Finite Group Databasebeta

← #11865219

Subgroups — #11865219

Order 1152.

1537 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic
2C2×#64160C211yesmaximal, characteristic, complemented
3#10594856C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C3×#5236C211yesmaximal, characteristic, complemented
6#10591689C214yesmaximal, complemented
7#10591688C214yesmaximal, complemented
8#10591111C211yesmaximal, characteristic, complemented
9#10591076C211yesmaximal, characteristic, complemented
10#84123—31nomaximal
11#78995—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×#634C2211yescharacteristic, complemented
14C3×#1010—21no—
15C3×#1010C2212yes—
16C3×#1009—21no—
17C3×#1009C2212yes—
18C3×D3×#41—22no—
19C3×D3×#41—22no—
20C3×#1007—21no—
21C3×#1004—21no—
22C3×#1004—22no—
23C2×C3×#235—22no—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2211yescharacteristic
26#64160—22no—
27#64160C2214yescomplemented
28C2×#3756—21no—
29C2×#3754—21no—
30C2×#3748C2211yescharacteristic, complemented
31C3×#926C2211yescharacteristic, complemented
32C2×C3×#208C2211yescharacteristic, complemented
33#63962—22no—
34#63866C2212yescomplemented
35#63860C2212yescomplemented
36#63857—22no—
37C2×#3719—21no—
38#63831—22no—
39#63831C2214yescomplemented
40C2×#3716—21no—
41C3×#837C2214yescomplemented
42#63569C2214yescomplemented
43#63560C2212yescomplemented
44#63558C2212yescomplemented
45C3×#585—31no—
46#5964D311yescharacteristic
47#5825—31no—
48C2×#951—31no—
49C2×#951—31no—
50C2×#951—31no—
51C2×#951—61no—
52C2×#909—31no—
53#5526—31no—
54C3×#421—31no—
55#5246—34no—
56#5242—34no—
57#5237—31no—
58#5236—31no—
59#5236D311yescharacteristic, complemented
60#5132—31no—
61#5005—31no—
62#4826—34no—
63#4825—34no—
64C32×#41—21no—
65C32×#41—21no—
66C32×#41D412yes—
67C32×#41C2312yes—
68C2×C32×Q8D411yescharacteristic
69C2×C32×D4—21no—
70C2×C32×D4D411yescharacteristic
71C22×C32×C4—21no—
72C22×C32×C4C2311yescharacteristic
73C22×C3⋊Dic3—21no—
74C2×#634—21no—
75C2×#634—21no—
76C2×#634—21no—
77C2×#634—21no—
78C2×#634—21no—
79C2×#634C2312yes—
80C2×C3×#67—24no—
81C2×C3×#67—21no—
82C2×C3×#67D412yes—
83C3×#239—22no—
84C3×#239—22no—
85C3×D3×Q8—22no—
86C3×D3×Q8—22no—
87C3×#237—24no—
88C3×#237—22no—
89C3×#237—22no—
90C3×#237—24no—
91C3×D3×D4—24no—
92C3×D3×D4—22no—
93C3×D3×D4—24no—
94C3×D3×D4—22no—
95C3×#235—24no—
96C3×#235—24no—
97C3×#235—21no—
98C3×#235—21no—
99C3×#235—21no—
100C3×#235—21no—
101C3×#235—21no—
102C3×#235—21no—
103C3×#235—22no—
104C3×#235—22no—
105C3×#235D412yes—
106C3×#235C2312yes—
107C2×C3×D12—22no—
108C2×C3×D12D411yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×C4×D3—24no—
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3D412yes—
113C2×C3×Dic6—22no—
114C2×C3×Dic6D411yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116#3756—24no—
117#3754—24no—
118#3748—21no—
119#3748C2312yes—
