Finite Group Databasebeta

← #11670554

Subgroups — #11670554

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
1C2×#5751C211yesmaximal, characteristic, complemented
2C22×#904C211yesmaximal, characteristic, complemented
3#86040C211yesmaximal, characteristic, complemented
4#86023C211yesmaximal, characteristic, complemented
5C3×#2929C211yesmaximal, characteristic, complemented
6#83798C211yesmaximal, characteristic, complemented
7#83742C211yesmaximal, characteristic, complemented
8#79498C214yesmaximal, complemented
9#79497C214yesmaximal, complemented
10#79437C214yesmaximal, complemented
11#79435C214yesmaximal, complemented
12#79100C211yesmaximal, characteristic, complemented
13#79086C211yesmaximal, characteristic, complemented
14#78679C211yesmaximal, characteristic, complemented
15#78670C211yesmaximal, characteristic, complemented
16#78638C211yesmaximal, characteristic, complemented
17#78638C211yesmaximal, characteristic, complemented
18#78572C211yesmaximal, characteristic, complemented
19#78564C211yesmaximal, characteristic, complemented
20#61052—31nomaximal, Sylow
21C2×#1010C2211yescharacteristic
22C2×#1009C2211yescharacteristic
23C22×#235C2211yescharacteristic
24C22×#235C2211yescharacteristic, complemented
25C2×C3×#131C2211yescharacteristic
26C23×C3×C8C2211yescharacteristic, complemented
27C3×#525C2211yescharacteristic
28#5830C2211yescharacteristic
29#5825C2211yescharacteristic
30#5791C2211yescharacteristic
31#5791C2211yescharacteristic, complemented
32#5751—28no—
33C2×#909C2211yescharacteristic
34C2×#909C2212yescomplemented
35C2×#909C2211yescharacteristic, complemented
36C2×#908C2211yescharacteristic
37C2×#908C2211yescharacteristic
38C2×#908C2212yescomplemented
39C22×Dic12C2211yescharacteristic, complemented
40C2×#904—28no—
41C2×#904C2211yescharacteristic
42C2×#904C2214yescomplemented
43C2×#904C2212yescomplemented
44C2×#904C2214yescomplemented
45C22×D24C2211yescharacteristic
46C22×#204C2211yescharacteristic
47C22×#204C2212yescomplemented
48C22×#204C2211yescharacteristic, complemented
49#5656—22no—
50D3×#123—22no—
51#5633—22no—
52#5631—22no—
53#5612—22no—
54#5599—22no—
55#5592—22no—
56#5589—22no—
57#5553C2214yescomplemented
58#5552C2214yescomplemented
59#5551C2214yescomplemented
60#5550C2214yescomplemented
61#5526C2211yescharacteristic
62#5525C2211yescharacteristic, complemented
63#5521C2211yescharacteristic
64#5516C2211yescharacteristic, complemented
65C3×#435C2214yescomplemented
66C3×C8×D4C2214yescomplemented
67C3×#424C2211yescharacteristic, complemented
68C3×#408C2211yescharacteristic
69C3×#407C2211yescharacteristic, complemented
70C3×#405C2211yescharacteristic, complemented
71#5134C2214yescomplemented
72#5131C2211yescharacteristic
