Finite Group Databasebeta

← #11670576

Subgroups — #11670576

Order 768.

2710 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3487C211yesmaximal, characteristic, complemented
2C2×#5838C211yesmaximal, characteristic, complemented
3C22×#950C211yesmaximal, characteristic, complemented
4#86023C211yesmaximal, characteristic, complemented
5#84113C211yesmaximal, characteristic, complemented
6#84081C211yesmaximal, characteristic, complemented
7#83585C214yesmaximal, complemented
8#83583C214yesmaximal, complemented
9#83549C214yesmaximal, complemented
10#83547C214yesmaximal, complemented
11#83391C211yesmaximal, characteristic, complemented
12#83390C211yesmaximal, characteristic, complemented
13#83382C211yesmaximal, characteristic, complemented
14#83378C211yesmaximal, characteristic, complemented
15#82928C211yesmaximal, characteristic, complemented
16#82922C211yesmaximal, characteristic, complemented
17#82916C211yesmaximal, characteristic, complemented
18#82551C211yesmaximal, characteristic, complemented
19#82549C211yesmaximal, characteristic, complemented
20#61054—31nomaximal, Sylow
21C2×C3×2−1+4C2211yescharacteristic
22C22×C3×#41C2211yescharacteristic
23C2×#1010C2211yescharacteristic
24C22×#235C2211yescharacteristic
25C3×#550—22no—
26C3×#550C2214yescomplemented
27C3×#548—22no—
28C3×#548C2214yescomplemented
29C3×#535—22no—
30C3×#535C2211yescharacteristic
31C3×#535C2211yescharacteristic
32C3×#525—22no—
33C3×#525C2211yescharacteristic
34C3×#525C2211yescharacteristic
35C3×#519C2211yescharacteristic
36#5838—28no—
37#5830C2211yescharacteristic
38C2×#951C2211yescharacteristic
39C2×#951C2212yescomplemented
40C2×#950—28no—
41C2×#950C2214yes—
42C2×#950C2214yes—
43C2×#950C2211yescharacteristic
44C2×#950C2212yescomplemented
45C2×#949C2211yescharacteristic
46C2×#948C2211yescharacteristic
47C22×#216C2211yescharacteristic
48C22×#216C2212yescomplemented
49C2×#942C2211yescharacteristic
50C2×#942C2212yescomplemented
51C22×#215C2211yescharacteristic
52C22×#214C2211yescharacteristic
53C2×#932C2211yescharacteristic
54C22×#213C2211yescharacteristic
55#5791C2211yescharacteristic
56C23×C3⋊C8C2211yescharacteristic
57#5656—22no—
58#5633—22no—
59#5599—22no—
60#5592—22no—
61#5553C2214yescomplemented
62#5552C2214yescomplemented
63#5525C2211yescharacteristic
64#5516C2211yescharacteristic
65#5239C2214yescomplemented
66#5238C2214yescomplemented
67#5238C2214yescomplemented
68#5234C2211yescharacteristic
69#5233C2211yescharacteristic
70#5227C2214yescomplemented
71#5225C2211yescharacteristic
72#5215C2211yescharacteristic
73#5207C2211yescharacteristic
74#5075C2214yescomplemented
75#5074C2212yescomplemented
76#5073C2212yescomplemented
77#5059C2212yescomplemented
