Finite Group Databasebeta

← #11664258

Subgroups — #11664258

Order 768.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3511C211yesmaximal, characteristic, complemented
2C4×#1009C211yesmaximal, characteristic, complemented
3#83461C214yesmaximal, complemented
4#83460C214yesmaximal, complemented
5#83424C212yesmaximal, complemented
6#83418C212yesmaximal, complemented
7#83353C212yesmaximal, complemented
8#83352C212yesmaximal, complemented
9#83301C212yesmaximal, complemented
10#83298C212yesmaximal, complemented
11#83297C211yesmaximal, characteristic, complemented
12#83296C211yesmaximal, characteristic, complemented
13#83212C211yesmaximal, characteristic, complemented
14C2×#5087C211yesmaximal, characteristic, complemented
15#82564C212yesmaximal, complemented
16#82557C212yesmaximal, complemented
17#82515C211yesmaximal, characteristic, complemented
18#60596—31nomaximal, Sylow
19C2×#1009C2211yescharacteristic
20C3×#556—21no—
21C3×#555—21no—
22C3×#554—21no—
23C3×#553—22no—
24C3×#548—22no—
25C3×#547—21no—
26C3×#542C2214yescomplemented
27C3×#537C2212yes—
28C3×#533C2212yescomplemented
29C3×#532C2211yescharacteristic, complemented
30C3×#532C2212yescomplemented
31C2×C3×C4⋊Q8C2211yescharacteristic, complemented
32C3×#520C2212yescomplemented
33C3×C4×#41C2211yescharacteristic
34#5827C2211yescharacteristic
35C2×#950C2212yes—
36C2×#949C2212yes—
37#5574—21no—
38C4×#239—21no—
39#5545—22no—
40#5545—21no—
41C4×D3×D4—21no—
42C4×D3×D4—22no—
43#5523C2212yes—
44#5523C2211yescharacteristic
45#5521C2212yes—
46#5521C2211yescharacteristic
47C4×#235C2211yescharacteristic
48C4×#235C2212yes—
49C2×C4×D12C2211yescharacteristic
50C2×C4×D12C2212yes—
51#5234C2212yes—
52#5233C2212yescomplemented
53#5232C2212yescomplemented
54#5094C2212yescomplemented
55#5091C2212yescomplemented
56#5090C2211yescharacteristic, complemented
57#5087C2214yescomplemented
58#5087C2212yescomplemented
59#5087C2212yescomplemented
60#5087C2212yescomplemented
61#5084C2212yescomplemented
62#5083C2211yescharacteristic, complemented
63#5083C2212yescomplemented
64#5075C2211yescharacteristic, complemented
65#5072C2211yescharacteristic, complemented
66#5072C2212yescomplemented
67#5057C2212yescomplemented
68#5057C2214yescomplemented
69#5054C2212yescomplemented
70#5047C2214yes—
71#5046C2214yes—
72#5045C2214yescomplemented
73#5044C2214yescomplemented
74#5037C2214yes—
75#5036C2214yes—
76#5035C2214yescomplemented
77#5033C2214yescomplemented
78C4×#216C2214yescomplemented
79#5026C2214yescomplemented
80#5026C2214yescomplemented
81C4×#215C2214yescomplemented
82#5018C2214yescomplemented
83#5014C2214yescomplemented
84C4×#213C2214yescomplemented
85C4×#213C2214yescomplemented
86#5000C2214yescomplemented
87#4997C2212yescomplemented
88#4966C2212yes—
89C2×#809C2212yes—
90#4964C2212yescomplemented
91C2×#807C2212yescomplemented
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic, complemented
