Finite Group Databasebeta

← #11887465

Subgroups — #11887465

Order 1152.

893 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595229C211yesmaximal, characteristic, complemented
2#10594437C211yesmaximal, characteristic, complemented
3#10592483C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×#4768C211yesmaximal, characteristic, complemented
6#10591455C211yesmaximal, characteristic, complemented
7#10591431C211yesmaximal, characteristic, complemented
8D3×#832C211yesmaximal, characteristic, complemented
9#10590963C211yesmaximal, characteristic, complemented
10Dic3×D24C211yesmaximal, characteristic, complemented
11#10590721C211yesmaximal, characteristic, complemented
12#10590682C211yesmaximal, characteristic, complemented
13#10590611C211yesmaximal, characteristic, complemented
14#10590514C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#81653—31nomaximal
17#80015—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64147C2211yescharacteristic
21#64101C2211yescharacteristic, complemented
22C3×#936C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27#63977—21no—
28#63971—21no—
29#63969—21no—
30D3×#217—21no—
31#63916C2211yescharacteristic, complemented
32C4×#626C2211yescharacteristic
33#63898—21no—
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic, complemented
36#63890—21no—
37D3×C4⋊Dic3C2211yescharacteristic
38#63886—21no—
39#63862—21no—
40#63856C2211yescharacteristic
41C2×#3715C2211yescharacteristic, complemented
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63659C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47#63645C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#832C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#5806—31no—
62#5695—31no—
63#5676—31no—
64#5618—31no—
65C3×#488—31no—
66C3×#447—31no—
67C2×#832—31no—
68#5158—31no—
69#5157—31no—
70#5153—31no—
71Dic3×D8—31no—
72#5066—31no—
73#5057—31no—
74#5041—31no—
75#4811—31no—
76#4810—31no—
77#4807—31no—
78#4804—31no—
79#4784—31no—
80#4784—31no—
81#4784—61no—
82#4775—31no—
83#4773D311yescharacteristic, complemented
84#4772—31no—
85D3×#102—31no—
86#4768D311yescharacteristic, complemented
87#4766—31no—
88#67⋊C8—31no—
89#4722—31no—
90C4×D24—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×#67—21no—
97C3×D3×D4—22no—
98C3×D3×D4—41no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626D411yescharacteristic
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3796—22no—
112#3796—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3757—21no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#213—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D24—22no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141#3715—41no—
142#3710—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C2×C3×D8—31no—
150C2×C3×D8—31no—
151C3×#125—31no—
152C3×#124—31no—
153C3×#121—31no—
154#953—61no—
155C2×#217—61no—
156#946—31no—
157C2×#215—31no—
158#939—61no—
159#939—61no—
160#938—31no—
161#938—31no—
162#938—31no—
163#938—61no—
164#936C2×D311yescharacteristic
165#935—61no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—61no—
169C2×#214—31no—
170C2×#213C2×D311yescharacteristic
171C4×#67—31no—
172C2×C4⋊Dic3—31no—
173#924—31no—
174C22×C3⋊C8—31no—
175C2×D24C2×D311yescharacteristic
176C2×D3×C8—31no—
177C2×D3×C8—31no—
178C2×D3×C8—31no—
179#898—61no—
180#895—31no—
181#895—61no—
182#895C2×D311yescharacteristic
183#894—61no—
184#893—61no—
185#892—31no—
186#892—31no—
187#892—61no—
188D3×C4⋊C4—31no—
189#890C2×D311yescharacteristic, complemented
190#886—61no—
191#884—61no—
192#883—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196C4×D12—31no—
197C4×D12—31no—
198C4×D12—31no—
199C3×#103—31no—
200C3×#103—31no—
201C3×#102—21no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102C2×D311yescharacteristic
205C3×#102C2×D311yescharacteristic
206C3×C22⋊C8—31no—
207C3×C4×C8—31no—
208#835—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#832—61no—
215#832C2×D311yescharacteristic
216#821—31no—
217#821—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—61no—
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818—31no—
223#818—31no—
224#818—31no—
225#818—61no—
226#816—31no—
227#816C2×D311yescharacteristic, complemented
228Dic3⋊C8—31no—
229C8×Dic3C2×D311yescharacteristic, complemented
230#810C2×D311yescharacteristic, complemented
231#809—31no—
232#809C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—61no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C32×D4—21no—
