Finite Group Databasebeta

← #11670556

Subgroups — #11670556

Order 768.

2722 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#916C211yesmaximal, characteristic, complemented
2C2×#5751C211yesmaximal, characteristic, complemented
3#86354C211yesmaximal, characteristic, complemented
4#86315C211yesmaximal, characteristic, complemented
5C3×#3057C211yesmaximal, characteristic, complemented
6#83854C211yesmaximal, characteristic, complemented
7#83794C211yesmaximal, characteristic, complemented
8#83411C211yesmaximal, characteristic, complemented
9#83383C211yesmaximal, characteristic, complemented
10#80837C214yesmaximal, complemented
11#80836C214yesmaximal, complemented
12#80679C214yesmaximal, complemented
13#80677C214yesmaximal, complemented
14#79180C211yesmaximal, characteristic, complemented
15#79168C211yesmaximal, characteristic, complemented
16#78977C211yesmaximal, characteristic, complemented
17#78959C211yesmaximal, characteristic, complemented
18#78944C211yesmaximal, characteristic, complemented
19#78927C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C2×#1010C2211yescharacteristic
22C2×#1009C2211yescharacteristic
23C22×#239C2211yescharacteristic
24C22×#237C2211yescharacteristic, complemented
25C22×C3×SD16C2211yescharacteristic, complemented
26C2×C3×#131C2211yescharacteristic
27C3×#536C2211yescharacteristic
28C3×#535C2211yescharacteristic
29#5828C2211yescharacteristic
30#5816C2211yescharacteristic
31C22×#216C2211yescharacteristic, complemented
32C2×#942C2211yescharacteristic, complemented
33#5805C2211yescharacteristic, complemented
34C2×#932C2211yescharacteristic
35C22×#213C2211yescharacteristic
36C2×#916—28no—
37C2×#916C2214yescomplemented
38C2×#916C2214yescomplemented
39#5751—28no—
40C2×#909C2211yescharacteristic
41C2×#909C2212yescomplemented
42C2×#908C2211yescharacteristic
43C2×#908C2212yescomplemented
44C2×#904C2211yescharacteristic
45C2×#904C2212yescomplemented
46C22×#204C2211yescharacteristic
47C22×#204C2212yescomplemented
48C22×D3×C8C2211yescharacteristic, complemented
49#5726—22no—
50#5718—22no—
51#5677—22no—
52#5676—22no—
53#5653—22no—
54D3×#123—22no—
55#5631C2214yescomplemented
56#5630C2214yescomplemented
57#5599C2214yescomplemented
58#5598C2214yescomplemented
59#5592—22no—
60#5586—22no—
61#5524C2211yescharacteristic
62#5524C2211yescharacteristic, complemented
63#5521C2211yescharacteristic
64#5516C2211yescharacteristic, complemented
65C3×#468C2214yescomplemented
66C3×#465C2214yescomplemented
67C3×#427C2211yescharacteristic, complemented
68C3×#419C2211yescharacteristic, complemented
69C3×#418C2211yescharacteristic, complemented
70#5234C2211yescharacteristic
71#5176C2212yescomplemented
72#5175C2212yescomplemented
73#5168C2212yescomplemented
74#5167C2212yescomplemented
75#5127C2214yescomplemented
