Finite Group Databasebeta

← #11904516

Subgroups — #11904516

Order 1152.

3119 conjugacy classes of subgroups.

The subgroup lattice has 805 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10596287C211yesmaximal, characteristic, complemented
4C3×#5816C211yesmaximal, characteristic, complemented
5#10595403C214yesmaximal, complemented
6#10595402C214yesmaximal, complemented
7#10595401C214yesmaximal, complemented
8#10595400C214yesmaximal, complemented
9#10595023C211yesmaximal, characteristic, complemented
10#10595022C211yesmaximal, characteristic, complemented
11#10594897C214yesmaximal, complemented
12#10594896C214yesmaximal, complemented
13#10594818C211yesmaximal, characteristic, complemented
14#87251—31nomaximal
15#86355—31nomaximal
16C22×C32×Q8C2211yescharacteristic
17C2×#3828C2211yescharacteristic
18C2×C3×D3×Q8—28no—
19C2×C3×D3×Q8C2214yes—
20C2×C3×D3×Q8C2214yes—
21C2×C3×#235C2211yescharacteristic
22C22×C3×C4×D3C2212yes—
23C22×C3×C4×D3C2211yescharacteristic
24C22×C3×Dic6C2212yes—
25C22×C3×Dic6C2211yescharacteristic
26C2×#3804C2214yes—
27C2×#3799C2212yescomplemented
28C2×#3797C2212yescomplemented
29#64297—28no—
30C2×#3796C2212yescomplemented
31C2×D3×Dic6C2212yescomplemented
32#64156C2212yescomplemented
33#64155C2214yescomplemented
34#64153C2212yescomplemented
35#64138C2214yes—
36#64135C2211yescharacteristic
37C3×#947C2212yescomplemented
38C3×#946C2214yescomplemented
39C3×#944C2212yescomplemented
40C3×#929C2214yes—
41C3×#926C2211yescharacteristic
42#63977C2212yes—
43#63976C2212yes—
44#63966C2212yes—
45#63961C2212yes—
46#63955C2214yes—
47#63909C2212yes—
48#63908C2212yes—
49#63907C2218yescomplemented
50#63906C2218yes—
51#63904C2218yes—
52C4×#626C2214yes—
53C4×#625C2214yes—
54#63888C2218yescomplemented
55#63887C2218yescomplemented
56#63879C2218yes—
57#63857C2212yes—
58#63856C2212yes—
59#63851C2218yes—
60#63843C2214yescomplemented
61Dic3×Dic6C2214yescomplemented
62#63839C2218yescomplemented
63C23×C3×Q8—31no—
64C2×#1010—31no—
65C2×#1007—31no—
66C22×D3×Q8D311yescharacteristic, complemented
67C3×#536—31no—
68#5828—31no—
69#5817—34no—
70#5817—34no—
71#5816—31no—
72#5816—31no—
73#5816—34no—
74#5816—61no—
75#5816D311yescharacteristic, complemented
76Q8×#67—34no—
77Q8×#67—34no—
78#5812—31no—
79#5791—31no—
80#5791—34no—
81#5791—31no—
82#5727—34no—
83#5677—34no—
84#5656—34no—
85#5648—34no—
86#5633—34no—
87#5632—34no—
88#5524—31no—
89#5516—31no—
90C23×C3×D3C2311yescharacteristic
91C2×C32×Q8—24no—
92C2×C32×Q8C2312yes—
93C2×C32×Q8C2312yes—
94C22×C32×C4C2312yes—
95C22×C32×C4C2311yescharacteristic
96C2×#638C2312yes—
97#3828—24no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4×C3⋊D3C2312yes—
100C2×#634C2311yescharacteristic
101C2×C3×#67C2312yes—
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2312yes—
104C3×D3×Q8—216no—
