Finite Group Databasebeta

← #11670681

Subgroups — #11670681

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
1#87251C211yesmaximal, characteristic, complemented
2C22×#942C211yesmaximal, characteristic, complemented
3C2×#5778C211yesmaximal, characteristic, complemented
4#86040C211yesmaximal, characteristic, complemented
5C3×#3004C211yesmaximal, characteristic, complemented
6#83982C211yesmaximal, characteristic, complemented
7#83975C211yesmaximal, characteristic, complemented
8#83970C211yesmaximal, characteristic, complemented
9#82923C211yesmaximal, characteristic, complemented
10#80206C214yesmaximal, complemented
11#80205C214yesmaximal, complemented
12#80062C214yesmaximal, complemented
13#80061C214yesmaximal, complemented
14#78976C211yesmaximal, characteristic, complemented
15#78964C211yesmaximal, characteristic, complemented
16#78961C211yesmaximal, characteristic, complemented
17#78947C211yesmaximal, characteristic, complemented
18#78638C211yesmaximal, characteristic, complemented
19#78627C211yesmaximal, characteristic, complemented
20#61060—31nomaximal, Sylow
21C23×C3×Q8C2211yescharacteristic, complemented
22C2×#1009C2211yescharacteristic
23C2×#1007C2211yescharacteristic
24C22×#235C2211yescharacteristic
25C2×C3×#137C2211yescharacteristic
26C2×C3×#137C2211yescharacteristic
27C3×#525C2211yescharacteristic
28#5825C2211yescharacteristic
29C2×#950C2211yescharacteristic
30#5817—22no—
31#5817C2214yescomplemented
32#5816—22no—
33#5816C2211yescharacteristic
34#5816C2211yescharacteristic, complemented
35Q8×#67—22no—
36Q8×#67C2214yescomplemented
37#5812C2211yescharacteristic, complemented
38C22×#216C2211yescharacteristic, complemented
39C22×#216C2211yescharacteristic, complemented
40C2×#942—28no—
41C2×#942C2214yescomplemented
42C2×#942C2214yescomplemented
43C22×#215C2211yescharacteristic
44C22×#215C2211yescharacteristic
45#5791—22no—
46#5791C2211yescharacteristic
47#5791C2211yescharacteristic, complemented
48C22×#208C2211yescharacteristic, complemented
49#5778—28no—
50C2×#919C2212yescomplemented
51C2×#918C2212yescomplemented
52C2×#914C2212yescomplemented
53C2×D3×SD16C2212yescomplemented
54C2×#909C2211yescharacteristic, complemented
55C2×#908C2211yescharacteristic
56C2×#907C2211yescharacteristic
57D3×#123—22no—
58#5631C2214yes—
59#5612C2214yes—
60#5589—22no—
61#5551—22no—
62#5550—22no—
63#5526C2211yescharacteristic
64#5521C2211yescharacteristic
65C3×#451C2214yescomplemented
66C3×#448C2214yescomplemented
67C3×#419C2211yescharacteristic, complemented
68C3×#419C2211yescharacteristic, complemented
69C3×#407C2211yescharacteristic, complemented
70#5233C2211yescharacteristic
71#5190C2212yescomplemented
72#5187C2214yescomplemented
