Finite Group Databasebeta

← #11664231

Subgroups — #11664231

Order 768.

1990 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86262C211yesmaximal, characteristic, complemented
2C4×#1010C211yesmaximal, characteristic
3C3×#3076C211yesmaximal, characteristic, complemented
4#83367C211yesmaximal, characteristic, complemented
5#82533C211yesmaximal, characteristic, complemented
6#81211C214yesmaximal, complemented
7#81145C214yesmaximal, complemented
8#81092C212yesmaximal, complemented
9#81047C212yesmaximal, complemented
10#80998C212yesmaximal, complemented
11#80949C212yesmaximal, complemented
12#79175C212yesmaximal, complemented
13#79169C212yesmaximal, complemented
14C2×#4849C211yesmaximal, characteristic, complemented
15#79000C211yesmaximal, characteristic, complemented
16#78837C212yesmaximal
17#78821C212yesmaximal, complemented
18#60594—31nomaximal, Sylow
19C2×#1010C2211yescharacteristic
20C3×#533C2211yescharacteristic
21C3×C4×#41C2211yescharacteristic
22#5827C2211yescharacteristic
23C2×#951C2212yes—
24C22×Dic12C2212yes—
25#5728C2212yes—
26#5728C2212yes—
27#5698C2214yes—
28#5642—22no—
29#5642—22no—
30#5584—21no—
31#5584—21no—
32#5572C2212yes—
33C4×D3×Q8C2212yes—
34#5570—21no—
35#5570—21no—
36#5546—22no—
37#5546C2212yes—
38C4×#237—22no—
39C4×#237C2212yes—
40#5526C2212yes—
41#5523—21no—
42#5523C2211yescharacteristic
43#5516—21no—
44#5516C2211yescharacteristic
45#5516C2212yes—
46C4×#235—21no—
47C4×#235C2211yescharacteristic
48C2×#869C2211yescharacteristic
49C2×C4×Dic6—21no—
50C2×C4×Dic6C2211yescharacteristic
51C3×#479C2212yes—
52C3×#478C2212yes—
53C3×#477C2211yescharacteristic
54C3×#476C2211yescharacteristic
55C3×#475C2211yescharacteristic
56C3×#474C2211yescharacteristic
57C3×#427C2212yes—
58C2×C3×C4⋊C8C2211yescharacteristic
59C3×#416C2212yes—
60#5110C2212yes—
61C2×#816C2212yes—
62#5101C2212yes—
63#5094C2212yes—
64#5091C2212yes—
65#5063C2214yes—
66#5031C2212yes—
67#5031C2212yes—
68#5019C2212yes—
69#5019C2212yes—
70#5004C2212yes—
71#5004C2212yes—
72#4995C2212yes—
73#4924C2211yescharacteristic
74#4888C2214yes—
75#4884C2214yes—
76#4873C2214yes—
77#4873C2214yes—
78#4868C2214yes—
79#4862C2214yes—
80#4853C2214yes—
81#4853C2214yes—
82#4849C2212yes—
83#4849C2214yes—
84#4849C2212yes—
85#4840C2214yes—
86#4835C2212yes—
87#4833C2212yes—
88#4809C2214yes—
89#4809C2214yes—
90#4790C2214yes—
91#4789C2214yes—
92#4783C2214yes—
93#4783C2214yes—
94#4758C2214yes—
95#4757C2214yes—
96#3509—31no—
97C4×2−1+4—31no—
98#3127—34no—
99#3120—34no—
100#3116—32no—
101#3113—32no—
102#3107—32no—
103#3104—32no—
104#3097—32no—
105#3078—31no—
106#3076D311yescharacteristic, complemented
107#3039—31no—
108C2×#462—31no—
109#3011—32no—
110#2950—32no—
111#2947—32no—
112#2925—31no—
113C2×C3×#41C2311yescharacteristic
114#1010—24no—
115#1010—24no—
116C2×D3×Q8C2312yes—
117C2×#237—22no—
118C2×#237C2312yes—
119C2×#235—21no—
120C2×#235C2311yescharacteristic
