Finite Group Databasebeta

← #11882320

Subgroups — #11882320

Order 1152.

863 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5596C211yesmaximal, characteristic, complemented
2#10594955C211yesmaximal, characteristic, complemented
3#10592737C211yesmaximal, characteristic, complemented
4C3×#5041C211yesmaximal, characteristic, complemented
5#10591471C211yesmaximal, characteristic, complemented
6#10591438C211yesmaximal, characteristic, complemented
7#10591429C211yesmaximal, characteristic, complemented
8#10591411C211yesmaximal, characteristic, complemented
9#10591179C211yesmaximal, characteristic, complemented
10#10591164C211yesmaximal, characteristic, complemented
11C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
12#10590545C211yesmaximal, characteristic, complemented
13#10590534C211yesmaximal, characteristic, complemented
14#10590489C211yesmaximal, characteristic, complemented
15#10590466C211yesmaximal, characteristic, complemented
16#83311—31nomaximal
17#80641—31nomaximal
18C2×C3×#237—21no—
19C32×#121C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21#64139C2211yescharacteristic
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#63966—21no—
36#63952—21no—
37#63894C2211yescharacteristic
38#63869C2211yescharacteristic
39#63868—21no—
40#63864C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
43C2×#3715C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45#63659C2211yescharacteristic
46#63636C2211yescharacteristic
47#63634C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#810C2211yescharacteristic
50C3×#808C2211yescharacteristic
51#63575C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55Dic3⋊(C3⋊C8)C2211yescharacteristic
56Dic3⋊(C3⋊C8)C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63562C2211yescharacteristic
61C3×#532—31no—
62#5624—31no—
63#5596D311yescharacteristic, complemented
64#5479—31no—
65C3×#465—31no—
66#5165—31no—
67#5163—31no—
68#5115—31no—
69C2×Dic3⋊C8—31no—
70#5091—31no—
71#5084—31no—
72#5075—31no—
73#5072—31no—
74#5048—31no—
75#5041—31no—
76#5041D311yescharacteristic, complemented
77#5038—31no—
78#5038—31no—
79#5038—31no—
80#5038—61no—
81#5016—31no—
82#5016—31no—
83#5009—31no—
84#5009—31no—
85C2×C4⋊(C3⋊C8)—31no—
86#4871—31no—
87#4870—31no—
88#4819—31no—
89#4793—31no—
90#4786—31no—
91#4766—31no—
92C2×C32×D4—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C32×C4C2311yescharacteristic
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C22×C3×Dic3D411yescharacteristic
102C22×C3×Dic3D411yescharacteristic
103C3×#237—44no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6C2311yescharacteristic
108C2×#624—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3753—41no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
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—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139Dic32—21no—
140#3715—41no—
141#3714—41no—
142#3247—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—
160#947—31no—
161Q8×Dic3—31no—
162C2×#215—31no—
163#940C2×D311yescharacteristic
164#939—21no—
165D4×Dic3C2×D311yescharacteristic
166C2×#214—31no—
167C2×#214C2×D311yescharacteristic
168C2×#213—31no—
169C2×#213—31no—
170C2×#213—31no—
171C2×#213—61no—
172#930—31no—
173#930—31no—
174#930—61no—
175#930C2×D311yescharacteristic
176#929—61no—
177C4×#67—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×D24—31no—
185#898—61no—
186#893—31no—
187#893C2×D311yescharacteristic
188#892—61no—
189#890—31no—
190#888C2×D311yescharacteristic
191#886—61no—
192#885—21no—
193#67⋊C4—21no—
194#67⋊C4—61no—
195#876—61no—
196#875—31no—
197C4×D12—31no—
198#872—61no—
199#870—31no—
200C4×Dic6—31no—
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#821—31no—
213#818—31no—
214Dic3⋊C8—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218#810—31no—
219#810C2×D311yescharacteristic
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—61no—
225#808—31no—
226#808—31no—
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230#807—31no—
231#807—61no—
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—
239C22×C3×D3—21no—
240C32×D4—21no—
241C32×D4—21no—
242C32×D4—42no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248#638—42no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C3×#67—42no—
