Finite Group Databasebeta

← #11670684

Subgroups — #11670684

Order 768.

2686 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5778C211yesmaximal, characteristic, complemented
2C22×#918C211yesmaximal, characteristic, complemented
3#86354C211yesmaximal, characteristic, complemented
4#85881C211yesmaximal, characteristic, complemented
5C3×#3044C211yesmaximal, characteristic, complemented
6#83979C211yesmaximal, characteristic, complemented
7#83884C211yesmaximal, characteristic, complemented
8#83403C211yesmaximal, characteristic, complemented
9#82548C211yesmaximal, characteristic, complemented
10#80629C214yesmaximal, complemented
11#80627C214yesmaximal, complemented
12#80501C214yesmaximal, complemented
13#80500C214yesmaximal, complemented
14#79087C211yesmaximal, characteristic, complemented
15#79074C211yesmaximal, characteristic, complemented
16#78964C211yesmaximal, characteristic, complemented
17#78959C211yesmaximal, characteristic, complemented
18#78839C211yesmaximal, characteristic, complemented
19#78835C211yesmaximal, characteristic, complemented
20#61060—31nomaximal, Sylow
21C2×#1009C2211yescharacteristic
22C2×#1007C2211yescharacteristic
23C22×#239C2211yescharacteristic
24C22×D3×Q8C2211yescharacteristic, complemented
25C2×C3×#137C2211yescharacteristic
26C22×C3×Q16C2211yescharacteristic, complemented
27C3×#536C2211yescharacteristic
28C3×#519C2211yescharacteristic, complemented
29#5828C2211yescharacteristic
30C2×#951C2211yescharacteristic
31C2×#950C2211yescharacteristic
32#5816C2211yescharacteristic
33C22×#216C2211yescharacteristic, complemented
34C2×#942C2211yescharacteristic, complemented
35C22×#215C2211yescharacteristic
36#5778—28no—
37C2×#919C2212yescomplemented
38C2×#918—28no—
39C2×#918C2214yescomplemented
40C2×#918C2212yescomplemented
41C2×#918C2214yescomplemented
42C2×#914C2212yescomplemented
43C2×D3×SD16C2212yescomplemented
44C2×#908C2211yescharacteristic
45C2×#907C2211yescharacteristic
46C22×#204C2211yescharacteristic
47C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
48#5726C2214yes—
49#5676C2214yes—
50#5653—22no—
51D3×#123—22no—
52#5631—22no—
53#5630—22no—
54#5576—22no—
55#5576C2214yescomplemented
56Q8×D12—22no—
57Q8×D12C2214yescomplemented
58#5526—22no—
59#5526C2211yescharacteristic
60#5526C2211yescharacteristic, complemented
61#5524—22no—
62#5524C2211yescharacteristic
63#5524C2211yescharacteristic, complemented
64#5521C2211yescharacteristic
65C3×#464C2214yescomplemented
66C3×#462C2214yescomplemented
67C3×#424C2211yescharacteristic, complemented
68C3×#419C2211yescharacteristic, complemented
69C3×#416C2211yescharacteristic
70#5225C2211yescharacteristic, complemented
71#5187C2214yescomplemented
72#5186C2214yescomplemented
73#5186C2214yescomplemented
74#5170C2214yescomplemented