78#5058C2212yescomplemented
79#5054C2214yescomplemented
80#5051C2212yescomplemented
81#5048C2212yescomplemented
82#5047C2214yescomplemented
83#5041C2212yescomplemented
84#5040C2214yescomplemented
85#5039C2214yescomplemented
86#5038C2214yescomplemented
87#5038C2212yescomplemented
88#5037C2214yescomplemented
89#5037C2214yescomplemented
90#5030C2214yescomplemented
91C4×#216C2214yescomplemented
92#5028C2214yescomplemented
93#5027C2214yescomplemented
94#5011C2214yescomplemented
95D4×C3⋊C8C2214yescomplemented
96#5004C2211yescharacteristic
97#5002C2211yescharacteristic
98#5001C2211yescharacteristic
99#4999C2211yescharacteristic
100#4998C2211yescharacteristic
101#4997C2211yescharacteristic
102C2×#578—31no—
103C22×#135—31no—
104#3487—31no—
105#3487D311yescharacteristic, complemented
106#3287—34no—
107#3285—34no—
108#3271—34no—
109#3271—34no—
110#3155—31no—
111#3058—31no—
112#3050—31no—
113#3043—31no—
114#3043—31no—
115#3010—31no—
116#3010—31no—
117#3005—31no—
118#3005—31no—
119#2950—31no—
120#2929—31no—
121C3×2−1+4—24no—
122C3×2−1+4—42no—
123C2×C3×#41—22no—
124C2×C3×#41—21no—
125C2×C3×#41—22no—
126C2×C3×#41—24no—
127C2×C3×#41—42no—
128C2×C3×#41C2311yescharacteristic
129C2×C3×#41C2314yes—
130C2×C3×#41C2312yes—
131C2×C3×#41C2311yescharacteristic
132C22×C3×Q8—21no—
133C22×C3×Q8C2312yes—
134C22×C3×Q8C2311yescharacteristic
135C22×C3×D4—21no—
136C22×C3×D4C2311yescharacteristic
137C23×C3×C4—21no—
138C23×C3×C4C2311yescharacteristic
139C22×#67—21no—
140#1010—24no—
141#1010—42no—
142C2×D3×Q8—21no—
143C2×#237—22no—
144C2×#237—21no—
145C2×#235—22no—
146C2×#235—24no—
147C2×#235—42no—
148C2×#235C2311yescharacteristic
149C2×#235C2314yes—
150C2×#235C2312yes—
151C22×D12C2311yescharacteristic
152C22×C4×D3—21no—
153C22×Dic6C2312yes—
154C22×Dic6C2311yescharacteristic
155C3×#127—24no—
156C3×#127—21no—
157C3×#127C2312yes—
158C3×#124—21no—
159C3×#124—24no—
160C3×#124C2312yes—
161C3×#123—21no—
162C3×#123D412yes—
163C3×C22⋊Q8—24no—
164C3×C22⋊Q8D412yes—
165C3×C22⋊Q8C2312yes—
166C3×#121—24no—
167C3×#121—22no—
168C3×#121—24no—
169C3×#121—24no—
170C3×#121D412yes—
171C3×#121C2312yes—
172C3×#121C2314yes—
173C3×#120—21no—
174C3×#120—22no—
175C3×#120—22no—
176C3×#120D412yes—
177C3×C4×Q8—22no—
178C3×C4×Q8C2314yes—
179C3×C4×D4—22no—
180C3×C4×D4—24no—
181C3×C4×D4—24no—
182C3×C4×D4C2314yes—
183C3×#117—22no—
184C3×#117C2311yescharacteristic
185C3×#117C2311yescharacteristic
186#953—21no—
187#951—24no—
188#951—28no—
189#950—216no—
190#950—216no—
191#950—28no—
192#950—24no—
193#949—42no—
194#948—24no—
195#947—21no—
196C2×#216—28no—
197C2×#216D418yescomplemented
198C2×#216C2312yes—
199C2×#216C2312yes—
200C2×#216C2311yescharacteristic
201C2×#216C2312yes—
202C2×#216C2312yes—