73#5183C2212yescomplemented
74#5182C2214yescomplemented
75#5169C2214yescomplemented
76#5168C2212yescomplemented
77#5167C2212yescomplemented
78#5166C2214yescomplemented
79#5131C2211yescharacteristic
80#5129C2211yescharacteristic
81#5122C2211yescharacteristic, complemented
82#5120C2211yescharacteristic, complemented
83#5119C2211yescharacteristic, complemented
84#5052C2212yescomplemented
85#5049C2212yescomplemented
86#5042C2212yescomplemented
87#5039C2212yescomplemented
88#5002C2211yescharacteristic, complemented
89#4998C2211yescharacteristic, complemented
90#4819C2214yescomplemented
91#4818C2214yescomplemented
92#4817C2214yescomplemented
93#4816C2214yescomplemented
94#4813C2214yescomplemented
95#4809C2214yescomplemented
96#4808C2214yescomplemented
97#4788C2214yescomplemented
98#4734C2214yescomplemented
99#4733C2214yescomplemented
100#4729C2214yescomplemented
101#4728C2214yescomplemented
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#3044—31no—
114#3042—31no—
115#3011—31no—
116#3009—31no—
117#3005—31no—
118#3004D311yescharacteristic, complemented
119#2949—31no—
120#2930—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8—22no—
123C22×C3×Q8—21no—
124C22×C3×Q8—24no—
125C22×C3×Q8—42no—
126C22×C3×Q8C2311yescharacteristic
127C22×C3×Q8C2314yes—
128C22×C3×Q8C2311yescharacteristic
129C23×C3×C4—21no—
130C23×C3×C4C2311yescharacteristic
131C22×#67—21no—
132#1009—24no—
133#1009—42no—
134#1007—24no—
135#1007—42no—
136C2×#239—21no—
137C2×#239C2312yes—
138C2×#239C2312yes—
139C2×D3×Q8—21no—
140C2×D3×Q8C2312yes—
141C2×D3×D4—22no—
142C2×D3×D4C2312yes—
143C2×#235—22no—
144C2×#235—22no—
145C2×#235—24no—
146C2×#235—21no—
147C2×#235—42no—
148C2×#235C2311yescharacteristic
149C2×#235C2311yescharacteristic
150C2×#235C2314yes—
151C22×D12—21no—
152C22×D12C2311yescharacteristic
153C22×C4×D3—21no—
154C22×Dic6C2311yescharacteristic
155C3×#137—24no—
156C3×#137—42no—
157C2×C3×Q16C2312yes—
158C2×C3×Q16C2312yes—
159C2×C3×SD16C2312yes—
160C2×C3×SD16C2312yes—
161C2×C3×M16C2311yescharacteristic
162C2×C3×M16C2311yescharacteristic
163C3×#123—21no—
164C3×C22⋊Q8C2312yes—
165C3×#121C2312yes—
166C3×#120—21no—
167C3×C4×D4—22no—
168C3×#117C2311yescharacteristic
169#953—21no—
170#953D412yes—
171#950—24no—
172#947—21no—
173#947—24no—
174#947C2312yes—
175#946—24no—
176#946—22no—
177#946—24no—
178#946C2314yes—
179Q8×Dic3—22no—
180Q8×Dic3C2314yes—
181#944—21no—
182#944—24no—
183#944C2312yes—
184#944C2312yes—
185C2×#216—24no—
186C2×#216—24no—
187C2×#216C2314yes—
188C2×#216C2312yes—
189C2×#216C2312yes—
190C2×#216C2311yescharacteristic
191#942—216no—
192#942—216no—
193C2×#215—24no—
194C2×#215D418yescomplemented
195C2×#215C2314yes—
196C2×#215C2311yescharacteristic
