Finite Group Databasebeta

← #11664315

Subgroups — #11664315

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
1C3×#3511C211yesmaximal, characteristic, complemented
2C4×#1010C211yesmaximal, characteristic, complemented
3#83467C214yesmaximal, complemented
4#83462C214yesmaximal, complemented
5#83427C212yesmaximal, complemented
6#83419C212yesmaximal, complemented
7#83369C212yesmaximal, complemented
8#83352C212yesmaximal, complemented
9#83315C212yesmaximal, complemented
10#83314C211yesmaximal, characteristic, complemented
11#83301C212yesmaximal, complemented
12#83296C211yesmaximal, characteristic, complemented
13C2×#5094C211yesmaximal, characteristic, complemented
14#83212C211yesmaximal, characteristic, complemented
15#82571C212yesmaximal, complemented
16#82558C212yesmaximal, complemented
17#82515C211yesmaximal, characteristic, complemented
18#60599—31nomaximal, Sylow
19C2×#1010C2211yescharacteristic
20C3×#556—21no—
21C3×#555—21no—
22C3×#554—21no—
23C3×#553—22no—
24C3×#548—22no—
25C3×#547—21no—
26C3×#542C2214yes—
27C3×#537C2212yes—
28C3×#533C2212yes—
29C3×#532C2211yescharacteristic
30C3×#532C2212yes—
31C2×C3×C4⋊Q8C2211yescharacteristic
32C3×#520C2212yes—
33C3×C4×#41C2211yescharacteristic
34#5827C2211yescharacteristic
35C2×#951C2212yes—
36C2×#950C2212yes—
37#5572—21no—
38C4×D3×Q8—21no—
39#5546—22no—
40#5546—21no—
41C4×#237—21no—
42C4×#237—22no—
43#5523C2212yes—
44#5523C2211yescharacteristic
45#5516C2212yes—
46#5516C2211yescharacteristic
47C4×#235C2211yescharacteristic
48C4×#235C2212yes—
49C2×C4×Dic6C2211yescharacteristic
50C2×C4×Dic6C2212yes—
51#5234C2212yes—
52#5233C2212yes—
53#5232C2212yes—
54#5094C2214yes—
55#5094C2212yes—
56#5094C2212yes—
57#5094C2212yes—
58#5091C2212yes—
59#5090C2211yescharacteristic
60#5090C2212yes—
61#5087C2212yes—
62#5084C2212yes—
63#5083C2211yescharacteristic
64#5075C2211yescharacteristic
65#5075C2212yes—
66#5072C2211yescharacteristic
67#5057C2212yes—
68#5054C2214yes—
69#5054C2212yes—
70#5050C2214yes—
71#5047C2214yes—
72#5045C2214yes—
73#5043C2214yes—
74#5040C2214yes—
75#5037C2214yes—
76#5035C2214yes—
77#5034C2214yes—
78#5030C2214yes—
79#5030C2214yes—
80C4×#216C2214yes—
81C4×#215C2214yes—
82#5018C2214yes—
83C4×#214C2214yes—
84C4×#214C2214yes—
85#5014C2214yes—
86#5000C2214yes—
87#4997C2212yes—
88C2×#810C2212yes—
89#4966C2212yes—
90#4964C2212yes—
91C2×#808C2212yes—
92#4926C2212yes—
93#4925C2212yes—
94#4924C2211yescharacteristic
95C2×C4⋊(C3⋊C8)C2211yescharacteristic
96#3511D311yescharacteristic, complemented
97C4×2−1+4—31no—
98#3125—34no—
99#3121—34no—
100#3115—32no—
101#3113—32no—
102#3107—32no—
103#3103—32no—
104#3099—32no—
105#3079—31no—
106C2×#475—31no—
107#3037—31no—
108#3035—31no—
109#3013—32no—
110#2952—32no—
111#2947—32no—
112#2925—31no—
113C2×C3×#41—22no—
114C2×C3×#41C2312yes—
115C2×C3×#41C2311yescharacteristic
116C22×C3×Q8—21no—
117#1010—24no—
118#1010—24no—
119C2×D3×Q8—21no—
120C2×#237—22no—
121C2×#237—21no—
122C2×#235C2312yes—
123C2×#235C2311yescharacteristic
124C22×Dic6C2312yes—
