Finite Group Databasebeta

← #11675537

Subgroups — #11675537

Order 768.

1782 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3507C211yesmaximal, characteristic, complemented
2#86281C211yesmaximal, characteristic, complemented
3#83719C212yesmaximal, complemented
4#83713C212yesmaximal, complemented
5#83696C212yesmaximal, complemented
6#83692C212yesmaximal, complemented
7#83678C214yesmaximal, complemented
8#83668C214yesmaximal, complemented
9#83406C212yesmaximal, complemented
10#83401C212yesmaximal, complemented
11#83330C211yesmaximal, characteristic, complemented
12#83296C211yesmaximal, characteristic
13#83283C211yesmaximal, characteristic, complemented
14#82559C212yesmaximal, complemented
15#82557C212yesmaximal, complemented
16C2×#5021C211yesmaximal, characteristic, complemented
17C4×#942C211yesmaximal, characteristic, complemented
18#61348—31nomaximal, Sylow
19C3×#559C2212yes—
20C3×#557C2212yes—
21C3×#556—21no—
22C3×#556C2214yes—
23C3×#554—21no—
24C3×#552—22no—
25C3×#539—22no—
26C3×#536C2212yes—
27C3×#533C2211yescharacteristic
28C3×#532C2211yescharacteristic
29C3×#529—22no—
30C3×#520C2212yes—
31C2×C3×C4×Q8C2211yescharacteristic
32C2×#950C2212yes—
33C2×#942C2211yescharacteristic
34#5728—21no—
35D3×C4⋊Q8—21no—
36#5689—22no—
37#5635—22no—
38#5632—22no—
39#5579C2212yes—
40Q8×D12C2212yes—
41#5567C2212yes—
42Q8×Dic6C2212yes—
43#5523C2212yes—
44#5519C2212yes—
45C4×#235C2211yescharacteristic
46C2×#869C2211yescharacteristic
47#5233C2212yes—
48#5232C2212yes—
49#5232C2212yes—
50#5225C2211yescharacteristic
51C2×#835C2212yes—
52#5090C2211yescharacteristic
53#5090C2214yes—
54#5083C2211yescharacteristic
55#5083C2214yes—
56#5082C2214yes—
57#5079C2212yes—
58#5079C2214yes—
59#5075C2211yescharacteristic
60#5072C2211yescharacteristic
61#5070C2212yes—
62#5057C2214yes—
63#5057C2212yes—
64#5056C2214yes—
65#5055C2214yes—
66#5055C2214yes—
67#5054C2214yes—
68#5054C2212yes—
69#5030C2212yes—
70C4×#216C2212yes—
71C4×#216C2214yes—
72#5026C2214yes—
73#5026C2212yes—
74C4×#215C2212yes—
75#5024C2212yes—
76#5024C2214yes—
77Q8×C3⋊C8C2212yes—
78#5022C2214yes—
79#5021C2212yes—
80#5021C2212yes—
81#5021C2214yes—
82#5021C2214yes—
83#5018C2214yes—
84C4×#213C2214yes—
85#5009C2214yes—
86#5007C2214yes—
87#4999C2212yes—
88#4997C2212yes—
89#4966C2211yescharacteristic
90#4964C2211yescharacteristic
91C2×#807C2212yes—
92C2×C4⋊(C3⋊C8)C2211yescharacteristic
93C4×#208C2211yescharacteristic
94#3507D311yescharacteristic, complemented
95#3503—31no—
96#3377—34no—
97#3375—32no—
98#3372—32no—
99#3367—34no—
100#3363—32no—
101#3361—32no—
102#3141—31no—
103#3137—32no—
104#3083—32no—
105C2×#477—31no—
106#3046—32no—
107#3035—31no—
