Finite Group Databasebeta

← #11023872

Subgroups — #11023872

Order 768.

3130 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5654C211yesmaximal, characteristic
2C2×D3×#123C211yesmaximal, characteristic, complemented
3C2×#5526C211yesmaximal, characteristic, complemented
4C22×#896C211yesmaximal, characteristic, complemented
5C3×#2413C211yesmaximal, characteristic, complemented
6#82864C211yesmaximal, characteristic, complemented
7#82859C211yesmaximal, characteristic, complemented
8#82271C211yesmaximal, characteristic, complemented
9#82192C211yesmaximal, characteristic, complemented
10#77969C212yesmaximal, complemented
11#77952C212yesmaximal, complemented
12#77431C212yesmaximal, complemented
13#77418C212yesmaximal, complemented
14#76257C212yesmaximal, complemented
15#75998C212yesmaximal, complemented
16#75915C212yesmaximal, complemented
17#75526C212yesmaximal, complemented
18#74781C211yesmaximal, characteristic, complemented
19#74686C211yesmaximal, characteristic, complemented
20#74406C211yesmaximal, characteristic, complemented
21#74384C211yesmaximal, characteristic, complemented
22#74146C211yesmaximal, characteristic, complemented
23#74075C211yesmaximal, characteristic, complemented
24#37647—31nomaximal, Sylow
25C22×D3×D4C2211yescharacteristic
26C22×#235C2211yescharacteristic
27C23×C4×D3C2211yescharacteristic
28C23×Dic6C2211yescharacteristic, complemented
29C2×C3×#123C2211yescharacteristic
30C2×C3×#123C2211yescharacteristic
31C2×C3×#117C2211yescharacteristic, complemented
32C22×C3×C4⋊C4C2211yescharacteristic, complemented
33C2×#939C2211yescharacteristic
34C2×#935C2211yescharacteristic
35C2×#935C2211yescharacteristic
36C2×#929C2211yescharacteristic
37C2×#929C2211yescharacteristic, complemented
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic
40C22×Dic3⋊C4C2211yescharacteristic, complemented
41C22×Dic3⋊C4C2211yescharacteristic, complemented
42#5654—28no—
43D3×#123—28no—
44#5526—28no—
45C2×#897C2212yescomplemented
46C2×#897C2212yescomplemented
47C2×#896—28no—
48C2×#896C2212yes—
49C2×#896C2212yes—
50C2×#896C2211yescharacteristic
51C2×#896C2212yescomplemented
52C2×#896C2212yescomplemented
53C2×#895C2211yescharacteristic
54C2×#894C2211yescharacteristic
55C2×#894C2212yes—
56C2×#893C2211yescharacteristic
57C2×D3×C4⋊C4C2212yes—
58C2×#886C2211yescharacteristic
59C2×#886C2211yescharacteristic
60C2×#886C2211yescharacteristic, complemented
61C2×#886C2211yescharacteristic, complemented
62C2×#885C2211yescharacteristic
63C2×#884C2211yescharacteristic
64C2×#883C2212yes—
65C2×#882C2211yescharacteristic
66C2×#882C2211yescharacteristic
67C2×#67⋊C4C2211yescharacteristic
68C2×D3×C22⋊C4C2212yes—
69C2×D3×C22⋊C4C2211yescharacteristic
70C2×D3×C22⋊C4C2211yescharacteristic
71C2×#875C2212yescomplemented
72C2×#869C2212yescomplemented
73C3×#398C2212yescomplemented
74C3×#396C2212yescomplemented
75C3×#389C2212yescomplemented
76C3×#388C2212yescomplemented
77C3×#386C2211yescharacteristic
78C3×#385C2211yescharacteristic, complemented
79C3×#381C2211yescharacteristic, complemented
80#5213C2211yescharacteristic
81#5213C2211yescharacteristic, complemented
82#5211C2211yescharacteristic, complemented
83#4993C2212yescomplemented
84#4991C2212yescomplemented
85#4991C2212yescomplemented
86#4990C2212yescomplemented
87#4989C2212yes—
88#4989C2212yescomplemented
89#4989C2212yescomplemented
90#4989C2212yescomplemented
91#4987C2212yes—
92#4979C2212yescomplemented
93#4979C2212yescomplemented