75#5126C2211yescharacteristic, complemented
76#5120C2211yescharacteristic, complemented
77#5113C2211yescharacteristic, complemented
78#5110C2211yescharacteristic
79#5092C2212yescomplemented
80#5086C2212yescomplemented
81#5060C2212yescomplemented
82#5059C2212yescomplemented
83#5026C2214yescomplemented
84C4×#215C2214yescomplemented
85#5001C2211yescharacteristic
86#4998C2211yescharacteristic, complemented
87#4997C2211yescharacteristic, complemented
88#4844C2214yescomplemented
89#4841C2214yescomplemented
90#4838C2214yescomplemented
91#4836C2214yescomplemented
92#4816C2214yescomplemented
93#4816C2212yescomplemented
94#4813C2214yescomplemented
95#4812C2212yescomplemented
96#4810C2214yescomplemented
97#4808C2214yescomplemented
98#4808C2214yescomplemented
99#4782C2212yescomplemented
100#4780C2212yescomplemented
101#4776C2214yescomplemented
102C2×#577—31no—
103C22×#137—31no—
104#3486—31no—
105#3485—31no—
106#3276—34no—
107#3275—34no—
108#3269—34no—
109#3266—34no—
110#3156—31no—
111#3059—31no—
112#3054—31no—
113#3044D311yescharacteristic, complemented
114#3042—31no—
115#3011—31no—
116#3009—31no—
117#3005—31no—
118#3004—31no—
119#2949—31no—
120#2930—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8C2311yescharacteristic
123C22×C3×Q8C2311yescharacteristic
124#1009—24no—
125#1009—42no—
126#1007—24no—
127#1007—42no—
128C2×#239—21no—
129C2×#239—22no—
130C2×#239—24no—
131C2×#239—42no—
132C2×#239C2314yes—
133C2×#239C2312yes—
134C2×#239C2312yes—
135C2×D3×Q8—22no—
136C2×D3×Q8—21no—
137C2×D3×Q8—24no—
138C2×D3×Q8—42no—
139C2×D3×Q8C2314yes—
140C2×D3×Q8C2312yes—
141C2×D3×D4—22no—
142C2×D3×D4C2312yes—
143C2×#235—22no—
144C2×#235—21no—
145C2×#235C2311yescharacteristic
146C2×#235C2311yescharacteristic
147C22×D12—21no—
148C22×D12—21no—
149C22×D12C2311yescharacteristic
150C22×C4×D3—21no—
151C22×C4×D3—21no—
152C22×C4×D3C2311yescharacteristic
153C22×Dic6—21no—
154C22×Dic6C2311yescharacteristic
155C3×#137—24no—
156C2×C3×Q16—24no—
157C2×C3×Q16C2314yes—
158C2×C3×Q16C2312yes—
159C2×C3×SD16C2312yes—
160C2×C3×M16C2311yescharacteristic
161C22×C3×C8C2311yescharacteristic
162C3×C4⋊Q8C2312yes—
163C3×#124C2312yes—
164C3×#123—22no—
165C3×C22⋊Q8—22no—
166C3×C4×Q8—22no—
167C3×C4×Q8C2314yes—
168C3×#117—22no—
169C3×#117C2311yescharacteristic
170C3×#117C2311yescharacteristic
171#951—42no—
172#950—24no—
173#947—21no—
174#946C2314yes—
175#946C2312yes—
176#944—21no—
177C2×#216—24no—
178C2×#216C2312yes—
179C2×#216C2312yes—
180C2×#216C2311yescharacteristic
181C2×#216C2312yes—
182C2×#216C2312yes—
183#942—42no—
184C2×#215D418yescomplemented
185C2×#215C2311yescharacteristic
186C2×#215C2312yes—
187C2×#215C2312yes—
188C2×#215C2312yes—
189#938C2312yes—
190#937—21no—
191#935—21no—
192C2×#214C2311yescharacteristic
193C2×#214C2312yes—
194C2×#213C2311yescharacteristic
