Finite Group Databasebeta

← #11675847

Subgroups — #11675847

Order 768.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#87046C211yesmaximal, characteristic
2#87031C211yesmaximal, characteristic
3C3×#3387C211yesmaximal, characteristic, complemented
4Q8×#216C211yesmaximal, characteristic, complemented
5#83682C211yesmaximal, characteristic, complemented
6#81975C212yesmaximal
7#81971C212yesmaximal, complemented
8#81906C211yesmaximal, characteristic, complemented
9#81891C211yesmaximal, characteristic
10#81233C212yesmaximal
11#81222C212yesmaximal, complemented
12#81108C211yesmaximal, characteristic
13#81102C211yesmaximal, characteristic, complemented
14#81013C212yesmaximal
15#81011C211yesmaximal, characteristic
16#81006C212yesmaximal, complemented
17#81006C211yesmaximal, characteristic, complemented
18#79986C211yesmaximal, characteristic, complemented
19#79958C211yesmaximal, characteristic
20#79831C212yesmaximal
21#79820C212yesmaximal, complemented
22C4×D3×Q16C211yesmaximal, characteristic
23#79708C211yesmaximal, characteristic, complemented
24#61372—31nomaximal, Sylow
25C3×Q82C2211yescharacteristic
26C3×#557C2211yescharacteristic
27C2×D3×Q16C2211yescharacteristic
28#5729—22no—
29#5729C2212yes—
30#5728—21no—
31#5728—21no—
32#5728C2211yescharacteristic
33#5728C2211yescharacteristic
34#5722—21no—
35#5722C2211yescharacteristic
36#5721—21no—
37#5721—22no—
38#5721C2212yes—
39#5721C2211yescharacteristic
40#5689—22no—
41#5689C2212yes—
42#5685—22no—
43#5685C2212yes—
44#5578—21no—
45#5578—21no—
46#5578C2211yescharacteristic
47#5572C2212yes—
48#5572C2212yes—
49C4×D3×Q8C2211yescharacteristic
50C4×D3×Q8C2211yescharacteristic
51#5570C2211yescharacteristic
52#5570C2212yes—
53#5569C2212yes—
54#5567—21no—
55#5567C2211yescharacteristic
56Q8×Dic6—21no—
57Q8×Dic6C2211yescharacteristic
58Q8×Dic6C2211yescharacteristic
59C3×#501C2212yes—
60C3×#498C2211yescharacteristic
61C3×#479C2212yes—
62C3×#477C2211yescharacteristic
63C3×#475C2211yescharacteristic
64C3×#475C2212yes—
65C3×#446C2211yescharacteristic
66C3×#441C2212yes—
67C3×C4×Q16C2211yescharacteristic
68#5184C2212yes—
69Dic3×Q16C2211yescharacteristic
70#5094C2211yescharacteristic
71#5091C2212yes—
72#5091C2211yescharacteristic
73#5078C2212yes—
74#5078C2211yescharacteristic
75#5078C2211yescharacteristic
76#5065C2212yes—
77#5063C2212yes—
78C4×#216C2212yes—
79C4×#216C2211yescharacteristic
80C4×#216C2211yescharacteristic
81C4×#216C2212yes—
82Q8×C3⋊C8C2211yescharacteristic
83#5022C2212yes—
84#5021C2212yes—
85#5021C2211yescharacteristic
86#5020C2211yescharacteristic
87#4881C2212yes—
88D3×#107C2211yescharacteristic