253C3×#67—42no—
254C3×#67—42no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271#624—42no—
272C3⋊(C3⋊C8)—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#532—31no—
277#529—91no—
278#478—91no—
279#478—91no—
280#477—91no—
281#476—91no—
282#466—91no—
283#466—91no—
284#465—31no—
285#465—91no—
286#463—91no—
287#463—91no—
288#460—91no—
289#459—91no—
290C2×C4⋊C8—91no—
291C3×#41—124no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×D4—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—41no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4—61no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—121no—
317C22×Dic3—21no—
318C22×Dic3#6711yescharacteristic
319C22×Dic3#6711yescharacteristic
320#237—44no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—21no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×Dic6—21no—
329C2×Dic6C22×D311yescharacteristic
330C3×SD16—121no—
331C2×C3×C8—31no—
332C2×C3×C8—31no—
333C2×C3×C8—121no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—31no—
336C3×C4⋊C4—31no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—41no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—31no—
350C3×C42—31no—
351C3×C42—31no—
352#217—21no—
353#217—21no—
354#215—121no—
355#214—41no—
356#214—121no—
357#213—121no—
358#213—121no—
359#213—121no—
360#213—122no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—121no—
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385C4×Dic3—61no—
386C4×Dic3—61no—
387C4×Dic3#6711yescharacteristic
388C4×Dic3#6711yescharacteristic
389C4×Dic3C22×D311yescharacteristic
390C4×Dic3C22×D311yescharacteristic
391C2×C3⋊C8—31no—
392C2×C3⋊C8—31no—
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—41no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8—121no—
399C2×C3⋊C8—121no—
400C2×C3⋊C8—122no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403D24—121no—
404C22×C32—21no—
405C22×C32—21no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32AGL(1,ℤ/8)12yes—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C32×C4—21no—
418C32×C4—41no—
419C32×C4H(5,𝔽2)11yescharacteristic
420C32×C42−1+411yescharacteristic
421C3⋊Dic3—41no—
422C3×Dic3—21no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3#13512yes—
429C2×#41—61no—
430C2×SD16—31no—
431C2×SD16—91no—
432C2×D8—91no—
433C2×D8—91no—
434C22×C8—31no—
435C22×C8—91no—
436C4⋊Q8—31no—
437#127—31no—
438#126—181no—
439#125—91no—
440#124—61no—
441#124—91no—
442#123—181no—
443C22⋊Q8—31no—
444#121—31no—
445#121—61no—
446#121—91no—
447#121D3211yescharacteristic
448C4×Q8—91no—
449C4×D4—31no—
450C4×D4—31no—
451C4×D4—61no—
452C4×D4—91no—
453C4×D4—181no—
454#117—181no—
455C2×C42—31no—
456#107—91no—
457#107—91no—
458#106—31no—
459#106—91no—
460C4⋊C8—91no—
461C4⋊C8—91no—
462C4⋊C8—91no—
463C4⋊C8—91no—
464#103—31no—
465#103—91no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3—61no—
477C23×C3D3×D411yescharacteristic
478C23×C3C2×#6711yescharacteristic
479C22×D3—21no—
480C22×D3—61no—
481C22×D3—61no—
482C22×D3—121no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—122no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—21no—
489C3×D4—21no—
490C3×D4—41no—
491C3×D4—41no—
492C3×D4—42no—
493C3×D4—42no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—82no—
497C3×D4—122no—
498C3×D4—122no—
499C3×D4—122no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—41no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—62no—
516C2×C3×C4—62no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4—122no—
522C2×C3×C4D3×D411yescharacteristic
523C2×C3×C4C2×#6711yescharacteristic
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—42no—
527#67—42no—
528#67—42no—
529#67—122no—
530#67—122no—
531#67—242no—
532C2×Dic3—22no—
533C2×Dic3—22no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—42no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3C2×#6711yescharacteristic
542C2×Dic3C2×#6711yescharacteristic
543C2×Dic3C2×#6711yescharacteristic
544C2×Dic3C2×#6711yescharacteristic
545D12—21no—
546D12—21no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—121no—
553C4×D3—42no—
554C4×D3—122no—
555C4×D3—122no—
556Dic6—21no—
557Dic6—21no—
558Dic6—42no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—62no—
