Finite Group Databasebeta

← #11888045

Subgroups — #11888045

Order 1152.

851 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5824C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592932C211yesmaximal, characteristic, complemented
4C3×#5239C211yesmaximal, characteristic, complemented
5#10591635C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8#10591559C211yesmaximal, characteristic, complemented
9#10591461C211yesmaximal, characteristic, complemented
10Dic3×#214C211yesmaximal, characteristic, complemented
11#10591420C211yesmaximal, characteristic, complemented
12#10591410C211yesmaximal, characteristic, complemented
13#10591188C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591127C211yesmaximal, characteristic, complemented
16#83510—31nomaximal
17#80248—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×C3×#237C2211yescharacteristic
20#64135C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#946C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C3×#939—21no—
26C3×#935—21no—
27C3×D4×Dic3C2211yescharacteristic
28C2×C3×#214C2211yescharacteristic
29C3×#929—21no—
30C3×C4×#67C2211yescharacteristic
31C3×#924C2211yescharacteristic
32C3×#924C2211yescharacteristic
33C2×C3×Dic3⋊C4—21no—
34#63959—21no—
35#63956—21no—
36#63918C2211yescharacteristic
37#63862—21no—
38#63856C2211yescharacteristic
39Dic3×Dic6C2211yescharacteristic
40#63841C2211yescharacteristic
41#63838—21no—
42C2×#3718C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63659C2211yescharacteristic
47#63659C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63576C2211yescharacteristic
52#63575C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#547—31no—
62#5824D311yescharacteristic
63#5641—31no—
64#5542—31no—
65C3×#452—31no—
66#5239—31no—
67#5239D311yescharacteristic, complemented
68#5233—31no—
69#5233—31no—
70#5233—31no—
71#5233—61no—
72#5188—31no—
73#5182—31no—
74#5173—31no—
75Dic3×SD16—31no—
76#5090—31no—
77#5079—31no—
78#5051—31no—
79#5051—31no—
80#5051—31no—
81#5045—31no—
82#5045—31no—
83C4×#214—31no—
84D4×C3⋊C8—31no—
85#5007—31no—
86#4815—31no—
87#4792—31no—
88#4772—31no—
89#4759—31no—
90#67⋊C8—31no—
91#4723—31no—
92C32×#41—22no—
93C32×#41—41no—
94C2×C32×Q8C2311yescharacteristic
95C2×C32×D4—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C22×C3×Dic3—21no—
103C3×#237—22no—
104C3×#237—41no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×C3×Dic6C2311yescharacteristic
108C2×#627—21no—
109#3757—21no—
110C4⋊(C3⋊Dic3)C2311yescharacteristic
111C4⋊(C3⋊Dic3)C2311yescharacteristic
112C4×C3⋊Dic3—21no—
113C2×C3⋊(C3⋊C8)—41no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#217—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×#216—41no—
121C3×#214—22no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4D411yescharacteristic
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
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—
143D3×C3⋊C8—41no—
144#3302—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41—31no—
147C2×C3×#41C2×D311yescharacteristic
148C2×C3×#41C2×D311yescharacteristic
149C2×#237C2×D311yescharacteristic
150C2×C3×Q16—31no—
151C2×C3×SD16—31no—
152C3×C4⋊Q8—31no—
153C3×#123—61no—
154C3×#123—61no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×#121—61no—
159C3×C4×D4—31no—
160C3×C4×D4—31no—
161C2×C3×C4⋊C4—61no—
162#946—31no—
163#946C2×D311yescharacteristic
164Q8×Dic3—31no—
165#944C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216C2×D311yescharacteristic
169#939—21no—
170#936—61no—
171#935—21no—
172D4×Dic3C2×D311yescharacteristic
173C2×#214C2×D311yescharacteristic
174#929—21no—
175C4×#67C2×D311yescharacteristic
176#926—31no—
177#926—31no—
178#926—31no—
179#926—61no—
180#924—31no—
181#924C2×D311yescharacteristic
182#924C2×D311yescharacteristic
183C2×Dic3⋊C4—21no—
184C22×C3⋊C8—31no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—61no—
188C2×D3×C8—31no—
189#898—61no—
190#892—31no—
191#888—31no—
192#887—61no—
193#887—61no—
194#885—61no—
195#879—61no—
196#879—61no—
197#879—61no—
198#869—31no—
199C4×Dic6—31no—
200C3×#103—31no—
201C3×#102—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—61no—
212#835—61no—
213#835C2×D311yescharacteristic
214#832—31no—
215#832—31no—
216#832—31no—
217#832—31no—
