Finite Group Databasebeta

← #11675202

Subgroups — #11675202

Order 768.

1896 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85848C211yesmaximal, characteristic, complemented
2#85828C211yesmaximal, characteristic, complemented
3C3×C4×#135C211yesmaximal, characteristic, complemented
4#83901C212yesmaximal, complemented
5#82526C211yesmaximal, characteristic, complemented
6#82508C211yesmaximal, characteristic, complemented
7#79703C212yesmaximal, complemented
8#79701C212yesmaximal, complemented
9#79629C212yesmaximal, complemented
10#79625C212yesmaximal, complemented
11#79622C212yesmaximal, complemented
12#79621C212yesmaximal, complemented
13#79570C212yesmaximal, complemented
14#79567C212yesmaximal, complemented
15#79197C212yesmaximal, complemented
16#78827C212yesmaximal, complemented
17#78820C212yesmaximal, complemented
18C2×#4694C211yesmaximal, characteristic, complemented
19#78445C211yesmaximal, characteristic, complemented
20#61329—31nomaximal, Sylow
21C2×C3×#135C2211yescharacteristic
22C3×C4×#41C2211yescharacteristic
23C3×C4×#41C2211yescharacteristic
24#5830C2212yes—
25#5827C2212yes—
26C2×#949C2212yes—
27#5585C2212yes—
28#5585C2212yes—
29#5570C2212yescomplemented
30Q8×Dic6C2212yescomplemented
31#5553C2212yes—
32#5553C2212yes—
33#5550—22no—
34#5550—22no—
35#5543—22no—
36#5543C2212yescomplemented
37D4×Dic6—22no—
38D4×Dic6C2212yescomplemented
39#5535—22no—
40#5521C2212yes—
41#5519—22no—
42#5519C2212yes—
43#5477—21no—
44#5477—21no—
45C2×#874C2211yescharacteristic
46#5470—21no—
47#5470C2211yescharacteristic
48C2×#869—21no—
49C2×#869C2211yescharacteristic
50C3×C4×Q16C2211yescharacteristic, complemented
51C3×C4×Q16C2211yescharacteristic, complemented
52C3×C4×SD16C2211yescharacteristic, complemented
53C3×C4×SD16C2211yescharacteristic, complemented
54C3×C4×SD16C2211yescharacteristic, complemented
55C3×C4×SD16C2211yescharacteristic, complemented
56C3×C4×D8C2211yescharacteristic, complemented
57C3×C4×D8C2211yescharacteristic, complemented
58C3×#427C2211yescharacteristic
59C3×#416C2211yescharacteristic
60C3×#416C2211yescharacteristic
61C2×C3×C4×C8C2211yescharacteristic
62#5232C2212yes—
63#5185C2214yescomplemented
64#5165C2214yescomplemented
65#5163C2214yescomplemented
66#5150C2214yescomplemented
67C2×#821C2212yes—
68C2×#821C2212yes—
69#5102C2212yes—
70#5101C2212yes—
71#5027C2212yes—
72#5027C2212yes—
73#5021C2212yescomplemented
74#5020C2212yescomplemented
75#5015C2212yes—
76#5015C2212yes—
77#5008C2212yescomplemented
78#5007C2212yescomplemented
79#5001C2212yes—
80#4995C2212yes—
81#4924C2211yescharacteristic
82#4891C2214yescomplemented
83#4890C2214yescomplemented
84#4871C2214yescomplemented
85#4870C2214yescomplemented
86#4817C2214yescomplemented
87#4800C2214yescomplemented
88#4794C2214yescomplemented
89#4788C2214yescomplemented
90#4785C2214yescomplemented
91#4764C2214yescomplemented