89#4877C2212yes—
90#4876C2212yes—
91#4875C2212yes—
92#4874C2212yes—
93#4873C2211yescharacteristic
94#4861C2212yes—
95#4860C2212yes—
96#4860C2212yes—
97#4858C2212yes—
98#4858C2212yes—
99#4858C2212yes—
100#4857C2212yes—
101#4857C2212yes—
102#4857C2212yes—
103#4856C2212yes—
104#4854C2212yes—
105#4853C2212yes—
106#4851C2212yes—
107#4851C2211yescharacteristic
108#4850C2211yescharacteristic
109#4839C2212yes—
110#4837C2211yescharacteristic
111#4830C2212yes—
112#4830C2211yescharacteristic
113#4829C2212yes—
114#4802C2212yes—
115#4802C2212yes—
116D3×#103C2211yescharacteristic
117D3×#103C2211yescharacteristic
118#4799C2212yes—
119#4799C2212yes—
120#4799C2212yes—
121#4796C2212yes—
122#4793C2212yes—
123#4791C2212yes—
124#4790C2211yescharacteristic
125#4790C2212yes—
126#4790C2211yescharacteristic
127#4790C2212yes—
128#4716C2212yes—
129#4708C2212yes—
130#4702C2212yes—
131#4701C2212yes—
132C4×Dic12C2211yescharacteristic
133C4×D3×C8C2211yescharacteristic
134#4680C2211yescharacteristic
135#4679C2211yescharacteristic
136#3502—31no—
137#3502—31no—
138#3390—32no—
139#3390—32no—
140#3387—31no—
141#3387—31no—
142#3387—31no—
143#3387D311yescharacteristic, complemented
144#3383—32no—
145#3383—31no—
146#3383—32no—
147#3383—31no—
148Q8×Q16—31no—
149Q8×Q16—31no—
150#3164—32no—
151#3160—31no—
152#3082—32no—
153#3082—32no—
154#3078—31no—
155#3078—31no—
156#2960—31no—
157#2950—32no—
158C2×C4×Q16—31no—
159C2×D3×Q8C2311yescharacteristic
160C2×D3×Q8C2311yescharacteristic
161C2×C3×Q16C2311yescharacteristic
162C3×C4⋊Q8—21no—
163C3×C4⋊Q8—22no—
164C3×C4⋊Q8—21no—
165C3×C4⋊Q8C2312yes—
166C3×C4⋊Q8C2311yescharacteristic
167C3×C4⋊Q8C2311yescharacteristic
168C3×#125—22no—
169C3×#125C2312yes—
170C3×C4×Q8—21no—
171C3×C4×Q8—21no—
172C3×C4×Q8C2311yescharacteristic
173C3×C4×Q8C2312yes—
174C3×C4×Q8C2311yescharacteristic
175C3×C4×Q8C2312yes—
176C3×C4×Q8C2311yescharacteristic
177#946—21no—
178#946—21no—
179#946—22no—
180#946D411yescharacteristic
181Q8×Dic3—21no—
182Q8×Dic3—22no—
183Q8×Dic3—21no—
184Q8×Dic3—21no—
185Q8×Dic3—21no—
186Q8×Dic3C2311yescharacteristic
187Q8×Dic3C2311yescharacteristic
188Q8×Dic3C2312yes—
189Q8×Dic3C2312yes—
190#944—21no—
191#944—21no—
192#944—22no—
193#944—22no—
194#944—22no—
195#944D411yescharacteristic
196C2×#216C2311yescharacteristic
197C2×#216C2311yescharacteristic
198D3×Q16Q818yescomplemented
199C2×Dic12C2311yescharacteristic
200C2×ΓL(1,𝔽25)C2312yes—
201C2×D3×C8C2311yescharacteristic
202C2×D3×C8C2311yescharacteristic
203#897—21no—
204#897—21no—
205#897—22no—
206#897D411yescharacteristic
207#896—22no—
208#896—22no—
209#896D412yes—
210#892—22no—
211#892—22no—