76#5126C2211yescharacteristic, complemented
77#5119C2211yescharacteristic, complemented
78C8×#67C2214yescomplemented
79#5101C2211yescharacteristic, complemented
80#5050C2214yescomplemented
81#5047C2214yescomplemented
82#5037C2214yescomplemented
83#5036C2214yescomplemented
84#5004C2211yescharacteristic, complemented
85#5002C2211yescharacteristic
86#5002C2211yescharacteristic, complemented
87#5001C2211yescharacteristic
88#4889C2214yescomplemented
89#4887C2212yescomplemented
90#4883C2212yescomplemented
91#4864C2212yescomplemented
92#4864C2212yescomplemented
93#4852C2214yescomplemented
94#4810C2214yescomplemented
95#4808C2214yescomplemented
96#4798C2214yescomplemented
97#4795C2214yescomplemented
98#4787C2214yescomplemented
99#4786C2214yescomplemented
100#4783C2214yescomplemented
101#4781C2214yescomplemented
102C2×#577—31no—
103C22×#135—31no—
104#3487—31no—
105#3485—31no—
106#3284—34no—
107#3282—34no—
108#3269—34no—
109#3268—34no—
110#3154—31no—
111#3057D311yescharacteristic, complemented
112#3050—31no—
113#3044—31no—
114#3041—31no—
115#3011—31no—
116#3008—31no—
117#3005—31no—
118#3005—31no—
119#2949—31no—
120#2929—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8C2311yescharacteristic
123C22×C3×D4C2311yescharacteristic
124C22×#67—21no—
125C23×Dic3—21no—
126#1010—24no—
127#1010—42no—
128#1009—24no—
129#1009—42no—
130C2×#239—21no—
131C2×#239—22no—
132C2×#239—24no—
133C2×#239—42no—
134C2×#239C2314yes—
135C2×D3×Q8—21no—
136C2×#237—21no—
137C2×#237—22no—
138C2×#237—22no—
139C2×#237—24no—
140C2×#237—42no—
141C2×#237C2314yes—
142C2×D3×D4—22no—
143C2×D3×D4—21no—
144C2×#235C2311yescharacteristic
145C2×#235C2311yescharacteristic
146C2×#235C2312yes—
147C2×#235C2312yes—
148C22×D12—21no—
149C22×D12C2312yes—
150C22×D12C2311yescharacteristic
151C22×C4×D3—21no—
152C22×C4×D3C2311yescharacteristic
153C22×Dic6C2312yes—
154C22×Dic6C2311yescharacteristic
155C2×C3×SD16—24no—
156C2×C3×SD16C2312yes—
157C2×C3×SD16C2312yes—
158C3×#131—24no—
159C2×C3×M16C2311yescharacteristic
160C2×C3×M16C2312yes—
161C22×C3×C8C2312yes—
162C22×C3×C8C2311yescharacteristic
163C3×C4⋊Q8—21no—
164C3×#127—21no—
165C3×#124—21no—
166C3×#124—21no—
167C3×#123—22no—
168C3×C22⋊Q8C2314yes—
169C3×#121C2314yes—
170C3×#120—22no—
171C3×#117C2311yescharacteristic
172C3×#117C2311yescharacteristic
173#953—22no—
174#947C2312yes—
175#946—22no—
176#946D412yes—
177#944C2312yes—
178C2×#216—24no—
179C2×#216C2314yes—
180C2×#216C2312yes—
181#942—42no—
182C2×#215C2312yes—
183#940—24no—
184#940C2312yes—
185#939—24no—
186#939—24no—
187#938—22no—
188#938D412yes—
189#937D412yes—
190#936C2312yes—
191#935D412yes—
192D4×Dic3—24no—
193C2×#214C2312yes—
194#932—42no—
195C2×#213—24no—
196C2×#213C2314yes—
197C2×#213C2312yes—
198#929—22no—
199C4×#67C2314yes—
200#926C2311yescharacteristic
201C2×#208C2311yescharacteristic
