Finite Group Databasebeta

← #11675872

Subgroups — #11675872

Order 768.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86926C211yesmaximal, characteristic, complemented
2#86747C211yesmaximal, characteristic, complemented
3C3×#3384C211yesmaximal, characteristic, complemented
4#83629C211yesmaximal, characteristic, complemented
5Q8×#214C211yesmaximal, characteristic, complemented
6#81974C212yesmaximal, complemented
7#81967C212yesmaximal, complemented
8#81906C211yesmaximal, characteristic, complemented
9D3×#498C211yesmaximal, characteristic, complemented
10#81171C212yesmaximal, complemented
11#81157C212yesmaximal, complemented
12#81063C212yesmaximal, complemented
13#81061C211yesmaximal, characteristic, complemented
14#81053C212yesmaximal, complemented
15#81053C211yesmaximal, characteristic, complemented
16#80966C211yesmaximal, characteristic, complemented
17#80958C211yesmaximal, characteristic, complemented
18#79986C211yesmaximal, characteristic, complemented
19#79958C211yesmaximal, characteristic, complemented
20#79868C212yesmaximal
21#79855C212yesmaximal, complemented
22C4×#912C211yesmaximal, characteristic
23#79576C211yesmaximal, characteristic, complemented
24#61374—31nomaximal, Sylow
25C3×#554C2211yescharacteristic
26C3×D4×Q8C2211yescharacteristic
27Q8×#67—21no—
28C2×#944—21no—
29C2×#912C2211yescharacteristic
30#5729C2212yes—
31D3×C4⋊Q8C2211yescharacteristic
32D3×C4⋊Q8C2211yescharacteristic
33#5722C2212yes—
34#5722C2211yescharacteristic
35#5721C2211yescharacteristic
36#5689C2212yes—
37#5685C2212yes—
38#5636—22no—
39#5635—21no—
40#5632—21no—
41#5632—22no—
42#5623—22no—
43#5623—22no—
44#5622—21no—
45#5622—21no—
46#5578C2211yescharacteristic
47#5567C2211yescharacteristic
48Q8×Dic6C2211yescharacteristic
49#5546C2212yes—
50#5546C2212yes—
51#5543C2211yescharacteristic
52#5539C2212yes—
53D4×Dic6C2212yes—
54D4×Dic6C2211yescharacteristic
55C4×#237C2211yescharacteristic
56C4×#237C2211yescharacteristic
57#5511—21no—
58C2×#888—21no—
59C3×#501C2212yes—
60C3×#498C2211yescharacteristic
61C3×#478C2212yes—
62C3×#476C2211yescharacteristic
63C3×#476C2212yes—
64C3×#474C2211yescharacteristic
65C3×#446C2211yescharacteristic
66C3×#442C2212yes—
67C3×C4×D8C2211yescharacteristic
68#5152C2212yes—
69Dic3×D8C2211yescharacteristic
70#5094C2212yes—
71#5094C2211yescharacteristic
72#5091C2211yescharacteristic
73#5080C2212yes—
74#5080C2211yescharacteristic
75#5080C2211yescharacteristic
76#5065C2212yes—
77#5063C2212yes—
78Q8×C3⋊C8C2211yescharacteristic
79C4×#214C2212yes—
80C4×#214C2211yescharacteristic
81C4×#214C2211yescharacteristic
82C4×#214C2212yes—
83#5009C2212yes—
84#5008C2212yes—
85#5008C2211yescharacteristic
86#5007C2211yescharacteristic
87#4881C2212yes—
88#4880C2211yescharacteristic
89#4878C2212yes—
90#4877C2212yes—
91#4876C2212yes—
92#4875C2212yes—
93#4873C2211yescharacteristic