94#4979C2212yescomplemented
95#4975C2212yescomplemented
96#4972C2212yescomplemented
97#4961C2212yes—
98#4959C2212yescomplemented
99#4957C2212yescomplemented
100#4955C2212yes—
101#4955C2211yescharacteristic
102#4949C2212yescomplemented
103#4948C2212yescomplemented
104#4947C2212yescomplemented
105#4947C2212yescomplemented
106#4943C2211yescharacteristic, complemented
107#4943C2211yescharacteristic, complemented
108#4942C2211yescharacteristic, complemented
109Dic3×C22⋊C4C2211yescharacteristic, complemented
110#4940C2212yescomplemented
111C4×(C2×D3)⋊C4C2212yes—
112#4676C2212yescomplemented
113#4675C2212yescomplemented
114#4674C2212yescomplemented
115#4672C2212yes—
116#4669C2212yescomplemented
117#4668C2212yes—
118#4668C2212yes—
119#4668C2212yescomplemented
120#4667C2212yescomplemented
121#4665C2212yes—
122#4665C2212yes—
123#4665C2212yescomplemented
124#4657C2212yescomplemented
125#4657C2212yescomplemented
126#4654C2212yescomplemented
127#4647C2212yescomplemented
128C2×#546—31no—
129C2×#536—31no—
130C22×#123—31no—
131C22×C22⋊Q8—31no—
132#2849—31no—
133#2681—32no—
134#2680—32no—
135#2674—32no—
136#2672—32no—
137#2618—31no—
138#2614—31no—
139#2501—31no—
140#2486—31no—
141#2472—32no—
142#2449—32no—
143#2440—32no—
144#2437—32no—
145#2413D311yescharacteristic, complemented
146#2412—31no—
147#2406—31no—
148#2405—31no—
149#2342—31no—
150#2322—31no—
151C24×D3C2311yescharacteristic
152C24×D3C2311yescharacteristic
153C22×C3×D4C2311yescharacteristic
154C23×C3×C4C2311yescharacteristic
155C23×C3×C4C2311yescharacteristic
156C23×C3×C4C2311yescharacteristic
157C22×#67C2311yescharacteristic
158C22×#67C2311yescharacteristic
159C22×#67C2311yescharacteristic
160C22×#67C2311yescharacteristic
161C23×Dic3C2311yescharacteristic
162C23×Dic3C2311yescharacteristic
163C23×Dic3C2311yescharacteristic
164C2×D3×D4—24no—
165C2×D3×D4—24no—
166C2×D3×D4—42no—
167C2×#235—24no—
168C2×#235—24no—
169C2×#235—42no—
170C22×D12C2311yescharacteristic
171C22×D12C2311yescharacteristic
172C22×D12C2311yescharacteristic
173C22×D12C2311yescharacteristic
174C22×C4×D3—24no—
175C22×C4×D3—24no—
176C22×C4×D3—42no—
177C22×C4×D3C2312yes—
178C22×C4×D3C2312yes—
179C22×C4×D3C2312yes—
180C22×C4×D3C2311yescharacteristic
181C22×C4×D3C2311yescharacteristic
182C22×C4×D3C2311yescharacteristic
183C22×C4×D3C2311yescharacteristic
184C22×Dic6—24no—
185C22×Dic6—24no—
186C22×Dic6—42no—
187C22×Dic6C2312yes—
188C22×Dic6C2312yes—
189C22×Dic6C2311yescharacteristic
190C3×#123—24no—
191C3×#123—24no—
192C3×#117—24no—
193C2×C3×C4⋊C4—24no—
194C2×C3×C4⋊C4C2312yes—
195C2×C3×C4⋊C4C2311yescharacteristic
196C2×C3×C4⋊C4C2311yescharacteristic
197C2×C3×C4⋊C4C2312yes—
198C2×C3×C4⋊C4C2312yes—
199C2×C3×C4⋊C4C2312yes—
200C2×C3×C4⋊C4C2312yes—
201C2×C3×C22⋊C4C2311yescharacteristic
202C2×C3×C22⋊C4C2311yescharacteristic
203C2×C3×C22⋊C4C2311yescharacteristic
204C2×C3×C22⋊C4C2311yescharacteristic
205C2×C3×C22⋊C4C2312yes—
206C2×C3×C22⋊C4C2312yes—
207C2×C3×C22⋊C4C2311yescharacteristic
208C2×C3×C42C2312yes—
209C2×#217C2311yescharacteristic
210C2×#217C2311yescharacteristic
211C2×#217C2312yes—
212C2×#217C2311yescharacteristic
213C2×#217C2312yes—
214#939—24no—
215#935—24no—
216#935—42no—
217#929—24no—
218#929—42no—
219C2×(C2×D3)⋊C4—24no—
220C2×(C2×D3)⋊C4D418yes—
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)⋊C4C2311yescharacteristic
228C2×(C2×D3)⋊C4C2311yescharacteristic
229C2×(C2×D3)⋊C4C2311yescharacteristic
230C2×(C2×D3)⋊C4C2312yes—
231C2×(C2×D3)⋊C4C2312yes—
232C2×(C2×D3)⋊C4C2311yescharacteristic