95C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
96#3511D311yescharacteristic, complemented
97C4×H(5,𝔽2)—31no—
98#3124—34no—
99#3118—34no—
100#3115—32no—
101#3110—32no—
102#3107—32no—
103#3100—32no—
104#3098—32no—
105#3079—31no—
106C2×#474—31no—
107#3036—31no—
108#3035—31no—
109#3012—32no—
110#2951—32no—
111#2946—32no—
112#2925—31no—
113C2×C3×#41—22no—
114C2×C3×#41C2312yes—
115C2×C3×#41C2311yescharacteristic
116C22×C3×Q8—21no—
117#1009—24no—
118#1009—24no—
119C2×#239—21no—
120C2×D3×D4—22no—
121C2×D3×D4—21no—
122C2×#235C2312yes—
123C2×#235C2311yescharacteristic
124C22×D12C2312yes—
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—22no—
128C3×C4⋊Q8—21no—
129C3×C4⋊Q8—21no—
130C3×C4⋊Q8C2311yescharacteristic
131C3×C4⋊Q8C2312yes—
132C3×C4⋊Q8C2312yes—
133C3×#127C2311yescharacteristic
134C3×#126—24no—
135C3×#125—22no—
136C3×#124—24no—
137C3×#124—22no—
138C3×#124C2312yes—
139C3×#123—24no—
140C3×C22⋊Q8—22no—
141C3×C22⋊Q8—22no—
142C3×C22⋊Q8—24no—
143C3×C22⋊Q8C2314yes—
144C3×#121—22no—
145C3×#121—24no—
146C3×#121—21no—
147C3×#121—21no—
148C3×#121—22no—
149C3×#121C2314yes—
150C3×C4×Q8—22no—
151C3×C4×Q8D411yescharacteristic
152C3×C4×Q8D411yescharacteristic
153C3×C4×Q8C2314yes—
154C3×C4×D4—24no—
155C3×C4×D4—21no—
156C3×C4×D4—22no—
157C3×C4×D4—21no—
158C3×C4×D4D411yescharacteristic
159C3×C4×D4D412yes—
160C3×C4×D4D412yes—
161C3×C4×D4D411yescharacteristic
162C3×C4×D4C2314yes—
163C3×#117—22no—
164C3×#117—22no—
165C3×#117C2311yescharacteristic
166C3×#117C2312yes—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—22no—
169C2×C3×C4⋊C4C2312yes—
170C2×C3×C42C2311yescharacteristic
171C2×C3×C42C2312yes—
172#950—28no—
173#949—28no—
174Q8×Dic3—21no—
175C2×#216C2312yes—
176C2×#215C2314yes—
177C2×#215C2312yes—
178D4×Dic3—22no—
179D4×Dic3—21no—
180C2×#214C2312yes—
181C2×#213C2312yes—
182C2×#213C2314yes—
183C4×#67—21no—
184C4×#67—22no—
185C4×#67—21no—
186C4×#67—22no—
187C2×(C2×D3)⋊C4—21no—
188C2×(C2×D3)⋊C4—22no—
189#926C2311yescharacteristic
190#926C2312yes—
191C2×C4⋊Dic3C2311yescharacteristic
192C2×C4⋊Dic3C2312yes—
193C2×#208C2312yes—
194C22×C3⋊C8C2312yes—
195#893—21no—
196#893—22no—
197#893—21no—
198#893—22no—
199#892—21no—
200#892—22no—
201D3×C4⋊C4—21no—
202D3×C4⋊C4—22no—
203#67⋊C4—22no—
204#67⋊C4—22no—
205#67⋊C4—22no—
206D3×C22⋊C4—22no—
207D3×C22⋊C4—22no—
208D3×C22⋊C4—22no—
209C4×D12—21no—
210C4×D12—22no—
211C4×D12—22no—
212C4×D12—21no—
213C4×D12C2312yes—
214C4×D12C2311yescharacteristic
215C4×D12C2312yes—
216C4×D12C2312yes—
217C4×D12C2312yes—
218C4×D12C2312yes—
219C4×D12C2311yescharacteristic
220#872—22no—
221#872—21no—
222C42×D3—21no—
223C42×D3—22no—
224C4×Dic6C2311yescharacteristic
225C4×Dic6C2312yes—
226C4×Dic6C2311yescharacteristic
227#835C2314yes—
228#835C2312yes—
229#835C2312yes—
230#832C2314yes—
231#832C2312yes—
232#832C2312yes—
233#830C2314yes—
234#830C2314yes—
235#810C2314yes—
236#809C2314yes—
237#809C2314yes—