125C22×Dic6C2311yescharacteristic
126C3×C4⋊Q8—21no—
127C3×C4⋊Q8—21no—
128C3×C4⋊Q8C2311yescharacteristic
129C3×C4⋊Q8C2312yes—
130C3×C4⋊Q8C2312yes—
131C3×#127C2311yescharacteristic
132C3×#126—24no—
133C3×#125—22no—
134C3×#124—24no—
135C3×#124—22no—
136C3×#124C2312yes—
137C3×#123—24no—
138C3×C22⋊Q8—22no—
139C3×C22⋊Q8—22no—
140C3×C22⋊Q8—24no—
141C3×C22⋊Q8C2314yes—
142C3×#121—22no—
143C3×#121—24no—
144C3×#121—21no—
145C3×#121—21no—
146C3×#121—22no—
147C3×#121C2314yes—
148C3×C4×Q8—22no—
149C3×C4×Q8D411yescharacteristic
150C3×C4×Q8D411yescharacteristic
151C3×C4×Q8C2314yes—
152C3×C4×D4—24no—
153C3×C4×D4—21no—
154C3×C4×D4—22no—
155C3×C4×D4—21no—
156C3×C4×D4D411yescharacteristic
157C3×C4×D4D412yes—
158C3×C4×D4D412yes—
159C3×C4×D4D411yescharacteristic
160C3×C4×D4C2314yes—
161C3×#117—22no—
162C3×#117—22no—
163C3×#117C2311yescharacteristic
164C3×#117C2312yes—
165C2×C3×C4⋊C4—21no—
166C2×C3×C4⋊C4—22no—
167C2×C3×C4⋊C4C2312yes—
168C2×C3×C42C2311yescharacteristic
169C2×C3×C42C2312yes—
170#951—28no—
171#950—28no—
172Q8×Dic3—21no—
173C2×#216C2314yes—
174C2×#216C2312yes—
175C2×#215C2312yes—
176D4×Dic3—22no—
177D4×Dic3—21no—
178C2×#214C2312yes—
179C2×#214C2314yes—
180C2×#213C2312yes—
181C4×#67—21no—
182C4×#67—22no—
183C4×#67—21no—
184C4×#67—22no—
185#926C2311yescharacteristic
186#926C2312yes—
187C2×C4⋊Dic3C2311yescharacteristic
188C2×C4⋊Dic3C2312yes—
189C2×Dic3⋊C4—21no—
190C2×Dic3⋊C4—22no—
191C2×C4×Dic3—21no—
192C2×C4×Dic3—22no—
193C2×#208C2312yes—
194C22×C3⋊C8C2312yes—
195#892—21no—
196#892—22no—
197D3×C4⋊C4—21no—
198D3×C4⋊C4—22no—
199#887—21no—
200#887—22no—
201#887—21no—
202#887—22no—
203#67⋊C4—22no—
204#67⋊C4—22no—
205#67⋊C4—22no—
206#877—22no—
207#877—22no—
208#877—22no—
209C4×D12C2311yescharacteristic
210C4×D12C2312yes—
211C4×D12C2311yescharacteristic
212#872—22no—
213#872—21no—
214C42×D3—21no—
215C42×D3—22no—
216C4×Dic6—21no—
217C4×Dic6—22no—
218C4×Dic6—22no—
219C4×Dic6—21no—
220C4×Dic6C2312yes—
221C4×Dic6C2311yescharacteristic
222C4×Dic6C2312yes—
223C4×Dic6C2312yes—
224C4×Dic6C2312yes—
225C4×Dic6C2312yes—
226C4×Dic6C2311yescharacteristic
227#835C2314yes—
228#835C2312yes—
229#835C2312yes—
230#832C2314yes—
231#832C2312yes—
232#832C2312yes—
233#830C2314yes—
234#830C2314yes—
235#810C2314yes—
236#810C2314yes—
237#810C2314yes—
238#809C2314yes—
239#808C2314yes—
240#808C2314yes—
241#808C2314yes—
242#807C2314yes—
243C4⋊(C3⋊C8)C2311yescharacteristic
244C4⋊(C3⋊C8)C2311yescharacteristic
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248#803C2314yes—
249C4×C3⋊C8C2314yes—
250C2×2−1+4—31no—
251C2×#137—32no—
252C2×#135—32no—
253#556—21no—
254#555—21no—
255#554—21no—
256#553—22no—
257#548—22no—
258#547—21no—
259#542C2×D314yes—
260#537C2×D312yes—
261#533C2×D312yes—
262#532C2×D311yescharacteristic
263#532C2×D312yes—
264C2×C4⋊Q8C2×D311yescharacteristic
265#520—31no—
266#520—32no—
267#520—31no—
268#520—62no—
269#520—61no—
270#520C2×D312yes—
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—31no—
280C2×C4×Q8—32no—
281C2×C4×Q8—61no—