203#942—24no—
204#942—28no—
205C2×#215—24no—
206C2×#215C2314yes—
207C2×#215C2312yes—
208C2×#215C2311yescharacteristic
209C2×#215C2312yes—
210#940—24no—
211#940—21no—
212#939—24no—
213#937—22no—
214C2×#214—24no—
215C2×#214C2314yes—
216C2×#214C2312yes—
217C2×#214C2311yescharacteristic
218C2×#214C2312yes—
219#932—42no—
220C2×#213—24no—
221C2×#213C2312yes—
222C2×#213C2312yes—
223C2×#213C2311yescharacteristic
224C2×#213C2312yes—
225C2×#213C2312yes—
226#930C2314yes—
227#930C2312yes—
228#929—21no—
229C4×#67—22no—
230#926C2311yescharacteristic
231#924C2312yes—
232C2×#208C2311yescharacteristic
233C2×#208C2311yescharacteristic
234C2×#208C2312yes—
235C22×C3⋊C8—24no—
236C22×C3⋊C8C2311yescharacteristic
237C22×C3⋊C8C2312yes—
238C22×C3⋊C8C2312yes—
239C22×C3⋊C8C2312yes—
240C22×C3⋊C8C2311yescharacteristic
241#896—24no—
242#895—22no—
243#893—24no—
244#887—22no—
245#885—24no—
246#884—24no—
247#884—24no—
248#882—22no—
249#67⋊C4—24no—
250#877—22no—
251#875C2312yes—
252#874C2312yes—
253C4×Dic6C2314yes—
254#835C2314yes—
255#835C2312yes—
256#832C2314yes—
257#832C2312yes—
258#830C2314yes—
259#830C2314yes—
260#810C2312yes—
261#810C2314yes—
262#809C2314yes—
263#809C2312yes—
264#808C2312yes—
265#807C2312yes—
266C4⋊(C3⋊C8)C2314yes—
267#803C2312yes—
268C4×C3⋊C8C2312yes—
269C2×2−1+4—31no—
270C2×2−1+4C2×D311yescharacteristic
271C22×#41—31no—
272C22×#41C2×D311yescharacteristic
273#578—68no—
274C2×#137—31no—
275C2×#137—32no—
276C2×#137—31no—
277C2×#137—32no—
278C2×AGL(1,ℤ/8)—31no—
279C2×AGL(1,ℤ/8)—31no—
280C2×#135—31no—
281C2×#135—34no—
282C2×#135—34no—
283C2×#135—32no—
284C2×#135—68no—
285C22×Q16—31no—
286C22×Q16—32no—
287C22×SD16—31no—
288C22×SD16—31no—
289C22×D8—31no—
290C2×#131—31no—
291C23×C8—31no—
292#550—22no—
293#550—34no—
294#550—62no—
295#550C2×D314yescomplemented
296#548—22no—
297#548—34no—
298#548—62no—
299#548C2×D314yescomplemented
300#535—22no—
301#535—31no—
302#535—31no—
303#535—62no—
304#535C2×D311yescharacteristic
305#535C2×D311yescharacteristic
306#525—22no—
307#525—31no—
308#525—62no—
309#525C2×D311yescharacteristic
310#525C2×D311yescharacteristic
311#519—31no—
312#519C2×D311yescharacteristic
313#496—32no—
314#496—32no—
315#495—32no—
316#493—32no—
317#469—34no—
318#467—32no—
319#466—34no—
320#466—32no—
321#465—32no—
322#465—32no—
323#464—34no—
324#464—34no—
325#460—34no—
326#460—34no—
327#452—34no—
328#452—34no—
329#449—34no—
330#449—34no—
331#449—34no—
332#449—34no—
333#448—34no—
334#448—34no—
335#441—34no—
336C4×Q16—34no—
337#435—34no—
338C8×D4—34no—
339#427—31no—
340#424—31no—
341#419—31no—
342#419—31no—
343#418—31no—
344#418—31no—
345#416—31no—
346#416—31no—
347#408—31no—
348#407—31no—
349#405—31no—
350C24×C3—21no—
351C24×C3C2×D411yescharacteristic
