Finite Group Databasebeta

← #11882248

Subgroups — #11882248

Order 1152.

846 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×#5596C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic, complemented
3#10592740C211yesmaximal, characteristic, complemented
4C3×#5041C211yesmaximal, characteristic, complemented
5#10591489C211yesmaximal, characteristic, complemented
6#10591439C211yesmaximal, characteristic, complemented
7#10591438C211yesmaximal, characteristic, complemented
8#10591408C211yesmaximal, characteristic, complemented
9#10591179C211yesmaximal, characteristic, complemented
10#10591175C211yesmaximal, characteristic, complemented
11C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#10590559C211yesmaximal, characteristic, complemented
13#10590558C211yesmaximal, characteristic, complemented
14#10590487C211yesmaximal, characteristic, complemented
15#10590486C211yesmaximal, characteristic, complemented
16#83320—31nomaximal
17#80640—31nomaximal
18C2×C3×#237—21no—
19C32×#121C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21#64133C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#940C2211yescharacteristic
24C3×#939—21no—
25C3×D4×Dic3C2211yescharacteristic
26C2×C3×#214C2211yescharacteristic
27C3×#930C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C22×C3×C3⋊C8C2211yescharacteristic
31C3×#893C2211yescharacteristic
32C3×#888C2211yescharacteristic
33C3×#885—21no—
34C3×#67⋊C4—21no—
35#63964—21no—
36#63955—21no—
37#63918C2211yescharacteristic
38#63867—21no—
39#63866C2211yescharacteristic
40#63844C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63837—21no—
43C2×#3716C2211yescharacteristic
44C2×#3715C2211yescharacteristic
45#63659C2211yescharacteristic
46#63637C2211yescharacteristic
47#63635C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63567C2211yescharacteristic
58#63565C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#532—31no—
62#5622—31no—
63#5596D311yescharacteristic
64#5470—31no—
65C3×#465—31no—
66#5163—31no—
67#5162—31no—
68#5114—31no—
69C2×Dic3⋊C8—31no—
70#5094—31no—
71#5094—31no—
72#5075—31no—
73#5075—31no—
74#5048—31no—
75#5041—31no—
76#5041—31no—
77#5041—31no—
78#5041—31no—
79#5041—61no—
80#5041D311yescharacteristic, complemented
81#5019—31no—
82#5019—31no—
83#5008—31no—
84#5008—31no—
85C2×C4⋊(C3⋊C8)—31no—
86#4870—31no—
87#4854—31no—
88#4818—31no—
89#4791—31no—
90#4762—31no—
91#4761—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C22×C3×Dic3—21no—
100C22×C3×Dic3D411yescharacteristic
101C22×C3×Dic3D411yescharacteristic
102C3×#237—44no—
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×#627—21no—
108C32×C4⋊C4C2311yescharacteristic
109C32×C22⋊C4—21no—
110#3757—21no—
111#3754—41no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C2×C3⋊(C3⋊C8)—41no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217—21no—
119C3×#214—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3D411yescharacteristic
127C3×C4×Dic3D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic32—21no—
139Dic32—21no—
140#3716—41no—
141#3715—41no—
142#3246—91noSylow
143C2×C3×#41—61no—
144C2×#237—21no—
145C2×C3×SD16—31no—
146C22×C3×C8—31no—
147C3×C4⋊Q8—31no—
148C3×#127—31no—
149C3×#124—61no—
150C3×C22⋊Q8—31no—
151C3×#121—21no—
152C3×#121—31no—
153C3×#121—61no—
154C3×#121C2×D311yescharacteristic
155C3×#121C2×D311yescharacteristic
156C3×C4×D4—31no—
157C3×C4×D4—31no—
158C3×C4×D4—61no—
159C2×C3×C42—31no—
160Q8×Dic3—31no—
161#944—31no—
162C2×#215—31no—
163#940C2×D311yescharacteristic
164#939—21no—
165D4×Dic3C2×D311yescharacteristic
166C2×#214—31no—
167C2×#214—31no—