233C2×(C2×D3)⋊C4C2312yes—
234C2×(C2×D3)⋊C4C2312yes—
235C2×(C2×D3)⋊C4C2312yes—
236C2×(C2×D3)⋊C4C2312yes—
237C2×(C2×D3)⋊C4C2312yes—
238C2×(C2×D3)⋊C4C2311yescharacteristic
239C2×(C2×D3)⋊C4C2311yescharacteristic
240C2×(C2×D3)⋊C4C2311yescharacteristic
241C2×(C2×D3)⋊C4C2311yescharacteristic
242C2×C4⋊Dic3C2312yes—
243C2×C4⋊Dic3C2312yes—
244C2×C4⋊Dic3C2312yes—
245C2×C4⋊Dic3C2312yes—
246C2×Dic3⋊C4—24no—
247C2×Dic3⋊C4—24no—
248C2×Dic3⋊C4C2312yes—
249C2×Dic3⋊C4C2312yes—
250C2×Dic3⋊C4C2312yes—
251C2×Dic3⋊C4C2311yescharacteristic
252C2×Dic3⋊C4C2311yescharacteristic
253C2×Dic3⋊C4C2312yes—
254C2×Dic3⋊C4C2312yes—
255C2×Dic3⋊C4C2312yes—
256C2×Dic3⋊C4C2312yes—
257C2×Dic3⋊C4C2312yes—
258C2×Dic3⋊C4C2312yes—
259C2×C4×Dic3C2311yescharacteristic
260C2×C4×Dic3C2312yes—
261#897—28no—
262#897—28no—
263#896—24no—
264#896—28no—
265#896—28no—
266#896—28no—
267#896—28no—
268#895—24no—
269#894—28no—
270#894—24no—
271#893—24no—
272D3×C4⋊C4—28no—
273#886—24no—
274#886—24no—
275#886—24no—
276#886D418yescomplemented
277#885—24no—
278#884—24no—
279#883—28no—
280#882—24no—
281#882—24no—
282#67⋊C4—24no—
283D3×C22⋊C4—24no—
284D3×C22⋊C4—28no—
285D3×C22⋊C4—24no—
286#875—28no—
287#869—28no—
288C3×#95C2312yes—
289C3×#95C2312yes—
290C3×#95C2312yes—
291C3×#95C2312yes—
292C3⋊#95C2312yes—
293C3⋊#95C2312yes—
294C3⋊#95C2312yes—
295C3⋊#95C2312yes—
296C3⋊#95C2312yes—
297C3⋊#95C2312yes—
298C3⋊#95C2312yes—
299C3⋊#95C2312yes—
300C3⋊#95C2312yes—
301C3⋊#95C2312yes—
302C22×#41—31no—
303C23×Q8—31no—
304C23×D4—31no—
305C24×C4—31no—
306#546—68no—
307#536—68no—
308C2×C4⋊Q8—32no—
309C2×#124—31no—
310C2×#124—32no—
311C2×#123—31no—
312C2×#123—31no—
313C2×#123—31no—
314C2×#123—31no—
315C2×#123—32no—
316C2×#123—31no—
317C2×#123—31no—
318C2×#123—31no—
319C2×#123—31no—
320C2×#123—32no—
321C2×#123—31no—
322C2×#123—68no—
323C2×#123C2×D311yescharacteristic
324C2×#123C2×D311yescharacteristic
325C2×C22⋊Q8—32no—
326C2×C22⋊Q8—32no—
327C2×C22⋊Q8—32no—
328C2×C22⋊Q8—32no—
329C2×C22⋊Q8—32no—
330C2×C22⋊Q8—32no—
331C2×C22⋊Q8—31no—
332C2×C22⋊Q8—68no—
333C2×#121—31no—
334C2×#121—31no—
335C2×#121—31no—
336C2×#120—31no—
337C2×#120—31no—
338C2×C4×D4—31no—
339C2×C4×D4—31no—
340C2×#117C2×D311yescharacteristic, complemented
341C22×C4⋊C4—31no—
342C22×C4⋊C4—31no—
343C22×C4⋊C4—32no—
344C22×C4⋊C4C2×D311yescharacteristic, complemented
345C22×C22⋊C4—31no—
346C22×C22⋊C4—31no—
347C22×C22⋊C4—31no—
348C22×C22⋊C4—32no—
349C22×C22⋊C4—31no—
350#399—32no—
351#399—32no—
352#398—32no—
353#398—32no—
354#398C2×D312yescomplemented
355#397—32no—
356#397—32no—
357#396—32no—
358#396—32no—
359#396C2×D312yescomplemented
360#395—32no—
361#395—32no—
362#395—32no—
363#394—32no—
364#394—32no—
365#394—32no—
366#394—32no—
367#394—32no—
368#393—32no—
369#393—32no—
370#390—32no—
371#389—32no—
372#389—32no—
373#389C2×D312yescomplemented
374#388—32no—
375#388—32no—
376#388—32no—
377#388C2×D312yescomplemented
378#387—32no—
379#386—31no—
380#386—31no—
381#386—32no—
382#386—32no—
383#386—32no—
384#386C2×D311yescharacteristic
385#385—32no—
386#385—32no—
387#385—32no—
388#385—32no—
389#385—32no—
390#385—32no—
391#385—32no—
392#385C2×D311yescharacteristic, complemented
393#384—32no—
394#381—31no—
395#381—31no—
396#381—31no—
397#381C2×D311yescharacteristic, complemented
398#380—32no—
399#380—31no—
400#380—32no—
401#379—31no—
402#379—32no—
403C4×C22⋊C4—31no—
404C4×C22⋊C4—32no—
405C24×C3C2411yescharacteristic
406C24×C3C2411yescharacteristic
407C23×D3—22no—
408C23×D3—22no—
