Finite Group Databasebeta

← #11664337

Subgroups — #11664337

Order 768.

2046 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86225C211yesmaximal, characteristic, complemented
2C4×#1010C211yesmaximal, characteristic, complemented
3C3×#3035C211yesmaximal, characteristic, complemented
4#83913C212yesmaximal, complemented
5#83898C212yesmaximal, complemented
6#83314C211yesmaximal, characteristic, complemented
7#82508C211yesmaximal, characteristic, complemented
8#80573C214yesmaximal, complemented
9#80510C214yesmaximal, complemented
10#80456C212yesmaximal, complemented
11#80411C212yesmaximal, complemented
12#80362C212yesmaximal, complemented
13#80313C212yesmaximal, complemented
14C2×#4850C211yesmaximal, characteristic, complemented
15#79000C211yesmaximal, characteristic, complemented
16#78843C212yesmaximal, complemented
17#78821C212yesmaximal, complemented
18#60600—31nomaximal, Sylow
19C2×#1010C2211yescharacteristic
20C2×C3×#135C2212yes—
21C3×#532C2211yescharacteristic
22C3×C4×#41C2211yescharacteristic
23#5833C2212yes—
24#5827C2211yescharacteristic
25#5827C2212yes—
26C2×#951C2212yes—
27#5728C2212yes—
28#5716C2212yes—
29#5682C2214yes—
30#5618—22no—
31#5598—22no—
32#5572C2212yes—
33C4×D3×Q8C2212yes—
34#5563—21no—
35#5555—21no—
36#5546—22no—
37#5546C2212yes—
38#5543—21no—
39#5542—21no—
40C4×#237—22no—
41C4×#237C2212yes—
42#5523—21no—
43#5523C2211yescharacteristic
44#5516—21no—
45#5516C2211yescharacteristic
46C4×#235—21no—
47C4×#235C2211yescharacteristic
48C2×#869C2211yescharacteristic
49C2×C4×Dic6—21no—
50C2×C4×Dic6C2211yescharacteristic
51C3×#464C2212yes—
52C3×#463C2212yes—
53C3×#462C2211yescharacteristic
54C3×#461C2211yescharacteristic
55C3×#460C2211yescharacteristic
56C3×#459C2211yescharacteristic
57C2×C3×C4⋊C8C2211yescharacteristic
58C3×#416C2212yes—
59#5232C2212yes—
60#5232C2212yes—
61#5186C2214yes—
62Dic3×Q16C2214yes—
63#5173C2214yes—
64#5170C2214yes—
65#5164C2214yes—
66#5164C2214yes—
67#5158C2214yes—
68Dic3×D8C2214yes—
69#5110C2212yes—
70C2×#818C2212yes—
71C2×#816C2212yes—
72#5101C2212yes—
73#5090C2212yes—
74#5075C2212yes—
75#5054C2214yes—
76#5021C2212yes—
77#5020C2212yes—
78#5008C2212yes—
79#5007C2212yes—
80#4995C2212yes—
81#4924C2211yescharacteristic
82#4850C2212yes—
83#4850C2212yes—
84#4850C2214yes—
85#4840C2214yes—
86#4835C2212yes—
87#4833C2212yes—
88#4814C2214yes—
89#4811C2214yes—
90#4790C2214yes—
91#4789C2214yes—
92#4784C2214yes—
93#4774C2214yes—
94#4758C2214yes—
95#4757C2214yes—
96#3511—31no—
97C4×2−1+4—31no—
98#3124—34no—
99#3121—34no—
100#3116—32no—
101#3112—32no—
102#3106—32no—
103#3104—32no—
104#3098—32no—
105#3079—31no—
106C2×#477—31no—
107#3037—31no—
108#3035D311yescharacteristic, complemented
109#3013—32no—
110#2951—32no—
111#2947—32no—
112#2925—31no—
113C2×C3×#41C2312yes—
114C2×C3×#41C2311yescharacteristic
115#1010—24no—
116#1010—24no—
117C2×D3×Q8C2312yes—
118C2×#237—22no—
119C2×#237—22no—
120C2×#237C2312yes—
121C2×#235—21no—
122C2×#235C2311yescharacteristic