202C22×C3⋊C8C2311yescharacteristic
203#916—216no—
204#916—216no—
205#909—24no—
206#909—28no—
207#908—24no—
208#908—28no—
209C2×Dic12C2311yescharacteristic
210C2×Dic12C2312yes—
211#904—24no—
212#904—28no—
213C2×D24C2311yescharacteristic
214C2×D24C2312yes—
215C2×#204—28no—
216C2×#204D418yescomplemented
217C2×#204C2311yescharacteristic
218C2×#204C2311yescharacteristic
219C2×#204C2312yes—
220C2×#204C2312yes—
221C2×#204C2312yes—
222C2×#204C2312yes—
223C2×D3×C8—24no—
224C2×D3×C8C2312yes—
225C2×D3×C8C2312yes—
226#897C2312yes—
227#897C2312yes—
228#895—24no—
229#895C2312yes—
230#895C2312yes—
231#894—24no—
232#894—24no—
233#893C2314yes—
234D3×C4⋊C4—24no—
235#887C2314yes—
236#886—21no—
237#886—21no—
238#885—24no—
239#884—24no—
240#884—24no—
241#883—24no—
242#882—21no—
243#882—21no—
244#882—24no—
245#67⋊C4—24no—
246D3×C22⋊C4—22no—
247D3×C22⋊C4—24no—
248#878—24no—
249#877—22no—
250C4×D12—22no—
251C4×D12—22no—
252C4×D12—22no—
253C4×Dic6—22no—
254C3×#107C2312yes—
255C3×#106C2312yes—
256C3×#103C2314yes—
257C3×#102C2314yes—
258#830C2314yes—
259(C2×D3)⋊C8C2314yes—
260#815C2312yes—
261Dic3⋊C8C2314yes—
262C8×Dic3C2312yes—
263#810C2312yes—
264#810C2312yes—
265#810C2314yes—
266#809C2312yes—
267#809C2312yes—
268#809C2314yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C22×#41—31no—
273#577—68no—
274C2×#137—31no—
275C2×#137—31no—
276C2×#137—32no—
277C2×AGL(1,ℤ/8)—31no—
278C2×AGL(1,ℤ/8)—31no—
279C2×AGL(1,ℤ/8)—32no—
280C2×#135—34no—
281C2×#135—34no—
282C2×#135—31no—
283C2×#135—32no—
284C2×#135—68no—
285C22×Q16—31no—
286C22×SD16—31no—
287C22×SD16—32no—
288C22×SD16C2×D311yescharacteristic, complemented
289C22×D8—31no—
290C2×#131C2×D311yescharacteristic
291C23×C8—31no—
292#550—34no—
293#550—62no—
294#548—34no—
295#548—62no—
296#547—34no—
297#547—62no—
298#546—34no—
299#546—62no—
300#536—31no—
301#536C2×D311yescharacteristic
302#535—31no—
303#535—62no—
304#535C2×D311yescharacteristic
305#534—62no—
306#525—31no—
307#525—31no—
308#525—31no—
309#525—62no—
310C2×#123—62no—
311#519—31no—
312#518—31no—
313#497—32no—
314#496—32no—
315#495—32no—
316#492—32no—
317#468C2×D314yescomplemented
318#467—32no—
319#466—32no—
320#465—32no—
321#465—32no—
322#465C2×D314yescomplemented
323#464—34no—
324#463—34no—
325#462—34no—
326#459—34no—
327#452—34no—
328#452—34no—
329#452—34no—
330#451—34no—
331#449—34no—
332#449—34no—
333#449—34no—
334#447—34no—
335#440—34no—
336C4×SD16—34no—
337#435—34no—
338C8×D4—34no—
339#427C2×D311yescharacteristic, complemented
340#424—31no—
341#419—31no—
342#419C2×D311yescharacteristic, complemented
343#418—31no—
344#418C2×D311yescharacteristic, complemented
345#416—31no—
346#416—31no—
347#408—31no—
348#407—31no—
349#405—31no—
350C24×C3—21no—
351C23×D3—21no—
352C23×D3—22no—
353C23×D3C2×D411yescharacteristic
354C3×#41—22no—