94#4861C2212yes—
95D3×#106C2212yes—
96D3×#106C2212yes—
97#4857C2212yes—
98#4856C2212yes—
99#4855C2212yes—
100#4855C2212yes—
101#4855C2212yes—
102#4854C2212yes—
103#4854C2212yes—
104#4854C2212yes—
105#4853C2212yes—
106#4851C2212yes—
107#4851C2211yescharacteristic
108#4850C2211yescharacteristic
109#4839C2212yes—
110#4837C2211yescharacteristic
111#4830C2212yes—
112#4830C2211yescharacteristic
113#4829C2212yes—
114#4772C2211yescharacteristic
115#4772C2211yescharacteristic
116#4771C2212yes—
117#4771C2212yes—
118#4766C2212yes—
119#4763C2212yes—
120#4761C2212yes—
121#4761C2212yes—
122#4761C2212yes—
123#4759C2212yes—
124#4758C2211yescharacteristic
125#4758C2212yes—
126#4758C2212yes—
127#4758C2211yescharacteristic
128#4716C2212yes—
129#4708C2212yes—
130#4702C2212yes—
131#4701C2212yes—
132C4×Dic12C2211yescharacteristic
133C4×D3×C8C2211yescharacteristic
134#4680C2211yescharacteristic
135#4679C2211yescharacteristic
136#3503—31no—
137#3503—31no—
138#3387—32no—
139#3387—31no—
140#3387—31no—
141#3384—32no—
142#3384—31no—
143#3384D311yescharacteristic, complemented
144#3381—32no—
145#3381—31no—
146#3381—31no—
147Q8×SD16—31no—
148Q8×SD16—32no—
149Q8×SD16—31no—
150#3163—32no—
151C2×#498—31no—
152#3084—32no—
153#3084—32no—
154#3079—31no—
155#3079—31no—
156#2960—31no—
157#2952—32no—
158C4×#135—31no—
159C22×C3×Q8—21no—
160C2×D3×Q8—21no—
161C2×D3×Q8—21no—
162C2×#237C2311yescharacteristic
163C2×#237C2311yescharacteristic
164C22×Dic6—22no—
165C22×Dic6—21no—
166C2×C3×D8C2311yescharacteristic
167C3×C4⋊Q8C2311yescharacteristic
168C3×C4⋊Q8C2311yescharacteristic
169C3×C4⋊Q8C2312yes—
170C3×#125C2312yes—
171C3×C22⋊Q8—21no—
172C3×C22⋊Q8—21no—
173C3×C22⋊Q8—22no—
174C3×C22⋊Q8—22no—
175C3×C4×Q8C2311yescharacteristic
176C3×C4×D4C2311yescharacteristic
177C3×C4×D4C2311yescharacteristic
178C3×C4×D4C2312yes—
179C3×C4×D4C2312yes—
180C2×C3×C4⋊C4—21no—
181#946—22no—
182#946D411yescharacteristic
183Q8×Dic3—21no—
184Q8×Dic3—21no—
185#944—21no—
186#944—21no—
187#944—22no—
188#944—22no—
189#944—22no—
190#944—22no—
191#944—21no—
192#944—21no—
193#944D411yescharacteristic
194D4×Dic3C2311yescharacteristic
195D4×Dic3C2311yescharacteristic
196D4×Dic3C2312yes—
197D4×Dic3C2312yes—
198C2×#214C2311yescharacteristic
199C2×#214C2311yescharacteristic
200C4×#67—21no—
201C4×#67—21no—
202C4×#67—22no—
203C4×#67—22no—
204C2×C4⋊Dic3—21no—
205#924—21no—
206#924—22no—
207#924—21no—
208#924—22no—
209C2×Dic3⋊C4—22no—
210C2×Dic3⋊C4—22no—
211C2×Dic3⋊C4—22no—
212C2×C4×Dic3—21no—
213C2×C4×Dic3—21no—
214#912Q818yescomplemented
215C2×Dic12C2311yescharacteristic
216C2×ΓL(1,𝔽25)C2312yes—
217C2×D3×C8C2311yescharacteristic
218C2×D3×C8C2311yescharacteristic
219#897—22no—
220#897D411yescharacteristic
221#896—22no—
222#896—22no—
223#896D412yes—
224#892C2311yescharacteristic
225#892C2311yescharacteristic
226D3×C4⋊C4—21no—
227D3×C4⋊C4—21no—