73#5131C2211yescharacteristic, complemented
74#5120C2211yescharacteristic, complemented
75#5120C2211yescharacteristic, complemented
76#5116C2212yescomplemented
77#5115C2212yescomplemented
78#5114C2212yescomplemented
79#5114C2212yescomplemented
80#5114C2214yescomplemented
81#5113C2211yescharacteristic
82#5113C2211yescharacteristic, complemented
83#5106C2211yescharacteristic, complemented
84#4849C2214yescomplemented
85#4845C2214yescomplemented
86#4844C2214yescomplemented
87#4843C2214yescomplemented
88#4739C2214yescomplemented
89#4734C2214yescomplemented
90#4734C2214yescomplemented
91#4734C2214yescomplemented
92#4733C2214yescomplemented
93#4733C2214yescomplemented
94#4733C2214yescomplemented
95#4732C2214yescomplemented
96#4715C2212yescomplemented
97#4712C2212yescomplemented
98#4710C2214yescomplemented
99#4696C2212yescomplemented
100#4693C2212yescomplemented
101C4×#204C2214yescomplemented
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#3057—31no—
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#2929D311yescharacteristic, complemented
121C2×C3×#41C2311yescharacteristic
122C23×C3×C4C2311yescharacteristic
123C22×#67—21no—
124C22×#67—21no—
125#1010—24no—
126#1010—42no—
127#1009—24no—
128#1009—42no—
129C2×#239—21no—
130C2×D3×Q8—21no—
131C2×#237—22no—
132C2×#237—21no—
133C2×D3×D4—22no—
134C2×D3×D4—21no—
135C2×#235—22no—
136C2×#235—22no—
137C2×#235—24no—
138C2×#235—24no—
139C2×#235—42no—
140C2×#235—42no—
141C2×#235C2311yescharacteristic
142C2×#235C2311yescharacteristic
143C2×#235C2314yes—
144C2×#235C2314yes—
145C2×#235C2312yes—
146C2×#235C2312yes—
147C22×D12C2311yescharacteristic
148C22×D12C2312yes—
149C22×D12C2311yescharacteristic
150C22×C4×D3—21no—
151C22×C4×D3—21no—
152C22×Dic6C2311yescharacteristic
153C22×Dic6C2312yes—
154C22×Dic6C2311yescharacteristic
155C3×#131—24no—
156C2×C3×M16C2311yescharacteristic
157C2×C3×M16C2311yescharacteristic
158C2×C3×M16C2312yes—
159C22×C3×C8—24no—
160C22×C3×C8C2311yescharacteristic
161C22×C3×C8C2312yes—
162C22×C3×C8C2312yes—
163C22×C3×C8C2312yes—
164C22×C3×C8C2311yescharacteristic
165C3×#123D412yes—
166C3×C22⋊Q8D412yes—
167C3×#121D412yes—
168C3×#120D412yes—
169C3×C4×D4C2314yes—
170C3×#117C2311yescharacteristic
171#953—21no—
172#953—21no—
173#947—21no—
174#944—21no—
175#940—24no—
176#940—21no—
177#939—24no—
178#938—24no—
179#937—22no—
180#937—24no—
181#936—21no—
182#935—22no—
183#930C2314yes—
184#930C2312yes—
185#930C2312yes—
186#929—21no—
187#929—21no—
188C4×#67—22no—
189C4×#67—22no—
190#926C2311yescharacteristic
191#926C2311yescharacteristic
192#924C2314yes—
193#924C2312yes—
194#924C2312yes—
195#909—24no—
196#909—28no—
197#909—42no—
198#908—24no—
199#908—28no—
200#908—42no—
201C2×Dic12—24no—