195#929—22no—
196C4×#67—22no—
197#926C2311yescharacteristic
198C2×#208C2311yescharacteristic
199C22×C3⋊C8C2311yescharacteristic
200#919—28no—
201#918—216no—
202#918—216no—
203#918—28no—
204#914—28no—
205D3×SD16—28no—
206#908—24no—
207#907—24no—
208C2×D24C2312yes—
209C2×#204—24no—
210C2×#204C2314yes—
211C2×#204C2312yes—
212C2×ΓL(1,𝔽25)—24no—
213C2×ΓL(1,𝔽25)C2312yes—
214C2×ΓL(1,𝔽25)C2312yes—
215C2×ΓL(1,𝔽25)C2312yes—
216C2×D3×C8C2312yes—
217#897—22no—
218#897—24no—
219#897—24no—
220#897—24no—
221#897D412yes—
222#897C2312yes—
223#897C2314yes—
224#895—24no—
225#895—24no—
226#895D412yes—
227#895C2312yes—
228#894—24no—
229#894—24no—
230#893—22no—
231D3×C4⋊C4—24no—
232#886—22no—
233#886—21no—
234#886—22no—
235#886D412yes—
236#884—24no—
237#883—24no—
238#882—21no—
239#882—24no—
240#882D412yes—
241D3×C22⋊C4—22no—
242D3×C22⋊C4—24no—
243#875—21no—
244#875—24no—
245#875C2312yes—
246C4×D12—24no—
247C4×D12—22no—
248C4×D12—24no—
249C4×D12C2314yes—
250C4×D12C2314yes—
251#869—21no—
252#869—24no—
253#869C2312yes—
254C3×C4⋊C8C2314yes—
255C3×#103C2312yes—
256C3×#103C2314yes—
257C3×#102C2312yes—
258#835C2314yes—
259#821C2312yes—
260(C2×D3)⋊C8C2314yes—
261(C2×D3)⋊C8C2314yes—
262#816C2314yes—
263#816C2312yes—
264#809C2314yes—
265#808C2312yes—
266#807C2312yes—
267#803C2312yes—
268C4×C3⋊C8C2312yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C23×Q8—31no—
273#577—68no—
274C2×#137—31no—
275C2×#137—31no—
276C2×#137—34no—
277C2×#137—34no—
278C2×#137—32no—
279C2×#137—68no—
280C2×#137C2×D311yescharacteristic
281C2×AGL(1,ℤ/8)—32no—
282C2×AGL(1,ℤ/8)—31no—
283C2×#135—31no—
284C2×#135—32no—
285C22×Q16—31no—
286C22×Q16C2×D311yescharacteristic, complemented
287C22×SD16—31no—
288C22×SD16—32no—
289C22×SD16—31no—
290C2×#131—31no—
291C22×M16—31no—
292D4×Q8—34no—
293D4×Q8—62no—
294#548—34no—
295#548—62no—
296#547—34no—
297#547—62no—
298#546—34no—
299#546—62no—
300#536—31no—
301#536—31no—
302#536—31no—
303#536—62no—
304#536C2×D311yescharacteristic
305#534—62no—
306#525—31no—
307#525—31no—
308#525—31no—
309#525—62no—
310C2×#123—62no—
311#519C2×D311yescharacteristic, complemented
312#518—31no—
313#497—32no—
314#497—32no—
315#495—32no—
316#494—32no—
317#470—34no—
318#470—32no—
319#469—32no—
320#468—32no—
321#468—32no—
322#467—34no—
323#464C2×D314yescomplemented
324#463—34no—
325#462C2×D314yescomplemented
326#461—34no—
327#452—34no—
328#452—34no—
329#452—34no—
330#451—34no—
331#451—34no—
332#450—34no—
333#449—34no—
334#448—34no—
335#440—34no—
336C4×SD16—34no—
337#436—34no—
338#435—34no—
339#427—31no—
340#424C2×D311yescharacteristic, complemented
341#419—31no—
342#419—31no—
343#419C2×D311yescharacteristic, complemented
344#418—31no—
345#416—31no—
346#416C2×D311yescharacteristic
347#408—31no—
348#407—31no—
349#405—31no—
350C23×D3—21no—