120C2×C3⋊(C3⋊C8)—21no—
121C3×#217—21no—
122C3×C4⋊Dic3—21no—
123C3×C4×Dic3C2312yes—
124C3×#208—21no—
125C3×#208C2312yes—
126C2×C3×C3⋊C8—21no—
127Dic3⋊Dic3—24no—
128(C2×D3)⋊Dic3—24no—
129#3719—24no—
130#3716—24no—
131#3022—91noSylow
132C3×2−1+4—32no—
133C3×2−1+4—61no—
134C3×2−1+4—61no—
135C3×H(5,𝔽2)—32no—
136C3×H(5,𝔽2)—62no—
137C3×H(5,𝔽2)—61no—
138C3×H(5,𝔽2)—61no—
139C2×C3×#41—21no—
140C2×C3×#41—31no—
141C2×C3×#41—31no—
142C2×C3×#41—62no—
143C2×C3×#41—62no—
144C2×C3×#41—62no—
145C2×C3×#41C2×D311yescharacteristic
146C2×C3×#41C2×D311yescharacteristic
147#1010—21no—
148#1010C2×D312yes—
149#1009—21no—
150#1009C2×D312yes—
151D3×#41—22no—
152D3×#41—22no—
153#1007—21no—
154#1004—21no—
155#1004—22no—
156C2×#235—22no—
157C2×#235C2×D311yescharacteristic
158C2×#235C2×D311yescharacteristic
159C22×Dic6—31no—
160C22×Dic6—31no—
161C22×Dic6—61no—
162C2×C3×M16—31no—
163C3×#117—31no—
164#951—34no—
165#951—34no—
166#951—34no—
167#951—64no—
168#951—62no—
169#951—64no—
170#951—62no—
171#951—62no—
172#944—32no—
173C2×#216—61no—
174C2×#216—62no—
175C2×#216—61no—
176C2×#216—61no—
177#936—32no—
178#935—62no—
179C2×#214—61no—
180C2×#214—62no—
181C2×#214—61no—
182C2×#214—61no—
183#926C2×D311yescharacteristic, complemented
184#924—62no—
185C2×#208—31no—
186C2×#208—31no—
187C2×#208—61no—
188C2×#208C2×D311yescharacteristic, complemented
189#909—34no—
190#909—62no—
191C2×Dic12—61no—
192C2×#204—61no—
193#897—62no—
194#886—62no—
195#875—32no—
196#869—32no—
197C3×#104—34no—
198#837—34no—
199#837C2×D314yescomplemented
200#836—32no—
201#833—32no—
202#824—32no—
203#823—32no—
204#805—34no—
205C23×C32—21no—
206C23×C32C2×D411yescharacteristic
207C22×C3×D3—24no—
208C22×C3×D3—21no—
209C22×C3×D3C2×D412yes—
210C32×Q8—21no—
211C32×Q8C2×D412yes—
212C32×D4—22no—
213C32×D4—22no—
214C32×D4—21no—
215C32×D4C2×D412yes—
216C2×C32×C4—21no—
217C2×C32×C4—22no—
218C2×C32×C4—22no—
219C2×C32×C4C2×D411yescharacteristic
220C2×C32×C4C2×D411yescharacteristic
221C2×C32×C4C2×D411yescharacteristic
222C2×C32×C4C2×D411yescharacteristic
223C2×C32×C4C2×D411yescharacteristic
224C2×C32×C4C2411yescharacteristic
225C2×C3⋊Dic3—22no—
226C2×C3⋊Dic3—41no—
227C2×C3⋊Dic3—41no—
228#634—22no—
229#634—22no—
230#634—41no—
231#634—41no—
232C3×#67—24no—
233C3×#67—24no—
234C3×#67—22no—
235C3×#67—22no—
236C3×#67—22no—
237C3×#67—22no—
238C2×C3×Dic3—24no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—22no—
241C2×C3×Dic3C2×D412yes—
242C3×D12—24no—
243C3×D12—21no—
244C3×D12—21no—
245C3×D12—21no—
246C3×D12C2×D412yes—
247C3×C4×D3—24no—
248C3×C4×D3—24no—
249C3×C4×D3—22no—
250C3×C4×D3—22no—
251C3×C4×D3—22no—
252C3×C4×D3—22no—
253C3×Dic6—24no—
254C3×Dic6—21no—
255C3×Dic6—21no—
256C3×Dic6—21no—
257C3×Dic6C2×D412yes—
258C3⋊(C3⋊C8)—22no—
259C3×C3⋊C8—22no—
260#585—31no—
261C2×#137—91no—
262C2×#137—91no—
263#536—91no—
264#456—94no—
265#455—94no—
266#421—31no—