123C22×Dic6—21no—
124C22×Dic6—21no—
125C22×Dic6C2311yescharacteristic
126C3×#135—28no—
127C2×C3×Q16C2312yes—
128C2×C3×SD16C2312yes—
129C2×C3×SD16C2312yes—
130C2×C3×D8C2312yes—
131C22×C3×C8C2312yes—
132C3×C4⋊Q8C2311yescharacteristic
133C3×#127C2311yescharacteristic
134C3×#124C2312yes—
135C3×#121—21no—
136C3×#121—21no—
137C3×C4×Q8C2311yescharacteristic
138C3×C4×Q8C2311yescharacteristic
139C3×C4×D4—21no—
140C3×C4×D4—21no—
141C3×C4×D4—21no—
142C3×C4×D4—21no—
143C3×C4×D4C2311yescharacteristic
144C3×C4×D4C2311yescharacteristic
145C3×#117—21no—
146C3×#117C2311yescharacteristic
147C2×C3×C42—21no—
148C2×C3×C42C2311yescharacteristic
149#951—28no—
150#946C2314yes—
151Q8×Dic3C2312yes—
152Q8×Dic3C2314yes—
153C2×#216C2314yes—
154#939—24no—
155#938—22no—
156#938C2314yes—
157#936—22no—
158D4×Dic3—22no—
159D4×Dic3—24no—
160D4×Dic3—22no—
161D4×Dic3C2312yes—
162D4×Dic3C2314yes—
163C2×#214C2314yes—
164#930—22no—
165C4×#67—22no—
166C4×#67—22no—
167C4×#67D412yes—
168C4×#67D412yes—
169#926—21no—
170#926—22no—
171#926C2311yescharacteristic
172C2×C4⋊Dic3—21no—
173C2×C4⋊Dic3—21no—
174C2×C4⋊Dic3—22no—
175C2×C4⋊Dic3C2311yescharacteristic
176C2×C4⋊Dic3C2312yes—
177#924—22no—
178C2×Dic3⋊C4—21no—
179C2×Dic3⋊C4—22no—
180C2×C4×Dic3—21no—
181C2×C4×Dic3—22no—
182C2×#208C2312yes—
183#897—22no—
184#892—22no—
185#892—22no—
186#892C2312yes—
187D3×C4⋊C4—22no—
188D3×C4⋊C4C2312yes—
189#890—22no—
190#887—22no—
191#887—22no—
192#887—22no—
193#887C2312yes—
194#887C2312yes—
195#886—24no—
196#885—24no—
197#67⋊C4—22no—
198#67⋊C4—22no—
199#67⋊C4—22no—
200#879—24no—
201#878—24no—
202#877—22no—
203#877—22no—
204#877—22no—
205C4×D12—21no—
206C4×D12D411yescharacteristic
207C4×D12D411yescharacteristic
208#872—22no—
209#872C2312yes—
210C42×D3—22no—
211C42×D3C2312yes—
212#869—21no—
213#869—21no—
214#869C2312yes—
215#869C2312yes—
216C4×Dic6—21no—
217C4×Dic6—21no—
218C4×Dic6—21no—
219C4×Dic6—21no—
220C4×Dic6—21no—
221C4×Dic6—22no—
222C4×Dic6—22no—
223C4×Dic6D411yescharacteristic
224C4×Dic6D411yescharacteristic
225C4×Dic6C2312yes—
226C4×Dic6C2312yes—
227C3×C4⋊C8C2311yescharacteristic
228C3×C4⋊C8C2311yescharacteristic
229C3×C4⋊C8C2312yes—
230C3×#103C2312yes—
231C3×#103C2312yes—
232C3×#102C2312yes—
233C3×#102C2312yes—
234#835C2314yes—
235#835C2314yes—
236#832C2314yes—
237#832C2314yes—
238(C2×D3)⋊C8C2314yes—
239(C2×D3)⋊C8C2314yes—
240#818C2314yes—
241#818C2314yes—
242#816C2314yes—
243#816C2314yes—
244#815C2314yes—
245C8×Dic3C2314yes—
246#808C2314yes—
247#807C2314yes—
248C4⋊(C3⋊C8)C2312yes—
249C4⋊(C3⋊C8)C2312yes—
250C2×2−1+4—31no—
251C2×#137—32no—
252C2×#135C2×D312yes—
253#556—61no—
254#555—61no—
255#554—61no—
256#553—62no—
257#548—62no—
258#547—61no—
259#542—34no—
260#537—32no—
261#533—32no—
262#532—32no—
263#532C2×D311yescharacteristic
264C2×C4⋊Q8—31no—
265#520—31no—
266#520—31no—
267#520—32no—
268#520—32no—
269#520—61no—
270#520—62no—
271#519—32no—
272#519—31no—
273#519—61no—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—61no—