351C23×D3—22no—
352C23×D3C2×D411yescharacteristic
353C3×#41—22no—
354C3×#41—22no—
355C2×C3×Q8—21no—
356C2×C3×Q8—21no—
357C2×C3×Q8—22no—
358C2×C3×Q8—22no—
359C2×C3×Q8—22no—
360C2×C3×Q8C2×D414yes—
361C2×C3×Q8C2412yes—
362C2×C3×Q8C2411yescharacteristic
363C2×C3×Q8C2412yes—
364C2×C3×D4—21no—
365C2×C3×D4C2411yescharacteristic
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4C2411yescharacteristic
370C2×#67—21no—
371C2×#67—22no—
372C2×#67—22no—
373C2×#67C2×D412yes—
374C22×Dic3—21no—
375C22×Dic3C2×D411yescharacteristic
376#239—24no—
377#239—28no—
378#239—24no—
379#239—44no—
380#239—42no—
381#239—42no—
382#239—48no—
383#239—44no—
384D3×Q8—24no—
385D3×Q8—28no—
386D3×Q8—44no—
387D3×Q8—42no—
388D3×Q8—44no—
389D3×Q8—48no—
390D3×D4—24no—
391D3×D4—42no—
392D3×D4—48no—
393#235—22no—
394#235—22no—
395#235—22no—
396#235—22no—
397#235—44no—
398#235—48no—
399C2×D12—21no—
400C2×D12—22no—
401C2×D12—22no—
402C2×D12—22no—
403C2×D12—24no—
404C2×D12—22no—
405C2×D12—44no—
406C2×D12—44no—
407C2×D12C2×D411yescharacteristic
408C2×D12C2×D414yes—
409C2×D12C2×D414yes—
410C2×D12C2411yescharacteristic
411C2×D12C2412yes—
412C2×C4×D3—22no—
413C2×C4×D3—22no—
414C2×C4×D3—24no—
415C2×C4×D3—22no—
416C2×C4×D3—21no—
417C2×C4×D3—22no—
418C2×C4×D3—24no—
419C2×C4×D3—22no—
420C2×C4×D3—24no—
421C2×C4×D3—44no—
422C2×C4×D3—44no—
423C2×C4×D3C2×D412yes—
424C2×C4×D3C2412yes—
425C2×C4×D3C2412yes—
426C2×Dic6—22no—
427C2×Dic6—22no—
428C2×Dic6—21no—
429C2×Dic6—22no—
430C2×Dic6—24no—
431C2×Dic6—44no—
432C2×Dic6C2×D411yescharacteristic
433C2×Dic6C2411yescharacteristic
434C2×Dic6C2412yes—
435C3×Q16—28no—
436C3×Q16—24no—
437C3×SD16—24no—
438C3×M16—22no—
439C2×C3×C8—22no—
440C2×C3×C8C2412yes—
441C2×C3×C8C2412yes—
442C3×C4⋊C4—24no—
443C3×C4⋊C4—24no—
444C3×C4⋊C4C2×D412yes—
445C3×C4⋊C4C2412yes—
446C3×C22⋊C4—21no—
447C3×C22⋊C4—24no—
448C3×C22⋊C4C2×D412yes—
449C3×C42—24no—
450C3×C42—21no—
451C3×C42C2412yes—
452#217—21no—
453#217—22no—
454#216—24no—
455#216—24no—
456#216—22no—
457#216—42no—
458#216—42no—
459#215—22no—
460#215—42no—
461#215C2×D418yes—
462#215C2×D418yes—
463#214—22no—
464#214—42no—
465#213—22no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—24no—
468(C2×D3)⋊C4—24no—
469(C2×D3)⋊C4—22no—
470(C2×D3)⋊C4—24no—
471(C2×D3)⋊C4—24no—
472(C2×D3)⋊C4—22no—
473(C2×D3)⋊C4C2×D414yes—
474(C2×D3)⋊C4C2×D414yes—
475C4⋊Dic3—24no—
476C4⋊Dic3—22no—
477C4⋊Dic3—24no—
478C4⋊Dic3C2×D414yes—
479C4⋊Dic3C2412yes—
480Dic3⋊C4—24no—
481Dic3⋊C4—22no—
482C4×Dic3—21no—
483#208—22no—
484C2×C3⋊C8C2×D414yes—
485C2×C3⋊C8C2412yes—
486C2×C3⋊C8C2411yescharacteristic
487C2×C3⋊C8C2411yescharacteristic
488D24—24no—
489#204—28no—
490#204—24no—
491ΓL(1,𝔽25)—24no—
492ΓL(1,𝔽25)—24no—
493ΓL(1,𝔽25)—24no—
494D3×C8—24no—
4952−1+4—64no—
4962−1+4—122no—
497H(5,𝔽2)—64no—
498H(5,𝔽2)—122no—