238#809C2314yes—
239#808C2314yes—
240#807C2314yes—
241#807C2314yes—
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×H(5,𝔽2)—31no—
251C2×AGL(1,ℤ/8)—32no—
252C2×#135—32no—
253#556—21no—
254#555—21no—
255#554—21no—
256#553—22no—
257#548—22no—
258#547—21no—
259#542C2×D314yescomplemented
260#537C2×D312yes—
261#533C2×D312yescomplemented
262#532C2×D311yescharacteristic, complemented
263#532C2×D312yescomplemented
264C2×C4⋊Q8C2×D311yescharacteristic, complemented
265#520—31no—
266#520—32no—
267#520—31no—
268#520—61no—
269#520C2×D312yescomplemented
270#518—32no—
271#518—31no—
272#518—62no—
273#518—61no—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—61no—
277C4×#41C2×D311yescharacteristic
278C2×C4×D4—32no—
279C2×C4×D4—31no—
280C2×C4×D4—61no—
281C2×C4×D4—62no—
282#485—34no—
283#484—34no—
284#482—34no—
285#480—34no—
286#477—32no—
287#476—32no—
288#475—32no—
289#474—32no—
290#474—32no—
291#474—32no—
292#474—34no—
293#464—32no—
294#463—32no—
295#463—34no—
296#462—31no—
297#461—32no—
298#461—31no—
299#460—31no—
300#459—31no—
301#459—32no—
302#452—34no—
303#450—34no—
304#449—34no—
305#447—34no—
306#442—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×D8—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318C2×#107—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#417—32no—
322#417—32no—
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C23×D3—22no—
328C23×D3—21no—
329C3×#41—22no—
330C3×#41—22no—
331C3×#41—24no—
332C3×#41—24no—
333C3×#41—84no—
334C2×C3×Q8—22no—
335C2×C3×Q8—22no—
336C2×C3×Q8—82no—
337C2×C3×Q8C2×D411yescharacteristic
338C2×C3×Q8C2412yes—
339C2×C3×D4—22no—
340C2×C3×D4—24no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4C2×D412yes—
344C2×C3×D4C2×D411yescharacteristic
345C2×C3×D4C2412yes—
346C22×C3×C4—22no—
347C22×C3×C4—22no—
348C22×C3×C4—24no—
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2×D412yes—
351C22×C3×C4C2×D411yescharacteristic
352C22×C3×C4C2×D412yes—
353C22×C3×C4C2412yes—
354C22×C3×C4C2411yescharacteristic
355C2×#67—22no—
356C2×#67—21no—
357C22×Dic3—22no—
358C22×Dic3—21no—
359#239—28no—
360D3×D4—216no—
361D3×D4—28no—
362#235—22no—
363#235—24no—
364#235—24no—
365#235#4114yescomplemented
366C2×D12—22no—
367C2×D12—21no—
368C2×D12—22no—
369C2×D12—24no—
370C2×D12—24no—
371C2×D12#4114yescomplemented
372C2×D12C2411yescharacteristic
373C2×D12C2412yes—
374C2×C4×D3—22no—
375C2×C4×D3—21no—
376C2×C4×D3—21no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—21no—
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—22no—
383C2×C4×D3—82no—
384C2×C4×D3—84no—
385C2×Dic6C2411yescharacteristic
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—24no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—24no—
393C3×C4⋊C4C2×D411yescharacteristic
394C3×C4⋊C4C2×D412yes—
395C3×C4⋊C4C2×D411yescharacteristic
396C3×C4⋊C4C2×D412yes—
397C3×C4⋊C4C2414yes—
398C3×C22⋊C4—24no—
399C3×C22⋊C4—24no—
