Finite Group Databasebeta

← #11887557

Subgroups — #11887557

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595361C211yesmaximal, characteristic, complemented
2#10594373C211yesmaximal, characteristic
3C3⋊D3×#103C211yesmaximal, characteristic, complemented
4C3×#4807C211yesmaximal, characteristic, complemented
5C3×#4792C211yesmaximal, characteristic, complemented
6#10591592C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8#10591549C211yesmaximal, characteristic, complemented
9#10590841C211yesmaximal, characteristic, complemented
10#10590744C211yesmaximal, characteristic, complemented
11C8×#626C211yesmaximal, characteristic, complemented
12D3×#816C211yesmaximal, characteristic, complemented
13#10590603C211yesmaximal, characteristic, complemented
14#10590529C211yesmaximal, characteristic, complemented
15#10590487C211yesmaximal, characteristic, complemented
16#81612—31nomaximal
17#80689—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3796—21no—
20C2×D3×Dic6C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic
22C4⋊C4×C3⋊D3C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#944C2211yescharacteristic
25C2×C3×#215C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27C3×#895C2211yescharacteristic
28C3×#888C2211yescharacteristic
29#63916C2211yescharacteristic
30C4×#626C2211yescharacteristic
31#63896—21no—
32Dic3×D12C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63887—21no—
35#63884—21no—
36#63881—21no—
37#63871C2211yescharacteristic
38#63865—21no—
39#63853—21no—
40#63844C2211yescharacteristic
41#63840—21no—
42C2×#3716C2211yescharacteristic
43C2×#3715C2211yescharacteristic
44C32×#103C2211yescharacteristic
45#63662C2211yescharacteristic
46#63643C2211yescharacteristic
47#63637C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×C8×Dic3C2211yescharacteristic
52C3×#810C2211yescharacteristic
53C3×#808C2211yescharacteristic
54#63574C2211yescharacteristic
55#63573C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63557C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5727—31no—
62#5726—31no—
63#5632—31no—
64#5611—31no—
65C3×#487—31no—
66C3×#465—31no—
67#5170—31no—
68#5162—31no—
69C8×#67—31no—
70C2×#816—31no—
71#5094—31no—
72#5083—31no—
73#5043—31no—
74#5040—31no—
75#4862—31no—
76#4854—31no—
77#4807—31no—
78#4807D311yescharacteristic, complemented
79#4806—31no—
80#4806—31no—
81#4805—31no—
82#4805—31no—
83D3×#103—31no—
84D3×#103—31no—
85D3×#103—31no—
86D3×#103—61no—
87#4792D311yescharacteristic, complemented
88#4778—31no—
89#4758—31no—
90C4×#204—31no—
91C8×D12—31no—
92C2×C32×Q8C2311yescharacteristic
93Q8×C3⋊D3—22no—
94Q8×C3⋊D3—41no—
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—21no—
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3796—44no—
112D3×Dic6—22no—
113D3×Dic6—41no—
114C2×C32×C8C2311yescharacteristic
115C32×C4⋊C4C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#215—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722D411yescharacteristic
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142Dic32—21no—
143#3716—22no—
144#3715—41no—
145#3298—91noSylow
146C2×#239—61no—
147C2×D3×Q8—31no—
148C2×D3×Q8—31no—
149C2×D3×Q8—31no—
150C2×D3×Q8—61no—
151C2×#237—61no—
152C22×Dic6—31no—
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×C4⋊Q8—31no—
156C3×C4⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×#121—31no—
159#946—31no—
160#946—61no—
161#946C2×D311yescharacteristic
162#944C2×D311yescharacteristic
163C2×#215—31no—
164C2×#215C2×D311yescharacteristic
165#938—31no—
166#935—61no—
167D4×Dic3—31no—
168C2×#214—31no—
169C2×#214—31no—
170C4×#67—31no—
171C2×C4⋊Dic3—31no—
172C2×#204—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8—61no—
176C2×D3×C8C2×D311yescharacteristic
177#897—31no—
178#896—61no—
179#896—61no—
180#896—61no—
181#895—31no—
182#895C2×D311yescharacteristic
183#894—61no—
184#894—61no—
185#893—61no—
186D3×C4⋊C4—31no—
187D3×C4⋊C4—31no—
188D3×C4⋊C4—31no—
189D3×C4⋊C4—61no—
190#888—61no—
191#888—61no—
192#888C2×D311yescharacteristic
193#887—31no—
194#883—61no—
195#67⋊C4—61no—
196#878—61no—