267#421—91no—
268#413—91no—
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—21no—
272C3×#41—21no—
273C3×#41—22no—
274C3×#41—22no—
275C3×#41—32no—
276C3×#41—32no—
277C3×#41—41no—
278C3×#41—41no—
279C3×#41—62no—
280C3×#41—62no—
281C3×#41—64no—
282C3×#41—64no—
283C3×#41—64no—
284C3×#41—64no—
285C3×#41—62no—
286C3×#41—62no—
287C3×#41—62no—
288C3×#41—62no—
289C3×#41—61no—
290C3×#41—61no—
291C3×#41—61no—
292C3×#41—61no—
293C3×#41—61no—
294C3×#41—61no—
295C3×#41D1212yes—
296C3×#41#6712yes—
297C3×#41C22×D312yes—
298C3×#41C22×D312yes—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—62no—
303C2×C3×Q8—62no—
304C2×C3×Q8—62no—
305C2×C3×Q8D1211yescharacteristic
306C2×C3×Q8#6711yescharacteristic
307C2×C3×D4—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—32no—
311C2×C3×D4—31no—
312C2×C3×D4—31no—
313C2×C3×D4—41no—
314C2×C3×D4—62no—
315C2×C3×D4—64no—
316C2×C3×D4—64no—
317C2×C3×D4—62no—
318C2×C3×D4—64no—
319C2×C3×D4—61no—
320C2×C3×D4—62no—
321C2×C3×D4D1211yescharacteristic
322C2×C3×D4#6711yescharacteristic
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—21no—
326C22×C3×C4—32no—
327C22×C3×C4—41no—
328C22×C3×C4—64no—
329C22×C3×C4—61no—
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C2×#67—24no—
333C2×#67—21no—
334C2×#67#6712yes—
335C22×Dic3—61no—
336C22×Dic3—61no—
337C22×Dic3—121no—
338#239—22no—
339#239—22no—
340D3×Q8—22no—
341D3×Q8—22no—
342#237—24no—
343#237—22no—
344#237—22no—
345#237—24no—
346D3×D4—24no—
347D3×D4—22no—
348D3×D4—24no—
349D3×D4—22no—
350#235—24no—
351#235—24no—
352#235—21no—
353#235—21no—
354#235—21no—
355#235—21no—
356#235—21no—
357#235—21no—
358#235—22no—
359#235—22no—
360#235#6712yes—
361#235C22×D312yes—
362C2×D12—22no—
363C2×D12#6711yescharacteristic
364C2×D12C22×D311yescharacteristic
365C2×C4×D3—24no—
366C2×C4×D3—21no—
367C2×C4×D3#6712yes—
368C2×Dic6—22no—
369C2×Dic6—32no—
370C2×Dic6—32no—
371C2×Dic6—62no—
372C2×Dic6—62no—
373C2×Dic6—62no—
374C2×Dic6—61no—
375C2×Dic6—61no—
376C2×Dic6—61no—
377C2×Dic6—61no—
378C2×Dic6—61no—
379C2×Dic6—61no—
380C2×Dic6—61no—
381C2×Dic6—61no—
382C2×Dic6—61no—
383C2×Dic6—61no—
384C2×Dic6—121no—
385C2×Dic6—121no—
386C2×Dic6—121no—
387C2×Dic6#6711yescharacteristic
388C2×Dic6C22×D311yescharacteristic
389C3×M16—32no—
390C3×M16—61no—
391C2×C3×C8—61no—
392C3×C4⋊C4—61no—
393C3×C22⋊C4—61no—
394C3×C42—32no—
395#217—21no—
396#217—64no—
397#216—64no—
398#216—68no—
399#216—64no—
400#216—64no—
401#214—64no—
402#214—68no—
403#214—64no—
404#214—64no—
405(C2×D3)⋊C4—64no—
406C4⋊Dic3—21no—
407C4⋊Dic3—64no—
408Dic3⋊C4—64no—
409C4×Dic3C22×D312yes—
410#208—21no—
411#208—32no—
412#208—32no—
413#208—62no—
414#208—62no—
415#208—61no—
416#208—61no—
417#208C22×D312yes—
418C2×C3⋊C8—21no—
419C2×C3⋊C8—62no—
420C2×C3⋊C8—61no—
421C2×C3⋊C8—61no—
422Dic12—64no—
423#204—64no—
424C22×C32—22no—
425C22×C32—41no—
426C22×C32—81no—
