Finite Group Databasebeta

← #11223211

Subgroups — #11223211

Order 768.

2890 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5733C211yesmaximal, characteristic, complemented
2C2×D4×D12C211yesmaximal, characteristic
3C3×#2452C211yesmaximal, characteristic, complemented
4#83257C211yesmaximal, characteristic, complemented
5#82829C212yesmaximal, complemented
6#82761C212yesmaximal, complemented
7#82344C211yesmaximal, characteristic, complemented
8#77437C212yesmaximal, complemented
9#77434C212yesmaximal, complemented
10#76876C212yesmaximal, complemented
11#76790C212yesmaximal, complemented
12#76431C211yesmaximal, characteristic, complemented
13#76428C211yesmaximal, characteristic, complemented
14#76315C211yesmaximal, characteristic, complemented
15#76315C211yesmaximal, characteristic, complemented
16#76218C211yesmaximal, characteristic, complemented
17#76210C211yesmaximal, characteristic, complemented
18#76004C211yesmaximal, characteristic, complemented
19#75985C211yesmaximal, characteristic, complemented
20#74599C212yesmaximal, complemented
21#74476C212yesmaximal, complemented
22#73801C211yesmaximal, characteristic, complemented
23#73777C211yesmaximal, characteristic, complemented
24#44874—31nomaximal, Sylow
25C22×D3×D4C2211yescharacteristic
26C22×D3×D4C2211yescharacteristic
27C23×D12C2212yes—
28C2×C3×C4⋊Q8C2211yescharacteristic, complemented
29C2×C3×C22⋊Q8C2212yescomplemented
30C2×C3×C4×D4C2211yescharacteristic
31C2×#947C2212yescomplemented
32C2×#947C2212yescomplemented
33C2×#946C2212yescomplemented
34C2×#936C2211yescharacteristic
35C2×#930C2212yes—
36#5733—28no—
37D4×D12—28no—
38C2×#898C2212yescomplemented
39C2×#897C2211yescharacteristic, complemented
40C2×#897C2211yescharacteristic, complemented
41C2×#895C2211yescharacteristic
42C2×#895C2211yescharacteristic
43C2×#894C2212yescomplemented
44C2×#894C2212yescomplemented
45C2×#893C2211yescharacteristic, complemented
46C2×#892C2211yescharacteristic, complemented
47C2×#887C2211yescharacteristic, complemented
48C2×#882C2212yes—
49C2×#882C2212yes—
50C2×D3×C22⋊C4C2212yescomplemented
51C2×#875C2211yescharacteristic, complemented
52C2×#875C2211yescharacteristic, complemented
53C2×#874C2211yescharacteristic
54C2×C4×D12C2211yescharacteristic
55C2×C4×D12C2211yescharacteristic, complemented
56C2×#872C2211yescharacteristic, complemented
57C3×#396C2212yescomplemented
58C3×#393C2212yescomplemented
59C3×#390C2211yescharacteristic
60C3×#390C2211yescharacteristic
61C3×#389C2211yescharacteristic, complemented
62C3×#389C2211yescharacteristic, complemented
63C3×#385C2212yescomplemented
64C3×C4×C4⋊C4C2211yescharacteristic, complemented
65#5231C2212yescomplemented
66#5221C2211yescharacteristic
67#5210C2212yescomplemented
68C4×#217C2212yescomplemented
69#4994C2212yescomplemented
70#4993C2211yescharacteristic, complemented
71#4992C2211yescharacteristic, complemented
72#4991C2211yescharacteristic
73#4991C2212yes—
74#4991C2212yescomplemented
75#4991C2212yescomplemented
76#4991C2212yescomplemented
77#4991C2212yescomplemented
78#4990C2212yescomplemented
79#4990C2212yescomplemented
80#4988C2211yescharacteristic, complemented
81#4988C2211yescharacteristic, complemented
82#4988C2212yescomplemented
83#4988C2212yescomplemented
84#4988C2211yescharacteristic, complemented
85#4987C2211yescharacteristic, complemented
86#4984C2212yescomplemented
87#4982C2211yescharacteristic, complemented
88Dic3×C4⋊C4C2211yescharacteristic, complemented
89#4961C2212yescomplemented
90#4961C2212yescomplemented