105C3×D3×Q8—216no—
106C3×#235—24no—
107C2×C3×D12C2311yescharacteristic
108C2×C3×C4×D3—24no—
109C2×C3×C4×D3—28no—
110C2×C3×C4×D3C2312yes—
111C2×C3×C4×D3C2318yes—
112C2×C3×C4×D3C2312yes—
113C2×C3×C4×D3C2312yes—
114C2×C3×Dic6—28no—
115C2×C3×Dic6D418yescomplemented
116C2×C3×Dic6C2311yescharacteristic
117C2×C3×Dic6C2318yes—
118C2×C3×Dic6C2312yes—
119C2×C3×Dic6C2312yes—
120C2×#627C2314yes—
121C2×#626C2314yes—
122C2×#626C2314yes—
123C2×#625C2314yes—
124C2×#624C2314yes—
125#3804—216no—
126C2×D3×Dic3C2314yes—
127#3799—28no—
128#3797—28no—
129#3796—28no—
130D3×Dic6—28no—
131#3757C2312yes—
132#3752C2318yes—
133C4⋊(C3⋊Dic3)C2312yes—
134#3750C2318yes—
135C4×C3⋊Dic3C2312yes—
136C3×#217C2312yes—
137C3×(C2×D3)⋊C4C2318yes—
138C3×C4⋊Dic3C2312yes—
139C3×Dic3⋊C4C2318yes—
140C3×C4×Dic3C2312yes—
141#3724C2314yes—
142Dic3⋊Dic3C2314yes—
143Dic3⋊Dic3C2318yes—
144#3722C2314yes—
145(C2×D3)⋊Dic3C2314yes—
146(C2×D3)⋊Dic3C2314yes—
147(C2×D3)⋊Dic3C2314yes—
148Dic32C2318yes—
149#3486—91noSylow
150C2×C3×#41—31no—
151C22×C3×Q8—21no—
152C22×C3×Q8—34no—
153C22×C3×Q8—34no—
154C22×C3×Q8—31no—
155C22×C3×Q8—32no—
156C22×C3×Q8—68no—
157C22×C3×Q8C2×D311yescharacteristic
158C22×C3×Q8C2×D311yescharacteristic
159C23×C3×C4—32no—
160C23×C3×C4—31no—
161#1010—68no—
162#1007—68no—
163C2×#239—32no—
164C2×#239—32no—
165C2×D3×Q8—28no—
166C2×D3×Q8—32no—
167C2×D3×Q8—32no—
168C2×D3×Q8—32no—
169C2×D3×Q8C2×D314yes—
170C2×D3×Q8C2×D314yes—
171C2×#237—34no—
172C2×#237—32no—
173C2×#235—31no—
174C2×#235—31no—
175C2×#235—34no—
176C2×#235—32no—
177C2×#235—61no—
178C2×#235C2×D311yescharacteristic
179C22×C4×D3C2×D312yes—
180C22×C4×D3C2×D311yescharacteristic
181C22×Dic6—32no—
182C22×Dic6C2×D312yes—
183C22×Dic6C2×D311yescharacteristic
184C3×C4⋊Q8—32no—
185C3×#124—32no—
186C3×#123—34no—
187C3×C22⋊Q8—34no—
188C3×#117—31no—
189#953—32no—
190#953—32no—
191#947—32no—
192#947—32no—
193#947—38no—
194#947—62no—
195#947C2×D312yescomplemented
196#946—34no—
197#946—34no—
198#946—32no—
199#946—38no—
200#946—38no—
201#946—64no—
202#946C2×D314yescomplemented
203Q8×Dic3—34no—
204Q8×Dic3—34no—
205#944—32no—
206#944—32no—
207#944—38no—
208#944—62no—
209#944C2×D312yescomplemented
210#938—32no—
211#937—32no—
212#935—32no—
213#930—32no—
214#930—38no—
215#930—32no—
216#929—34no—
217#929—34no—
218#929—32no—
219#929—32no—
220#929—64no—
221#929C2×D314yes—
222C4×#67—34no—
223C4×#67—34no—
224C4×#67—38no—
225C4×#67—38no—
226C4×#67—34no—
227#926—31no—
228#926—31no—
229#926—34no—
230#926—61no—
231#926C2×D311yescharacteristic
232#924—32no—
233#924—32no—
234#924—38no—
235#897—32no—
236#896—38no—
237#896—38no—
238#895—32no—
239#893—38no—
240#888—38no—
241#887—34no—
242#886—32no—
243#885—38no—
244#884—38no—
245#882—32no—
246#67⋊C4—38no—
247#878—38no—
248#877—34no—
249C4×D12—34no—
250C4×Dic6—34no—
251C23×C32C2411yescharacteristic