355C3×#41—22no—
356C2×C3×Q8—21no—
357C2×C3×Q8—22no—
358C2×C3×Q8—22no—
359C2×C3×Q8C2×D411yescharacteristic
360C2×C3×Q8C2412yes—
361C2×C3×D4—24no—
362C2×C3×D4—22no—
363C2×C3×D4—21no—
364C2×C3×D4—22no—
365C2×C3×D4C2×D412yes—
366C2×C3×D4C2×D411yescharacteristic
367C2×C3×D4C2412yes—
368C22×C3×C4—21no—
369C22×C3×C4C2412yes—
370C22×C3×C4C2411yescharacteristic
371C2×#67—21no—
372C2×#67—21no—
373C2×#67—22no—
374C2×#67—22no—
375C2×#67—24no—
376C2×#67—24no—
377C2×#67—44no—
378C2×#67C2×D414yes—
379C22×Dic3—21no—
380C22×Dic3—22no—
381C22×Dic3—24no—
382C22×Dic3—44no—
383C22×Dic3C2×D411yescharacteristic
384#239—28no—
385#239—44no—
386#239—48no—
387#239—44no—
388D3×Q8—44no—
389#237—28no—
390#237—44no—
391#237—48no—
392#237—44no—
393#237—48no—
394D3×D4—44no—
395D3×D4—48no—
396#235—22no—
397#235—22no—
398#235—22no—
399#235—22no—
400#235—24no—
401#235—24no—
402#235—42no—
403#235—42no—
404C2×D12—21no—
405C2×D12—22no—
406C2×D12—24no—
407C2×D12—24no—
408C2×D12—22no—
409C2×D12—22no—
410C2×D12—22no—
411C2×D12—42no—
412C2×D12—44no—
413C2×D12C2×D414yes—
414C2×D12C2411yescharacteristic
415C2×D12C2411yescharacteristic
416C2×D12C2412yes—
417C2×C4×D3—22no—
418C2×C4×D3—22no—
419C2×C4×D3—21no—
420C2×C4×D3—21no—
421C2×C4×D3—22no—
422C2×C4×D3—22no—
423C2×C4×D3—24no—
424C2×C4×D3—24no—
425C2×C4×D3—44no—
426C2×C4×D3C2×D412yes—
427C2×C4×D3C2412yes—
428C2×Dic6—21no—
429C2×Dic6—22no—
430C2×Dic6—24no—
431C2×Dic6—22no—
432C2×Dic6—42no—
433C2×Dic6C2×D414yes—
434C2×Dic6C2411yescharacteristic
435C2×Dic6C2411yescharacteristic
436C2×Dic6C2412yes—
437C3×SD16—24no—
438C3×SD16—24no—
439C3×M16—22no—
440C3×M16—24no—
441C2×C3×C8—24no—
442C2×C3×C8C2×D414yes—
443C2×C3×C8C2412yes—
444C2×C3×C8C2411yescharacteristic
445C2×C3×C8C2411yescharacteristic
446C3×C4⋊C4—24no—
447C3×C4⋊C4C2412yes—
448C3×C4⋊C4C2412yes—
449C3×C22⋊C4—21no—
450C3×C22⋊C4—21no—
451C3×C22⋊C4—24no—
452C3×C22⋊C4—24no—
453C3×C42—21no—
454C3×C42—21no—
455#217—24no—
456#217C2×D412yes—
457#217C2×D414yes—
458#216—28no—
459#216—42no—
460#215—42no—
461#214—42no—
462#213—28no—
463#213—42no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—22no—
467(C2×D3)⋊C4—24no—
468(C2×D3)⋊C4—22no—
469(C2×D3)⋊C4—24no—
470(C2×D3)⋊C4C2×D414yes—
471C4⋊Dic3—22no—
472C4⋊Dic3—22no—
473C4⋊Dic3C2×D412yes—
474Dic3⋊C4—24no—
475Dic3⋊C4—24no—
476Dic3⋊C4C2×D414yes—
477C4×Dic3—24no—
478C4×Dic3C2412yes—
479#208—22no—
480C2×C3⋊C8—22no—
481C2×C3⋊C8C2412yes—
482C2×C3⋊C8C2412yes—
483Dic12—24no—
484Dic12—22no—
485D24—24no—
486D24—22no—
487#204—24no—
488#204—24no—
489#204—22no—
490#204—22no—
491#204C2×D418yes—
492#204C2×D418yes—
493D3×C8—24no—
494D3×C8—24no—
4952−1+4—64no—
4962−1+4—122no—
497H(5,𝔽2)—64no—
498H(5,𝔽2)—122no—
499C2×#41—34no—
500C2×#41—34no—
501C2×#41—31no—
502C2×#41—31no—
503C2×#41—32no—
504C2×#41—32no—
505C2×#41—62no—
506C2×#41—62no—
507C2×#41—61no—