91#4961C2212yescomplemented
92#4961C2212yescomplemented
93#4957C2212yescomplemented
94#4957C2212yescomplemented
95#4956C2212yescomplemented
96#4956C2212yescomplemented
97#4955C2212yescomplemented
98#4955C2212yescomplemented
99#4955C2212yescomplemented
100#4955C2212yescomplemented
101#4955C2212yescomplemented
102#4955C2212yescomplemented
103#4955C2212yescomplemented
104#4945C2212yescomplemented
105#4944C2212yescomplemented
106#4939C2211yescharacteristic, complemented
107C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
109C4×(C2×D3)⋊C4C2211yescharacteristic, complemented
110C4×Dic3⋊C4C2211yescharacteristic, complemented
111#4929C2211yescharacteristic, complemented
112#4675C2211yescharacteristic, complemented
113#4675C2211yescharacteristic, complemented
114#4674C2212yescomplemented
115#4672C2211yescharacteristic
116#4672C2212yescomplemented
117#4672C2212yescomplemented
118#4670C2212yescomplemented
119#4670C2212yescomplemented
120#4666C2212yescomplemented
121#4665C2212yescomplemented
122#4665C2212yescomplemented
123#4665C2212yescomplemented
124#4665C2212yescomplemented
125#4660C2211yescharacteristic, complemented
126C2×D42—31no—
127C2×#542—31no—
128#2697—32no—
129#2685—32no—
130#2684—32no—
131#2681—32no—
132#2559—32no—
133#2544—31no—
134#2491—31no—
135#2472—32no—
136#2452D311yescharacteristic, complemented
137#2445—31no—
138#2435—31no—
139#2435—31no—
140#2435—32no—
141#2426—31no—
142#2415—31no—
143#2405—32no—
144#2395—31no—
145#2367—31no—
146#2363—31no—
147D4×C22⋊C4—31no—
148#2309—31no—
149C24×D3C2312yes—
150C24×D3C2312yes—
151C22×C3×Q8C2312yes—
152C22×C3×D4C2311yescharacteristic
153C23×C3×C4C2312yes—
154C22×#67C2312yes—
155C22×#67C2312yes—
156C2×D3×D4—24no—
157C2×D3×D4—24no—
158C2×D3×D4—24no—
159C2×D3×D4—24no—
160C2×D3×D4—42no—
161C2×D3×D4—42no—
162C22×D12—28no—
163C22×D12—44no—
164C22×D12—44no—
165C22×D12C2311yescharacteristic
166C22×D12C2311yescharacteristic
167C22×D12C2312yes—
168C22×D12C2312yes—
169C22×D12C2311yescharacteristic
170C22×D12C2312yes—
171C22×D12C2312yes—
172C22×C4×D3C2311yescharacteristic
173C22×C4×D3C2311yescharacteristic
174C22×C4×D3C2312yes—
175C22×C4×D3C2312yes—
176C22×Dic6C2311yescharacteristic
177C3×C4⋊Q8—24no—
178C3×C22⋊Q8—44no—
179C3×C4×D4—24no—
180C2×C3×C4⋊C4C2311yescharacteristic
181C2×C3×C4⋊C4C2312yes—
182C2×C3×C4⋊C4C2311yescharacteristic
183C2×C3×C4⋊C4C2311yescharacteristic
184C2×C3×C4⋊C4C2312yes—
185C2×C3×C4⋊C4C2312yes—
186C2×C3×C4⋊C4C2311yescharacteristic
187C2×C3×C4⋊C4C2311yescharacteristic
188C2×C3×C22⋊C4C2312yes—
189C2×C3×C22⋊C4C2312yes—
190C2×C3×C22⋊C4C2312yes—
191C2×C3×C22⋊C4C2312yes—
192C2×C3×C22⋊C4C2312yes—
193C2×C3×C42C2311yescharacteristic
194C2×C3×C42C2311yescharacteristic
195C2×C3×C42C2311yescharacteristic
196C2×#217C2312yes—
197C2×#217C2312yes—
198C2×#217C2312yes—
199C2×#217C2312yes—
200#947—28no—
201#947—44no—
202#946—28no—
203#936—24no—
204#930—28no—
205C2×(C2×D3)⋊C4C2312yes—
206C2×(C2×D3)⋊C4C2312yes—
207C2×(C2×D3)⋊C4C2311yescharacteristic
208C2×(C2×D3)⋊C4C2312yes—
209C2×(C2×D3)⋊C4C2312yes—
210C2×(C2×D3)⋊C4C2311yescharacteristic
211C2×(C2×D3)⋊C4C2311yescharacteristic
212C2×(C2×D3)⋊C4C2312yes—
213C2×(C2×D3)⋊C4C2311yescharacteristic
214C2×(C2×D3)⋊C4C2312yes—
215C2×(C2×D3)⋊C4C2311yescharacteristic
216C2×(C2×D3)⋊C4C2311yescharacteristic
217C2×(C2×D3)⋊C4C2312yes—
218C2×(C2×D3)⋊C4C2311yescharacteristic
219C2×(C2×D3)⋊C4C2312yes—
220C2×(C2×D3)⋊C4C2312yes—
221C2×(C2×D3)⋊C4C2312yes—
222C2×(C2×D3)⋊C4C2312yes—
223C2×(C2×D3)⋊C4C2312yes—
224C2×(C2×D3)⋊C4C2312yes—