247C32×D4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250#638—81no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3C2×D411yescharacteristic
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—22no—
272#626—42no—
273#626—81no—
274D3×Dic3—42no—
275D3×Dic3—81no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—31no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—31no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×Q8—31no—
300C2×C3×D4—21no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—61no—
304C2×C3×D4—61no—
305C2×C3×D4—62no—
306C2×C3×D4—121no—
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C2×#67—21no—
311C2×#67—31no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—121no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321#239—62no—
322#239—121no—
323#237—62no—
324#237—121no—
325D3×D4—22no—
326D3×D4—41no—
327C2×D12—21no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12C22×D311yescharacteristic
332C2×D12C22×D311yescharacteristic
333C2×C4×D3—31no—
334C2×C4×D3—31no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3C22×D311yescharacteristic
341C2×Dic6C22×D311yescharacteristic
342C3×D8—62no—
343C3×D8—121no—
344C2×C3×C8—21no—
345C2×C3×C8—31no—
346C2×C3×C8—31no—
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359#217—21no—
360#217—21no—
361#217—31no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—121no—
369#215—121no—
370#214—121no—
371#213—41no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—31no—
374(C2×D3)⋊C4—31no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—121no—
383C4⋊Dic3—21no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3C22×D311yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—31no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—22no—
409D3×C8—121no—
410D3×C8—121no—
411D3×C8—121no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—22no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—84no—
428C2×C3×D3#13512yes—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—21no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—31no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×D8—31no—
445C22×C8—91no—
446C22×C8—91no—
447#126—181no—
448#125—31no—
449#124—31no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453#121—31no—
454#121—91no—
455#121—91no—
456#121—181no—
457#121—181no—
458#120—181no—
459C4×D4—91no—
460C4×D4—91no—
461C4×D4—91no—
462C4×D4—181no—
463#117—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466#107—91no—
467#107—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—31no—
471#103—31no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102D3211yescharacteristic
480C22⋊C8—31no—
481C22⋊C8—91no—
482C4×C8—31no—
483C23×C3—21no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—41no—
487C23×C3—61no—
488C23×C3—61no—
489C23×C3—122no—
490C23×C3—122no—
491C23×C3—241no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—31no—
495C22×D3—31no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—61no—
499C22×D3—81no—
500C22×D3D3×D411yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—41no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—122no—
514C3×D4—122no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—31no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4C23×D311yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528#67—42no—
529#67—62no—
530#67—122no—
531#67—241no—
532#67—241no—
533#67—241no—
534#67—242no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3D3×D411yescharacteristic
551C2×Dic3D3×D411yescharacteristic
552C2×Dic3D3×D411yescharacteristic
553D12—21no—
554D12—21no—
555D12—21no—
556D12—42no—
557D12—62no—
558D12—122no—
559D12—241no—
560D12#23712yes—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—61no—
564C4×D3—61no—
565C4×D3—61no—
566C4×D3—61no—
567C4×D3—121no—
568C4×D3—121no—
569C4×D3—122no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573Dic6—21no—
574Dic6—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—121no—
585C2×C32—81no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57611yescharacteristic
589C3⋊D3—41no—
590C3×D3—22no—
591C3×D3—42no—
592C3×D3—81no—
593C24—61no—
594#41—182no—
595#41—361no—
596C2×Q8—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—62no—
602C2×D4—91no—
603C2×D4—121no—
604C2×D4—181no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4C2×D3211yescharacteristic
608C22×C4—31no—
