×D3—21no—
1029C22×D3—21no—
1030C22×D3—21no—
1031C22×D3—21no—
1032C22×D3—21no—
1033C22×D3—21no—
1034C22×D3—21no—
1035C22×D3—21no—
1036C22×D3—21no—
1037C22×D3—21no—
1038C22×D3—21no—
1039C22×D3—21no—
1040C22×D3—21no—
1041C22×D3—21no—
1042C22×D3—21no—
1043C22×D3—21no—
1044C22×D3—21no—
1045C22×D3—44no—
1046C22×D3—44no—
1047C22×D3—44no—
1048C22×D3—44no—
1049C22×D3—44no—
1050C22×D3—44no—
1051C22×D3H(5,𝔽2)12yes—
1052C22×D32−1+412yes—
1053C3×Q8—28no—
1054C3×D4—28no—
1055C3×D4—28no—
1056C3×D4—28no—
1057C2×C3×C4—28no—
1058C2×C3×C4—28no—
1059C2×C3×C4—28no—
1060C2×C3×C4—21no—
1061C2×C3×C4—21no—
1062C2×C3×C4—21no—
1063C2×C3×C4—21no—
1064C2×C3×C4—21no—
1065C2×C3×C4—21no—
1066C2×C3×C4—21no—
1067C2×C3×C4—21no—
1068C2×C3×C4—21no—
1069C2×C3×C4—21no—
1070C2×C3×C4—21no—
1071C2×C3×C4—21no—
1072C2×C3×C4—21no—
1073C2×C3×C4—21no—
1074C2×C3×C4—21no—
1075C2×C3×C4—21no—
1076C2×C3×C4—21no—
1077C2×C3×C4—21no—
1078C2×C3×C4—21no—
1079C2×C3×C4—21no—
1080C2×C3×C4—21no—
1081C2×C3×C4—21no—
1082C2×C3×C4—21no—
1083C2×C3×C4—21no—
1084C2×C3×C4—21no—
1085C2×C3×C4—21no—
1086C2×C3×C4—21no—
1087C2×C3×C4—21no—
1088C2×C3×C4—44no—
1089C2×C3×C4—44no—
1090C2×C3×C4—82no—
1091C2×C3×C4—82no—
1092C2×C3×C4—82no—
1093C2×C3×C4—82no—
1094C2×C3×C4C22×D412yes—
1095C2×C3×C4C22×D412yes—
1096C2×C3×C4C22×D412yes—
1097C2×C3×C4C22×D412yes—
1098C2×C3×C4C22×D412yes—
1099C2×C3×C4C2×#4112yes—
1100C2×C3×C4C2×#4112yes—
1101C2×C3×C4C2×#4112yes—
1102#67—44no—
1103#67—44no—
1104#67—44no—
1105#67—44no—
1106#67—44no—
1107#67—44no—
1108#67—82no—
1109C2×Dic3—21no—
1110C2×Dic3—21no—
1111C2×Dic3—21no—
1112C2×Dic3—21no—
1113C2×Dic3—21no—
1114C2×Dic3—21no—
1115C2×Dic3—21no—
1116C2×Dic3—21no—
1117C2×Dic3—21no—
1118C2×Dic3—21no—
1119C2×Dic3—21no—
1120C2×Dic3—21no—
1121C2×Dic3—21no—
1122C2×Dic3—21no—
1123C2×Dic3—21no—
1124C2×Dic3—21no—
1125C2×Dic3—21no—
1126C2×Dic3—21no—
1127C2×Dic3—21no—
1128C2×Dic3—21no—
1129C2×Dic3—21no—
1130C2×Dic3—21no—
1131C2×Dic3—21no—
1132C2×Dic3—21no—
1133C2×Dic3—21no—
1134C2×Dic3—21no—
1135C2×Dic3—21no—
1136C2×Dic3—21no—
1137C2×Dic3—21no—
1138C2×Dic3—21no—
1139C2×Dic3—21no—
1140C2×Dic3—21no—
1141C2×Dic3—21no—
1142C2×Dic3—21no—
1143C2×Dic3—21no—
1144C2×Dic3—21no—
1145C2×Dic3—21no—
1146C2×Dic3—21no—
1147C2×Dic3—44no—
1148C2×Dic3—44no—
1149C2×Dic3—82no—
1150C2×Dic3H(5,𝔽2)12yes—
1151D12—44no—
1152D12—44no—
1153C4×D3—28no—
1154C4×D3—44no—
1155C4×D3—44no—
1156C4×D3—44no—
1157C4×D3—44no—
1158Dic6—44no—
1159C24—31no—
1160C24—31no—
1161C24—31no—
1162C24—62no—
1163C24—62no—
