Finite Group Databasebeta

← #11889409

Subgroups — #11889409

Order 1152.

809 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5642C211yesmaximal, characteristic
2Dic6×#67C211yesmaximal, characteristic
3#10592750C211yesmaximal, characteristic, complemented
4C3×#5050C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591638C211yesmaximal, characteristic, complemented
7#10591625C211yesmaximal, characteristic, complemented
8#10591576C211yesmaximal, characteristic, complemented
9#10591158C211yesmaximal, characteristic
10#10591124C211yesmaximal, characteristic, complemented
11C2×#63565C211yesmaximal, characteristic, complemented
12#10590600C211yesmaximal, characteristic, complemented
13#10590562C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590493C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#80195—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64133C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C3×#898—21no—
31C3×#892C2211yescharacteristic
32C3×#890—21no—
33C3×#890C2211yescharacteristic
34C3×#886—21no—
35C3×#877—21no—
36Dic3×#67—21no—
37#63964—21no—
38#63887—21no—
39#63866C2211yescharacteristic
40#63856C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63839—21no—
43C2×#3711C2211yescharacteristic
44#63662C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#810C2211yescharacteristic
50#63573C2211yescharacteristic
51#63573C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#552—31no—
62Q8×#67—31no—
63#5642D311yescharacteristic
64D4×Dic6—31no—
65C3×#451—31no—
66C2×#835—31no—
67#5189—31no—
68#5186—31no—
69#5184—31no—
70#5182—31no—
71#5069—31no—
72#5063—31no—
73#5052—31no—
74#5051—31no—
75#5051—31no—
76#5051—61no—
77#5050—31no—
78#5050D311yescharacteristic, complemented
79#5031—31no—
80#5030—31no—
81#5011—31no—
82#5004—31no—
83#4996—31no—
84#4971—31no—
85C2×#810—31no—
86#4815—31no—
87#4802—31no—
88#4799—31no—
89#4797—31no—
90#4730—31no—
91#4721—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C22×C3×Dic3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×Dic6—22no—
100C2×C3×Dic6—21no—
101C2×C3×Dic6—41no—
102C2×C3×Dic6C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×D3×Dic3—21no—
106D3×Dic6—22no—
107D3×Dic6—41no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3757—21no—
112#3756—41no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C2×C3⋊(C3⋊C8)—41no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217D411yescharacteristic
119C3×#216—22no—
120C3×#216—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3—21no—
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3711—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C22×Dic6C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×Q16—31no—
151C3×#126—61no—
152C3×#125—31no—
153C3×#125—61no—
154C3×#123—61no—
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8C2×D311yescharacteristic
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C4×Q8—31no—
160C3×C4×D4—31no—
161C3×#117—31no—
162C3×#117—61no—
163C2×C3×C4⋊C4—31no—
164#946—31no—
165#946—61no—
166#946C2×D311yescharacteristic
167Q8×Dic3—31no—
168Q8×Dic3C2×D311yescharacteristic
169#944—31no—
170#944—61no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—61no—
174C2×#216C2×D311yescharacteristic
175C2×#216C2×D311yescharacteristic
176D4×Dic3—61no—
177C4×#67—61no—
178C4×#67C2×D311yescharacteristic
179C2×C4⋊Dic3C2×D311yescharacteristic
180#924—31no—
181#924—31no—
182#924—31no—
183#924—61no—
184#924—61no—
185C2×#208—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C2×ΓL(1,𝔽25)—31no—
190#898—21no—
191#892C2×D311yescharacteristic
192#890—21no—
193#890C2×D311yescharacteristic
194#888—61no—
195#886—21no—
196#878—61no—
197#878—61no—
198#877—21no—
199#869—31no—
200C4×Dic6—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×C22⋊C8—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—61no—
211#830—31no—
212#830C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214#817—31no—
215#817—31no—
216#816—31no—
217#816—31no—
218#815—31no—