609C22×C4—91no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4—181no—
614SD16—361no—
615D8—62no—
616D8—121no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—91no—
620C2×C8—361no—
621C2×C8—361no—
622C2×C8C2×D3211yescharacteristic
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—91no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4C2×D3211yescharacteristic
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C42—31no—
644C42—181no—
645C22×C3—21no—
646C22×C3—32no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—62no—
656C22×C3—81no—
657C22×C3—81no—
658C22×C3—81no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—244no—
665C22×C3C2×D3×D411yescharacteristic
666C22×C3C2×D3×D411yescharacteristic
667C2×D3—21no—
668C2×D3—21no—
669C2×D3—22no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—41no—
674C2×D3—41no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—61no—
680C2×D3—61no—
681C2×D3—84no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3#91212yes—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—61no—
693C3×C4—81no—
694C3×C4—121no—
695C3×C4—121no—
696C3×C4C2×#23711yescharacteristic
697C3×C4#100411yescharacteristic
698C3×C4D3×#4111yescharacteristic
699C3×C4#100911yescharacteristic
700Dic3—21no—
701Dic3—21no—
702Dic3—21no—
703Dic3—41no—
704Dic3—41no—
705Dic3—61no—
706Dic3—61no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711Dic3—121no—
712Dic3—241no—
713Dic3—241no—
714C32#329711yescharacteristic, complemented, Sylow
715C23—21no—
716C23—31no—
717C23—61no—
718C23—61no—
719C23—91no—
720C23—122no—
721C23—122no—
722C23—241no—
723Q8—61no—
724Q8—61no—
725D4—21no—
726D4—21no—
727D4—32no—
728D4—61no—
729D4—61no—
730D4—61no—
731D4—122no—
732D4—122no—
733D4—182no—
734D4—362no—
735D4—721no—
736D4—721no—
737C2×C4—21no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—31no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—91no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—362no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4C22×D3211yescharacteristic
755C8—21no—
756C8—61no—
757C8—61no—
758C8—181no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—62no—
763C2×C3—81no—
764C2×C3—81no—
765C2×C3—122no—
766C2×C3—161no—
767C2×C3—241no—
768C2×C3#559111yescharacteristic
769C2×C3#567611yescharacteristic
770C2×C3C2×#91211yescharacteristic
771C2×C3D3×#13511yescharacteristic
772C2×C3#576911yescharacteristic
773C2×C3#577411yescharacteristic
774D3—22no—
775D3—42no—
776D3—81no—
777D3—121no—
778D3—121no—
779D3—241no—
780C22—32no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—61no—
785C22—61no—
786C22—62no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—181no—
793C22—181no—
794C22—181no—
795C22—244no—
796C22D32×D411yescharacteristic
797C4—41no—
798C4—61no—
799C4—61no—
800C4—61no—
801C4—121no—
802C4—121no—
803C4—181no—
804C4—361no—
805C4—361no—
806C4#6430711yescharacteristic
807C4D3×#23711yescharacteristic
808C3—21no—
809C3#8001511yescharacteristic, complemented
810C3#8165311yescharacteristic, complemented
811C2—62no—
812C2—81no—
813C2—122no—
814C2—241no—
815C2—361no—
816C2#1059428111yescharacteristic
817C2D3×#91211yescharacteristic
818C2#1059475511yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595229C2semidirect
2. #10594437C2semidirect
3. #10592483C2semidirect
4. C3×#4773C2semidirect
5. C3×#4768C2semidirect
6. #10591455C2semidirect
7. #10591431C2semidirect
8. D3×#832C2semidirect
9. #10590963C2semidirect
10. Dic3×D24C2semidirect
11. #10590721C2semidirect
12. #10590682C2semidirect
13. #10590611C2semidirect
14. #10590514C2semidirect
15. #10590469C2semidirect
21. #64101C22semidirect
26. C3×#890C22semidirect
31. #63916C22semidirect
35. Dic3×D12C22semidirect
41. C2×#3715C22semidirect
42. C2×#3710C22semidirect
46. #63647C22semidirect
47. #63645C22semidirect
48. #63635C22semidirect
51. C3×#816C22semidirect
52. C3×C8×Dic3C22semidirect
53. C3×#810C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63566C22semidirect
59. #63563C22semidirect
83. #4773D3semidirect
86. #4768D3semidirect
189. #890C2×D3semidirect
227. #816C2×D3semidirect
229. C8×Dic3C2×D3semidirect
230. #810C2×D3semidirect
714. C32#3297semidirect
809. C3#80015semidirect
810. C3#81653semidirect

Maximal subgroups

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

subgroupindex
#105952292
#105944372
#105924832
C3×#47732
C3×#47682
#105914552
#105914312
D3×#8322
#105909632
Dic3×D242
#105907212
#105906822
#105906112
#105905142
#105904692
#816533
#800153