Finite Group Databasebeta

← #11889223

Subgroups — #11889223

Order 1152.

899 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592830C211yesmaximal, characteristic, complemented
4C3×#5137C211yesmaximal, characteristic, complemented
5C3×#5127C211yesmaximal, characteristic, complemented
6#10591183C211yesmaximal, characteristic, complemented
7#10591127C211yesmaximal, characteristic, complemented
8#10590966C211yesmaximal, characteristic, complemented
9#10590893C211yesmaximal, characteristic, complemented
10#10590847C211yesmaximal, characteristic, complemented
11#10590801C211yesmaximal, characteristic, complemented
12#10590795C211yesmaximal, characteristic, complemented
13#10590759C211yesmaximal, characteristic, complemented
14#10590704C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#80914—31nomaximal
17#79502—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×M16C2211yescharacteristic
21#64135C2211yescharacteristic
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C3×#924C2211yescharacteristic
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic, complemented
27#63981—21no—
28#63974—21no—
29#63959—21no—
30#63956—21no—
31#63918C2211yescharacteristic, complemented
32#63910—21no—
33#63909C2211yescharacteristic
34#63897—21no—
35#63894C2211yescharacteristic
36#63864C2211yescharacteristic
37#63862—21no—
38#63856C2211yescharacteristic, complemented
39Dic3×Dic6C2211yescharacteristic, complemented
40#63841C2211yescharacteristic, complemented
41#63838—21no—
42C2×#3717C2211yescharacteristic
43C2×#3717C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63648C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5641—31no—
62#5630—31no—
63#5550—31no—
64#5542—31no—
65C3×#470—31no—
66C3×#435—31no—
67#5187—31no—
68#5185—31no—
69#5137D311yescharacteristic, complemented
70#5131—31no—
71#5131—31no—
72#5131—61no—
73#5127D311yescharacteristic, complemented
74#5114—31no—
75#5113—31no—
76#5046—31no—
77#5045—31no—
78#4870—31no—
79#4866—31no—
80#4845—31no—
81#4842—31no—
82#4817—31no—
83#4807—31no—
84#4804—31no—
85#4794—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4723—31no—
90#4714—31no—
91#4710—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C3×#67D411yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—41no—
110C32×M16—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×Dic12—41no—
130C3×D3×C8—41no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3717—22no—
143#3717—41no—
144#3311—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C2×C3×Q16—31no—
151C2×C3×M16—21no—
152C2×C3×M16C2×D311yescharacteristic
153C2×C3×M16C2×D311yescharacteristic
154C22×C3×C8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C4×D4—31no—
158#947—31no—
159#946—31no—
160Q8×Dic3—31no—
161C2×#215—31no—
162C2×#215—31no—
163#937—61no—
164#936—61no—
165#930—31no—
166C4×#67C2×D311yescharacteristic
167#926—31no—
168#926—31no—
169#926—31no—
170#926—61no—
171#924—31no—
172#924C2×D311yescharacteristic
173#924C2×D311yescharacteristic
174C2×Dic12C2×D311yescharacteristic, complemented
175C2×#204—31no—
176C2×#204—31no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#898—61no—
179#895—31no—
180#895—61no—
181#894—61no—
182#894—61no—
183#893—31no—
184#892—31no—
185#888—31no—
186#887—61no—
187#887—61no—
188#885—61no—
189#884—61no—
190#882—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—61no—
193#879—61no—
194#879—61no—
195#879—61no—
196#875—31no—
197C4×D12—31no—
198#869—31no—
199C4×Dic6—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207#835—31no—
208#835—31no—
209#830C2×D311yescharacteristic
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821—61no—
222#821—61no—
223#821—61no—
224(C2×D3)⋊C8C2×D311yescharacteristic, complemented
225#818—31no—
226#817—31no—
227#817C2×D311yescharacteristic, complemented
228#816—31no—
229#816—31no—
230#816C2×D311yescharacteristic, complemented
231#816C2×D311yescharacteristic, complemented
232#815C2×D311yescharacteristic, complemented
233Dic3⋊C8C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#808—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—42no—
255C4⋊(C3⋊D3)#4112yes—
256C3×#67—41no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#627—42no—
271#626—42no—
272#626—81no—
273#624—42no—
274#624—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—31no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—31no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×D4—31no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—61no—
305C2×#67—61no—
306C2×#67D1211yescharacteristic
307#239—62no—
308#239—121no—
309#235—62no—
310#235—121no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—62no—
319C2×D12—64no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—121no—
325C2×D12—121no—
326C2×D12—121no—
327C2×D12—122no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6C22×D311yescharacteristic
336C2×Dic6C22×D311yescharacteristic
337C3×Q16—121no—
338C3×M16—41no—
339C3×M16—41no—
340C3×M16—42no—
341C2×C3×C8—21no—
342C2×C3×C8—21no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C2×C3×C8—121no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—31no—
360#217—21no—
361#217—21no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—121no—
367#217D1211yescharacteristic
368#215—62no—
369#215—121no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
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—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—21no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4D1211yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—121no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—41no—
409#204—62no—
410#204—121no—
411D3×C8—41no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—84no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—31no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×M16D3211yescharacteristic
444C22×C8—31no—
445C4⋊Q8—91no—
446#126—181no—
447#126—181no—
448#124—91no—
449#124—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454#121—91no—