197C2×#215C2312yes—
198C2×#215C2312yes—
199#938—24no—
200#937—24no—
201#936C2312yes—
202#935—22no—
203C2×#214C2311yescharacteristic
204C2×#213C2311yescharacteristic
205#930—24no—
206#930D412yes—
207#930C2312yes—
208#929—21no—
209#929—22no—
210#929—22no—
211#929D412yes—
212C4×#67—22no—
213C4×#67—24no—
214C4×#67—24no—
215C4×#67C2314yes—
216#926—22no—
217#926C2311yescharacteristic
218#926C2311yescharacteristic
219#924—24no—
220#924—22no—
221#924D412yes—
222#924C2312yes—
223C2×#208—24no—
224C2×#208C2312yes—
225C2×#208C2312yes—
226C22×C3⋊C8C2311yescharacteristic
227C22×C3⋊C8C2311yescharacteristic
228#919—28no—
229#918—28no—
230#914—28no—
231D3×SD16—28no—
232#909—42no—
233#908—24no—
234#907—24no—
235C2×Dic12C2312yes—
236C2×D24C2312yes—
237C2×#204C2312yes—
238C2×#204C2312yes—
239C2×ΓL(1,𝔽25)C2312yes—
240C2×D3×C8C2312yes—
241#897C2314yes—
242#894—24no—
243#893C2314yes—
244D3×C4⋊C4—24no—
245#886—22no—
246#884—24no—
247#883—24no—
248#883—24no—
249D3×C22⋊C4—22no—
250D3×C22⋊C4—24no—
251#875—21no—
252C4×D12—22no—
253#869—21no—
254C3×#103C2314yes—
255C3×#103C2314yes—
256C3×C22⋊C8C2314yes—
257#835C2312yes—
258#832C2312yes—
259#821C2314yes—
260(C2×D3)⋊C8C2314yes—
261#816C2314yes—
262#815C2312yes—
263Dic3⋊C8C2314yes—
264C8×Dic3C2312yes—
265#810C2312yes—
266#809C2312yes—
267#808C2312yes—
268#807C2312yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C23×Q8C2×D311yescharacteristic, complemented
273#577—68no—
274C2×#137—34no—
275C2×#137—34no—
276C2×#137—32no—
277C2×#137—31no—
278C2×#137—68no—
279C2×#137C2×D311yescharacteristic
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×Q16—31no—
287C22×SD16—31no—
288C22×SD16—31no—
289C22×SD16—32no—
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—31no—
304#536—62no—
305#534—62no—
306#525—31no—
307#525—31no—
308#525—62no—
309#525C2×D311yescharacteristic
310C2×#123—62no—
311#519—31no—
312#518—31no—
313#497—32no—
314#497—32no—
315#495—32no—
316#494—32no—
317#470—32no—
318#470—34no—
319#469—32no—
320#468—32no—
321#468—32no—
322#467—34no—
323#464—34no—
324#463—34no—
325#462—34no—
326#461—34no—
327#452—34no—
328#452—34no—
329#452—34no—
330#451—34no—
331#451C2×D314yescomplemented
332#450—34no—
333#449—34no—
334#448C2×D314yescomplemented
335#440—34no—
336C4×SD16—34no—
337#436—34no—
338#435—34no—
339#427—31no—
340#424—31no—
341#419—31no—
342#419C2×D311yescharacteristic, complemented
343#419C2×D311yescharacteristic, complemented
344#418—31no—
345#416—31no—
346#416—31no—
347#408—31no—
348#407C2×D311yescharacteristic, complemented
349#405—31no—
350C24×C3C2×D411yescharacteristic
351C23×D3—21no—
352C23×D3—22no—
353C3×#41—22no—
354C3×#41—22no—
355C2×C3×Q8—21no—
356C2×C3×Q8—24no—
357C2×C3×Q8—21no—