1164C24—62no—
1165C24—62no—
1166C24—62no—
1167C24—121no—
1168C24—121no—
1169C24C23×D311yescharacteristic
1170C24C23×D311yescharacteristic
1171C24C23×D311yescharacteristic
1172#41—232no—
1173#41—1216no—
1174C2×Q8—22no—
1175C2×Q8—22no—
1176C2×Q8—22no—
1177C2×Q8—62no—
1178C2×Q8—62no—
1179C2×Q8—121no—
1180C2×D4—22no—
1181C2×D4—22no—
1182C2×D4—22no—
1183C2×D4—22no—
1184C2×D4—22no—
1185C2×D4—22no—
1186C2×D4—22no—
1187C2×D4—62no—
1188C2×D4—62no—
1189C2×D4—62no—
1190C2×D4—62no—
1191C2×D4—62no—
1192C2×D4—62no—
1193C2×D4—62no—
1194C2×D4—62no—
1195C2×D4—62no—
1196C2×D4—62no—
1197C2×D4—62no—
1198C2×D4—62no—
1199C2×D4—62no—
1200C2×D4—62no—
1201C2×D4—62no—
1202C2×D4—62no—
1203C2×D4—62no—
1204C2×D4—62no—
1205C2×D4—121no—
1206C2×D4—121no—
1207C2×D4—121no—
1208C2×D4—121no—
1209C2×D4—121no—
1210C2×D4—121no—
1211C2×D4—121no—
1212C2×D4—121no—
1213C2×D4—121no—
1214C2×D4#23514yescomplemented
1215C2×D4C2×#6714yes—
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—22no—
1219C22×C4—22no—
1220C22×C4—22no—
1221C22×C4—22no—
1222C22×C4—22no—
1223C22×C4—22no—
1224C22×C4—22no—
1225C22×C4—22no—
1226C22×C4—22no—
1227C22×C4—22no—
1228C22×C4—31no—
1229C22×C4—31no—
1230C22×C4—31no—
1231C22×C4—31no—
1232C22×C4—31no—
1233C22×C4—31no—
1234C22×C4—31no—
1235C22×C4—31no—
1236C22×C4—31no—
1237C22×C4—31no—
1238C22×C4—31no—
1239C22×C4—31no—
1240C22×C4—31no—
1241C22×C4—41no—
1242C22×C4—41no—
1243C22×C4—41no—
1244C22×C4—41no—
1245C22×C4—41no—
1246C22×C4—41no—
1247C22×C4—41no—
1248C22×C4—41no—
1249C22×C4—41no—
1250C22×C4—41no—
1251C22×C4—41no—
1252C22×C4—41no—
1253C22×C4—62no—
1254C22×C4—62no—
1255C22×C4—62no—
1256C22×C4—62no—
1257C22×C4—62no—
1258C22×C4—62no—
1259C22×C4—62no—
1260C22×C4—62no—
1261C22×C4—62no—
1262C22×C4—62no—
1263C22×C4—62no—
1264C22×C4—62no—
1265C22×C4—62no—
1266C22×C4—121no—
1267C22×C4—121no—
1268C22×C4—121no—
1269C22×C4—121no—
1270C22×C4—121no—
1271C22×C4—121no—
1272C22×C4—1216no—
1273C22×C4—121no—
1274C22×C4—121no—
1275C22×C4—121no—
1276C22×C4—121no—
1277C22×C4—121no—
1278C22×C4#23514yescomplemented
1279C22×C4C2×#6714yes—
1280C22×C4C2×#6714yes—
1281C22×C4C23×D311yescharacteristic
1282C22×C4C23×D311yescharacteristic
1283C22×C4C23×D311yescharacteristic
1284C22×C4C23×D311yescharacteristic
1285C22×C4C23×D311yescharacteristic
1286C22×C4C23×D311yescharacteristic
1287C22×C4C23×D311yescharacteristic
1288C22×C4C23×D311yescharacteristic
1289C22×C4C23×D311yescharacteristic
1290C22×C4C23×D311yescharacteristic
1291C22×C4C23×D311yescharacteristic