228D3×C4⋊C4C2312yes—
229D3×C4⋊C4C2312yes—
230#890C2312yes—
231#890C2312yes—
232#889—22no—
233#889—22no—
234#889—22no—
235#889—22no—
236#889—22no—
237#889—22no—
238#889D412yes—
239#888—22no—
240#888—22no—
241#888—21no—
242#888—22no—
243#888—21no—
244#888—22no—
245#888—21no—
246#888—21no—
247#888D411yescharacteristic
248#888C2312yes—
249#888C2312yes—
250#888C2312yes—
251#888C2312yes—
252#887—22no—
253#887—21no—
254#887—21no—
255#887—22no—
256#887C2311yescharacteristic
257#887C2311yescharacteristic
258#887C2312yes—
259#887C2312yes—
260#67⋊C4—21no—
261#67⋊C4—21no—
262#67⋊C4—22no—
263#67⋊C4—22no—
264#878—22no—
265#878—22no—
266#878—22no—
267#878—22no—
268#878—22no—
269#878—22no—
270#877—22no—
271#877—22no—
272#877—21no—
273#877—21no—
274#872C2312yes—
275C42×D3C2311yescharacteristic
276#870C2312yes—
277#869C2312yes—
278#869C2311yescharacteristic
279#869C2311yescharacteristic
280C4×Dic6C2312yes—
281C4×Dic6C2311yescharacteristic
282C4×Dic6C2311yescharacteristic
283C4×Dic6C2312yes—
284C4×Dic6C2312yes—
285C4×Dic6C2311yescharacteristic
286C3×#107C2311yescharacteristic
287C3×#107C2312yes—
288C3×#106C2312yes—
289C3×#106C2312yes—
290C3×#106C2312yes—
291C3×C4⋊C8C2312yes—
292C3×C4⋊C8C2311yescharacteristic
293C3×#102C2312yes—
294C3×#102C2311yescharacteristic
295C3×#102C2312yes—
296C3×#102C2311yescharacteristic
297C3×#97C2312yes—
298C3×C4×C8C2311yescharacteristic
299#832C2311yescharacteristic
300#832C2311yescharacteristic
301#832C2312yes—
302#832C2312yes—
303#818C2312yes—
304#818C2311yescharacteristic
305#817C2312yes—
306#817C2312yes—
307#817C2312yes—
308#816C2312yes—
309#816C2312yes—
310#816C2311yescharacteristic
311#816C2311yescharacteristic
312#815C2312yes—
313Dic3⋊C8C2312yes—
314Dic3⋊C8C2312yes—
315Dic3⋊C8C2312yes—
316C8×Dic3C2311yescharacteristic
317C8×Dic3C2312yes—
318C8×Dic3C2311yescharacteristic
319#810C2311yescharacteristic
320#810C2311yescharacteristic
321#810C2312yes—
322#810C2312yes—
323#808C2312yes—
324#808C2312yes—
325#808C2311yescharacteristic
326#808C2312yes—
327#808C2311yescharacteristic
328#808C2312yes—
329#808C2312yes—
330#808C2312yes—
331#807C2312yes—
332#807C2312yes—
333C4⋊(C3⋊C8)C2311yescharacteristic
334C4⋊(C3⋊C8)C2312yes—
335C4×C3⋊C8C2311yescharacteristic
336C4×C3⋊C8C2312yes—
337C2×#135—31no—
338Q82—32no—
339Q82—31no—
340Q82—31no—
341#557—31no—
342#557—32no—
343#557—31no—
344#554—32no—
345#554—31no—
346#554—61no—
347#554—61no—
348#554—62no—
349#554C2×D311yescharacteristic
350D4×Q8—32no—
351D4×Q8—31no—
352D4×Q8—61no—
353D4×Q8—62no—
354D4×Q8—61no—
355D4×Q8C2×D311yescharacteristic
356#544—32no—
357#544—32no—
358#544—62no—
359#544—62no—
360#533—31no—
361#533—61no—
362#533—61no—
363C2×C4⋊Q8—31no—
364C2×C4⋊Q8—31no—
365C2×C4⋊Q8—61no—
366C2×C4⋊Q8—61no—
367#520—32no—
368#520—32no—
369C4×#41—31no—
370C4×#41—31no—
371#501—32no—
372#501—32no—
373#501—32no—
374#501C2×D312yes—