202C2×Dic12C2311yescharacteristic
203C2×Dic12C2314yes—
204C2×Dic12C2312yes—
205C2×Dic12C2312yes—
206#904—24no—
207#904—216no—
208#904—216no—
209#904—28no—
210C2×D24—24no—
211C2×D24C2311yescharacteristic
212C2×D24C2314yes—
213C2×D24C2312yes—
214C2×D24C2312yes—
215C2×#204—24no—
216C2×#204—28no—
217C2×#204D418yescomplemented
218C2×#204C2312yes—
219C2×#204C2311yescharacteristic
220C2×#204C2312yes—
221C2×#204C2311yescharacteristic
222C2×#204C2312yes—
223C2×#204C2312yes—
224C2×#204C2312yes—
225C2×#204C2312yes—
226C2×#204C2312yes—
227C2×#204C2312yes—
228#897—22no—
229#896—24no—
230#895—22no—
231#894—24no—
232#893—24no—
233#893—22no—
234D3×C4⋊C4—24no—
235#887—22no—
236#886—22no—
237#885—24no—
238#884—24no—
239#884—24no—
240#884—24no—
241#883—24no—
242#883—24no—
243#882—22no—
244#67⋊C4—24no—
245D3×C22⋊C4—22no—
246D3×C22⋊C4—24no—
247#877—22no—
248#875C2312yes—
249#875C2312yes—
250#874C2312yes—
251C4×D12C2314yes—
252#869C2312yes—
253C4×Dic6C2314yes—
254C3×C4⋊C8C2314yes—
255C3×C22⋊C8C2314yes—
256C3×C22⋊C8C2314yes—
257C3×#97C2312yes—
258C3×C4×C8C2312yes—
259#821C2314yes—
260#821C2314yes—
261#821C2312yes—
262#821C2312yes—
263#818C2312yes—
264#817C2312yes—
265#816C2314yes—
266#816C2314yes—
267#816C2312yes—
268#816C2312yes—
269C2×2−1+4—31no—
270C2×H(5,𝔽2)—31no—
271C22×#41—31no—
272C22×#41—31no—
273#577—68no—
274C2×#137—31no—
275C2×#137—32no—
276C2×#137—31no—
277C2×AGL(1,ℤ/8)—31no—
278C2×AGL(1,ℤ/8)—32no—
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×SD16—31no—
287C22×SD16—31no—
288C22×SD16—32no—
289C22×D8—31no—
290C2×#131C2×D311yescharacteristic
291C23×C8C2×D311yescharacteristic, complemented
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#536—31no—
302#535—31no—
303#535—31no—
304#535—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#496—32no—
315#495—32no—
316#492—32no—
317#468—34no—
318#467—32no—
319#466—32no—
320#465—32no—
321#465—34no—
322#465—32no—
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#435C2×D314yescomplemented
338C8×D4C2×D314yescomplemented
339#427—31no—
340#424C2×D311yescharacteristic, complemented
341#419—31no—
342#419—31no—
343#418—31no—
344#418—31no—
345#416—31no—
346#416—31no—
347#408C2×D311yescharacteristic
348#407C2×D311yescharacteristic, complemented
349#405C2×D311yescharacteristic, complemented
350C24×C3C2×D411yescharacteristic
351C23×D3—21no—
352C23×D3—22no—
353C23×D3—21no—
354C3×#41—22no—
355C3×#41—22no—
356C2×C3×Q8C2×D411yescharacteristic
357C2×C3×D4C2×D412yes—
358C2×C3×D4C2×D411yescharacteristic
359C2×C3×D4C2×D414yes—
360C22×C3×C4—22no—
361C22×C3×C4—22no—
362C22×C3×C4C2×D412yes—
363C22×C3×C4C2×D411yescharacteristic
364C22×C3×C4C2412yes—
365C22×C3×C4C2412yes—
366C22×C3×C4C2411yescharacteristic
367C2×#67—21no—