1292C22×C4C23×D311yescharacteristic
1293C4⋊C4—22no—
1294C4⋊C4—22no—
1295C4⋊C4—22no—
1296C4⋊C4—22no—
1297C4⋊C4—22no—
1298C4⋊C4—22no—
1299C4⋊C4—22no—
1300C4⋊C4—22no—
1301C4⋊C4—22no—
1302C4⋊C4—62no—
1303C4⋊C4—62no—
1304C4⋊C4—62no—
1305C4⋊C4—62no—
1306C4⋊C4—62no—
1307C4⋊C4—62no—
1308C4⋊C4—62no—
1309C4⋊C4—62no—
1310C4⋊C4—62no—
1311C4⋊C4—62no—
1312C4⋊C4—62no—
1313C4⋊C4—121no—
1314C4⋊C4—121no—
1315C4⋊C4—121no—
1316C4⋊C4—121no—
1317C4⋊C4—121no—
1318C4⋊C4—121no—
1319C4⋊C4—121no—
1320C4⋊C4—121no—
1321C4⋊C4—121no—
1322C4⋊C4—121no—
1323C4⋊C4—121no—
1324C4⋊C4C2×#6714yes—
1325C22⋊C4—22no—
1326C22⋊C4—22no—
1327C22⋊C4—22no—
1328C22⋊C4—22no—
1329C22⋊C4—62no—
1330C22⋊C4—62no—
1331C22⋊C4—62no—
1332C22⋊C4—62no—
1333C22⋊C4—62no—
1334C22⋊C4—62no—
1335C22⋊C4—62no—
1336C22⋊C4—62no—
1337C22⋊C4—62no—
1338C22⋊C4—62no—
1339C22⋊C4—62no—
1340C22⋊C4—62no—
1341C22⋊C4—62no—
1342C22⋊C4—62no—
1343C22⋊C4—62no—
1344C22⋊C4—62no—
1345C22⋊C4—62no—
1346C22⋊C4—62no—
1347C22⋊C4—62no—
1348C22⋊C4—62no—
1349C22⋊C4—62no—
1350C22⋊C4—62no—
1351C22⋊C4—62no—
1352C22⋊C4—62no—
1353C22⋊C4—62no—
1354C22⋊C4—121no—
1355C22⋊C4—121no—
1356C22⋊C4—121no—
1357C22⋊C4—121no—
1358C22⋊C4—121no—
1359C22⋊C4—121no—
1360C22⋊C4—121no—
1361C22⋊C4—121no—
1362C22⋊C4—121no—
1363C22⋊C4—121no—
1364C22⋊C4—121no—
1365C22⋊C4—121no—
1366C22⋊C4—121no—
1367C22⋊C4—121no—
1368C22⋊C4—121no—
1369C22⋊C4C2×#6714yes—
1370C22⋊C4C2×#6714yes—
1371C42—22no—
1372C42—22no—
1373C42—22no—
1374C42—22no—
1375C42—22no—
1376C42—62no—
1377C42—121no—
1378C42—121no—
1379C42C2×#6714yes—
1380C22×C3—22no—
1381C22×C3—22no—
1382C22×C3—22no—
1383C22×C3—22no—
1384C22×C3—22no—
1385C22×C3—22no—
1386C22×C3—22no—
1387C22×C3—22no—
1388C22×C3—22no—
1389C22×C3—22no—
1390C22×C3—22no—
1391C22×C3—22no—
1392C22×C3—41no—
1393C22×C3—41no—
1394C22×C3—41no—
1395C22×C3—41no—
1396C22×C3—41no—
1397C22×C3—41no—
1398C22×C3—41no—
1399C22×C3—41no—
1400C22×C3#52514yes—
1401C22×C3C23×D411yescharacteristic
1402C22×C3C22×#4111yescharacteristic
1403C22×C3C22×#4111yescharacteristic
1404C22×C3C2×H(5,𝔽2)11yescharacteristic
1405C22×C3C2×H(5,𝔽2)11yescharacteristic
1406C22×C3C2×2−1+411yescharacteristic
1407C22×C3#58511yescharacteristic
1408C2×D3—22no—
1409C2×D3—22no—
1410C2×D3—22no—
1411C2×D3—22no—
1412C2×D3—22no—
1413C2×D3—22no—
1414C2×D3—416no—
1415C2×D3—41no—
1416C2×D3—41no—
1417C2×D3—41no—
1418C2×D3—41no—
1419C2×D3—41no—
1420C2×D3—41no—
1421C2×D3—41no—
1422C2×D3—41no—
1423C2×D3—41no—
1424C2×D3—41no—
1425C2×D3—41no—
1426C2×D3—41no—