427C22×C32#12011yescharacteristic
428C22×C32#12011yescharacteristic
429C22×C32C22×D411yescharacteristic
430C2×C3×D3—22no—
431C2×C3×D3—22no—
432C2×C3×D3—42no—
433C2×C3×D3—81no—
434C2×C3×D3—84no—
435C32×C4—22no—
436C32×C4#12011yescharacteristic
437C32×C4#12011yescharacteristic
438C32×C4C22×D411yescharacteristic
439C32×C4C22×D411yescharacteristic
440C3⋊Dic3—42no—
441C3×Dic3—22no—
442C3×Dic3—22no—
443C3×Dic3—42no—
4442−1+4—32no—
4452−1+4—61no—
4462−1+4—61no—
447H(5,𝔽2)—32no—
448H(5,𝔽2)—62no—
449H(5,𝔽2)—61no—
450H(5,𝔽2)—61no—
451C2×#41—31no—
452C2×#41—31no—
453C2×#41—62no—
454C2×#41—62no—
455C2×#41—62no—
456C2×#41D3211yescharacteristic
457C22×Q8—91no—
458#137—94no—
459#137—94no—
460#137—182no—
461#137—182no—
462C2×Q16—181no—
463C2×Q16—181no—
464C2×SD16—181no—
465C2×SD16—181no—
466C2×M16—31no—
467C2×M16—91no—
468C4⋊Q8—92no—
469#124—92no—
470#123—182no—
471C22⋊Q8—182no—
472#117—31no—
473#104—34no—
474#104—94no—
475#101—92no—
476#100—92no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—32no—
481C23×C3—41no—
482C23×C3—64no—
483C23×C3—61no—
484C23×C3D3×D411yescharacteristic
485C23×C3C2×#6711yescharacteristic
486C22×D3—24no—
487C22×D3—21no—
488C22×D3C2×#6712yes—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—22no—
492C3×Q8—32no—
493C3×Q8—41no—
494C3×Q8—64no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8C2×D1212yes—
499C3×Q8C2×#6712yes—
500C3×D4—22no—
501C3×D4—22no—
502C3×D4—22no—
503C3×D4—22no—
504C3×D4—21no—
505C3×D4—21no—
506C3×D4—22no—
507C3×D4—32no—
508C3×D4—41no—
509C3×D4—42no—
510C3×D4—42no—
511C3×D4—64no—
512C3×D4—64no—
513C3×D4—64no—
514C3×D4—62no—
515C3×D4—62no—
516C3×D4—62no—
517C3×D4—62no—
518C3×D4—61no—
519C3×D4—61no—
520C3×D4—61no—
521C3×D4C2×D1212yes—
522C3×D4C2×#6712yes—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—22no—
526C2×C3×C4—22no—
527C2×C3×C4—22no—
528C2×C3×C4—22no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—32no—
536C2×C3×C4—42no—
537C2×C3×C4—42no—
538C2×C3×C4—41no—
539C2×C3×C4—64no—
540C2×C3×C4—64no—
541C2×C3×C4—64no—
542C2×C3×C4—61no—
543C2×C3×C4—62no—
544C2×C3×C4—62no—
545C2×C3×C4—62no—
546C2×C3×C4—62no—
547C2×C3×C4—62no—
548C2×C3×C4C2×D1211yescharacteristic
549C2×C3×C4C2×D1211yescharacteristic
550C2×C3×C4D3×D411yescharacteristic
551C2×C3×C4D3×D411yescharacteristic
552C2×C3×C4D3×D411yescharacteristic
553C2×C3×C4C2×#6711yescharacteristic
554C2×C3×C4C2×#6711yescharacteristic
555C2×C3×C4C2×#6711yescharacteristic
556C2×C3×C4C2×#6711yescharacteristic
557C2×C3×C4C2×#6711yescharacteristic
558C2×C3×C4C23×D311yescharacteristic
559C2×C3×C4C23×D311yescharacteristic
560#67—24no—
561#67—24no—
562#67—22no—
563#67—22no—
564#67—22no—
565#67—22no—
566C2×Dic3—24no—
567C2×Dic3—21no—
568C2×Dic3—22no—
569C2×Dic3—62no—
570C2×Dic3—62no—
571C2×Dic3—122no—
572C2×Dic3—122no—
573C2×Dic3—122no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3—121no—