212#892C2312yes—
213#892C2312yes—
214D3×C4⋊C4—21no—
215D3×C4⋊C4—21no—
216D3×C4⋊C4C2311yescharacteristic
217D3×C4⋊C4C2311yescharacteristic
218#890—22no—
219#890—22no—
220#890—22no—
221#890—22no—
222#890C2312yes—
223#890C2312yes—
224#890C2312yes—
225#890C2312yes—
226#889—22no—
227#889—22no—
228#889—22no—
229#889—22no—
230#889—22no—
231#889—22no—
232#889—22no—
233#889—22no—
234#889D412yes—
235#888—22no—
236#888—22no—
237#888—22no—
238#888—21no—
239#888—21no—
240#888—22no—
241#888—22no—
242#888D411yescharacteristic
243#888C2312yes—
244#888C2312yes—
245#887—21no—
246#887—21no—
247#887—22no—
248#887—22no—
249#887—22no—
250#887—21no—
251#887—21no—
252#887—21no—
253#887—21no—
254#887C2311yescharacteristic
255#887C2311yescharacteristic
256#887C2312yes—
257#887C2312yes—
258#872—22no—
259#872—22no—
260#872C2312yes—
261C42×D3—21no—
262C42×D3—21no—
263C42×D3C2311yescharacteristic
264#870—22no—
265#870C2312yes—
266#869—22no—
267#869—21no—
268#869—21no—
269#869C2312yes—
270#869C2311yescharacteristic
271#869C2311yescharacteristic
272C4×Dic6—21no—
273C4×Dic6—22no—
274C4×Dic6—21no—
275C4×Dic6—22no—
276C4×Dic6—22no—
277C4×Dic6—22no—
278C4×Dic6—21no—
279C4×Dic6—21no—
280C4×Dic6C2312yes—
281C4×Dic6C2311yescharacteristic
282C4×Dic6C2312yes—
283C4×Dic6C2311yescharacteristic
284C4×Dic6C2312yes—
285C4×Dic6C2311yescharacteristic
286C3×#107C2311yescharacteristic
287C3×#107C2312yes—
288C3×#106C2312yes—
289C3×#106C2312yes—
290C3×#106C2312yes—
291C3×C4⋊C8C2312yes—
292C3×C4⋊C8C2311yescharacteristic
293C3×#103C2311yescharacteristic
294C3×#103C2312yes—
295C3×#103C2312yes—
296C3×#103C2311yescharacteristic
297C3×#97C2312yes—
298C3×C4×C8C2311yescharacteristic
299#835C2311yescharacteristic
300#835C2311yescharacteristic
301#835C2312yes—
302#835C2312yes—
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#807C2311yescharacteristic
326#807C2312yes—
327#807C2312yes—
328#807C2312yes—
329#807C2311yescharacteristic
330#807C2312yes—
331#807C2312yes—
332#807C2312yes—
333C4⋊(C3⋊C8)C2311yescharacteristic
334C4⋊(C3⋊C8)C2312yes—
335C4×C3⋊C8C2311yescharacteristic
336C4×C3⋊C8C2312yes—
337C22×Q16—31no—
338Q82—31no—
339Q82—31no—
340Q82—31no—
341Q82—61no—
342Q82—61no—
343Q82C2×D311yescharacteristic
344#557—31no—
345#557—32no—
346#557—32no—
347#557—31no—
348#557—32no—
349#557—32no—
350#557—31no—
351#557—61no—
352#557—62no—
353#557—62no—
354#557—61no—
355#557C2×D311yescharacteristic
356#544—32no—
357#544—32no—
358#544—62no—
359#544—62no—
360#533—31no—
361#533—31no—
362#533—31no—
363#533—61no—
364#533—61no—
365#533—61no—
366#533—61no—
367#519—32no—
368#519—32no—
369C2×C4×Q8—31no—