168C2×#214—31no—
169C2×#214—31no—
170C2×#214—61no—
171C2×#214C2×D311yescharacteristic
172#930C2×D311yescharacteristic
173#926—61no—
174#924—31no—
175#924—31no—
176#924—61no—
177#924—61no—
178#924C2×D311yescharacteristic
179C2×C4×Dic3C2×D311yescharacteristic
180C22×C3⋊C8—31no—
181C22×C3⋊C8—31no—
182C22×C3⋊C8—61no—
183C22×C3⋊C8C2×D311yescharacteristic
184C2×#204—31no—
185#893C2×D311yescharacteristic
186#889—61no—
187#888—31no—
188#888C2×D311yescharacteristic
189#887—31no—
190#887—61no—
191#885—21no—
192#67⋊C4—21no—
193#878—61no—
194#877—61no—
195#870—61no—
196#869—31no—
197#869—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#102—31no—
204#835—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—31no—
209#832—61no—
210#832C2×D311yescharacteristic
211#821—31no—
212#817—31no—
213#816—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—61no—
223#810C2×D311yescharacteristic
224#809—31no—
225#808—31no—
226#808—31no—
227#808—31no—
228#808—31no—
229#808—31no—
230#808—61no—
231#808C2×D311yescharacteristic
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C23×C32—21no—
237C23×C32C2×D411yescharacteristic
238C22×C3×D3—21no—
239C32×D4—21no—
240C32×D4—21no—
241C32×D4—42no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249#634—21no—
250#634—21no—
251C3×#67—42no—
252C3×#67—42no—
253C3×#67—42no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—41no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3SD1614yescomplemented
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—42no—
270#627—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#533—91no—
276#532—31no—
277#476—91no—
278#476—91no—
279#475—91no—
280#475—91no—
281#465—31no—
282#465—91no—
283#465—91no—
284#465—91no—
285#461—91no—
286#461—91no—
287#460—91no—
288#460—91no—
289C2×C4⋊C8—91no—
290C3×#41—124no—
291C2×C3×Q8—31no—
292C2×C3×Q8—61no—
293C2×C3×D4—21no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—41no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—21no—
311C2×#67—21no—
312C2×#67—21no—
313C22×Dic3—21no—
314C22×Dic3#6711yescharacteristic
315C22×Dic3#6711yescharacteristic
316#237—44no—
317C2×D12C22×D311yescharacteristic
318C2×C4×D3—21no—
319C2×Dic6—21no—
320C2×Dic6—31no—
321C2×Dic6—31no—
322C2×Dic6—61no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6C22×D311yescharacteristic
326C3×SD16—121no—
327C2×C3×C8—31no—
328C2×C3×C8—31no—
329C2×C3×C8—121no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—61no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4C22×D311yescharacteristic
336C3×C4⋊C4C22×D311yescharacteristic
337C3×C22⋊C4—21no—
338C3×C22⋊C4—21no—
339C3×C22⋊C4—41no—
340C3×C22⋊C4—61no—
341C3×C22⋊C4—61no—
342C3×C22⋊C4—61no—
343C3×C22⋊C4—61no—
344C3×C42—31no—
345C3×C42—31no—
346C3×C42—31no—
347C3×C42—31no—
348#217—21no—
349#217—21no—
350#217—61no—
351#217—61no—
352#217—121no—
353#215—121no—
354#214—41no—
355#214—121no—
356#214—121no—
357#214—121no—
358#214—121no—
359#214—122no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362C4⋊Dic3—31no—
363C4⋊Dic3—31no—
364C4⋊Dic3—61no—
365C4⋊Dic3—61no—
366C4⋊Dic3—61no—
367C4⋊Dic3—61no—
368C4⋊Dic3—61no—
369C4⋊Dic3C22×D311yescharacteristic
370C4⋊Dic3C22×D311yescharacteristic
371Dic3⋊C4—21no—
372Dic3⋊C4—21no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—61no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—121no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3—61no—
386C4×Dic3#6711yescharacteristic
387C4×Dic3#6711yescharacteristic
388C4×Dic3C22×D311yescharacteristic
389C4×Dic3C22×D311yescharacteristic
390C2×C3⋊C8—31no—