499C2×#41—31no—
500C2×#41—34no—
501C2×#41—32no—
502C2×#41—32no—
503C2×#41—31no—
504C2×#41—62no—
505C2×#41—61no—
506C2×#41—62no—
507C2×#41—61no—
508C2×#41—64no—
509C2×#41—122no—
510C2×#41C22×D311yescharacteristic
511C22×Q8—34no—
512C22×Q8—32no—
513C22×Q8—31no—
514C22×Q8—61no—
515C22×Q8—62no—
516C22×Q8—61no—
517C22×Q8—64no—
518C22×Q8—122no—
519C22×Q8C22×D311yescharacteristic
520C22×Q8C22×D311yescharacteristic
521C22×D4—32no—
522C22×D4—31no—
523C22×D4—61no—
524C22×D4—61no—
525C22×D4—62no—
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—24no—
530#137—616no—
531#137—616no—
532#137—68no—
533#137—122no—
534#137—122no—
535AGL(1,ℤ/8)—64no—
536AGL(1,ℤ/8)—68no—
537#135—64no—
538#135—68no—
539C2×Q16—24no—
540C2×Q16—32no—
541C2×Q16—32no—
542C2×Q16—31no—
543C2×Q16—32no—
544C2×Q16—32no—
545C2×Q16—64no—
546C2×Q16C22×D314yes—
547C2×Q16C22×D312yes—
548C2×SD16—38no—
549C2×SD16—32no—
550C2×SD16—32no—
551C2×SD16—31no—
552C2×SD16—31no—
553C2×SD16—32no—
554C2×SD16—32no—
555C2×SD16—32no—
556C2×SD16—34no—
557C2×SD16—64no—
558C2×SD16—68no—
559C2×SD16C22×D312yes—
560C2×D8—31no—
561C2×D8—32no—
562#131—64no—
563C2×M16—31no—
564C2×M16—32no—
565C2×M16—32no—
566C2×M16—32no—
567C2×M16—64no—
568C2×M16C22×D311yescharacteristic
569C22×C8—31no—
570C22×C8—32no—
571C22×C8C22×D311yescharacteristic
572C4⋊Q8—32no—
573C4⋊Q8—64no—
574C4⋊Q8—61no—
575C4⋊Q8—61no—
576C4⋊Q8C22×D312yes—
577#124—32no—
578#124—64no—
579#124—61no—
580#124—61no—
581#124C22×D312yes—
582#123—22no—
583#123—32no—
584#123—64no—
585#123—61no—
586#123—62no—
587#123—64no—
588#123—64no—
589#123—62no—
590#123—61no—
591#123—62no—
592C22⋊Q8—22no—
593C22⋊Q8—32no—
594C22⋊Q8—32no—
595C22⋊Q8—34no—
596C22⋊Q8—32no—
597C22⋊Q8—34no—
598C22⋊Q8—64no—
599C22⋊Q8—64no—
600C22⋊Q8—64no—
601C22⋊Q8—62no—
602#121—32no—
603#121—32no—
604#121—32no—
605#121—64no—
606#121—64no—
607#121—64no—
608#120—32no—
609#120—64no—
610#120—61no—
611#120—61no—
612C4×Q8—22no—
613C4×Q8C22×D314yes—
614C4×D4—34no—
615C4×D4—34no—
616C4×D4—64no—
617C4×D4—62no—
618C4×D4—64no—
619C4×D4—62no—
620C4×D4—62no—
621#117—22no—
622#117—31no—
623#117C22×D311yescharacteristic
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—64no—
627C2×C22⋊C4—62no—
628#107—32no—
629#106—32no—
630C4⋊C8C22×D314yes—
631#103—34no—
632#103—32no—
633#103—34no—
634#103C22×D312yes—
635#103C22×D314yes—
636#102—32no—
637#102—34no—
638#102C22×D312yes—
639C22⋊C8—34no—
640C22⋊C8—34no—
641#97—32no—
642C4×C8—32no—
643C23×C3—21no—
644C23×C3C22×D411yescharacteristic
645C22×D3—22no—
646C22×D3—22no—
647C22×D3—24no—
648C22×D3—21no—
649C22×D3—42no—
650C22×D3—44no—
651C22×D3—84no—
652C22×D3—82no—
653C22×D3C22×D412yes—
654C22×D3C22×D412yes—
655C3×Q8—24no—
656C3×Q8—22no—
657C3×Q8—21no—
658C3×Q8—22no—
659C3×Q8—22no—
660C3×Q8—21no—
661C3×Q8—42no—
662C3×Q8C22×D414yes—