370C2×C4×Q8—31no—
371#501—32no—
372#501—32no—
373#501—32no—
374#501C2×D312yes—
375#500—31no—
376#500—32no—
377#500—31no—
378#500—32no—
379#499—32no—
380#499—32no—
381#499—32no—
382#499—32no—
383#498—31no—
384#498C2×D311yescharacteristic
385#479—32no—
386#479—32no—
387#479—32no—
388#479—32no—
389#479—32no—
390#479—32no—
391#479—32no—
392#479—32no—
393#479—32no—
394#479—32no—
395#479—32no—
396#479C2×D312yes—
397#477—31no—
398#477—32no—
399#477—31no—
400#477—32no—
401#477—32no—
402#477—31no—
403#477—32no—
404#477C2×D311yescharacteristic
405#475—31no—
406#475—31no—
407#475—32no—
408#475—31no—
409#475—32no—
410#475—32no—
411#475C2×D311yescharacteristic
412#475C2×D312yes—
413#446—32no—
414#446—31no—
415#446C2×D311yescharacteristic
416C8×Q8—31no—
417C8×Q8—31no—
418C8×Q8—32no—
419#441—32no—
420#441—32no—
421#441—32no—
422#441C2×D312yes—
423C4×Q16—31no—
424C4×Q16—31no—
425C4×Q16—31no—
426C4×Q16—32no—
427C4×Q16—32no—
428C4×Q16—31no—
429C4×Q16—32no—
430C4×Q16—31no—
431C4×Q16—31no—
432C4×Q16—32no—
433C4×Q16—31no—
434C4×Q16C2×D311yescharacteristic
435#428—32no—
436#428—32no—
437#427—32no—
438#427—32no—
439C2×#107—31no—
440#424—32no—
441#423—31no—
442#419—32no—
443#419—32no—
444C2×#103—31no—
445C2×#103—31no—
446#405—32no—
447C2×C4×C8—31no—
448C2×C3×Q8—21no—
449C2×C3×Q8—21no—
450C2×C3×Q8—22no—
451C2×C3×Q8C2×D411yescharacteristic
452C2×C3×Q8C2411yescharacteristic
453C2×C3×Q8C2411yescharacteristic
454D3×Q8—22no—
455D3×Q8—22no—
456D3×Q8C2×Q814yes—
457D3×Q8C2×Q814yes—
458C2×C4×D3—21no—
459C2×C4×D3—21no—
460C2×C4×D3—21no—
461C2×C4×D3—21no—
462C2×C4×D3C2×D411yescharacteristic
463C2×C4×D3C2×D411yescharacteristic
464C2×C4×D3C2411yescharacteristic
465C2×Dic6—21no—
466C2×Dic6—21no—
467C2×Dic6—21no—
468C2×Dic6—22no—
469C2×Dic6—21no—
470C2×Dic6—22no—
471C2×Dic6—22no—
472C2×Dic6C2×D411yescharacteristic
473C2×Dic6C2×D412yes—
474C2×Dic6C2411yescharacteristic
475C2×Dic6C2411yescharacteristic
476C3×Q16C2×Q814yes—
477C2×C3×C8C2411yescharacteristic
478C2×C3×C8C2412yes—
479C2×C3×C8C2411yescharacteristic
480C3×C4⋊C4—21no—
481C3×C4⋊C4—21no—
482C3×C4⋊C4—22no—
483C3×C4⋊C4—21no—
484C3×C4⋊C4—22no—
485C3×C4⋊C4—21no—
486C3×C4⋊C4—22no—
487C3×C4⋊C4—22no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4C2×D411yescharacteristic
490C3×C4⋊C4C2×D412yes—
491C3×C4⋊C4C2412yes—
492C3×C4⋊C4C2411yescharacteristic
493C3×C4⋊C4C2412yes—
494C3×C4⋊C4C2411yescharacteristic
495C3×C42—21no—
496C3×C42—21no—
497C3×C42—22no—
498C3×C42—22no—
499C3×C42C2411yescharacteristic
500C3×C42C2412yes—
501#216C2×Q814yes—
502#216C2×Q814yes—
503(C2×D3)⋊C4—22no—
504(C2×D3)⋊C4—22no—
505(C2×D3)⋊C4C2×D412yes—