1427C2×D3—41no—
1428C2×D3—41no—
1429C2×D3—41no—
1430C3×C4—22no—
1431C3×C4—22no—
1432C3×C4—22no—
1433C3×C4—22no—
1434C3×C4—22no—
1435C3×C4—22no—
1436C3×C4—22no—
1437C3×C4—22no—
1438C3×C4—41no—
1439C3×C4—41no—
1440C3×C4—41no—
1441C3×C4—41no—
1442Dic3—22no—
1443Dic3—41no—
1444Dic3—41no—
1445Dic3—41no—
1446Dic3—41no—
1447Dic3—41no—
1448Dic3—41no—
1449Dic3—41no—
1450Dic3—41no—
1451Dic3—41no—
1452Dic3—41no—
1453Dic3—41no—
1454Dic3—41no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23—21no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—21no—
1470C23—21no—
1471C23—32no—
1472C23—32no—
1473C23—68no—
1474C23—61no—
1475C23—61no—
1476C23—61no—
1477C23—61no—
1478C23—61no—
1479C23—61no—
1480C23—61no—
1481C23—61no—
1482C23—61no—
1483C23—61no—
1484C23—61no—
1485C23—61no—
1486C23—61no—
1487C23—61no—
1488C23—61no—
1489C23—61no—
1490C23—61no—
1491C23—61no—
1492C23—61no—
1493C23—124no—
1494C23—124no—
1495C23—124no—
1496C23—124no—
1497C23—124no—
1498C23—124no—
1499C23C2×#23512yes—
1500C23C2×#23512yes—
1501C23C2×#23512yes—
1502C23C22×#6712yes—
1503C23C22×#6712yes—
1504C23C24×D311yescharacteristic
1505Q8—28no—
1506Q8—124no—
1507D4—28no—
1508D4—28no—
1509D4—28no—
1510D4—124no—
1511D4—124no—
1512D4—124no—
1513D4—124no—
1514D4—124no—
1515D4—124no—
1516D4—124no—
1517D4—124no—
1518D4—242no—
1519C2×C4—28no—
1520C2×C4—28no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—28no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—32no—
1551C2×C4—44no—
1552C2×C4—44no—
1553C2×C4—68no—
1554C2×C4—61no—
1555C2×C4—61no—
1556C2×C4—61no—
1557C2×C4—61no—
1558C2×C4—61no—
1559C2×C4—61no—
1560C2×C4—61no—
1561C2×C4—61no—
1562C2×C4—61no—
1563C2×C4—61no—
1564C2×C4—61no—
1565C2×C4—61no—
1566C2×C4—61no—
1567C2×C4—61no—
1568C2×C4—61no—
1569C2×C4—61no—
1570C2×C4—61no—
1571C2×C4—61no—
1572C2×C4—61no—
1573C2×C4—61no—
1574C2×C4—61no—
1575C2×C4—61no—
1576C2×C4—61no—
1577C2×C4—61no—
1578C2×C4—61no—
1579C2×C4—61no—
1580C2×C4—61no—
1581C2×C4—61no—
1582C2×C4—61no—
1583C2×C4—61no—
1584C2×C4—61no—
1585C2×C4—61no—
1586C2×C4—61no—
1587C2×C4—61no—
1588C2×C4—61no—
1589C2×C4—61no—
1590C2×C4—61no—
1591C2×C4—61no—
1592C2×C4—82no—
1593C2×C4—82no—
1594C2×C4—82no—
1595C2×C4—82no—
1596C2×C4—124no—
1597C2×C4—124no—
1598C2×C4—124no—
1599C2×C4—124no—
1600C2×C4—124no—
1601C2×C4—124no—
1602C2×C4—242no—
1603C2×C4C2×#23512yes—
1604C2×C4C2×#23512yes—
1605C2×C4C2×#23512yes—
1606C2×C4C22×#6712yes—
1607C2×C4C22×#6712yes—
1608C2×C4C22×#6712yes—
1609C2×C4C22×#6712yes—
