Finite Group Databasebeta

← #11887425

Subgroups — #11887425

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594995C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic, complemented
3#10592421C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591175C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590962C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590863C211yesmaximal, characteristic, complemented
11#10590834C211yesmaximal, characteristic, complemented
12#10590831C211yesmaximal, characteristic, complemented
13#10590767C211yesmaximal, characteristic, complemented
14Dic3×D24C211yesmaximal, characteristic, complemented
15#10590755C211yesmaximal, characteristic, complemented
16#80015—31nomaximal
17#79441—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C2×C3×D24C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63980—21no—
29#63976—21no—
30#67⋊Dic3—21no—
31D3×#217—21no—
32#63908C2211yescharacteristic
33#63908C2211yescharacteristic, complemented
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic, complemented
36#63891—21no—
37#63885—21no—
38#63884—21no—
39#63869C2211yescharacteristic, complemented
40#63861—21no—
41#63860C2211yescharacteristic
42#63841C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63645C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47#63643C2211yescharacteristic, complemented
48#63643C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63563C2211yescharacteristic
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic, complemented
61#5806—31no—
62#5618—31no—
63#5565—31no—
64#5550—31no—
65C3×#447—31no—
66C3×C8×D4—31no—
67C2×#832—31no—
68#5158—31no—
69#5157—31no—
70#5153—31no—
71Dic3×D8—31no—
72#5115—31no—
73#5114—31no—
74#5113—31no—
75C2×#821—31no—
76#5041—31no—
77#4847—31no—
78#4844—31no—
79#4784—31no—
80#4772—31no—
81#4768—31no—
82#4766—31no—
83#4737—31no—
84#4734—31no—
85#4732D311yescharacteristic, complemented
86#67⋊C8D311yescharacteristic, complemented
87#4722—31no—
88#4722—31no—
89#4722—61no—
90#4697—31no—
91C4×D24—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#625—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111#3795—22no—
112#3795—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3757—21no—
116C4⋊(C3⋊Dic3)—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8—41no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—22no—
131C3×D24—41no—
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3716—41no—
144#3297—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C2×C3×D8—31no—
150C2×C3×D8—31no—
151C22×C3×C8—31no—
152C22×C3×C8—31no—
153C3×#121—31no—
154C3×C4×D4—31no—
155#953—61no—
156C2×#217—61no—
157#939—61no—
158#939—61no—
159#939—61no—
160#938—31no—
161#938—31no—
162#937—61no—
163#936—31no—
164#935—61no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—61no—
168C2×#214—31no—
169#930—31no—
170#930—31no—
171#930C2×D311yescharacteristic
172C4×#67C2×D311yescharacteristic
173#926—31no—
174C2×C4⋊Dic3—31no—
175C2×C4⋊Dic3—31no—
176C2×C4⋊Dic3—61no—
177#924—31no—
178#924—31no—
179#924—61no—
180C22×C3⋊C8C2×D311yescharacteristic
181C2×D24C2×D311yescharacteristic
182C2×D24C2×D311yescharacteristic
183C2×#204—31no—
184C2×D3×C8C2×D311yescharacteristic, complemented
185#898—61no—
186#894—61no—
187#892—31no—
188#890—31no—
189#886—61no—
190#884—61no—
191#883—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194#879—61no—
195#875—31no—
196C4×D12—31no—
197C4×D12—31no—
198#870—31no—
199C3×C4⋊C8—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×C4×C8—31no—
207#832—31no—
208#832—31no—
209#832—31no—
210#832—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8C2×D311yescharacteristic, complemented
220#818—31no—
221#818—31no—
222#818—31no—
223#818—31no—
224#818—61no—
225#818—61no—
226#817—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—31no—
232#816—61no—
233#816—61no—
234Dic3⋊C8C2×D311yescharacteristic, complemented
235C8×Dic3C2×D311yescharacteristic, complemented
236#810—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—42no—
243C22×C3×D3—42no—
244C22×C3×D3—81no—
245C22×C3×D3C2×D411yescharacteristic
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—81no—
255#634—21no—