358C2×C3×Q8—22no—
359C2×C3×Q8—28no—
360C2×C3×Q8—22no—
361C2×C3×Q8—22no—
362C2×C3×Q8—44no—
363C2×C3×Q8—44no—
364C2×C3×Q8—48no—
365C2×C3×Q8C2×D414yes—
366C2×C3×Q8C2411yescharacteristic
367C2×C3×Q8C2412yes—
368C2×C3×Q8C2412yes—
369C2×C3×D4—21no—
370C2×C3×D4—22no—
371C2×C3×D4C2411yescharacteristic
372C22×C3×C4—21no—
373C22×C3×C4—22no—
374C22×C3×C4—22no—
375C22×C3×C4—24no—
376C22×C3×C4—21no—
377C22×C3×C4—21no—
378C22×C3×C4—44no—
379C22×C3×C4C2×D412yes—
380C22×C3×C4C2×D411yescharacteristic
381C22×C3×C4C2412yes—
382C22×C3×C4C2411yescharacteristic
383C2×#67—24no—
384C2×#67—22no—
385C2×#67—21no—
386C2×#67—22no—
387C2×#67—44no—
388C2×#67C2×D412yes—
389C2×#67C2×D414yes—
390C22×Dic3—21no—
391#239—24no—
392#239—24no—
393#239—42no—
394#239—42no—
395#239—44no—
396D3×Q8—24no—
397D3×Q8—42no—
398D3×Q8—44no—
399D3×D4—24no—
400D3×D4—42no—
401D3×D4—48no—
402#235—22no—
403#235—22no—
404#235—22no—
405#235—22no—
406#235—28no—
407#235—44no—
408#235—44no—
409#235—48no—
410#235—48no—
411C2×D12—21no—
412C2×D12—22no—
413C2×D12—22no—
414C2×D12—22no—
415C2×D12—44no—
416C2×D12C2×D411yescharacteristic
417C2×D12C2×D414yes—
418C2×D12C2411yescharacteristic
419C2×D12C2412yes—
420C2×C4×D3—22no—
421C2×C4×D3—24no—
422C2×C4×D3—21no—
423C2×C4×D3—22no—
424C2×C4×D3—22no—
425C2×C4×D3—24no—
426C2×C4×D3—44no—
427C2×C4×D3C2412yes—
428C2×Dic6—22no—
429C2×Dic6—22no—
430C2×Dic6—21no—
431C2×Dic6—22no—
432C2×Dic6C2×D411yescharacteristic
433C2×Dic6C2411yescharacteristic
434C2×Dic6C2412yes—
435C3×Q16—24no—
436C3×Q16—42no—
437C3×SD16—24no—
438C3×SD16—42no—
439C3×M16—22no—
440C3×M16—22no—
441C2×C3×C8C2412yes—
442C2×C3×C8C2412yes—
443C3×C4⋊C4—22no—
444C3×C4⋊C4C2412yes—
445C3×C22⋊C4—21no—
446C3×C22⋊C4—22no—
447C3×C22⋊C4—22no—
448C3×C42—21no—
449#217—22no—
450#217—21no—
451#217—24no—
452#217C2×D412yes—
453#217C2×D414yes—
454#216—28no—
455#216—22no—
456#216—24no—
457#216—24no—
458#215—28no—
459#215—22no—
460#215C2×D418yes—
461#215C2×D418yes—
462#214—22no—
463#213—22no—
464(C2×D3)⋊C4—24no—
465(C2×D3)⋊C4—24no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—24no—
468(C2×D3)⋊C4—24no—
469(C2×D3)⋊C4C2×D414yes—
470C4⋊Dic3—24no—
471C4⋊Dic3—24no—
472C4⋊Dic3C2×D412yes—
473C4⋊Dic3C2412yes—
474Dic3⋊C4—22no—
475Dic3⋊C4—24no—
476Dic3⋊C4—24no—
477Dic3⋊C4—24no—
478Dic3⋊C4C2×D414yes—
479C4×Dic3—21no—
480C4×Dic3—24no—
481C4×Dic3C2412yes—
482#208—24no—
483#208—24no—
484C2×C3⋊C8—22no—
485C2×C3⋊C8C2×D414yes—
486C2×C3⋊C8C2412yes—
487C2×C3⋊C8C2411yescharacteristic
488C2×C3⋊C8C2411yescharacteristic
489Dic12—42no—
490D24—24no—
491#204—24no—
492#204—42no—
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—32no—
501C2×#41—32no—
502C2×#41—31no—
503C2×#41—34no—
504C2×#41—62no—
505C2×#41—61no—
506C2×#41—64no—