225C2×(C2×D3)⋊C4C2312yes—
226C2×(C2×D3)⋊C4C2312yes—
227C2×(C2×D3)⋊C4C2312yes—
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2312yes—
230C2×(C2×D3)⋊C4C2311yescharacteristic
231C2×(C2×D3)⋊C4C2311yescharacteristic
232C2×(C2×D3)⋊C4C2312yes—
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×C4⋊Dic3C2311yescharacteristic
236C2×C4⋊Dic3C2312yes—
237C2×C4⋊Dic3C2311yescharacteristic
238C2×C4⋊Dic3C2312yes—
239C2×Dic3⋊C4C2311yescharacteristic
240C2×Dic3⋊C4C2311yescharacteristic
241C2×Dic3⋊C4C2312yes—
242C2×Dic3⋊C4C2311yescharacteristic
243C2×Dic3⋊C4C2311yescharacteristic
244C2×C4×Dic3C2312yes—
245C2×C4×Dic3C2311yescharacteristic
246C2×C4×Dic3C2311yescharacteristic
247C2×C4×Dic3C2312yes—
248C2×C4×Dic3C2312yes—
249#898—28no—
250#897—24no—
251#897—42no—
252#895—24no—
253#895D418yes—
254#894—28no—
255#894—44no—
256#893—24no—
257#892—42no—
258#887—24no—
259#882—28no—
260#882—28no—
261D3×C22⋊C4—44no—
262#875—24no—
263#875—42no—
264#874—24no—
265C4×D12—24no—
266C4×D12—42no—
267#872—24no—
268C3×#95C2311yescharacteristic
269C3×#95C2311yescharacteristic
270C3×#95C2312yes—
271C3×#95C2312yes—
272C3⋊#95C2311yescharacteristic
273C3⋊#95C2311yescharacteristic
274C3⋊#95C2311yescharacteristic
275C3⋊#95C2311yescharacteristic
276C3⋊#95C2311yescharacteristic
277C3⋊#95C2312yes—
278C3⋊#95C2312yes—
279C3⋊#95C2312yes—
280C3⋊#95C2312yes—
281C3⋊#95C2311yescharacteristic
282C3⋊#95C2311yescharacteristic
283C3⋊#95C2311yescharacteristic
284C23×D4—31no—
285C23×D4—31no—
286C23×D4—32no—
287D42—68no—
288#542—68no—
289C2×C4⋊Q8C2×D311yescharacteristic, complemented
290C2×#127—31no—
291C2×#126—32no—
292C2×#124—32no—
293C2×#124—31no—
294C2×#124—32no—
295C2×#124—31no—
296C2×#124—31no—
297C2×#123—32no—
298C2×#123—32no—
299C2×C22⋊Q8—32no—
300C2×C22⋊Q8—31no—
301C2×C22⋊Q8—31no—
302C2×C22⋊Q8C2×D312yescomplemented
303C2×#121—32no—
304C2×#121—31no—
305C2×#121—31no—
306C2×#120—32no—
307C2×#120—32no—
308C2×C4×Q8—31no—
309C2×C4×D4—31no—
310C2×C4×D4—31no—
311C2×C4×D4—31no—
312C2×C4×D4C2×D311yescharacteristic
313C2×#117—31no—
314C2×#117—31no—
315C22×C22⋊C4—32no—
316#400—31no—
317#399—31no—
318#398—31no—
319#397—31no—
320#397—32no—
321#397—31no—
322#397—31no—
323#396—32no—
324#396C2×D312yescomplemented
325#394—31no—
326#394—32no—
327#394—32no—
328#394—32no—
329#394—32no—
330#394—32no—
331#394—32no—
332#394—32no—
333#394—32no—
334#394—32no—
335#394—31no—
336#394—32no—
337#394—32no—
338#393—32no—
339#393C2×D312yescomplemented
340#391—31no—
341#390—31no—
342#390—31no—
343#390—32no—
344#390—31no—
345#390—32no—
346#390—31no—
347#390—32no—
348#390—32no—
349#390—31no—
350#390C2×D311yescharacteristic
351#390C2×D311yescharacteristic
352#389—32no—
353#389C2×D311yescharacteristic, complemented
354#389C2×D311yescharacteristic, complemented
355#388—32no—
356#388—32no—
357#388—32no—
358#388—32no—
359#388—32no—
360#388—32no—
361#386—32no—
362#386—32no—
363#386—32no—
364#386—32no—
365#386—32no—
366#386—32no—
367#385—32no—
368#385C2×D312yescomplemented
369#380—31no—
370#379—32no—
371#379—32no—
372#379—32no—
373#379—32no—
374#379—32no—
375#379—32no—
376#379—32no—
377C4×C4⋊C4—31no—
378C4×C4⋊C4—31no—
379C4×C4⋊C4C2×D311yescharacteristic, complemented
380C4×C22⋊C4—32no—
381C4×C22⋊C4—31no—
382C4×C22⋊C4—31no—
383C4×C22⋊C4—31no—
384C4×C22⋊C4—32no—
385C24×C3C2412yes—
386C23×D3—24no—
387C23×D3—24no—
388C23×D3—24no—
389C23×D3—24no—
390C23×D3—24no—
391C23×D3—42no—
392C23×D3—42no—
393C23×D3—42no—
394C23×D3—42no—
395C23×D3—42no—
396C23×D3—42no—
397C23×D3—42no—
398C23×D3—42no—
399C23×D3—42no—
400C23×D3C2412yes—