506(C2×D3)⋊C4C2×D412yes—
507C4⋊Dic3—21no—
508C4⋊Dic3—22no—
509C4⋊Dic3—21no—
510C4⋊Dic3—22no—
511C4⋊Dic3—21no—
512C4⋊Dic3—22no—
513C4⋊Dic3—21no—
514C4⋊Dic3—22no—
515C4⋊Dic3—22no—
516C4⋊Dic3—22no—
517C4⋊Dic3—22no—
518C4⋊Dic3C2×D411yescharacteristic
519C4⋊Dic3C2×D412yes—
520C4⋊Dic3C2412yes—
521C4⋊Dic3C2411yescharacteristic
522C4⋊Dic3C2412yes—
523C4⋊Dic3C2411yescharacteristic
524Dic3⋊C4—22no—
525Dic3⋊C4—22no—
526Dic3⋊C4—22no—
527Dic3⋊C4—21no—
528Dic3⋊C4—21no—
529Dic3⋊C4—22no—
530Dic3⋊C4—22no—
531Dic3⋊C4—21no—
532Dic3⋊C4—21no—
533Dic3⋊C4—21no—
534Dic3⋊C4—21no—
535Dic3⋊C4—22no—
536Dic3⋊C4—22no—
537Dic3⋊C4—22no—
538Dic3⋊C4—22no—
539Dic3⋊C4—22no—
540Dic3⋊C4—22no—
541Dic3⋊C4—22no—
542Dic3⋊C4C2×D412yes—
543Dic3⋊C4C2×D412yes—
544Dic3⋊C4C2×D412yes—
545Dic3⋊C4C2×D412yes—
546Dic3⋊C4C2×D412yes—
547C4×Dic3—21no—
548C4×Dic3—21no—
549C4×Dic3—22no—
550C4×Dic3—22no—
551C4×Dic3—21no—
552C4×Dic3—21no—
553C4×Dic3—22no—
554C4×Dic3—22no—
555C4×Dic3—22no—
556C4×Dic3—22no—
557C4×Dic3—22no—
558C4×Dic3—22no—
559C4×Dic3—21no—
560C4×Dic3—21no—
561C4×Dic3C2×D411yescharacteristic
562C4×Dic3C2×D411yescharacteristic
563C4×Dic3C2411yescharacteristic
564C4×Dic3C2412yes—
565C2×C3⋊C8C2411yescharacteristic
566C2×C3⋊C8C2412yes—
567C2×C3⋊C8C2411yescharacteristic
568Dic12C2×Q814yes—
569ΓL(1,𝔽25)—24no—
570D3×C8—22no—
571D3×C8C2×Q814yes—
572C22×Q8—31no—
573C22×Q8—31no—
574C2×Q16—31no—
575C2×Q16—31no—
576C2×Q16—38no—
577C2×Q16—31no—
578C2×Q16C22×D311yescharacteristic
579C2×M16—32no—
580C22×C8—31no—
581C22×C8—31no—
582C4⋊Q8—21no—
583C4⋊Q8—21no—
584C4⋊Q8—22no—
585C4⋊Q8—31no—
586C4⋊Q8—31no—
587C4⋊Q8—32no—
588C4⋊Q8—32no—
589C4⋊Q8—31no—
590C4⋊Q8—31no—
591C4⋊Q8—32no—
592C4⋊Q8—61no—
593C4⋊Q8—61no—
594C4⋊Q8—62no—
595C4⋊Q8—61no—
596C4⋊Q8—62no—
597C4⋊Q8—62no—
598C4⋊Q8—62no—
599C4⋊Q8—62no—
600C4⋊Q8—62no—
601C4⋊Q8—62no—
602C4⋊Q8—61no—
603C4⋊Q8—62no—
604C4⋊Q8—61no—
605C4⋊Q8—61no—
606C4⋊Q8—62no—
607C4⋊Q8C22×D311yescharacteristic
608C4⋊Q8C22×D311yescharacteristic
609C4⋊Q8C22×D312yes—
610#125—22no—
611#125—32no—
612#125—32no—
613#125—32no—
614#125—32no—
615#125—32no—
616#125—32no—
617#125—62no—
618#125—62no—
619#125—62no—
620#125—62no—
621#125—62no—
622#125—62no—
623#125—62no—
624#125—62no—
625#125—62no—
626#125—62no—
627#125—62no—
628#125—62no—
629#125—62no—
630#125C22×D312yes—
631C22⋊Q8—31no—
632C22⋊Q8—31no—
633C22⋊Q8—32no—
634C22⋊Q8—62no—
635C22⋊Q8—62no—
636C22⋊Q8—62no—
637C22⋊Q8—62no—
638C22⋊Q8—61no—
639C22⋊Q8—61no—
640C22⋊Q8—61no—
641C22⋊Q8—61no—
642C4×Q8—21no—
643C4×Q8—21no—
644C4×Q8—32no—
645C4×Q8—31no—
646C4×Q8—31no—
647C4×Q8—31no—
648C4×Q8—32no—
649C4×Q8—32no—
650C4×Q8—31no—
651C4×Q8—31no—