108#2962—31no—
109#2951—32no—
110C4×#137—31no—
111C2×C3×#41C2312yes—
112C22×C3×Q8C2311yescharacteristic
113C2×D3×Q8—22no—
114C2×#235C2311yescharacteristic
115C22×Dic6—21no—
116C3×C4⋊Q8D411yescharacteristic
117C3×C4⋊Q8D411yescharacteristic
118C3×C4⋊Q8C2311yescharacteristic
119C3×C4⋊Q8C2314yes—
120C3×#127C2311yescharacteristic
121C3×#126—24no—
122C3×#126—24no—
123C3×#125—22no—
124C3×#125—24no—
125C3×#125D412yes—
126C3×#124—22no—
127C3×#124C2314yes—
128C3×#124C2312yes—
129C3×#123—24no—
130C3×#123—24no—
131C3×C22⋊Q8—24no—
132C3×C22⋊Q8—22no—
133C3×C22⋊Q8—22no—
134C3×C22⋊Q8D412yes—
135C3×C22⋊Q8D412yes—
136C3×#121—21no—
137C3×#121—21no—
138C3×C4×Q8—22no—
139C3×C4×Q8—21no—
140C3×C4×Q8—21no—
141C3×C4×Q8C2312yes—
142C3×C4×Q8C2312yes—
143C3×C4×Q8C2314yes—
144C3×C4×Q8C2312yes—
145C3×C4×Q8C2312yes—
146C3×C4×D4—22no—
147C3×C4×D4—24no—
148C3×C4×D4—21no—
149C3×C4×D4—21no—
150C3×C4×D4C2314yes—
151C3×#117—22no—
152C3×#117—24no—
153C3×#117C2312yes—
154C2×C3×C4⋊C4—21no—
155C2×C3×C4⋊C4—22no—
156C2×C3×C4⋊C4C2311yescharacteristic
157C2×C3×C42—21no—
158C2×C3×C42C2311yescharacteristic
159#950—28no—
160#946—22no—
161Q8×Dic3—22no—
162#944—22no—
163C2×#216C2312yes—
164C2×#216C2312yes—
165#942—24no—
166C2×#215C2312yes—
167C2×#215C2312yes—
168C2×#214C2312yes—
169C2×#213C2312yes—
170C4×#67—21no—
171C4×#67—21no—
172#926C2311yescharacteristic
173C2×C4⋊Dic3—21no—
174C2×C4⋊Dic3C2312yes—
175C2×#208C2311yescharacteristic
176C2×#208C2311yescharacteristic
177C22×C3⋊C8C2312yes—
178#897—22no—
179#897—24no—
180#896—24no—
181#892—22no—
182D3×C4⋊C4—22no—
183D3×C4⋊C4—22no—
184#890—22no—
185#889—24no—
186#888—24no—
187#888—22no—
188#888—22no—
189#887—22no—
190#67⋊C4—24no—
191#878—24no—
192C4×D12C2311yescharacteristic
193C4×D12C2311yescharacteristic
194C4×D12C2314yes—
195#872—21no—
196C42×D3—21no—
197#870C2314yes—
198#869—21no—
199#869—21no—
200#869C2312yes—
201#869C2312yes—
202#869C2314yes—
203C4×Dic6C2311yescharacteristic
204C4×Dic6C2311yescharacteristic
205C4×Dic6C2314yes—
206#835C2314yes—
207#835C2314yes—
208#835C2312yes—
209#835C2312yes—
210#835C2314yes—
211#835C2314yes—
212#835C2312yes—
213#835C2312yes—
214#832C2314yes—
215#832C2314yes—
216#832C2312yes—
217#832C2312yes—
218#810C2312yes—
219#809C2312yes—
220#808C2312yes—
221#807C2314yes—
222#807C2314yes—
223#807C2312yes—
224C4⋊(C3⋊C8)C2311yescharacteristic
225C4⋊(C3⋊C8)C2312yes—
226C4⋊(C3⋊C8)C2311yescharacteristic
227C4⋊(C3⋊C8)C2314yes—
228C4⋊(C3⋊C8)C2314yes—
229#803C2312yes—
230#803C2314yes—
231C4×C3⋊C8C2312yes—
232C4×C3⋊C8C2314yes—
233C2×#137—31no—
234C2×#135—32no—
235#559C2×D312yes—
236Q82—32no—
237#557—32no—
238#557C2×D312yes—
239#556—21no—
240#556C2×D314yes—
