Finite Group Databasebeta

← #11889404

Subgroups — #11889404

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic
2#10594853C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic, complemented
4C3×#5228C211yesmaximal, characteristic, complemented
5#10591638C211yesmaximal, characteristic, complemented
6#10591613C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic, complemented
8#10591576C211yesmaximal, characteristic, complemented
9#10591574C211yesmaximal, characteristic, complemented
10#10591559C211yesmaximal, characteristic, complemented
11#10591557C211yesmaximal, characteristic, complemented
12#10591545C211yesmaximal, characteristic, complemented
13#10591188C211yesmaximal, characteristic, complemented
14#10591158C211yesmaximal, characteristic
15#10591126C211yesmaximal, characteristic, complemented
16#83552—31nomaximal
17#80195—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#946—21no—
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C3×#944—21no—
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×#216C2211yescharacteristic
29C3×C4×#67—21no—
30C3×C4×#67C2211yescharacteristic
31C3×#924—21no—
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic
34#63962—21no—
35#63957—21no—
36#63869C2211yescharacteristic
37#63861—21no—
38#63856C2211yescharacteristic
39#63845—21no—
40Dic3×Dic6C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×D4×Q8—31no—
62Q8×#67D311yescharacteristic
63#5642—31no—
64#5541—31no—
65C3×#451—31no—
66#5228—31no—
67#5228D311yescharacteristic, complemented
68#5225—31no—
69C2×#835—31no—
70C2×#835—31no—
71C2×#835—61no—
72#5189—31no—
73#5186—31no—
74#5184—31no—
75#5182—31no—
76#5090—31no—
77#5082—31no—
78#5052—31no—
79#5051—31no—
80#5051—31no—
81#5045—31no—
82#5043—31no—
83#5030—31no—
84#5022—31no—
85#5011—31no—
86#4815—31no—
87#4802—31no—
88#4799—31no—
89#4797—31no—
90#4730—31no—
91#4721—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C22×C3⋊Dic3—21no—
100C2×C3×#67D411yescharacteristic
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C4⋊(C3⋊Dic3)—21no—
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊C8)—41no—
112C2×C3⋊(C3⋊C8)C2311yescharacteristic
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C3×#217—21no—
115C3×#217—21no—
116C3×#217D411yescharacteristic
117C3×#216—22no—
118C3×#216—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3718—41no—
143#3711—41no—
144#3312—91noSylow
145C22×C3×Q8—21no—
146C22×C3×Q8—31no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C2×D311yescharacteristic
149C2×D3×Q8C2×D311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×Q16—31no—
152C3×C4⋊Q8—31no—
153C3×C4⋊Q8—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8—61no—
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×C4×D4—61no—
162#946—21no—
163#946—31no—
164#946C2×D311yescharacteristic
165Q8×Dic3—31no—
166Q8×Dic3C2×D311yescharacteristic
167#944—21no—
168#944C2×D311yescharacteristic
169C2×#216—31no—
170C2×#216—31no—
171C2×#216C2×D311yescharacteristic
172C2×#216C2×D311yescharacteristic
173#935—61no—
174C4×#67—21no—
175C4×#67C2×D311yescharacteristic
176#926—31no—
177C2×C4⋊Dic3—31no—
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—61no—
180#924—21no—
181#924—31no—
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic
184C2×#208—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—61no—
188C2×ΓL(1,𝔽25)—31no—
189#898—61no—
190#892—31no—
191#890—31no—
192#890—61no—
193#889—61no—
194#886—61no—
195#879—61no—
196#877—61no—
197#877—61no—
198#870—31no—
199C4×Dic6—31no—
200C3×#103—31no—
201C3×#103—31no—
202C3×C22⋊C8—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835—61no—
217#835—61no—
218#835—61no—
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224#817—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228#815—31no—
229Dic3⋊C8—31no—
230#810—31no—
231#810—31no—
232#808—31no—
233#808—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—42no—
244C32×Q8#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—42no—
255C3×#67—22no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—91no—
276D4×Q8—31no—
277#491—91no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—91no—
282#467—91no—
283#462—91no—
284#451—31no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—24no—
293C2×C3×Q8—22no—
294C2×C3×Q8—22no—
295C2×C3×Q8—21no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—41no—
300C2×C3×Q8—41no—
301C2×C3×Q8—41no—
302C2×C3×Q8—42no—
303C2×C3×Q8—61no—
304C2×C3×Q8—62no—
305C2×C3×Q8—121no—
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×Q8C22×D311yescharacteristic
308C2×C3×Q8C22×D311yescharacteristic
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×D4—31no—
311C22×C3×C4—21no—
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—31no—
315C22×C3×C4—41no—
316C22×C3×C4—61no—
317C22×C3×C4C22×D311yescharacteristic
318C22×C3×C4C22×D311yescharacteristic
319C2×#67#6711yescharacteristic
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—121no—
323D3×Q8—22no—
324D3×Q8—41no—
325C2×C4×D3—21no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—21no—
328C2×Dic6C22×D311yescharacteristic
329C2×Dic6C22×D311yescharacteristic
330C3×Q16—62no—
331C3×Q16—121no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—61no—
350#217—21no—
351#217—21no—
352#217—61no—
353#217—61no—
354#217#6711yescharacteristic
355#216—22no—
356#216—41no—
357#216—121no—
358#216—121no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4#6711yescharacteristic
363C4⋊Dic3—21no—
364C4⋊Dic3—31no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—61no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—121no—