508C2×#41—62no—
509C2×#41—61no—
510C2×#41—64no—
511C2×#41—64no—
512C2×#41—122no—
513C2×#41—122no—
514C2×#41C22×D311yescharacteristic
515C22×Q8—31no—
516C22×Q8—32no—
517C22×Q8—61no—
518C22×Q8C22×D311yescharacteristic
519C22×D4—31no—
520C22×D4—32no—
521C22×D4—61no—
522C22×D4—61no—
523C22×D4—62no—
524C22×D4—61no—
525C22×D4C22×D311yescharacteristic
526C23×C4—31no—
527C23×C4—61no—
528C23×C4—61no—
529#137—68no—
530#137—64no—
531#137—122no—
532AGL(1,ℤ/8)—68no—
533AGL(1,ℤ/8)—64no—
534AGL(1,ℤ/8)—122no—
535#135—68no—
536#135—616no—
537#135—616no—
538#135—64no—
539C2×Q16—34no—
540C2×Q16—32no—
541C2×Q16—32no—
542C2×Q16—31no—
543C2×Q16—64no—
544C2×SD16—24no—
545C2×SD16—32no—
546C2×SD16—32no—
547C2×SD16—38no—
548C2×SD16—32no—
549C2×SD16—32no—
550C2×SD16—31no—
551C2×SD16—32no—
552C2×SD16—32no—
553C2×SD16—31no—
554C2×SD16—68no—
555C2×SD16C22×D312yes—
556C2×SD16C22×D312yes—
557C2×D8—34no—
558C2×D8—32no—
559C2×D8—32no—
560C2×D8—31no—
561C2×D8—64no—
562#131—24no—
563C2×M16—31no—
564C2×M16C22×D311yescharacteristic
565C2×M16C22×D312yes—
566C22×C8—31no—
567C22×C8—32no—
568C22×C8—32no—
569C22×C8—64no—
570C22×C8C22×D312yes—
571C22×C8C22×D311yescharacteristic
572C4⋊Q8—21no—
573C4⋊Q8—32no—
574#127—21no—
575#127—32no—
576#127—64no—
577#124—21no—
578#124—21no—
579#124—32no—
580#124—32no—
581#124—64no—
582#123—22no—
583#123—32no—
584#123—64no—
585#123—61no—
586#123—61no—
587#123—64no—
588#123—62no—
589#123—64no—
590C22⋊Q8—32no—
591C22⋊Q8—32no—
592C22⋊Q8—32no—
593C22⋊Q8—64no—
594C22⋊Q8—62no—
595C22⋊Q8C22×D314yes—
596#121—32no—
597#121—32no—
598#121—32no—
599#121—64no—
600#121—64no—
601#121—64no—
602#121—64no—
603#121—62no—
604#121—64no—
605#121C22×D314yes—
606#120—22no—
607#120—32no—
608#120—64no—
609#120—61no—
610#120—61no—
611#120—62no—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—34no—
615C4×D4—34no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4—62no—
619C4×D4—64no—
620C4×D4—64no—
621#117—31no—
622#117—62no—
623#117C22×D311yescharacteristic
624#117C22×D311yescharacteristic
625C2×C4⋊C4—64no—
626C2×C22⋊C4—62no—
627C2×C22⋊C4—64no—
628#107C22×D312yes—
629#106C22×D312yes—
630C4⋊C8—34no—
631#103—32no—
632#103—32no—
633#103—34no—
634#103C22×D314yes—
635#102—32no—
636#102—32no—
637#102—34no—
638#102C22×D314yes—
639C22⋊C8—34no—
640C22⋊C8—34no—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—42no—
645C23×C3—82no—
646C23×C3C22×D412yes—
647C23×C3C22×D411yescharacteristic
648C22×D3—22no—
649C22×D3—22no—
650C22×D3—24no—
651C22×D3—21no—
652C22×D3—21no—
653C22×D3—42no—
654C22×D3—44no—
655C22×D3—82no—
656C22×D3—84no—
657C22×D3C22×D412yes—
658C3×Q8—22no—
659C3×Q8—22no—
660C3×Q8—22no—
661C3×Q8—42no—
662C3×D4—24no—
663C3×D4—22no—
664C3×D4—22no—
665C3×D4—22no—
666C3×D4—42no—
667C3×D4—84no—
668C2×C3×C4—22no—
669C2×C3×C4—22no—
670C2×C3×C4—22no—