241#554—21no—
242#554—32no—
243#554—62no—
244#552—22no—
245D4×Q8—32no—
246D4×Q8—62no—
247#544—32no—
248#544—62no—
249#539—22no—
250#536C2×D312yes—
251#533—61no—
252#533C2×D311yescharacteristic
253#532C2×D311yescharacteristic
254C2×C4⋊Q8—31no—
255C2×C4⋊Q8—61no—
256#529—22no—
257#520—32no—
258#520C2×D312yes—
259C4×#41—31no—
260C2×C4×Q8C2×D311yescharacteristic
261#491—34no—
262#489—34no—
263#489—34no—
264#488—34no—
265#487—34no—
266#487—32no—
267#486—32no—
268#479—34no—
269#478—34no—
270#477—32no—
271#477—34no—
272#477—32no—
273#477—34no—
274#474—34no—
275#464—34no—
276#464—32no—
277#463—34no—
278#463—32no—
279#462—31no—
280#462—34no—
281#461—34no—
282#461—31no—
283#460—31no—
284#459—31no—
285#446—34no—
286#446—32no—
287C8×Q8—32no—
288#441—32no—
289#440—32no—
290#440—34no—
291#440—34no—
292C4×Q16—32no—
293C4×Q16—34no—
294C4×SD16—32no—
295C4×D8—34no—
296#428—31no—
297C2×#107—32no—
298#424—32no—
299C2×C4⋊C8—31no—
300#419—31no—
301#417—32no—
302#417—32no—
303#417—31no—
304#416—32no—
305C2×#103—32no—
306#405—32no—
307C4×M16—31no—
308C3×#41—24no—
309C3×#41—24no—
310C2×C3×Q8—21no—
311C2×C3×Q8—22no—
312C2×C3×Q8—22no—
313C2×C3×Q8C2×D412yes—
314C2×C3×Q8C2×D412yes—
315C2×C3×Q8C2412yes—
316C2×C3×Q8C2412yes—
317C2×C3×D4—22no—
318C2×C3×D4—21no—
319C2×C3×D4—21no—
320C2×C3×D4C2412yes—
321C22×C3×C4—21no—
322C22×C3×C4—21no—
323C22×C3×C4—22no—
324C22×C3×C4—24no—
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2×D411yescharacteristic
327C22×C3×C4C2411yescharacteristic
328C2×#67—21no—
329C22×Dic3—22no—
330D3×Q8—84no—
331#235—22no—
332#235#4114yes—
333C2×D12C2411yescharacteristic
334C2×C4×D3—21no—
335C2×C4×D3—21no—
336C2×C4×D3—21no—
337C2×C4×D3—24no—
338C2×Dic6—22no—
339C2×Dic6—22no—
340C2×Dic6—24no—
341C2×Dic6—82no—
342C2×Dic6C2411yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—24no—
345C3×C4⋊C4—22no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—24no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—24no—
351C3×C4⋊C4C2×D412yes—
352C3×C4⋊C4C2×D412yes—
353C3×C4⋊C4C2×D412yes—
354C3×C4⋊C4C2×D414yes—
355C3×C4⋊C4C2×D414yes—
356C3×C4⋊C4C2×D412yes—
357C3×C4⋊C4C2412yes—
358C3×C22⋊C4—22no—
359C3×C22⋊C4—24no—
360C3×C22⋊C4—24no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—24no—
363C3×C22⋊C4C2×D414yes—
364C3×C42—22no—
365C3×C42—22no—
366C3×C42—24no—
367C3×C42C2×D411yescharacteristic
368C3×C42C2×D411yescharacteristic
369C3×C42C2411yescharacteristic
370C3×C42C2414yes—
371C3×C42C2411yescharacteristic
372#217—21no—
373#216—24no—
374#216—24no—
375#215—24no—
376#215—24no—
377#214—24no—
378#213—24no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—21no—
381(C2×D3)⋊C4—24no—
