Finite Group Databasebeta

← #11904508

Subgroups — #11904508

Order 1152.

3117 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64298C211yesmaximal, characteristic, complemented
2C22×D3×Dic6C211yesmaximal, characteristic, complemented
3#10595987C211yesmaximal, characteristic, complemented
4C3×#5526C211yesmaximal, characteristic, complemented
5C3×#5524C211yesmaximal, characteristic, complemented
6#10595022C211yesmaximal, characteristic, complemented
7#10594855C211yesmaximal, characteristic, complemented
8#10594526C214yesmaximal, complemented
9#10594525C214yesmaximal, complemented
10#10594084C214yesmaximal, complemented
11#10594082C214yesmaximal, complemented
12#10593905C214yesmaximal, complemented
13#10593904C214yesmaximal, complemented
14#86355—31nomaximal
15#86022—31nomaximal
16C22×#634C2211yescharacteristic
17C2×C3×#235C2211yescharacteristic
18C2×C3×#235C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2212yes—
22C2×#3805C2214yes—
23C22×D3×Dic3C2212yes—
24#64298—28no—
25C2×#3795C2212yescomplemented
26C2×#3795C2212yescomplemented
27C2×D3×Dic6—28no—
28C2×D3×Dic6C2214yes—
29C2×D3×Dic6C2214yes—
30C2×D3×Dic6C2212yescomplemented
31C2×D3×Dic6C2212yescomplemented
32C32×#117C2211yescharacteristic
33#64135C2211yescharacteristic
34#64096C2214yescomplemented
35#64086C2214yes—
36C4×#634C2214yescomplemented
37C3×#897C2212yes—
38C3×#897C2214yescomplemented
39C3×#895C2212yes—
40C3×#886C2214yes—
41C3×#886C2212yes—
42C3×#882C2212yes—
43C3×#875C2212yescomplemented
44C3×C4×D12C2214yes—
45C3×#869C2212yescomplemented
46#63976C2212yes—
47#63961C2214yes—
48#63961C2212yes—
49#63919C2218yescomplemented
50#63915C2218yescomplemented
51#63908C2212yes—
52#63902C2218yes—
53C4×#625C2214yes—
54#63899C2218yes—
55#63899C2218yescomplemented
56#63899C2218yescomplemented
57#63898C2218yes—
58#63885C2218yes—
59#63873C2212yescomplemented
60#63863C2212yescomplemented
61#63856C2212yes—
62#63856C2214yescomplemented
63C2×#1010—31no—
64C2×#1010—31no—
65C22×D3×Q8—31no—
66C23×Dic6—31no—
67C3×#536—31no—
68C3×#525—31no—
69#5828—31no—
70#5825—31no—
71#5816—31no—
72#5791—31no—
73#5727—34no—
74#5677—34no—
75#5656—34no—
76#5648—34no—
77#5648—34no—
78#5633—34no—
79#5632—34no—
80#5632—34no—
81#5598—34no—
82#5586—34no—
83#5552—34no—
84D4×Dic6—34no—
85#5526D311yescharacteristic, complemented
86#5524D311yescharacteristic, complemented
87#5516—31no—
88#5516—31no—
89#5516—61no—
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2312yes—
93C2×#634D418yescomplemented
94C2×#634C2312yes—
95C2×#634C2312yes—
96C2×C3×#67C2312yes—
97C2×C3×#67C2312yes—
98C22×C3×Dic3C2312yes—
99C22×C3×Dic3C2311yescharacteristic
100C3×#235—24no—
101C3×#235—24no—
102C2×C3×D12C2314yes—
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—24no—
106C2×C3×C4×D3C2312yes—
107C2×C3×C4×D3C2312yes—