671C2×C3×C4—22no—
672C2×C3×C4—22no—
673C2×C3×C4—42no—
674C2×C3×C4C22×D412yes—
675C2×C3×C4C22×D411yescharacteristic
676C2×C3×C4C22×D412yes—
677C2×C3×C4H(5,𝔽2)12yes—
678C2×C3×C4C2511yescharacteristic
679#67—44no—
680#67—48no—
681#67—44no—
682#67—44no—
683#67—42no—
684#67—42no—
685#67—84no—
686C2×Dic3—24no—
687C2×Dic3—22no—
688C2×Dic3—22no—
689C2×Dic3—21no—
690C2×Dic3—21no—
691C2×Dic3—48no—
692C2×Dic3—44no—
693C2×Dic3C22×D414yes—
694C2×Dic3C22×D412yes—
695D12—24no—
696D12—21no—
697D12—21no—
698D12—22no—
699D12—21no—
700D12—21no—
701D12—44no—
702D12—48no—
703D12—82no—
704D12—82no—
705D12C22×D414yes—
706C4×D3—24no—
707C4×D3—22no—
708C4×D3—22no—
709C4×D3—44no—
710C4×D3—48no—
711C4×D3—44no—
712C4×D3—42no—
713C4×D3—42no—
714C4×D3—84no—
715Dic6—24no—
716Dic6—22no—
717Dic6—21no—
718Dic6—21no—
719Dic6—21no—
720Dic6—21no—
721Dic6—44no—
722Dic6C22×D414yes—
723C3×C8—22no—
724C3×C8C22×D412yes—
725C3×C8C22×D412yes—
726C3⋊C8—22no—
727C3⋊C8—22no—
728C24—21no—
729C24—31no—
730C24—61no—
731C24—62no—
732#41—22no—
733#41—22no—
734#41—64no—
735#41—64no—
736#41—68no—
737#41—68no—
738#41—62no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—122no—
743#41—122no—
744#41—124no—
745#41—128no—
746#41—128no—
747#41—124no—
748#41—128no—
749#41—124no—
750#41—124no—
751C2×Q8—21no—
752C2×Q8—22no—
753C2×Q8—22no—
754C2×Q8—34no—
755C2×Q8—32no—
756C2×Q8—31no—
757C2×Q8—31no—
758C2×Q8—64no—
759C2×Q8—61no—
760C2×Q8—62no—
761C2×Q8—62no—
762C2×Q8—122no—
763C2×Q8—124no—
764C2×Q8D3×D411yescharacteristic
765C2×Q8C23×D312yes—
766C2×D4—24no—
767C2×D4—22no—
768C2×D4—21no—
769C2×D4—22no—
770C2×D4—34no—
771C2×D4—34no—
772C2×D4—32no—
773C2×D4—31no—
774C2×D4—31no—
775C2×D4—64no—
776C2×D4—64no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—64no—
780C2×D4—64no—
781C2×D4—61no—
782C2×D4—61no—
783C2×D4—62no—
784C2×D4—62no—
785C2×D4—61no—
786C2×D4—62no—
787C2×D4—62no—
788C2×D4—122no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—124no—
792C2×D4—128no—
793C2×D4D3×D412yes—
794C2×D4D3×D411yescharacteristic
795C2×D4C23×D312yes—
796C22×C4—21no—
797C22×C4—31no—
798C22×C4—32no—
799C22×C4—32no—
800C22×C4—64no—
801C22×C4—64no—
802C22×C4—64no—
803C22×C4—61no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—62no—
809C22×C4—61no—
810C22×C4—61no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4C23×D312yes—
814C22×C4C23×D311yescharacteristic
815Q16—64no—
816Q16—68no—
817Q16—62no—
818Q16—122no—
819SD16—24no—
820SD16—24no—
821SD16—38no—
822SD16—38no—
823SD16—64no—
824SD16—64no—
825SD16—62no—
826SD16—62no—
827SD16—122no—
828SD16—122no—
829D8—64no—
830D8—68no—
831D8—62no—
832D8—122no—
833M16—22no—
834M16—24no—
835M16—62no—
836C2×C8—24no—
837C2×C8—32no—
838C2×C8—32no—
839C2×C8—62no—
840C2×C8—64no—
841C2×C8—64no—
842C2×C8D3×D414yes—
843C2×C8C23×D312yes—
844C2×C8C23×D311yescharacteristic