277C4×#41—62no—
278C4×#41C2×D311yescharacteristic
279C2×C4×Q8—32no—
280C2×C4×Q8—31no—
281C2×C4×Q8—61no—
282#485—34no—
283#484—34no—
284#482—34no—
285#480—34no—
286#477—32no—
287#477—32no—
288#477—32no—
289#477—34no—
290#476—32no—
291#475—32no—
292#474—32no—
293#464—34no—
294#464C2×D312yes—
295#463C2×D312yes—
296#462—32no—
297#462C2×D311yescharacteristic
298#461C2×D311yescharacteristic
299#460—32no—
300#460C2×D311yescharacteristic
301#459C2×D311yescharacteristic
302#452—34no—
303#451—34no—
304#449—34no—
305#448—34no—
306#441—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×Q16—34no—
312C4×SD16—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318C2×#107—32no—
319#423—31no—
320C2×C4⋊C8C2×D311yescharacteristic
321#417—32no—
322#417—32no—
323#416C2×D312yes—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C3×#41—22no—
328C3×#41—24no—
329C3×#41—24no—
330C3×#41#4114yescomplemented
331C2×C3×Q8C2412yes—
332C2×C3×Q8C2411yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—22no—
335C2×C3×D4—21no—
336C2×C3×D4—21no—
337C2×C3×D4C2412yes—
338C2×C3×D4C2411yescharacteristic
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4—22no—
342C22×C3×C4—21no—
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2411yescharacteristic
346C2×#67—22no—
347C2×#67—24no—
348C2×#67C2×D412yes—
349C22×Dic3—21no—
350C22×Dic3—22no—
351C22×Dic3—21no—
352C22×Dic3—22no—
353C22×Dic3—24no—
354C22×Dic3—22no—
355D3×Q8—24no—
356D3×Q8—24no—
357#237—216no—
358#237—24no—
359#237—24no—
360#237—84no—
361#235—28no—
362#235—22no—
363#235—22no—
364C2×D12C2×D411yescharacteristic
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3C2×D412yes—
368C2×C4×D3C2×D412yes—
369C2×C4×D3C2412yes—
370C2×Dic6—28no—
371C2×Dic6—21no—
372C2×Dic6—22no—
373C2×Dic6—22no—
374C2×Dic6—22no—
375C2×Dic6—22no—
376C2×Dic6—82no—
377C2×Dic6C2×D411yescharacteristic
378C2×Dic6#4114yescomplemented
379C2×Dic6C2412yes—
380C3×Q16—24no—
381C3×SD16—24no—
382C3×SD16—24no—
383C3×D8—24no—
384C2×C3×C8—24no—
385C2×C3×C8C2412yes—
386C2×C3×C8C2412yes—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4C2411yescharacteristic
392C3×C4⋊C4C2411yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—21no—
395C3×C22⋊C4—21no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—22no—
398C3×C42—21no—
399C3×C42—21no—
400C3×C42—21no—
401C3×C42C2×D411yescharacteristic
402C3×C42C2×D411yescharacteristic
403C3×C42C2411yescharacteristic
404C3×C42C2411yescharacteristic
405#217—22no—
406#217—24no—
407#217—24no—
408#217C2×D412yes—
409#216—28no—
410#214—28no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—24no—
413(C2×D3)⋊C4C2×D412yes—
414(C2×D3)⋊C4C2×D412yes—
415C4⋊Dic3—21no—
416C4⋊Dic3—22no—
417C4⋊Dic3—22no—
418C4⋊Dic3—22no—
419C4⋊Dic3—22no—
420C4⋊Dic3—24no—
421C4⋊Dic3C2×D411yescharacteristic
422C4⋊Dic3C2×D411yescharacteristic
423C4⋊Dic3C2414yes—
424C4⋊Dic3C2412yes—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—22no—
430Dic3⋊C4—24no—
431Dic3⋊C4C2×D412yes—