400C3×C22⋊C4—24no—
401C3×C22⋊C4—22no—
402C3×C22⋊C4—22no—
403C3×C22⋊C4C2×D412yes—
404C3×C22⋊C4C2×D412yes—
405C3×C22⋊C4C2×D412yes—
406C3×C42—24no—
407C3×C42C2×D411yescharacteristic
408C3×C42C2×D412yes—
409C3×C42C2×D412yes—
410C3×C42C2×D411yescharacteristic
411C3×C42C2412yes—
412C3×C42C2411yescharacteristic
413C3×C42C2411yescharacteristic
414#217—22no—
415#217—21no—
416#216—24no—
417#215—28no—
418#215—24no—
419#214—24no—
420#213—28no—
421#213—24no—
422(C2×D3)⋊C4—22no—
423(C2×D3)⋊C4—21no—
424(C2×D3)⋊C4—21no—
425(C2×D3)⋊C4—22no—
426(C2×D3)⋊C4—22no—
427(C2×D3)⋊C4—22no—
428(C2×D3)⋊C4—22no—
429C4⋊Dic3—22no—
430C4⋊Dic3—21no—
431C4⋊Dic3C2412yes—
432C4⋊Dic3C2411yescharacteristic
433C4⋊Dic3C2411yescharacteristic
434Dic3⋊C4—21no—
435Dic3⋊C4—21no—
436Dic3⋊C4—22no—
437C4×Dic3—21no—
438C4×Dic3—22no—
439C4×Dic3—21no—
440C4×Dic3—22no—
441C4×Dic3—21no—
442#208—24no—
443C2×C3⋊C8—24no—
444C2×C3⋊C8C2412yes—
445C2×C3⋊C8C2414yes—
446C2×C3⋊C8C2412yes—
447H(5,𝔽2)—64no—
448H(5,𝔽2)—64no—
449C2×#41—22no—
450C2×#41—31no—
451C2×#41—32no—
452C2×#41—61no—
453C2×#41C22×D312yes—
454C2×#41C22×D311yescharacteristic
455C22×Q8—21no—
456C22×D4—31no—
457C22×D4—32no—
458C22×D4—62no—
459C22×D4—61no—
460C23×C4—61no—
461C23×C4—62no—
462AGL(1,ℤ/8)—68no—
463#135—68no—
464C2×Q16—32no—
465C2×SD16—32no—
466C2×SD16—34no—
467C2×SD16—32no—
468C2×D8—32no—
469C2×D8—34no—
470C2×M16—32no—
471C22×C8—32no—
472C4⋊Q8—21no—
473C4⋊Q8—21no—
474C4⋊Q8C22×D311yescharacteristic
475C4⋊Q8C22×D312yes—
476C4⋊Q8C22×D312yes—
477#127C22×D311yescharacteristic
478#126—24no—
479#125—22no—
480#124—24no—
481#124—22no—
482#124C22×D312yes—
483#123—24no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—24no—
487C22⋊Q8C22×D314yes—
488#121—22no—
489#121—24no—
490#121—21no—
491#121—21no—
492#121—22no—
493#121C22×D314yes—
494C4×Q8—22no—
495C4×Q8—31no—
496C4×Q8—32no—
497C4×Q8—31no—
498C4×Q8—61no—
499C4×Q8#6711yescharacteristic
500C4×Q8#6711yescharacteristic
501C4×Q8C22×D314yes—
502C4×D4—24no—
503C4×D4—21no—
504C4×D4—22no—
505C4×D4—21no—
506C4×D4—31no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—32no—
510C4×D4—32no—
511C4×D4—32no—
512C4×D4—31no—
513C4×D4—62no—
514C4×D4—61no—
515C4×D4—61no—
516C4×D4—62no—
517C4×D4—61no—
518C4×D4—62no—
519C4×D4—61no—
520C4×D4—62no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—61no—
527C4×D4—62no—
528C4×D4—62no—
529C4×D4—61no—
530C4×D4#6711yescharacteristic
531C4×D4#6712yes—
532C4×D4#6712yes—
533C4×D4#6711yescharacteristic
534C4×D4C22×D314yes—
535#117—22no—
536#117—22no—
537#117—31no—
538#117—32no—
539#117—61no—
540#117—62no—
541#117—62no—
542#117—61no—
543#117C22×D311yescharacteristic
544#117C22×D312yes—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—22no—
547C2×C4⋊C4—31no—
548C2×C4⋊C4—32no—
549C2×C4⋊C4—61no—
550C2×C4⋊C4—62no—
551C2×C4⋊C4C22×D312yes—
552C2×C22⋊C4—61no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C22⋊C4—62no—
556C2×C22⋊C4—62no—