92#4760C2214yescomplemented
93#4756C2214yescomplemented
94#4694C2212yes—
95#4694C2212yes—
96#4694C2212yes—
97#4694C2212yes—
98#4679C2212yescomplemented
99#4679C2212yescomplemented
100C8×Dic6C2212yescomplemented
101C8×Dic6C2212yescomplemented
102#3508—31no—
103#3503—31no—
104#3375—32no—
105#3373—32no—
106#3368—32no—
107#3366—32no—
108#3365—32no—
109#3362—32no—
110#3361—32no—
111#3358—32no—
112#3136—32no—
113C2×#486—31no—
114#3081—32no—
115#3079—31no—
116#3045—32no—
117#3038—31no—
118#2960—31no—
119#2946—32no—
120C4×#135D311yescharacteristic, complemented
121C2×C3×#41C2311yescharacteristic
122C2×C3×#41C2311yescharacteristic
123C2×#235—22no—
124C2×#235—22no—
125C22×D12—21no—
126C22×D12—21no—
127C22×D12C2312yes—
128C22×Dic6—21no—
129C22×Dic6—22no—
130C3×#135—24no—
131C2×C3×Q16C2311yescharacteristic
132C2×C3×SD16C2311yescharacteristic
133C2×C3×SD16C2311yescharacteristic
134C2×C3×D8C2311yescharacteristic
135C22×C3×C8C2311yescharacteristic
136C22×C3×C8C2311yescharacteristic
137C3×C4×Q8C2311yescharacteristic
138C3×C4×Q8C2311yescharacteristic
139C3×C4×Q8C2311yescharacteristic
140C3×C4×Q8C2311yescharacteristic
141C3×C4×D4—21no—
142C3×C4×D4—21no—
143C3×C4×D4—21no—
144C3×C4×D4—21no—
145C3×C4×D4C2311yescharacteristic
146C3×C4×D4C2311yescharacteristic
147C3×C4×D4C2311yescharacteristic
148C3×C4×D4C2311yescharacteristic
149C3×#117—21no—
150C3×#117—21no—
151C3×#117C2311yescharacteristic
152C3×#117C2311yescharacteristic
153C2×C3×C42—21no—
154C2×C3×C42—21no—
155C2×C3×C42C2311yescharacteristic
156#949—28no—
157#947C2314yes—
158Q8×Dic3C2314yes—
159C2×#215C2314yes—
160#940C2314yes—
161#937—24no—
162D4×Dic3—24no—
163D4×Dic3C2314yes—
164C2×#213C2314yes—
165#930—22no—
166#930—22no—
167#930—22no—
168#930—22no—
169#926—22no—
170#926C2312yes—
171C2×C4⋊Dic3—21no—
172C2×C4⋊Dic3—22no—
173C2×C4⋊Dic3—22no—
174C2×C4⋊Dic3C2312yes—
175#924—22no—
176#924—22no—
177#924D412yes—
178#924D412yes—
179C2×#208C2312yes—
180#894—24no—
181#894—24no—
182#893C2314yes—
183#893C2314yes—
184#890—24no—
185#890C2314yes—
186#888—24no—
187#888C2314yes—
188#884—24no—
189#884—24no—
190D3×C22⋊C4—24no—
191#878—24no—
192#878—24no—
193#878—24no—
194#875—22no—
195#875—22no—
196#874—21no—
197#874—21no—
198#874C2312yes—
199#874C2312yes—
200C4×D12—22no—
201C4×D12—22no—
202C4×D12—22no—
203C4×D12—22no—
204#870—22no—
205#870D412yes—
206#869—22no—
207#869—21no—
208#869—21no—
209#869—22no—
210#869—22no—
211#869D411yescharacteristic
212#869D411yescharacteristic
213#869C2312yes—
214#869C2312yes—
215C4×Dic6—22no—
216C4×Dic6—22no—
217C4×Dic6C2312yes—
218C4×Dic6C2312yes—
219C3×#107C2311yescharacteristic
220C3×#107C2311yescharacteristic
221C3×#106C2311yescharacteristic
222C3×#106C2311yescharacteristic
223C3×#103C2311yescharacteristic
224C3×#103C2311yescharacteristic
225C3×#103C2311yescharacteristic
226C3×#103C2311yescharacteristic
227C3×#102C2311yescharacteristic