375#499—32no—
376#499—32no—
377#498—32no—
378#498—31no—
379#498—31no—
380#498—32no—
381#498—32no—
382#498—32no—
383#498—31no—
384#498C2×D311yescharacteristic
385#479—32no—
386#479—32no—
387#479—32no—
388#479—32no—
389#478—32no—
390#478—32no—
391#478—32no—
392#478C2×D312yes—
393#477—31no—
394#477—32no—
395#477—31no—
396#476—31no—
397#476—32no—
398#476—32no—
399#476—32no—
400#476—32no—
401#476C2×D311yescharacteristic
402#476C2×D312yes—
403#475—31no—
404#475—32no—
405#475—32no—
406#475—32no—
407#475—32no—
408#475—31no—
409#475—32no—
410#474—31no—
411#474—32no—
412#474C2×D311yescharacteristic
413#446—32no—
414#446—31no—
415#446C2×D311yescharacteristic
416C8×Q8—31no—
417C8×Q8—32no—
418C8×Q8—31no—
419#442—32no—
420#442C2×D312yes—
421#441—32no—
422#441—32no—
423C4×Q16—31no—
424C4×Q16—31no—
425C4×SD16—31no—
426C4×SD16—32no—
427C4×SD16—32no—
428C4×SD16—31no—
429C4×SD16—31no—
430C4×SD16—32no—
431C4×SD16—32no—
432C4×SD16—31no—
433C4×D8—31no—
434C4×D8C2×D311yescharacteristic
435#428—32no—
436#428—32no—
437#427—31no—
438C2×#106—32no—
439C2×#106—32no—
440#424—32no—
441#423—31no—
442#417—32no—
443#417—32no—
444#416—31no—
445#416—31no—
446#405—32no—
447C2×C4×C8—31no—
448C2×C3×Q8—21no—
449C2×C3×Q8—22no—
450C2×C3×Q8—21no—
451C2×C3×Q8—82no—
452C2×C3×Q8C2×D411yescharacteristic
453C2×C3×D4C2411yescharacteristic
454C2×C3×D4C2411yescharacteristic
455C22×C3×C4—21no—
456C22×C3×C4—21no—
457C22×C3×C4—22no—
458C22×C3×C4—22no—
459C2×#67—21no—
460C2×#67—21no—
461C22×Dic3—21no—
462C22×Dic3—21no—
463C22×Dic3—21no—
464C22×Dic3—21no—
465C22×Dic3—22no—
466C22×Dic3—22no—
467D3×Q8—82no—
468D3×Q8—82no—
469#237—22no—
470#237—22no—
471#237C2×Q814yescomplemented
472#237C2×Q814yescomplemented
473C2×C4×D3—22no—
474C2×C4×D3—22no—
475C2×C4×D3C2×D411yescharacteristic
476C2×C4×D3C2×D411yescharacteristic
477C2×C4×D3C2411yescharacteristic
478C2×Dic6—21no—
479C2×Dic6—22no—
480C2×Dic6—21no—
481C2×Dic6—22no—
482C2×Dic6—22no—
483C2×Dic6—22no—
484C2×Dic6—22no—
485C2×Dic6—84no—
486C2×Dic6—82no—
487C2×Dic6C2×D412yes—
488C2×Dic6C2×D411yescharacteristic
489C2×Dic6C2411yescharacteristic
490C2×Dic6C2411yescharacteristic
491C3×D8C2×Q814yescomplemented
492C2×C3×C8C2411yescharacteristic
493C2×C3×C8C2412yes—
494C2×C3×C8C2411yescharacteristic
495C3×C4⋊C4—21no—
496C3×C4⋊C4—22no—
497C3×C4⋊C4—22no—
498C3×C4⋊C4—22no—
499C3×C4⋊C4—21no—
500C3×C4⋊C4C2×D411yescharacteristic
501C3×C4⋊C4C2×D412yes—
502C3×C4⋊C4C2411yescharacteristic
503C3×C4⋊C4C2412yes—
504C3×C4⋊C4C2411yescharacteristic
505C3×C4⋊C4C2412yes—
506C3×C22⋊C4—21no—
507C3×C22⋊C4—21no—
508C3×C22⋊C4—22no—
509C3×C22⋊C4—22no—
510C3×C42C2411yescharacteristic
511C3×C42C2412yes—
512#217—21no—
513#217—21no—
514#217—22no—
515#217—22no—
516#214C2×Q814yescomplemented
517#214C2×Q814yescomplemented
518(C2×D3)⋊C4—21no—
519(C2×D3)⋊C4—21no—
520(C2×D3)⋊C4C2×D412yes—
521(C2×D3)⋊C4C2×D412yes—