557C2×C42—61no—
558C2×C42—62no—
559C2×C42C22×D311yescharacteristic
560C2×C42C22×D312yes—
561#107—34no—
562#107—34no—
563#107—34no—
564#106—34no—
565C4⋊C8—31no—
566C4⋊C8—31no—
567C4⋊C8—32no—
568C4⋊C8—32no—
569C4⋊C8—32no—
570#103—32no—
571#103—32no—
572#103—34no—
573#103—34no—
574#102—32no—
575#102—32no—
576#102—34no—
577#102—34no—
578#102—34no—
579#102—34no—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—22no—
585C23×C3C22×D412yes—
586C23×C3C22×D411yescharacteristic
587C22×D3—22no—
588C22×D3—21no—
589C22×D3—28no—
590C22×D3—24no—
591C22×D3—81no—
592C22×D3—82no—
593C22×D3—81no—
594C22×D3—82no—
595C3×Q8—22no—
596C3×Q8—22no—
597C3×Q8—22no—
598C3×Q8—44no—
599C3×Q8—82no—
600C3×D4—24no—
601C3×D4—22no—
602C3×D4—22no—
603C3×D4—22no—
604C3×D4—42no—
605C3×D4—44no—
606C3×D4—42no—
607C3×D4—84no—
608C2×C3×C4—22no—
609C2×C3×C4—24no—
610C2×C3×C4—22no—
611C2×C3×C4—22no—
612C2×C3×C4—22no—
613C2×C3×C4—24no—
614C2×C3×C4—41no—
615C2×C3×C4—42no—
616C2×C3×C4—44no—
617C2×C3×C4—84no—
618C2×C3×C4—82no—
619C2×C3×C4C22×D412yes—
620C2×C3×C4C22×D412yes—
621C2×C3×C4C22×D411yescharacteristic
622C2×C3×C4C22×D411yescharacteristic
623C2×C3×C4C22×D411yescharacteristic
624C2×C3×C4C22×D412yes—
625C2×C3×C4C22×D411yescharacteristic
626C2×C3×C4C22×D411yescharacteristic
627C2×C3×C4C2×#4112yes—
628C2×C3×C4C2×#4112yes—
629C2×C3×C4C2511yescharacteristic
630#67—28no—
631#67—24no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—22no—
635C2×Dic3—21no—
636C2×Dic3—81no—
637C2×Dic3—82no—
638D12—28no—
639D12—24no—
640D12—21no—
641D12—22no—
642D12C2×#4112yes—
643D12C2×#4114yes—
644C4×D3—28no—
645C4×D3—24no—
646C4×D3—44no—
647C4×D3—42no—
648C4×D3—82no—
649C4×D3—81no—
650C4×D3—82no—
651C4×D3—82no—
652C4×D3—82no—
653Dic6—21no—
654Dic6C2×#4112yes—
655C3⋊C8—22no—
656C3⋊C8—22no—
657C3⋊C8—24no—
658C24—62no—
659C24—61no—
660#41—22no—
661#41—22no—
662#41—24no—
663#41—24no—
664#41—34no—
665#41—64no—
666#41—64no—
667#41—68no—
668#41—62no—
669#41—84no—
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—31no—
673C2×Q8—82no—
674C2×Q8C2×#6711yescharacteristic
675C2×Q8C23×D312yes—
676C2×D4—22no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—34no—
681C2×D4—32no—
682C2×D4—31no—
683C2×D4—64no—
684C2×D4—64no—
685C2×D4—616no—
686C2×D4—68no—
687C2×D4—62no—
688C2×D4—61no—
689C2×D4—62no—
690C2×D4—62no—
691C2×D4—61no—
692C2×D4C2×#6712yes—
693C2×D4C2×#6711yescharacteristic
694C2×D4C23×D312yes—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—24no—
698C22×C4—62no—
699C22×C4—61no—
700C22×C4—62no—
701C22×C4—61no—
702C22×C4—61no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—61no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—62no—
709C22×C4—242no—
710C22×C4—244no—
711C22×C4C2×#6711yescharacteristic
712C22×C4C2×#6712yes—
713C22×C4C2×#6711yescharacteristic
714C22×C4C2×#6712yes—
715C22×C4C23×D312yes—
716C22×C4C23×D311yescharacteristic
717Q16—64no—
718SD16—64no—