382C4⋊Dic3—22no—
383C4⋊Dic3—22no—
384C4⋊Dic3—22no—
385C4⋊Dic3—24no—
386C4⋊Dic3C2411yescharacteristic
387C4⋊Dic3C2414yes—
388C4⋊Dic3C2411yescharacteristic
389Dic3⋊C4—21no—
390Dic3⋊C4—21no—
391Dic3⋊C4—24no—
392Dic3⋊C4—24no—
393Dic3⋊C4—24no—
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3—24no—
397C4×Dic3—21no—
398#208—22no—
399#208—22no—
400C2×C3⋊C8—24no—
401C2×C3⋊C8C2412yes—
402C2×C3⋊C8C2412yes—
403C2×C3⋊C8C2412yes—
404C2×C3⋊C8C2412yes—
405C2×#41—31no—
406C2×#41C22×D312yes—
407C22×Q8—62no—
408C22×Q8—61no—
409C22×Q8C22×D311yescharacteristic
410#137—64no—
411#135—68no—
412C2×Q16—32no—
413C2×Q16—32no—
414C2×SD16—32no—
415C2×SD16—32no—
416C2×SD16—32no—
417C2×D8—32no—
418C2×M16—31no—
419C2×M16—31no—
420C22×C8—32no—
421C4⋊Q8—32no—
422C4⋊Q8—32no—
423C4⋊Q8—34no—
424C4⋊Q8—62no—
425C4⋊Q8—62no—
426C4⋊Q8—62no—
427C4⋊Q8—64no—
428C4⋊Q8—61no—
429C4⋊Q8—61no—
430C4⋊Q8#6711yescharacteristic
431C4⋊Q8#6711yescharacteristic
432C4⋊Q8C22×D311yescharacteristic
433C4⋊Q8C22×D314yes—
434#127C22×D311yescharacteristic
435#126—24no—
436#126—24no—
437#125—22no—
438#125—24no—
439#125—34no—
440#125—62no—
441#125—64no—
442#125#6712yes—
443#124—22no—
444#124C22×D312yes—
445#124C22×D314yes—
446#123—24no—
447#123—24no—
448C22⋊Q8—24no—
449C22⋊Q8—22no—
450C22⋊Q8—22no—
451C22⋊Q8—62no—
452C22⋊Q8—62no—
453C22⋊Q8—64no—
454C22⋊Q8—64no—
455C22⋊Q8—64no—
456C22⋊Q8#6712yes—
457C22⋊Q8#6712yes—
458#121—21no—
459#121—21no—
460C4×Q8—22no—
461C4×Q8—21no—
462C4×Q8—21no—
463C4×Q8—31no—
464C4×Q8—31no—
465C4×Q8—34no—
466C4×Q8—62no—
467C4×Q8—62no—
468C4×Q8C22×D312yes—
469C4×Q8C22×D312yes—
470C4×Q8C22×D314yes—
471C4×Q8C22×D312yes—
472C4×Q8C22×D312yes—
473C4×D4—22no—
474C4×D4—24no—
475C4×D4—21no—
476C4×D4—21no—
477C4×D4—31no—
478C4×D4—31no—
479C4×D4—34no—
480C4×D4—61no—
481C4×D4—61no—
482C4×D4—64no—
483C4×D4C22×D314yes—
484#117—22no—
485#117—24no—
486#117—31no—
487#117—62no—
488#117—61no—
489#117C22×D312yes—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—22no—
492C2×C4⋊C4—32no—
493C2×C4⋊C4—61no—
494C2×C4⋊C4—62no—
495C2×C4⋊C4—62no—
496C2×C4⋊C4C22×D311yescharacteristic
497C2×C42—21no—
498C2×C42—61no—
499C2×C42C22×D311yescharacteristic
500#107—34no—
501#107—34no—
502#107—32no—
503#106—32no—
504C4⋊C8—31no—
505C4⋊C8—31no—
506C4⋊C8—32no—
507C4⋊C8—34no—
508C4⋊C8—34no—
509#103—34no—
510#103—34no—
511#103—32no—
512#103—32no—
513#103—34no—
514#103—34no—
515#103—32no—
516#103—32no—
517#103—32no—
518#102—32no—
519#102—32no—
520#102—34no—
521#102—34no—
522#102—32no—
523#97—32no—
524#97—34no—
525C4×C8—32no—
526C4×C8—34no—
527C23×C3—22no—
528C23×C3C22×D411yescharacteristic
529C22×D3—21no—
530C3×Q8—24no—
531C3×Q8—22no—
532C3×Q8—22no—