218#832—61no—
219#832—61no—
220#832C2×D311yescharacteristic
221#830—31no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224#818—31no—
225#817—31no—
226#816—31no—
227#816—31no—
228Dic3⋊C8—31no—
229C8×Dic3—31no—
230#810—31no—
231#810—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32—21no—
239C23×C32C2×D411yescharacteristic
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×D4—21no—
244C32×D4—42no—
245C32×D4#4112yes—
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—
254C3×#67—22no—
255C3×#67—42no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3—42no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#627—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—91no—
277#547—31no—
278#487—91no—
279#485—91no—
280#485—91no—
281#474—91no—
282#467—91no—
283#467—91no—
284#462—91no—
285#452—31no—
286#452—91no—
287C4×SD16—91no—
288C8×D4—91no—
289#416—91no—
290#416—91no—
291C3×#41—24no—
292C3×#41—22no—
293C3×#41—22no—
294C3×#41—41no—
295C3×#41—41no—
296C3×#41—42no—
297C3×#41—62no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×Q8C22×D311yescharacteristic
304C2×C3×D4—21no—
305C2×C3×D4—21no—
306C2×C3×D4—21no—
307C2×C3×D4—31no—
308C2×C3×D4—41no—
309C2×C3×D4—61no—
310C2×C3×D4C22×D311yescharacteristic
311C2×C3×D4C22×D311yescharacteristic
312C22×C3×C4—21no—
313C22×C3×C4—21no—
314C22×C3×C4—21no—
315C22×C3×C4—31no—
316C22×C3×C4—41no—
317C22×C3×C4—61no—
318C22×C3×C4—61no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C2×#67—21no—
322C2×#67#6711yescharacteristic
323C22×Dic3—21no—
324C22×Dic3—21no—
325#237—22no—
326#237—41no—
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—61no—
329C2×Dic6—61no—
330C2×Dic6C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C3×Q16—121no—
333C3×SD16—62no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—31no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351#217—21no—
352#217—21no—
353#217—21no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359#217#6711yescharacteristic
360#216—41no—
361#216—121no—
362#216—121no—
363#214—22no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4#6711yescharacteristic
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
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—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4#6711yescharacteristic
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—121no—
395C4×Dic3C22×D311yescharacteristic
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—121no—
405C2×C3⋊C8—122no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—22no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C32×C4—21no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4H(5,𝔽2)11yescharacteristic
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C3×Dic3#13512yes—
432C2×#41—31no—
433C2×#41D3211yescharacteristic
434C2×Q16—31no—
435C2×Q16—91no—
436C2×SD16—31no—
437C22×C8—91no—
438C22×C8—91no—
439C4⋊Q8—31no—
440C4⋊Q8—91no—
441#126—181no—
442#126—181no—
443#124—181no—
444#123—61no—
445#123—61no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450#121—61no—
451C4×Q8—91no—
452C4×Q8—181no—
453C4×D4—31no—
454C4×D4—31no—
455#117—91no—
456#117—91no—
457C2×C4⋊C4—61no—
458#107—91no—
459#107—91no—
460#106—91no—
461C4⋊C8—91no—
462#103—31no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102—91no—
472C22⋊C8—31no—
473C22⋊C8—91no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C23×C3D3×D411yescharacteristic
481C23×C3C2×#6711yescharacteristic
482C22×D3C2×#6711yescharacteristic
483C3×Q8—22no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—41no—
489C3×Q8—61no—
490C3×Q8—61no—
491C3×Q8—61no—
492C3×Q8—61no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—22no—
496C3×D4—41no—
497C3×D4—42no—
498C3×D4—42no—
499C3×D4—44no—
500C3×D4—62no—
501C3×D4—122no—
502C3×D4#23712yes—
503C3×D4#23712yes—
504C2×C3×C4—22no—
505C2×C3×C4—22no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—44no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—122no—
528C2×C3×C4—122no—
529C2×C3×C4D3×D411yescharacteristic
530C2×C3×C4C2×#6711yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532C2×C3×C4C23×D311yescharacteristic
533#67—22no—
534#67—42no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—42no—