663C3×D4—21no—
664C3×D4—21no—
665C3×D4—42no—
666C2×C3×C4—24no—
667C2×C3×C4—22no—
668C2×C3×C4—22no—
669C2×C3×C4—21no—
670C2×C3×C4—22no—
671C2×C3×C4—42no—
672C2×C3×C4—42no—
673C2×C3×C4C22×D414yes—
674C2×C3×C4C22×D411yescharacteristic
675C2×C3×C4C22×D412yes—
676C2×C3×C4H(5,𝔽2)12yes—
677C2×C3×C4C2511yescharacteristic
678#67—24no—
679#67—44no—
680#67—42no—
681#67—82no—
682C2×Dic3—22no—
683C2×Dic3—22no—
684C2×Dic3—21no—
685C2×Dic3—22no—
686C2×Dic3—42no—
687C2×Dic3C22×D412yes—
688C2×Dic3C22×D412yes—
689D12—24no—
690D12—22no—
691D12—21no—
692D12—22no—
693D12—21no—
694D12—44no—
695D12—44no—
696D12—44no—
697D12—48no—
698D12—44no—
699D12C22×D414yes—
700C4×D3—24no—
701C4×D3—22no—
702C4×D3—22no—
703C4×D3—22no—
704C4×D3—22no—
705C4×D3—44no—
706C4×D3—48no—
707C4×D3—44no—
708C4×D3—48no—
709C4×D3—44no—
710C4×D3—42no—
711C4×D3—84no—
712Dic6—22no—
713Dic6—21no—
714Dic6—22no—
715Dic6—22no—
716Dic6—21no—
717Dic6—48no—
718Dic6—44no—
719Dic6—42no—
720C3×C8—22no—
721C3×C8—22no—
722C3⋊C8—22no—
723C3⋊C8C22×D412yes—
724C3⋊C8C22×D412yes—
725C24—31no—
726C24—62no—
727C24—61no—
728#41—22no—
729#41—22no—
730#41—62no—
731#41—62no—
732#41—64no—
733#41—68no—
734#41—64no—
735#41—62no—
736#41—62no—
737#41—128no—
738#41—124no—
739#41—124no—
740#41—122no—
741#41—122no—
742#41—128no—
743#41—124no—
744C2×Q8—21no—
745C2×Q8—21no—
746C2×Q8—22no—
747C2×Q8—22no—
748C2×Q8—22no—
749C2×Q8—31no—
750C2×Q8—32no—
751C2×Q8—31no—
752C2×Q8—64no—
753C2×Q8—62no—
754C2×Q8—61no—
755C2×Q8—64no—
756C2×Q8—68no—
757C2×Q8—62no—
758C2×Q8—62no—
759C2×Q8—124no—
760C2×Q8—124no—
761C2×Q8—122no—
762C2×Q8—128no—
763C2×Q8—124no—
764C2×Q8D3×D414yes—
765C2×Q8C23×D312yes—
766C2×Q8C23×D311yescharacteristic
767C2×Q8C23×D312yes—
768C2×D4—21no—
769C2×D4—32no—
770C2×D4—34no—
771C2×D4—31no—
772C2×D4—34no—
773C2×D4—32no—
774C2×D4—31no—
775C2×D4—62no—
776C2×D4—64no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—62no—
780C2×D4—64no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—61no—
784C2×D4—62no—
785C2×D4—124no—
786C2×D4—124no—
787C2×D4—122no—
788C2×D4—128no—
789C2×D4C23×D311yescharacteristic
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—31no—
794C22×C4—32no—
795C22×C4—32no—
796C22×C4—32no—
797C22×C4—64no—
798C22×C4—62no—
799C22×C4—62no—
800C22×C4—64no—
801C22×C4—62no—
802C22×C4—62no—
803C22×C4—62no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—64no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4C23×D311yescharacteristic
810Q16—28no—
811Q16—24no—
812Q16—64no—
813Q16—64no—
814Q16—62no—
815Q16—122no—
816Q16—122no—
817SD16—24no—
818SD16—38no—
819SD16—38no—
820SD16—64no—
821SD16—68no—
822SD16—62no—
823SD16—62no—
824SD16—122no—
825SD16—122no—
826D8—64no—
827D8—62no—
828M16—22no—
829M16—64no—
830M16—64no—
831M16—64no—
832M16—62no—
833C2×C8—22no—
