Finite Group Databasebeta

← #11664161

Subgroups — #11664161

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3509C211yesmaximal, characteristic, complemented
2C4×#1009C211yesmaximal, characteristic
3#83447C214yesmaximal, complemented
4#83446C214yesmaximal, complemented
5#83404C212yesmaximal
6#83397C212yesmaximal, complemented
7#83354C212yesmaximal, complemented
8#83353C212yesmaximal, complemented
9#83352C212yesmaximal, complemented
10#83351C212yesmaximal, complemented
11#83350C211yesmaximal, characteristic, complemented
12#83349C211yesmaximal, characteristic, complemented
13#83209C211yesmaximal, characteristic, complemented
14C2×#5083C211yesmaximal, characteristic, complemented
15#82548C212yesmaximal, complemented
16#82547C212yesmaximal, complemented
17#82515C211yesmaximal, characteristic, complemented
18#60591—31nomaximal, Sylow
19C2×#1009C2211yescharacteristic
20C3×#557—21no—
21C3×#557—21no—
22C3×#556—21no—
23C3×#556—21no—
24C3×#552—22no—
25C3×#552—22no—
26C3×#541C2214yescomplemented
27C3×#536C2212yes—
28C3×#533C2212yescomplemented
29C3×#533C2212yescomplemented
30C3×#533C2211yescharacteristic, complemented
31C2×C3×C4⋊Q8C2211yescharacteristic, complemented
32C3×#519C2212yescomplemented
33C3×C4×#41C2211yescharacteristic
34#5827C2211yescharacteristic
35C2×#942C2212yes—
36C22×#215C2212yes—
37#5574—21no—
38C4×#239—21no—
39#5545—22no—
40#5545—21no—
41C4×D3×D4—22no—
42C4×D3×D4—21no—
43#5523C2211yescharacteristic
44#5523C2212yes—
45#5521C2211yescharacteristic
46#5521C2212yes—
47C4×#235C2211yescharacteristic
48C4×#235C2212yes—
49C2×C4×D12C2211yescharacteristic
50C2×C4×D12C2212yes—
51#5234C2212yes—
52#5225C2212yescomplemented
53C2×#835C2212yescomplemented
54#5094C2211yescharacteristic, complemented
55#5091C2211yescharacteristic, complemented
56#5090C2212yescomplemented
57#5090C2212yescomplemented
58#5087C2211yescharacteristic, complemented
59#5087C2212yescomplemented
60#5084C2211yescharacteristic, complemented
61#5084C2212yescomplemented
62#5083C2212yescomplemented
63#5083C2212yescomplemented
64#5083C2214yescomplemented
65#5083C2212yescomplemented
66#5083C2212yescomplemented
67#5066C2212yescomplemented
68#5066C2214yescomplemented
69#5063C2212yescomplemented
70#5047C2214yes—
71#5047C2214yes—
72#5046C2214yes—
73#5046C2214yes—
74#5045C2214yescomplemented
75#5045C2214yescomplemented
76#5044C2214yescomplemented
77#5043C2214yescomplemented
78#5030C2214yescomplemented
79C4×#216C2214yescomplemented
80#5026C2214yescomplemented
81#5026C2214yescomplemented
82#5026C2214yescomplemented
83C4×#215C2214yescomplemented
84C4×#215C2214yescomplemented
85C4×#215C2214yescomplemented
86#5002C2212yes—
87#5001C2212yes—
88#5000C2214yescomplemented
89#4998C2212yescomplemented
90#4997C2212yescomplemented
91#4995C2212yescomplemented
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic, complemented
95C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
96#3509D311yescharacteristic, complemented
97C4×H(5,𝔽2)—31no—
98#3123—34no—
99#3120—34no—
100#3116—32no—
101#3110—32no—
102#3107—32no—
103#3101—32no—
104#3097—32no—
105#3077—31no—
106#3076—31no—
107#3039—31no—
108C2×#461—31no—
109#3009—32no—