252C22×C3⋊D3C2412yes—
253C22×C3×D3—22no—
254C22×C3×D3—24no—
255C22×C3×D3C2412yes—
256C22×C3×D3C2412yes—
257C32×Q8—24no—
258C32×Q8—24no—
259C2×C32×C4—24no—
260C2×C32×C4C2×D414yes—
261C2×C32×C4C2414yes—
262C2×C32×C4C2411yescharacteristic
263C2×C32×C4C2411yescharacteristic
264#638—24no—
265C2×C3⋊Dic3C2414yes—
266C2×C3⋊Dic3C2412yes—
267C4⋊(C3⋊D3)—22no—
268C4×C3⋊D3—24no—
269#634—22no—
270C3×#67—24no—
271C2×C3×Dic3—22no—
272C2×C3×Dic3C2×D418yes—
273C2×C3×Dic3C2414yes—
274C2×C3×Dic3C2412yes—
275C2×C3×Dic3C2412yes—
276C2×C3×Dic3C2414yes—
277C3×D12—22no—
278C3×C4×D3—24no—
279C3×C4×D3—24no—
280C3×C4×D3—24no—
281C3×C4×D3—216no—
282C3×Dic6—22no—
283C3×Dic6—216no—
284C3×Dic6C2×D418yes—
285C3×Dic6C2×D418yes—
286#627—28no—
287#626—28no—
288#626—28no—
289#625—28no—
290#624—28no—
291D3×Dic3—28no—
292C2×2−1+4—91no—
293C23×Q8—31no—
294D4×Q8—94no—
295D4×Q8—94no—
296#548—94no—
297#548—94no—
298#536—31no—
299#536—94no—
300#536—91no—
301#525—91no—
302#525—94no—
303#525—91no—
304#519—91no—
305C24×C3—31no—
306C23×D3C22×D311yescharacteristic
307C3×#41—64no—
308C2×C3×Q8—24no—
309C2×C3×Q8—24no—
310C2×C3×Q8—22no—
311C2×C3×Q8—22no—
312C2×C3×Q8—38no—
313C2×C3×Q8—32no—
314C2×C3×Q8—32no—
315C2×C3×Q8—38no—
316C2×C3×Q8—31no—
317C2×C3×Q8—44no—
318C2×C3×Q8—68no—
319C2×C3×Q8—616no—
320C2×C3×Q8—616no—
321C2×C3×Q8C22×D312yes—
322C2×C3×Q8C22×D312yes—
323C2×C3×Q8C22×D312yes—
324C2×C3×Q8C22×D312yes—
325C2×C3×D4—32no—
326C2×C3×D4—31no—
327C22×C3×C4—21no—
328C22×C3×C4—22no—
329C22×C3×C4—32no—
330C22×C3×C4—31no—
331C22×C3×C4—38no—
332C22×C3×C4—32no—
333C22×C3×C4—32no—
334C22×C3×C4—32no—
335C22×C3×C4—68no—
336C22×C3×C4—64no—
337C22×C3×C4C22×D312yes—
338C22×C3×C4C22×D312yes—
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—32no—
342C2×#67—32no—
343C2×#67—34no—
344C2×#67—34no—
345C2×#67—34no—
346C2×#67—34no—
347C2×#67—62no—
348C2×#67C22×D312yes—
349C22×Dic3—34no—
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D312yes—
352#239—68no—
353#239—68no—
354D3×Q8—216no—
355D3×Q8—216no—
356D3×Q8—68no—
357D3×Q8—68no—
358D3×Q8—68no—
359#237—616no—
360#237—68no—
361#235—24no—
362#235—616no—
363#235—64no—
364#235—64no—
365#235—68no—
366#235—124no—
367C2×D12—34no—
368C2×D12—34no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—61no—
372C2×D12C22×D311yescharacteristic
373C2×C4×D3—24no—
374C2×C4×D3—28no—
375C2×C4×D3—34no—
376C2×C4×D3—32no—
377C2×C4×D3—32no—
378C2×C4×D3—34no—
379C2×C4×D3—34no—
380C2×C4×D3—62no—
381C2×C4×D3C22×D312yes—
382C2×C4×D3C22×D318yes—
383C2×C4×D3C22×D312yes—
384C2×C4×D3C22×D312yes—
385C2×Dic6—28no—
386C2×Dic6—31no—
387C2×Dic6—31no—
388C2×Dic6—34no—
389C2×Dic6—34no—
390C2×Dic6—61no—
391C2×Dic6—68no—
392C2×Dic6#6718yescomplemented
393C2×Dic6C22×D318yes—
394C2×Dic6C22×D311yescharacteristic
395C2×Dic6C22×D312yes—
396C2×Dic6C22×D312yes—
397C3×C4⋊C4—32no—