652C4×Q8—32no—
653C4×Q8—32no—
654C4×Q8—31no—
655C4×Q8—31no—
656C4×Q8—32no—
657C4×Q8—32no—
658C4×Q8—61no—
659C4×Q8—61no—
660C4×Q8—62no—
661C4×Q8—62no—
662C4×Q8—62no—
663C4×Q8—62no—
664C4×Q8—61no—
665C4×Q8—61no—
666C4×Q8—61no—
667C4×Q8—61no—
668C4×Q8—61no—
669C4×Q8—61no—
670C4×Q8—61no—
671C4×Q8—61no—
672C4×Q8—62no—
673C4×Q8—62no—
674C4×Q8—62no—
675C4×Q8—61no—
676C4×Q8—62no—
677C4×Q8—61no—
678C4×Q8—61no—
679C4×Q8—61no—
680C4×Q8C22×D311yescharacteristic
681C4×Q8C22×D311yescharacteristic
682C4×Q8C22×D312yes—
683C4×Q8C22×D312yes—
684C4×Q8C22×D311yescharacteristic
685#117—32no—
686#117—32no—
687#117—32no—
688#117—62no—
689#117—62no—
690#117—62no—
691#117—62no—
692C2×C4⋊C4—31no—
693C2×C4⋊C4—31no—
694C2×C4⋊C4—61no—
695C2×C4⋊C4—61no—
696C2×C42—31no—
697C2×C42—61no—
698C2×C42—61no—
699#107—31no—
700#107—32no—
701#107—31no—
702#107—31no—
703#107—32no—
704#107—32no—
705#107—32no—
706#107—32no—
707#107—32no—
708#107—32no—
709#107C22×D311yescharacteristic
710#107C22×D312yes—
711#106—32no—
712#106—32no—
713#106—32no—
714#106—32no—
715#106—32no—
716#106C22×D312yes—
717#106C22×D312yes—
718#106C22×D312yes—
719C4⋊C8—32no—
720C4⋊C8—32no—
721C4⋊C8—32no—
722C4⋊C8—31no—
723C4⋊C8—32no—
724C4⋊C8C22×D311yescharacteristic
725C4⋊C8C22×D312yes—
726#103—31no—
727#103—31no—
728#103—32no—
729#103—32no—
730#103—31no—
731#103—31no—
732#103—32no—
733#103—32no—
734#103—31no—
735#103—31no—
736#103—32no—
737#103—32no—
738#103C22×D311yescharacteristic
739#103C22×D311yescharacteristic
740#103C22×D312yes—
741#103C22×D312yes—
742#97—32no—
743#97C22×D312yes—
744C4×C8—31no—
745C4×C8—31no—
746C4×C8—32no—
747C4×C8—31no—
748C4×C8—32no—
749C4×C8C22×D311yescharacteristic
750C22×D3C22×D411yescharacteristic
751C3×Q8—22no—
752C3×Q8—21no—
753C3×Q8—21no—
754C3×Q8—42no—
755C3×Q8—82no—
756C3×Q8—81no—
757C3×Q8C22×Q812yes—
758C3×Q8C22×Q812yes—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—22no—
762C2×C3×C4—22no—
763C2×C3×C4—21no—
764C2×C3×C4—21no—
765C2×C3×C4C22×D412yes—
766C2×C3×C4C22×D412yes—
767C2×C3×C4C22×D411yescharacteristic
768C2×C3×C4C22×D411yescharacteristic
769C2×C3×C4C2511yescharacteristic
770C2×Dic3—21no—
771C2×Dic3—21no—
772C2×Dic3—22no—
773C2×Dic3—22no—
774C2×Dic3—21no—
775C2×Dic3—21no—
776C2×Dic3C22×D411yescharacteristic
777C2×Dic3C22×D412yes—
778C2×Dic3C22×D412yes—
779C2×Dic3C22×D411yescharacteristic
780C2×Dic3C22×D411yescharacteristic
781C4×D3—24no—
782C4×D3—24no—
783C4×D3—22no—
784C4×D3—41no—
785C4×D3—81no—
786C4×D3—81no—
787C4×D3C22×Q812yes—
788C4×D32−1+412yes—
789Dic6—22no—
790Dic6—21no—
791Dic6—21no—
792Dic6—24no—
793Dic6—24no—
794Dic6—42no—
795Dic6—42no—
796Dic6—82no—
