Finite Group Databasebeta

← #11888030

Subgroups — #11888030

Order 1152.

829 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5641C211yesmaximal, characteristic, complemented
2#10594887C211yesmaximal, characteristic
3#10592750C211yesmaximal, characteristic, complemented
4C3×#5047C211yesmaximal, characteristic, complemented
5#10591655C211yesmaximal, characteristic, complemented
6#10591635C211yesmaximal, characteristic, complemented
7#10591625C211yesmaximal, characteristic, complemented
8Dic3×#215C211yesmaximal, characteristic, complemented
9#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10591134C211yesmaximal, characteristic, complemented
11#10591083C211yesmaximal, characteristic, complemented
12#10590608C211yesmaximal, characteristic, complemented
13#10590560C211yesmaximal, characteristic, complemented
14#10590521C211yesmaximal, characteristic, complemented
15#10590463C211yesmaximal, characteristic, complemented
16#83664—31nomaximal
17#80248—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22#64133C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C2×C3×#216C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C3×C4×#67C2211yescharacteristic
29C3×#926C2211yescharacteristic
30C3×#898—21no—
31C3×#892C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#887—21no—
34C3×#885—21no—
35C3×#879—21no—
36#63970—21no—
37#63969—21no—
38#63905—21no—
39Dic3×D12C2211yescharacteristic
40D3×Dic3⋊C4—21no—
41#63866C2211yescharacteristic
42#63856C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63637C2211yescharacteristic
46#63634C2211yescharacteristic
47C3×#830C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#809C2211yescharacteristic
50#63575C2211yescharacteristic
51#63573C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#556—31no—
62#5824—31no—
63#5641D311yescharacteristic, complemented
64#5551—31no—
65C3×#452—31no—
66#5233—31no—
67#5188—31no—
68#5182—31no—
69#5173—31no—
70Dic3×SD16—31no—
71#5093—31no—
72#5087—31no—
73#5051—31no—
74#5051—31no—
75#5051—31no—
76#5051—61no—
77#5047—31no—
78#5047D311yescharacteristic, complemented
79#5031—31no—
80C4×#215—31no—
81D4×C3⋊C8—31no—
82#5002—31no—
83#5002—31no—
84#4996—31no—
85#4996—31no—
86#4815—31no—
87#4792—31no—
88#4772—31no—
89#4759—31no—
90#67⋊C8—31no—
91#4723—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×#67—21no—
96C2×C3×#67D411yescharacteristic
97C3×#235—22no—
98C3×#235—41no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2311yescharacteristic
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107#3795—22no—
108#3795—41no—
109C32×C4⋊C4—21no—
110C32×C4⋊C4C2311yescharacteristic
111C32×C22⋊C4—21no—
112#3757—21no—
113#3756—41no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)—41no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×#216—41no—
122C3×#215—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
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×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138#3724—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143D3×C3⋊C8—41no—
144#3302—91noSylow
145C2×C3×#41—31no—
146C2×#237—31no—
147C2×#235—31no—
148C2×#235C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C3×C4⋊Q8—31no—
152C3×#126—61no—
153C3×#126—61no—
154C3×#124—61no—
155C3×C22⋊Q8—21no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8C2×D311yescharacteristic
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C4×Q8—31no—
160C3×C4×Q8—61no—
161C3×C4×D4—31no—
162C3×#117—31no—
163C3×#117—31no—
164#946—31no—
165#946C2×D311yescharacteristic
166Q8×Dic3C2×D311yescharacteristic
167#944—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216—61no—
171C2×#216C2×D311yescharacteristic
172C2×#215C2×D311yescharacteristic
173#939—61no—
174#938—61no—
175#935—61no—
176D4×Dic3—31no—
177#929—61no—
178C4×#67C2×D311yescharacteristic
179#926C2×D311yescharacteristic
180#924—31no—
181#924—31no—
182#924—31no—
183#924—61no—
184C2×Dic3⋊C4—61no—
185C22×C3⋊C8—31no—
186C22×C3⋊C8—31no—
187C22×C3⋊C8—31no—
188C22×C3⋊C8—61no—
189C2×D3×C8—31no—
190#898—21no—
191#892C2×D311yescharacteristic
192D3×C4⋊C4—61no—
193#888C2×D311yescharacteristic
194#887—21no—
195#885—21no—
196#883—61no—
197#883—61no—
198#879—21no—
199C4×D12—31no—
200#869—31no—
201C3×#103—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—61no—