401C23×D3C2411yescharacteristic
402C23×D3C2412yes—
403C23×D3C2411yescharacteristic
404C2×C3×Q8—24no—
405C2×C3×Q8—42no—
406C2×C3×Q8—42no—
407C2×C3×D4—22no—
408C2×C3×D4—22no—
409C2×C3×D4#4114yes—
410C22×C3×C4—24no—
411C22×C3×C4—24no—
412C22×C3×C4—42no—
413C22×C3×C4C2411yescharacteristic
414C22×C3×C4C2411yescharacteristic
415C22×C3×C4C2411yescharacteristic
416C22×C3×C4C2411yescharacteristic
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2412yes—
419C22×C3×C4C2412yes—
420C22×C3×C4C2412yes—
421C22×C3×C4C2411yescharacteristic
422C22×C3×C4C2411yescharacteristic
423C2×#67—24no—
424C2×#67—24no—
425C2×#67—24no—
426C2×#67—24no—
427C2×#67—42no—
428C2×#67—42no—
429C22×Dic3C2411yescharacteristic
430C22×Dic3C2411yescharacteristic
431C22×Dic3C2412yes—
432C22×Dic3C2411yescharacteristic
433C22×Dic3C2411yescharacteristic
434C22×Dic3C2411yescharacteristic
435C22×Dic3C2412yes—
436C22×Dic3C2411yescharacteristic
437D3×D4—416no—
438D3×D4—416no—
439C2×D12—22no—
440C2×D12—22no—
441C2×D12—22no—
442C2×D12—22no—
443C2×D12—22no—
444C2×D12—24no—
445C2×D12—24no—
446C2×D12—22no—
447C2×D12—24no—
448C2×D12—22no—
449C2×D12—22no—
450C2×D12—24no—
451C2×D12—24no—
452C2×D12—432no—
453C2×D12—42no—
454C2×D12—42no—
455C2×D12—42no—
456C2×D12—42no—
457C2×D12—42no—
458C2×D12—42no—
459C2×D12C2×D414yes—
460C2×D12C2×D418yes—
461C2×C4×D3—22no—
462C2×C4×D3—22no—
463C2×C4×D3—22no—
464C2×C4×D3—22no—
465C2×C4×D3—22no—
466C2×C4×D3—24no—
467C2×C4×D3—42no—
468C2×C4×D3—42no—
469C2×C4×D3—42no—
470C2×C4×D3—42no—
471C2×C4×D3—42no—
472C2×C4×D3C2×D414yes—
473C2×Dic6—22no—
474C2×Dic6—22no—
475C2×Dic6—22no—
476C3×C4⋊C4—22no—
477C3×C4⋊C4—24no—
478C3×C4⋊C4—22no—
479C3×C4⋊C4—24no—
480C3×C4⋊C4—22no—
481C3×C4⋊C4—41no—
482C3×C4⋊C4—42no—
483C3×C4⋊C4C2×D414yes—
484C3×C22⋊C4—24no—
485C3×C22⋊C4—42no—
486C3×C22⋊C4—42no—
487C3×C22⋊C4—42no—
488C3×C22⋊C4—42no—
489C3×C42—22no—
490C3×C42—22no—
491C3×C42—22no—
492#217—24no—
493#217—24no—
494#217—42no—
495#217—42no—
496(C2×D3)⋊C4—22no—
497(C2×D3)⋊C4—22no—
498(C2×D3)⋊C4—22no—
499(C2×D3)⋊C4—24no—
500(C2×D3)⋊C4—24no—
501(C2×D3)⋊C4—24no—
502(C2×D3)⋊C4—24no—
503(C2×D3)⋊C4—22no—
504(C2×D3)⋊C4—24no—
505(C2×D3)⋊C4—22no—
506(C2×D3)⋊C4—24no—
507(C2×D3)⋊C4—22no—
508(C2×D3)⋊C4—42no—
509(C2×D3)⋊C4—42no—
510(C2×D3)⋊C4—42no—
511(C2×D3)⋊C4—42no—
512(C2×D3)⋊C4—42no—
513(C2×D3)⋊C4—42no—
514(C2×D3)⋊C4—42no—
515(C2×D3)⋊C4—42no—
516(C2×D3)⋊C4—41no—
517(C2×D3)⋊C4—41no—
518(C2×D3)⋊C4—42no—
519(C2×D3)⋊C4—42no—
520(C2×D3)⋊C4—41no—
521(C2×D3)⋊C4—41no—
522(C2×D3)⋊C4—42no—
523(C2×D3)⋊C4—42no—
524(C2×D3)⋊C4—42no—
525(C2×D3)⋊C4C2×D418yes—
526C4⋊Dic3—22no—
527C4⋊Dic3—22no—
528C4⋊Dic3—24no—
529C4⋊Dic3—42no—
530Dic3⋊C4—24no—
531Dic3⋊C4—22no—
532Dic3⋊C4—22no—
533Dic3⋊C4—22no—
534Dic3⋊C4—41no—
535C4×Dic3—22no—
536C4×Dic3—24no—
537C4×Dic3—22no—
538C4×Dic3—42no—
539C4×Dic3—42no—
540C25—32no—
541C25—32no—
542C22×Q8—31no—
543C22×Q8C22×D312yes—
544C22×D4—32no—
545C22×D4—32no—
546C22×D4—31no—
547C22×D4—32no—
548C22×D4—31no—
549C22×D4—31no—
550C22×D4—32no—
551C22×D4—32no—
552C22×D4—32no—
553C22×D4—68no—
554C22×D4—64no—
555C22×D4—64no—
556C22×D4—64no—
557C22×D4—64no—
558C22×D4—124no—
559C22×D4—124no—
560C22×D4—122no—
561C22×D4—122no—
562C22×D4C22×D311yescharacteristic
563C23×C4—31no—
564C23×C4—31no—
565C23×C4—32no—
566C23×C4—32no—
567C23×C4C22×D312yes—
568C4⋊Q8—24no—
569#127—64no—
570#126—68no—
571#124—64no—
572#124—68no—
573#124—64no—
574#124—122no—
575#124—124no—
576#123—68no—
577#123—124no—
578C22⋊Q8—44no—
579C22⋊Q8—68no—
580C22⋊Q8—64no—
581C22⋊Q8—122no—
582#121—38no—