797Dic6—82no—
798Dic6—81no—
799Dic6—82no—
800Dic6C22×Q812yes—
801Dic6C22×Q812yes—
802C3×C8—21no—
803C3×C8—22no—
804C3×C8C22×Q812yes—
805C3⋊C8—21no—
806C3⋊C8—22no—
807C3⋊C8C22×Q812yes—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—22no—
811C2×Q8—31no—
812C2×Q8—32no—
813C2×Q8—34no—
814C2×Q8—34no—
815C2×Q8—31no—
816C2×Q8—31no—
817C2×Q8—61no—
818C2×Q8—61no—
819C2×Q8—62no—
820C2×Q8—62no—
821C2×Q8—62no—
822C2×Q8—62no—
823C2×Q8—61no—
824C2×Q8—61no—
825C2×Q8—62no—
826C2×Q8D3×D411yescharacteristic
827C2×Q8C23×D311yescharacteristic
828C2×Q8C23×D311yescharacteristic
829C22×C4—31no—
830C22×C4—31no—
831C22×C4—31no—
832C22×C4—61no—
833C22×C4—61no—
834C22×C4—61no—
835C22×C4—61no—
836Q16—34no—
837Q16—34no—
838Q16—34no—
839Q16D3×Q814yes—
840M16—64no—
841C2×C8—31no—
842C2×C8—34no—
843C2×C8—31no—
844C2×C8—32no—
845C2×C8—62no—
846C2×C8C23×D311yescharacteristic
847C2×C8C23×D312yes—
848C2×C8C23×D311yescharacteristic
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—21no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—21no—
857C4⋊C4—22no—
858C4⋊C4—32no—
859C4⋊C4—32no—
860C4⋊C4—32no—
861C4⋊C4—32no—
862C4⋊C4—31no—
863C4⋊C4—32no—
864C4⋊C4—32no—
865C4⋊C4—32no—
866C4⋊C4—31no—
867C4⋊C4—31no—
868C4⋊C4—32no—
869C4⋊C4—61no—
870C4⋊C4—61no—
871C4⋊C4—61no—
872C4⋊C4—61no—
873C4⋊C4—61no—
874C4⋊C4—61no—
875C4⋊C4—62no—
876C4⋊C4—62no—
877C4⋊C4—62no—
878C4⋊C4—62no—
879C4⋊C4—62no—
880C4⋊C4—62no—
881C4⋊C4—62no—
882C4⋊C4—62no—
883C4⋊C4—62no—
884C4⋊C4—62no—
885C4⋊C4—62no—
886C4⋊C4—62no—
887C4⋊C4—62no—
888C4⋊C4—62no—
889C4⋊C4—61no—
890C4⋊C4—61no—
891C4⋊C4—62no—
892C4⋊C4—62no—
893C4⋊C4—61no—
894C4⋊C4—62no—
895C4⋊C4—62no—
896C4⋊C4—61no—
897C4⋊C4—62no—
898C4⋊C4D3×D411yescharacteristic
899C4⋊C4D3×D412yes—
900C4⋊C4C23×D311yescharacteristic
901C4⋊C4C23×D312yes—
902C4⋊C4C23×D311yescharacteristic
903C4⋊C4C23×D312yes—
904C22⋊C4—32no—
905C22⋊C4—32no—
906C22⋊C4—62no—
907C22⋊C4—62no—
908C42—21no—
909C42—21no—
910C42—22no—
911C42—22no—
912C42—31no—
913C42—31no—
914C42—31no—
915C42—32no—
916C42—61no—
917C42—61no—
918C42—61no—
919C42—61no—
920C42—62no—
921C42—62no—
922C42—62no—
923C42—62no—
924C42—62no—
925C42—62no—
926C42—61no—
927C42—61no—
928C42—62no—
929C42—62no—
930C42C23×D311yescharacteristic
931C42C23×D312yes—
932C22×C3C23×D411yescharacteristic
933C2×D3—21no—
934C2×D3—21no—
935C2×D3D4×Q812yes—
936C3×C4—22no—
937C3×C4—21no—
938C3×C4—22no—
939C3×C4—22no—
940C3×C4—22no—
941C3×C4—41no—
942C3×C4—42no—
943C3×C4—41no—
944C3×C4—42no—
945C3×C4#57812yes—
946C3×C4C23×Q811yescharacteristic
947C3×C4C2×2−1+411yescharacteristic
948Dic3—21no—
949Dic3—22no—
950Dic3—22no—
951Dic3—22no—