1610C2×C4C22×#6712yes—
1611C2×C3—24no—
1612C2×C3—42no—
1613C2×C3—42no—
1614C2×C3C2×#52511yescharacteristic
1615C2×C3#348411yescharacteristic
1616C2×C3#348911yescharacteristic
1617C2×C3#349211yescharacteristic
1618C2×C3#350611yescharacteristic
1619C2×C3#351311yescharacteristic
1620C2×C3#352011yescharacteristic
1621D3—42no—
1622D3—42no—
1623D3—81no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—62no—
1645C22—62no—
1646C22—62no—
1647C22—62no—
1648C22—62no—
1649C22—62no—
1650C22—1216no—
1651C22—121no—
1652C22—121no—
1653C22—121no—
1654C22—121no—
1655C22—121no—
1656C22—121no—
1657C22—121no—
1658C22—121no—
1659C22—121no—
1660C22—121no—
1661C22—121no—
1662C22—121no—
1663C22—121no—
1664C22—121no—
1665C22—121no—
1666C22#579114yes—
1667C22C22×#23511yescharacteristic
1668C22C22×#23511yescharacteristic
1669C22D3×H(5,𝔽2)11yescharacteristic
1670C22D3×H(5,𝔽2)11yescharacteristic
1671C22D3×2−1+411yescharacteristic
1672C22#596811yescharacteristic
1673C22C23×#6711yescharacteristic
1674C4—22no—
1675C4—22no—
1676C4—22no—
1677C4—22no—
1678C4—22no—
1679C4—22no—
1680C4—22no—
1681C4—22no—
1682C4—41no—
1683C4—41no—
1684C4—41no—
1685C4—41no—
1686C4—62no—
1687C4—121no—
1688C4—121no—
1689C4—121no—
1690C4—121no—
1691C4—121no—
1692C4—121no—
1693C4—121no—
1694C4—121no—
1695C4—121no—
1696C4—121no—
1697C4—121no—
1698C4—121no—
1699C3#3535311yescharacteristic, complemented, Sylow
1700C2—24no—
1701C2—42no—
1702C2—42no—
1703C2—122no—
1704C2—122no—
1705C2—241no—
1706C2#8589111yescharacteristic
1707C2#8590211yescharacteristic
1708C2#8590511yescharacteristic
1709C2#8590711yescharacteristic
1710C2C2×#579111yescharacteristic
1711C2#8728411yescharacteristic
1712C2#8729511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC2×C3×#520C2
hypercenterC2×#520D3
hypocenterC3#35353
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#520

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#520C2semidirect
2. C2×#5547C2semidirect
3. #84096C2semidirect
4. #84091C2semidirect
5. #82502C2semidirect
6. #82501C2semidirect
7. #82498C2semidirect
8. #82497C2semidirect
9. #82419C2semidirect
10. #82410C2semidirect
11. #82407C2semidirect
12. #82404C2semidirect
13. #82402C2semidirect
14. C4×#937C2semidirect
15. #82364C2semidirect
16. #82360C2semidirect
17. #82356C2semidirect
18. #82327C2semidirect
19. #82324C2semidirect
20. #82285C2semidirect
21. #82284C2semidirect
22. #82280C2semidirect
23. #82278C2semidirect
24. #82275C2semidirect
25. #82247C2semidirect