455#121—181no—
456#120—181no—
457C4×Q8—91no—
458C4×Q8—181no—
459C4×D4—31no—
460C4×D4—91no—
461#117—91no—
462#117—91no—
463C2×C22⋊C4—181no—
464#107—91no—
465#106—31no—
466#106—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—31no—
480#97—31no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3C2×D1211yescharacteristic
484C23×C3D3×D411yescharacteristic
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3—121no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—124no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—242no—
497C22×D3—241no—
498C22×D3—241no—
499C22×D3—242no—
500C22×D3C2×D1211yescharacteristic
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—61no—
505C3×D4—121no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
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—41no—
528#67—122no—
529#67—241no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3C2×D1211yescharacteristic
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543D12—32no—
544D12—32no—
545D12—62no—
546D12—62no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12—121no—
555D12—122no—
556D12—122no—
557D12—124no—
558D12—122no—
559D12—241no—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—241no—
565C4×D3—241no—
566Dic6—21no—
567Dic6—21no—
568Dic6—21no—
569Dic6—21no—
570Dic6—122no—
571Dic6—122no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—41no—
577C3×C8—41no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C2×C32—41no—
583C2×C32#54611yescharacteristic
584C2×C32#57511yescharacteristic
585C2×C32#57711yescharacteristic
586C3⋊D3—42no—
587C3⋊D3—81no—
588C3×D3—41no—
589C24—181no—
590#41—182no—
591#41—361no—
592C2×Q8—31no—
593C2×Q8—31no—
594C2×Q8—181no—
595C2×D4—31no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—361no—
603C22×C4—31no—
604C22×C4—181no—
605C22×C4—181no—
606C22×C4C2×D3211yescharacteristic
607Q16—121no—
608SD16—182no—
609SD16—361no—
610M16—41no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—121no—
614C2×C8C2×D3211yescharacteristic
615C2×C8C2×D3211yescharacteristic
616C4⋊C4—31no—
617C4⋊C4—31no—
618C4⋊C4—31no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C22⋊C4—31no—
627C22⋊C4—31no—
628C22⋊C4—61no—
629C22⋊C4—61no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C42—31no—
638C42—181no—
639C42—181no—
640C42—181no—
641C22×C3—22no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3C22×D1211yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—62no—
660C2×D3—62no—
661C2×D3—122no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—122no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—244no—
678C2×D3—244no—
679C2×D3—248no—
680C3×C4—22no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—61no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4—121no—
692C3×C4#100411yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4D3×#4111yescharacteristic
695C3×C4D3×#4111yescharacteristic
696Dic3—21no—
697Dic3—21no—
698Dic3—21no—
699Dic3—41no—
700Dic3—41no—
701Dic3—41no—
702Dic3—41no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—241no—
708Dic3—241no—
709C32#331111yescharacteristic, complemented, Sylow
710C23—31no—
711C23—181no—
712C23—181no—
713C23—362no—
714C23—362no—
715C23—721no—
716C23D3×D1211yescharacteristic
717Q8—61no—
718Q8—61no—
719Q8—61no—
720Q8—61no—
721Q8—362no—
722D4—92no—
723D4—121no—
724D4—181no—
725D4—181no—
726D4—181no—
727D4—362no—
728D4—362no—
729D4—721no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—31no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—181no—
742C2×C4—181no—
743C2×C4—362no—
744C2×C4—721no—
745C2×C4D3×D1211yescharacteristic
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—21no—
749C8—61no—
750C8—61no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—42no—
755C2×C3—41no—
756C2×C3—41no—
757C2×C3—121no—
758C2×C3#555411yescharacteristic
759C2×C3#561011yescharacteristic
760C2×C3#574811yescharacteristic
761C2×C3#575111yescharacteristic
762C2×C3#577711yescharacteristic
763C2×C3#577811yescharacteristic
764D3—41no—
765D3—122no—
766D3—122no—
767D3—242no—
768D3—242no—
769D3—241no—
770D3—241no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—61no—
775C22—61no—
776C22—61no—
777C22—182no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—724no—
784C22C2×D3×D1211yescharacteristic
785C4—21no—
786C4—61no—
787C4—61no—
788C4—61no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—361no—
794C4—361no—
795C4#6430611yescharacteristic
796C4#6433011yescharacteristic
797C3—21no—
798C3#7950211yescharacteristic, complemented
799C3#8091411yescharacteristic, complemented
800C2—41no—
801C2—121no—
802C2—362no—
803C2—721no—
804C2#1059471111yescharacteristic
805C2#1059471511yescharacteristic
806C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10595018C2
hypercenterC2×M16D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594841C2semidirect
3. #10592830C2semidirect
4. C3×#5137C2semidirect
5. C3×#5127C2semidirect
6. #10591183C2semidirect
7. #10591127C2semidirect
8. #10590966C2semidirect
9. #10590893C2semidirect
10. #10590847C2semidirect
11. #10590801C2semidirect
12. #10590795C2semidirect
13. #10590759C2semidirect
14. #10590704C2semidirect
15. #10590690C2semidirect
25. C2×C3×Dic12C22semidirect
26. C2×C3×D3×C8C22semidirect
31. #63918C22semidirect
38. #63856C22semidirect
39. Dic3×Dic6C22semidirect
40. #63841C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
58. #63566C22semidirect
69. #5137D3semidirect
73. #5127D3semidirect
174. C2×Dic12C2×D3semidirect
177. C2×D3×C8C2×D3semidirect
224. (C2×D3)⋊C8C2×D3semidirect
227. #817C2×D3semidirect
230. #816C2×D3semidirect
231. #816C2×D3semidirect
232. #815C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
709. C32#3311semidirect
798. C3#79502semidirect
799. C3#80914semidirect

Maximal subgroups

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

subgroupindex
#105950182
#105948412
#105928302
C3×#51372
C3×#51272
#105911832
#105911272
#105909662
#105908932
#105908472
#105908012
#105907952
#105907592
#105907042
#105906902
#809143
#795023