256#634—21no—
257C3×#67—22no—
258C3×#67—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×D12#4112yes—
270C3×C4×D3—21no—
271C3×C4×D3—21no—
272#625—42no—
273#625—81no—
274#625—81no—
275D3×Dic3—42no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
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—31no—
295#416—91no—
296C2×#102—91no—
297C24×C3—61no—
298C23×D3—21no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—31no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4—61no—
306C2×C3×D4—121no—
307C22×C3×C4—21no—
308C22×C3×C4—31no—
309C22×C3×C4C22×D311yescharacteristic
310C22×C3×C4C22×D311yescharacteristic
311C2×#67—21no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67D1211yescharacteristic
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—121no—
325#237—62no—
326#237—121no—
327#235—62no—
328#235—121no—
329C2×D12—22no—
330C2×D12—21no—
331C2×D12—41no—
332C2×D12C22×D311yescharacteristic
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3C22×D311yescharacteristic
339C2×Dic6—31no—
340C2×Dic6—31no—
341C2×Dic6—61no—
342C3×D8—62no—
343C3×D8—121no—
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—121no—
349C2×C3×C8—121no—
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—31no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—121no—
370#217D1211yescharacteristic
371#214—121no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4D1211yescharacteristic
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—121no—
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—121no—
401Dic3⋊C4D1211yescharacteristic
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—41no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—22no—
409D24—41no—
410#204—121no—
411D3×C8—41no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32#13512yes—
415C22×C32C22×D411yescharacteristic
416C2×C3×D3—22no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—84no—
429C32×C4—21no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—31no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×D8—31no—
445C22×C8—31no—
446C22×C8—31no—
447#126—181no—
448#125—91no—
449#124—91no—
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—31no—
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—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8D3211yescharacteristic
482C4×C8—31no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—61no—
487C23×C3—61no—
488C23×C3—122no—
489C23×C3—122no—
490C23×C3—241no—
491C23×C3C2×D1211yescharacteristic
492C23×C3D3×D411yescharacteristic
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—42no—
497C22×D3—42no—
498C22×D3—81no—
499C22×D3C2×D1211yescharacteristic
500C3×D4—32no—
501C3×D4—62no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—122no—
508C3×D4—122no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4C2×D1211yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—22no—
528#67—42no—
529#67—122no—
530#67—122no—
531#67—241no—
532#67—241no—
533#67—241no—
534#67—241no—
535C2×Dic3—21no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—121no—
545C2×Dic3—121no—
546C2×Dic3—121no—
547C2×Dic3—121no—
548C2×Dic3—122no—
549C2×Dic3—241no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3—241no—
553C2×Dic3—242no—
554C2×Dic3C2×D1211yescharacteristic
555C2×Dic3C2×D1211yescharacteristic
556C2×Dic3C2×D1211yescharacteristic
557D12—21no—
558D12—21no—
559D12—21no—
560D12—21no—
561D12—21no—
562D12—42no—
563D12#23712yes—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—122no—
567C4×D3—241no—
568C4×D3—241no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—121no—
574Dic6—121no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—41no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C2×C32—22no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57611yescharacteristic
589C3×D3—41no—
590C3×D3—42no—
591C3×D3—81no—
592C3×D3—81no—
593C24—61no—
594#41—182no—
595#41—361no—
596C2×Q8—91no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—31no—
601C2×D4—62no—
602C2×D4—61no—
603C2×D4—61no—
604C2×D4—121no—
605C2×D4—181no—
606C2×D4—181no—
607C2×D4—181no—
608C22×C4—31no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4—181no—
612C22×C4—181no—