533C3×Q8—22no—
534C3×Q8—22no—
535C3×Q8—42no—
536C3×Q8—42no—
537C3×D4—22no—
538C3×D4—22no—
539C3×D4—44no—
540C3×D4—42no—
541C3×D4—81no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—44no—
549C2×C3×C4—84no—
550C2×C3×C4—81no—
551C2×C3×C4C22×D414yes—
552C2×C3×C4C22×D411yescharacteristic
553C2×C3×C4C22×D414yes—
554C2×C3×C4C22×D411yescharacteristic
555C2×C3×C4C22×D411yescharacteristic
556C2×C3×C4C22×D411yescharacteristic
557C2×C3×C4C22×D411yescharacteristic
558C2×C3×C4C2×#4112yes—
559C2×C3×C42−1+412yes—
560C2×C3×C4C2511yescharacteristic
561#67—24no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—24no—
566C2×Dic3—82no—
567D12—21no—
568D12C2×#4112yes—
569C4×D3—24no—
570C4×D3—42no—
571C4×D3—42no—
572C4×D3—84no—
573Dic6—21no—
574Dic6—44no—
575Dic6—82no—
576Dic6—84no—
577Dic6C2×#4112yes—
578C3⋊C8—22no—
579C3⋊C8—22no—
580C3⋊C8—22no—
581C3⋊C8—22no—
582#41—24no—
583#41—24no—
584#41—34no—
585#41—62no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—31no—
590C2×Q8—62no—
591C2×Q8—64no—
592C2×Q8—62no—
593C2×Q8—242no—
594C2×Q8—244no—
595C2×Q8C2×#6712yes—
596C2×Q8C2×#6712yes—
597C2×Q8C23×D312yes—
598C2×Q8C23×D312yes—
599C2×D4—22no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—31no—
603C2×D4—61no—
604C2×D4C23×D312yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—22no—
608C22×C4—24no—
609C22×C4—61no—
610C22×C4—62no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—64no—
614C22×C4C2×#6711yescharacteristic
615C22×C4C2×#6711yescharacteristic
616C22×C4C23×D311yescharacteristic
617Q16—64no—
618Q16—64no—
619SD16—64no—
620SD16—64no—
621SD16—64no—
622D8—64no—
623M16—62no—
624M16—62no—
625C2×C8—32no—
626C2×C8—32no—
627C2×C8—32no—
628C2×C8—32no—
629C2×C8—64no—
630C4⋊C4—21no—
631C4⋊C4—24no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—24no—
638C4⋊C4—31no—
639C4⋊C4—34no—
640C4⋊C4—31no—
641C4⋊C4—62no—
642C4⋊C4—62no—
643C4⋊C4—64no—
644C4⋊C4—64no—
645C4⋊C4—62no—
646C4⋊C4—61no—
647C4⋊C4—61no—
648C4⋊C4—64no—
649C4⋊C4—64no—
650C4⋊C4C2×#6712yes—
651C4⋊C4C2×#6712yes—
652C4⋊C4C2×#6712yes—
653C4⋊C4C2×#6714yes—
654C4⋊C4C2×#6712yes—
655C4⋊C4C2×#6714yes—
656C4⋊C4C23×D312yes—
657C22⋊C4—22no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—22no—
661C22⋊C4—24no—
662C22⋊C4—61no—
663C22⋊C4—61no—
664C22⋊C4—61no—
665C22⋊C4—64no—
666C22⋊C4C2×#6714yes—
667C42—22no—
668C42—22no—
669C42—24no—
670C42—61no—
671C42—61no—
672C42—61no—
673C42—64no—
674C42C2×#6711yescharacteristic
675C42C2×#6711yescharacteristic
676C42C23×D311yescharacteristic
677C42C23×D314yes—
678C42C23×D311yescharacteristic
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3#54812yes—
685C22×C3C23×D411yescharacteristic