578C2×Dic3C2×#6712yes—
579D12—24no—
580D12—21no—
581D12—21no—
582D12—21no—
583D12C2×#6712yes—
584C4×D3—24no—
585C4×D3—24no—
586C4×D3—22no—
587C4×D3—22no—
588C4×D3—22no—
589C4×D3—22no—
590Dic6—24no—
591Dic6—21no—
592Dic6—21no—
593Dic6—21no—
594Dic6—64no—
595Dic6—62no—
596Dic6—62no—
597Dic6—62no—
598Dic6—62no—
599Dic6—122no—
600Dic6—122no—
601Dic6—122no—
602Dic6—121no—
603Dic6—121no—
604Dic6—121no—
605Dic6—121no—
606Dic6C2×#6712yes—
607C3×C8—62no—
608C3⋊C8—22no—
609C3⋊C8—64no—
610C3⋊C8—62no—
611C3⋊C8—62no—
612C2×C32—21no—
613C2×C32—21no—
614C2×C32—21no—
615C2×C32—42no—
616C2×C32C2×#12011yescharacteristic
617C3×D3—42no—
618C3×D3—42no—
619#41—21no—
620#41—21no—
621#41—32no—
622#41—32no—
623#41—62no—
624#41—62no—
625#41—64no—
626#41—64no—
627#41—64no—
628#41—64no—
629#41—62no—
630#41—62no—
631#41—62no—
632#41—62no—
633#41—61no—
634#41—61no—
635#41—61no—
636#41—61no—
637#41—61no—
638#41—61no—
639#41#62612yes—
640#41C2×D3212yes—
641C2×Q8—31no—
642C2×Q8—31no—
643C2×Q8—62no—
644C2×Q8—62no—
645C2×Q8—62no—
646C2×Q8—92no—
647C2×Q8—181no—
648C2×Q8—181no—
649C2×Q8—181no—
650C2×Q8—181no—
651C2×Q8—181no—
652C2×Q8#62611yescharacteristic
653C2×D4—21no—
654C2×D4—32no—
655C2×D4—31no—
656C2×D4—31no—
657C2×D4—62no—
658C2×D4—64no—
659C2×D4—64no—
660C2×D4—62no—
661C2×D4—64no—
662C2×D4—61no—
663C2×D4—62no—
664C2×D4#62611yescharacteristic
665C22×C4—21no—
666C22×C4—32no—
667C22×C4—64no—
668C22×C4—61no—
669C22×C4—181no—
670C22×C4C2×D3211yescharacteristic
671Q16—184no—
672Q16—184no—
673SD16—184no—
674SD16—184no—
675M16—32no—
676M16—61no—
677M16—92no—
678M16—181no—
679C2×C8—61no—
680C2×C8—181no—
681C4⋊C4—61no—
682C4⋊C4—184no—
683C22⋊C4—61no—
684C22⋊C4—184no—
685C42—32no—
686C22×C3—22no—
687C22×C3—22no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—42no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—42no—
695C22×C3—62no—
696C22×C3—62no—
697C22×C3—81no—
698C22×C3—81no—
699C22×C3—82no—
700C22×C3—122no—
701C22×C3—241no—
702C22×C3—244no—
703C22×C3#88211yescharacteristic
704C22×C3#88211yescharacteristic
705C22×C3#95311yescharacteristic
706C22×C3#95311yescharacteristic
707C22×C3C2×D3×D411yescharacteristic
708C22×C3C22×#6711yescharacteristic
709C2×D3—22no—
710C2×D3—22no—
711C2×D3—42no—
712C2×D3—81no—
713C2×D3—84no—
714C3×C4—22no—
715C3×C4—22no—
716C3×C4—21no—
717C3×C4—21no—
718C3×C4—21no—
719C3×C4—21no—
720C3×C4—42no—
721C3×C4—62no—
722C3×C4—62no—
723C3×C4—122no—
724C3×C4#88211yescharacteristic
725C3×C4#88211yescharacteristic
726C3×C4#95311yescharacteristic
727C3×C4#95311yescharacteristic
728C3×C4C22×D1211yescharacteristic
729C3×C4C2×D3×D411yescharacteristic
730C3×C4C22×#6711yescharacteristic
731C3×C4C22×#6711yescharacteristic
732Dic3—22no—
733Dic3—22no—
734Dic3—42no—
735Dic3—124no—
736Dic3—122no—
737Dic3—122no—
738C32#302211yescharacteristic, complemented, Sylow