952Dic3—22no—
953Dic3—21no—
954Dic3—42no—
955Dic3—41no—
956Dic3—41no—
957Dic3—42no—
958Dic3D4×Q812yes—
959C23—31no—
960Q8—21no—
961Q8—21no—
962Q8—22no—
963Q8—32no—
964Q8—32no—
965Q8—42no—
966Q8—64no—
967Q8—64no—
968Q8—61no—
969Q8—61no—
970Q8—62no—
971Q8—81no—
972Q8—82no—
973Q8—122no—
974Q8—122no—
975Q8—241no—
976Q8—242no—
977Q8—242no—
978Q8—242no—
979Q8C2×D3×Q812yes—
980Q8C2×D3×Q812yes—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—31no—
988C2×C4—32no—
989C2×C4—32no—
990C2×C4—31no—
991C2×C4—31no—
992C2×C4—32no—
993C2×C4—32no—
994C2×C4—64no—
995C2×C4—64no—
996C2×C4—61no—
997C2×C4—61no—
998C2×C4—62no—
999C2×C4—62no—
1000C2×C4—62no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—121no—
1004C2×C4—241no—
1005C2×C4—241no—
1006C2×C4C2×D3×D412yes—
1007C2×C4C2×D3×D412yes—
1008C2×C4C2×D3×D411yescharacteristic
1009C2×C4C2×D3×D411yescharacteristic
1010C2×C4C24×D311yescharacteristic
1011C8—21no—
1012C8—22no—
1013C8—32no—
1014C8—61no—
1015C8—62no—
1016C8C2×D3×Q812yes—
1017C2×C3C2×D4×Q811yescharacteristic
1018C2×C3C2×#57811yescharacteristic
1019C2×C3#358411yescharacteristic
1020D3—22no—
1021C22—32no—
1022C22—61no—
1023C22—61no—
1024C22C22×D3×D411yescharacteristic
1025C4—22no—
1026C4—21no—
1027C4—22no—
1028C4—22no—
1029C4—22no—
1030C4—32no—
1031C4—42no—
1032C4—41no—
1033C4—41no—
1034C4—42no—
1035C4—61no—
1036C4—62no—
1037C4—61no—
1038C4—62no—
1039C4—62no—
1040C4—62no—
1041C4—122no—
1042C4—121no—
1043C4—121no—
1044C4—122no—
1045C4#577912yes—
1046C4C22×D3×Q811yescharacteristic
1047C4D3×2−1+411yescharacteristic
1048C3#6137211yescharacteristic, complemented, Sylow
1049C2—62no—
1050C2D3×D4×Q811yescharacteristic
1051C2C2×#577911yescharacteristic
1052C2#8720611yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3387C2
socleC22×C3C23×D4
prime radicalC22×D3C22×D4
hypercenter#3387D3
hypocenterC3#61372
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #3387

Complements

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

NH ≅ G/Ntype
3. C3×#3387C2semidirect
4. Q8×#216C2semidirect
5. #83682C2semidirect
7. #81971C2semidirect
8. #81906C2semidirect
11. #81222C2semidirect
13. #81102C2semidirect
16. #81006C2semidirect
17. #81006C2semidirect
18. #79986C2semidirect
21. #79820C2semidirect
23. #79708C2semidirect
143. #3387D3semidirect
198. D3×Q16Q8semidirect
1048. C3#61372semidirect

Maximal subgroups

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

subgroupindex
#870462
#870312
C3×#33872
Q8×#2162
#836822
#819752
#819712
#819062
#818912
#812332
#812222
#811082
#811022
#810132
#810112
#810062
#799862
#799582
#798312
#798202
C4×D3×Q162
#797082
#613723