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—21no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395#208—121no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—61no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8—122no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407ΓL(1,𝔽25)—121no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32#13712yes—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C32×C4—21no—
416C32×C4—22no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C22×Q8—31no—
430C22×Q8D3211yescharacteristic
431C2×Q16—31no—
432C2×Q16—31no—
433C2×Q16—91no—
434C2×M16—91no—
435C22×C8—91no—
436C4⋊Q8—31no—
437C4⋊Q8—61no—
438#126—181no—
439#125—91no—
440#125—181no—
441#123—181no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C22⋊Q8—91no—
448C4×Q8—31no—
449C4×Q8—91no—
450C4×D4—31no—
451C4×D4—61no—
452#117—91no—
453#117—181no—
454C2×C4⋊C4—91no—
455#107—91no—
456#106—91no—
457#106—91no—
458C4⋊C8—91no—
459#103—31no—
460#103—31no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469C22⋊C8—31no—
470C22⋊C8—91no—
471#97—91no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3D3×D411yescharacteristic
475C23×C3C2×#6711yescharacteristic
476C22×D3C2×#6711yescharacteristic
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—22no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—22no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—42no—
488C3×Q8—42no—
489C3×Q8—44no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×Q8—61no—
494C3×Q8—122no—
495C3×Q8#23712yes—
496C3×Q8#23712yes—
497C3×D4—62no—
498C2×C3×C4—22no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—44no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—22no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—122no—
542C2×Dic3—242no—
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549Dic6—21no—
550Dic6—21no—
551Dic6—21no—
552Dic6—21no—
553Dic6—42no—
554C3×C8—61no—
555C3×C8—61no—
556C3⋊C8—21no—
557C3⋊C8—21no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C3⋊C8—121no—
564C2×C32—22no—
565C2×C32#54611yescharacteristic
566C2×C32C2×#13711yescharacteristic
567C2×C32#57811yescharacteristic
568C3×D3—41no—
569C2×Q8—21no—
570C2×Q8—22no—
571C2×Q8—31no—
572C2×Q8—31no—
573C2×Q8—41no—
574C2×Q8—61no—
575C2×Q8—62no—
576C2×Q8—121no—
577C2×Q8C2×D3211yescharacteristic
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C22×C4—21no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—181no—
584C22×C4C2×D3211yescharacteristic
585Q16—62no—
586Q16—121no—
587Q16—361no—
588M16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C2×C8—361no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—31no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—31no—
611C22⋊C4—31no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C42—31no—
618C42—61no—
619C42—181no—
620C42—181no—
621C22×C3—22no—
622C22×C3—22no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—22no—
629C22×C3—61no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3#91812yes—
633C22×C3#94212yes—
634C22×C3C2×D3×D411yescharacteristic
635C22×C3C22×#6711yescharacteristic
636C2×D3—21no—
637C2×D3—21no—
638C2×D3—21no—
639C3×C4—22no—
640C3×C4—22no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—22no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—42no—
647C3×C4—42no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4C2×#23711yescharacteristic
658C3×C4C2×#23711yescharacteristic
659C3×C4#100411yescharacteristic
660C3×C4#100411yescharacteristic
661Dic3—21no—
662Dic3—21no—
663Dic3—21no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—41no—
668Dic3—121no—
669Dic3—121no—
670Dic3—121no—
671Dic3—121no—
672Dic3—241no—
673Dic3—241no—
674C32#331211yescharacteristic, complemented, Sylow
675C23—31no—
676C23D3×#6711yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—21no—
680Q8—42no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—61no—
685Q8—122no—
686Q8#380512yes—
687D4—62no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—42no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—122no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—362no—
706C2×C4D3×#6711yescharacteristic
707C2×C4C22×D3211yescharacteristic
708C8—61no—
709C8—61no—
710C8—181no—
711C8—181no—
712C2×C3—24no—
713C2×C3—22no—
714C2×C3—22no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—21no—
718C2×C3—121no—
719C2×C3#559111yescharacteristic
720C2×C3C2×#91811yescharacteristic
721C2×C3#577911yescharacteristic
722C2×C3#580611yescharacteristic
723C2×C3C2×#94211yescharacteristic
724C2×C3#583811yescharacteristic
725D3—41no—
726C22—21no—
727C22—21no—
728C22—61no—
729C22—61no—
730C22—61no—
731C22#6394812yes—
732C22C2×D3×#6711yescharacteristic
733C4—21no—
734C4—22no—
735C4—41no—
736C4—61no—
737C4—61no—
738C4—61no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—361no—
744C4—361no—
745C4C2×#380511yescharacteristic
746C4#6433011yescharacteristic
747C3—21no—
748C3#8019511yescharacteristic, complemented
749C3#8355211yescharacteristic, complemented
750C2—22no—
751C2—121no—
752C2#1059532811yescharacteristic
753C2C2×#6394811yescharacteristic
754C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC22×Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#63662C2semidirect
4. C3×#5228C2semidirect
5. #10591638C2semidirect
6. #10591613C2semidirect
7. #10591594C2semidirect
8. #10591576C2semidirect
9. #10591574C2semidirect
10. #10591559C2semidirect
11. #10591557C2semidirect
12. #10591545C2semidirect
13. #10591188C2semidirect
15. #10591126C2semidirect
67. #5228D3semidirect
674. C32#3312semidirect
748. C3#80195semidirect
749. C3#83552semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
#105948532
C2×#636622
C3×#52282
#105916382
#105916132
#105915942
#105915762
#105915742
#105915592
#105915572
#105915452
#105911882
#105911582
#105911262
#835523
#801953