282#485—34no—
283#483—34no—
284#482—34no—
285#481—34no—
286#477—32no—
287#476—32no—
288#475—32no—
289#475—32no—
290#475—34no—
291#475—32no—
292#474—32no—
293#464—32no—
294#464—34no—
295#463—32no—
296#462—32no—
297#462—31no—
298#461—31no—
299#460—31no—
300#460—32no—
301#459—31no—
302#452—34no—
303#451—34no—
304#449—34no—
305#448—34no—
306#442—34no—
307#441—34no—
308#441—34no—
309#440—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×SD16—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318C2×#106—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#417—32no—
322#417—32no—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C3×#41—22no—
328C3×#41—22no—
329C3×#41—24no—
330C3×#41—24no—
331C3×#41—84no—
332C2×C3×Q8—22no—
333C2×C3×Q8—22no—
334C2×C3×Q8—82no—
335C2×C3×Q8C2×D411yescharacteristic
336C2×C3×Q8C2412yes—
337C2×C3×D4—22no—
338C2×C3×D4—24no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4C2×D412yes—
342C2×C3×D4C2×D411yescharacteristic
343C2×C3×D4C2412yes—
344C22×C3×C4—22no—
345C22×C3×C4—22no—
346C22×C3×C4—24no—
347C22×C3×C4C2×D411yescharacteristic
348C22×C3×C4C2×D412yes—
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2×D412yes—
351C22×C3×C4C2412yes—
352C22×C3×C4C2411yescharacteristic
353C2×#67—22no—
354C2×#67—21no—
355C22×Dic3—22no—
356C22×Dic3—21no—
357C22×Dic3—22no—
358C22×Dic3—21no—
359D3×Q8—28no—
360#237—216no—
361#237—28no—
362#235—22no—
363#235—24no—
364#235—24no—
365#235#4114yescomplemented
366C2×D12C2411yescharacteristic
367C2×C4×D3—22no—
368C2×C4×D3—21no—
369C2×C4×D3—21no—
370C2×C4×D3—22no—
371C2×C4×D3—21no—
372C2×Dic6—22no—
373C2×Dic6—21no—
374C2×Dic6—22no—
375C2×Dic6—24no—
376C2×Dic6—24no—
377C2×Dic6#4114yescomplemented
378C2×Dic6C2411yescharacteristic
379C2×Dic6C2412yes—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—24no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—21no—
385C3×C4⋊C4—21no—
386C3×C4⋊C4—24no—
387C3×C4⋊C4C2×D411yescharacteristic
388C3×C4⋊C4C2×D412yes—
389C3×C4⋊C4C2×D411yescharacteristic
390C3×C4⋊C4C2×D412yes—
391C3×C4⋊C4C2414yes—
392C3×C22⋊C4—24no—
393C3×C22⋊C4—24no—
394C3×C22⋊C4—24no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4C2×D412yes—
398C3×C22⋊C4C2×D412yes—
399C3×C22⋊C4C2×D412yes—
400C3×C42—24no—
401C3×C42C2×D411yescharacteristic
402C3×C42C2×D412yes—
403C3×C42C2×D412yes—
404C3×C42C2×D411yescharacteristic
405C3×C42C2412yes—
406C3×C42C2411yescharacteristic
407C3×C42C2411yescharacteristic
408#217—22no—
409#217—21no—
410#216—24no—
411#216—28no—
412#215—24no—
413#214—24no—
414#214—28no—
415#213—24no—
416(C2×D3)⋊C4—21no—
417(C2×D3)⋊C4—21no—
418(C2×D3)⋊C4—22no—
419C4⋊Dic3—22no—
420C4⋊Dic3—21no—
421C4⋊Dic3C2411yescharacteristic
422C4⋊Dic3C2412yes—
423C4⋊Dic3C2411yescharacteristic
424Dic3⋊C4—21no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—22no—
429Dic3⋊C4—21no—
430Dic3⋊C4—22no—
431C4×Dic3—22no—
432C4×Dic3—21no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—22no—
436C4×Dic3—22no—
437C4×Dic3—21no—
438C4×Dic3—22no—
439C4×Dic3—21no—