583#121—68no—
584#121—64no—
585#120—68no—
586#120—68no—
587C4×Q8—64no—
588C4×D4—24no—
589C4×D4—64no—
590C4×D4—64no—
591C4×D4—122no—
592#117—64no—
593#117—122no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—31no—
597C2×C4⋊C4—31no—
598C2×C4⋊C4—32no—
599C2×C4⋊C4—32no—
600C2×C4⋊C4—31no—
601C2×C4⋊C4—32no—
602C2×C4⋊C4—31no—
603C2×C4⋊C4C22×D311yescharacteristic
604C2×C4⋊C4C22×D311yescharacteristic
605C2×C4⋊C4C22×D311yescharacteristic
606C2×C4⋊C4C22×D312yes—
607C2×C4⋊C4C22×D312yes—
608C2×C4⋊C4C22×D312yes—
609C2×C4⋊C4C22×D311yescharacteristic
610C2×C4⋊C4C22×D311yescharacteristic
611C2×C22⋊C4—32no—
612C2×C22⋊C4—32no—
613C2×C22⋊C4—32no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—32no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—32no—
621C2×C22⋊C4—32no—
622C2×C22⋊C4—32no—
623C2×C22⋊C4—32no—
624C2×C22⋊C4—32no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—32no—
627C2×C22⋊C4—32no—
628C2×C22⋊C4—32no—
629C2×C22⋊C4—32no—
630C2×C22⋊C4—32no—
631C2×C22⋊C4—32no—
632C2×C22⋊C4—32no—
633C2×C22⋊C4—32no—
634C2×C22⋊C4—32no—
635C2×C22⋊C4—32no—
636C2×C22⋊C4—32no—
637C2×C22⋊C4—32no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—31no—
641C2×C22⋊C4—31no—
642C2×C22⋊C4—32no—
643C2×C22⋊C4—32no—
644C2×C22⋊C4—32no—
645C2×C22⋊C4—124no—
646C2×C22⋊C4C22×D312yes—
647C2×C22⋊C4C22×D312yes—
648C2×C22⋊C4C22×D312yes—
649C2×C22⋊C4C22×D312yes—
650C2×C22⋊C4C22×D312yes—
651C2×C42—31no—
652C2×C42—32no—
653C2×C42—31no—
654C2×C42—32no—
655C2×C42—32no—
656C2×C42C22×D311yescharacteristic
657C2×C42C22×D311yescharacteristic
658C2×C42C22×D311yescharacteristic
659#95—31no—
660#95—31no—
661#95—32no—
662#95—31no—
663#95—31no—
664#95—31no—
665#95—31no—
666#95—31no—
667#95—32no—
668#95—31no—
669#95—32no—
670#95—32no—
671#95C22×D312yes—
672#95C22×D311yescharacteristic
673#95C22×D311yescharacteristic
674#95C22×D312yes—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—22no—
678C23×C3—22no—
679C23×C3—22no—
680C23×C3—22no—
681C23×C3C2×#4114yes—
682C23×C3C2511yescharacteristic
683C22×D3—21no—
684C22×D3—21no—
685C22×D3—21no—
686C22×D3—22no—
687C22×D3—21no—
688C22×D3—21no—
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—21no—
693C22×D3—21no—
694C22×D3—21no—
695C22×D3—22no—
696C22×D3—21no—
697C22×D3—21no—
698C22×D3—21no—
699C22×D3—21no—
700C22×D3—22no—
701C22×D3—22no—
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—22no—
706C22×D3—22no—
707C22×D3—22no—
708C22×D3—48no—
709C22×D3—48no—
710C22×D3—48no—
711C22×D3—48no—
712C22×D3—48no—
713C22×D3—84no—
714C22×D3—84no—
715C22×D3—84no—
716C22×D3—84no—
717C22×D3—84no—
718C22×D3—84no—
719C22×D3—84no—
720C22×D3—84no—
721C22×D3—84no—
722C22×D3C22×D412yes—
723C22×D3C22×D414yes—
724C22×D3H(5,𝔽2)12yes—
725C3×Q8—84no—
726C3×D4—28no—
727C2×C3×C4—21no—
728C2×C3×C4—22no—
729C2×C3×C4—22no—
730C2×C3×C4—21no—
731C2×C3×C4—21no—
732C2×C3×C4—21no—
733C2×C3×C4—22no—
734C2×C3×C4—21no—
735C2×C3×C4—22no—
736C2×C3×C4—21no—
737C2×C3×C4—22no—
738C2×C3×C4—21no—
739C2×C3×C4—21no—
740C2×C3×C4—21no—
741C2×C3×C4—22no—
742C2×C3×C4—22no—
743C2×C3×C4—21no—
744C2×C3×C4—21no—
745C2×C3×C4—21no—
746C2×C3×C4—21no—
747C2×C3×C4—22no—
748C2×C3×C4—21no—
749C2×C3×C4—21no—
750C2×C3×C4—21no—
751C2×C3×C4—21no—
752C2×C3×C4—48no—
753C2×C3×C4C22×D414yes—
754C2×C3×C4C22×D412yes—
755C2×C3×C4C2×#4112yes—
756C2×C3×C4H(5,𝔽2)12yes—
757C2×C3×C4H(5,𝔽2)12yes—
758#67—48no—
759#67—48no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3—21no—
763C2×Dic3—21no—
764C2×Dic3—22no—
765C2×Dic3—21no—
766C2×Dic3—21no—
767C2×Dic3—21no—
768C2×Dic3—22no—
