Finite Group Databasebeta

← #11889403

Subgroups — #11889403

Order 1152.

814 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×#5541C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic
3#10592710C211yesmaximal, characteristic
4#10591189C211yesmaximal, characteristic, complemented
5#10591188C211yesmaximal, characteristic, complemented
6#10591185C211yesmaximal, characteristic, complemented
7#10591185C211yesmaximal, characteristic, complemented
8#10591102C211yesmaximal, characteristic, complemented
9#10591101C211yesmaximal, characteristic, complemented
10#10591099C211yesmaximal, characteristic, complemented
11C2×#63565C211yesmaximal, characteristic, complemented
12#10590384C211yesmaximal, characteristic, complemented
13#10590381C211yesmaximal, characteristic, complemented
14#10590291C211yesmaximal, characteristic, complemented
15#10590286C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#83552—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C2×#3748C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#935—21no—
24C3×D4×Dic3—21no—
25C3×#926C2211yescharacteristic
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#924C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C3×#924C2211yescharacteristic
30C3×#924C2211yescharacteristic
31C3×#889—21no—
32C3×#888—21no—
33C3×#879—21no—
34C3×#878—21no—
35C3×#878—21no—
36C3×#877—21no—
37C3×#870C2211yescharacteristic
38C3×#869C2211yescharacteristic
39C3×C4×Dic6C2211yescharacteristic
40C3×C4×Dic6C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×#3718C2211yescharacteristic
44#63657C2211yescharacteristic
45#63657C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47#63630C2211yescharacteristic
48#63576C2211yescharacteristic
49#63574C2211yescharacteristic
50#63574C2211yescharacteristic
51#63565C2211yescharacteristic
52#63565C2211yescharacteristic
53#63565C2211yescharacteristic
54#63565C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59#63565C2211yescharacteristic
60#63565C2211yescharacteristic
61C3×#552—31no—
62C3×D4×Q8—31no—
63#5541D311yescharacteristic
64D4×Dic6D311yescharacteristic
65#5228—31no—
66#5228—31no—
67#5225—31no—
68C2×#835—31no—
69#5090—31no—
70#5082—31no—
71#5069—31no—
72#5063—31no—
73#5052—31no—
74#5052—31no—
75#5051—31no—
76#5051—31no—
77#5050—31no—
78#5050—31no—
79#5045—31no—
80#5043—31no—
81#5031—31no—
82#5030—31no—
83#5030—31no—
84#5022—31no—
85#5011—31no—
86#5011—31no—
87#5011—61no—
88#5004—31no—
89#4996—31no—
90#4971—31no—
91C2×#810—31no—
92C2×C32×D4D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C22×C3×Dic3—21no—
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×Dic6—22no—
99C2×C3×Dic6—22no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—41no—
103C2×C3×Dic6—41no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C32×C4⋊C4D411yescharacteristic
109C32×C22⋊C4D411yescharacteristic
110C32×C22⋊C4D411yescharacteristic
111C32×C42C2311yescharacteristic
112#3748—41no—
113C2×C3⋊(C3⋊C8)—41no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217—21no—
120C3×#217—21no—
121C3×#217—21no—
122C3×#217—21no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4—21no—
135C3×Dic3⋊C4—21no—
136C3×Dic3⋊C4—21no—
137C3×Dic3⋊C4—21no—
138C3×C4×Dic3—21no—
139C3×C4×Dic3—21no—
140C3×C4×Dic3—21no—
141#3718—22no—
142#3718—41no—
143#3718—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C22×Dic6C2×D311yescharacteristic
148C22×Dic6C2×D311yescharacteristic
149C3×C4⋊Q8—31no—
150C3×C4⋊Q8—61no—
151C3×#126—61no—
152C3×#125—31no—
153C3×#125—61no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8—61no—
161C3×C4×Q8—31no—
162C3×C4×Q8—31no—
163C3×C4×D4—21no—
164C3×C4×D4—61no—
165C3×C4×D4C2×D311yescharacteristic
166C3×C4×D4C2×D311yescharacteristic
167C3×#117—31no—
168C3×#117—61no—
169C2×C3×C4⋊C4—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—31no—
174C2×#216—31no—
175C2×#216—31no—
176#935—21no—
177D4×Dic3—21no—
178#926C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924C2×D311yescharacteristic
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic
183#924C2×D311yescharacteristic
184C2×#208—31no—
185C2×#208—31no—