108C2×C3×C4×D3C2312yes—
109C2×C3×C4×D3C2312yes—
110C2×C3×Dic6—24no—
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2312yes—
113C2×C3×Dic6C2312yes—
114C2×C3×Dic6C2311yescharacteristic
115C2×#627—28no—
116C2×#627C2318yes—
117C2×#627C2314yes—
118C2×#625C2314yes—
119C2×#625C2314yes—
120#3805—216no—
121C2×D3×Dic3—28no—
122C2×D3×Dic3C2318yes—
123C2×D3×Dic3C2314yes—
124C2×D3×Dic3C2314yes—
125#3795—28no—
126#3795—28no—
127D3×Dic6—216no—
128D3×Dic6—216no—
129D3×Dic6—28no—
130D3×Dic6—28no—
131C32×C4⋊C4C2312yes—
132C32×C22⋊C4C2312yes—
133C32×C42C2312yes—
134#3757C2312yes—
135C4⋊(C3⋊Dic3)C2312yes—
136#3750C2318yes—
137C4×C3⋊Dic3C2318yes—
138C4×C3⋊Dic3C2312yes—
139C3×(C2×D3)⋊C4C2314yes—
140C3×(C2×D3)⋊C4C2314yes—
141C3×(C2×D3)⋊C4C2318yes—
142C3×C4⋊Dic3C2314yes—
143C3×C4⋊Dic3C2318yes—
144#3724C2314yes—
145#3724C2318yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2318yes—
148(C2×D3)⋊Dic3C2314yes—
149#3486—91noSylow
150C2×C3×#41—31no—
151C2×C3×#41—31no—
152C22×C3×Q8—31no—
153C23×C3×C4—31no—
154C23×Dic3—32no—
155#1010—68no—
156#1010—68no—
157C2×D3×Q8—32no—
158C2×D3×Q8—34no—
159C2×D3×Q8—34no—
160C2×D3×Q8—32no—
161C2×D3×Q8—68no—
162C2×#237—34no—
163C2×#237—34no—
164C2×#237—32no—
165C2×#237—32no—
166C2×#235—32no—
167C2×#235—32no—
168C2×#235C2×D311yescharacteristic
169C2×#235C2×D311yescharacteristic
170C22×C4×D3—32no—
171C22×C4×D3C2×D311yescharacteristic
172C22×Dic6—31no—
173C22×Dic6—31no—
174C22×Dic6—32no—
175C22×Dic6—32no—
176C22×Dic6—32no—
177C22×Dic6—34no—
178C22×Dic6—34no—
179C22×Dic6—32no—
180C22×Dic6—61no—
181C22×Dic6—68no—
182C22×Dic6C2×D311yescharacteristic
183C3×C4⋊Q8—32no—
184C3×#124—32no—
185C3×#123—32no—
186C3×#123—34no—
187C3×C22⋊Q8—32no—
188C3×C22⋊Q8—34no—
189C3×#121—32no—
190C3×#120—32no—
191C3×C4×D4—34no—
192C3×#117—21no—
193C3×#117C2×D311yescharacteristic
194C3×#117C2×D311yescharacteristic
195#953—32no—
196#947—32no—
197#946—34no—
198#946—32no—
199#944—32no—
200#944—32no—
201#939—38no—
202#938—32no—
203#937—32no—
204#936—32no—
205#935—32no—
206#935—34no—
207D4×Dic3—38no—
208#930—32no—
209#929—32no—
210#929—34no—
211C4×#67—34no—
212C4×#67—34no—
213#926—31no—
214#926—31no—
215#926—61no—
216#924—32no—
217#924—34no—
218#897C2×D312yes—
219#897C2×D314yescomplemented
220#896—38no—
221#896—38no—
222#896—38no—
223#895C2×D312yes—
224#893—38no—
225#888—38no—
226#888—38no—
227#887—34no—
228#887—34no—
229#887—64no—
230#886C2×D312yes—
231#886C2×D314yes—
232#885—38no—
233#885—38no—
234#884—38no—
235#882C2×D312yes—
236#67⋊C4—38no—
237#67⋊C4—38no—
238#878—38no—
239#878—38no—
240#878—38no—
241#877—34no—
242#877—34no—
243#877—64no—
244#875C2×D312yescomplemented
245C4×D12C2×D314yes—
246#869C2×D312yescomplemented
247C4×Dic6—34no—
248C4×Dic6—34no—
249C4×Dic6—64no—
250C23×C32C2411yescharacteristic
251C22×C3×D3—22no—