540C2×Dic3—42no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550C4×D3—21no—
551C4×D3—21no—
552Dic6—21no—
553Dic6—21no—
554Dic6—21no—
555Dic6—21no—
556Dic6—122no—
557Dic6—122no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—121no—
567C3⋊C8—121no—
568C2×C32—41no—
569C2×C32—42no—
570C2×C32#54611yescharacteristic
571C2×C32C2×#13511yescharacteristic
572C2×C32#57811yescharacteristic
573C3×D3—41no—
574#41—22no—
575#41—41no—
576#41—62no—
577#41—121no—
578C2×Q8—31no—
579C2×Q8—31no—
580C2×Q8—181no—
581C2×Q8C2×D3211yescharacteristic
582C2×D4—21no—
583C2×D4—31no—
584C2×D4—61no—
585C2×D4C2×D3211yescharacteristic
586C22×C4—21no—
587C22×C4—31no—
588C22×C4—61no—
589C22×C4—61no—
590C22×C4C2×D3211yescharacteristic
591Q16—121no—
592Q16—361no—
593SD16—62no—
594C2×C8—31no—
595C2×C8—31no—
596C2×C8—91no—
597C2×C8—91no—
598C2×C8—361no—
599C2×C8—361no—
600C4⋊C4—31no—
601C4⋊C4—31no—
602C4⋊C4—31no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—31no—
623C42—181no—
624C42—181no—
625C42—181no—
626C22×C3—22no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—22no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—42no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—61no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—81no—
647C22×C3—81no—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×#6711yescharacteristic
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C3×C4—22no—
654C3×C4—21no—
655C3×C4—21no—
656C3×C4—21no—
657C3×C4—21no—
658C3×C4—32no—
659C3×C4—42no—
660C3×C4—41no—
661C3×C4—41no—
662C3×C4—61no—
663C3×C4—61no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4C2×#23711yescharacteristic
669C3×C4C2×#23711yescharacteristic
670C3×C4#100411yescharacteristic
671C3×C4#100411yescharacteristic
672Dic3—21no—
673Dic3—21no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—121no—
679Dic3—121no—
680Dic3—121no—
681Dic3—121no—
682Dic3—241no—
683Dic3—241no—
684Dic3#95012yes—
685C32#330211yescharacteristic, complemented, Sylow
686C23—21no—
687C23—31no—
688C23D3×#6711yescharacteristic
689Q8—21no—
690Q8—21no—
691Q8—61no—
692Q8—61no—
693Q8—61no—
694Q8—61no—
695Q8—362no—
696D4—21no—
697D4—42no—
698D4—62no—
699D4—122no—
700D4#380512yes—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—42no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—122no—
715C2×C4—122no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4D3×#6711yescharacteristic
719C2×C4C22×D3211yescharacteristic
720C8—61no—
721C8—61no—
722C8—181no—
723C8—181no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—42no—
728C2×C3—41no—
729C2×C3—42no—
730C2×C3—41no—
731C2×C3—42no—
732C2×C3—82no—
733C2×C3—121no—
734C2×C3#559111yescharacteristic
735C2×C3D3×#13511yescharacteristic
736C2×C3#577911yescharacteristic
737C2×C3#580611yescharacteristic
738C2×C3C2×#95011yescharacteristic
739C2×C3#583811yescharacteristic
740D3—41no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—61no—
748C22—61no—
749C22—61no—
750C22C2×D3×#6711yescharacteristic
751C4—21no—
752C4—32no—
753C4—41no—
754C4—61no—
755C4—61no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—121no—
760C4—361no—
761C4—361no—
762C4C2×#380511yescharacteristic
763C4#6433011yescharacteristic
764C3—21no—
765C3#8024811yescharacteristic, complemented
766C3#8351011yescharacteristic, complemented
767C2—41no—
768C2—42no—
769C2—121no—
770C2D3×#95011yescharacteristic
771C2#1059546511yescharacteristic
772C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radicalC3×#5824C2
hypercenterC2×#41D32
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594841C2semidirect
3. #10592932C2semidirect
4. C3×#5239C2semidirect
5. #10591635C2semidirect
6. #10591623C2semidirect
7. #10591574C2semidirect
8. #10591559C2semidirect
9. #10591461C2semidirect
10. Dic3×#214C2semidirect
11. #10591420C2semidirect
12. #10591410C2semidirect
13. #10591188C2semidirect
14. #67⋊(C3⋊C8)C2semidirect
15. #10591127C2semidirect
67. #5239D3semidirect
685. C32#3302semidirect
765. C3#80248semidirect
766. C3#83510semidirect

Maximal subgroups

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

subgroupindex
C3×#58242
#105948412
#105929322
C3×#52392
#105916352
#105916232
#105915742
#105915592
#105914612
Dic3×#2142
#105914202
#105914102
#105911882
#67⋊(C3⋊C8)2
#105911272
#835103
#802483