522C4⋊Dic3—21no—
523C4⋊Dic3—22no—
524C4⋊Dic3—21no—
525C4⋊Dic3—22no—
526C4⋊Dic3—22no—
527C4⋊Dic3C2×D412yes—
528C4⋊Dic3C2×D411yescharacteristic
529C4⋊Dic3C2411yescharacteristic
530C4⋊Dic3C2412yes—
531C4⋊Dic3C2411yescharacteristic
532C4⋊Dic3C2412yes—
533Dic3⋊C4—21no—
534Dic3⋊C4—21no—
535Dic3⋊C4—22no—
536Dic3⋊C4—22no—
537Dic3⋊C4—22no—
538Dic3⋊C4—22no—
539Dic3⋊C4—21no—
540Dic3⋊C4—21no—
541Dic3⋊C4—22no—
542Dic3⋊C4—22no—
543Dic3⋊C4—22no—
544Dic3⋊C4—22no—
545Dic3⋊C4—22no—
546Dic3⋊C4—22no—
547Dic3⋊C4—22no—
548Dic3⋊C4—22no—
549Dic3⋊C4—22no—
550Dic3⋊C4—22no—
551Dic3⋊C4C2×D412yes—
552Dic3⋊C4C2×D412yes—
553Dic3⋊C4C2×D412yes—
554Dic3⋊C4C2×D412yes—
555Dic3⋊C4C2×D412yes—
556C4×Dic3—22no—
557C4×Dic3—22no—
558C4×Dic3—21no—
559C4×Dic3—21no—
560C4×Dic3—22no—
561C4×Dic3—22no—
562C4×Dic3—21no—
563C4×Dic3—21no—
564C4×Dic3—21no—
565C4×Dic3—21no—
566C4×Dic3C2×D411yescharacteristic
567C4×Dic3C2×D411yescharacteristic
568C4×Dic3C2411yescharacteristic
569C4×Dic3C2412yes—
570C2×C3⋊C8C2412yes—
571C2×C3⋊C8C2411yescharacteristic
572C2×C3⋊C8C2411yescharacteristic
573Dic12C2×Q814yescomplemented
574ΓL(1,𝔽25)—24no—
575D3×C8—22no—
576D3×C8C2×Q814yescomplemented
577C2×#41—31no—
578C2×#41—31no—
579C22×Q8—21no—
580C22×Q8—61no—
581C22×Q8—62no—
582C22×Q8—61no—
583C22×Q8—61no—
584#135—38no—
585C2×Q16—31no—
586C2×SD16—31no—
587C2×SD16—31no—
588C2×D8C22×D311yescharacteristic
589C2×M16—32no—
590C22×C8—31no—
591C22×C8—31no—
592C4⋊Q8—31no—
593C4⋊Q8—31no—
594C4⋊Q8—32no—
595C4⋊Q8—32no—
596C4⋊Q8—32no—
597C4⋊Q8—32no—
598C4⋊Q8—31no—
599C4⋊Q8—31no—
600C4⋊Q8—32no—
601C4⋊Q8—61no—
602C4⋊Q8—61no—
603C4⋊Q8—61no—
604C4⋊Q8—61no—
605C4⋊Q8—62no—
606C4⋊Q8—61no—
607C4⋊Q8—62no—
608C4⋊Q8—62no—
609C4⋊Q8—62no—
610C4⋊Q8—62no—
611C4⋊Q8—62no—
612C4⋊Q8—62no—
613C4⋊Q8—61no—
614C4⋊Q8—61no—
615C4⋊Q8—61no—
616C4⋊Q8—62no—
617C4⋊Q8C22×D311yescharacteristic
618C4⋊Q8C22×D311yescharacteristic
619C4⋊Q8C22×D312yes—
620#125—32no—
621#125—32no—
622#125—32no—
623#125—32no—
624#125—62no—
625#125—62no—
626#125—62no—
627#125—62no—
628#125—62no—
629#125—62no—
630#125C22×D312yes—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—22no—
634C22⋊Q8—22no—
635C22⋊Q8—31no—
636C22⋊Q8—32no—
637C22⋊Q8—31no—
638C22⋊Q8—62no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—62no—
643C22⋊Q8—62no—
644C22⋊Q8—62no—
645C22⋊Q8—62no—
646C22⋊Q8—62no—
647C22⋊Q8—62no—
648C22⋊Q8—61no—
649C22⋊Q8—62no—
650C22⋊Q8—62no—
651C22⋊Q8—61no—
652C4×Q8—32no—
653C4×Q8—31no—
654C4×Q8—31no—
655C4×Q8—31no—
656C4×Q8—32no—
657C4×Q8—32no—
658C4×Q8—31no—
659C4×Q8—31no—
660C4×Q8—32no—
661C4×Q8—32no—
662C4×Q8—62no—
663C4×Q8—62no—
664C4×Q8—61no—
665C4×Q8—61no—
666C4×Q8—61no—
667C4×Q8—61no—
668C4×Q8C22×D311yescharacteristic
669C4×D4—31no—
670C4×D4—31no—
671C4×D4—32no—
672C4×D4—32no—
673C4×D4—62no—
674C4×D4—62no—
675C4×D4—61no—
676C4×D4—61no—
677C4×D4—62no—
678C4×D4—62no—
679C4×D4—61no—
680C4×D4—61no—