769C2×Dic3—21no—
770C2×Dic3—21no—
771C2×Dic3—22no—
772C2×Dic3—22no—
773C2×Dic3—21no—
774C2×Dic3—21no—
775C2×Dic3—21no—
776C2×Dic3—22no—
777C2×Dic3—21no—
778C2×Dic3—21no—
779C2×Dic3—21no—
780C2×Dic3—21no—
781C2×Dic3—21no—
782C2×Dic3—22no—
783C2×Dic3C22×D412yes—
784D12—28no—
785D12—28no—
786D12—48no—
787D12—48no—
788D12—48no—
789D12—44no—
790D12—84no—
791C4×D3—28no—
792C4×D3—44no—
793C4×D3—84no—
794C4×D3—84no—
795Dic6—44no—
796C24—31no—
797C24—31no—
798C24—32no—
799C24—32no—
800C24—64no—
801C24—64no—
802C24—64no—
803C24—64no—
804C24—64no—
805C24—122no—
806C24—122no—
807C24—122no—
808C24—122no—
809C24—122no—
810C24—122no—
811C24—122no—
812C24—122no—
813C24—122no—
814C24C23×D312yes—
815C2×Q8—24no—
816C2×Q8—42no—
817C2×Q8—42no—
818C2×Q8—62no—
819C2×Q8—62no—
820C2×Q8—62no—
821C2×D4—22no—
822C2×D4—22no—
823C2×D4—34no—
824C2×D4—38no—
825C2×D4—62no—
826C2×D4—62no—
827C2×D4—64no—
828C2×D4—64no—
829C2×D4—64no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—64no—
833C2×D4—64no—
834C2×D4—64no—
835C2×D4—62no—
836C2×D4—62no—
837C2×D4—64no—
838C2×D4—62no—
839C2×D4—62no—
840C2×D4—62no—
841C2×D4—62no—
842C2×D4—122no—
843C2×D4—122no—
844C2×D4—122no—
845C2×D4—122no—
846C2×D4—122no—
847C2×D4—122no—
848C2×D4—1232no—
849C2×D4—1216no—
850C2×D4—122no—
851C2×D4—122no—
852C2×D4—1216no—
853C2×D4#23914yes—
854C22×C4—24no—
855C22×C4—24no—
856C22×C4—31no—
857C22×C4—34no—
858C22×C4—31no—
859C22×C4—31no—
860C22×C4—32no—
861C22×C4—31no—
862C22×C4—31no—
863C22×C4—32no—
864C22×C4—31no—
865C22×C4—42no—
866C22×C4—64no—
867C22×C4—62no—
868C22×C4—62no—
869C22×C4—62no—
870C22×C4—62no—
871C22×C4—62no—
872C22×C4—122no—
873C22×C4—122no—
874C22×C4—122no—
875C22×C4—122no—
876C22×C4—122no—
877C22×C4C23×D311yescharacteristic
878C22×C4C23×D311yescharacteristic
879C22×C4C23×D311yescharacteristic
880C22×C4C23×D311yescharacteristic
881C22×C4C23×D311yescharacteristic
882C22×C4C23×D312yes—
883C22×C4C23×D312yes—
884C22×C4C23×D312yes—
885C22×C4C23×D311yescharacteristic
886C22×C4C23×D311yescharacteristic
887C4⋊C4—22no—
888C4⋊C4—24no—
889C4⋊C4—22no—
890C4⋊C4—24no—
891C4⋊C4—22no—
892C4⋊C4—42no—
893C4⋊C4—41no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—62no—
897C4⋊C4—64no—
898C4⋊C4—64no—
899C4⋊C4—62no—
900C4⋊C4—62no—
901C4⋊C4—122no—
902C4⋊C4—121no—
903C4⋊C4D3×D414yes—
904C22⋊C4—24no—
905C22⋊C4—38no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—42no—
910C22⋊C4—62no—
911C22⋊C4—62no—
912C22⋊C4—64no—
913C22⋊C4—62no—
914C22⋊C4—62no—
915C22⋊C4—62no—
916C22⋊C4—64no—
917C22⋊C4—64no—
918C22⋊C4—64no—
919C22⋊C4—64no—
920C22⋊C4—62no—
921C22⋊C4—64no—
922C22⋊C4—64no—
923C22⋊C4—64no—
924C22⋊C4—122no—
925C22⋊C4—122no—
926C22⋊C4—122no—
927C22⋊C4—122no—
928C22⋊C4—122no—
929C22⋊C4—122no—
930C22⋊C4—122no—
931C22⋊C4—122no—
932C22⋊C4—122no—
933C22⋊C4—122no—
934C22⋊C4—122no—
935C22⋊C4—122no—
936C22⋊C4—121no—
937C22⋊C4—121no—
938C22⋊C4—121no—
939C22⋊C4—122no—
940C22⋊C4—121no—
941C22⋊C4—122no—
942C22⋊C4—122no—
943C42—22no—
944C42—22no—
945C42—22no—
946C42—62no—
947C42—64no—
948C42—62no—
949C42—122no—
950C42—122no—
951C22×C3—24no—
952C22×C3—24no—
953C22×C3—24no—
954C22×C3—42no—
955C22×C3—42no—
956C22×C3—42no—
957C22×C3—42no—
958C22×C3C23×D411yescharacteristic
959C22×C3C22×#4111yescharacteristic
960C22×C3C2×H(5,𝔽2)11yescharacteristic
961C22×C3C2×H(5,𝔽2)11yescharacteristic
962C22×C3C2×H(5,𝔽2)11yescharacteristic
963C22×C3#58511yescharacteristic
964C22×C3#58511yescharacteristic
965C2×D3—22no—
966C2×D3—24no—
967C2×D3—24no—
968C2×D3—22no—
969C2×D3—22no—
970C2×D3—24no—