739C23—21no—
740C23—32no—
741C23—64no—
742C23—61no—
743C23D3×#6711yescharacteristic
744Q8—21no—
745Q8—32no—
746Q8—64no—
747Q8—61no—
748Q8—61no—
749Q8—61no—
750Q8—182no—
751Q8—182no—
752Q8—361no—
753Q8—361no—
754Q8C2×#62612yes—
755D4—22no—
756D4—22no—
757D4—21no—
758D4—32no—
759D4—64no—
760D4—64no—
761D4—64no—
762D4—62no—
763D4—62no—
764D4—62no—
765D4—62no—
766D4—61no—
767D4—61no—
768D4—61no—
769D4C2×#62612yes—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—32no—
774C2×C4—64no—
775C2×C4—64no—
776C2×C4—64no—
777C2×C4—61no—
778C2×C4—62no—
779C2×C4—62no—
780C2×C4—62no—
781C2×C4—62no—
782C2×C4—62no—
783C2×C4—182no—
784C2×C4—361no—
785C2×C4—361no—
786C2×C4C2×#62611yescharacteristic
787C2×C4C2×#62611yescharacteristic
788C2×C4D3×#6711yescharacteristic
789C2×C4D3×#6711yescharacteristic
790C2×C4D3×#6711yescharacteristic
791C2×C4C22×D3211yescharacteristic
792C8—62no—
793C8—182no—
794C2×C3—22no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—21no—
800C2×C3—21no—
801C2×C3—21no—
802C2×C3—41no—
803C2×C3—41no—
804C2×C3—42no—
805C2×C3—42no—
806C2×C3—82no—
807C2×C3—122no—
808C2×C3—122no—
809C2×C3C2×#88211yescharacteristic
810C2×C3C2×#95311yescharacteristic
811D3—42no—
812D3—42no—
813C22—22no—
814C22—41no—
815C22—62no—
816C22—62no—
817C22—81no—
818C22—122no—
819C22—241no—
820C22—244no—
821C22#6397711yescharacteristic
822C22#6397711yescharacteristic
823C22C2×D3×#6711yescharacteristic
824C4—22no—
825C4—62no—
826C4—62no—
827C4—122no—
828C4—362no—
829C4#6397711yescharacteristic
830C4#6397711yescharacteristic
831C4C22×#62611yescharacteristic
832C4C2×D3×#6711yescharacteristic
833C3—21no—
834C3#7899511yescharacteristic, complemented
835C3#8412311yescharacteristic, complemented
836C2—21no—
837C2—21no—
838C2—21no—
839C2—42no—
840C2—122no—
841C2—122no—
842C2C2×#6397711yescharacteristic
subgroupG/H
centerC2C2×#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
prime radicalC3×#5964C2
hypercenterC2×#41D32
hypocenterC32#3022
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#64160C2semidirect
3. #10594856C2semidirect
4. C2×#63831C2semidirect
5. C3×#5236C2semidirect
6. #10591689C2semidirect
7. #10591688C2semidirect
8. #10591111C2semidirect
9. #10591076C2semidirect
13. C22×#634C22semidirect
27. #64160C22semidirect
30. C2×#3748C22semidirect
31. C3×#926C22semidirect
32. C2×C3×#208C22semidirect
34. #63866C22semidirect
35. #63860C22semidirect
39. #63831C22semidirect
41. C3×#837C22semidirect
42. #63569C22semidirect
43. #63560C22semidirect
44. #63558C22semidirect
59. #5236D3semidirect
183. #926C2×D3semidirect
188. C2×#208C2×D3semidirect
199. #837C2×D3semidirect
738. C32#3022semidirect
834. C3#78995semidirect
835. C3#84123semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
C2×#641602
#105948562
C2×#638312
C3×#52362
#105916892
#105916882
#105911112
#105910762
#841233
#789953