432Dic3⋊C4C2×D412yes—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—22no—
437C4×Dic3—22no—
438C4×Dic3—22no—
439C4×Dic3—24no—
440C4×Dic3C2×D412yes—
441C4×Dic3C2×D412yes—
442C4×Dic3C2412yes—
443#208—24no—
444C2×C3⋊C8C2414yes—
4452−1+4—64no—
4462−1+4—64no—
447C2×#41—31no—
448C2×#41—32no—
449C2×#41—61no—
450C2×#41—62no—
451C2×#41—62no—
452C2×#41C22×D312yes—
453C2×#41C22×D311yescharacteristic
454C22×Q8—32no—
455C22×Q8—31no—
456C22×Q8—61no—
457C22×Q8—61no—
458#137—68no—
459#135—28no—
460C2×Q16—34no—
461C2×Q16C22×D312yes—
462C2×SD16—34no—
463C2×SD16C22×D312yes—
464C2×SD16C22×D312yes—
465C2×D8C22×D312yes—
466C2×M16—32no—
467C22×C8C22×D312yes—
468C4⋊Q8—32no—
469C4⋊Q8—32no—
470C4⋊Q8—61no—
471C4⋊Q8—61no—
472C4⋊Q8C22×D311yescharacteristic
473#127C22×D311yescharacteristic
474#126—64no—
475#125—62no—
476#124—62no—
477#124—64no—
478#124C22×D312yes—
479#123—64no—
480C22⋊Q8—34no—
481C22⋊Q8—64no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484#121—21no—
485#121—21no—
486#121—34no—
487#121—62no—
488#121—62no—
489#121—64no—
490C4×Q8—31no—
491C4×Q8—31no—
492C4×Q8—32no—
493C4×Q8—34no—
494C4×Q8—32no—
495C4×Q8—32no—
496C4×Q8—32no—
497C4×Q8—32no—
498C4×Q8—62no—
499C4×Q8—61no—
500C4×Q8—62no—
501C4×Q8—61no—
502C4×Q8—61no—
503C4×Q8—62no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—61no—
507C4×Q8—61no—
508C4×Q8C22×D311yescharacteristic
509C4×Q8C22×D311yescharacteristic
510C4×D4—21no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—32no—
515C4×D4—32no—
516C4×D4—32no—
517C4×D4—34no—
518C4×D4—31no—
519C4×D4—31no—
520C4×D4—61no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4—64no—
528C4×D4—62no—
529C4×D4C22×D311yescharacteristic
530C4×D4C22×D311yescharacteristic
531#117—21no—
532#117—31no—
533#117—32no—
534#117—32no—
535#117—62no—
536#117—62no—
537#117—62no—
538#117—62no—
539#117—62no—
540#117—62no—
541#117—61no—
542#117—62no—
543#117C22×D311yescharacteristic
544C2×C4⋊C4—31no—
545C2×C4⋊C4—32no—
546C2×C4⋊C4—32no—
547C2×C4⋊C4—62no—
548C2×C4⋊C4—62no—
549C2×C4⋊C4—61no—
550C2×C4⋊C4—62no—
551C2×C4⋊C4—61no—
552C2×C4⋊C4—61no—
553C2×C42—21no—
554C2×C42—32no—
555C2×C42—62no—
556C2×C42—62no—
557C2×C42—61no—
558C2×C42C22×D311yescharacteristic
559#107—34no—
560#107—34no—
561#107—34no—
562#106—34no—
563C4⋊C8—32no—
564C4⋊C8—32no—
565C4⋊C8C22×D311yescharacteristic
566C4⋊C8C22×D311yescharacteristic
567C4⋊C8C22×D312yes—
568#103—34no—
569#103—34no—
570#103—34no—
571#103—34no—
572#103C22×D312yes—
573#103C22×D312yes—
574#102—34no—
575#102—34no—
576#102C22×D312yes—
577#102C22×D312yes—
578C22⋊C8—34no—
579C22⋊C8—34no—
580#97—34no—
581C4×C8—34no—
582C23×C3—21no—
583C23×C3—22no—
584C23×C3C22×D411yescharacteristic
585C22×D3C22×D412yes—
586C3×Q8—21no—
587C3×Q8—22no—
588C3×Q8—22no—
589C3×Q8C2×#4112yes—
590C3×D4—24no—
591C3×D4—21no—
592C3×D4—22no—
593C3×D4—22no—
594C3×D4—42no—
595C3×D4—44no—
596C3×D4—42no—
597C3×D4C2×#4112yes—
598C2×C3×C4—21no—
599C2×C3×C4—24no—
600C2×C3×C4—22no—
601C2×C3×C4—21no—
602C2×C3×C4—21no—