368C2×#67—22no—
369C2×#67—24no—
370C2×#67—22no—
371C2×#67—24no—
372C2×#67—21no—
373C2×#67—24no—
374C2×#67—22no—
375C2×#67—22no—
376C2×#67—44no—
377C2×#67—44no—
378C22×Dic3—21no—
379C22×Dic3—22no—
380C22×Dic3—21no—
381#239—44no—
382D3×Q8—44no—
383#237—44no—
384#237—48no—
385D3×D4—44no—
386D3×D4—48no—
387#235—22no—
388#235—22no—
389#235—22no—
390#235—22no—
391#235—28no—
392#235—24no—
393#235—28no—
394#235—24no—
395#235—44no—
396#235—44no—
397#235—42no—
398#235—42no—
399#235—48no—
400#235—48no—
401C2×D12—21no—
402C2×D12—22no—
403C2×D12—22no—
404C2×D12—22no—
405C2×D12—24no—
406C2×D12—22no—
407C2×D12—21no—
408C2×D12—24no—
409C2×D12—42no—
410C2×D12C2×D414yes—
411C2×D12C2411yescharacteristic
412C2×D12C2412yes—
413C2×D12C2411yescharacteristic
414C2×D12C2412yes—
415C2×C4×D3—24no—
416C2×C4×D3—24no—
417C2×C4×D3—22no—
418C2×C4×D3—22no—
419C2×C4×D3—21no—
420C2×C4×D3—21no—
421C2×C4×D3—24no—
422C2×C4×D3—44no—
423C2×C4×D3—44no—
424C2×Dic6—21no—
425C2×Dic6—22no—
426C2×Dic6—22no—
427C2×Dic6—22no—
428C2×Dic6—24no—
429C2×Dic6—22no—
430C2×Dic6—21no—
431C2×Dic6—42no—
432C2×Dic6C2×D414yes—
433C2×Dic6C2411yescharacteristic
434C2×Dic6C2412yes—
435C2×Dic6C2411yescharacteristic
436C2×Dic6C2412yes—
437C3×M16—22no—
438C3×M16—22no—
439C3×M16—24no—
440C2×C3×C8—22no—
441C2×C3×C8—24no—
442C2×C3×C8—24no—
443C2×C3×C8—24no—
444C2×C3×C8C2×D414yes—
445C2×C3×C8C2412yes—
446C2×C3×C8C2412yes—
447C2×C3×C8C2412yes—
448C2×C3×C8C2411yescharacteristic
449C2×C3×C8C2411yescharacteristic
450C3×C4⋊C4C2×D412yes—
451C3×C4⋊C4C2×D414yes—
452C3×C22⋊C4C2×D412yes—
453C3×C22⋊C4C2×D414yes—
454C3×C22⋊C4C2×D414yes—
455C3×C42C2412yes—
456#217—21no—
457#217—21no—
458#217—24no—
459#217—22no—
460#217—22no—
461(C2×D3)⋊C4—24no—
462(C2×D3)⋊C4—24no—
463(C2×D3)⋊C4—24no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—24no—
467C4⋊Dic3—24no—
468C4⋊Dic3C2412yes—
469C4⋊Dic3C2412yes—
470Dic3⋊C4—24no—
471Dic3⋊C4—22no—
472Dic3⋊C4—22no—
473Dic3⋊C4—24no—
474C4×Dic3—24no—
475C4×Dic3—21no—
476C4×Dic3—21no—
477Dic12—28no—
478Dic12—24no—
479Dic12—22no—
480Dic12—42no—
481D24—28no—
482D24—24no—
483D24—22no—
484D24—42no—
485#204—24no—
486#204—24no—
487#204—22no—
488#204—24no—
489#204—24no—
490#204—22no—
491#204—42no—
492#204—42no—
493#204C2×D418yes—
494#204C2×D418yes—
4952−1+4—64no—
4962−1+4—122no—
497H(5,𝔽2)—64no—
498H(5,𝔽2)—122no—
499C2×#41—31no—
500C2×#41—31no—
501C2×#41—34no—
502C2×#41—32no—
503C2×#41—34no—
504C2×#41—32no—
505C2×#41—64no—
506C2×#41—64no—
507C2×#41—61no—
508C2×#41—62no—
509C2×#41—61no—
510C2×#41—62no—
511C2×#41—62no—
512C2×#41—122no—
513C2×#41—122no—
514C2×#41C22×D311yescharacteristic
515C22×Q8—31no—
516C22×Q8—31no—
517C22×Q8—32no—
518C22×Q8—61no—
519C22×D4—31no—
520C22×D4—31no—
521C22×D4—32no—