110#2949—32no—
111#2947—32no—
112#2925—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8C2312yes—
115#1009—24no—
116#1009—24no—
117C2×#239—21no—
118C2×D3×D4—22no—
119C2×D3×D4—21no—
120C2×#235C2312yes—
121C2×#235C2311yescharacteristic
122C22×D12C2312yes—
123C22×D12C2311yescharacteristic
124C22×C4×D3—21no—
125C22×C4×D3—22no—
126C3×C4⋊Q8—22no—
127C3×C4⋊Q8—21no—
128C3×C4⋊Q8—21no—
129C3×C4⋊Q8C2312yes—
130C3×C4⋊Q8C2312yes—
131C3×C4⋊Q8C2311yescharacteristic
132C3×C4⋊Q8C2311yescharacteristic
133C3×#126—24no—
134C3×#126—24no—
135C3×#125—24no—
136C3×#125—24no—
137C3×#125—22no—
138C3×#125—22no—
139C3×#125C2312yes—
140C3×#124—22no—
141C3×#123—24no—
142C3×C22⋊Q8—21no—
143C3×C22⋊Q8—21no—
144C3×C22⋊Q8—22no—
145C3×C22⋊Q8—22no—
146C3×C22⋊Q8C2314yes—
147C3×C22⋊Q8C2314yes—
148C3×C4×Q8—22no—
149C3×C4×Q8—22no—
150C3×C4×Q8—22no—
151C3×C4×Q8—22no—
152C3×C4×Q8—21no—
153C3×C4×Q8—21no—
154C3×C4×Q8D411yescharacteristic
155C3×C4×Q8D411yescharacteristic
156C3×C4×Q8C2314yes—
157C3×C4×Q8C2314yes—
158C3×C4×D4D412yes—
159C3×C4×D4D411yescharacteristic
160C3×C4×D4D412yes—
161C3×C4×D4D411yescharacteristic
162C3×#117—22no—
163C3×#117—22no—
164C3×#117—24no—
165C3×#117C2312yes—
166C3×#117C2311yescharacteristic
167C3×#117C2312yes—
168C2×C3×C4⋊C4—21no—
169C2×C3×C4⋊C4—21no—
170C2×C3×C42C2311yescharacteristic
171C2×C3×C42C2312yes—
172Q8×Dic3—21no—
173C2×#216C2314yes—
174#942—28no—
175C2×#215—28no—
176C2×#215C2314yes—
177C2×#215C2314yes—
178C2×#215C2314yes—
179D4×Dic3—22no—
180D4×Dic3—21no—
181C4×#67—21no—
182C4×#67—22no—
183C4×#67—21no—
184C4×#67—22no—
185C2×(C2×D3)⋊C4—21no—
186C2×(C2×D3)⋊C4—22no—
187#926C2311yescharacteristic
188#926C2312yes—
189C2×C4⋊Dic3C2311yescharacteristic
190C2×C4⋊Dic3C2312yes—
191C2×#208C2312yes—
192C22×C3⋊C8C2312yes—
193#893—21no—
194#893—22no—
195#893—21no—
196#893—22no—
197#892—21no—
198#892—22no—
199D3×C4⋊C4—21no—
200D3×C4⋊C4—22no—
201#67⋊C4—22no—
202#67⋊C4—22no—
203#67⋊C4—22no—
204D3×C22⋊C4—22no—
205D3×C22⋊C4—22no—
206D3×C22⋊C4—22no—
207C4×D12—22no—
208C4×D12—21no—
209C4×D12—22no—
210C4×D12—21no—
211C4×D12C2312yes—
212C4×D12C2311yescharacteristic
213C4×D12C2312yes—
214C4×D12C2312yes—
215C4×D12C2312yes—
216C4×D12C2312yes—
217C4×D12C2311yescharacteristic
218#872—22no—
219#872—21no—
220C42×D3—22no—
221C42×D3—21no—
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2312yes—
224C4×Dic6C2311yescharacteristic
225#835C2314yes—
226#835C2314yes—
227#835C2314yes—
228#835C2314yes—
229#830C2314yes—
230#830C2314yes—
231#810C2312yes—
232#810C2312yes—
233#809C2314yes—
234#809C2314yes—
235#809C2312yes—
236#809C2312yes—
237#808C2314yes—
238#808C2312yes—
239#808C2312yes—
240#807C2314yes—
241#807C2312yes—
242#807C2312yes—
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×#137—32no—
252C22×SD16—32no—
253#557—21no—
254#557—21no—
255#556—21no—
256#556—21no—
257#552—22no—
258#552—22no—
259#541C2×D314yescomplemented
260#536C2×D312yes—
261#533C2×D312yescomplemented
262#533C2×D312yescomplemented
263#533C2×D311yescharacteristic, complemented
264C2×C4⋊Q8C2×D311yescharacteristic, complemented
265#520—31no—
266#520—32no—
267#520—31no—
268#520—61no—
269#519C2×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—31no—