352C23×D3—21no—
353C3×#41—22no—
354C3×#41—22no—
355C3×#41—28no—
356C3×#41—24no—
357C3×#41—22no—
358C3×#41—22no—
359C3×#41—44no—
360C3×#41—42no—
361C3×#41—48no—
362C3×#41—48no—
363C3×#41—44no—
364C2×C3×Q8—21no—
365C2×C3×Q8—22no—
366C2×C3×Q8—22no—
367C2×C3×Q8—24no—
368C2×C3×Q8—42no—
369C2×C3×Q8—44no—
370C2×C3×Q8C2×D414yes—
371C2×C3×Q8C2×D411yescharacteristic
372C2×C3×Q8C2411yescharacteristic
373C2×C3×Q8C2412yes—
374C2×C3×D4—21no—
375C2×C3×D4—24no—
376C2×C3×D4—22no—
377C2×C3×D4—24no—
378C2×C3×D4—22no—
379C2×C3×D4—22no—
380C2×C3×D4—21no—
381C2×C3×D4—24no—
382C2×C3×D4—22no—
383C2×C3×D4—44no—
384C2×C3×D4C2×D412yes—
385C2×C3×D4C2×D411yescharacteristic
386C2×C3×D4C2×D414yes—
387C2×C3×D4C2412yes—
388C2×C3×D4C2411yescharacteristic
389C22×C3×C4—21no—
390C22×C3×C4—22no—
391C22×C3×C4—22no—
392C22×C3×C4—22no—
393C22×C3×C4—22no—
394C22×C3×C4—21no—
395C22×C3×C4—24no—
396C22×C3×C4—44no—
397C22×C3×C4C2×D412yes—
398C22×C3×C4C2×D411yescharacteristic
399C22×C3×C4C2412yes—
400C22×C3×C4C2412yes—
401C22×C3×C4C2411yescharacteristic
402C2×#67—21no—
403C2×#67—22no—
404C2×#67—24no—
405C2×#67—24no—
406C2×#67—22no—
407C2×#67—44no—
408C22×Dic3—21no—
409C22×Dic3—22no—
410D3×Q8—44no—
411#237—44no—
412#237—48no—
413#235—22no—
414#235—22no—
415#235—24no—
416#235—28no—
417#235—44no—
418#235—42no—
419#235—48no—
420C2×D12—22no—
421C2×D12—22no—
422C2×D12—21no—
423C2×D12—24no—
424C2×D12C2411yescharacteristic
425C2×D12C2412yes—
426C2×C4×D3—24no—
427C2×C4×D3—22no—
428C2×C4×D3—21no—
429C2×C4×D3—44no—
430C2×Dic6—21no—
431C2×Dic6—22no—
432C2×Dic6—24no—
433C2×Dic6—22no—
434C2×Dic6—42no—
435C2×Dic6C2×D414yes—
436C2×Dic6C2411yescharacteristic
437C2×Dic6C2412yes—
438C3×C4⋊C4—24no—
439C3×C4⋊C4—22no—
440C3×C4⋊C4C2×D412yes—
441C3×C4⋊C4C2×D414yes—
442C3×C4⋊C4C2412yes—
443C3×C22⋊C4—21no—
444C3×C22⋊C4—22no—
445C3×C22⋊C4—22no—
446C3×C22⋊C4—24no—
447C3×C22⋊C4—24no—
448C3×C22⋊C4C2×D412yes—
449C3×C22⋊C4C2×D414yes—
450C3×C22⋊C4C2×D414yes—
451C3×C42—24no—
452C3×C42—21no—
453C3×C42C2412yes—
454#217—21no—
455#217—22no—
456#216—24no—
457#216—24no—
458#216—22no—
459#216C2×D418yes—
460#216C2×D418yes—
461#215—28no—
462#215—24no—
463#215—22no—
464#215—42no—
465#214—28no—
466#214—24no—
467#214—22no—
468#214—42no—
469#213—24no—
470#213—24no—
471#213—22no—
472#213—42no—
473#213—42no—
474(C2×D3)⋊C4—24no—
475(C2×D3)⋊C4—22no—
476(C2×D3)⋊C4—24no—
477C4⋊Dic3C2412yes—
478Dic3⋊C4—24no—
479Dic3⋊C4—22no—
480C4×Dic3—24no—
481C4×Dic3—21no—
482#208—22no—
483#208—22no—
484#208—24no—
485C2×C3⋊C8—22no—
486C2×C3⋊C8—24no—
487C2×C3⋊C8—24no—
488C2×C3⋊C8—24no—
489C2×C3⋊C8C2×D414yes—
490C2×C3⋊C8C2412yes—
491C2×C3⋊C8C2412yes—
492C2×C3⋊C8C2412yes—
493C2×C3⋊C8C2411yescharacteristic
494C2×C3⋊C8C2411yescharacteristic