398C3×C4⋊C4—38no—
399C3×C22⋊C4—32no—
400C3×C22⋊C4—38no—
401C3×C42—32no—
402#217—32no—
403#217—32no—
404#217—34no—
405#217—34no—
406#217—34no—
407#217—62no—
408#217C22×D312yes—
409(C2×D3)⋊C4—34no—
410(C2×D3)⋊C4—34no—
411(C2×D3)⋊C4—34no—
412(C2×D3)⋊C4—38no—
413(C2×D3)⋊C4—38no—
414(C2×D3)⋊C4—34no—
415(C2×D3)⋊C4—34no—
416(C2×D3)⋊C4—68no—
417(C2×D3)⋊C4C22×D318yes—
418C4⋊Dic3—32no—
419C4⋊Dic3—32no—
420C4⋊Dic3—34no—
421C4⋊Dic3—38no—
422C4⋊Dic3—62no—
423C4⋊Dic3C22×D312yes—
424Dic3⋊C4—38no—
425Dic3⋊C4—38no—
426Dic3⋊C4—38no—
427Dic3⋊C4—34no—
428Dic3⋊C4—34no—
429Dic3⋊C4—34no—
430Dic3⋊C4—68no—
431Dic3⋊C4C22×D318yes—
432C4×Dic3—32no—
433C4×Dic3—32no—
434C4×Dic3—38no—
435C4×Dic3—38no—
436C4×Dic3—62no—
437C4×Dic3C22×D312yes—
438C22×C32—22no—
439C22×C32C22×D412yes—
440C22×C32C2511yescharacteristic
441C2×C3⋊D3—22no—
442C2×C3⋊D3—24no—
443C2×C3×D3—28no—
444C2×C3×D3—22no—
445C2×C3×D3—22no—
446C2×C3×D3—22no—
447C2×C3×D3—24no—
448C2×C3×D32−1+414yescomplemented
449C32×C4—24no—
450C32×C4C22×D412yes—
451C32×C4C22×D412yes—
452C3⋊Dic3—22no—
453C3⋊Dic3—24no—
454C3×Dic3—22no—
455C3×Dic3—22no—
456C3×Dic3—24no—
457C3×Dic3C22×D418yes—
4582−1+4—188no—
459C2×#41—31no—
460C2×#41—94no—
461C2×#41—92no—
462C2×#41—92no—
463C2×#41—91no—
464C22×Q8—34no—
465C22×Q8—34no—
466C22×Q8—31no—
467C22×Q8—32no—
468C22×Q8—68no—
469C22×Q8—92no—
470C22×Q8—92no—
471C22×Q8D3211yescharacteristic
472C23×C4—32no—
473C23×C4—31no—
474C4⋊Q8—32no—
475C4⋊Q8—98no—
476C4⋊Q8—92no—
477#124—32no—
478#124—98no—
479#124—92no—
480#123—34no—
481#123—92no—
482#123—92no—
483#123—94no—
484C22⋊Q8—34no—
485C22⋊Q8—98no—
486C22⋊Q8—98no—
487C22⋊Q8—92no—
488C22⋊Q8—98no—
489C22⋊Q8—92no—
490C22⋊Q8—94no—
491#121—98no—
492#121—92no—
493#121—92no—
494#120—92no—
495#120—92no—
496C4×Q8—94no—
497C4×Q8—94no—
498C4×D4—94no—
499C4×D4—98no—
500C4×D4—98no—
501C4×D4—94no—
502#117—31no—
503#117—94no—
504#117—91no—
505C23×C3—21no—
506C23×C3—32no—
507C23×C3—32no—
508C23×C3—64no—
509C23×C3—62no—
510C23×C3C23×D311yescharacteristic
511C23×C3C23×D311yescharacteristic
512C22×D3—22no—
513C22×D3—24no—
514C22×D3—32no—
515C22×D3—32no—
516C22×D3—62no—
517C22×D3C23×D312yes—
518C22×D3C23×D312yes—
519C3×Q8—24no—
520C3×Q8—24no—
521C3×Q8—24no—
522C3×Q8—24no—
523C3×Q8—38no—
524C3×Q8—38no—
525C3×Q8—44no—
526C3×Q8—44no—
527C3×Q8—616no—
528C3×Q8—62no—
529C3×D4—64no—
530C3×D4—62no—
531C2×C3×C4—24no—
532C2×C3×C4—24no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—24no—
536C2×C3×C4—24no—
537C2×C3×C4—38no—
538C2×C3×C4—34no—
539C2×C3×C4—34no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—44no—
543C2×C3×C4—616no—
544C2×C3×C4—62no—
545C2×C3×C4—64no—
546C2×C3×C4—64no—
547C2×C3×C4—64no—
548C2×C3×C4D3×D414yes—
549C2×C3×C4C2×#6714yes—
550C2×C3×C4C23×D314yes—
551C2×C3×C4C23×D314yes—
552C2×C3×C4C23×D311yescharacteristic
553C2×C3×C4C23×D311yescharacteristic