409C23×D3—24no—
410C23×D3—22no—
411C23×D3—22no—
412C23×D3—24no—
413C23×D3—42no—
414C23×D3—41no—
415C23×D3—42no—
416C23×D3C2×D414yes—
417C23×D3C2411yescharacteristic
418C23×D3C2411yescharacteristic
419C23×D3C2411yescharacteristic
420C23×D3C2411yescharacteristic
421C2×C3×D4—22no—
422C2×C3×D4—22no—
423C2×C3×D4—22no—
424C22×C3×C4—22no—
425C22×C3×C4—22no—
426C22×C3×C4—22no—
427C22×C3×C4—22no—
428C22×C3×C4—22no—
429C22×C3×C4—22no—
430C22×C3×C4—42no—
431C22×C3×C4C2×D414yes—
432C22×C3×C4C2411yescharacteristic
433C22×C3×C4C2411yescharacteristic
434C22×C3×C4C2412yes—
435C22×C3×C4C2412yes—
436C22×C3×C4C2411yescharacteristic
437C22×C3×C4C2412yes—
438C22×C3×C4C2411yescharacteristic
439C22×C3×C4C2411yescharacteristic
440C22×C3×C4C2412yes—
441C2×#67—22no—
442C2×#67—22no—
443C2×#67—22no—
444C2×#67—22no—
445C2×#67—22no—
446C2×#67—22no—
447C2×#67—22no—
448C2×#67—22no—
449C2×#67—41no—
450C2×#67—42no—
451C2×#67C2×D414yes—
452C22×Dic3—22no—
453C22×Dic3—22no—
454C22×Dic3—22no—
455C22×Dic3—22no—
456C22×Dic3—22no—
457C22×Dic3—42no—
458C22×Dic3C2×D414yes—
459C22×Dic3C2×D414yes—
460C22×Dic3C2412yes—
461C22×Dic3C2412yes—
462C22×Dic3C2411yescharacteristic
463C22×Dic3C2412yes—
464C22×Dic3C2411yescharacteristic
465C22×Dic3C2411yescharacteristic
466C22×Dic3C2411yescharacteristic
467C22×Dic3C2412yes—
468D3×D4—416no—
469#235—416no—
470C2×D12—22no—
471C2×D12—22no—
472C2×D12—22no—
473C2×D12—22no—
474C2×D12—24no—
475C2×D12—22no—
476C2×D12—22no—
477C2×D12—41no—
478C2×D12—41no—
479C2×D12—42no—
480C2×C4×D3—22no—
481C2×C4×D3—24no—
482C2×C4×D3—24no—
483C2×C4×D3—22no—
484C2×C4×D3—24no—
485C2×C4×D3—24no—
486C2×C4×D3—22no—
487C2×C4×D3—22no—
488C2×C4×D3—24no—
489C2×C4×D3—24no—
490C2×C4×D3—22no—
491C2×C4×D3—22no—
492C2×C4×D3—22no—
493C2×C4×D3—42no—
494C2×C4×D3—42no—
495C2×C4×D3—42no—
496C2×C4×D3—41no—
497C2×C4×D3—41no—
498C2×C4×D3—41no—
499C2×C4×D3—416no—
500C2×C4×D3—42no—
501C2×Dic6—22no—
502C2×Dic6—24no—
503C2×Dic6—24no—
504C2×Dic6—22no—
505C2×Dic6—24no—
506C2×Dic6—24no—
507C2×Dic6—42no—
508C2×Dic6—42no—
509C2×Dic6—41no—
510C2×Dic6—416no—
511C3×C4⋊C4—24no—
512C3×C4⋊C4—22no—
513C3×C4⋊C4—22no—
514C3×C4⋊C4—24no—
515C3×C4⋊C4—24no—
516C3×C4⋊C4—24no—
517C3×C4⋊C4—42no—
518C3×C22⋊C4—22no—
519C3×C22⋊C4—22no—
520C3×C22⋊C4—24no—
521C3×C22⋊C4—22no—
522C3×C22⋊C4—22no—
523C3×C22⋊C4—42no—
524C3×C22⋊C4C2×D414yes—
525C3×C42—24no—
526#217—22no—
527#217—22no—
528#217—24no—
529#217—22no—
530#217—42no—
531(C2×D3)⋊C4—24no—
532(C2×D3)⋊C4—22no—
533(C2×D3)⋊C4—24no—
534(C2×D3)⋊C4—22no—
535(C2×D3)⋊C4—24no—
536(C2×D3)⋊C4—24no—
537(C2×D3)⋊C4—24no—
538(C2×D3)⋊C4—24no—
539(C2×D3)⋊C4—24no—
540(C2×D3)⋊C4—24no—
541(C2×D3)⋊C4—22no—
542(C2×D3)⋊C4—22no—
543(C2×D3)⋊C4—42no—
544(C2×D3)⋊C4—42no—
545(C2×D3)⋊C4—42no—
546(C2×D3)⋊C4—42no—
547(C2×D3)⋊C4C2×D418yes—
548(C2×D3)⋊C4C2×D414yes—
549(C2×D3)⋊C4C2×D414yes—
550(C2×D3)⋊C4C2×D414yes—
551(C2×D3)⋊C4C2×D414yes—
552C4⋊Dic3—24no—
553C4⋊Dic3—24no—
554C4⋊Dic3—24no—
555C4⋊Dic3C2×D418yes—
556Dic3⋊C4—22no—
557Dic3⋊C4—24no—
558Dic3⋊C4—24no—
559Dic3⋊C4—22no—
560Dic3⋊C4—24no—
561Dic3⋊C4—24no—
562Dic3⋊C4—24no—
563Dic3⋊C4—24no—
564Dic3⋊C4—42no—
565Dic3⋊C4—42no—
566Dic3⋊C4—42no—
567C4×Dic3—22no—
568C4×Dic3—42no—
569C25—31no—
570C25—31no—
571C2×#41—64no—
572C2×#41—64no—
573C2×#41—122no—
574C22×Q8—32no—
575C22×Q8—32no—
576C22×Q8—31no—
577C22×Q8—64no—
578C22×Q8—64no—
579C22×Q8—122no—
580C22×D4—31no—
581C22×D4—31no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—64no—
589C22×D4—64no—
590C22×D4—122no—