4952−1+4—24no—
4962−1+4—42no—
4972−1+4—64no—
4982−1+4—122no—
499C2×#41—22no—
500C2×#41—21no—
501C2×#41—22no—
502C2×#41—24no—
503C2×#41—31no—
504C2×#41—34no—
505C2×#41—32no—
506C2×#41—42no—
507C2×#41—64no—
508C2×#41—62no—
509C2×#41—61no—
510C2×#41—62no—
511C2×#41—122no—
512C2×#41C22×D311yescharacteristic
513C2×#41C22×D314yes—
514C2×#41C22×D312yes—
515C2×#41C22×D311yescharacteristic
516C22×Q8—21no—
517C22×Q8—31no—
518C22×Q8—32no—
519C22×Q8—61no—
520C22×Q8C22×D312yes—
521C22×Q8C22×D311yescharacteristic
522C22×D4—21no—
523C22×D4—31no—
524C22×D4—61no—
525C22×D4C22×D311yescharacteristic
526C23×C4—21no—
527C23×C4—61no—
528C23×C4C22×D311yescharacteristic
529#137—68no—
530#137—68no—
531#137—64no—
532#137—64no—
533AGL(1,ℤ/8)—122no—
534AGL(1,ℤ/8)—122no—
535#135—64no—
536#135—616no—
537#135—616no—
538#135—68no—
539C2×Q16—38no—
540C2×Q16—32no—
541C2×Q16—32no—
542C2×Q16—31no—
543C2×Q16—32no—
544C2×Q16—32no—
545C2×Q16—68no—
546C2×SD16—34no—
547C2×SD16—32no—
548C2×SD16—31no—
549C2×SD16—34no—
550C2×SD16—32no—
551C2×SD16—31no—
552C2×SD16—32no—
553C2×SD16—32no—
554C2×SD16—64no—
555C2×SD16—64no—
556C2×D8—32no—
557C2×D8—32no—
558C2×D8—31no—
559C2×D8—32no—
560C2×D8—32no—
561C2×D8—64no—
562#131—64no—
563C2×M16—31no—
564C2×M16—32no—
565C2×M16—31no—
566C22×C8—31no—
567C22×C8—31no—
568C22×C8—32no—
569C22×C8—32no—
570C22×C8—32no—
571C22×C8—64no—
572#127—24no—
573#127—21no—
574#127—32no—
575#127—61no—
576#127—64no—
577#127C22×D312yes—
578#124—21no—
579#124—24no—
580#124—32no—
581#124—61no—
582#124—64no—
583#124C22×D312yes—
584#123—21no—
585#123—61no—
586#123#6712yes—
587C22⋊Q8—24no—
588C22⋊Q8—32no—
589C22⋊Q8—64no—
590C22⋊Q8#6712yes—
591C22⋊Q8C22×D312yes—
592#121—24no—
593#121—22no—
594#121—24no—
595#121—24no—
596#121—32no—
597#121—34no—
598#121—64no—
599#121—62no—
600#121—64no—
601#121—64no—
602#121#6712yes—
603#121C22×D312yes—
604#121C22×D314yes—
605#120—21no—
606#120—22no—
607#120—22no—
608#120—61no—
609#120—62no—
610#120—62no—
611#120#6712yes—
612C4×Q8—22no—
613C4×Q8—34no—
614C4×Q8—62no—
615C4×Q8C22×D314yes—
616C4×D4—22no—
617C4×D4—24no—
618C4×D4—24no—
619C4×D4—62no—
620C4×D4—64no—
621C4×D4—64no—
622C4×D4C22×D314yes—
623#117—22no—
624#117—31no—
625#117—62no—
626#117C22×D311yescharacteristic
627#117C22×D311yescharacteristic
628#107—32no—
629#106—32no—
630C4⋊C8—34no—
631#103—32no—
632#103—34no—
633#103—32no—
634#103—34no—
635#102—32no—
636#102—34no—
637#102—32no—
638#102—34no—
639C22⋊C8—34no—
640C22⋊C8—34no—
641#97—32no—
642C4×C8—32no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—21no—
646C23×C3—42no—
647C23×C3—42no—
648C23×C3—82no—
649C23×C3C22×D412yes—
650C23×C3C22×D412yes—
651C23×C3C22×D411yescharacteristic
652C22×D3—22no—
653C22×D3—21no—