522C22×D4—61no—
523C22×D4—61no—
524C22×D4—62no—
525C22×D4—61no—
526C23×C4—61no—
527C23×C4—61no—
528C23×C4C22×D311yescharacteristic
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—616no—
536#135—616no—
537#135—68no—
538#135—64no—
539C2×Q16—34no—
540C2×Q16—32no—
541C2×Q16—31no—
542C2×Q16—32no—
543C2×Q16—64no—
544C2×SD16—38no—
545C2×SD16—32no—
546C2×SD16—32no—
547C2×SD16—31no—
548C2×SD16—32no—
549C2×SD16—32no—
550C2×SD16—32no—
551C2×SD16—32no—
552C2×SD16—31no—
553C2×SD16—32no—
554C2×SD16—32no—
555C2×SD16—68no—
556C2×SD16—64no—
557C2×D8—34no—
558C2×D8—32no—
559C2×D8—31no—
560C2×D8—32no—
561C2×D8—64no—
562#131—24no—
563C2×M16C22×D311yescharacteristic
564C2×M16C22×D312yes—
565C2×M16C22×D311yescharacteristic
566C22×C8—24no—
567C22×C8C22×D311yescharacteristic
568C22×C8C22×D312yes—
569C22×C8C22×D312yes—
570C22×C8C22×D312yes—
571C22×C8C22×D311yescharacteristic
572C4⋊Q8—32no—
573C4⋊Q8—61no—
574#127—32no—
575#127—61no—
576#127—64no—
577#124—32no—
578#124—32no—
579#124—61no—
580#124—61no—
581#124—64no—
582#123—62no—
583#123—61no—
584#123—61no—
585#123—64no—
586#123—62no—
587#123—64no—
588#123—64no—
589#123D1212yes—
590C22⋊Q8—32no—
591C22⋊Q8—32no—
592C22⋊Q8—34no—
593C22⋊Q8—64no—
594C22⋊Q8—62no—
595C22⋊Q8D1212yes—
596#121—32no—
597#121—32no—
598#121—34no—
599#121—64no—
600#121—64no—
601#121—62no—
602#121—64no—
603#121—64no—
604#121—64no—
605#121D1212yes—
606#120—61no—
607#120—61no—
608#120—62no—
609#120—64no—
610#120—62no—
611#120D1212yes—
612C4×Q8—34no—
613C4×Q8—62no—
614C4×D4—34no—
615C4×D4—62no—
616C4×D4—62no—
617C4×D4—62no—
618C4×D4—64no—
619C4×D4—64no—
620C4×D4C22×D314yes—
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⋊C8C22×D314yes—
631#103—32no—
632#103—32no—
633#103—34no—
634#103—34no—
635#102—32no—
636#102—32no—
637#102—34no—
638#102—34no—
639C22⋊C8C22×D314yes—
640C22⋊C8C22×D314yes—
641#97C22×D312yes—
642C4×C8C22×D312yes—
643C23×C3—22no—
644C23×C3—42no—
645C23×C3C22×D412yes—
646C23×C3C22×D412yes—
647C23×C3C22×D411yescharacteristic
648C22×D3—22no—
649C22×D3—24no—
650C22×D3—21no—
651C22×D3—22no—
652C22×D3—21no—
653C22×D3—44no—
654C22×D3—42no—
655C22×D3—82no—
656C22×D3—82no—
657C22×D3—84no—
658C3×Q8—22no—
659C3×D4—24no—
660C3×D4—22no—
661C3×D4—44no—
662C2×C3×C4—22no—
663C2×C3×C4—24no—
664C2×C3×C4—22no—
665C2×C3×C4—22no—
666C2×C3×C4—22no—
667C2×C3×C4—22no—
668C2×C3×C4C22×D414yes—
669C2×C3×C4C22×D412yes—
670C2×C3×C4C22×D412yes—
671C2×C3×C4C22×D411yescharacteristic
672C2×C3×C4C22×D412yes—
673C2×C3×C4H(5,𝔽2)12yes—
674C2×C3×C4C2511yescharacteristic
675#67—48no—
676#67—44no—
677#67—48no—
678#67—44no—
679#67—42no—
680#67—42no—
681#67—82no—
682#67—82no—
683#67—84no—
684C2×Dic3—24no—
685C2×Dic3—22no—
686C2×Dic3—22no—
687C2×Dic3—22no—