279C2×C4×D4—32no—
280C2×C4×D4—62no—
281C2×C4×D4—61no—
282#485—34no—
283#485—34no—
284#484—34no—
285#483—34no—
286#479—32no—
287#478—32no—
288#478—34no—
289#477—31no—
290#476—31no—
291#476—32no—
292#475—31no—
293#474—31no—
294#474—32no—
295#462—32no—
296#462—32no—
297#461—32no—
298#461—32no—
299#461—32no—
300#461—34no—
301#461—32no—
302#452—34no—
303#452—34no—
304#450—34no—
305#450—34no—
306#441—34no—
307#440—34no—
308#440—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—
318#427—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#419—32no—
322#418—32no—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C23×D3—22no—
328C23×D3—21no—
329C3×#41—22no—
330C3×#41—22no—
331C2×C3×Q8—21no—
332C2×C3×Q8—21no—
333C2×C3×Q8—22no—
334C2×C3×Q8—24no—
335C2×C3×Q8—24no—
336C2×C3×Q8C2×D411yescharacteristic
337C2×C3×Q8C2414yes—
338C2×C3×D4C2×D412yes—
339C2×C3×D4C2×D411yescharacteristic
340C22×C3×C4—22no—
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D412yes—
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2×D412yes—
345C22×C3×C4C2412yes—
346C22×C3×C4C2411yescharacteristic
347C2×#67—22no—
348C2×#67—21no—
349C22×Dic3—22no—
350C22×Dic3—21no—
351#239—28no—
352D3×D4—216no—
353D3×D4—28no—
354#235—22no—
355#235—24no—
356#235—24no—
357#235#4114yes—
358C2×D12—22no—
359C2×D12—21no—
360C2×D12—22no—
361C2×D12—24no—
362C2×D12—24no—
363C2×D12#4114yes—
364C2×D12C2411yescharacteristic
365C2×D12C2412yes—
366C2×C4×D3—22no—
367C2×C4×D3—21no—
368C2×C4×D3—22no—
369C2×C4×D3—21no—
370C2×C4×D3—22no—
371C2×C4×D3—21no—
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—82no—
376C2×C4×D3—84no—
377C2×Dic6C2411yescharacteristic
378C3×C4⋊C4—22no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4—22no—
382C3×C4⋊C4—21no—
383C3×C4⋊C4—21no—
384C3×C4⋊C4—24no—
385C3×C4⋊C4—24no—
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—24no—
389C3×C4⋊C4—24no—
390C3×C4⋊C4C2×D411yescharacteristic
391C3×C4⋊C4C2×D412yes—
392C3×C4⋊C4C2×D411yescharacteristic
393C3×C4⋊C4C2×D412yes—
394C3×C4⋊C4C2412yes—
395C3×C4⋊C4C2412yes—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—24no—
398C3×C22⋊C4—24no—
399C3×C22⋊C4C2×D412yes—
400C3×C22⋊C4C2×D412yes—
401C3×C22⋊C4C2×D412yes—
402C3×C42—24no—
403C3×C42—24no—
404C3×C42—22no—
405C3×C42C2×D412yes—
406C3×C42C2×D411yescharacteristic
407C3×C42C2×D412yes—
408C3×C42C2×D411yescharacteristic
409C3×C42C2412yes—
410C3×C42C2411yescharacteristic
411C3×C42C2411yescharacteristic
412#217—22no—
413#217—21no—
414#216—28no—
415#215—28no—
416#215—28no—
417#215—28no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—21no—
420(C2×D3)⋊C4—22no—
421(C2×D3)⋊C4—21no—
422(C2×D3)⋊C4—22no—
423(C2×D3)⋊C4—22no—
424(C2×D3)⋊C4—22no—
425C4⋊Dic3—22no—
426C4⋊Dic3—21no—
427C4⋊Dic3C2412yes—
428C4⋊Dic3C2411yescharacteristic
429C4⋊Dic3C2411yescharacteristic
430Dic3⋊C4—21no—
431Dic3⋊C4—22no—
432Dic3⋊C4—21no—
433C4×Dic3—21no—
434C4×Dic3—22no—
435C4×Dic3—21no—
436C4×Dic3—22no—
437C4×Dic3—21no—
438#208—24no—
439C2×C3⋊C8—24no—
440C2×C3⋊C8C2412yes—
441C2×C3⋊C8C2414yes—
442C2×C3⋊C8C2412yes—
443H(5,𝔽2)—64no—
444H(5,𝔽2)—64no—
445C2×#41—31no—
446C2×#41—32no—
447C2×#41—61no—