209#832—31no—
210#832—31no—
211#830—31no—
212#830C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214#818—31no—
215#817—31no—
216#816—31no—
217#816—31no—
218Dic3⋊C8—31no—
219C8×Dic3—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—61no—
227#810C2×D311yescharacteristic
228#809—31no—
229#809—31no—
230#809C2×D311yescharacteristic
231#808—31no—
232#807—31no—
233#807—31no—
234#807—31no—
235#807—61no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251#634—21no—
252#634—21no—
253C3×#67—22no—
254C3×#67—42no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—42no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—42no—
269#625—42no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#556—31no—
277#547—91no—
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—62no—
292C3×#41—121no—
293C2×C3×Q8—21no—
294C2×C3×Q8—31no—
295C2×C3×Q8—61no—
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—61no—
301C22×C3×C4—21no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67#6711yescharacteristic
310C22×Dic3—61no—
311C22×Dic3—61no—
312#237—62no—
313#237—121no—
314#235—22no—
315#235—41no—
316#235—62no—
317#235—121no—
318C2×D12C22×D311yescharacteristic
319C2×C4×D3—21no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3C22×D311yescharacteristic
323C2×Dic6—21no—
324C2×Dic6—31no—
325C2×Dic6—31no—
326C2×Dic6—61no—
327C2×Dic6C22×D311yescharacteristic
328C3×Q16—121no—
329C3×SD16—62no—
330C2×C3×C8—31no—
331C2×C3×C8—31no—
332C3×C4⋊C4—21no—
333C3×C4⋊C4—21no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—41no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C22⋊C4—21no—
345C3×C22⋊C4—21no—
346C3×C22⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—41no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C42—31no—
353C3×C42—61no—
354C3×C42—61no—
355C3×C42—61no—
356#217—21no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362#217#6711yescharacteristic
363#216—41no—
364#216—121no—
365#216—121no—
366#216—122no—
367#215—22no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4#6711yescharacteristic
373C4⋊Dic3—21no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—121no—
390Dic3⋊C4#6711yescharacteristic
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—21no—
394C4×Dic3C22×D311yescharacteristic
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—121no—
404C2×C3⋊C8—122no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407D3×C8—121no—
408C22×C32—21no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32C22×D411yescharacteristic
412C2×C3×D3—22no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C32×C4—21no—
419C32×C4—41no—
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#13512yes—
431C2×#41—31no—
432C2×#41—91no—
433C2×Q16—31no—
434C2×Q16—91no—
435C2×SD16—31no—
436C22×C8—91no—
437C22×C8—91no—
438C4⋊Q8—31no—
439C4⋊Q8—91no—
440#126—61no—
441#126—61no—
442#124—61no—
443#123—181no—
444#123—181no—
445C22⋊Q8—31no—
446C22⋊Q8—91no—
447C22⋊Q8—91no—
448C22⋊Q8D3211yescharacteristic
449#121—181no—
450C4×Q8—31no—
451C4×Q8—61no—
452C4×D4—31no—
453C4×D4—91no—
454#117—31no—
455#117—31no—
456C2×C4⋊C4—181no—
457#107—91no—
458#107—91no—
459#106—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#102—31no—
469#102—91no—
470#102—91no—
471C22⋊C8—31no—
472C22⋊C8—91no—
473C4×C8—91no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—61no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3—21no—
480C22×D3C2×#6711yescharacteristic
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—61no—
488C3×Q8—61no—
489C3×Q8—122no—
490C3×D4—32no—
491C3×D4—62no—
492C3×D4—61no—
493C3×D4—122no—
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—21no—
504C2×C3×C4—31no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
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×C4—122no—
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C2×#6711yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—22no—
522#67—42no—
523#67—122no—
524#67—122no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—122no—
535C2×Dic3—122no—
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—21no—
540D12#23712yes—
541C4×D3—21no—
542C4×D3—21no—
543C4×D3—42no—
544C4×D3—122no—
545C4×D3—122no—
546Dic6—21no—
547Dic6—21no—
548Dic6—42no—
549Dic6—61no—