613C22×C4C2×D3211yescharacteristic
614SD16—361no—
615D8—62no—
616D8—121no—
617C2×C8—31no—
618C2×C8—31no—
619C2×C8—121no—
620C2×C8—121no—
621C2×C8C2×D3211yescharacteristic
622C2×C8C2×D3211yescharacteristic
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C4⋊C4—181no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
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—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—62no—
656C22×C3—61no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3—121no—
663C22×C3—121no—
664C22×C3—121no—
665C22×C3—244no—
666C22×C3#90412yes—
667C22×C3#91212yes—
668C22×C3C22×D1211yescharacteristic
669C22×C3C2×D3×D411yescharacteristic
670C2×D3—21no—
671C2×D3—21no—
672C2×D3—21no—
673C2×D3—22no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—41no—
681C2×D3—41no—
682C2×D3—84no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—121no—
692C3×C4C2×#23711yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4#100411yescharacteristic
695C3×C4D3×#4111yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—121no—
701Dic3—121no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709Dic3—241no—
710Dic3—241no—
711Dic3—241no—
712C32#329711yescharacteristic, complemented, Sylow
713C23—31no—
714C23—61no—
715C23—61no—
716C23—61no—
717C23—122no—
718C23—122no—
719C23—241no—
720C23D3×D1211yescharacteristic
721Q8—181no—
722Q8—181no—
723D4—32no—
724D4—62no—
725D4—61no—
726D4—61no—
727D4—61no—
728D4—61no—
729D4—61no—
730D4—122no—
731D4—122no—
732D4—362no—
733D4—721no—
734D4—721no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—31no—
738C2×C4—31no—
739C2×C4—31no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—362no—
748C2×C4—721no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4D3×D1211yescharacteristic
752C2×C4C22×D3211yescharacteristic
753C8—21no—
754C8—21no—
755C8—61no—
756C8—61no—
757C2×C3—22no—
758C2×C3—22no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—42no—
763C2×C3—122no—
764C2×C3—121no—
765C2×C3—241no—
766C2×C3—241no—
767C2×C3#555411yescharacteristic
768C2×C3#559111yescharacteristic
769C2×C3C2×#90411yescharacteristic
770C2×C3#575211yescharacteristic
771C2×C3C2×#91211yescharacteristic
772C2×C3#577411yescharacteristic
773D3—41no—
774D3—42no—
775D3—81no—
776D3—81no—
777C22—21no—
778C22—21no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—62no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—244no—
792C22#6380712yes—
793C22C2×D3×D1211yescharacteristic
794C4—21no—
795C4—61no—
796C4—61no—
797C4—61no—
798C4—121no—
799C4—361no—
800C4—361no—
801C4—361no—
802C4—361no—
803C4D3×#23711yescharacteristic
804C4#6431311yescharacteristic
805C3—21no—
806C3#7944111yescharacteristic, complemented
807C3#8001511yescharacteristic, complemented
808C2—22no—
809C2—121no—
810C2—122no—
811C2—241no—
812C2—241no—
813C2#1059429211yescharacteristic
814C2C2×#6380711yescharacteristic
815C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #10594995C2semidirect
2. #10594886C2semidirect
3. #10592421C2semidirect
4. C3×#4732C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591175C2semidirect
7. C2×#63563C2semidirect
8. #10590962C2semidirect
9. #10590954C2semidirect
10. #10590863C2semidirect
11. #10590834C2semidirect
12. #10590831C2semidirect
13. #10590767C2semidirect
14. Dic3×D24C2semidirect
15. #10590755C2semidirect
27. C2×C3×D3×C8C22semidirect
33. #63908C22semidirect
35. Dic3×D12C22semidirect
39. #63869C22semidirect
42. #63841C22semidirect
43. C2×#3716C22semidirect
45. #63645C22semidirect
46. #63645C22semidirect
47. #63643C22semidirect
48. #63643C22semidirect
51. C3×(C2×D3)⋊C8C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
60. #63563C22semidirect
85. #4732D3semidirect
86. #67⋊C8D3semidirect
184. C2×D3×C8C2×D3semidirect
219. (C2×D3)⋊C8C2×D3semidirect
234. Dic3⋊C8C2×D3semidirect
235. C8×Dic3C2×D3semidirect
712. C32#3297semidirect
806. C3#79441semidirect
807. C3#80015semidirect

Maximal subgroups

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

subgroupindex
#105949952
#105948862
#105924212
C3×#47322
C3×#67⋊C82
#105911752
C2×#635632
#105909622
#105909542
#105908632
#105908342
#105908312
#105907672
Dic3×D242
#105907552
#800153
#794413