834C2×C8—34no—
835C2×C8—31no—
836C2×C8—31no—
837C2×C8—32no—
838C2×C8—64no—
839C2×C8C23×D312yes—
840C2×C8C23×D312yes—
841C4⋊C4—24no—
842C4⋊C4—24no—
843C4⋊C4—34no—
844C4⋊C4—32no—
845C4⋊C4—62no—
846C4⋊C4—64no—
847C4⋊C4—62no—
848C4⋊C4—64no—
849C4⋊C4—64no—
850C4⋊C4D3×D412yes—
851C4⋊C4C23×D312yes—
852C22⋊C4—21no—
853C22⋊C4—24no—
854C22⋊C4—34no—
855C22⋊C4—34no—
856C22⋊C4—62no—
857C22⋊C4—64no—
858C22⋊C4—62no—
859C22⋊C4—62no—
860C22⋊C4—64no—
861C22⋊C4—62no—
862C22⋊C4—61no—
863C22⋊C4—64no—
864C22⋊C4—64no—
865C22⋊C4D3×D412yes—
866C42—24no—
867C42—21no—
868C42—61no—
869C42C23×D312yes—
870C22×C3—22no—
871C22×C3—42no—
872C22×C3—41no—
873C22×C3D4212yes—
874C22×C3C23×D411yescharacteristic
875C2×D3—22no—
876C2×D3—24no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—24no—
881C2×D3—44no—
882C2×D3—44no—
883C2×D3—42no—
884C2×D3—41no—
885C2×D3—84no—
886C2×D3—164no—
887C3×C4—24no—
888C3×C4—24no—
889C3×C4—42no—
890C3×C4—41no—
891C3×C4—42no—
892C3×C4D4212yes—
893C3×C4C23×D411yescharacteristic
894C3×C4C2×H(5,𝔽2)11yescharacteristic
895Dic3—22no—
896Dic3—22no—
897Dic3—42no—
898Dic3—42no—
899Dic3—41no—
900C23—21no—
901C23—32no—
902C23—32no—
903C23—62no—
904C23—62no—
905C23—64no—
906C23—61no—
907C23—122no—
908C23—124no—
909C23—242no—
910C23—244no—
911C23C2×D3×D411yescharacteristic
912Q8—22no—
913Q8—24no—
914Q8—21no—
915Q8—22no—
916Q8—22no—
917Q8—21no—
918Q8—42no—
919Q8—62no—
920Q8—61no—
921Q8—62no—
922Q8—62no—
923Q8—61no—
924Q8—128no—
925Q8—124no—
926Q8—122no—
927Q8C2×D3×D414yes—
928D4—21no—
929D4—21no—
930D4—34no—
931D4—42no—
932D4—64no—
933D4—61no—
934D4—62no—
935D4—61no—
936D4—64no—
937D4—62no—
938D4—124no—
939D4—124no—
940D4—124no—
941D4—128no—
942D4—124no—
943D4—124no—
944D4—122no—
945D4—242no—
946C2×C4—22no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—21no—
951C2×C4—32no—
952C2×C4—32no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—62no—
956C2×C4—62no—
957C2×C4—62no—
958C2×C4—62no—
959C2×C4—62no—
960C2×C4—64no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—61no—
964C2×C4—124no—
965C2×C4—128no—
966C2×C4—124no—
967C2×C4—128no—
968C2×C4—124no—
969C2×C4—122no—
970C2×C4—122no—
971C2×C4—244no—
972C2×C4C2×D3×D414yes—
973C2×C4C2×D3×D412yes—
974C2×C4C2×D3×D411yescharacteristic
975C2×C4#100912yes—
976C2×C4C24×D311yescharacteristic
977C8—22no—
978C8—22no—
979C8—32no—
980C8—32no—
981C8—62no—
982C2×C3—22no—
983C2×C3—81no—
984C2×C3C2×D4211yescharacteristic
985C2×C3#358612yes—
986D3—42no—
987D3—42no—
988D3—44no—
989D3—81no—
990C22—22no—
991C22—42no—
992C22—41no—
993C22—62no—
994C22—64no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—64no—
999C22—124no—
1000C22—124no—
1001C22—122no—
1002C22—121no—
1003C22—244no—
1004C22—484no—
1005C22#560912yes—
1006C22C22×D3×D411yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—41no—