448C2×#41C22×D311yescharacteristic
449C22×Q8C22×D312yes—
450C22×D4—31no—
451C22×D4—32no—
452C22×D4—62no—
453C22×D4—61no—
454C23×C4—61no—
455C23×C4—62no—
456#137—68no—
457C2×Q16—34no—
458C2×SD16—34no—
459C2×SD16—34no—
460C2×SD16—34no—
461C2×SD16—68no—
462C2×M16—32no—
463C22×C8—32no—
464C4⋊Q8—22no—
465C4⋊Q8—21no—
466C4⋊Q8—21no—
467C4⋊Q8C22×D312yes—
468C4⋊Q8C22×D312yes—
469C4⋊Q8C22×D311yescharacteristic
470C4⋊Q8C22×D311yescharacteristic
471#126—24no—
472#126—24no—
473#125—24no—
474#125—24no—
475#125—22no—
476#125—22no—
477#125C22×D312yes—
478#124—22no—
479#123—24no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—22no—
483C22⋊Q8—22no—
484C22⋊Q8C22×D314yes—
485C22⋊Q8C22×D314yes—
486C4×Q8—22no—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—31no—
493C4×Q8—32no—
494C4×Q8—31no—
495C4×Q8—61no—
496C4×Q8#6711yescharacteristic
497C4×Q8#6711yescharacteristic
498C4×Q8C22×D314yes—
499C4×Q8C22×D314yes—
500C4×D4—32no—
501C4×D4—31no—
502C4×D4—32no—
503C4×D4—32no—
504C4×D4—32no—
505C4×D4—32no—
506C4×D4—31no—
507C4×D4—62no—
508C4×D4—61no—
509C4×D4—61no—
510C4×D4—62no—
511C4×D4—61no—
512C4×D4—62no—
513C4×D4—61no—
514C4×D4—62no—
515C4×D4—61no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—61no—
524C4×D4#6712yes—
525C4×D4#6711yescharacteristic
526C4×D4#6712yes—
527C4×D4#6711yescharacteristic
528#117—22no—
529#117—22no—
530#117—24no—
531#117—31no—
532#117—32no—
533#117—61no—
534#117—62no—
535#117—62no—
536#117—61no—
537#117C22×D312yes—
538#117C22×D311yescharacteristic
539#117C22×D312yes—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—32no—
544C2×C4⋊C4—61no—
545C2×C4⋊C4—62no—
546C2×C22⋊C4—61no—
547C2×C22⋊C4—62no—
548C2×C22⋊C4—62no—
549C2×C22⋊C4—62no—
550C2×C22⋊C4—62no—
551C2×C42—62no—
552C2×C42—61no—
553C2×C42C22×D311yescharacteristic
554C2×C42C22×D312yes—
555#107—32no—
556#107—32no—
557#107—34no—
558#106—32no—
559#106—32no—
560#106—34no—
561C4⋊C8—31no—
562C4⋊C8—31no—
563C4⋊C8—32no—
564C4⋊C8—32no—
565C4⋊C8—32no—
566#103—34no—
567#103—34no—
568#103—34no—
569#103—34no—
570#103—32no—
571#103—32no—
572#102—32no—
573#102—32no—
574#102—34no—
575#102—34no—
576C22⋊C8—34no—
577C22⋊C8—34no—
578#97—34no—
579C4×C8—34no—
580C23×C3C22×D412yes—
581C23×C3C22×D411yescharacteristic
582C22×D3—22no—
583C22×D3—21no—
584C22×D3—28no—
585C22×D3—24no—
586C22×D3—81no—
587C22×D3—82no—
588C22×D3—81no—
589C22×D3—82no—
590C3×Q8—22no—
591C3×Q8—24no—
592C3×Q8—24no—
593C3×Q8—42no—
594C3×Q8—44no—
595C3×Q8—42no—
596C3×D4—24no—
597C3×D4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—24no—
600C2×C3×C4—22no—
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×C4C22×D412yes—
609C2×C3×C4C22×D412yes—
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D412yes—
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C2×#4112yes—
617C2×C3×C4C2×#4112yes—
618C2×C3×C4C2511yescharacteristic
619#67—28no—
620#67—24no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—22no—
624C2×Dic3—21no—
625C2×Dic3—81no—
626C2×Dic3—82no—
627D12—28no—
628D12—24no—
629D12—21no—
630D12—22no—
631D12C2×#4112yes—
632D12C2×#4114yes—
633C4×D3—28no—
634C4×D3—24no—
635C4×D3—44no—
636C4×D3—42no—
637C4×D3—82no—
638C4×D3—81no—