688C2×Dic3—21no—
689C2×Dic3—22no—
690C2×Dic3—21no—
691C2×Dic3—44no—
692C2×Dic3—42no—
693D12—24no—
694D12—21no—
695D12—22no—
696D12—21no—
697D12—22no—
698D12—21no—
699D12—22no—
700D12—21no—
701D12—44no—
702D12—42no—
703D12—84no—
704D12C22×D414yes—
705C4×D3—48no—
706C4×D3—44no—
707C4×D3—48no—
708C4×D3—44no—
709C4×D3—42no—
710C4×D3—42no—
711C4×D3—84no—
712Dic6—24no—
713Dic6—22no—
714Dic6—21no—
715Dic6—22no—
716Dic6—21no—
717Dic6—21no—
718Dic6—22no—
719Dic6—21no—
720Dic6—44no—
721Dic6—42no—
722Dic6C22×D414yes—
723C3×C8—22no—
724C3×C8—22no—
725C3×C8—22no—
726C3×C8C22×D412yes—
727C3×C8C22×D412yes—
728C24—61no—
729C24—62no—
730C24—61no—
731C24C2×D1211yescharacteristic
732#41—22no—
733#41—22no—
734#41—68no—
735#41—64no—
736#41—68no—
737#41—64no—
738#41—62no—
739#41—62no—
740#41—62no—
741#41—62no—
742#41—124no—
743#41—124no—
744#41—122no—
745#41—122no—
746#41—128no—
747#41—128no—
748#41—128no—
749#41—124no—
750#41—124no—
751C2×Q8—34no—
752C2×Q8—32no—
753C2×Q8—31no—
754C2×Q8—32no—
755C2×Q8—31no—
756C2×Q8—64no—
757C2×Q8—61no—
758C2×Q8—62no—
759C2×Q8—61no—
760C2×Q8—62no—
761C2×Q8—62no—
762C2×Q8—62no—
763C2×Q8—122no—
764C2×Q8—124no—
765C2×Q8C2×D1211yescharacteristic
766C2×D4—34no—
767C2×D4—32no—
768C2×D4—31no—
769C2×D4—32no—
770C2×D4—31no—
771C2×D4—64no—
772C2×D4—61no—
773C2×D4—64no—
774C2×D4—61no—
775C2×D4—62no—
776C2×D4—64no—
777C2×D4—62no—
778C2×D4—62no—
779C2×D4—64no—
780C2×D4—62no—
781C2×D4—61no—
782C2×D4—62no—
783C2×D4—61no—
784C2×D4—64no—
785C2×D4—62no—
786C2×D4—62no—
787C2×D4—62no—
788C2×D4—122no—
789C2×D4—124no—
790C2×D4—124no—
791C2×D4—128no—
792C2×D4—124no—
793C2×D4C2×D1212yes—
794C2×D4C2×D1211yescharacteristic
795C2×D4C2×D1214yes—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—61no—
799C22×C4—62no—
800C22×C4—61no—
801C22×C4—64no—
802C22×C4—62no—
803C22×C4—62no—
804C22×C4—61no—
805C22×C4—64no—
806C22×C4—61no—
807C22×C4—64no—
808C22×C4—124no—
809C22×C4—124no—
810C22×C4C2×D1212yes—
811C22×C4C2×D1211yescharacteristic
812C22×C4C23×D312yes—
813C22×C4C23×D312yes—
814C22×C4C23×D311yescharacteristic
815Q16—68no—
816Q16—64no—
817Q16—62no—
818Q16—122no—
819SD16—38no—
820SD16—38no—
821SD16—64no—
822SD16—64no—
823SD16—62no—
824SD16—64no—
825SD16—64no—
826SD16—62no—
827SD16—122no—
828SD16—122no—
829D8—68no—
830D8—64no—
831D8—62no—
832D8—122no—
833M16—22no—
834M16—22no—
835M16—24no—
836C2×C8—22no—
837C2×C8—24no—
838C2×C8—24no—
839C2×C8—24no—
840C2×C8D3×D414yes—
841C2×C8C23×D312yes—
842C2×C8C23×D312yes—
843C2×C8C23×D312yes—
844C2×C8C23×D311yescharacteristic
845C2×C8C23×D311yescharacteristic
846C4⋊C4—32no—
847C4⋊C4—32no—
848C4⋊C4—62no—
849C4⋊C4—64no—
850C4⋊C4—64no—
851C4⋊C4—64no—
852C4⋊C4—62no—
853C4⋊C4C2×D1214yes—
854C4⋊C4C2×D1212yes—
855C22⋊C4—61no—