121C22×Dic6—21no—
122C22×Dic6C2312yes—
123C22×Dic6C2311yescharacteristic
124C22×C3×C8C2312yes—
125C3×C4⋊Q8C2311yescharacteristic
126C3×C4⋊Q8C2311yescharacteristic
127C3×#125C2312yes—
128C3×C22⋊Q8—21no—
129C3×C22⋊Q8—21no—
130C3×C4×Q8—21no—
131C3×C4×Q8—21no—
132C3×C4×Q8C2311yescharacteristic
133C3×C4×Q8C2311yescharacteristic
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4C2311yescharacteristic
137C3×C4×D4C2311yescharacteristic
138C3×#117—21no—
139C3×#117C2312yes—
140C3×#117C2311yescharacteristic
141C2×C3×C42—21no—
142C2×C3×C42C2311yescharacteristic
143#951—28no—
144#946—22no—
145#946—22no—
146Q8×Dic3—22no—
147Q8×Dic3—22no—
148Q8×Dic3C2312yes—
149C2×#216C2314yes—
150D4×Dic3—22no—
151D4×Dic3C2312yes—
152C2×#214C2314yes—
153C4×#67—22no—
154C4×#67—22no—
155C4×#67D412yes—
156C4×#67D412yes—
157#926—21no—
158#926C2311yescharacteristic
159C2×C4⋊Dic3—21no—
160C2×C4⋊Dic3—21no—
161C2×C4⋊Dic3—21no—
162C2×C4⋊Dic3C2311yescharacteristic
163C2×Dic3⋊C4—21no—
164C2×Dic3⋊C4—22no—
165C2×C4×Dic3—21no—
166C2×C4×Dic3—22no—
167C2×#208C2312yes—
168C2×Dic12—28no—
169C2×Dic12C2314yes—
170C2×Dic12C2314yes—
171#898—24no—
172#898—24no—
173#897C2314yes—
174#897C2314yes—
175#892—22no—
176#892—22no—
177#892—22no—
178#892C2312yes—
179D3×C4⋊C4—22no—
180D3×C4⋊C4C2312yes—
181#890—24no—
182#890—24no—
183#890—22no—
184#890—22no—
185#887—22no—
186#887—22no—
187#887C2312yes—
188#887C2312yes—
189#887C2314yes—
190#887C2314yes—
191#886—24no—
192#67⋊C4—22no—
193#67⋊C4—22no—
194#67⋊C4—22no—
195#877—24no—
196#877—22no—
197#877—22no—
198#877—22no—
199#875—22no—
200C4×D12—21no—
201C4×D12D411yescharacteristic
202C4×D12D411yescharacteristic
203#872—22no—
204#872C2312yes—
205C42×D3—22no—
206C42×D3C2312yes—
207#869—22no—
208#869—21no—
209#869—21no—
210#869C2312yes—
211#869C2312yes—
212C4×Dic6—21no—
213C4×Dic6—21no—
214C4×Dic6—21no—
215C4×Dic6—21no—
216C4×Dic6—21no—
217C4×Dic6—22no—
218C4×Dic6—22no—
219C4×Dic6—22no—
220C4×Dic6—22no—
221C4×Dic6D411yescharacteristic
222C4×Dic6D411yescharacteristic
223C4×Dic6C2312yes—
224C4×Dic6C2312yes—
225C3×#107C2312yes—
226C3×#107C2312yes—
227C3×#106C2312yes—
228C3×#106C2312yes—
229C3×C4⋊C8C2311yescharacteristic
230C3×C4⋊C8C2311yescharacteristic
231C3×C4⋊C8C2312yes—
232C3×#103C2312yes—
233C3×#103C2312yes—
234C3×#102C2312yes—
235C3×#102C2312yes—
236(C2×D3)⋊C8C2314yes—
237(C2×D3)⋊C8C2314yes—
238#816C2314yes—
239#816C2314yes—
240#815C2314yes—
241C8×Dic3C2314yes—
242#810C2314yes—
243#810C2314yes—
244#810C2314yes—
245#810C2314yes—
246#808C2314yes—
247#807C2314yes—
248C4⋊(C3⋊C8)C2312yes—
249C4⋊(C3⋊C8)C2312yes—
250C2×2−1+4—31no—
251C2×#137—32no—
252C22×Q16—32no—
253#557—61no—
254#557—61no—
255#556—61no—
256#556—61no—
257#552—62no—
258#552—62no—
259#541—34no—
260#536—32no—
261#533—32no—
262#533—32no—
263#533C2×D311yescharacteristic
264C2×C4⋊Q8—31no—
265#520—31no—
266#520—31no—
267#520—32no—
268#520—61no—