654C22×D3—42no—
655C22×D3—82no—
656C3×Q8—22no—
657C3×Q8—24no—
658C3×Q8—22no—
659C3×Q8—21no—
660C3×Q8—21no—
661C3×Q8—44no—
662C3×Q8C22×D414yes—
663C3×D4—24no—
664C3×D4—22no—
665C3×D4—22no—
666C3×D4—21no—
667C3×D4—21no—
668C3×D4—22no—
669C3×D4—44no—
670C3×D4—48no—
671C3×D4—44no—
672C3×D4—42no—
673C3×D4—42no—
674C3×D4—84no—
675C3×D4—84no—
676C3×D4—82no—
677C2×C3×C4—22no—
678C2×C3×C4—24no—
679C2×C3×C4—22no—
680C2×C3×C4—24no—
681C2×C3×C4—22no—
682C2×C3×C4—22no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—22no—
686C2×C3×C4—21no—
687C2×C3×C4—48no—
688C2×C3×C4—44no—
689C2×C3×C4—44no—
690C2×C3×C4—42no—
691C2×C3×C4C22×D412yes—
692C2×C3×C4C22×D414yes—
693C2×C3×C4C22×D412yes—
694C2×C3×C4C22×D412yes—
695C2×C3×C4C22×D411yescharacteristic
696C2×C3×C4H(5,𝔽2)12yes—
697C2×C3×C4C2511yescharacteristic
698#67—48no—
699#67—44no—
700#67—42no—
701#67—82no—
702#67—84no—
703C2×Dic3—24no—
704C2×Dic3—22no—
705C2×Dic3—22no—
706C2×Dic3—21no—
707C2×Dic3—44no—
708D12—22no—
709D12—21no—
710D12—21no—
711D12—22no—
712D12—42no—
713D12—84no—
714C4×D3—48no—
715C4×D3—44no—
716C4×D3—42no—
717Dic6—24no—
718Dic6—22no—
719Dic6—21no—
720Dic6—21no—
721Dic6—44no—
722Dic6C22×D414yes—
723C3⋊C8—22no—
724C3⋊C8—22no—
725C3⋊C8—22no—
726C3⋊C8C22×D412yes—
727C3⋊C8C22×D412yes—
728C24—21no—
729C24—61no—
730C24C2×#6711yescharacteristic
731#41—22no—
732#41—22no—
733#41—28no—
734#41—24no—
735#41—22no—
736#41—22no—
737#41—44no—
738#41—42no—
739#41—48no—
740#41—48no—
741#41—44no—
742#41—68no—
743#41—64no—
744#41—62no—
745#41—62no—
746#41—124no—
747#41—122no—
748#41—128no—
749#41—128no—
750#41—124no—
751C2×Q8—22no—
752C2×Q8—21no—
753C2×Q8—22no—
754C2×Q8—24no—
755C2×Q8—34no—
756C2×Q8—32no—
757C2×Q8—31no—
758C2×Q8—42no—
759C2×Q8—44no—
760C2×Q8—64no—
761C2×Q8—62no—
762C2×Q8—61no—
763C2×Q8—62no—
764C2×Q8—122no—
765C2×Q8—124no—
766C2×Q8D3×D414yes—
767C2×Q8C2×#6711yescharacteristic
768C2×Q8C23×D311yescharacteristic
769C2×Q8C23×D312yes—
770C2×D4—21no—
771C2×D4—24no—
772C2×D4—22no—
773C2×D4—24no—
774C2×D4—22no—
775C2×D4—22no—
776C2×D4—22no—
777C2×D4—21no—
778C2×D4—24no—
779C2×D4—32no—
780C2×D4—31no—
781C2×D4—44no—
782C2×D4—61no—
783C2×D4—64no—
784C2×D4—62no—
785C2×D4—64no—
786C2×D4—62no—
787C2×D4—62no—
788C2×D4—62no—
789C2×D4—61no—
790C2×D4—64no—
791C2×D4—124no—
792C2×D4C2×#6712yes—
793C2×D4C2×#6711yescharacteristic
794C2×D4C2×#6714yes—
795C2×D4C23×D312yes—
796C2×D4C23×D311yescharacteristic
797C22×C4—21no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—24no—
804C22×C4—44no—
805C22×C4—61no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—61no—
809C22×C4—64no—
810C22×C4—124no—
811C22×C4C2×#6712yes—
812C22×C4C2×#6711yescharacteristic
813C22×C4C23×D312yes—
814C22×C4C23×D312yes—