252C22×C3×D3—24no—
253C22×C3×D3C2412yes—
254C22×C3×D3C2412yes—
255C22×C3×D3C2412yes—
256C2×C32×C4C2×D414yes—
257C2×C32×C4C2414yes—
258C2×C32×C4C2411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260C2×C3⋊Dic3C2×D418yes—
261C2×C3⋊Dic3C2414yes—
262C2×C3⋊Dic3C2414yes—
263#634C2×D418yes—
264#634C2×D418yes—
265C3×#67—24no—
266C3×#67—24no—
267C2×C3×Dic3—24no—
268C2×C3×Dic3—22no—
269C2×C3×Dic3C2412yes—
270C2×C3×Dic3C2414yes—
271C2×C3×Dic3C2412yes—
272C2×C3×Dic3C2412yes—
273C3×D12—28no—
274C3×D12—22no—
275C3×D12—22no—
276C3×C4×D3—24no—
277C3×C4×D3—24no—
278C3×C4×D3—24no—
279C3×C4×D3—24no—
280C3×Dic6—24no—
281C3×Dic6—24no—
282C3×Dic6—22no—
283C3×Dic6—22no—
284#627—28no—
285#627—216no—
286#625—28no—
287#625—28no—
288D3×Dic3—216no—
289D3×Dic3—28no—
290D3×Dic3—28no—
291C2×2−1+4—91no—
292C23×Q8—91no—
293D4×Q8—94no—
294D4×Q8—94no—
295#548—94no—
296#548—94no—
297#536—31no—
298#536—94no—
299#536—91no—
300#525—31no—
301#525—94no—
302#525—91no—
303#519—91no—
304C24×C3—31no—
305C23×D3C22×D311yescharacteristic
306C3×#41—64no—
307C3×#41—64no—
308C2×C3×Q8—31no—
309C2×C3×Q8—32no—
310C2×C3×Q8—32no—
311C2×C3×Q8—31no—
312C2×C3×Q8—64no—
313C2×C3×D4—32no—
314C2×C3×D4—32no—
315C2×C3×D4—34no—
316C2×C3×D4—31no—
317C2×C3×D4—31no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—32no—
321C22×C3×C4—32no—
322C22×C3×C4—32no—
323C22×C3×C4—32no—
324C22×C3×C4—32no—
325C22×C3×C4—64no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C2×#67—34no—
329C2×#67—34no—
330C2×#67—34no—
331C2×#67—34no—
332C2×#67C22×D312yes—
333C2×#67C22×D312yes—
334C22×Dic3—32no—
335C22×Dic3—32no—
336C22×Dic3—34no—
337C22×Dic3—34no—
338C22×Dic3—38no—
339C22×Dic3—62no—
340C22×Dic3—68no—
341C22×Dic3C22×D311yescharacteristic
342C22×Dic3C22×D312yes—
343D3×Q8—616no—
344D3×Q8—616no—
345D3×Q8—68no—
346D3×Q8—68no—
347#237—68no—
348#237—68no—
349#237—616no—
350#237—616no—
351#235—24no—
352#235—24no—
353#235—68no—
354#235—68no—
355C2×D12C22×D314yes—
356C2×D12C22×D311yescharacteristic
357C2×D12C22×D311yescharacteristic
358C2×C4×D3—24no—
359C2×C4×D3—34no—
360C2×C4×D3—38no—
361C2×C4×D3—34no—
362C2×C4×D3—68no—
363C2×C4×D3C22×D312yes—
364C2×C4×D3C22×D312yes—
365C2×C4×D3C22×D312yes—
366C2×C4×D3C22×D312yes—
367C2×Dic6—24no—
368C2×Dic6—38no—
369C2×Dic6—38no—
370C2×Dic6—32no—
371C2×Dic6—32no—
372C2×Dic6—32no—
373C2×Dic6—32no—
374C2×Dic6—34no—
375C2×Dic6—38no—
376C2×Dic6—38no—
377C2×Dic6—34no—
378C2×Dic6—62no—
379C2×Dic6—62no—
380C2×Dic6—68no—
381C2×Dic6—616no—
382C2×Dic6—616no—
383C2×Dic6—68no—
384C2×Dic6—68no—
385C2×Dic6—68no—
386C2×Dic6—68no—
387C2×Dic6C22×D311yescharacteristic
388C2×Dic6C22×D312yes—
389C2×Dic6C22×D311yescharacteristic
390C2×Dic6C22×D312yes—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—34no—
393C3×C4⋊C4—38no—
394C3×C4⋊C4C22×D312yes—