507C2×#41—61no—
508C2×#41—62no—
509C2×#41—122no—
510C2×#41C22×D311yescharacteristic
511C22×Q8—21no—
512C22×Q8—22no—
513C22×Q8—24no—
514C22×Q8—32no—
515C22×Q8—31no—
516C22×Q8—42no—
517C22×Q8—61no—
518C22×Q8C22×D311yescharacteristic
519C22×Q8C22×D314yes—
520C22×Q8C22×D311yescharacteristic
521C22×D4—32no—
522C22×D4—31no—
523C22×D4—61no—
524C22×D4—62no—
525C22×D4—61no—
526C23×C4—21no—
527C23×C4—61no—
528C23×C4C22×D311yescharacteristic
529#137—24no—
530#137—42no—
531#137—68no—
532#137—616no—
533#137—616no—
534#137—122no—
535AGL(1,ℤ/8)—64no—
536AGL(1,ℤ/8)—68no—
537#135—64no—
538#135—68no—
539C2×Q16—34no—
540C2×Q16—32no—
541C2×Q16—32no—
542C2×Q16—31no—
543C2×Q16—32no—
544C2×Q16—64no—
545C2×Q16—64no—
546C2×Q16C22×D312yes—
547C2×Q16C22×D312yes—
548C2×SD16—38no—
549C2×SD16—32no—
550C2×SD16—32no—
551C2×SD16—34no—
552C2×SD16—31no—
553C2×SD16—31no—
554C2×SD16—32no—
555C2×SD16—32no—
556C2×SD16—68no—
557C2×SD16—64no—
558C2×SD16C22×D312yes—
559C2×SD16C22×D312yes—
560C2×D8—31no—
561C2×D8—32no—
562#131—64no—
563C2×M16—32no—
564C2×M16—32no—
565C2×M16—32no—
566C2×M16—64no—
567C2×M16C22×D311yescharacteristic
568C2×M16C22×D311yescharacteristic
569C22×C8—31no—
570C22×C8—31no—
571C22×C8—32no—
572C4⋊Q8—32no—
573C4⋊Q8—32no—
574C4⋊Q8—61no—
575C4⋊Q8—64no—
576C4⋊Q8—61no—
577#124—32no—
578#124—32no—
579#124—61no—
580#124—64no—
581#124—61no—
582#123—21no—
583#123—32no—
584#123—64no—
585#123—64no—
586#123—62no—
587#123—64no—
588#123—62no—
589#123—62no—
590#123—62no—
591#123—61no—
592C22⋊Q8—32no—
593C22⋊Q8—34no—
594C22⋊Q8—32no—
595C22⋊Q8—34no—
596C22⋊Q8—64no—
597C22⋊Q8—64no—
598C22⋊Q8—62no—
599C22⋊Q8—62no—
600C22⋊Q8—64no—
601C22⋊Q8C22×D312yes—
602#121—32no—
603#121—32no—
604#121—64no—
605#121—64no—
606#121—64no—
607#121C22×D312yes—
608#120—21no—
609#120—32no—
610#120—64no—
611#120—61no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—22no—
615C4×D4—34no—
616C4×D4—34no—
617C4×D4—62no—
618C4×D4—64no—
619C4×D4—64no—
620C4×D4—62no—
621#117—31no—
622#117—31no—
623#117—62no—
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—62no—
627C2×C22⋊C4—64no—
628#107—32no—
629#106—32no—
630C4⋊C8—34no—
631#103—32no—
632#103—34no—
633#103—32no—
634#103C22×D314yes—
635#103C22×D314yes—
636#102—32no—
637#102—34no—
638#102—32no—
639C22⋊C8—34no—
640C22⋊C8C22×D314yes—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—21no—
645C23×C3—42no—
646C23×C3C22×D412yes—
647C23×C3C22×D411yescharacteristic
648C22×D3—22no—
649C22×D3—24no—
650C22×D3—21no—
651C22×D3—44no—
652C22×D3—84no—
653C22×D3—82no—
654C22×D3C22×D412yes—
655C3×Q8—24no—
656C3×Q8—22no—
657C3×Q8—22no—
658C3×Q8—21no—
659C3×Q8—22no—
660C3×Q8—21no—
661C3×Q8—48no—
662C3×Q8—42no—
663C3×Q8C22×D414yes—
664C3×D4—21no—