681C4×D4C22×D311yescharacteristic
682C4×D4C22×D311yescharacteristic
683C4×D4C22×D312yes—
684C4×D4C22×D312yes—
685#117—32no—
686#117—31no—
687#117—31no—
688#117—61no—
689#117—61no—
690#117—62no—
691#117—62no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—32no—
694C2×C4⋊C4—32no—
695C2×C4⋊C4—61no—
696C2×C4⋊C4—61no—
697C2×C4⋊C4—62no—
698C2×C4⋊C4—62no—
699C2×C4⋊C4—62no—
700C2×C4⋊C4—61no—
701C2×C42—31no—
702C2×C42—61no—
703C2×C42—61no—
704#107—31no—
705#107—32no—
706#107—32no—
707#107—32no—
708#107C22×D311yescharacteristic
709#107C22×D312yes—
710#106—32no—
711#106—32no—
712#106—32no—
713#106—32no—
714#106—32no—
715#106—32no—
716#106—32no—
717#106—31no—
718#106—31no—
719#106—32no—
720#106—32no—
721#106C22×D312yes—
722#106C22×D312yes—
723#106C22×D312yes—
724C4⋊C8—32no—
725C4⋊C8—32no—
726C4⋊C8—32no—
727C4⋊C8—31no—
728C4⋊C8—32no—
729C4⋊C8C22×D311yescharacteristic
730C4⋊C8C22×D312yes—
731#103—31no—
732#103—31no—
733#103—32no—
734#103—32no—
735#103—31no—
736#103—31no—
737#103—32no—
738#103—32no—
739#102—31no—
740#102—31no—
741#102—32no—
742#102—32no—
743#102C22×D311yescharacteristic
744#102C22×D311yescharacteristic
745#102C22×D312yes—
746#102C22×D312yes—
747#97—32no—
748#97C22×D312yes—
749C4×C8—31no—
750C4×C8—31no—
751C4×C8—32no—
752C4×C8—31no—
753C4×C8—32no—
754C4×C8C22×D311yescharacteristic
755C23×C3—21no—
756C23×C3—21no—
757C22×D3C22×D411yescharacteristic
758C3×Q8—22no—
759C3×Q8—42no—
760C3×Q8—81no—
761C3×Q8—82no—
762C3×D4—21no—
763C3×D4—21no—
764C3×D4C22×Q812yes—
765C3×D4C22×Q812yes—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—22no—
769C2×C3×C4—22no—
770C2×C3×C4—42no—
771C2×C3×C4—42no—
772C2×C3×C4—82no—
773C2×C3×C4—82no—
774C2×C3×C4C22×D412yes—
775C2×C3×C4C22×D412yes—
776C2×C3×C4C22×D411yescharacteristic
777C2×C3×C4C22×D411yescharacteristic
778C2×C3×C4C2511yescharacteristic
779#67—24no—
780#67—24no—
781C2×Dic3—21no—
782C2×Dic3—21no—
783C2×Dic3—24no—
784C2×Dic3—24no—
785C2×Dic3—21no—
786C2×Dic3—21no—
787C2×Dic3—22no—
788C2×Dic3—22no—
789C2×Dic3—42no—
790C2×Dic3—42no—
791C2×Dic3—82no—
792C2×Dic3—82no—
793C2×Dic3C22×D412yes—
794C2×Dic3C22×D412yes—
795C2×Dic3C22×D411yescharacteristic
796C2×Dic3C22×D411yescharacteristic
797C2×Dic3C22×D411yescharacteristic
798C4×D3—22no—
799C4×D3—22no—
800C4×D3—82no—
801C4×D3—82no—
802C4×D3C22×Q812yes—
803C4×D32−1+412yes—
804Dic6—22no—
805Dic6—21no—
806Dic6—21no—
807Dic6—24no—
808Dic6—42no—
809Dic6—44no—
810Dic6—82no—
811Dic6—82no—
812Dic6—82no—
813Dic6—82no—
814Dic6—81no—
815Dic6C22×Q812yes—
816Dic6C22×Q812yes—
817C3×C8—21no—
818C3×C8—22no—
819C3×C8C22×Q812yes—
820C3⋊C8—21no—
821C3⋊C8—22no—
822C3⋊C8C22×Q812yes—
823#41—34no—
824#41—34no—
825#41—62no—
826#41—62no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—22no—
830C2×Q8—32no—
831C2×Q8—31no—
832C2×Q8—31no—
833C2×Q8—31no—
834C2×Q8—62no—
835C2×Q8—62no—
836C2×Q8—62no—