228C3×#102C2311yescharacteristic
229C3×#102C2311yescharacteristic
230C3×#102C2311yescharacteristic
231C3×C4×C8C2311yescharacteristic
232C3×C4×C8C2311yescharacteristic
233C3×C4×C8C2311yescharacteristic
234C3×C4×C8C2311yescharacteristic
235#835C2314yes—
236#832C2314yes—
237#821C2314yes—
238#821C2314yes—
239#821C2314yes—
240#821C2314yes—
241#815C2314yes—
242Dic3⋊C8C2314yes—
243Dic3⋊C8C2314yes—
244C8×Dic3C2314yes—
245#809C2314yes—
246#809C2314yes—
247#808C2314yes—
248#807C2314yes—
249C4⋊(C3⋊C8)C2312yes—
250C4⋊(C3⋊C8)C2312yes—
251C2×AGL(1,ℤ/8)—32no—
252C2×#135C2×D311yescharacteristic
253#559—32no—
254#559—32no—
255Q82—32no—
256#557—32no—
257#554—32no—
258#554—62no—
259#550—32no—
260#550—32no—
261D4×Q8—32no—
262D4×Q8—62no—
263#546—62no—
264#546—62no—
265#544—32no—
266#544—62no—
267#540—62no—
268#535—32no—
269#533—31no—
270#533—61no—
271#532—61no—
272#532—61no—
273C2×C4⋊Q8—31no—
274C2×C4⋊Q8—61no—
275C2×#127—31no—
276#520—32no—
277#518—32no—
278C4×#41C2×D311yescharacteristic
279C4×#41C2×D311yescharacteristic
280#490—34no—
281#489—34no—
282#488—34no—
283#486—34no—
284#486—32no—
285#486—32no—
286#486—32no—
287#486—32no—
288#478—34no—
289#478—34no—
290#477—32no—
291#476—32no—
292#476—34no—
293#475—32no—
294#474—32no—
295#474—34no—
296#464—34no—
297#463—34no—
298#460—34no—
299#460—32no—
300#460—32no—
301#459—34no—
302#459—32no—
303#459—32no—
304#446—32no—
305#446—32no—
306C8×Q8—32no—
307C8×Q8—32no—
308#442—34no—
309#440—34no—
310C4×Q16C2×D311yescharacteristic, complemented
311C4×Q16C2×D311yescharacteristic, complemented
312C4×SD16—34no—
313C4×SD16C2×D311yescharacteristic, complemented
314C4×SD16C2×D311yescharacteristic, complemented
315C4×SD16C2×D311yescharacteristic, complemented
316C4×SD16C2×D311yescharacteristic, complemented
317C4×D8—34no—
318C4×D8C2×D311yescharacteristic, complemented
319C4×D8C2×D311yescharacteristic, complemented
320#428—32no—
321#427C2×D311yescharacteristic
322#424—32no—
323#423—31no—
324#418—32no—
325#417—32no—
326#416C2×D311yescharacteristic
327#416C2×D311yescharacteristic
328C2×#102—32no—
329C2×#102—32no—
330#405—32no—
331C2×C4×C8C2×D311yescharacteristic
332C23×D3—22no—
333C3×#41—22no—
334C3×#41—22no—
335C3×#41—22no—
336C3×#41#4114yescomplemented
337C2×C3×Q8C2411yescharacteristic
338C2×C3×Q8C2411yescharacteristic
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4C2411yescharacteristic
342C2×C3×D4C2411yescharacteristic
343C22×C3×C4—21no—
344C22×C3×C4—21no—
345C22×C3×C4—21no—
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4C2×D411yescharacteristic
350C22×C3×C4C2×D411yescharacteristic
351C22×C3×C4C2411yescharacteristic
352C2×#67—24no—
353C2×#67—24no—
354C22×Dic3—22no—
355C22×Dic3—24no—
356#235—84no—
357#235—84no—
358C2×D12—24no—
359C2×D12—24no—
360C2×D12—22no—
361C2×D12—22no—
362C2×D12—22no—
363C2×D12—22no—
364C2×D12—22no—
365C2×D12—82no—
366C2×D12—82no—