564C3⋊C8—61no—
565C3⋊C8—61no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—121no—
569C2×C32—22no—
570C2×C32—81no—
571C2×C32#53711yescharacteristic
572C2×C32C2×#13511yescharacteristic
573C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
574C3⋊D3—81no—
575C3×D3—81no—
576#41—124no—
577C2×Q8—31no—
578C2×Q8—61no—
579C2×D4—21no—
580C2×D4—31no—
581C2×D4—61no—
582C2×D4—61no—
583C2×D4—61no—
584C2×D4—91no—
585C2×D4—181no—
586C2×D4C2×D3211yescharacteristic
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—61no—
590C22×C4—61no—
591C22×C4—181no—
592C22×C4C2×D3211yescharacteristic
593SD16—121no—
594SD16—361no—
595D8—361no—
596D8—361no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8—91no—
601C2×C8—121no—
602C2×C8—361no—
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—91no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C42—31no—
622C42—31no—
623C42—31no—
624C42—31no—
625C42—181no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—22no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—81no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3#91412yes—
647C22×C3#93212yes—
648C22×C3C2×D3×D411yescharacteristic
649C22×C3C22×#6711yescharacteristic
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3—241no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—32no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—81no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4#100411yescharacteristic
678C3×C4#100911yescharacteristic
679C3×C4#101011yescharacteristic
680C3×C4#101011yescharacteristic
681Dic3—21no—
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—121no—
688Dic3—121no—
689Dic3—241no—
690Dic3#95012yes—
691C32#324711yescharacteristic, complemented, Sylow
692C23—21no—
693C23—61no—
694C23—181no—
695C23D3×#6711yescharacteristic
696Q8—61no—
697Q8—61no—
698Q8—122no—
699D4—21no—
700D4—21no—
701D4—42no—
702D4—61no—
703D4—61no—
704D4—122no—
705D4—122no—
706D4—122no—
707D4—181no—
708D4—181no—
709D4—362no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—31no—
714C2×C4—31no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—122no—
723C2×C4—122no—
724C2×C4—181no—
725C2×C4—362no—
726C2×C4D3×#6711yescharacteristic
727C2×C4C22×D3211yescharacteristic
728C8—61no—
729C8—61no—
730C8—181no—
731C8—181no—
732C2×C3—22no—
733C2×C3—22no—
734C2×C3—21no—
735C2×C3—21no—
736C2×C3—21no—
737C2×C3—42no—
738C2×C3—81no—
739C2×C3—81no—
740C2×C3—161no—
741C2×C3—241no—
742C2×C3#559711yescharacteristic
743C2×C3C2×#91411yescharacteristic
744C2×C3D3×#13511yescharacteristic
745C2×C3C2×#93211yescharacteristic
746C2×C3C2×#95011yescharacteristic
747C2×C3#583311yescharacteristic
748D3—81no—
749D3—241no—
750D3—241no—
751D3—481no—
752C22—21no—
753C22—21no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22—361no—
761C22—361no—
762C22—361no—
763C22#6393412yes—
764C22C2×D3×#6711yescharacteristic
765C4—21no—
766C4—32no—
767C4—41no—
768C4—61no—
769C4—61no—
770C4—61no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—361no—
775C4#6430911yescharacteristic
776C4#6431411yescharacteristic
777C3—21no—
778C3#8064111yescharacteristic, complemented
779C3#8331111yescharacteristic, complemented
780C2—22no—
781C2—81no—
782C2—241no—
783C2—721no—
784C2C2×#6393411yescharacteristic
785C2#1059515611yescharacteristic
786C2D3×#95011yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3247
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
1. C3×#5596C2semidirect
2. #10594955C2semidirect
3. #10592737C2semidirect
4. C3×#5041C2semidirect
5. #10591471C2semidirect
6. #10591438C2semidirect
7. #10591429C2semidirect
8. #10591411C2semidirect
9. #10591179C2semidirect
10. #10591164C2semidirect
11. C2×Dic3⋊(C3⋊C8)C2semidirect
12. #10590545C2semidirect
13. #10590534C2semidirect
14. #10590489C2semidirect
15. #10590466C2semidirect
63. #5596D3semidirect
76. #5041D3semidirect
691. C32#3247semidirect
778. C3#80641semidirect
779. C3#83311semidirect

Maximal subgroups

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

subgroupindex
C3×#55962
#105949552
#105927372
C3×#50412
#105914712
#105914382
#105914292
#105914112
#105911792
#105911642
C2×Dic3⋊(C3⋊C8)2
#105905452
#105905342
#105904892
#105904662
#833113
#806413