219Dic3⋊C8—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#810C2×D311yescharacteristic
230#810C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250#634—21no—
251#634—21no—
252C3×#67—22no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—42no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6#4112yes—
269#627—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—91no—
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—31no—
292C2×C3×Q8—31no—
293C2×C3×Q8—62no—
294C2×C3×Q8—61no—
295C2×C3×Q8—121no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×D4—31no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67#6711yescharacteristic
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—61no—
309D3×Q8—62no—
310D3×Q8—121no—
311C2×C4×D3—61no—
312C2×C4×D3C22×D311yescharacteristic
313C2×Dic6—22no—
314C2×Dic6—21no—
315C2×Dic6—31no—
316C2×Dic6—31no—
317C2×Dic6—41no—
318C2×Dic6—61no—
319C2×Dic6—62no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6—121no—
323C2×Dic6C22×D311yescharacteristic
324C2×Dic6C22×D311yescharacteristic
325C3×Q16—62no—
326C3×Q16—121no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—21no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4C22×D311yescharacteristic
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C22⋊C4—21no—
344C3×C22⋊C4—21no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—41no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352C3×C42—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—121no—
357#217#6711yescharacteristic
358#216—22no—
359#216—41no—
360#216—121no—
361#216—121no—
362#216—122no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4#6711yescharacteristic
367C4⋊Dic3—21no—
368C4⋊Dic3—21no—
369C4⋊Dic3—21no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3C22×D311yescharacteristic
377C4⋊Dic3C22×D311yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—121no—
388Dic3⋊C4#6711yescharacteristic
389C4×Dic3—21no—
390C4×Dic3—21no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3C22×D311yescharacteristic
394#208—121no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8—121no—
403C2×C3⋊C8—122no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406ΓL(1,𝔽25)—121no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32#13712yes—
410C22×C32C22×D411yescharacteristic
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C32×C4—21no—
415C32×C4—41no—
416C32×C4—41no—
417C32×C4C2×#4111yescharacteristic
418C32×C4H(5,𝔽2)11yescharacteristic
419C3⋊Dic3—41no—
420C3⋊Dic3—41no—
421C3×Dic3—22no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—31no—
429C22×Q8—91no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×Q16—91no—
433C2×M16—91no—
434C22×C8—91no—
435C4⋊Q8—91no—
436C4⋊Q8—181no—
437#126—61no—
438#125—31no—
439#125—61no—
440#123—61no—
441C22⋊Q8—31no—
442C22⋊Q8—91no—
443C22⋊Q8—91no—
444C22⋊Q8—181no—
445C22⋊Q8—181no—
446C22⋊Q8D3211yescharacteristic
447C4×Q8—31no—
448C4×Q8—91no—
449C4×D4—31no—
450C4×D4—181no—
451#117—31no—
452#117—61no—
453C2×C4⋊C4—31no—
454#107—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
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—31no—
469C22⋊C8—91no—
470#97—91no—
471C23×C3—21no—
472C23×C3—31no—
473C23×C3D3×D411yescharacteristic
474C23×C3C2×#6711yescharacteristic
475C22×D3C2×#6711yescharacteristic
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—32no—
481C3×Q8—41no—
482C3×Q8—41no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
487C3×D4—62no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
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—31no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—122no—
512C2×C3×C4—122no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C2×#6711yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—22no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—42no—
523C2×Dic3—42no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—122no—
537Dic6—21no—
538Dic6—21no—
539Dic6—21no—
540Dic6—42no—
541Dic6—61no—
542Dic6—61no—