719SD16—64no—
720SD16—68no—
721D8—64no—
722D8—68no—
723M16—64no—
724C2×C8—32no—
725C2×C8—34no—
726C2×C8—32no—
727C2×C8—64no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—24no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—24no—
735C4⋊C4—31no—
736C4⋊C4—31no—
737C4⋊C4—32no—
738C4⋊C4—62no—
739C4⋊C4—61no—
740C4⋊C4—61no—
741C4⋊C4—62no—
742C4⋊C4—61no—
743C4⋊C4C2×#6711yescharacteristic
744C4⋊C4C2×#6712yes—
745C4⋊C4C2×#6711yescharacteristic
746C4⋊C4C2×#6712yes—
747C4⋊C4C23×D314yes—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—22no—
753C22⋊C4—62no—
754C22⋊C4—61no—
755C22⋊C4—61no—
756C22⋊C4—62no—
757C22⋊C4—62no—
758C22⋊C4—62no—
759C22⋊C4—62no—
760C22⋊C4—62no—
761C22⋊C4—61no—
762C22⋊C4C2×#6712yes—
763C22⋊C4C2×#6712yes—
764C22⋊C4C2×#6712yes—
765C42—24no—
766C42—61no—
767C42—62no—
768C42—61no—
769C42—62no—
770C42—61no—
771C42C2×#6711yescharacteristic
772C42C2×#6712yes—
773C42C2×#6712yes—
774C42C2×#6711yescharacteristic
775C42C23×D312yes—
776C42C23×D311yescharacteristic
777C42C23×D311yescharacteristic
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—42no—
784C22×C3—42no—
785C22×C3—42no—
786C22×C3#52512yes—
787C22×C3C23×D411yescharacteristic
788C2×D3—24no—
789C2×D3—22no—
790C2×D3—42no—
791C2×D3—41no—
792C2×D3—42no—
793C2×D3—41no—
794C2×D3—84no—
795C2×D3—88no—
796C3×C4—22no—
797C3×C4—21no—
798C3×C4—21no—
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—21no—
802C3×C4—42no—
803C3×C4—44no—
804C3×C4#52512yes—
805C3×C4#57612yes—
806C3×C4C22×#4111yescharacteristic
807C3×C4C22×#4111yescharacteristic
808Dic3—22no—
809Dic3—41no—
810Dic3—41no—
811Dic3—42no—
812C23—22no—
813C23—68no—
814C23—62no—
815C23—61no—
816C23—64no—
817C23—241no—
818C23—242no—
819C23—241no—
820C23—242no—
821C23C22×#6712yes—
822C23C22×#6711yescharacteristic
823Q8—22no—
824Q8—22no—
825Q8—22no—
826Q8—32no—
827Q8—44no—
828Q8—61no—
829Q8—82no—
830D4—24no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—34no—
835D4—32no—
836D4—42no—
837D4—44no—
838D4—42no—
839D4—68no—
840D4—68no—
841D4—64no—
842D4—61no—
843D4—62no—
844D4—64no—
845D4—84no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—24no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—44no—
855C2×C4—68no—
856C2×C4—61no—
857C2×C4—64no—
858C2×C4—61no—
859C2×C4—62no—
860C2×C4—61no—
861C2×C4—84no—
862C2×C4—82no—
863C2×C4—124no—
864C2×C4—122no—
865C2×C4—242no—
866C2×C4—242no—
867C2×C4—242no—
868C2×C4—242no—
869C2×C4—241no—
870C2×C4—241no—
871C2×C4—242no—
872C2×C4D3×#4112yes—
873C2×C4D3×#4112yes—
874C2×C4C22×#6712yes—
875C2×C4C22×#6712yes—
876C2×C4C22×#6711yescharacteristic
877C2×C4C22×#6711yescharacteristic
878C2×C4C22×#6711yescharacteristic
879C2×C4C22×#6712yes—
880C2×C4C22×#6711yescharacteristic
881C2×C4C22×#6711yescharacteristic
882C2×C4C24×D311yescharacteristic
883C8—62no—
884C8—62no—
885C8—64no—
886C2×C3—22no—
887C2×C3—42no—
888C2×C3—82no—
889C2×C3C2×#52511yescharacteristic