845C2×C8C23×D311yescharacteristic
846C4⋊C4—24no—
847C4⋊C4—34no—
848C4⋊C4—32no—
849C4⋊C4—62no—
850C4⋊C4—64no—
851C4⋊C4—64no—
852C4⋊C4—62no—
853C4⋊C4C23×D312yes—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—24no—
857C22⋊C4—21no—
858C22⋊C4—24no—
859C22⋊C4—32no—
860C22⋊C4—34no—
861C22⋊C4—34no—
862C22⋊C4—62no—
863C22⋊C4—64no—
864C22⋊C4—64no—
865C22⋊C4—62no—
866C22⋊C4—62no—
867C22⋊C4—62no—
868C22⋊C4—64no—
869C42—21no—
870C42—21no—
871C42—32no—
872C42—64no—
873C22×C3—22no—
874C22×C3—24no—
875C22×C3—22no—
876C22×C3—44no—
877C22×C3—42no—
878C22×C3—84no—
879C22×C3D4212yes—
880C22×C3C23×D411yescharacteristic
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—24no—
885C2×D3—44no—
886C2×D3—44no—
887C2×D3—42no—
888C2×D3—42no—
889C2×D3—41no—
890C2×D3—41no—
891C2×D3—84no—
892C2×D3—164no—
893C3×C4—22no—
894C3×C4—42no—
895C3×C4—42no—
896C3×C4—42no—
897C3×C4D4212yes—
898C3×C4C23×D411yescharacteristic
899C3×C4C2×H(5,𝔽2)11yescharacteristic
900Dic3—24no—
901Dic3—24no—
902Dic3—22no—
903Dic3—41no—
904Dic3—41no—
905C23—22no—
906C23—32no—
907C23—42no—
908C23—62no—
909C23—62no—
910C23—64no—
911C23—61no—
912C23—61no—
913C23—82no—
914C23—122no—
915C23—124no—
916C23—242no—
917C23—244no—
918C23C2×D3×D412yes—
919C23C2×D3×D411yescharacteristic
920Q8—22no—
921Q8—22no—
922Q8—22no—
923Q8—34no—
924Q8—42no—
925Q8—62no—
926Q8—64no—
927Q8—61no—
928Q8—61no—
929Q8—61no—
930Q8—61no—
931Q8—124no—
932D4—24no—
933D4—22no—
934D4—22no—
935D4—22no—
936D4—34no—
937D4—42no—
938D4—61no—
939D4—61no—
940D4—62no—
941D4—61no—
942D4—61no—
943D4—64no—
944D4—84no—
945D4—124no—
946D4—128no—
947D4—124no—
948D4—124no—
949D4—128no—
950D4—124no—
951D4—122no—
952D4—122no—
953D4—242no—
954D4—242no—
955D4—244no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—34no—
962C2×C4—32no—
963C2×C4—42no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—64no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—64no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—124no—
973C2×C4—124no—
974C2×C4—128no—
975C2×C4—128no—
976C2×C4—124no—
977C2×C4—122no—
978C2×C4—122no—
979C2×C4—244no—
980C2×C4C2×D3×D412yes—
981C2×C4C2×D3×D412yes—
982C2×C4C2×D3×D411yescharacteristic
983C2×C4#100912yes—
984C2×C4C24×D311yescharacteristic
985C8—22no—
986C8—62no—
987C8—62no—
988C8C2×D3×D412yes—
989C8C2×D3×D412yes—
990C2×C3—22no—
991C2×C3—42no—
992C2×C3—82no—
993C2×C3C2×D4211yescharacteristic
994C2×C3#358412yes—
995D3—42no—
996D3—44no—
997D3—81no—
998D3—81no—
999C22—22no—
1000C22—24no—
1001C22—22no—
1002C22—44no—
1003C22—42no—
1004C22—62no—
1005C22—62no—
1006C22—62no—
1007C22—64no—
1008C22—84no—
1009C22—124no—
1010C22—124no—
1011C22—122no—
1012C22—122no—
1013C22—121no—
1014C22—121no—
1015C22—244no—
1016C22—484no—
1017C22#560912yes—
1018C22C22×D3×D411yescharacteristic