186C2×#208—61no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—61no—
190#889—21no—
191#888—21no—
192#879—21no—
193#878—21no—
194#878—21no—
195#877—21no—
196#870C2×D311yescharacteristic
197#869C2×D311yescharacteristic
198C4×Dic6C2×D311yescharacteristic
199C4×Dic6C2×D311yescharacteristic
200#835—31no—
201#835—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#830—31no—
211#830—31no—
212#830—31no—
213#830—31no—
214#830—61no—
215#830—61no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—61no—
235#803—31no—
236#803—31no—
237#803—61no—
238C23×C32C2×D411yescharacteristic
239C23×C32C2×D411yescharacteristic
240C32×D4—22no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—42no—
261C3×Dic6—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269C3×Dic6—42no—
270C3×Dic6#4112yes—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3⋊(C3⋊C8)—21no—
275#552—31no—
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—91no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—31no—
291C2×C3×Q8—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—62no—
295C2×C3×Q8—62no—
296C2×C3×Q8—61no—
297C2×C3×Q8—61no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×D4—21no—
301C2×C3×D4#6711yescharacteristic
302C2×C3×D4#6711yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C22×C3×C4C22×D311yescharacteristic
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C2×Dic6—22no—
316C2×Dic6—22no—
317C2×Dic6—21no—
318C2×Dic6—21no—
319C2×Dic6—41no—
320C2×Dic6—41no—
321C2×Dic6C22×D311yescharacteristic
322C2×Dic6C22×D311yescharacteristic
323C2×Dic6C22×D311yescharacteristic
324C2×Dic6C22×D311yescharacteristic
325C3×C4⋊C4—21no—
326C3×C4⋊C4—31no—
327C3×C4⋊C4—31no—
328C3×C4⋊C4—31no—
329C3×C4⋊C4—31no—
330C3×C4⋊C4—61no—
331C3×C4⋊C4—61no—
332C3×C4⋊C4—61no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4#6711yescharacteristic
342C3×C4⋊C4#6711yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4#6711yescharacteristic
351C3×C22⋊C4#6711yescharacteristic
352C3×C22⋊C4#6711yescharacteristic
353C3×C22⋊C4#6711yescharacteristic
354C3×C42—21no—
355C3×C42—61no—
356C3×C42—61no—
357C3×C42—61no—
358C3×C42C22×D311yescharacteristic
359C3×C42C22×D311yescharacteristic
360#217—21no—
361#217—21no—
362#217—21no—
363#217—21no—
364#217—21no—
365#216—62no—
366#216—62no—
367#216—121no—
368#216—121no—
369#216—121no—
370#216—121no—
371C4⋊Dic3—21no—
372C4⋊Dic3—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386C4×Dic3—21no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389#208—121no—
390#208—121no—
391#208—122no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
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—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8—122no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32#13712yes—
413C22×C32C22×D411yescharacteristic
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—21no—
417C32×C4—21no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3×Dic3—22no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—31no—
429C22×Q8—31no—
430C2×Q16—91no—
431C2×Q16—91no—
432C2×Q16—91no—
433C2×M16—91no—
434C22×C8—91no—
435C4⋊Q8—31no—
436C4⋊Q8—61no—
437#126—61no—
438#125—31no—
439#125—61no—
440#123—61no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—61no—
446C22⋊Q8—61no—
447C4×Q8—31no—
448C4×Q8—31no—
449C4×D4—61no—
450C4×D4D3211yescharacteristic
451#117—31no—
452#117—61no—
453C2×C4⋊C4—31no—
454#107—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458#103—91no—
459#103—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470#97—91no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3C2×#6711yescharacteristic
474C23×C3C2×#6711yescharacteristic
475C23×C3C2×#6711yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C3×Q8—32no—
478C3×Q8—61no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C3×Q8—122no—
487C3×D4—22no—
488C3×D4—22no—
489C3×D4—42no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—122no—
516C2×C3×C4—122no—
517C2×C3×C4—122no—
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C2×#6711yescharacteristic
520C2×C3×C4C2×#6711yescharacteristic
521C2×C3×C4C2×#6711yescharacteristic