440#208—24no—
441C2×C3⋊C8—24no—
442C2×C3⋊C8C2412yes—
443C2×C3⋊C8C2414yes—
444C2×C3⋊C8C2412yes—
4452−1+4—64no—
4462−1+4—64no—
447C2×#41—22no—
448C2×#41—31no—
449C2×#41—32no—
450C2×#41—61no—
451C2×#41—62no—
452C2×#41C22×D312yes—
453C2×#41C22×D311yescharacteristic
454C22×Q8—21no—
455C22×Q8—31no—
456C22×Q8—32no—
457C22×Q8—61no—
458#137—68no—
459#135—68no—
460C2×Q16—32no—
461C2×Q16—34no—
462C2×SD16—32no—
463C2×SD16—32no—
464C2×SD16—34no—
465C2×D8—32no—
466C2×M16—32no—
467C22×C8—32no—
468C4⋊Q8—21no—
469C4⋊Q8—21no—
470C4⋊Q8C22×D311yescharacteristic
471C4⋊Q8C22×D312yes—
472C4⋊Q8C22×D312yes—
473#127C22×D311yescharacteristic
474#126—24no—
475#125—22no—
476#124—24no—
477#124—22no—
478#124C22×D312yes—
479#123—24no—
480C22⋊Q8—22no—
481C22⋊Q8—22no—
482C22⋊Q8—24no—
483C22⋊Q8C22×D314yes—
484#121—22no—
485#121—24no—
486#121—21no—
487#121—21no—
488#121—22no—
489#121C22×D314yes—
490C4×Q8—22no—
491C4×Q8—32no—
492C4×Q8—31no—
493C4×Q8—32no—
494C4×Q8—32no—
495C4×Q8—32no—
496C4×Q8—32no—
497C4×Q8—31no—
498C4×Q8—61no—
499C4×Q8—61no—
500C4×Q8—62no—
501C4×Q8—61no—
502C4×Q8—62no—
503C4×Q8—61no—
504C4×Q8—62no—
505C4×Q8—62no—
506C4×Q8—61no—
507C4×Q8#6711yescharacteristic
508C4×Q8#6711yescharacteristic
509C4×Q8C22×D314yes—
510C4×D4—24no—
511C4×D4—21no—
512C4×D4—22no—
513C4×D4—21no—
514C4×D4—31no—
515C4×D4—32no—
516C4×D4—31no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—61no—
520C4×D4—62no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4#6711yescharacteristic
527C4×D4#6712yes—
528C4×D4#6712yes—
529C4×D4#6711yescharacteristic
530C4×D4C22×D314yes—
531#117—22no—
532#117—22no—
533#117—31no—
534#117—32no—
535#117—61no—
536#117—62no—
537#117—62no—
538#117—62no—
539#117—62no—
540#117—62no—
541#117—61no—
542#117C22×D311yescharacteristic
543#117C22×D312yes—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—31no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—61no—
549C2×C4⋊C4—62no—
550C2×C4⋊C4—61no—
551C2×C4⋊C4—62no—
552C2×C4⋊C4C22×D312yes—
553C2×C42—61no—
554C2×C42—62no—
555C2×C42—61no—
556C2×C42—62no—
557C2×C42C22×D311yescharacteristic
558C2×C42C22×D312yes—
559#107—34no—
560#106—34no—
561#106—34no—
562#106—34no—
563C4⋊C8—31no—
564C4⋊C8—31no—
565C4⋊C8—32no—
566C4⋊C8—32no—
567C4⋊C8—32no—
568#103—32no—
569#103—32no—
570#103—34no—
571#103—34no—
572#103—34no—
573#103—34no—
574#102—32no—
575#102—32no—
576#102—34no—
577#102—34no—
578C22⋊C8—34no—
579C22⋊C8—34no—
580#97—34no—
581C4×C8—34no—
582C23×C3—22no—
583C23×C3C22×D412yes—
584C23×C3C22×D411yescharacteristic
585C22×D3—21no—
586C3×Q8—22no—
587C3×Q8—22no—
588C3×Q8—22no—
589C3×Q8—44no—
590C3×Q8—82no—
591C3×D4—24no—
592C3×D4—22no—
593C3×D4—22no—
594C3×D4—22no—
595C3×D4—42no—
596C3×D4—44no—
597C3×D4—42no—
598C3×D4—84no—
599C2×C3×C4—22no—
600C2×C3×C4—24no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—22no—
604C2×C3×C4—24no—
605C2×C3×C4—41no—
606C2×C3×C4—42no—
607C2×C3×C4—44no—
608C2×C3×C4—84no—
609C2×C3×C4—82no—
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D412yes—
612C2×C3×C4C22×D412yes—