856C22⋊C4—64no—
857C22⋊C4—61no—
858C22⋊C4—62no—
859C22⋊C4—62no—
860C22⋊C4—62no—
861C22⋊C4—64no—
862C22⋊C4—64no—
863C22⋊C4—62no—
864C22⋊C4—64no—
865C22⋊C4—64no—
866C22⋊C4C2×D1212yes—
867C22⋊C4C2×D1214yes—
868C22⋊C4C2×D1214yes—
869C42—61no—
870C42—61no—
871C42—64no—
872C42C23×D312yes—
873C22×C3—22no—
874C22×C3—22no—
875C22×C3—24no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—44no—
880C22×C3D4212yes—
881C22×C3C23×D411yescharacteristic
882C2×D3—24no—
883C2×D3—44no—
884C2×D3—42no—
885C2×D3—44no—
886C2×D3—42no—
887C2×D3—41no—
888C2×D3—42no—
889C2×D3—41no—
890C2×D3—84no—
891C2×D3—84no—
892C2×D3—164no—
893C3×C4—24no—
894C3×C4—22no—
895C3×C4—22no—
896C3×C4D4212yes—
897C3×C4C23×D411yescharacteristic
898C3×C4C2×H(5,𝔽2)11yescharacteristic
899Dic3—24no—
900Dic3—42no—
901Dic3—42no—
902Dic3—41no—
903Dic3—42no—
904Dic3—41no—
905C23—22no—
906C23—42no—
907C23—62no—
908C23—64no—
909C23—61no—
910C23—62no—
911C23—61no—
912C23—124no—
913C23—122no—
914C23—242no—
915C23—242no—
916C23—244no—
917C23C22×D1212yes—
918C23C22×D1212yes—
919C23C22×D1211yescharacteristic
920Q8—22no—
921Q8—34no—
922Q8—62no—
923Q8—64no—
924Q8—61no—
925Q8—62no—
926Q8—61no—
927Q8—61no—
928Q8—62no—
929Q8—61no—
930Q8—124no—
931Q8—122no—
932D4—24no—
933D4—22no—
934D4—34no—
935D4—44no—
936D4—61no—
937D4—62no—
938D4—61no—
939D4—62no—
940D4—61no—
941D4—62no—
942D4—61no—
943D4—64no—
944D4—124no—
945D4—128no—
946D4—124no—
947D4—124no—
948D4—128no—
949D4—122no—
950D4—122no—
951D4—122no—
952D4—244no—
953D4—242no—
954D4—244no—
955D4—242no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—24no—
962C2×C4—62no—
963C2×C4—64no—
964C2×C4—62no—
965C2×C4—62no—
966C2×C4—61no—
967C2×C4—62no—
968C2×C4—61no—
969C2×C4—128no—
970C2×C4—124no—
971C2×C4—128no—
972C2×C4—124no—
973C2×C4—124no—
974C2×C4—122no—
975C2×C4—122no—
976C2×C4—122no—
977C2×C4—244no—
978C2×C4C22×D1214yes—
979C2×C4C22×D1212yes—
980C2×C4C22×D1212yes—
981C2×C4C22×D1211yescharacteristic
982C2×C4C2×D3×D412yes—
983C2×C4#100912yes—
984C2×C4C24×D311yescharacteristic
985C8—22no—
986C8—22no—
987C8—22no—
988C8C2×D3×D412yes—
989C8C2×D3×D412yes—
990C2×C3—22no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3C2×D4211yescharacteristic
994C2×C3#358412yes—
995D3—44no—
996D3—81no—
997D3—82no—
998D3—81no—
999C22—22no—
1000C22—22no—
1001C22—22no—
1002C22—22no—
1003C22—24no—
1004C22—22no—
1005C22—44no—
1006C22—64no—
1007C22—124no—
1008C22—121no—
1009C22—122no—
1010C22—121no—
1011C22—122no—
1012C22—124no—
1013C22—122no—
1014C22—244no—
1015C22—244no—
1016C22—484no—
1017C22D4×D1212yes—
1018C22C23×D1211yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—24no—
1022C4—64no—
1023C4—121no—
1024C4—122no—
1025C4—121no—
1026C4—122no—
1027C4—122no—