197#878—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×#103—21no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic
207C3×#103C2×D311yescharacteristic
208C3×#102—31no—
209C3×C4×C8—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835C2×D311yescharacteristic
215#830—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220#817—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816C2×D311yescharacteristic
227Dic3⋊C8—31no—
228C8×Dic3C2×D311yescharacteristic
229#810—31no—
230#810—31no—
231#810—31no—
232#810—61no—
233#810C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#808—31no—
237#808C2×D311yescharacteristic
238C4⋊(C3⋊C8)—31no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—42no—
253C4×C3⋊D3—42no—
254#634—21no—
255#634—42no—
256#634#4112yescomplemented
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×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#627—42no—
272#626—42no—
273#626SD1614yescomplemented
274D3×Dic3—42no—
275D3×Dic3—42no—
276D3×Dic3—42no—
277C32×C8—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—91no—
282#547—91no—
283#487—31no—
284#483—91no—
285#483—91no—
286#475—91no—
287#465—31no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—61no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C2×#67—31no—
305C2×#67—61no—
306C22×Dic3—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309#239—124no—
310D3×Q8—62no—
311D3×Q8—62no—
312D3×Q8—62no—
313D3×Q8—64no—
314D3×Q8—121no—
315D3×Q8—121no—
316D3×Q8—121no—
317D3×Q8—122no—
318#237—124no—
319C2×D12—21no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×C4×D3—121no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—21no—
337C2×Dic6—31no—
338C2×Dic6—31no—
339C2×Dic6—61no—
340C2×Dic6—62no—
341C2×Dic6—61no—
342C2×Dic6—61no—
343C2×Dic6—61no—
344C2×Dic6—61no—
345C2×Dic6—121no—
346C2×Dic6—121no—
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—121no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C4⋊C4C22×D311yescharacteristic
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367#217—31no—
368#217—61no—
369#217—61no—
370#215—41no—
371#215—121no—
372#214—62no—
373#214—121no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—31no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—121no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411#204—62no—
412D3×C8—41no—
413D3×C8—121no—
414D3×C8—121no—
415D3×C8—122no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3C2×SD1612yes—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3C2×SD1612yes—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—22no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3C2×SD1612yes—
439C2×#41—181no—
440C22×Q8—91no—
441C22×Q8—91no—
442C2×SD16—31no—
443C2×SD16—91no—
444C2×SD16—91no—
445C22×C8—31no—
446C22×C8—91no—
447C4⋊Q8—31no—
448C4⋊Q8—31no—
449C4⋊Q8—181no—
450#123—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—181no—
455C22⋊Q8—181no—
456C22⋊Q8—181no—
457#121—31no—
458#121—91no—
459C4×Q8—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465#106—31no—
466#106—91no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—31no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103D3211yescharacteristic
478#102—31no—
479C22⋊C8—91no—
480C22⋊C8—91no—
481C4×C8—31no—
482C23×C3—31no—
483C23×C3—61no—
484C22×D3—21no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—61no—
488C22×D3D3×D411yescharacteristic
489C3×Q8—22no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—41no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—122no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—122no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—34no—
519#67—122no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3—122no—
535C2×Dic3D3×D411yescharacteristic
536C2×Dic3D3×D411yescharacteristic
537C2×Dic3D3×D411yescharacteristic
538D12—21no—
539D12—21no—
540D12—34no—
541D12—42no—
542D12—122no—
543C4×D3—21no—
544C4×D3—21no—
545C4×D3—62no—
546C4×D3—62no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—124no—
558C4×D3—122no—
559C4×D3—242no—
560Dic6—21no—