665C3×D4—21no—
666C3×D4—42no—
667C3×D4—82no—
668C2×C3×C4—22no—
669C2×C3×C4—24no—
670C2×C3×C4—22no—
671C2×C3×C4—24no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—21no—
676C2×C3×C4—22no—
677C2×C3×C4—48no—
678C2×C3×C4—42no—
679C2×C3×C4—42no—
680C2×C3×C4C22×D412yes—
681C2×C3×C4C22×D411yescharacteristic
682C2×C3×C4C22×D412yes—
683C2×C3×C4H(5,𝔽2)12yes—
684C2×C3×C4C2511yescharacteristic
685#67—24no—
686#67—44no—
687#67—44no—
688#67—48no—
689#67—44no—
690#67—42no—
691C2×Dic3—22no—
692C2×Dic3—21no—
693C2×Dic3—22no—
694C2×Dic3—42no—
695C2×Dic3C22×D414yes—
696C2×Dic3C22×D412yes—
697D12—24no—
698D12—22no—
699D12—21no—
700D12—22no—
701D12—21no—
702D12—44no—
703D12—44no—
704D12C22×D414yes—
705C4×D3—22no—
706C4×D3—22no—
707C4×D3—44no—
708C4×D3—44no—
709C4×D3—48no—
710C4×D3—44no—
711C4×D3—42no—
712C4×D3—84no—
713Dic6—22no—
714Dic6—21no—
715Dic6—22no—
716Dic6—22no—
717Dic6—21no—
718Dic6—44no—
719Dic6—42no—
720C3×C8—22no—
721C3×C8—22no—
722C3⋊C8—22no—
723C3⋊C8C22×D412yes—
724C3⋊C8C22×D412yes—
725C24—62no—
726C24—61no—
727C24D3×D411yescharacteristic
728#41—22no—
729#41—22no—
730#41—68no—
731#41—62no—
732#41—62no—
733#41—64no—
734#41—64no—
735#41—62no—
736#41—62no—
737#41—124no—
738#41—128no—
739#41—128no—
740#41—124no—
741#41—122no—
742#41—122no—
743#41—124no—
744C2×Q8—21no—
745C2×Q8—24no—
746C2×Q8—21no—
747C2×Q8—22no—
748C2×Q8—28no—
749C2×Q8—22no—
750C2×Q8—22no—
751C2×Q8—31no—
752C2×Q8—32no—
753C2×Q8—31no—
754C2×Q8—44no—
755C2×Q8—44no—
756C2×Q8—48no—
757C2×Q8—62no—
758C2×Q8—61no—
759C2×Q8—64no—
760C2×Q8—62no—
761C2×Q8—62no—
762C2×Q8—122no—
763C2×Q8—124no—
764C2×Q8D3×D414yes—
765C2×Q8C23×D311yescharacteristic
766C2×Q8C23×D312yes—
767C2×Q8C23×D312yes—
768C2×D4—21no—
769C2×D4—22no—
770C2×D4—32no—
771C2×D4—34no—
772C2×D4—34no—
773C2×D4—31no—
774C2×D4—32no—
775C2×D4—31no—
776C2×D4—62no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—64no—
780C2×D4—62no—
781C2×D4—64no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—62no—
785C2×D4—124no—
786C2×D4—122no—
787C2×D4—128no—
788C2×D4—124no—
789C2×D4C23×D311yescharacteristic
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—24no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—32no—
797C22×C4—44no—
798C22×C4—62no—
799C22×C4—62no—
800C22×C4—64no—
801C22×C4—62no—
802C22×C4—61no—
803C22×C4—64no—
804C22×C4—61no—
805C22×C4—124no—
806C22×C4D3×D412yes—
807C22×C4D3×D411yescharacteristic
808C22×C4C23×D312yes—
809C22×C4C23×D311yescharacteristic
810Q16—24no—
811Q16—42no—
812Q16—64no—
813Q16—64no—
814Q16—62no—
815Q16—68no—
816Q16—122no—
817SD16—24no—
818SD16—38no—
819SD16—38no—
820SD16—42no—
821SD16—64no—
822SD16—62no—
823SD16—62no—
824SD16—68no—
825SD16—122no—
826D8—64no—
827D8—62no—