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D412yes—
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C22×D411yescharacteristic
618C2×C3×C4C2×#4112yes—
619C2×C3×C4C2×#4112yes—
620C2×C3×C4C2511yescharacteristic
621#67—28no—
622#67—24no—
623C2×Dic3—28no—
624C2×Dic3—24no—
625C2×Dic3—21no—
626C2×Dic3—22no—
627C2×Dic3—21no—
628C2×Dic3—22no—
629C2×Dic3—21no—
630C2×Dic3—81no—
631C2×Dic3—82no—
632D12—21no—
633D12C2×#4112yes—
634C4×D3—28no—
635C4×D3—24no—
636C4×D3—42no—
637C4×D3—82no—
638C4×D3—81no—
639Dic6—28no—
640Dic6—24no—
641Dic6—22no—
642Dic6—21no—
643Dic6C2×#4112yes—
644Dic6C2×#4114yes—
645C3⋊C8—22no—
646C3⋊C8—22no—
647C3⋊C8—24no—
648#41—22no—
649#41—22no—
650#41—24no—
651#41—24no—
652#41—34no—
653#41—64no—
654#41—64no—
655#41—616no—
656#41—68no—
657#41—62no—
658#41—84no—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—34no—
662C2×Q8—32no—
663C2×Q8—31no—
664C2×Q8—64no—
665C2×Q8—64no—
666C2×Q8—68no—
667C2×Q8—62no—
668C2×Q8—62no—
669C2×Q8—61no—
670C2×Q8—82no—
671C2×Q8C2×#6711yescharacteristic
672C2×Q8C23×D312yes—
673C2×D4—22no—
674C2×D4—24no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—31no—
678C2×D4—62no—
679C2×D4—61no—
680C2×D4C2×#6712yes—
681C2×D4C2×#6711yescharacteristic
682C2×D4C23×D312yes—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—24no—
686C22×C4—62no—
687C22×C4—61no—
688C22×C4—62no—
689C22×C4—61no—
690C22×C4—62no—
691C22×C4—61no—
692C22×C4—61no—
693C22×C4—62no—
694C22×C4—61no—
695C22×C4C2×#6711yescharacteristic
696C22×C4C2×#6712yes—
697C22×C4C2×#6711yescharacteristic
698C22×C4C2×#6712yes—
699C22×C4C23×D312yes—
700C22×C4C23×D311yescharacteristic
701Q16—64no—
702Q16—68no—
703SD16—64no—
704SD16—68no—
705SD16—64no—
706D8—64no—
707M16—64no—
708C2×C8—32no—
709C2×C8—34no—
710C2×C8—32no—
711C2×C8—64no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—24no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—24no—
719C4⋊C4—31no—
720C4⋊C4—32no—
721C4⋊C4—31no—
722C4⋊C4—62no—
723C4⋊C4—61no—
724C4⋊C4—62no—
725C4⋊C4—62no—
726C4⋊C4—62no—
727C4⋊C4—62no—
728C4⋊C4—61no—
729C4⋊C4—61no—
730C4⋊C4—62no—
731C4⋊C4C2×#6711yescharacteristic
732C4⋊C4C2×#6711yescharacteristic
733C4⋊C4C2×#6712yes—
734C4⋊C4C2×#6712yes—
735C4⋊C4C23×D314yes—
736C22⋊C4—24no—
737C22⋊C4—24no—
738C22⋊C4—24no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—62no—
742C22⋊C4—61no—
743C22⋊C4—61no—
744C22⋊C4—61no—
745C22⋊C4—62no—
746C22⋊C4C2×#6712yes—
747C22⋊C4C2×#6712yes—
748C22⋊C4C2×#6712yes—
749C42—24no—
750C42—62no—
751C42—61no—
752C42—62no—
753C42—61no—
754C42—62no—
755C42—61no—
756C42—62no—
757C42—62no—
758C42—62no—
759C42C2×#6711yescharacteristic
760C42C2×#6712yes—
761C42C2×#6712yes—
762C42C2×#6711yescharacteristic
763C42C23×D312yes—
764C42C23×D311yescharacteristic
765C42C23×D311yescharacteristic
766C22×C3—21no—
767C22×C3—21no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—42no—
772C22×C3—42no—
773C22×C3—42no—
774C22×C3#52512yes—
775C22×C3C23×D411yescharacteristic
776C2×D3—22no—
777C2×D3—41no—
778C2×D3—41no—