543Dic6—61no—
544Dic6—61no—
545Dic6—121no—
546Dic6—121no—
547Dic6—122no—
548Dic6—122no—
549Dic6#23712yes—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—62no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—61no—
559C3⋊C8—121no—
560C2×C32—22no—
561C2×C32#54611yescharacteristic
562C2×C32C2×#13711yescharacteristic
563C2×C32#57811yescharacteristic
564C3×D3—41no—
565C2×Q8—31no—
566C2×Q8—31no—
567C2×Q8—62no—
568C2×Q8—61no—
569C2×Q8—91no—
570C2×Q8—121no—
571C2×Q8—181no—
572C2×Q8—182no—
573C2×Q8—361no—
574C2×Q8C2×D3211yescharacteristic
575C2×D4—31no—
576C22×C4—31no—
577C22×C4—61no—
578C22×C4—61no—
579C22×C4—181no—
580C22×C4C2×D3211yescharacteristic
581Q16—62no—
582Q16—121no—
583Q16—361no—
584M16—361no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—91no—
589C2×C8—361no—
590C4⋊C4—21no—
591C4⋊C4—31no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—61no—
595C4⋊C4—61no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—91no—
600C4⋊C4—181no—
601C4⋊C4—181no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4C2×D3211yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—31no—
608C22⋊C4—31no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—31no—
614C42—61no—
615C42—61no—
616C42—181no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3#91812yes—
629C22×C3#95112yes—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C22×#6711yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—61no—
648C3×C4—81no—
649C3×C4—81no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4—121no—
653C3×C4C2×#23711yescharacteristic
654C3×C4#100411yescharacteristic
655C3×C4D3×#4111yescharacteristic
656C3×C4#100911yescharacteristic
657Dic3—21no—
658Dic3—21no—
659Dic3—21no—
660Dic3—22no—
661Dic3—41no—
662Dic3—41no—
663Dic3—41no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—121no—
668Dic3—241no—
669Dic3—241no—
670C32#331211yescharacteristic, complemented, Sylow
671C23—31no—
672C23D3×#6711yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—32no—
676Q8—61no—
677Q8—61no—
678Q8—61no—
679Q8—122no—
680Q8—181no—
681Q8—181no—
682Q8—362no—
683D4—62no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—31no—
689C2×C4—31no—
690C2×C4—31no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—122no—
698C2×C4—122no—
699C2×C4—181no—
700C2×C4—181no—
701C2×C4—362no—
702C2×C4D3×#6711yescharacteristic
703C2×C4C22×D3211yescharacteristic
704C8—61no—
705C8—61no—
706C8—181no—
707C8—181no—
708C2×C3—22no—
709C2×C3—22no—
710C2×C3—21no—
711C2×C3—21no—
712C2×C3—21no—
713C2×C3—42no—
714C2×C3—121no—
715C2×C3#559111yescharacteristic
716C2×C3C2×#91811yescharacteristic
717C2×C3#577911yescharacteristic
718C2×C3C2×#95111yescharacteristic
719C2×C3#582911yescharacteristic
720C2×C3#583811yescharacteristic
721D3—41no—
722C22—21no—
723C22—21no—
724C22—61no—
725C22—61no—
726C22—61no—
727C22#6394312yes—
728C22C2×D3×#6711yescharacteristic
729C4—21no—
730C4—41no—
731C4—41no—
732C4—61no—
733C4—61no—
734C4—62no—
735C4—61no—
736C4—121no—
737C4—121no—
738C4—121no—
739C4—361no—
740C4—361no—
741C4D3×#23711yescharacteristic
742C4#6431411yescharacteristic
743C3—21no—
744C3#8019511yescharacteristic, complemented
745C3#8360311yescharacteristic, complemented
746C2—22no—
747C2—121no—
748C2#1059530411yescharacteristic
749C2C2×#6394311yescharacteristic
750C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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. #10592750C2semidirect
4. C3×#5050C2semidirect
5. #10591653C2semidirect
6. #10591638C2semidirect
7. #10591625C2semidirect
8. #10591576C2semidirect
10. #10591124C2semidirect
11. C2×#63565C2semidirect
12. #10590600C2semidirect
13. #10590562C2semidirect
14. #10590521C2semidirect
15. #10590493C2semidirect
78. #5050D3semidirect
670. C32#3312semidirect
744. C3#80195semidirect
745. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#56422
Dic6×#672
#105927502
C3×#50502
#105916532
#105916382
#105916252
#105915762
#105911582
#105911242
C2×#635652
#105906002
#105905622
#105905212
#105904932
#836033
#801953