367C2×D12C2414yes—
368C2×C4×D3—24no—
369C2×C4×D3—24no—
370C2×Dic6—22no—
371C2×Dic6—22no—
372C2×Dic6—24no—
373C2×Dic6—84no—
374C2×Dic6—82no—
375C2×Dic6C2×D412yes—
376C2×Dic6C2×D412yes—
377C3×Q16—22no—
378C3×SD16—22no—
379C3×SD16—22no—
380C3×D8—22no—
381C2×C3×C8—22no—
382C2×C3×C8—22no—
383C2×C3×C8C2411yescharacteristic
384C2×C3×C8C2411yescharacteristic
385C2×C3×C8C2411yescharacteristic
386C2×C3×C8C2411yescharacteristic
387C3×C4⋊C4—21no—
388C3×C4⋊C4—21no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—21no—
391C3×C4⋊C4C2411yescharacteristic
392C3×C4⋊C4C2411yescharacteristic
393C3×C4⋊C4C2411yescharacteristic
394C3×C4⋊C4C2411yescharacteristic
395C3×C22⋊C4—21no—
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—21no—
400C3×C22⋊C4—21no—
401C3×C42—21no—
402C3×C42—21no—
403C3×C42—21no—
404C3×C42—21no—
405C3×C42—21no—
406C3×C42—21no—
407C3×C42C2×D411yescharacteristic
408C3×C42C2×D411yescharacteristic
409C3×C42C2411yescharacteristic
410C3×C42C2411yescharacteristic
411#217—24no—
412#217C2×D414yes—
413#215—28no—
414#213—28no—
415(C2×D3)⋊C4—24no—
416(C2×D3)⋊C4—24no—
417(C2×D3)⋊C4—24no—
418(C2×D3)⋊C4—24no—
419C4⋊Dic3—22no—
420C4⋊Dic3—22no—
421C4⋊Dic3—22no—
422C4⋊Dic3—24no—
423C4⋊Dic3—24no—
424C4⋊Dic3C2×D412yes—
425C4⋊Dic3C2×D412yes—
426C4⋊Dic3C2×D412yes—
427C4⋊Dic3C2×D412yes—
428C4⋊Dic3C2414yes—
429Dic3⋊C4—24no—
430Dic3⋊C4—24no—
431Dic3⋊C4C2×D414yes—
432Dic3⋊C4C2×D414yes—
433C4×Dic3—24no—
434C4×Dic3C2414yes—
435#208—24no—
436C2×C3⋊C8C2414yes—
437C2×#41—62no—
438C2×#41—62no—
439C2×#41C22×D311yescharacteristic
440C2×#41C22×D311yescharacteristic
441C22×Q8—62no—
442C22×Q8—61no—
443C22×D4—32no—
444C22×D4—61no—
445C22×D4—61no—
446AGL(1,ℤ/8)—68no—
447#135—24no—
448C2×Q16C22×D311yescharacteristic
449C2×SD16—34no—
450C2×SD16C22×D311yescharacteristic
451C2×SD16C22×D311yescharacteristic
452C2×D8—34no—
453C2×D8C22×D311yescharacteristic
454C2×M16—32no—
455C22×C8C22×D311yescharacteristic
456C22×C8C22×D311yescharacteristic
457C4⋊Q8—34no—
458C4⋊Q8—31no—
459C4⋊Q8—31no—
460C4⋊Q8—32no—
461C4⋊Q8—32no—
462C4⋊Q8—62no—
463C4⋊Q8—62no—
464C4⋊Q8—62no—
465C4⋊Q8—64no—
466C4⋊Q8—61no—
467C4⋊Q8—61no—
468#127—34no—
469#127—32no—
470#127—32no—
471#127—61no—
472#127—61no—
473#125—34no—
474#125—32no—
475#125—62no—
476#125—64no—
477#124—34no—
478#124—62no—
479#124—62no—
480#123—64no—
481#123—64no—
482C22⋊Q8—32no—
483C22⋊Q8—32no—
484C22⋊Q8—64no—
485C22⋊Q8—64no—
486C22⋊Q8—64no—
487C22⋊Q8—62no—
488C22⋊Q8—62no—
489#121—64no—
490#121—64no—
491#121—62no—
492#121—62no—
493#121—62no—
494#121—62no—
495#120—64no—
496C4×Q8—32no—
497C4×Q8—32no—
498C4×Q8—34no—
499C4×Q8—62no—
500C4×Q8—62no—
501C4×Q8C22×D311yescharacteristic
502C4×Q8C22×D311yescharacteristic
503C4×Q8C22×D311yescharacteristic
504C4×Q8C22×D311yescharacteristic
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4—34no—
510C4×D4—34no—
511C4×D4—34no—
512C4×D4—62no—
513C4×D4—62no—