639C4×D3—82no—
640C4×D3—82no—
641C4×D3—82no—
642Dic6—21no—
643Dic6C2×#4112yes—
644C3⋊C8—22no—
645C3⋊C8—22no—
646C3⋊C8—24no—
647C24—62no—
648C24—61no—
649#41—22no—
650#41—22no—
651#41—34no—
652#41—64no—
653#41—64no—
654#41—68no—
655#41—62no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—22no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—31no—
662C2×Q8C2×#6711yescharacteristic
663C2×Q8C23×D314yes—
664C2×D4—34no—
665C2×D4—32no—
666C2×D4—31no—
667C2×D4—64no—
668C2×D4—64no—
669C2×D4—616no—
670C2×D4—68no—
671C2×D4—62no—
672C2×D4—61no—
673C2×D4—62no—
674C2×D4—62no—
675C2×D4—61no—
676C2×D4C2×#6712yes—
677C2×D4C2×#6711yescharacteristic
678C22×C4—22no—
679C22×C4—62no—
680C22×C4—61no—
681C22×C4—62no—
682C22×C4—61no—
683C22×C4—62no—
684C22×C4—61no—
685C22×C4—62no—
686C22×C4—61no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—242no—
691C22×C4—244no—
692C22×C4C2×#6711yescharacteristic
693C22×C4C2×#6712yes—
694C22×C4C2×#6711yescharacteristic
695C22×C4C2×#6712yes—
696C22×C4C23×D312yes—
697C22×C4C23×D311yescharacteristic
698Q16—68no—
699SD16—68no—
700SD16—68no—
701SD16—68no—
702M16—64no—
703C2×C8—32no—
704C2×C8—34no—
705C2×C8—32no—
706C2×C8—64no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—24no—
714C4⋊C4—24no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—32no—
720C4⋊C4—31no—
721C4⋊C4—31no—
722C4⋊C4—62no—
723C4⋊C4—61no—
724C4⋊C4—62no—
725C4⋊C4—61no—
726C4⋊C4—61no—
727C4⋊C4C2×#6711yescharacteristic
728C4⋊C4C2×#6712yes—
729C4⋊C4C2×#6711yescharacteristic
730C4⋊C4C2×#6712yes—
731C4⋊C4C23×D312yes—
732C4⋊C4C23×D312yes—
733C22⋊C4—22no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—62no—
737C22⋊C4—61no—
738C22⋊C4—62no—
739C22⋊C4—61no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—61no—
745C22⋊C4C2×#6712yes—
746C22⋊C4C2×#6712yes—
747C22⋊C4C2×#6712yes—
748C42—24no—
749C42—24no—
750C42—22no—
751C42—61no—
752C42—62no—
753C42—61no—
754C42—62no—
755C42—61no—
756C42C2×#6712yes—
757C42C2×#6711yescharacteristic
758C42C2×#6712yes—
759C42C2×#6711yescharacteristic
760C42C23×D312yes—
761C42C23×D311yescharacteristic
762C42C23×D311yescharacteristic
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3#52512yes—
769C22×C3C23×D411yescharacteristic
770C2×D3—24no—
771C2×D3—22no—
772C2×D3—42no—
773C2×D3—41no—
774C2×D3—42no—
775C2×D3—41no—
776C2×D3—84no—
777C2×D3—88no—
778C3×C4—22no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—21no—
784C3×C4—42no—
785C3×C4—44no—
786C3×C4—42no—
787C3×C4#52512yes—
788C3×C4#57712yes—
789C3×C4C22×#4111yescharacteristic
790C3×C4C22×#4111yescharacteristic
791Dic3—22no—
792Dic3—41no—
793Dic3—42no—
794Dic3—41no—
795C23—68no—
796C23—62no—
797C23—61no—
798C23—64no—
799C23—241no—
800C23—242no—
801C23—241no—
802C23—242no—
803C23C22×#6712yes—
804C23C22×#6711yescharacteristic
805Q8—22no—
806Q8—24no—
807Q8—24no—
808Q8—32no—
809Q8—42no—
810Q8—44no—
811Q8—42no—
812Q8—61no—
813D4—24no—
814D4—22no—
815D4—34no—
816D4—32no—
817D4—68no—
818D4—68no—
819D4—64no—
820D4—61no—
821D4—62no—
822D4—64no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—44no—
833C2×C4—68no—
834C2×C4—61no—
835C2×C4—64no—
836C2×C4—61no—
837C2×C4—62no—
838C2×C4—61no—