269#520—62no—
270#519—32no—
271#519—31no—
272#519—32no—
273#519—61no—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—61no—
277C4×#41—62no—
278C4×#41C2×D311yescharacteristic
279C2×C4×Q8—32no—
280C2×C4×Q8—31no—
281C2×C4×Q8—61no—
282#485—34no—
283#485—34no—
284#484—34no—
285#483—34no—
286#479—34no—
287#479C2×D312yes—
288#478C2×D312yes—
289#477—32no—
290#477C2×D311yescharacteristic
291#476C2×D311yescharacteristic
292#475—32no—
293#475C2×D311yescharacteristic
294#474C2×D311yescharacteristic
295#462—32no—
296#462—32no—
297#462—32no—
298#462—32no—
299#462—34no—
300#461—32no—
301#461—32no—
302#452—34no—
303#452—34no—
304#451—34no—
305#451—34no—
306#441—34no—
307#441—34no—
308#441—34no—
309#440—34no—
310C4×Q16—34no—
311C4×Q16—34no—
312C4×Q16—34no—
313C4×SD16—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427C2×D312yes—
319#423—31no—
320C2×C4⋊C8C2×D311yescharacteristic
321#419—32no—
322#419—32no—
323#416C2×D312yes—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C3×#41—22no—
328C3×#41#4114yes—
329C2×C3×Q8—21no—
330C2×C3×Q8—21no—
331C2×C3×Q8C2411yescharacteristic
332C2×C3×D4—21no—
333C2×C3×D4C2411yescharacteristic
334C22×C3×C4—21no—
335C22×C3×C4—21no—
336C22×C3×C4—21no—
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2×D411yescharacteristic
339C22×C3×C4C2411yescharacteristic
340C2×#67—22no—
341C2×#67C2×D412yes—
342C22×Dic3—21no—
343C22×Dic3—22no—
344C22×Dic3—22no—
345C22×Dic3—21no—
346C22×Dic3—22no—
347D3×Q8—24no—
348D3×Q8—24no—
349#237—216no—
350#237—24no—
351#237—24no—
352#235—28no—
353#235—22no—
354#235—22no—
355C2×D12C2×D411yescharacteristic
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3C2×D412yes—
359C2×C4×D3C2×D412yes—
360C2×C4×D3C2412yes—
361C2×Dic6—28no—
362C2×Dic6—21no—
363C2×Dic6—22no—
364C2×Dic6—22no—
365C2×Dic6—24no—
366C2×Dic6—24no—
367C2×Dic6—22no—
368C2×Dic6C2×D411yescharacteristic
369C2×Dic6#4114yes—
370C2×Dic6C2414yes—
371C2×Dic6C2412yes—
372C2×C3×C8—24no—
373C2×C3×C8C2412yes—
374C2×C3×C8C2412yes—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—21no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4—21no—
379C3×C4⋊C4—22no—
380C3×C4⋊C4—22no—
381C3×C4⋊C4C2412yes—
382C3×C4⋊C4C2412yes—
383C3×C4⋊C4C2411yescharacteristic
384C3×C4⋊C4C2411yescharacteristic
385C3×C22⋊C4—21no—
386C3×C22⋊C4—22no—
387C3×C22⋊C4—21no—
388C3×C22⋊C4—21no—
389C3×C42—21no—
390C3×C42—22no—
391C3×C42—21no—
392C3×C42—21no—
393C3×C42C2×D411yescharacteristic
394C3×C42C2×D411yescharacteristic
395C3×C42C2411yescharacteristic
396C3×C42C2411yescharacteristic
397#217—22no—
398#217C2×D412yes—
399#216—28no—
400#214—28no—
401(C2×D3)⋊C4—22no—
402(C2×D3)⋊C4—24no—
403(C2×D3)⋊C4—24no—
404(C2×D3)⋊C4C2×D412yes—
405(C2×D3)⋊C4C2×D412yes—
406C4⋊Dic3—21no—
407C4⋊Dic3—22no—
408C4⋊Dic3—22no—
409C4⋊Dic3—22no—
410C4⋊Dic3—22no—
411C4⋊Dic3—22no—
412C4⋊Dic3—24no—
413C4⋊Dic3—24no—
414C4⋊Dic3C2×D411yescharacteristic