971C2×D3—22no—
972C2×D3—22no—
973C2×D3—22no—
974C2×D3—41no—
975C2×D3—41no—
976C2×D3—42no—
977C2×D3—41no—
978C2×D3—42no—
979C2×D3—41no—
980C2×D3—41no—
981C2×D3—42no—
982C2×D3—41no—
983C2×D3—41no—
984C2×D3—42no—
985C2×D3—41no—
986C2×D3—42no—
987C2×D3—42no—
988C2×D3—42no—
989C2×D3—42no—
990C2×D3—42no—
991C2×D3—42no—
992C2×D3—42no—
993C2×D3—816no—
994C2×D3—816no—
995C3×C4—22no—
996C3×C4—24no—
997C3×C4—42no—
998C3×C4—41no—
999C3×C4—41no—
1000C3×C4—41no—
1001C3×C4—42no—
1002C3×C4—41no—
1003C3×C4—41no—
1004C3×C4#54614yes—
1005Dic3—22no—
1006Dic3—42no—
1007Dic3—41no—
1008Dic3—41no—
1009Dic3—41no—
1010Dic3—41no—
1011Dic3—41no—
1012Dic3—42no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—34no—
1020C23—32no—
1021C23—32no—
1022C23—61no—
1023C23—62no—
1024C23—61no—
1025C23—61no—
1026C23—61no—
1027C23—61no—
1028C23—62no—
1029C23—61no—
1030C23—61no—
1031C23—62no—
1032C23—62no—
1033C23—61no—
1034C23—61no—
1035C23—62no—
1036C23—61no—
1037C23—61no—
1038C23—61no—
1039C23—62no—
1040C23—62no—
1041C23—62no—
1042C23—62no—
1043C23—62no—
1044C23—62no—
1045C23—62no—
1046C23—62no—
1047C23—128no—
1048C23—128no—
1049C23—128no—
1050C23—128no—
1051C23—128no—
1052C23—244no—
1053C23—244no—
1054C23—244no—
1055C23—244no—
1056C23—244no—
1057C23—244no—
1058C23—244no—
1059C23—244no—
1060C23—244no—
1061C23C2×#23914yes—
1062C23C24×D311yescharacteristic
1063Q8—84no—
1064Q8—124no—
1065D4—28no—
1066D4—68no—
1067D4—68no—
1068D4—128no—
1069D4—128no—
1070D4—128no—
1071D4—128no—
1072D4—128no—
1073D4—124no—
1074D4—244no—
1075C2×C4—21no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—32no—
1101C2×C4—48no—
1102C2×C4—61no—
1103C2×C4—61no—
1104C2×C4—68no—
1105C2×C4—61no—
1106C2×C4—62no—
1107C2×C4—61no—
1108C2×C4—61no—
1109C2×C4—61no—
1110C2×C4—61no—
1111C2×C4—61no—
1112C2×C4—61no—
1113C2×C4—62no—
1114C2×C4—61no—
1115C2×C4—62no—
1116C2×C4—62no—
1117C2×C4—61no—
1118C2×C4—61no—
1119C2×C4—61no—
1120C2×C4—61no—
1121C2×C4—62no—
1122C2×C4—61no—
1123C2×C4—61no—
1124C2×C4—61no—
1125C2×C4—62no—
1126C2×C4—124no—
1127C2×C4—244no—
1128C2×C4—244no—
1129C2×C4C2×D3×D414yes—
1130C2×C4C2×D3×D412yes—
1131C2×C4#100412yes—
1132C2×C4C2×#23912yes—
1133C2×C4#100912yes—
1134C2×C3—44no—
1135C2×C3C2×#54611yescharacteristic
1136C2×C3#348411yescharacteristic
1137C2×C3#350011yescharacteristic
1138C2×C3#351311yescharacteristic
1139C2×C3#351411yescharacteristic
1140C2×C3#354611yescharacteristic
1141C2×C3#355811yescharacteristic
1142D3—44no—
1143D3—42no—
1144D3—42no—
1145D3—82no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—62no—
1154C22—64no—
1155C22—62no—
1156C22—62no—
1157C22—62no—
1158C22—64no—
1159C22—62no—
1160C22—62no—
1161C22—64no—
1162C22—122no—
1163C22—121no—
1164C22—122no—
1165C22—121no—
1166C22—121no—
1167C22—121no—
1168C22—121no—
1169C22—121no—
1170C22—122no—
1171C22—121no—
1172C22—121no—
1173C22—122no—
1174C22—122no—
1175C22—122no—
1176C22—122no—
1177C22—122no—
1178C22—122no—
1179C22—122no—
1180C22—122no—
1181C22—2416no—
1182C22—2416no—
1183C22C22×D3×D411yescharacteristic
1184C22C2×#100411yescharacteristic
1185C22C22×#23911yescharacteristic
1186C22C2×#100911yescharacteristic
1187C22#596411yescharacteristic
1188C22D3×H(5,𝔽2)11yescharacteristic
1189C22#596811yescharacteristic
1190C4—22no—
1191C4—24no—
1192C4—41no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—42no—
1199C4—62no—
1200C4—122no—
1201C4—121no—
1202C4—121no—
1203C4—121no—
1204C4—121no—
1205C4—122no—
1206C4—121no—
1207C4#563014yes—
1208C3#4487411yescharacteristic, complemented, Sylow
1209C2—44no—