554C2×C3×C4C23×D311yescharacteristic
555C2×C3×C4C23×D311yescharacteristic
556#67—24no—
557#67—68no—
558#67—68no—
559#67—64no—
560#67—64no—
561#67—68no—
562#67—68no—
563#67—124no—
564C2×Dic3—22no—
565C2×Dic3—34no—
566C2×Dic3—34no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—64no—
570C2×Dic3—62no—
571C2×Dic3—68no—
572C2×Dic3C2×#6718yes—
573C2×Dic3C23×D314yes—
574C2×Dic3C23×D312yes—
575C2×Dic3C23×D312yes—
576C2×Dic3C23×D314yes—
577D12—22no—
578D12—68no—
579D12—68no—
580D12—62no—
581D12—62no—
582D12—122no—
583C4×D3—24no—
584C4×D3—24no—
585C4×D3—24no—
586C4×D3—216no—
587C4×D3—68no—
588C4×D3—68no—
589C4×D3—64no—
590C4×D3—64no—
591C4×D3—68no—
592C4×D3—124no—
593Dic6—22no—
594Dic6—216no—
595Dic6—68no—
596Dic6—62no—
597Dic6—62no—
598Dic6—68no—
599Dic6—122no—
600Dic6C2×#6718yes—
601Dic6C2×#6718yes—
602C2×C32—22no—
603C2×C32C23×D411yescharacteristic
604C2×C32C2×2−1+412yes—
605C3⋊D3—42no—
606C3×D3—24no—
607C3×D3—42no—
608C24—31no—
609#41—64no—
610#41—1816no—
611#41—188no—
612#41—188no—
613#41—184no—
614C2×Q8—24no—
615C2×Q8—32no—
616C2×Q8—32no—
617C2×Q8—38no—
618C2×Q8—31no—
619C2×Q8—38no—
620C2×Q8—68no—
621C2×Q8—616no—
622C2×Q8—616no—
623C2×Q8—94no—
624C2×Q8—91no—
625C2×Q8—188no—
626C2×Q8—188no—
627C2×Q8C2×D3212yes—
628C2×Q8C2×D3212yes—
629C2×D4—32no—
630C2×D4—31no—
631C2×D4—94no—
632C2×D4—94no—
633C2×D4—94no—
634C2×D4—92no—
635C2×D4—91no—
636C22×C4—32no—
637C22×C4—31no—
638C22×C4—38no—
639C22×C4—32no—
640C22×C4—32no—
641C22×C4—32no—
642C22×C4—68no—
643C22×C4—64no—
644C22×C4—94no—
645C22×C4—94no—
646C22×C4—92no—
647C22×C4C2×D3212yes—
648C22×C4C2×D3211yescharacteristic
649C4⋊C4—32no—
650C4⋊C4—38no—
651C4⋊C4—98no—
652C4⋊C4—94no—
653C4⋊C4—94no—
654C4⋊C4—92no—
655C4⋊C4—98no—
656C22⋊C4—32no—
657C22⋊C4—38no—
658C22⋊C4—94no—
659C22⋊C4—94no—
660C22⋊C4—94no—
661C22⋊C4—94no—
662C22⋊C4—92no—
663C22⋊C4—98no—
664C42—32no—
665C42—98no—
666C42—92no—
667C22×C3—22no—
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—21no—
671C22×C3—34no—
672C22×C3—42no—
673C22×C3—68no—
674C22×C3—62no—
675C22×C3—62no—
676C22×C3—64no—
677C22×C3—62no—
678C22×C3C2×D3×D412yes—
679C22×C3C22×#6712yes—
680C22×C3C24×D311yescharacteristic
681C22×C3C24×D311yescharacteristic
682C2×D3—28no—
683C2×D3—22no—
684C2×D3—22no—
685C2×D3—22no—
686C2×D3—24no—
687C2×D3—62no—
688C2×D3—64no—
689C2×D3—64no—
690C2×D3—62no—
691C2×D3—122no—
692C2×D3—124no—
693C2×D3#100714yescomplemented
694C3×C4—24no—
695C3×C4—24no—
696C3×C4—22no—
697C3×C4—22no—
698C3×C4—38no—
699C3×C4—44no—
700C3×C4—62no—
701C3×C4—64no—
702C3×C4—62no—
703C3×C4C2×D3×D412yes—
704C3×C4C2×D3×D412yes—
705C3×C4C22×#6712yes—
706C3×C4C22×#6712yes—
707Dic3—22no—
708Dic3—24no—
709Dic3—22no—
710Dic3—62no—
711Dic3—64no—
712Dic3—64no—
713Dic3—62no—
714Dic3—122no—
715Dic3—124no—
716Dic3C22×#6718yes—