395C3×C4⋊C4C22×D312yes—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—34no—
398C3×C22⋊C4—34no—
399C3×C22⋊C4—38no—
400C3×C22⋊C4C22×D312yes—
401C3×C22⋊C4C22×D312yes—
402C3×C42—22no—
403C3×C42C22×D312yes—
404C3×C42C22×D312yes—
405#217—32no—
406#217—32no—
407#217—34no—
408#217—34no—
409#217—38no—
410#217—62no—
411(C2×D3)⋊C4—38no—
412(C2×D3)⋊C4—34no—
413(C2×D3)⋊C4—34no—
414(C2×D3)⋊C4C22×D314yes—
415(C2×D3)⋊C4C22×D314yes—
416(C2×D3)⋊C4C22×D318yes—
417C4⋊Dic3—32no—
418C4⋊Dic3—32no—
419C4⋊Dic3—62no—
420C4⋊Dic3C22×D318yes—
421C4⋊Dic3C22×D314yes—
422Dic3⋊C4—38no—
423Dic3⋊C4—38no—
424Dic3⋊C4—34no—
425Dic3⋊C4—38no—
426Dic3⋊C4—38no—
427Dic3⋊C4—34no—
428Dic3⋊C4—68no—
429C4×Dic3—38no—
430C4×Dic3—38no—
431C4×Dic3—32no—
432C4×Dic3—32no—
433C4×Dic3—68no—
434C4×Dic3—62no—
435C22×C32—22no—
436C22×C32C22×D412yes—
437C22×C32C2511yescharacteristic
438C2×C3×D3—28no—
439C2×C3×D3—22no—
440C2×C3×D3—22no—
441C2×C3×D3—22no—
442C2×C3×D3—22no—
443C2×C3×D3—24no—
444C2×C3×D3—24no—
445C2×C3×D32−1+414yescomplemented
446C32×C4—24no—
447C32×C4C22×D412yes—
448C32×C4C22×D412yes—
449C3⋊Dic3—24no—
450C3⋊Dic3C22×D418yes—
451C3×Dic3—24no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—22no—
4552−1+4—188no—
456C2×#41—31no—
457C2×#41—31no—
458C2×#41—92no—
459C2×#41—92no—
460C2×#41—94no—
461C22×Q8—31no—
462C22×Q8—92no—
463C22×Q8—94no—
464C22×Q8—94no—
465C22×Q8—92no—
466C22×Q8—92no—
467C22×Q8—91no—
468C22×Q8—188no—
469C23×C4—31no—
470C23×C4—92no—
471C4⋊Q8—32no—
472C4⋊Q8—98no—
473C4⋊Q8—92no—
474#124—32no—
475#124—98no—
476#124—92no—
477#123—32no—
478#123—34no—
479#123—92no—
480#123—94no—
481C22⋊Q8—32no—
482C22⋊Q8—34no—
483C22⋊Q8—98no—
484C22⋊Q8—98no—
485C22⋊Q8—98no—
486C22⋊Q8—92no—
487C22⋊Q8—94no—
488#121—32no—
489#121—98no—
490#121—92no—
491#120—32no—
492#120—92no—
493C4×Q8—94no—
494C4×Q8—94no—
495C4×D4—34no—
496C4×D4—98no—
497C4×D4—98no—
498C4×D4—94no—
499#117—91no—
500#117—94no—
501#117D3211yescharacteristic
502C23×C3—21no—
503C23×C3—32no—
504C23×C3—32no—
505C23×C3—32no—
506C23×C3—64no—
507C23×C3—62no—
508C23×C3C23×D311yescharacteristic
509C23×C3C23×D311yescharacteristic
510C22×D3—22no—
511C22×D3—24no—
512C22×D3C23×D312yes—
513C22×D3C23×D312yes—
514C22×D3C23×D312yes—
515C3×Q8—64no—
516C3×Q8—64no—
517C3×Q8—62no—
518C3×Q8—62no—
519C3×D4—68no—
520C3×D4—64no—
521C3×D4—64no—
522C3×D4—62no—
523C3×D4—62no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—24no—
527C2×C3×C4—24no—
528C2×C3×C4—32no—
529C2×C3×C4—32no—
530C2×C3×C4—34no—
531C2×C3×C4—32no—
532C2×C3×C4—62no—
533C2×C3×C4—64no—
534C2×C3×C4—64no—
535C2×C3×C4—64no—
536C2×C3×C4—64no—
537C2×C3×C4—64no—
538C2×C3×C4D3×D414yes—
539C2×C3×C4D3×D414yes—
540C2×C3×C4C23×D314yes—
541C2×C3×C4C23×D314yes—
542C2×C3×C4C23×D311yescharacteristic
543C2×C3×C4C23×D311yescharacteristic
544C2×C3×C4C23×D311yescharacteristic