603C2×C3×C4—22no—
604C2×C3×C4—41no—
605C2×C3×C4—44no—
606C2×C3×C4—42no—
607C2×C3×C4—81no—
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C2×#4112yes—
614C2×C3×C4C2×#4112yes—
615C2×C3×C4C2511yescharacteristic
616#67—28no—
617#67—24no—
618#67—84no—
619C2×Dic3—28no—
620C2×Dic3—24no—
621C2×Dic3—22no—
622C2×Dic3—22no—
623C2×Dic3—24no—
624C2×Dic3—84no—
625C2×Dic3—82no—
626C2×Dic3—82no—
627C2×Dic3—81no—
628C2×Dic3C22×D412yes—
629C2×Dic3C22×D412yes—
630C2×Dic3C22×D412yes—
631D12—22no—
632C4×D3—28no—
633C4×D3—24no—
634C4×D3—22no—
635C4×D3—22no—
636C4×D3—42no—
637C4×D3—82no—
638Dic6—28no—
639Dic6—22no—
640Dic6—24no—
641Dic6—22no—
642Dic6—44no—
643Dic6—82no—
644Dic6C2×#4114yes—
645C3×C8—22no—
646C3×C8—22no—
647C3⋊C8—24no—
648#41—22no—
649#41—24no—
650#41—24no—
651#41—68no—
652#41—64no—
653#41—616no—
654#41—64no—
655#41—62no—
656#41—62no—
657#41—244no—
658#41#23714yescomplemented
659C2×Q8—31no—
660C2×Q8—34no—
661C2×Q8—32no—
662C2×Q8—62no—
663C2×Q8—68no—
664C2×Q8—64no—
665C2×Q8—64no—
666C2×Q8—61no—
667C2×Q8—62no—
668C2×Q8—62no—
669C2×Q8—62no—
670C2×Q8—242no—
671C2×Q8C23×D312yes—
672C2×Q8C23×D311yescharacteristic
673C2×D4—21no—
674C2×D4—22no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—32no—
678C2×D4—31no—
679C2×D4—62no—
680C2×D4—64no—
681C2×D4C23×D312yes—
682C2×D4C23×D311yescharacteristic
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—21no—
687C22×C4—32no—
688C22×C4—32no—
689C22×C4—32no—
690C22×C4—62no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—62no—
694C22×C4—64no—
695C22×C4—61no—
696C22×C4—61no—
697C22×C4—62no—
698C22×C4D3×D411yescharacteristic
699C22×C4D3×D411yescharacteristic
700C22×C4C23×D311yescharacteristic
701Q16—24no—
702Q16—68no—
703SD16—24no—
704SD16—24no—
705SD16—68no—
706D8—24no—
707M16—64no—
708C2×C8—24no—
709C2×C8—34no—
710C2×C8C23×D312yes—
711C2×C8C23×D312yes—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—31no—
717C4⋊C4—32no—
718C4⋊C4—31no—
719C4⋊C4—32no—
720C4⋊C4—32no—
721C4⋊C4—34no—
722C4⋊C4—62no—
723C4⋊C4—62no—
724C4⋊C4—62no—
725C4⋊C4—64no—
726C4⋊C4—62no—
727C4⋊C4—64no—
728C4⋊C4—61no—
729C4⋊C4—62no—
730C4⋊C4—62no—
731C4⋊C4—62no—
732C4⋊C4—62no—
733C4⋊C4—62no—
734C4⋊C4C23×D311yescharacteristic
735C4⋊C4C23×D311yescharacteristic
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—32no—
742C22⋊C4—32no—
743C22⋊C4—32no—
744C22⋊C4—62no—
745C22⋊C4—64no—
746C22⋊C4—62no—
747C22⋊C4—64no—
748C22⋊C4—64no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—32no—
753C42—32no—
754C42—32no—
755C42—62no—
756C42—62no—
757C42—62no—
758C42—62no—
759C42—64no—
760C42—62no—
761C42—62no—
762C42D3×D411yescharacteristic
763C42D3×D411yescharacteristic
764C42C23×D311yescharacteristic
765C42C23×D311yescharacteristic
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—22no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3#52512yes—
775C22×C3C23×D411yescharacteristic
776C2×D3—22no—
777C2×D3—22no—
778C2×D3—22no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—21no—