717C32#348611yescharacteristic, complemented, Sylow
718C23—32no—
719C23—32no—
720C23—64no—
721C23—62no—
722C23—92no—
723C23C22×D3211yescharacteristic
724Q8—24no—
725Q8—24no—
726Q8—38no—
727Q8—38no—
728Q8—616no—
729Q8—62no—
730Q8—188no—
731Q8—182no—
732D4—64no—
733D4—62no—
734D4—188no—
735D4—188no—
736D4—188no—
737D4—184no—
738D4—182no—
739C2×C4—24no—
740C2×C4—38no—
741C2×C4—34no—
742C2×C4—34no—
743C2×C4—32no—
744C2×C4—32no—
745C2×C4—616no—
746C2×C4—62no—
747C2×C4—64no—
748C2×C4—64no—
749C2×C4—64no—
750C2×C4—94no—
751C2×C4—92no—
752C2×C4—188no—
753C2×C4—188no—
754C2×C4—184no—
755C2×C4D3×#6714yes—
756C2×C4C22×D3214yes—
757C2×C4C22×D3211yescharacteristic
758C2×C4C22×D3211yescharacteristic
759C2×C3—22no—
760C2×C3—22no—
761C2×C3—22no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—64no—
765C2×C3—122no—
766C2×C3C22×D3×D411yescharacteristic
767C2×C3C2×#100712yes—
768C2×C3D3×2−1+412yes—
769C2×C3C23×#6711yescharacteristic
770D3—24no—
771D3—42no—
772D3—122no—
773D3—122no—
774D3—242no—
775C22—22no—
776C22—34no—
777C22—68no—
778C22—62no—
779C22—62no—
780C22—64no—
781C22—62no—
782C22—184no—
783C22—182no—
784C22C2×D3×#6712yes—
785C22C23×D3211yescharacteristic
786C4—24no—
787C4—38no—
788C4—64no—
789C4—62no—
790C4—62no—
791C4—184no—
792C4—182no—
793C4C2×D3×#6712yes—
794C4C2×D3×#6712yes—
795C3—21no—
796C3#8635511yescharacteristic, complemented
797C3#8725111yescharacteristic, complemented
798C2—22no—
799C2—64no—
800C2—122no—
801C2—362no—
802C2D3×#100712yes—
803C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3486
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×Q8C2semidirect
2. C2×#64297C2semidirect
3. #10596287C2semidirect
4. C3×#5816C2semidirect
5. #10595403C2semidirect
6. #10595402C2semidirect
7. #10595401C2semidirect
8. #10595400C2semidirect
9. #10595023C2semidirect
10. #10595022C2semidirect
11. #10594897C2semidirect
12. #10594896C2semidirect
13. #10594818C2semidirect
27. C2×#3799C22semidirect
28. C2×#3797C22semidirect
30. C2×#3796C22semidirect
31. C2×D3×Dic6C22semidirect
32. #64156C22semidirect
33. #64155C22semidirect
34. #64153C22semidirect
37. C3×#947C22semidirect
38. C3×#946C22semidirect
39. C3×#944C22semidirect
49. #63907C22semidirect
54. #63888C22semidirect
55. #63887C22semidirect
60. #63843C22semidirect
61. Dic3×Dic6C22semidirect
62. #63839C22semidirect
66. C22×D3×Q8D3semidirect
75. #5816D3semidirect
115. C2×C3×Dic6D4semidirect
195. #947C2×D3semidirect
202. #946C2×D3semidirect
209. #944C2×D3semidirect
392. C2×Dic6#67semidirect
448. C2×C3×D32−1+4semidirect
693. C2×D3#1007semidirect
717. C32#3486semidirect
796. C3#86355semidirect
797. C3#87251semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C2×#642972
#105962872
C3×#58162
#105954032
#105954022
#105954012
#105954002
#105950232
#105950222
#105948972
#105948962
#105948182
#872513
#863553