1019C4—22no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—64no—
1024C4—62no—
1025C4—64no—
1026C4—121no—
1027C4—121no—
1028C4#560912yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100911yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—42no—
1034C2—82no—
1035C2—122no—
1036C2—124no—
1037C2—241no—
1038C2—241no—
1039C2C2×#560911yescharacteristic
1040C2#8720612yes—
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3057C2
socleC22×C3C23×D4
hypercenter#3057D3
hypocenterC3#61052
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3057

Complements

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

NH ≅ G/Ntype
1. C22×#916C2semidirect
2. C2×#5751C2semidirect
3. #86354C2semidirect
4. #86315C2semidirect
5. C3×#3057C2semidirect
6. #83854C2semidirect
7. #83794C2semidirect
8. #83411C2semidirect
9. #83383C2semidirect
10. #80837C2semidirect
11. #80836C2semidirect
12. #80679C2semidirect
13. #80677C2semidirect
14. #79180C2semidirect
15. #79168C2semidirect
16. #78977C2semidirect
17. #78959C2semidirect
18. #78944C2semidirect
19. #78927C2semidirect
24. C22×#237C22semidirect
25. C22×C3×SD16C22semidirect
31. C22×#216C22semidirect
32. C2×#942C22semidirect
33. #5805C22semidirect
37. C2×#916C22semidirect
38. C2×#916C22semidirect
41. C2×#909C22semidirect
43. C2×#908C22semidirect
45. C2×#904C22semidirect
47. C22×#204C22semidirect
48. C22×D3×C8C22semidirect
55. #5631C22semidirect
56. #5630C22semidirect
57. #5599C22semidirect
58. #5598C22semidirect
62. #5524C22semidirect
64. #5516C22semidirect
65. C3×#468C22semidirect
66. C3×#465C22semidirect
67. C3×#427C22semidirect
68. C3×#419C22semidirect
69. C3×#418C22semidirect
71. #5176C22semidirect
72. #5175C22semidirect
73. #5168C22semidirect
74. #5167C22semidirect
75. #5127C22semidirect
76. #5126C22semidirect
77. #5119C22semidirect
78. C8×#67C22semidirect
79. #5101C22semidirect
80. #5050C22semidirect
81. #5047C22semidirect
82. #5037C22semidirect
83. #5036C22semidirect
84. #5004C22semidirect
86. #5002C22semidirect
88. #4889C22semidirect
89. #4887C22semidirect
90. #4883C22semidirect
91. #4864C22semidirect
92. #4864C22semidirect
93. #4852C22semidirect
94. #4810C22semidirect
95. #4808C22semidirect
96. #4798C22semidirect
97. #4795C22semidirect
98. #4787C22semidirect
99. #4786C22semidirect
100. #4783C22semidirect
101. #4781C22semidirect
111. #3057D3semidirect
216. C2×#204D4semidirect
288. C22×SD16C2×D3semidirect
317. #468C2×D3semidirect
322. #465C2×D3semidirect
339. #427C2×D3semidirect
342. #419C2×D3semidirect
344. #418C2×D3semidirect
1031. C3#61052semidirect

Maximal subgroups

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

subgroupindex
C22×#9162
C2×#57512
#863542
#863152
C3×#30572
#838542
#837942
#834112
#833832
#808372
#808362
#806792
#806772
#791802
#791682
#789772
#789592
#789442
#789272
#610523