1028C4D4×D1212yes—
1029C4C22×D3×D411yescharacteristic
1030C4C2×#100911yescharacteristic
1031C3#6105211yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—42no—
1034C2—42no—
1035C2—124no—
1036C2—242no—
1037C2—241no—
1038C2—241no—
1039C2C2×D4×D1211yescharacteristic
1040C2#8716312yes—
subgroupG/H
centerC22C23×D12
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#2929C2
socleC22×C3C23×D4
hypercenter#2929D3
hypocenterC3#61052
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #525 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. C2×#5751C2semidirect
2. C22×#904C2semidirect
3. #86040C2semidirect
4. #86023C2semidirect
5. C3×#2929C2semidirect
6. #83798C2semidirect
7. #83742C2semidirect
8. #79498C2semidirect
9. #79497C2semidirect
10. #79437C2semidirect
11. #79435C2semidirect
12. #79100C2semidirect
13. #79086C2semidirect
14. #78679C2semidirect
15. #78670C2semidirect
16. #78638C2semidirect
17. #78638C2semidirect
18. #78572C2semidirect
19. #78564C2semidirect
24. C22×#235C22semidirect
26. C23×C3×C8C22semidirect
31. #5791C22semidirect
34. C2×#909C22semidirect
35. C2×#909C22semidirect
38. C2×#908C22semidirect
39. C22×Dic12C22semidirect
42. C2×#904C22semidirect
43. C2×#904C22semidirect
44. C2×#904C22semidirect
47. C22×#204C22semidirect
48. C22×#204C22semidirect
57. #5553C22semidirect
58. #5552C22semidirect
59. #5551C22semidirect
60. #5550C22semidirect
62. #5525C22semidirect
64. #5516C22semidirect
65. C3×#435C22semidirect
66. C3×C8×D4C22semidirect
67. C3×#424C22semidirect
69. C3×#407C22semidirect
70. C3×#405C22semidirect
71. #5134C22semidirect
73. #5131C22semidirect
74. #5120C22semidirect
75. #5120C22semidirect
76. #5116C22semidirect
77. #5115C22semidirect
78. #5114C22semidirect
79. #5114C22semidirect
80. #5114C22semidirect
82. #5113C22semidirect
83. #5106C22semidirect
84. #4849C22semidirect
85. #4845C22semidirect
86. #4844C22semidirect
87. #4843C22semidirect
88. #4739C22semidirect
89. #4734C22semidirect
90. #4734C22semidirect
91. #4734C22semidirect
92. #4733C22semidirect
93. #4733C22semidirect
94. #4733C22semidirect
95. #4732C22semidirect
96. #4715C22semidirect
97. #4712C22semidirect
98. #4710C22semidirect
99. #4696C22semidirect
100. #4693C22semidirect
101. C4×#204C22semidirect
120. #2929D3semidirect
217. C2×#204D4semidirect
291. C23×C8C2×D3semidirect
337. #435C2×D3semidirect
338. C8×D4C2×D3semidirect
340. #424C2×D3semidirect
348. #407C2×D3semidirect
349. #405C2×D3semidirect
1031. C3#61052semidirect

Maximal subgroups

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

subgroupindex
C2×#57512
C22×#9042
#860402
#860232
C3×#29292
#837982
#837422
#794982
#794972
#794372
#794352
#791002
#790862
#786792
#786702
#786382
#785722
#785642
#610523