828M16—22no—
829M16—22no—
830M16—64no—
831M16—64no—
832M16—64no—
833C2×C8—34no—
834C2×C8—31no—
835C2×C8—31no—
836C2×C8—32no—
837C2×C8—64no—
838C2×C8—62no—
839C2×C8C23×D312yes—
840C2×C8C23×D312yes—
841C4⋊C4—22no—
842C4⋊C4—34no—
843C4⋊C4—32no—
844C4⋊C4—32no—
845C4⋊C4—64no—
846C4⋊C4—64no—
847C4⋊C4—64no—
848C4⋊C4—64no—
849C4⋊C4—64no—
850C4⋊C4—62no—
851C4⋊C4C23×D312yes—
852C22⋊C4—21no—
853C22⋊C4—22no—
854C22⋊C4—22no—
855C22⋊C4—32no—
856C22⋊C4—34no—
857C22⋊C4—34no—
858C22⋊C4—64no—
859C22⋊C4—64no—
860C22⋊C4—64no—
861C22⋊C4—64no—
862C22⋊C4—64no—
863C22⋊C4—61no—
864C22⋊C4—62no—
865C22⋊C4—62no—
866C42—21no—
867C42—32no—
868C42—64no—
869C42—61no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—22no—
874C22×C3—44no—
875C22×C3—42no—
876C22×C3—41no—
877C22×C3D4212yes—
878C22×C3C23×D411yescharacteristic
879C2×D3—24no—
880C2×D3—22no—
881C2×D3—24no—
882C2×D3—44no—
883C2×D3—42no—
884C2×D3—41no—
885C2×D3—84no—
886C2×D3—164no—
887C3×C4—24no—
888C3×C4—22no—
889C3×C4—42no—
890C3×C4—41no—
891C3×C4—42no—
892C3×C4D4212yes—
893C3×C4C23×D411yescharacteristic
894C3×C4C2×H(5,𝔽2)11yescharacteristic
895Dic3—24no—
896Dic3—22no—
897Dic3—42no—
898Dic3—41no—
899Dic3—42no—
900C23—22no—
901C23—21no—
902C23—32no—
903C23—42no—
904C23—62no—
905C23—64no—
906C23—61no—
907C23—124no—
908C23—242no—
909C23—244no—
910C23C2×D3×D412yes—
911C23C2×D3×D411yescharacteristic
912Q8—22no—
913Q8—24no—
914Q8—22no—
915Q8—21no—
916Q8—22no—
917Q8—21no—
918Q8—48no—
919Q8—42no—
920Q8—62no—
921Q8—61no—
922Q8—62no—
923Q8—62no—
924Q8—61no—
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—82no—
939D4—124no—
940D4—124no—
941D4—124no—
942D4—124no—
943D4—128no—
944D4—124no—
945D4—122no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—21no—
954C2×C4—22no—
955C2×C4—34no—
956C2×C4—32no—
957C2×C4—48no—
958C2×C4—42no—
959C2×C4—42no—
960C2×C4—62no—
961C2×C4—62no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—61no—
965C2×C4—124no—
966C2×C4—128no—
967C2×C4—124no—
968C2×C4—124no—
969C2×C4—122no—
970C2×C4—122no—
971C2×C4—244no—
972C2×C4C2×D3×D412yes—
973C2×C4C2×D3×D412yes—
974C2×C4C2×D3×D411yescharacteristic
975C2×C4#100412yes—
976C2×C4C24×D311yescharacteristic
977C8—22no—
978C8—22no—
979C8—32no—
980C8—32no—
981C8—62no—
982C2×C3—22no—
983C2×C3—42no—
984C2×C3—81no—
985C2×C3C2×D4211yescharacteristic
986C2×C3#358612yes—
987D3—42no—
988D3—44no—
989D3—81no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—44no—
995C22—41no—
996C22—42no—
997C22—62no—
998C22—64no—
999C22—64no—
1000C22—124no—
1001C22—121no—
1002C22—122no—
1003C22—244no—
1004C22—484no—
1005C22#559012yes—
1006C22C22×D3×D411yescharacteristic
1007C4—22no—
1008C4—24no—
1009C4—42no—
1010C4—41no—
1011C4—42no—
1012C4—62no—