591C22×D4C22×D311yescharacteristic
592C23×C4—31no—
593C23×C4—31no—
594C23×C4—31no—
595C23×C4—32no—
596C23×C4—32no—
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—31no—
600C23×C4—32no—
601C23×C4—31no—
602C23×C4—64no—
603C23×C4—64no—
604C23×C4—122no—
605C23×C4C22×D311yescharacteristic
606C23×C4C22×D311yescharacteristic
607C23×C4C22×D311yescharacteristic
608C4⋊Q8—68no—
609#124—68no—
610#124—64no—
611#123—24no—
612#123—24no—
613#123—38no—
614#123—68no—
615#123—64no—
616#123—64no—
617#123—68no—
618#123—64no—
619#123—64no—
620#123—64no—
621#123—64no—
622#123—122no—
623#123—122no—
624C22⋊Q8—68no—
625C22⋊Q8—68no—
626C22⋊Q8—68no—
627C22⋊Q8—68no—
628C22⋊Q8—68no—
629C22⋊Q8—64no—
630C22⋊Q8—68no—
631#121—64no—
632#121—64no—
633#121—64no—
634#120—64no—
635#120—64no—
636C4×D4—64no—
637C4×D4—64no—
638#117—24no—
639C2×C4⋊C4—24no—
640C2×C4⋊C4—32no—
641C2×C4⋊C4—32no—
642C2×C4⋊C4—32no—
643C2×C4⋊C4—32no—
644C2×C4⋊C4—32no—
645C2×C4⋊C4—32no—
646C2×C4⋊C4—32no—
647C2×C4⋊C4—31no—
648C2×C4⋊C4—31no—
649C2×C4⋊C4—32no—
650C2×C4⋊C4—32no—
651C2×C4⋊C4—32no—
652C2×C4⋊C4—32no—
653C2×C4⋊C4—32no—
654C2×C4⋊C4—32no—
655C2×C4⋊C4—68no—
656C2×C4⋊C4—64no—
657C2×C4⋊C4—64no—
658C2×C4⋊C4C22×D312yes—
659C2×C4⋊C4C22×D312yes—
660C2×C4⋊C4C22×D312yes—
661C2×C4⋊C4C22×D312yes—
662C2×C4⋊C4C22×D311yescharacteristic
663C2×C4⋊C4C22×D311yescharacteristic
664C2×C4⋊C4C22×D312yes—
665C2×C22⋊C4—38no—
666C2×C22⋊C4—31no—
667C2×C22⋊C4—31no—
668C2×C22⋊C4—31no—
669C2×C22⋊C4—31no—
670C2×C22⋊C4—32no—
671C2×C22⋊C4—31no—
672C2×C22⋊C4—31no—
673C2×C22⋊C4—32no—
674C2×C22⋊C4—31no—
675C2×C22⋊C4—31no—
676C2×C22⋊C4—32no—
677C2×C22⋊C4—32no—
678C2×C22⋊C4—32no—
679C2×C22⋊C4—32no—
680C2×C22⋊C4—31no—
681C2×C22⋊C4—31no—
682C2×C22⋊C4—31no—
683C2×C22⋊C4—32no—
684C2×C22⋊C4—32no—
685C2×C22⋊C4—32no—
686C2×C22⋊C4—32no—
687C2×C22⋊C4—32no—
688C2×C22⋊C4—32no—
689C2×C22⋊C4—32no—
690C2×C22⋊C4—32no—
691C2×C22⋊C4—32no—
692C2×C22⋊C4—68no—
693C2×C22⋊C4—64no—
694C2×C22⋊C4—64no—
695C2×C22⋊C4—64no—
696C2×C22⋊C4C22×D311yescharacteristic
697C2×C22⋊C4C22×D312yes—
698C2×C22⋊C4C22×D311yescharacteristic
699C2×C22⋊C4C22×D311yescharacteristic
700C2×C22⋊C4C22×D311yescharacteristic
701C2×C22⋊C4C22×D312yes—
702C2×C22⋊C4C22×D311yescharacteristic
703C2×C42—31no—
704C2×C42—32no—
705C2×C42C22×D312yes—
706#95—32no—
707#95—32no—
708#95—32no—
709#95—32no—
710#95—32no—
711#95—32no—
712#95—32no—
713#95—32no—
714#95—32no—
715#95—32no—
716#95C22×D312yes—
717#95C22×D312yes—
718#95C22×D312yes—
719#95C22×D312yes—
720C23×C3—22no—
721C23×C3—22no—
722C23×C3—21no—
723C23×C3—21no—
724C23×C3—21no—
725C23×C3—22no—
726C23×C3—22no—
727C23×C3C22×D412yes—
728C23×C3C22×D412yes—
729C23×C3H(5,𝔽2)12yes—
730C23×C3C2511yescharacteristic
731C22×D3—21no—
732C22×D3—21no—
733C22×D3—22no—
734C22×D3—28no—
735C22×D3—21no—
736C22×D3—21no—
737C22×D3—21no—
738C22×D3—21no—
739C22×D3—22no—
740C22×D3—22no—
741C22×D3—22no—
742C22×D3—22no—
743C22×D3—28no—
744C22×D3—21no—
745C22×D3—21no—
746C22×D3—21no—
747C22×D3—22no—
748C22×D3—22no—
749C22×D3—44no—
750C22×D3—44no—
751C22×D3—48no—
752C22×D3—48no—
753C22×D3—48no—
754C22×D3—44no—
755C22×D3—82no—
756C22×D3—84no—
757C22×D3C22×D412yes—
758C22×D3C22×D412yes—
759C22×D3C22×D412yes—
760C22×D32−1+414yes—
761C3×D4—44no—
762C2×C3×C4—28no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4—21no—
766C2×C3×C4—21no—
767C2×C3×C4—22no—
768C2×C3×C4—22no—
769C2×C3×C4—21no—
770C2×C3×C4—22no—
771C2×C3×C4—22no—
772C2×C3×C4—21no—
773C2×C3×C4—21no—
774C2×C3×C4—22no—
775C2×C3×C4—21no—
776C2×C3×C4—22no—