1210C2—122no—
1211C2—122no—
1212C2—124no—
1213C2—242no—
1214C2C2×#563011yescharacteristic
1215C2#8624911yescharacteristic
1216C2#8656711yescharacteristic
1217C2#8662011yescharacteristic
1218C2#8671511yescharacteristic
1219C2#8674811yescharacteristic
1220C2#8692911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2452C2
prime radicalC2×D4×D12C2
hypercenter#2452D3
hypocenterC3#44874
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. C2×#5733C2semidirect
3. C3×#2452C2semidirect
4. #83257C2semidirect
5. #82829C2semidirect
6. #82761C2semidirect
7. #82344C2semidirect
8. #77437C2semidirect
9. #77434C2semidirect
10. #76876C2semidirect
11. #76790C2semidirect
12. #76431C2semidirect
13. #76428C2semidirect
14. #76315C2semidirect
15. #76315C2semidirect
16. #76218C2semidirect
17. #76210C2semidirect
18. #76004C2semidirect
19. #75985C2semidirect
20. #74599C2semidirect
21. #74476C2semidirect
22. #73801C2semidirect
23. #73777C2semidirect
28. C2×C3×C4⋊Q8C22semidirect
29. C2×C3×C22⋊Q8C22semidirect
31. C2×#947C22semidirect
32. C2×#947C22semidirect
33. C2×#946C22semidirect
38. C2×#898C22semidirect
39. C2×#897C22semidirect
40. C2×#897C22semidirect
43. C2×#894C22semidirect
44. C2×#894C22semidirect
45. C2×#893C22semidirect
46. C2×#892C22semidirect
47. C2×#887C22semidirect
50. C2×D3×C22⋊C4C22semidirect
51. C2×#875C22semidirect
52. C2×#875C22semidirect
55. C2×C4×D12C22semidirect
56. C2×#872C22semidirect
57. C3×#396C22semidirect
58. C3×#393C22semidirect
61. C3×#389C22semidirect
62. C3×#389C22semidirect
63. C3×#385C22semidirect
64. C3×C4×C4⋊C4C22semidirect
65. #5231C22semidirect
67. #5210C22semidirect
68. C4×#217C22semidirect
69. #4994C22semidirect
70. #4993C22semidirect
71. #4992C22semidirect
74. #4991C22semidirect
75. #4991C22semidirect
76. #4991C22semidirect
77. #4991C22semidirect
78. #4990C22semidirect
79. #4990C22semidirect
80. #4988C22semidirect
81. #4988C22semidirect
82. #4988C22semidirect
83. #4988C22semidirect
84. #4988C22semidirect
85. #4987C22semidirect
86. #4984C22semidirect
87. #4982C22semidirect
88. Dic3×C4⋊C4C22semidirect
89. #4961C22semidirect
90. #4961C22semidirect
91. #4961C22semidirect
92. #4961C22semidirect
93. #4957C22semidirect
94. #4957C22semidirect
95. #4956C22semidirect
96. #4956C22semidirect
97. #4955C22semidirect
98. #4955C22semidirect
99. #4955C22semidirect
100. #4955C22semidirect
101. #4955C22semidirect
102. #4955C22semidirect
103. #4955C22semidirect
104. #4945C22semidirect
105. #4944C22semidirect
106. #4939C22semidirect
107. C4×(C2×D3)⋊C4C22semidirect
108. C4×(C2×D3)⋊C4C22semidirect
109. C4×(C2×D3)⋊C4C22semidirect
110. C4×Dic3⋊C4C22semidirect
111. #4929C22semidirect
112. #4675C22semidirect
113. #4675C22semidirect
114. #4674C22semidirect
116. #4672C22semidirect
117. #4672C22semidirect
118. #4670C22semidirect
119. #4670C22semidirect
120. #4666C22semidirect
121. #4665C22semidirect
122. #4665C22semidirect
123. #4665C22semidirect
124. #4665C22semidirect
125. #4660C22semidirect
136. #2452D3semidirect
289. C2×C4⋊Q8C2×D3semidirect
302. C2×C22⋊Q8C2×D3semidirect
324. #396C2×D3semidirect
339. #393C2×D3semidirect
353. #389C2×D3semidirect
354. #389C2×D3semidirect
368. #385C2×D3semidirect
379. C4×C4⋊C4C2×D3semidirect
1208. C3#44874semidirect

Maximal subgroups

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

subgroupindex
C2×#57332
C2×D4×D122
C3×#24522
#832572
#828292
#827612
#823442
#774372
#774342
#768762
#767902
#764312
#764282
#763152
#762182
#762102
#760042
#759852
#745992
#744762
#738012
#737772
#448743