1011C4—42no—
1012C4—62no—
1013C4—62no—
1014C4—122no—
1015C4—121no—
1016C4—122no—
1017C4#560912yes—
1018C4C22×D3×D411yescharacteristic
1019C4C2×#100911yescharacteristic
1020C3#6106011yescharacteristic, complemented, Sylow
1021C2—22no—
1022C2—81no—
1023C2—122no—
1024C2—122no—
1025C2—124no—
1026C2—241no—
1027C2C2×#560911yescharacteristic
1028C2#8721112yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3044C2
socleC22×C3C23×D4
hypercenter#3044D3
hypocenterC3#61060
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #117 ◁ #3044

Complements

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

NH ≅ G/Ntype
1. C2×#5778C2semidirect
2. C22×#918C2semidirect
3. #86354C2semidirect
4. #85881C2semidirect
5. C3×#3044C2semidirect
6. #83979C2semidirect
7. #83884C2semidirect
8. #83403C2semidirect
9. #82548C2semidirect
10. #80629C2semidirect
11. #80627C2semidirect
12. #80501C2semidirect
13. #80500C2semidirect
14. #79087C2semidirect
15. #79074C2semidirect
16. #78964C2semidirect
17. #78959C2semidirect
18. #78839C2semidirect
19. #78835C2semidirect
24. C22×D3×Q8C22semidirect
26. C22×C3×Q16C22semidirect
28. C3×#519C22semidirect
33. C22×#216C22semidirect
34. C2×#942C22semidirect
37. C2×#919C22semidirect
39. C2×#918C22semidirect
40. C2×#918C22semidirect
41. C2×#918C22semidirect
42. C2×#914C22semidirect
43. C2×D3×SD16C22semidirect
47. C22×ΓL(1,𝔽25)C22semidirect
55. #5576C22semidirect
57. Q8×D12C22semidirect
60. #5526C22semidirect
63. #5524C22semidirect
65. C3×#464C22semidirect
66. C3×#462C22semidirect
67. C3×#424C22semidirect
68. C3×#419C22semidirect
70. #5225C22semidirect
71. #5187C22semidirect
72. #5186C22semidirect
73. #5186C22semidirect
74. #5170C22semidirect
75. #5126C22semidirect
76. #5120C22semidirect
77. #5113C22semidirect
79. #5092C22semidirect
80. #5086C22semidirect
81. #5060C22semidirect
82. #5059C22semidirect
83. #5026C22semidirect
84. C4×#215C22semidirect
86. #4998C22semidirect
87. #4997C22semidirect
88. #4844C22semidirect
89. #4841C22semidirect
90. #4838C22semidirect
91. #4836C22semidirect
92. #4816C22semidirect
93. #4816C22semidirect
94. #4813C22semidirect
95. #4812C22semidirect
96. #4810C22semidirect
97. #4808C22semidirect
98. #4808C22semidirect
99. #4782C22semidirect
100. #4780C22semidirect
101. #4776C22semidirect
113. #3044D3semidirect
184. C2×#215D4semidirect
286. C22×Q16C2×D3semidirect
311. #519C2×D3semidirect
323. #464C2×D3semidirect
325. #462C2×D3semidirect
340. #424C2×D3semidirect
343. #419C2×D3semidirect
1020. C3#61060semidirect

Maximal subgroups

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

subgroupindex
C2×#57782
C22×#9182
#863542
#858812
C3×#30442
#839792
#838842
#834032
#825482
#806292
#806272
#805012
#805002
#790872
#790742
#789642
#789592
#788392
#788352
#610603