1013C4—64no—
1014C4—122no—
1015C4—121no—
1016C4—122no—
1017C4#559012yes—
1018C4C22×D3×D411yescharacteristic
1019C4C2×#100411yescharacteristic
1020C3#6106011yescharacteristic, complemented, Sylow
1021C2—22no—
1022C2—42no—
1023C2—81no—
1024C2—122no—
1025C2—124no—
1026C2—241no—
1027C2C2×#559011yescharacteristic
1028C2#8719712yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3004C2
socleC22×C3C23×D4
hypercenter#3004D3
hypocenterC3#61060
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

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

NH ≅ G/Ntype
1. #87251C2semidirect
2. C22×#942C2semidirect
3. C2×#5778C2semidirect
4. #86040C2semidirect
5. C3×#3004C2semidirect
6. #83982C2semidirect
7. #83975C2semidirect
8. #83970C2semidirect
9. #82923C2semidirect
10. #80206C2semidirect
11. #80205C2semidirect
12. #80062C2semidirect
13. #80061C2semidirect
14. #78976C2semidirect
15. #78964C2semidirect
16. #78961C2semidirect
17. #78947C2semidirect
18. #78638C2semidirect
19. #78627C2semidirect
21. C23×C3×Q8C22semidirect
31. #5817C22semidirect
34. #5816C22semidirect
36. Q8×#67C22semidirect
37. #5812C22semidirect
38. C22×#216C22semidirect
39. C22×#216C22semidirect
41. C2×#942C22semidirect
42. C2×#942C22semidirect
47. #5791C22semidirect
48. C22×#208C22semidirect
50. C2×#919C22semidirect
51. C2×#918C22semidirect
52. C2×#914C22semidirect
53. C2×D3×SD16C22semidirect
54. C2×#909C22semidirect
65. C3×#451C22semidirect
66. C3×#448C22semidirect
67. C3×#419C22semidirect
68. C3×#419C22semidirect
69. C3×#407C22semidirect
71. #5190C22semidirect
72. #5187C22semidirect
73. #5183C22semidirect
74. #5182C22semidirect
75. #5169C22semidirect
76. #5168C22semidirect
77. #5167C22semidirect
78. #5166C22semidirect
81. #5122C22semidirect
82. #5120C22semidirect
83. #5119C22semidirect
84. #5052C22semidirect
85. #5049C22semidirect
86. #5042C22semidirect
87. #5039C22semidirect
88. #5002C22semidirect
89. #4998C22semidirect
90. #4819C22semidirect
91. #4818C22semidirect
92. #4817C22semidirect
93. #4816C22semidirect
94. #4813C22semidirect
95. #4809C22semidirect
96. #4808C22semidirect
97. #4788C22semidirect
98. #4734C22semidirect
99. #4733C22semidirect
100. #4729C22semidirect
101. #4728C22semidirect
118. #3004D3semidirect
194. C2×#215D4semidirect
272. C23×Q8C2×D3semidirect
331. #451C2×D3semidirect
334. #448C2×D3semidirect
342. #419C2×D3semidirect
343. #419C2×D3semidirect
348. #407C2×D3semidirect
1020. C3#61060semidirect

Maximal subgroups

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

subgroupindex
#872512
C22×#9422
C2×#57782
#860402
C3×#30042
#839822
#839752
#839702
#829232
#802062
#802052
#800622
#800612
#789762
#789642
#789612
#789472
#786382
#786272
#610603