815C22×C4C23×D311yescharacteristic
816Q16—38no—
817Q16—38no—
818Q16—62no—
819Q16—64no—
820Q16—64no—
821SD16—62no—
822SD16—62no—
823SD16—68no—
824SD16—64no—
825SD16—68no—
826SD16—64no—
827SD16—122no—
828SD16—122no—
829D8—64no—
830D8—64no—
831D8—62no—
832D8—122no—
833D8—122no—
834M16—64no—
835M16—62no—
836M16—62no—
837C2×C8—34no—
838C2×C8—31no—
839C2×C8—31no—
840C2×C8—32no—
841C2×C8—32no—
842C2×C8—32no—
843C2×C8—64no—
844C2×C8—64no—
845C2×C8—64no—
846C2×C8—62no—
847C4⋊C4—24no—
848C4⋊C4—22no—
849C4⋊C4—32no—
850C4⋊C4—64no—
851C4⋊C4—62no—
852C4⋊C4C2×#6712yes—
853C4⋊C4C2×#6714yes—
854C4⋊C4C23×D312yes—
855C22⋊C4—21no—
856C22⋊C4—22no—
857C22⋊C4—22no—
858C22⋊C4—24no—
859C22⋊C4—24no—
860C22⋊C4—61no—
861C22⋊C4—62no—
862C22⋊C4—62no—
863C22⋊C4—64no—
864C22⋊C4—64no—
865C22⋊C4C2×#6712yes—
866C22⋊C4C2×#6714yes—
867C22⋊C4C2×#6714yes—
868C42—24no—
869C42—21no—
870C42—61no—
871C42—64no—
872C42C23×D312yes—
873C22×C3—22no—
874C22×C3—24no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—44no—
880C22×C3—42no—
881C22×C3—44no—
882C22×C3—41no—
883C22×C3—42no—
884C22×C3—84no—
885C22×C3D4212yes—
886C22×C3C23×D411yescharacteristic
887C2×D3—42no—
888C2×D3—44no—
889C2×D3—41no—
890C2×D3—42no—
891C2×D3—84no—
892C3×C4—24no—
893C3×C4—22no—
894C3×C4—22no—
895C3×C4—24no—
896C3×C4—42no—
897C3×C4—41no—
898C3×C4D4212yes—
899C3×C4C23×D411yescharacteristic
900C3×C4C2×H(5,𝔽2)11yescharacteristic
901Dic3—24no—
902Dic3—42no—
903Dic3—41no—
904C23—22no—
905C23—22no—
906C23—21no—
907C23—42no—
908C23—42no—
909C23—62no—
910C23—61no—
911C23—82no—
912C23—122no—
913C23—242no—
914C23C22×#6712yes—
915C23C22×#6712yes—
916C23C22×#6711yescharacteristic
917Q8—22no—
918Q8—24no—
919Q8—22no—
920Q8—21no—
921Q8—21no—
922Q8—34no—
923Q8—44no—
924Q8—62no—
925Q8—64no—
926Q8—61no—
927Q8—61no—
928Q8—124no—
929Q8C2×D3×D414yes—
930D4—24no—
931D4—22no—
932D4—21no—
933D4—21no—
934D4—22no—
935D4—22no—
936D4—44no—
937D4—48no—
938D4—44no—
939D4—42no—
940D4—42no—
941D4—62no—
942D4—61no—
943D4—61no—
944D4—62no—
945D4—84no—
946D4—84no—
947D4—82no—
948D4—128no—
949D4—124no—
950D4—122no—
951D4—122no—
952D4—244no—
953D4—244no—
954D4—242no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—24no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—22no—
964C2×C4—21no—
965C2×C4—48no—
966C2×C4—44no—
967C2×C4—44no—
968C2×C4—42no—
969C2×C4—62no—
970C2×C4—64no—
971C2×C4—62no—
972C2×C4—61no—
973C2×C4—128no—
974C2×C4—124no—
975C2×C4—124no—
976C2×C4—122no—
977C2×C4C2×D3×D412yes—
978C2×C4#100412yes—
979C2×C4C22×#6714yes—
980C2×C4C22×#6712yes—
981C2×C4C22×#6712yes—
982C2×C4C22×#6711yescharacteristic
983C2×C4C24×D311yescharacteristic
984C8—32no—
985C8—32no—
986C8—62no—
987C8—62no—
988C8—62no—
989C2×C3—22no—