550Dic6—61no—
551Dic6—61no—
552Dic6—61no—
553Dic6—121no—
554Dic6—121no—
555C3×C8—61no—
556C3×C8—61no—
557C3⋊C8—21no—
558C3⋊C8—21no—
559C3⋊C8—62no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C2×C32—41no—
566C2×C32#54611yescharacteristic
567C2×C32C2×#13511yescharacteristic
568C2×C32#57811yescharacteristic
569C3×D3—41no—
570C3×D3—42no—
571#41—62no—
572#41—121no—
573#41—182no—
574#41—361no—
575C2×Q8—31no—
576C2×Q8—61no—
577C2×Q8—91no—
578C2×Q8C2×D3211yescharacteristic
579C2×D4—31no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—61no—
585C22×C4—181no—
586C22×C4—181no—
587C22×C4C2×D3211yescharacteristic
588Q16—121no—
589Q16—361no—
590SD16—62no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C2×C8—361no—
596C2×C8—361no—
597C4⋊C4—21no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4C2×D3211yescharacteristic
610C22⋊C4—21no—
611C22⋊C4—31no—
612C22⋊C4—31no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—31no—
620C42—61no—
621C42—61no—
622C42—61no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—61no—
634C22×C3—61no—
635C22×C3—62no—
636C22×C3—61no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3C2×D3×D411yescharacteristic
640C22×C3C22×#6711yescharacteristic
641C2×D3—21no—
642C2×D3—21no—
643C2×D3—21no—
644C2×D3—22no—
645C2×D3—41no—
646C2×D3—41no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—21no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—41no—
656C3×C4—41no—
657C3×C4—61no—
658C3×C4—61no—
659C3×C4—81no—
660C3×C4—81no—
661C3×C4—121no—
662C3×C4—121no—
663C3×C4—121no—
664C3×C4C2×#23711yescharacteristic
665C3×C4#100411yescharacteristic
666C3×C4D3×#4111yescharacteristic
667C3×C4#100911yescharacteristic
668Dic3—21no—
669Dic3—21no—
670Dic3—41no—
671Dic3—41no—
672Dic3—41no—
673Dic3—121no—
674Dic3—121no—
675Dic3—121no—
676Dic3—121no—
677Dic3—241no—
678Dic3—241no—
679Dic3#95012yes—
680C32#330211yescharacteristic, complemented, Sylow
681C23—31no—
682C23—61no—
683C23D3×#6711yescharacteristic
684Q8—21no—
685Q8—21no—
686Q8—61no—
687Q8—61no—
688Q8—122no—
689Q8—181no—
690Q8—181no—
691D4—32no—
692D4—62no—
693D4—61no—
694D4—122no—
695D4—362no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—31no—
701C2×C4—31no—
702C2×C4—31no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—122no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—362no—
712C2×C4—362no—
713C2×C4D3×#6711yescharacteristic
714C2×C4C22×D3211yescharacteristic
715C8—61no—
716C8—61no—
717C8—181no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—42no—
723C2×C3—41no—
724C2×C3—41no—
725C2×C3—121no—
726C2×C3—122no—
727C2×C3#559111yescharacteristic
728C2×C3D3×#13511yescharacteristic
729C2×C3#577911yescharacteristic
730C2×C3C2×#95011yescharacteristic
731C2×C3#582911yescharacteristic
732C2×C3#583811yescharacteristic
733D3—42no—
734D3—41no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—62no—
742C22—121no—
743C22—121no—
744C22C2×D3×#6711yescharacteristic
745C4—21no—
746C4—32no—
747C4—41no—
748C4—41no—
749C4—61no—
750C4—61no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—361no—
755C4—361no—
756C4D3×#23711yescharacteristic
757C4#6431411yescharacteristic
758C3—21no—
759C3#8024811yescharacteristic, complemented
760C3#8366411yescharacteristic, complemented
761C2—41no—
762C2—121no—
763C2—122no—
764C2#1059530411yescharacteristic
765C2#1059532811yescharacteristic
766C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radical#10594887C2
hypercenterC22⋊Q8D32
hypocenterC32#3302
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
1. C3×#5641C2semidirect
3. #10592750C2semidirect
4. C3×#5047C2semidirect
5. #10591655C2semidirect
6. #10591635C2semidirect
7. #10591625C2semidirect
8. Dic3×#215C2semidirect
9. #67⋊(C3⋊C8)C2semidirect
10. #10591134C2semidirect
11. #10591083C2semidirect
12. #10590608C2semidirect
13. #10590560C2semidirect
14. #10590521C2semidirect
15. #10590463C2semidirect
63. #5641D3semidirect
78. #5047D3semidirect
680. C32#3302semidirect
759. C3#80248semidirect
760. C3#83664semidirect

Maximal subgroups

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

subgroupindex
C3×#56412
#105948872
#105927502
C3×#50472
#105916552
#105916352
#105916252
Dic3×#2152
#67⋊(C3⋊C8)2
#105911342
#105910832
#105906082
#105905602
#105905212
#105904632
#836643
#802483