839C2×C4—124no—
840C2×C4—122no—
841C2×C4—242no—
842C2×C4—242no—
843C2×C4—242no—
844C2×C4—242no—
845C2×C4—241no—
846C2×C4—241no—
847C2×C4—242no—
848C2×C4D3×#4112yes—
849C2×C4D3×#4112yes—
850C2×C4C22×#6712yes—
851C2×C4C22×#6712yes—
852C2×C4C22×#6712yes—
853C2×C4C22×#6711yescharacteristic
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×C3C2×#52511yescharacteristic
865C2×C3C2×#57711yescharacteristic
866C2×C3#358611yescharacteristic
867D3—44no—
868D3—42no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—64no—
875C22—62no—
876C22—122no—
877C22—121no—
878C22—122no—
879C22—121no—
880C22—244no—
881C22—248no—
882C22#582812yes—
883C22C23×#6711yescharacteristic
884C4—22no—
885C4—22no—
886C4—21no—
887C4—21no—
888C4—22no—
889C4—21no—
890C4—44no—
891C4—42no—
892C4—42no—
893C4—62no—
894C4—122no—
895C4—121no—
896C4—121no—
897C4#582812yes—
898C4#583712yes—
899C4C2×D3×#4111yescharacteristic
900C4C2×D3×#4111yescharacteristic
901C3#6059111yescharacteristic, complemented, Sylow
902C2—22no—
903C2—42no—
904C2—124no—
905C2—122no—
906C2C2×#582811yescharacteristic
907C2C2×#583711yescharacteristic
908C2#8728711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3509C2
socleC22×C3C23×D4
prime radicalC2×#1009C22
hypercenter#3509D3
hypocenterC3#60591
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. C3×#3509C2semidirect
3. #83447C2semidirect
4. #83446C2semidirect
6. #83397C2semidirect
7. #83354C2semidirect
8. #83353C2semidirect
9. #83352C2semidirect
10. #83351C2semidirect
11. #83350C2semidirect
12. #83349C2semidirect
13. #83209C2semidirect
14. C2×#5083C2semidirect
15. #82548C2semidirect
16. #82547C2semidirect
17. #82515C2semidirect
26. C3×#541C22semidirect
28. C3×#533C22semidirect
29. C3×#533C22semidirect
30. C3×#533C22semidirect
31. C2×C3×C4⋊Q8C22semidirect
32. C3×#519C22semidirect
52. #5225C22semidirect
53. C2×#835C22semidirect
54. #5094C22semidirect
55. #5091C22semidirect
56. #5090C22semidirect
57. #5090C22semidirect
58. #5087C22semidirect
59. #5087C22semidirect
60. #5084C22semidirect
61. #5084C22semidirect
62. #5083C22semidirect
63. #5083C22semidirect
64. #5083C22semidirect
65. #5083C22semidirect
66. #5083C22semidirect
67. #5066C22semidirect
68. #5066C22semidirect
69. #5063C22semidirect
74. #5045C22semidirect
75. #5045C22semidirect
76. #5044C22semidirect
77. #5043C22semidirect
78. #5030C22semidirect
79. C4×#216C22semidirect
80. #5026C22semidirect
81. #5026C22semidirect
82. #5026C22semidirect
83. C4×#215C22semidirect
84. C4×#215C22semidirect
85. C4×#215C22semidirect
88. #5000C22semidirect
89. #4998C22semidirect
90. #4997C22semidirect
91. #4995C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
94. #4924C22semidirect
95. C2×C4⋊(C3⋊C8)C22semidirect
96. #3509D3semidirect
259. #541C2×D3semidirect
261. #533C2×D3semidirect
262. #533C2×D3semidirect
263. #533C2×D3semidirect
264. C2×C4⋊Q8C2×D3semidirect
269. #519C2×D3semidirect
901. C3#60591semidirect

Maximal subgroups

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

subgroupindex
C3×#35092
C4×#10092
#834472
#834462
#834042
#833972
#833542
#833532
#833522
#833512
#833502
#833492
#832092
C2×#50832
#825482
#825472
#825152
#605913