837C2×Q8—62no—
838C2×Q8—61no—
839C2×Q8—62no—
840C2×Q8—61no—
841C2×Q8—82no—
842C2×Q8—242no—
843C2×Q8—242no—
844C2×Q8—242no—
845C2×Q8—244no—
846C2×Q8D3×D411yescharacteristic
847C2×D4—61no—
848C2×D4—61no—
849C2×D4C23×D311yescharacteristic
850C2×D4C23×D311yescharacteristic
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—31no—
856C22×C4—31no—
857C22×C4—31no—
858C22×C4—62no—
859C22×C4—62no—
860C22×C4—61no—
861C22×C4—61no—
862C22×C4—61no—
863C22×C4—61no—
864C22×C4—62no—
865C22×C4—62no—
866Q16—34no—
867SD16—34no—
868SD16—34no—
869D8D3×Q814yescomplemented
870M16—64no—
871C2×C8—31no—
872C2×C8—34no—
873C2×C8—31no—
874C2×C8—32no—
875C2×C8—62no—
876C2×C8C23×D311yescharacteristic
877C2×C8C23×D312yes—
878C2×C8C23×D311yescharacteristic
879C4⋊C4—21no—
880C4⋊C4—22no—
881C4⋊C4—21no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—32no—
885C4⋊C4—32no—
886C4⋊C4—32no—
887C4⋊C4—31no—
888C4⋊C4—32no—
889C4⋊C4—32no—
890C4⋊C4—32no—
891C4⋊C4—32no—
892C4⋊C4—32no—
893C4⋊C4—31no—
894C4⋊C4—31no—
895C4⋊C4—62no—
896C4⋊C4—62no—
897C4⋊C4—62no—
898C4⋊C4—62no—
899C4⋊C4—62no—
900C4⋊C4—62no—
901C4⋊C4—62no—
902C4⋊C4—62no—
903C4⋊C4—61no—
904C4⋊C4—61no—
905C4⋊C4—62no—
906C4⋊C4—62no—
907C4⋊C4—62no—
908C4⋊C4—62no—
909C4⋊C4—61no—
910C4⋊C4—62no—
911C4⋊C4—62no—
912C4⋊C4—62no—
913C4⋊C4—61no—
914C4⋊C4—61no—
915C4⋊C4—61no—
916C4⋊C4—62no—
917C4⋊C4—62no—
918C4⋊C4D3×D411yescharacteristic
919C4⋊C4D3×D412yes—
920C4⋊C4C23×D312yes—
921C4⋊C4C23×D311yescharacteristic
922C4⋊C4C23×D312yes—
923C4⋊C4C23×D311yescharacteristic
924C22⋊C4—21no—
925C22⋊C4—21no—
926C22⋊C4—22no—
927C22⋊C4—22no—
928C22⋊C4—32no—
929C22⋊C4—32no—
930C22⋊C4—61no—
931C22⋊C4—61no—
932C22⋊C4—61no—
933C22⋊C4—61no—
934C22⋊C4—62no—
935C22⋊C4—62no—
936C42—31no—
937C42—31no—
938C42—31no—
939C42—32no—
940C42—61no—
941C42—61no—
942C42—61no—
943C42—61no—
944C42—62no—
945C42—62no—
946C42—61no—
947C42—61no—
948C42—62no—
949C42—62no—
950C42C23×D311yescharacteristic
951C42C23×D312yes—
952C22×C3—22no—
953C22×C3—22no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3C23×D411yescharacteristic
959C2×D3—21no—
960C2×D3—21no—
961C2×D3D4×Q812yes—
962C3×C4—22no—
963C3×C4—21no—
964C3×C4—22no—
965C3×C4—42no—
966C3×C4—41no—
967C3×C4—42no—
968C3×C4—41no—
969C3×C4#57712yes—
970C3×C4C23×Q811yescharacteristic
971C3×C4C2×2−1+411yescharacteristic
972Dic3—22no—
973Dic3—22no—
974Dic3—22no—
975Dic3—22no—
976Dic3—21no—
977Dic3—42no—
978Dic3—42no—
979Dic3—41no—
980Dic3—41no—
981Dic3D4×Q812yes—
982Dic3#57712yes—
983C23—21no—
984C23—21no—
985C23—31no—
986Q8—22no—
987Q8—32no—
988Q8—32no—
989Q8—42no—
990Q8—64no—
991Q8—61no—
992Q8—61no—
993Q8—62no—
994Q8—82no—
995Q8—81no—
996Q8—124no—
997Q8—122no—
998Q8—241no—
999Q8—242no—
1000Q8—242no—
1001Q8—242no—
1002Q8—242no—
1003D4—21no—
1004D4—21no—
1005D4—64no—
1006D4—64no—
1007D4C2×D3×Q812yes—
1008D4C2×D3×Q812yes—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—31no—