26. #82198C2semidirect
27. #82195C2semidirect
28. #82192C2semidirect
29. C2×#4989C2semidirect
30. #82173C2semidirect
31. #82158C2semidirect
37. C2×C3×C4×Q8C22semidirect
38. C2×C3×C4×Q8C22semidirect
43. C2×C3×C4×D4C22semidirect
44. C2×C3×C4×D4C22semidirect
46. C2×C3×#117C22semidirect
47. C2×C3×#117C22semidirect
49. C22×C3×C4⋊C4C22semidirect
50. C22×C3×C4⋊C4C22semidirect
58. C2×#929C22semidirect
65. C2×#924C22semidirect
78. #5231C22semidirect
79. #5230C22semidirect
82. #5223C22semidirect
83. #5222C22semidirect
95. #5213C22semidirect
96. #5213C22semidirect
97. #5213C22semidirect
98. #5212C22semidirect
100. #5211C22semidirect
102. #5210C22semidirect
103. #5210C22semidirect
104. #5210C22semidirect
105. #5210C22semidirect
106. #5210C22semidirect
114. #4993C22semidirect
119. #4990C22semidirect
120. #4990C22semidirect
131. #4989C22semidirect
132. #4989C22semidirect
133. #4989C22semidirect
134. #4986C22semidirect
135. #4983C22semidirect
136. #4982C22semidirect
137. #4982C22semidirect
138. #4982C22semidirect
139. #4980C22semidirect
140. #4980C22semidirect
141. #4979C22semidirect
142. #4979C22semidirect
143. #4978C22semidirect
144. #4978C22semidirect
145. #4978C22semidirect
146. #4976C22semidirect
147. #4976C22semidirect
152. #4959C22semidirect
156. #4956C22semidirect
158. #4952C22semidirect
159. #4951C22semidirect
160. #4951C22semidirect
163. #4949C22semidirect
164. #4948C22semidirect
166. #4944C22semidirect
173. #4940C22semidirect
174. #4940C22semidirect
180. #4937C22semidirect
181. #4936C22semidirect
182. #4933C22semidirect
183. #4933C22semidirect
184. #4933C22semidirect
185. #4933C22semidirect
186. #4933C22semidirect
187. #4929C22semidirect
188. #4928C22semidirect
189. #4928C22semidirect
191. C2×#520D3semidirect
269. C3×C4×D4D4semidirect
443. C2×C4×Q8C2×D3semidirect
444. C2×C4×Q8C2×D3semidirect
454. C2×C4×D4C2×D3semidirect
455. C2×C4×D4C2×D3semidirect
458. C2×#117C2×D3semidirect
459. C2×#117C2×D3semidirect
462. C22×C4⋊C4C2×D3semidirect
463. C22×C4⋊C4C2×D3semidirect
605. C2×C3×D4#41semidirect
632. C22×C3×C4#41semidirect
869. C4×D4#67semidirect
1214. C2×D4#235semidirect
1278. C22×C4#235semidirect
1699. C3#35353semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×#5202
C2×#55472
#840962
#840912
#825022
#825012
#824982
#824972
#824192
#824102
#824072
#824042
#824022
C4×#9372
#823642
#823602
#823562
#823272
#823242
#822852
#822842
#822802
#822782
#822752
#822472
#821982
#821952
#821922
C2×#49892
#821732
#821582
#353533