415C4⋊Dic3C2×D411yescharacteristic
416C4⋊Dic3C2412yes—
417Dic3⋊C4—22no—
418Dic3⋊C4—22no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—22no—
422Dic3⋊C4—24no—
423Dic3⋊C4—24no—
424Dic3⋊C4C2×D412yes—
425Dic3⋊C4C2×D412yes—
426C4×Dic3—22no—
427C4×Dic3—22no—
428C4×Dic3—22no—
429C4×Dic3—22no—
430C4×Dic3—22no—
431C4×Dic3—24no—
432C4×Dic3—24no—
433C4×Dic3—22no—
434C4×Dic3C2×D412yes—
435C4×Dic3C2×D412yes—
436C4×Dic3C2412yes—
437#208—24no—
438C2×C3⋊C8C2414yes—
439Dic12—28no—
440Dic12—28no—
4412−1+4—64no—
4422−1+4—64no—
443C2×#41—31no—
444C2×#41—32no—
445C2×#41—61no—
446C2×#41—62no—
447C2×#41C22×D311yescharacteristic
448C22×Q8—32no—
449C22×Q8—31no—
450C22×Q8—32no—
451C22×Q8—61no—
452#137—68no—
453C2×Q16—34no—
454C2×Q16—34no—
455C2×Q16—34no—
456C2×Q16—68no—
457C2×SD16—34no—
458C2×M16—32no—
459C22×C8C22×D312yes—
460C4⋊Q8—32no—
461C4⋊Q8—32no—
462C4⋊Q8—62no—
463C4⋊Q8—61no—
464C4⋊Q8—61no—
465C4⋊Q8C22×D311yescharacteristic
466C4⋊Q8C22×D311yescharacteristic
467#126—64no—
468#126—64no—
469#125—62no—
470#125—62no—
471#125—64no—
472#125—64no—
473#125C22×D312yes—
474#124—62no—
475#123—64no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—34no—
479C22⋊Q8—34no—
480C22⋊Q8—62no—
481C22⋊Q8—62no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8—31no—
485C4×Q8—31no—
486C4×Q8—32no—
487C4×Q8—32no—
488C4×Q8—32no—
489C4×Q8—34no—
490C4×Q8—34no—
491C4×Q8—32no—
492C4×Q8—32no—
493C4×Q8—62no—
494C4×Q8—61no—
495C4×Q8—62no—
496C4×Q8—61no—
497C4×Q8—62no—
498C4×Q8—62no—
499C4×Q8—61no—
500C4×Q8—62no—
501C4×Q8—62no—
502C4×Q8—62no—
503C4×Q8—62no—
504C4×Q8—61no—
505C4×Q8—61no—
506C4×Q8C22×D311yescharacteristic
507C4×Q8C22×D311yescharacteristic
508C4×D4—21no—
509C4×D4—21no—
510C4×D4—32no—
511C4×D4—32no—
512C4×D4—32no—
513C4×D4—31no—
514C4×D4—31no—
515C4×D4—61no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4C22×D311yescharacteristic
523C4×D4C22×D311yescharacteristic
524#117—21no—
525#117—31no—
526#117—32no—
527#117—32no—
528#117—62no—
529#117—62no—
530#117—62no—
531#117—64no—
532#117—62no—
533#117—62no—
534#117—62no—
535#117—62no—
536#117—61no—
537#117C22×D311yescharacteristic
538#117C22×D312yes—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—32no—
541C2×C4⋊C4—62no—
542C2×C4⋊C4—62no—
543C2×C4⋊C4—61no—
544C2×C4⋊C4—61no—
545C2×C4⋊C4—61no—
546C2×C4⋊C4—61no—
547C2×C42—21no—
548C2×C42—32no—
549C2×C42—62no—
550C2×C42—62no—
551C2×C42—61no—
552C2×C42C22×D311yescharacteristic
553#107—34no—
554#107C22×D312yes—
555#107C22×D312yes—
556#106—34no—
557#106C22×D312yes—
558#106C22×D312yes—
559C4⋊C8—32no—
560C4⋊C8—32no—
561C4⋊C8C22×D311yescharacteristic
562C4⋊C8C22×D311yescharacteristic
563C4⋊C8C22×D312yes—
564#103—34no—
565#103—34no—
566#103—34no—
567#103—34no—
568#103—34no—
569#103—34no—
570#103C22×D312yes—
571#103C22×D312yes—
572#102C22×D312yes—
573#102C22×D312yes—
574C22⋊C8—34no—
575C22⋊C8—34no—
576#97—34no—
577C4×C8—34no—