545C2×C3×C4C23×D311yescharacteristic
546#67—24no—
547#67—24no—
548#67—68no—
549#67—68no—
550#67—68no—
551#67—68no—
552C2×Dic3—24no—
553C2×Dic3—22no—
554C2×Dic3—38no—
555C2×Dic3—38no—
556C2×Dic3—34no—
557C2×Dic3—34no—
558C2×Dic3—34no—
559C2×Dic3—34no—
560C2×Dic3—68no—
561C2×Dic3—64no—
562C2×Dic3—64no—
563C2×Dic3—616no—
564C2×Dic3—68no—
565C2×Dic3—68no—
566C2×Dic3C23×D312yes—
567C2×Dic3C23×D312yes—
568C2×Dic3C23×D312yes—
569C2×Dic3C23×D314yes—
570D12—28no—
571D12—22no—
572D12—22no—
573C4×D3—24no—
574C4×D3—24no—
575C4×D3—24no—
576C4×D3—24no—
577C4×D3—616no—
578C4×D3—68no—
579C4×D3—68no—
580Dic6—24no—
581Dic6—24no—
582Dic6—22no—
583Dic6—22no—
584Dic6—38no—
585Dic6—38no—
586Dic6—38no—
587Dic6—38no—
588Dic6—68no—
589Dic6—68no—
590Dic6—616no—
591Dic6—68no—
592Dic6—68no—
593Dic6—616no—
594C2×C32—22no—
595C2×C32C23×D411yescharacteristic
596C2×C32C2×2−1+412yes—
597C3×D3—24no—
598C3×D3—42no—
599C3×D3—42no—
600C24—31no—
601#41—64no—
602#41—64no—
603#41—188no—
604#41—188no—
605#41—1816no—
606C2×Q8—32no—
607C2×Q8—31no—
608C2×Q8—32no—
609C2×Q8—31no—
610C2×Q8—64no—
611C2×Q8—98no—
612C2×Q8—94no—
613C2×Q8—92no—
614C2×Q8—92no—
615C2×Q8—98no—
616C2×Q8—188no—
617C2×Q8—1816no—
618C2×Q8—1816no—
619C2×Q8—188no—
620C2×Q8—188no—
621C2×D4—32no—
622C2×D4—32no—
623C2×D4—34no—
624C2×D4—31no—
625C2×D4—31no—
626C2×D4—94no—
627C2×D4—94no—
628C22×C4—31no—
629C22×C4—32no—
630C22×C4—32no—
631C22×C4—32no—
632C22×C4—32no—
633C22×C4—32no—
634C22×C4—64no—
635C22×C4—98no—
636C22×C4—94no—
637C22×C4—94no—
638C22×C4—92no—
639C22×C4—188no—
640C22×C4C2×D3211yescharacteristic
641C4⋊C4—34no—
642C4⋊C4—38no—
643C4⋊C4—94no—
644C4⋊C4—98no—
645C4⋊C4—98no—
646C4⋊C4—92no—
647C4⋊C4C2×D3212yes—
648C22⋊C4—34no—
649C22⋊C4—34no—
650C22⋊C4—38no—
651C22⋊C4—94no—
652C22⋊C4—94no—
653C22⋊C4—98no—
654C22⋊C4—92no—
655C22⋊C4C2×D3212yes—
656C42—98no—
657C42—92no—
658C42C2×D3212yes—
659C22×C3—22no—
660C22×C3—22no—
661C22×C3—22no—
662C22×C3—21no—
663C22×C3—34no—
664C22×C3—42no—
665C22×C3—68no—
666C22×C3—62no—
667C22×C3—62no—
668C22×C3—62no—
669C22×C3—62no—
670C22×C3—64no—
671C22×C3—64no—
672C22×C3C2×D3×D412yes—
673C22×C3C2×D3×D412yes—
674C22×C3C24×D311yescharacteristic
675C22×C3C24×D311yescharacteristic
676C2×D3—28no—
677C2×D3—22no—
678C2×D3—22no—
679C2×D3—22no—
680C2×D3—22no—
681C2×D3—24no—
682C2×D3—24no—
683C2×D3#101014yescomplemented
684C3×C4—24no—
685C3×C4—24no—
686C3×C4—22no—
687C3×C4—22no—
688C3×C4—44no—
689C3×C4—62no—
690C3×C4—62no—
691C3×C4—62no—
692C3×C4—64no—
693C3×C4C2×D3×D412yes—
694C3×C4C2×D3×D412yes—
695C3×C4C2×D3×D412yes—
696C3×C4C2×D3×D412yes—
697Dic3—24no—
698Dic3—22no—
699Dic3—22no—
700Dic3—22no—
701Dic3—38no—
702Dic3—38no—
703Dic3—68no—
704Dic3—64no—
705Dic3—64no—
706Dic3—124no—
707C32#348611yescharacteristic, complemented, Sylow
708C23—32no—
709C23—32no—