514C4×D4—62no—
515C4×D4—62no—
516C4×D4—64no—
517C4×D4C22×D311yescharacteristic
518C4×D4C22×D311yescharacteristic
519C4×D4C22×D311yescharacteristic
520C4×D4C22×D311yescharacteristic
521#117—21no—
522#117—21no—
523#117—32no—
524#117—62no—
525#117C22×D311yescharacteristic
526#117C22×D311yescharacteristic
527C2×C4⋊C4—32no—
528C2×C4⋊C4—62no—
529C2×C4⋊C4—62no—
530C2×C4⋊C4—61no—
531C2×C22⋊C4—64no—
532C2×C42—21no—
533C2×C42—21no—
534C2×C42C22×D311yescharacteristic
535#107—34no—
536#107C22×D311yescharacteristic
537#107C22×D311yescharacteristic
538#106—34no—
539#106C22×D311yescharacteristic
540#106C22×D311yescharacteristic
541C4⋊C8—34no—
542C4⋊C8—34no—
543C4⋊C8—32no—
544C4⋊C8—32no—
545#103—34no—
546#103C22×D311yescharacteristic
547#103C22×D311yescharacteristic
548#103C22×D311yescharacteristic
549#103C22×D311yescharacteristic
550#102—34no—
551#102—34no—
552#102—34no—
553#102—34no—
554#102—34no—
555#102—34no—
556#102—34no—
557#102C22×D311yescharacteristic
558#102C22×D311yescharacteristic
559#102C22×D311yescharacteristic
560#102C22×D311yescharacteristic
561#97—34no—
562C4×C8—34no—
563C4×C8C22×D311yescharacteristic
564C4×C8C22×D311yescharacteristic
565C4×C8C22×D311yescharacteristic
566C4×C8C22×D311yescharacteristic
567C23×C3—21no—
568C23×C3—21no—
569C23×C3C22×D411yescharacteristic
570C22×D3—24no—
571C22×D3—44no—
572C22×D3—82no—
573C22×D3—82no—
574C3×Q8—21no—
575C3×Q8—21no—
576C3×Q8—21no—
577C3×Q8C2×#4112yes—
578C3×D4—24no—
579C3×D4—21no—
580C3×D4—21no—
581C3×D4—21no—
582C3×D4—42no—
583C3×D4C2×#4112yes—
584C2×C3×C4—21no—
585C2×C3×C4—24no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—42no—
594C2×C3×C4—42no—
595C2×C3×C4—42no—
596C2×C3×C4—42no—
597C2×C3×C4—42no—
598C2×C3×C4C22×D411yescharacteristic
599C2×C3×C4C22×D411yescharacteristic
600C2×C3×C4C22×D411yescharacteristic
601C2×C3×C4C22×D411yescharacteristic
602C2×C3×C4C22×D411yescharacteristic
603C2×C3×C4C2×#4112yes—
604C2×C3×C42−1+412yes—
605C2×C3×C4C2511yescharacteristic
606#67—84no—
607#67—84no—
608C2×Dic3—24no—
609C2×Dic3—84no—
610C2×Dic3—82no—
611C2×Dic3C22×D414yes—
612C2×Dic3C22×D414yes—
613D12—24no—
614D12—24no—
615D12—44no—
616D12—44no—
617D12—44no—
618D12—82no—
619D12—82no—
620C4×D3—84no—
621C4×D3—84no—
622Dic6—24no—
623Dic6—24no—
624Dic6—44no—
625Dic6—84no—
626Dic6—82no—
627C3×C8—21no—
628C3×C8—21no—
629C3×C8—21no—
630C3×C8—21no—
631C3⋊C8—24no—
632C24—62no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—244no—
637#41—244no—
638#41#23514yescomplemented
639C2×Q8—32no—
640C2×Q8—32no—
641C2×Q8—64no—
642C2×Q8—62no—
643C2×Q8—62no—
644C2×Q8—242no—
645C2×Q8—244no—
646C2×Q8C23×D311yescharacteristic
647C2×Q8C23×D311yescharacteristic
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—34no—
651C2×D4—64no—
652C2×D4—64no—
653C2×D4—64no—
654C2×D4—62no—
655C2×D4—62no—
656C2×D4—62no—
657C2×D4—62no—
658C2×D4—62no—
659C2×D4—64no—