522C2×C3×C4C2×#6711yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C2×#6711yescharacteristic
525C2×C3×C4C2×#6711yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—42no—
537C2×Dic3—42no—
538C2×Dic3—42no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—21no—
546Dic6—42no—
547Dic6—42no—
548Dic6#23712yes—
549C3⋊C8—62no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C3⋊C8—121no—
560C3⋊C8—121no—
561C2×C32—22no—
562C2×C32—41no—
563C2×C32#54611yescharacteristic
564C2×C32C2×#13711yescharacteristic
565C2×C32#57811yescharacteristic
566C2×Q8—31no—
567C2×Q8—31no—
568C2×Q8—31no—
569C2×Q8—31no—
570C2×Q8—62no—
571C2×Q8—62no—
572C2×Q8—61no—
573C2×Q8—61no—
574C2×Q8—121no—
575C2×Q8—121no—
576C2×D4#62511yescharacteristic
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4C2×D3211yescharacteristic
581C22×C4C2×D3211yescharacteristic
582Q16—182no—
583Q16—361no—
584Q16—361no—
585M16—361no—
586C2×C8—91no—
587C2×C8—91no—
588C2×C8—91no—
589C2×C8—91no—
590C2×C8—361no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4#62511yescharacteristic
607C22⋊C4—61no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4#62511yescharacteristic
613C22⋊C4#62511yescharacteristic
614C42—61no—
615C42—61no—
616C42—61no—
617C42C2×D3211yescharacteristic
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3#94212yes—
636C22×C3#95112yes—
637C22×C3C22×#6711yescharacteristic
638C22×C3C22×#6711yescharacteristic
639C3×C4—21no—
640C3×C4—21no—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—21no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—41no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—62no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4C2×#23711yescharacteristic
662C3×C4#100411yescharacteristic
663C3×C4D3×#4111yescharacteristic
664C3×C4#100911yescharacteristic
665Dic3—22no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673C32#331211yescharacteristic, complemented, Sylow
674C23C2×#62511yescharacteristic
675C23C2×#62511yescharacteristic
676Q8—32no—
677Q8—61no—
678Q8—61no—
679Q8—61no—
680Q8—61no—
681Q8—61no—
682Q8—61no—
683Q8—61no—
684Q8—122no—
685Q8—122no—
686D4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—122no—
700C2×C4—122no—
701C2×C4—122no—
702C2×C4C2×#62511yescharacteristic
703C2×C4C2×#62511yescharacteristic
704C2×C4C2×#62511yescharacteristic
705C2×C4C2×#62511yescharacteristic
706C2×C4C22×D3211yescharacteristic
707C8—181no—
708C8—181no—
709C8—181no—
710C8—181no—
711C2×C3—22no—
712C2×C3—22no—
713C2×C3—21no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—42no—
717C2×C3—41no—
718C2×C3—41no—
719C2×C3—81no—
720C2×C3#580611yescharacteristic
721C2×C3C2×#94211yescharacteristic
722C2×C3C2×#95111yescharacteristic
723C2×C3#582911yescharacteristic
724C2×C3#583811yescharacteristic
725C2×C3#583811yescharacteristic
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22#6382712yes—
732C22C22×#62511yescharacteristic
733C4—21no—
734C4—21no—
735C4—21no—
736C4—21no—
737C4—62no—
738C4—121no—
739C4—121no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—121no—
745C4D3×#23711yescharacteristic
746C4#6431411yescharacteristic
747C3—21no—
748C3#8355211yescharacteristic, complemented
749C3#8360311yescharacteristic, complemented
750C2—22no—
751C2—41no—
752C2C2×#6382711yescharacteristic
753C2#1059524411yescharacteristic
754C2#1059544511yescharacteristic
subgroupG/H
centerC22C22×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radicalC2×C32×D4D4
hypercenterC4×D4D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
4. #10591189C2semidirect
5. #10591188C2semidirect
6. #10591185C2semidirect
7. #10591185C2semidirect
8. #10591102C2semidirect
9. #10591101C2semidirect
10. #10591099C2semidirect
11. C2×#63565C2semidirect
12. #10590384C2semidirect
13. #10590381C2semidirect
14. #10590291C2semidirect
15. #10590286C2semidirect
673. C32#3312semidirect
748. C3#83552semidirect
749. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#55412
C3×D4×Dic62
#105927102
#105911892
#105911882
#105911852
#105911022
#105911012
#105910992
C2×#635652
#105903842
#105903812
#105902912
#105902862
#836033
#835523