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—41no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—121no—
398C2×C3⋊C8—121no—
399C2×C3⋊C8—122no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402#204—121no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32C2×SD1612yes—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C32×C4—21no—
414C32×C4—41no—
415C32×C4H(5,𝔽2)11yescharacteristic
416C32×C42−1+411yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—21no—
420C3×Dic3—21no—
421C3×Dic3—41no—
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3C2×SD1612yes—
425C3×Dic3C2×SD1612yes—
426C2×#41—61no—
427C2×SD16—31no—
428C2×SD16—91no—
429C2×SD16—91no—
430C2×SD16—91no—
431C22×C8—31no—
432C22×C8—91no—
433C4⋊Q8—31no—
434C4⋊Q8—91no—
435C4⋊Q8—91no—
436#127—31no—
437#125—181no—
438#124—61no—
439C22⋊Q8—31no—
440C22⋊Q8—91no—
441C22⋊Q8—181no—
442#121—31no—
443#121—61no—
444#121D3211yescharacteristic
445C4×Q8—91no—
446C4×Q8—91no—
447C4×Q8—181no—
448C4×D4—31no—
449C4×D4—31no—
450C4×D4—61no—
451#117—181no—
452C2×C42—31no—
453#106—31no—
454#106—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458C4⋊C8—91no—
459C4⋊C8—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#102—31no—
466#102—91no—
467#102—91no—
468#102—91no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—41no—
473C23×C3—61no—
474C23×C3D3×D411yescharacteristic
475C23×C3C2×#6711yescharacteristic
476C22×D3—21no—
477C3×Q8—61no—
478C3×Q8—61no—
479C3×Q8—122no—
480C3×D4—21no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—41no—
485C3×D4—41no—
486C3×D4—42no—
487C3×D4—42no—
488C3×D4—61no—
489C3×D4—61no—
490C3×D4—82no—
491C3×D4—122no—
492C3×D4—122no—
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—34no—
503C2×C3×C4—31no—
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—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4—122no—
515C2×C3×C4—121no—
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4C2×#6711yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—42no—
521#67—42no—
522#67—42no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—41no—
527C2×Dic3—42no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3#21414yescomplemented
535C2×Dic3C2×#6711yescharacteristic
536C2×Dic3C2×#6711yescharacteristic
537C2×Dic3C2×#6711yescharacteristic
538C2×Dic3C2×#6711yescharacteristic
539D12—21no—
540D12—21no—
541C4×D3—42no—
542Dic6—21no—
543Dic6—21no—
544Dic6—42no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—121no—
550Dic6—121no—
551Dic6—122no—
552Dic6—122no—
553C3×C8—61no—
554C3×C8—61no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—62no—
558C3⋊C8—61no—
559C3⋊C8—61no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—121no—
563C2×C32—22no—
564C2×C32—81no—
565C2×C32#53711yescharacteristic
566C2×C32C22×SD1611yescharacteristic
567C2×C32#57511yescharacteristic
568C3×D3—81no—
569#41—124no—
570C2×Q8—31no—
571C2×Q8—61no—
572C2×Q8—91no—
573C2×Q8—181no—
574C2×D4—21no—
575C2×D4—31no—
576C2×D4—61no—
577C2×D4—61no—
578C2×D4—61no—
579C2×D4C2×D3211yescharacteristic
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—61no—
583C22×C4—61no—
584C22×C4C2×D3211yescharacteristic
585SD16—121no—
586SD16—361no—
587SD16—361no—
588SD16—361no—
589C2×C8—31no—
590C2×C8—31no—
591C2×C8—91no—
592C2×C8—91no—
593C2×C8—121no—
594C2×C8—361no—
595C4⋊C4—31no—
596C4⋊C4—31no—
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⋊C4—181no—
606C4⋊C4C2×D3211yescharacteristic
607C22⋊C4—21no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—181no—
613C42—31no—
614C42—31no—
615C42—31no—
616C42—31no—
617C42—181no—