1014C2×C4—31no—
1015C2×C4—32no—
1016C2×C4—32no—
1017C2×C4—31no—
1018C2×C4—32no—
1019C2×C4—32no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—62no—
1023C2×C4—64no—
1024C2×C4—64no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—62no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—82no—
1033C2×C4—82no—
1034C2×C4—122no—
1035C2×C4—122no—
1036C2×C4—242no—
1037C2×C4—242no—
1038C2×C4—242no—
1039C2×C4—242no—
1040C2×C4C2×D3×D411yescharacteristic
1041C2×C4C2×D3×D412yes—
1042C2×C4C2×D3×D412yes—
1043C2×C4C2×D3×D411yescharacteristic
1044C2×C4C24×D311yescharacteristic
1045C8—21no—
1046C8—22no—
1047C8—32no—
1048C8—61no—
1049C8—62no—
1050C8C2×D3×Q812yes—
1051C2×C3—42no—
1052C2×C3—42no—
1053C2×C3C2×D4×Q811yescharacteristic
1054C2×C3C2×#57711yescharacteristic
1055C2×C3C2×#57711yescharacteristic
1056D3—22no—
1057C22—22no—
1058C22—22no—
1059C22—32no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—41no—
1064C22—61no—
1065C22—61no—
1066C22C22×D3×D411yescharacteristic
1067C4—22no—
1068C4—21no—
1069C4—22no—
1070C4—32no—
1071C4—32no—
1072C4—41no—
1073C4—41no—
1074C4—42no—
1075C4—42no—
1076C4—61no—
1077C4—62no—
1078C4—62no—
1079C4—62no—
1080C4—62no—
1081C4—122no—
1082C4—121no—
1083C4—121no—
1084C4—122no—
1085C4#577512yes—
1086C4C22×D3×Q811yescharacteristic
1087C4D3×2−1+411yescharacteristic
1088C3#6137411yescharacteristic, complemented, Sylow
1089C2—42no—
1090C2—42no—
1091C2—62no—
1092C2D3×D4×Q811yescharacteristic
1093C2C2×#577511yescharacteristic
1094C2D3×#57711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3384C2
socleC22×C3C23×D4
prime radicalC2×#912C22
hypercenter#3384D3
hypocenterC3#61374
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3384

Complements

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

NH ≅ G/Ntype
1. #86926C2semidirect
2. #86747C2semidirect
3. C3×#3384C2semidirect
4. #83629C2semidirect
5. Q8×#214C2semidirect
6. #81974C2semidirect
7. #81967C2semidirect
8. #81906C2semidirect
9. D3×#498C2semidirect
10. #81171C2semidirect
11. #81157C2semidirect
12. #81063C2semidirect
13. #81061C2semidirect
14. #81053C2semidirect
15. #81053C2semidirect
16. #80966C2semidirect
17. #80958C2semidirect
18. #79986C2semidirect
19. #79958C2semidirect
21. #79855C2semidirect
23. #79576C2semidirect
143. #3384D3semidirect
214. #912Q8semidirect
471. #237C2×Q8semidirect
472. #237C2×Q8semidirect
491. C3×D8C2×Q8semidirect
516. #214C2×Q8semidirect
517. #214C2×Q8semidirect
573. Dic12C2×Q8semidirect
576. D3×C8C2×Q8semidirect
869. D8D3×Q8semidirect
1088. C3#61374semidirect

Maximal subgroups

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

subgroupindex
#869262
#867472
C3×#33842
#836292
Q8×#2142
#819742
#819672
#819062
D3×#4982
#811712
#811572
#810632
#810612
#810532
#809662
#809582
#799862
#799582
#798682
#798552
C4×#9122
#795762
#613743