561Dic6—21no—
562Dic6—32no—
563Dic6—32no—
564Dic6—42no—
565Dic6—62no—
566Dic6—61no—
567Dic6—61no—
568Dic6—121no—
569Dic6—122no—
570Dic6—122no—
571Dic6—122no—
572Dic6—122no—
573Dic6—124no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—41no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—121no—
584C2×C32#54611yescharacteristic
585C2×C32C22×SD1611yescharacteristic
586C2×C32#57811yescharacteristic
587C3⋊D3—22no—
588C3×D3—22no—
589C3×D3—81no—
590#41—364no—
591C2×Q8—31no—
592C2×Q8—61no—
593C2×Q8—91no—
594C2×Q8—181no—
595C2×Q8—181no—
596C2×Q8—182no—
597C2×Q8—182no—
598C2×Q8—361no—
599C2×Q8—361no—
600C2×Q8C2×D3211yescharacteristic
601C2×D4—31no—
602C2×D4—61no—
603C2×D4—91no—
604C2×D4—181no—
605C22×C4—31no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612SD16—121no—
613SD16—182no—
614SD16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—121no—
619C2×C8—361no—
620C2×C8C2×D3211yescharacteristic
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—91no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4C2×D3211yescharacteristic
634C22⋊C4—61no—
635C22⋊C4—61no—
636C22⋊C4—91no—
637C22⋊C4—91no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—181no—
643C22×C3—21no—
644C22×C3—32no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3C2×D3×D411yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—32no—
655C2×D3—32no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3D3×SD1612yes—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—32no—
670C3×C4—42no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4#100411yescharacteristic
682C3×C4D3×#4111yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—62no—
691Dic3—62no—
692Dic3—61no—
693Dic3—62no—
694Dic3—61no—
695Dic3—122no—
696Dic3—121no—
697Dic3—121no—
698Dic3—241no—
699Dic3D3×SD1612yes—
700C32#329811yescharacteristic, complemented, Sylow
701C23—31no—
702C23—61no—
703C23—91no—
704Q8—21no—
705Q8—21no—
706Q8—61no—
707Q8—61no—
708Q8—92no—
709Q8—122no—
710Q8—181no—
711Q8—362no—
712Q8—362no—
713D4—61no—
714D4—61no—
715D4—94no—
716D4—122no—
717D4—362no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4—362no—
738C2×C4C22×D3211yescharacteristic
739C8—21no—
740C8—61no—
741C8—61no—
742C8—181no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—62no—
747C2×C3—241no—
748C2×C3#561011yescharacteristic
749C2×C3#567611yescharacteristic
750C2×C3C2×D3×SD1611yescharacteristic
751C2×C3C2×D3×SD1611yescharacteristic
752C2×C3#576611yescharacteristic
753C2×C3#577111yescharacteristic
754D3—22no—
755D3—64no—
756D3—62no—
757D3—62no—
758D3—81no—
759C22—32no—
760C22—61no—
761C22—61no—
762C22—92no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—181no—
767C22—181no—
768C22D32×D411yescharacteristic
769C4—32no—
770C4—41no—
771C4—41no—
772C4—61no—
773C4—61no—
774C4—121no—
775C4—121no—
776C4—121no—
777C4—181no—
778C4—182no—
779C4—361no—
780C4#6430611yescharacteristic
781C4#6431411yescharacteristic
782C3—21no—
783C3#8068911yescharacteristic, complemented
784C3#8161211yescharacteristic, complemented
785C2—62no—
786C2—182no—
787C2—241no—
788C2#1059428511yescharacteristic
789C2D32×SD1611yescharacteristic
790C2#1059476811yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10594373C2
hypercenter#103D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595361C2semidirect
3. C3⋊D3×#103C2semidirect
4. C3×#4807C2semidirect
5. C3×#4792C2semidirect
6. #10591592C2semidirect
7. #10591564C2semidirect
8. #10591549C2semidirect
9. #10590841C2semidirect
10. #10590744C2semidirect
11. C8×#626C2semidirect
12. D3×#816C2semidirect
13. #10590603C2semidirect
14. #10590529C2semidirect
15. #10590487C2semidirect
78. #4807D3semidirect
87. #4792D3semidirect
256. #634#41semidirect
273. #626SD16semidirect
700. C32#3298semidirect
783. C3#80689semidirect
784. C3#81612semidirect

Maximal subgroups

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

subgroupindex
#105953612
#105943732
C3⋊D3×#1032
C3×#48072
C3×#47922
#105915922
#105915642
#105915492
#105908412
#105907442
C8×#6262
D3×#8162
#105906032
#105905292
#105904872
#816123
#806893