779C3×C4—22no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—42no—
786C3×C4—44no—
787C3×C4#52512yes—
788C3×C4#57712yes—
789C3×C4C22×#4111yescharacteristic
790C3×C4C22×#4111yescharacteristic
791Dic3—22no—
792Dic3—24no—
793Dic3—42no—
794Dic3—41no—
795Dic3—41no—
796C23—22no—
797C23—61no—
798C23C22×#6712yes—
799C23C22×#6711yescharacteristic
800Q8—22no—
801Q8—22no—
802Q8—22no—
803Q8—34no—
804Q8—32no—
805Q8—44no—
806Q8—68no—
807Q8—62no—
808Q8—61no—
809Q8—64no—
810Q8—82no—
811D4—24no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—32no—
816D4—42no—
817D4—44no—
818D4—42no—
819D4—68no—
820D4—64no—
821D4—61no—
822D4—84no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—24no—
829C2×C4—41no—
830C2×C4—42no—
831C2×C4—44no—
832C2×C4—68no—
833C2×C4—68no—
834C2×C4—62no—
835C2×C4—61no—
836C2×C4—64no—
837C2×C4—64no—
838C2×C4—61no—
839C2×C4—62no—
840C2×C4—61no—
841C2×C4—84no—
842C2×C4—82no—
843C2×C4—122no—
844C2×C4—242no—
845C2×C4—241no—
846C2×C4—241no—
847C2×C4—242no—
848C2×C4D3×#4112yes—
849C2×C4D3×#4112yes—
850C2×C4C22×#6712yes—
851C2×C4C22×#6711yescharacteristic
852C2×C4C22×#6712yes—
853C2×C4C22×#6712yes—
854C2×C4C22×#6711yescharacteristic
855C2×C4C22×#6711yescharacteristic
856C2×C4C22×#6711yescharacteristic
857C2×C4C22×#6711yescharacteristic
858C2×C4C24×D311yescharacteristic
859C8—62no—
860C8—62no—
861C8—64no—
862C2×C3—22no—
863C2×C3—42no—
864C2×C3—82no—
865C2×C3C2×#52511yescharacteristic
866C2×C3C2×#57711yescharacteristic
867C2×C3#358611yescharacteristic
868D3—42no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—62no—
878C22—121no—
879C22—121no—
880C22#582812yes—
881C22C23×#6711yescharacteristic
882C4—22no—
883C4—22no—
884C4—21no—
885C4—21no—
886C4—22no—
887C4—21no—
888C4—42no—
889C4—44no—
890C4—64no—
891C4—62no—
892C4—121no—
893C4—122no—
894C4—121no—
895C4#582812yes—
896C4#583612yes—
897C4C2×D3×#4111yescharacteristic
898C4C2×D3×#4111yescharacteristic
899C3#6059911yescharacteristic, complemented, Sylow
900C2—22no—
901C2—42no—
902C2—82no—
903C2—122no—
904C2C2×#582811yescharacteristic
905C2C2×#583611yescharacteristic
906C2#8728711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3511C2
socleC22×C3C23×D4
hypercenter#3511D3
hypocenterC3#60599
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. C3×#3511C2semidirect
2. C4×#1010C2semidirect
3. #83467C2semidirect
4. #83462C2semidirect
5. #83427C2semidirect
6. #83419C2semidirect
7. #83369C2semidirect
8. #83352C2semidirect
9. #83315C2semidirect
10. #83314C2semidirect
11. #83301C2semidirect
12. #83296C2semidirect
13. C2×#5094C2semidirect
14. #83212C2semidirect
15. #82571C2semidirect
16. #82558C2semidirect
17. #82515C2semidirect
96. #3511D3semidirect
365. #235#41semidirect
377. C2×Dic6#41semidirect
899. C3#60599semidirect

Maximal subgroups

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

subgroupindex
C3×#35112
C4×#10102
#834672
#834622
#834272
#834192
#833692
#833522
#833152
#833142
#833012
#832962
C2×#50942
#832122
#825712
#825582
#825152
#605993