777C2×C3×C4—21no—
778C2×C3×C4—22no—
779C2×C3×C4—22no—
780C2×C3×C4—22no—
781C2×C3×C4—22no—
782C2×C3×C4—22no—
783C2×C3×C4—22no—
784C2×C3×C4—22no—
785C2×C3×C4—44no—
786C2×C3×C4—44no—
787C2×C3×C4C22×D414yes—
788C2×C3×C4C22×D412yes—
789C2×C3×C4C22×D412yes—
790#67—28no—
791#67—44no—
792#67—44no—
793#67—82no—
794C2×Dic3—28no—
795C2×Dic3—21no—
796C2×Dic3—22no—
797C2×Dic3—22no—
798C2×Dic3—21no—
799C2×Dic3—22no—
800C2×Dic3—22no—
801C2×Dic3—22no—
802C2×Dic3—22no—
803C2×Dic3—21no—
804C2×Dic3—21no—
805C2×Dic3—22no—
806C2×Dic3—22no—
807C2×Dic3—21no—
808C2×Dic3—22no—
809C2×Dic3—22no—
810C2×Dic3—22no—
811C2×Dic3—22no—
812C2×Dic3—22no—
813C2×Dic3—44no—
814C2×Dic3—44no—
815C2×Dic3C22×D412yes—
816C2×Dic3C22×D412yes—
817C2×Dic3C22×D412yes—
818C2×Dic3C22×D414yes—
819D12—44no—
820D12—44no—
821D12—44no—
822D12—82no—
823C4×D3—44no—
824C4×D3—48no—
825C4×D3—48no—
826C4×D3—44no—
827C4×D3—48no—
828C4×D3—44no—
829C4×D3—82no—
830Dic6—48no—
831Dic6—48no—
832Dic6—44no—
833C24—31no—
834C24—31no—
835C24—31no—
836C24—34no—
837C24—31no—
838C24—64no—
839C24—62no—
840C24—62no—
841C24—64no—
842C24—62no—
843C24—62no—
844C24—122no—
845C24—121no—
846C24—122no—
847C24C23×D311yescharacteristic
848C24C23×D311yescharacteristic
849#41—1216no—
850C2×Q8—64no—
851C2×Q8—64no—
852C2×Q8—62no—
853C2×Q8—64no—
854C2×Q8—64no—
855C2×Q8—62no—
856C2×Q8—122no—
857C2×Q8—122no—
858C2×Q8—121no—
859C2×Q8—1216no—
860C2×D4—22no—
861C2×D4—22no—
862C2×D4—22no—
863C2×D4—34no—
864C2×D4—62no—
865C2×D4—62no—
866C2×D4—62no—
867C2×D4—62no—
868C2×D4—64no—
869C2×D4—62no—
870C2×D4—62no—
871C2×D4—62no—
872C2×D4—62no—
873C2×D4—62no—
874C2×D4—62no—
875C2×D4—62no—
876C2×D4—62no—
877C2×D4—62no—
878C2×D4—62no—
879C2×D4—121no—
880C2×D4—121no—
881C2×D4—122no—
882C2×D4—121no—
883C2×D4—122no—
884C2×D4—1216no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—22no—
891C22×C4—34no—
892C22×C4—31no—
893C22×C4—31no—
894C22×C4—31no—
895C22×C4—32no—
896C22×C4—34no—
897C22×C4—32no—
898C22×C4—32no—
899C22×C4—32no—
900C22×C4—31no—
901C22×C4—42no—
902C22×C4—64no—
903C22×C4—62no—
904C22×C4—62no—
905C22×C4—64no—
906C22×C4—62no—
907C22×C4—62no—
908C22×C4—64no—
909C22×C4—64no—
910C22×C4—62no—
911C22×C4—64no—
912C22×C4—62no—
913C22×C4—62no—
914C22×C4—62no—
915C22×C4—62no—
916C22×C4—62no—
917C22×C4—64no—
918C22×C4—62no—
919C22×C4—62no—
920C22×C4—122no—
921C22×C4—122no—
922C22×C4—121no—
923C22×C4—121no—
924C22×C4—121no—
925C22×C4—122no—
926C22×C4—122no—
927C22×C4—1216no—
928C22×C4—122no—
929C22×C4D3×D414yes—
930C22×C4C23×D311yescharacteristic
931C22×C4C23×D311yescharacteristic
932C22×C4C23×D312yes—
933C22×C4C23×D312yes—
934C22×C4C23×D312yes—
935C22×C4C23×D311yescharacteristic
936C22×C4C23×D311yescharacteristic
937C22×C4C23×D311yescharacteristic
938C22×C4C23×D312yes—
939C4⋊C4—24no—
940C4⋊C4—24no—
941C4⋊C4—24no—
942C4⋊C4—24no—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—38no—
946C4⋊C4—42no—
947C4⋊C4—64no—
948C4⋊C4—64no—
949C4⋊C4—64no—
950C4⋊C4—64no—
951C4⋊C4—64no—
952C4⋊C4—64no—
953C4⋊C4—62no—
954C4⋊C4—62no—
955C4⋊C4—64no—
956C4⋊C4—64no—
957C4⋊C4—64no—
958C4⋊C4—122no—
959C4⋊C4—122no—
960C4⋊C4—122no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—24no—
965C22⋊C4—22no—
966C22⋊C4—34no—
967C22⋊C4—34no—
968C22⋊C4—34no—
969C22⋊C4—34no—
970C22⋊C4—38no—
971C22⋊C4—42no—
972C22⋊C4—62no—
973C22⋊C4—62no—
974C22⋊C4—64no—
975C22⋊C4—62no—
976C22⋊C4—64no—
977C22⋊C4—64no—
978C22⋊C4—64no—
979C22⋊C4—62no—
980C22⋊C4—64no—
981C22⋊C4—64no—
982C22⋊C4—62no—
983C22⋊C4—64no—
984C22⋊C4—62no—