618C42—181no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3—21no—
623C22×C3—21no—
624C22×C3—22no—
625C22×C3—41no—
626C22×C3—41no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—41no—
630C22×C3—41no—
631C22×C3—41no—
632C22×C3—41no—
633C22×C3—81no—
634C22×C3—81no—
635C22×C3—81no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3D3×SD1612yes—
640C22×C3C2×#21412yes—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C22×#6711yescharacteristic
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C3×C4—21no—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—21no—
650C3×C4—32no—
651C3×C4—32no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—41no—
655C3×C4—61no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4#100411yescharacteristic
662C3×C4#100911yescharacteristic
663C3×C4#101011yescharacteristic
664C3×C4#101011yescharacteristic
665Dic3—21no—
666Dic3—21no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—121no—
671Dic3—121no—
672Dic3—121no—
673Dic3—121no—
674Dic3—241no—
675Dic3—241no—
676Dic3C2×#21412yes—
677Dic3C2×#21412yes—
678C32#324611yescharacteristic, complemented, Sylow
679C23—21no—
680C23—61no—
681C23D3×#6711yescharacteristic
682Q8—61no—
683Q8—61no—
684Q8—122no—
685Q8—181no—
686Q8—181no—
687Q8—362no—
688D4—21no—
689D4—21no—
690D4—42no—
691D4—61no—
692D4—61no—
693D4—122no—
694D4—122no—
695D4—122no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—31no—
700C2×C4—31no—
701C2×C4—34no—
702C2×C4—31no—
703C2×C4—31no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—122no—
708C2×C4—122no—
709C2×C4—121no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4D3×#6711yescharacteristic
713C2×C4C22×D3211yescharacteristic
714C8—61no—
715C8—61no—
716C8—181no—
717C8—181no—
718C2×C3—22no—
719C2×C3—22no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—21no—
723C2×C3—42no—
724C2×C3—81no—
725C2×C3—81no—
726C2×C3—161no—
727C2×C3—241no—
728C2×C3#559711yescharacteristic
729C2×C3C2×D3×SD1611yescharacteristic
730C2×C3#576811yescharacteristic
731C2×C3C22×#21411yescharacteristic
732C2×C3#582211yescharacteristic
733C2×C3#583311yescharacteristic
734D3—81no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—121no—
741C22—121no—
742C22—121no—
743C22D3×#21412yes—
744C22C2×D3×#6711yescharacteristic
745C4—21no—
746C4—32no—
747C4—32no—
748C4—41no—
749C4—61no—
750C4—61no—
751C4—121no—
752C4—121no—
753C4—121no—
754C4—361no—
755C4—361no—
756C4#6430911yescharacteristic
757C4#6431411yescharacteristic
758C3—21no—
759C3#8064011yescharacteristic, complemented
760C3#8332011yescharacteristic, complemented
761C2—22no—
762C2—81no—
763C2—241no—
764C2C2×D3×#21411yescharacteristic
765C2#1059515611yescharacteristic
766C2#1059545311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
prime radicalC3×#5596C2
hypercenter#121D32
hypocenterC32#3246
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10594808C2semidirect
3. #10592740C2semidirect
4. C3×#5041C2semidirect
5. #10591489C2semidirect
6. #10591439C2semidirect
7. #10591438C2semidirect
8. #10591408C2semidirect
9. #10591179C2semidirect
10. #10591175C2semidirect
11. C2×Dic3⋊(C3⋊C8)C2semidirect
12. #10590559C2semidirect
13. #10590558C2semidirect
14. #10590487C2semidirect
15. #10590486C2semidirect
80. #5041D3semidirect
259. C2×C3×Dic3SD16semidirect
534. C2×Dic3#214semidirect
678. C32#3246semidirect
759. C3#80640semidirect
760. C3#83320semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
#105948082
#105927402
C3×#50412
#105914892
#105914392
#105914382
#105914082
#105911792
#105911752
C2×Dic3⋊(C3⋊C8)2
#105905592
#105905582
#105904872
#105904862
#833203
#806403