890C2×C3C2×#57611yescharacteristic
891C2×C3#358611yescharacteristic
892D3—44no—
893D3—42no—
894C22—21no—
895C22—21no—
896C22—22no—
897C22—22no—
898C22—22no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—64no—
903C22—62no—
904C22—122no—
905C22—121no—
906C22—122no—
907C22—121no—
908C22—244no—
909C22—248no—
910C22#582812yes—
911C22C23×#6711yescharacteristic
912C4—22no—
913C4—22no—
914C4—21no—
915C4—21no—
916C4—22no—
917C4—21no—
918C4—42no—
919C4—44no—
920C4—62no—
921C4—121no—
922C4—122no—
923C4—121no—
924C4#582812yes—
925C4#583512yes—
926C4C2×D3×#4111yescharacteristic
927C4C2×D3×#4111yescharacteristic
928C3#6059611yescharacteristic, complemented, Sylow
929C2—22no—
930C2—42no—
931C2—82no—
932C2—124no—
933C2—122no—
934C2C2×#582811yescharacteristic
935C2C2×#583511yescharacteristic
936C2#8728711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3511C2
socleC22×C3C23×D4
hypercenter#3511D3
hypocenterC3#60596
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×#1009C2semidirect
3. #83461C2semidirect
4. #83460C2semidirect
5. #83424C2semidirect
6. #83418C2semidirect
7. #83353C2semidirect
8. #83352C2semidirect
9. #83301C2semidirect
10. #83298C2semidirect
11. #83297C2semidirect
12. #83296C2semidirect
13. #83212C2semidirect
14. C2×#5087C2semidirect
15. #82564C2semidirect
16. #82557C2semidirect
17. #82515C2semidirect
26. C3×#542C22semidirect
28. C3×#533C22semidirect
29. C3×#532C22semidirect
30. C3×#532C22semidirect
31. C2×C3×C4⋊Q8C22semidirect
32. C3×#520C22semidirect
52. #5233C22semidirect
53. #5232C22semidirect
54. #5094C22semidirect
55. #5091C22semidirect
56. #5090C22semidirect
57. #5087C22semidirect
58. #5087C22semidirect
59. #5087C22semidirect
60. #5087C22semidirect
61. #5084C22semidirect
62. #5083C22semidirect
63. #5083C22semidirect
64. #5075C22semidirect
65. #5072C22semidirect
66. #5072C22semidirect
67. #5057C22semidirect
68. #5057C22semidirect
69. #5054C22semidirect
72. #5045C22semidirect
73. #5044C22semidirect
76. #5035C22semidirect
77. #5033C22semidirect
78. C4×#216C22semidirect
79. #5026C22semidirect
80. #5026C22semidirect
81. C4×#215C22semidirect
82. #5018C22semidirect
83. #5014C22semidirect
84. C4×#213C22semidirect
85. C4×#213C22semidirect
86. #5000C22semidirect
87. #4997C22semidirect
90. #4964C22semidirect
91. C2×#807C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
94. #4924C22semidirect
95. C2×C4⋊(C3⋊C8)C22semidirect
96. #3511D3semidirect
259. #542C2×D3semidirect
261. #533C2×D3semidirect
262. #532C2×D3semidirect
263. #532C2×D3semidirect
264. C2×C4⋊Q8C2×D3semidirect
269. #520C2×D3semidirect
365. #235#41semidirect
371. C2×D12#41semidirect
928. C3#60596semidirect

Maximal subgroups

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

subgroupindex
C3×#35112
C4×#10092
#834612
#834602
#834242
#834182
#833532
#833522
#833012
#832982
#832972
#832962
#832122
C2×#50872
#825642
#825572
#825152
#605963