783C3×C4—41no—
784C3×C4—42no—
785C3×C4—41no—
786C3×C4#52512yes—
787C3×C4#57812yes—
788C3×C4C22×#4111yescharacteristic
789C3×C4C22×#4111yescharacteristic
790Dic3—22no—
791Dic3—22no—
792Dic3—24no—
793Dic3—22no—
794Dic3—44no—
795Dic3—42no—
796C23—21no—
797C23—22no—
798C23—32no—
799C23C2×D3×D411yescharacteristic
800Q8—21no—
801Q8—22no—
802Q8—22no—
803Q8—34no—
804Q8—68no—
805Q8—62no—
806Q8—62no—
807Q8—64no—
808Q8—124no—
809Q8—242no—
810Q8C2×#23712yes—
811D4—24no—
812D4—22no—
813D4—21no—
814D4—22no—
815D4—42no—
816D4—44no—
817D4—42no—
818D4—68no—
819D4—64no—
820D4—62no—
821D4—244no—
822D4C2×#23712yes—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—44no—
835C2×C4—68no—
836C2×C4—68no—
837C2×C4—62no—
838C2×C4—64no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—64no—
842C2×C4—62no—
843C2×C4—64no—
844C2×C4—81no—
845C2×C4—122no—
846C2×C4—242no—
847C2×C4—244no—
848C2×C4—242no—
849C2×C4—242no—
850C2×C4—241no—
851C2×C4C2×D3×D411yescharacteristic
852C2×C4C2×D3×D411yescharacteristic
853C2×C4C2×D3×D411yescharacteristic
854C2×C4C2×D3×D411yescharacteristic
855C2×C4C2×D3×D411yescharacteristic
856C2×C4C2×#23712yes—
857C2×C4D3×#4112yes—
858C2×C4C24×D311yescharacteristic
859C8—22no—
860C8—22no—
861C8—64no—
862C2×C3—22no—
863C2×C3—42no—
864C2×C3—82no—
865C2×C3C2×#52511yescharacteristic
866C2×C3C2×#57811yescharacteristic
867C2×C3#358511yescharacteristic
868D3—42no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—41no—
873C22—41no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—62no—
878C22—62no—
879C22—62no—
880C22#560612yes—
881C22C22×D3×D411yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—22no—
886C4—41no—
887C4—41no—
888C4—42no—
889C4—62no—
890C4—62no—
891C4—62no—
892C4—64no—
893C4—122no—
894C4—124no—
895C4#560612yes—
896C4#577112yes—
897C4C22×#23711yescharacteristic
898C4C2×D3×#4111yescharacteristic
899C3#6060011yescharacteristic, complemented, Sylow
900C2—22no—
901C2—42no—
902C2—82no—
903C2—122no—
904C2C2×#560611yescharacteristic
905C2C2×#577111yescharacteristic
906C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3035C2
socleC22×C3C23×D4
hypercenter#3035D3
hypocenterC3#60600
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #86225C2semidirect
2. C4×#1010C2semidirect
3. C3×#3035C2semidirect
4. #83913C2semidirect
5. #83898C2semidirect
6. #83314C2semidirect
7. #82508C2semidirect
8. #80573C2semidirect
9. #80510C2semidirect
10. #80456C2semidirect
11. #80411C2semidirect
12. #80362C2semidirect
13. #80313C2semidirect
14. C2×#4850C2semidirect
15. #79000C2semidirect
16. #78843C2semidirect
17. #78821C2semidirect
108. #3035D3semidirect
330. C3×#41#41semidirect
378. C2×Dic6#41semidirect
658. #41#237semidirect
899. C3#60600semidirect

Maximal subgroups

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

subgroupindex
#862252
C4×#10102
C3×#30352
#839132
#838982
#833142
#825082
#805732
#805102
#804562
#804112
#803622
#803132
C2×#48502
#790002
#788432
#788212
#606003