990C2×C3—42no—
991C2×C3—42no—
992C2×C3—81no—
993C2×C3—82no—
994C2×C3C2×D4211yescharacteristic
995C2×C3#358412yes—
996D3—81no—
997D3—82no—
998C22—22no—
999C22—22no—
1000C22—24no—
1001C22—22no—
1002C22—22no—
1003C22—22no—
1004C22—44no—
1005C22—42no—
1006C22—44no—
1007C22—41no—
1008C22—42no—
1009C22—84no—
1010C22—122no—
1011C22—124no—
1012C22—121no—
1013C22—122no—
1014C22—244no—
1015C22D4×#6712yes—
1016C22C23×#6711yescharacteristic
1017C4—24no—
1018C4—22no—
1019C4—24no—
1020C4—22no—
1021C4—42no—
1022C4—41no—
1023C4—64no—
1024C4—122no—
1025C4—121no—
1026C4D4×#6712yes—
1027C4C22×D3×D411yescharacteristic
1028C4C2×#100411yescharacteristic
1029C3#6105411yescharacteristic, complemented, Sylow
1030C2—22no—
1031C2—42no—
1032C2—42no—
1033C2—82no—
1034C2—81no—
1035C2—242no—
1036C2—241no—
1037C2C2×D4×#6711yescharacteristic
1038C2#8729712yes—
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3487C2
socleC22×C3C23×D4
hypercenter#3487D3
hypocenterC3#61054
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #525 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. C3×#3487C2semidirect
2. C2×#5838C2semidirect
3. C22×#950C2semidirect
4. #86023C2semidirect
5. #84113C2semidirect
6. #84081C2semidirect
7. #83585C2semidirect
8. #83583C2semidirect
9. #83549C2semidirect
10. #83547C2semidirect
11. #83391C2semidirect
12. #83390C2semidirect
13. #83382C2semidirect
14. #83378C2semidirect
15. #82928C2semidirect
16. #82922C2semidirect
17. #82916C2semidirect
18. #82551C2semidirect
19. #82549C2semidirect
26. C3×#550C22semidirect
28. C3×#548C22semidirect
39. C2×#951C22semidirect
44. C2×#950C22semidirect
48. C22×#216C22semidirect
50. C2×#942C22semidirect
61. #5553C22semidirect
62. #5552C22semidirect
65. #5239C22semidirect
66. #5238C22semidirect
67. #5238C22semidirect
70. #5227C22semidirect
74. #5075C22semidirect
75. #5074C22semidirect
76. #5073C22semidirect
77. #5059C22semidirect
78. #5058C22semidirect
79. #5054C22semidirect
80. #5051C22semidirect
81. #5048C22semidirect
82. #5047C22semidirect
83. #5041C22semidirect
84. #5040C22semidirect
85. #5039C22semidirect
86. #5038C22semidirect
87. #5038C22semidirect
88. #5037C22semidirect
89. #5037C22semidirect
90. #5030C22semidirect
91. C4×#216C22semidirect
92. #5028C22semidirect
93. #5027C22semidirect
94. #5011C22semidirect
95. D4×C3⋊C8C22semidirect
105. #3487D3semidirect
197. C2×#216D4semidirect
295. #550C2×D3semidirect
299. #548C2×D3semidirect
1029. C3#61054semidirect

Maximal subgroups

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

subgroupindex
C3×#34872
C2×#58382
C22×#9502
#860232
#841132
#840812
#835852
#835832
#835492
#835472
#833912
#833902
#833822
#833782
#829282
#829222
#829162
#825512
#825492
#610543