578C23×C3—21no—
579C23×C3C22×D411yescharacteristic
580C22×D3C22×D412yes—
581C3×Q8—21no—
582C3×Q8—42no—
583C3×Q8—42no—
584C3×Q8C2×#4112yes—
585C3×D4—24no—
586C3×D4—21no—
587C3×D4C2×#4112yes—
588C2×C3×C4—21no—
589C2×C3×C4—24no—
590C2×C3×C4—22no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—41no—
596C2×C3×C4—42no—
597C2×C3×C4—81no—
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×C4C2×#4112yes—
605C2×C3×C4C2511yescharacteristic
606#67—28no—
607#67—24no—
608C2×Dic3—28no—
609C2×Dic3—24no—
610C2×Dic3—22no—
611C2×Dic3—22no—
612C2×Dic3—24no—
613C2×Dic3—44no—
614C2×Dic3—82no—
615C2×Dic3—81no—
616C2×Dic3C22×D412yes—
617C2×Dic3C22×D412yes—
618C2×Dic3C22×D412yes—
619D12—22no—
620C4×D3—28no—
621C4×D3—24no—
622C4×D3—22no—
623C4×D3—22no—
624C4×D3—42no—
625C4×D3—82no—
626Dic6—28no—
627Dic6—22no—
628Dic6—24no—
629Dic6—22no—
630Dic6—24no—
631Dic6—24no—
632Dic6—44no—
633Dic6C2×#4114yes—
634C3×C8—22no—
635C3×C8—22no—
636C3⋊C8—24no—
637#41—22no—
638#41—68no—
639#41—64no—
640#41—616no—
641#41—64no—
642#41—62no—
643#41—62no—
644#41#23914yes—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—31no—
648C2×Q8—34no—
649C2×Q8—32no—
650C2×Q8—34no—
651C2×Q8—62no—
652C2×Q8—68no—
653C2×Q8—64no—
654C2×Q8—64no—
655C2×Q8—61no—
656C2×Q8—62no—
657C2×Q8—62no—
658C2×Q8—64no—
659C2×Q8—64no—
660C2×Q8C23×D311yescharacteristic
661C2×D4—21no—
662C2×D4—32no—
663C2×D4—31no—
664C2×D4—62no—
665C2×D4C23×D311yescharacteristic
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—32no—
670C22×C4—32no—
671C22×C4—32no—
672C22×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4—61no—
677C22×C4—62no—
678C22×C4—61no—
679C22×C4D3×D411yescharacteristic
680C22×C4D3×D411yescharacteristic
681C22×C4C23×D311yescharacteristic
682Q16—68no—
683Q16—68no—
684Q16—68no—
685SD16—68no—
686M16—64no—
687C2×C8—24no—
688C2×C8—34no—
689C2×C8C23×D312yes—
690C2×C8C23×D312yes—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—31no—
698C4⋊C4—32no—
699C4⋊C4—31no—
700C4⋊C4—32no—
701C4⋊C4—32no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—62no—
706C4⋊C4—64no—
707C4⋊C4—64no—
708C4⋊C4—64no—
709C4⋊C4—64no—
710C4⋊C4—61no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—62no—
715C4⋊C4—62no—
716C4⋊C4—62no—
717C4⋊C4C23×D312yes—
718C4⋊C4C23×D312yes—
719C4⋊C4C23×D311yescharacteristic
720C4⋊C4C23×D311yescharacteristic
721C22⋊C4—21no—
722C22⋊C4—22no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—32no—
726C22⋊C4—32no—
727C22⋊C4—32no—
728C22⋊C4—62no—
729C22⋊C4—64no—
730C22⋊C4—64no—
731C22⋊C4—62no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—22no—
736C42—32no—
737C42—32no—
738C42—32no—
739C42—62no—
740C42—62no—
741C42—62no—
742C42—62no—
743C42—64no—
744C42—64no—
745C42—62no—
746C42—62no—
747C42D3×D411yescharacteristic
748C42D3×D411yescharacteristic
749C42C23×D311yescharacteristic
750C42C23×D311yescharacteristic
751C22×C3—21no—
752C22×C3—21no—