710C23—32no—
711C23—64no—
712C23—62no—
713C23C22×D3211yescharacteristic
714Q8—64no—
715Q8—64no—
716Q8—62no—
717Q8—62no—
718Q8—98no—
719Q8—98no—
720Q8—1816no—
721Q8—188no—
722D4—68no—
723D4—64no—
724D4—64no—
725D4—62no—
726D4—62no—
727D4—188no—
728D4—188no—
729C2×C4—32no—
730C2×C4—34no—
731C2×C4—32no—
732C2×C4—32no—
733C2×C4—62no—
734C2×C4—64no—
735C2×C4—64no—
736C2×C4—64no—
737C2×C4—64no—
738C2×C4—64no—
739C2×C4—98no—
740C2×C4—94no—
741C2×C4—94no—
742C2×C4—1816no—
743C2×C4—188no—
744C2×C4—188no—
745C2×C4#380214yes—
746C2×C4C22×D3214yes—
747C2×C4C22×D3211yescharacteristic
748C2×C4C22×D3211yescharacteristic
749C2×C3—22no—
750C2×C3—22no—
751C2×C3—21no—
752C2×C3—22no—
753C2×C3—42no—
754C2×C3—64no—
755C2×C3—122no—
756C2×C3—122no—
757C2×C3C22×D3×D411yescharacteristic
758C2×C3C22×D3×D411yescharacteristic
759C2×C3C2×#101012yes—
760C2×C3D3×2−1+412yes—
761D3—24no—
762D3—42no—
763D3—42no—
764C22—22no—
765C22—34no—
766C22—68no—
767C22—62no—
768C22—62no—
769C22—62no—
770C22—62no—
771C22—64no—
772C22—64no—
773C22C2×#380212yes—
774C22C23×D3211yescharacteristic
775C4—24no—
776C4—62no—
777C4—62no—
778C4—62no—
779C4—64no—
780C4—98no—
781C4—184no—
782C4C2×#380212yes—
783C4C2×#380212yes—
784C3—21no—
785C3#8602211yescharacteristic, complemented
786C3#8635511yescharacteristic, complemented
787C2—22no—
788C2—64no—
789C2—122no—
790C2—122no—
791C2C22×#380211yescharacteristic
792C2D3×#101012yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#117C22
hypercenter#117D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C2×#64298C2semidirect
2. C22×D3×Dic6C2semidirect
3. #10595987C2semidirect
4. C3×#5526C2semidirect
5. C3×#5524C2semidirect
6. #10595022C2semidirect
7. #10594855C2semidirect
8. #10594526C2semidirect
9. #10594525C2semidirect
10. #10594084C2semidirect
11. #10594082C2semidirect
12. #10593905C2semidirect
13. #10593904C2semidirect
25. C2×#3795C22semidirect
26. C2×#3795C22semidirect
30. C2×D3×Dic6C22semidirect
31. C2×D3×Dic6C22semidirect
34. #64096C22semidirect
36. C4×#634C22semidirect
38. C3×#897C22semidirect
43. C3×#875C22semidirect
45. C3×#869C22semidirect
49. #63919C22semidirect
50. #63915C22semidirect
55. #63899C22semidirect
56. #63899C22semidirect
59. #63873C22semidirect
60. #63863C22semidirect
62. #63856C22semidirect
85. #5526D3semidirect
86. #5524D3semidirect
93. C2×#634D4semidirect
219. #897C2×D3semidirect
244. #875C2×D3semidirect
246. #869C2×D3semidirect
445. C2×C3×D32−1+4semidirect
683. C2×D3#1010semidirect
707. C32#3486semidirect
785. C3#86022semidirect
786. C3#86355semidirect

Maximal subgroups

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

subgroupindex
C2×#642982
C22×D3×Dic62
#105959872
C3×#55262
C3×#55242
#105950222
#105948552
#105945262
#105945252
#105940842
#105940822
#105939052
#105939042
#863553
#860223