660C2×D4—242no—
661C2×D4—242no—
662C2×D4C23×D311yescharacteristic
663C2×D4C23×D311yescharacteristic
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—64no—
671C22×C4—64no—
672C22×C4—64no—
673C22×C4—62no—
674C22×C4D3×D411yescharacteristic
675C22×C4D3×D411yescharacteristic
676C22×C4C23×D311yescharacteristic
677Q16—22no—
678SD16—22no—
679SD16—22no—
680SD16—68no—
681D8—22no—
682D8—68no—
683M16—64no—
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—34no—
687C2×C8C23×D311yescharacteristic
688C2×C8C23×D311yescharacteristic
689C2×C8C23×D311yescharacteristic
690C2×C8C23×D311yescharacteristic
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—32no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—32no—
699C4⋊C4—34no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—64no—
703C4⋊C4—64no—
704C4⋊C4—64no—
705C4⋊C4—64no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4C23×D311yescharacteristic
710C4⋊C4C23×D311yescharacteristic
711C4⋊C4C23×D311yescharacteristic
712C4⋊C4C23×D311yescharacteristic
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—34no—
720C22⋊C4—64no—
721C22⋊C4—64no—
722C22⋊C4—64no—
723C22⋊C4—64no—
724C22⋊C4—64no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—21no—
731C42—34no—
732C42—64no—
733C42D3×D411yescharacteristic
734C42D3×D411yescharacteristic
735C42C23×D311yescharacteristic
736C42C23×D311yescharacteristic
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—22no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3#54812yes—
746C22×C3C23×D411yescharacteristic
747C2×D3—44no—
748C2×D3—44no—
749C2×D3—44no—
750C2×D3—164no—
751C3×C4—22no—
752C3×C4—21no—
753C3×C4—21no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—41no—
759C3×C4#54812yes—
760C3×C4#57612yes—
761C3×C4#57712yes—
762C3×C4C22×#4111yescharacteristic
763C3×C4C2×2−1+411yescharacteristic
764Dic3—24no—
765Dic3—24no—
766Dic3—44no—
767C23—21no—
768C23—21no—
769C23—64no—
770C23—124no—
771C23—242no—
772C23—242no—
773C23C2×D3×D411yescharacteristic
774Q8—21no—
775Q8—21no—
776Q8—21no—
777Q8—64no—
778Q8—64no—
779Q8—124no—
780Q8—242no—
781Q8—244no—
782Q8C2×#23512yes—
783D4—24no—
784D4—21no—
785D4—21no—
786D4—21no—
787D4—42no—
788D4—64no—
789D4—64no—
790D4—124no—
791D4—124no—
792D4—124no—
793D4—242no—
794D4—242no—
795D4—244no—
796D4—244no—
797D4C2×#23512yes—
798C2×C4—21no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—34no—
808C2×C4—34no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—64no—
815C2×C4—244no—
816C2×C4—244no—
817C2×C4—244no—
818C2×C4—242no—
819C2×C4C2×#23512yes—
820C2×C4C2×D3×D411yescharacteristic
821C2×C4C2×D3×D411yescharacteristic
822C2×C4C2×D3×D411yescharacteristic
823C2×C4C2×D3×D411yescharacteristic
824C2×C4C2×D3×D411yescharacteristic
825C2×C4#101012yes—
826C2×C4C24×D311yescharacteristic
827C8—21no—
828C8—21no—
829C8—21no—
830C8—21no—
831C8—64no—
832C2×C3—22no—
833C2×C3—42no—