985C22⋊C4—62no—
986C22⋊C4—64no—
987C22⋊C4—64no—
988C22⋊C4—122no—
989C22⋊C4—122no—
990C22⋊C4—122no—
991C22⋊C4—122no—
992C22⋊C4—122no—
993C22⋊C4D3×D414yes—
994C42—24no—
995C42—62no—
996C42—122no—
997C22×C3—22no—
998C22×C3—22no—
999C22×C3—24no—
1000C22×C3—24no—
1001C22×C3—41no—
1002C22×C3—41no—
1003C22×C3—41no—
1004C22×C3—42no—
1005C22×C3—42no—
1006C22×C3D4214yes—
1007C22×C3C23×D411yescharacteristic
1008C22×C3C23×D411yescharacteristic
1009C22×C3C2×H(5,𝔽2)11yescharacteristic
1010C22×C3C2×2−1+412yes—
1011C22×C3#58512yes—
1012C2×D3—22no—
1013C2×D3—22no—
1014C2×D3—24no—
1015C2×D3—24no—
1016C2×D3—22no—
1017C2×D3—22no—
1018C2×D3—22no—
1019C2×D3—22no—
1020C2×D3—24no—
1021C2×D3—416no—
1022C2×D3—41no—
1023C2×D3—41no—
1024C2×D3—42no—
1025C2×D3—42no—
1026C2×D3—42no—
1027C2×D3—41no—
1028C2×D3—41no—
1029C2×D3—41no—
1030C2×D3—42no—
1031C2×D3—42no—
1032C2×D3—88no—
1033C2×D3#53614yescomplemented
1034C3×C4—22no—
1035C3×C4—22no—
1036C3×C4—24no—
1037C3×C4—41no—
1038C3×C4—42no—
1039C3×C4—41no—
1040C3×C4—41no—
1041C3×C4—42no—
1042C3×C4—42no—
1043Dic3—24no—
1044Dic3—22no—
1045Dic3—22no—
1046Dic3—22no—
1047Dic3—42no—
1048Dic3—41no—
1049Dic3—42no—
1050Dic3—42no—
1051C23—22no—
1052C23—22no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—22no—
1057C23—22no—
1058C23—32no—
1059C23—34no—
1060C23—32no—
1061C23—32no—
1062C23—68no—
1063C23—61no—
1064C23—61no—
1065C23—62no—
1066C23—61no—
1067C23—61no—
1068C23—61no—
1069C23—61no—
1070C23—62no—
1071C23—62no—
1072C23—62no—
1073C23—62no—
1074C23—68no—
1075C23—61no—
1076C23—61no—
1077C23—61no—
1078C23—62no—
1079C23—62no—
1080C23—124no—
1081C23—128no—
1082C23—128no—
1083C23—124no—
1084C23—124no—
1085C23—128no—
1086C23—242no—
1087C23—244no—
1088C23C2×D3×D412yes—
1089C23C2×D3×D412yes—
1090C23#100912yes—
1091C23C24×D311yescharacteristic
1092Q8—128no—
1093Q8—128no—
1094Q8—124no—
1095D4—44no—
1096D4—68no—
1097D4—124no—
1098D4—124no—
1099D4—124no—
1100D4—124no—
1101D4—124no—
1102D4—242no—
1103D4—242no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—28no—
1111C2×C4—22no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—21no—
1119C2×C4—22no—
1120C2×C4—21no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—32no—
1128C2×C4—32no—
1129C2×C4—34no—
1130C2×C4—32no—
1131C2×C4—44no—
1132C2×C4—44no—
1133C2×C4—61no—
1134C2×C4—62no—
1135C2×C4—62no—
1136C2×C4—61no—
1137C2×C4—62no—
1138C2×C4—62no—
1139C2×C4—68no—
1140C2×C4—62no—
1141C2×C4—61no—
1142C2×C4—62no—
1143C2×C4—62no—
1144C2×C4—61no—
1145C2×C4—62no—
1146C2×C4—62no—
1147C2×C4—61no—
1148C2×C4—62no—
1149C2×C4—62no—
1150C2×C4—62no—
1151C2×C4—62no—
1152C2×C4—124no—
1153C2×C4—124no—
1154C2×C4—128no—
1155C2×C4—128no—
1156C2×C4—128no—
1157C2×C4—124no—
1158C2×C4—124no—
1159C2×C4—124no—
1160C2×C4—242no—
1161C2×C4C2×D3×D414yes—
1162C2×C4C2×D3×D412yes—
1163C2×C4C2×D3×D412yes—
1164C2×C3—24no—
1165C2×C3—81no—
1166C2×C3C2×#53611yescharacteristic
1167C2×C3C2×D4211yescharacteristic
1168C2×C3#348511yescharacteristic
1169C2×C3#348912yes—
1170C2×C3#353512yes—
1171D3—24no—
1172D3—42no—
1173D3—42no—
1174D3—81no—
1175C22—22no—
1176C22—24no—
1177C22—22no—
1178C22—24no—
1179C22—34no—
1180C22—41no—
1181C22—42no—
1182C22—41no—
1183C22—42no—
1184C22—41no—
1185C22—62no—
1186C22—64no—
1187C22—64no—
1188C22—62no—
1189C22—62no—
1190C22—62no—
1191C22—64no—
1192C22—62no—
1193C22—62no—
1194C22—1216no—
1195C22—121no—
1196C22—122no—
1197C22—122no—
1198C22—121no—
1199C22—122no—
1200C22—121no—
1201C22—122no—
1202C22—121no—
1203C22—122no—