753C22×C3—22no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3#52512yes—
757C22×C3C23×D411yescharacteristic
758C2×D3—22no—
759C2×D3—22no—
760C2×D3—22no—
761C3×C4—21no—
762C3×C4—21no—
763C3×C4—22no—
764C3×C4—21no—
765C3×C4—41no—
766C3×C4—42no—
767C3×C4—41no—
768C3×C4—42no—
769C3×C4#52512yes—
770C3×C4#57812yes—
771C3×C4C22×#4111yescharacteristic
772C3×C4C22×#4111yescharacteristic
773Dic3—22no—
774Dic3—22no—
775Dic3—24no—
776Dic3—22no—
777Dic3—42no—
778Dic3—44no—
779C23—21no—
780C23—32no—
781C23C2×D3×D411yescharacteristic
782Q8—21no—
783Q8—34no—
784Q8—42no—
785Q8—42no—
786Q8—68no—
787Q8—62no—
788Q8—62no—
789Q8—64no—
790Q8—64no—
791Q8—64no—
792Q8—124no—
793Q8C2×#23912yes—
794D4—24no—
795D4—21no—
796D4—68no—
797D4—64no—
798D4—62no—
799D4C2×#23912yes—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—68no—
813C2×C4—68no—
814C2×C4—62no—
815C2×C4—64no—
816C2×C4—62no—
817C2×C4—62no—
818C2×C4—64no—
819C2×C4—62no—
820C2×C4—64no—
821C2×C4—81no—
822C2×C4—122no—
823C2×C4—124no—
824C2×C4—242no—
825C2×C4—242no—
826C2×C4—241no—
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×D411yescharacteristic
830C2×C4C2×D3×D411yescharacteristic
831C2×C4C2×D3×D411yescharacteristic
832C2×C4C2×#23912yes—
833C2×C4D3×#4112yes—
834C2×C4C24×D311yescharacteristic
835C8—22no—
836C8—22no—
837C8—64no—
838C2×C3—22no—
839C2×C3—42no—
840C2×C3C2×#52511yescharacteristic
841C2×C3C2×#57811yescharacteristic
842C2×C3#358611yescharacteristic
843D3—42no—
844C22—21no—
845C22—21no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—62no—
850C22—62no—
851C22—62no—
852C22#562712yes—
853C22C22×D3×D411yescharacteristic
854C4—21no—
855C4—21no—
856C4—21no—
857C4—22no—
858C4—41no—
859C4—42no—
860C4—41no—
861C4—42no—
862C4—62no—
863C4—62no—
864C4—62no—
865C4—64no—
866C4—122no—
867C4—124no—
868C4#562712yes—
869C4#577112yes—
870C4C22×#23911yescharacteristic
871C4C2×D3×#4111yescharacteristic
872C3#6059411yescharacteristic, complemented, Sylow
873C2—22no—
874C2—42no—
875C2—122no—
876C2C2×#562711yescharacteristic
877C2C2×#577111yescharacteristic
878C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3076C2
socleC22×C3C23×D4
prime radicalC2×#1010C22
hypercenter#3076D3
hypocenterC3#60594
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
1. #86262C2semidirect
3. C3×#3076C2semidirect
4. #83367C2semidirect
5. #82533C2semidirect
6. #81211C2semidirect
7. #81145C2semidirect
8. #81092C2semidirect
9. #81047C2semidirect
10. #80998C2semidirect
11. #80949C2semidirect
12. #79175C2semidirect
13. #79169C2semidirect
14. C2×#4849C2semidirect
15. #79000C2semidirect
17. #78821C2semidirect
106. #3076D3semidirect
872. C3#60594semidirect

Maximal subgroups

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

subgroupindex
#862622
C4×#10102
C3×#30762
#833672
#825332
#812112
#811452
#810922
#810472
#809982
#809492
#791752
#791692
C2×#48492
#790002
#788372
#788212
#605943