834C2×C3—81no—
835C2×C3C2×#54811yescharacteristic
836C2×C3C2×#57611yescharacteristic
837C2×C3C2×#57711yescharacteristic
838D3—84no—
839C22—21no—
840C22—21no—
841C22—22no—
842C22—41no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—41no—
847C22—124no—
848C22—124no—
849C22—124no—
850C22—484no—
851C22#555212yes—
852C22C22×D3×D411yescharacteristic
853C4—21no—
854C4—21no—
855C4—22no—
856C4—41no—
857C4—41no—
858C4—41no—
859C4—41no—
860C4—41no—
861C4—64no—
862C4—64no—
863C4—124no—
864C4#555212yes—
865C4#576912yes—
866C4#577012yes—
867C4C22×#23511yescharacteristic
868C4C2×#101011yescharacteristic
869C3#6132911yescharacteristic, complemented, Sylow
870C2—22no—
871C2—42no—
872C2—81no—
873C2—244no—
874C2C2×#555211yescharacteristic
875C2C2×#576911yescharacteristic
876C2C2×#577011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×C4×#135C2
socleC22×C3C23×D4
hypercenterC4×#135D3
hypocenterC3#61329
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #85848C2semidirect
2. #85828C2semidirect
3. C3×C4×#135C2semidirect
4. #83901C2semidirect
5. #82526C2semidirect
6. #82508C2semidirect
7. #79703C2semidirect
8. #79701C2semidirect
9. #79629C2semidirect
10. #79625C2semidirect
11. #79622C2semidirect
12. #79621C2semidirect
13. #79570C2semidirect
14. #79567C2semidirect
15. #79197C2semidirect
16. #78827C2semidirect
17. #78820C2semidirect
18. C2×#4694C2semidirect
19. #78445C2semidirect
29. #5570C22semidirect
30. Q8×Dic6C22semidirect
36. #5543C22semidirect
38. D4×Dic6C22semidirect
50. C3×C4×Q16C22semidirect
51. C3×C4×Q16C22semidirect
52. C3×C4×SD16C22semidirect
53. C3×C4×SD16C22semidirect
54. C3×C4×SD16C22semidirect
55. C3×C4×SD16C22semidirect
56. C3×C4×D8C22semidirect
57. C3×C4×D8C22semidirect
63. #5185C22semidirect
64. #5165C22semidirect
65. #5163C22semidirect
66. #5150C22semidirect
73. #5021C22semidirect
74. #5020C22semidirect
77. #5008C22semidirect
78. #5007C22semidirect
82. #4891C22semidirect
83. #4890C22semidirect
84. #4871C22semidirect
85. #4870C22semidirect
86. #4817C22semidirect
87. #4800C22semidirect
88. #4794C22semidirect
89. #4788C22semidirect
90. #4785C22semidirect
91. #4764C22semidirect
92. #4760C22semidirect
93. #4756C22semidirect
98. #4679C22semidirect
99. #4679C22semidirect
100. C8×Dic6C22semidirect
101. C8×Dic6C22semidirect
120. C4×#135D3semidirect
310. C4×Q16C2×D3semidirect
311. C4×Q16C2×D3semidirect
313. C4×SD16C2×D3semidirect
314. C4×SD16C2×D3semidirect
315. C4×SD16C2×D3semidirect
316. C4×SD16C2×D3semidirect
318. C4×D8C2×D3semidirect
319. C4×D8C2×D3semidirect
336. C3×#41#41semidirect
638. #41#235semidirect
869. C3#61329semidirect

Maximal subgroups

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

subgroupindex
#858482
#858282
C3×C4×#1352
#839012
#825262
#825082
#797032
#797012
#796292
#796252
#796222
#796212
#795702
#795672
#791972
#788272
#788202
C2×#46942
#784452
#613293