1204C22—121no—
1205C22—248no—
1206C22#560914yes—
1207C22C22×D3×D411yescharacteristic
1208C22C22×D3×D411yescharacteristic
1209C22C2×#100911yescharacteristic
1210C22#596412yes—
1211C22D3×2−1+412yes—
1212C4—24no—
1213C4—22no—
1214C4—22no—
1215C4—42no—
1216C4—41no—
1217C4—41no—
1218C4—42no—
1219C4—42no—
1220C4—41no—
1221C4—62no—
1222C4—62no—
1223C4—64no—
1224C4—62no—
1225C4—122no—
1226C4—122no—
1227C4—121no—
1228C4—122no—
1229C3#3764711yescharacteristic, complemented, Sylow
1230C2—24no—
1231C2—64no—
1232C2—81no—
1233C2—122no—
1234C2—122no—
1235C2—241no—
1236C2C2×#560911yescharacteristic
1237C2#8604011yescharacteristic
1238C2D3×#53611yescharacteristic
1239C2#8667712yes—
1240C2#8684412yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2413C2
prime radicalC2×#5654C2
hypercenter#2413D3
hypocenterC3#37647
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2413

Complements

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

NH ≅ G/Ntype
2. C2×D3×#123C2semidirect
3. C2×#5526C2semidirect
4. C22×#896C2semidirect
5. C3×#2413C2semidirect
6. #82864C2semidirect
7. #82859C2semidirect
8. #82271C2semidirect
9. #82192C2semidirect
10. #77969C2semidirect
11. #77952C2semidirect
12. #77431C2semidirect
13. #77418C2semidirect
14. #76257C2semidirect
15. #75998C2semidirect
16. #75915C2semidirect
17. #75526C2semidirect
18. #74781C2semidirect
19. #74686C2semidirect
20. #74406C2semidirect
21. #74384C2semidirect
22. #74146C2semidirect
23. #74075C2semidirect
28. C23×Dic6C22semidirect
31. C2×C3×#117C22semidirect
32. C22×C3×C4⋊C4C22semidirect
37. C2×#929C22semidirect
40. C22×Dic3⋊C4C22semidirect
41. C22×Dic3⋊C4C22semidirect
45. C2×#897C22semidirect
46. C2×#897C22semidirect
51. C2×#896C22semidirect
52. C2×#896C22semidirect
60. C2×#886C22semidirect
61. C2×#886C22semidirect
71. C2×#875C22semidirect
72. C2×#869C22semidirect
73. C3×#398C22semidirect
74. C3×#396C22semidirect
75. C3×#389C22semidirect
76. C3×#388C22semidirect
78. C3×#385C22semidirect
79. C3×#381C22semidirect
81. #5213C22semidirect
82. #5211C22semidirect
83. #4993C22semidirect
84. #4991C22semidirect
85. #4991C22semidirect
86. #4990C22semidirect
88. #4989C22semidirect
89. #4989C22semidirect
90. #4989C22semidirect
92. #4979C22semidirect
93. #4979C22semidirect
94. #4979C22semidirect
95. #4975C22semidirect
96. #4972C22semidirect
98. #4959C22semidirect
99. #4957C22semidirect
102. #4949C22semidirect
103. #4948C22semidirect
104. #4947C22semidirect
105. #4947C22semidirect
106. #4943C22semidirect
107. #4943C22semidirect
108. #4942C22semidirect
109. Dic3×C22⋊C4C22semidirect
110. #4940C22semidirect
112. #4676C22semidirect
113. #4675C22semidirect
114. #4674C22semidirect
116. #4669C22semidirect
119. #4668C22semidirect
120. #4667C22semidirect
123. #4665C22semidirect
124. #4657C22semidirect
125. #4657C22semidirect
126. #4654C22semidirect
127. #4647C22semidirect
145. #2413D3semidirect
276. #886D4semidirect
340. C2×#117C2×D3semidirect
344. C22×C4⋊C4C2×D3semidirect
354. #398C2×D3semidirect
359. #396C2×D3semidirect
373. #389C2×D3semidirect
377. #388C2×D3semidirect
392. #385C2×D3semidirect
397. #381C2×D3semidirect
1033. C2×D3#536semidirect
1229. C3#37647semidirect

Maximal subgroups

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

subgroupindex
C2×#56542
C2×D3×#1232
C2×#55262
C22×#8962
C3×#24132
#828642
#828592
#822712
#821922
#779692
#779522
#774312
#774182
#762572
#759982
#759152
#755262
#747812
#746862
#744062
#743842
#741462
#740752
#376473