686C2×D3—22no—
687C2×D3—41no—
688C2×D3—41no—
689C3×C4—21no—
690C3×C4—21no—
691C3×C4—24no—
692C3×C4—21no—
693C3×C4—24no—
694C3×C4—42no—
695C3×C4—42no—
696C3×C4—42no—
697C3×C4#54812yes—
698C3×C4#57812yes—
699C3×C4C22×#4111yescharacteristic
700C3×C4C2×2−1+411yescharacteristic
701Dic3—22no—
702Dic3—44no—
703Dic3—41no—
704Dic3—41no—
705C23—22no—
706C23—61no—
707C23C22×#6711yescharacteristic
708Q8—24no—
709Q8—22no—
710Q8—22no—
711Q8—22no—
712Q8—22no—
713Q8—32no—
714Q8—42no—
715Q8—42no—
716Q8—61no—
717Q8—124no—
718Q8—242no—
719Q8—244no—
720D4—22no—
721D4—22no—
722D4—32no—
723D4—44no—
724D4—42no—
725D4—64no—
726D4—61no—
727D4—81no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—41no—
733C2×C4—42no—
734C2×C4—44no—
735C2×C4—61no—
736C2×C4—64no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—64no—
740C2×C4—84no—
741C2×C4—81no—
742C2×C4—122no—
743C2×C4—122no—
744C2×C4—244no—
745C2×C4—242no—
746C2×C4D3×#4112yes—
747C2×C4#101012yes—
748C2×C4C22×#6711yescharacteristic
749C2×C4C22×#6714yes—
750C2×C4C22×#6711yescharacteristic
751C2×C4C22×#6711yescharacteristic
752C2×C4C22×#6714yes—
753C2×C4C22×#6711yescharacteristic
754C2×C4C22×#6711yescharacteristic
755C2×C4C24×D311yescharacteristic
756C8—62no—
757C8—62no—
758C8—62no—
759C8—62no—
760C2×C3—22no—
761C2×C3—82no—
762C2×C3C2×#54811yescharacteristic
763C2×C3C2×#57811yescharacteristic
764C2×C3#358511yescharacteristic
765D3—42no—
766C22—21no—
767C22—21no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—62no—
772C22—121no—
773C22—121no—
774C22#583112yes—
775C22C23×#6711yescharacteristic
776C4—21no—
777C4—21no—
778C4—24no—
779C4—21no—
780C4—24no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—62no—
785C4—121no—
786C4—124no—
787C4—121no—
788C4#583112yes—
789C4#583812yes—
790C4C2×D3×#4111yescharacteristic
791C4C2×#101011yescharacteristic
792C3#6134811yescharacteristic, complemented, Sylow
793C2—22no—
794C2—82no—
795C2—122no—
796C2C2×#583111yescharacteristic
797C2C2×#583811yescharacteristic
798C2#8729811yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3507C2
socleC22×C3C23×D4
prime radical#83296C2
hypercenter#3507D3
hypocenterC3#61348
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ #533 ◁ #3507

Complements

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

NH ≅ G/Ntype
1. C3×#3507C2semidirect
2. #86281C2semidirect
3. #83719C2semidirect
4. #83713C2semidirect
5. #83696C2semidirect
6. #83692C2semidirect
7. #83678C2semidirect
8. #83668C2semidirect
9. #83406C2semidirect
10. #83401C2semidirect
11. #83330C2semidirect
13. #83283C2semidirect
14. #82559C2semidirect
15. #82557C2semidirect
16. C2×#5021C2semidirect
17. C4×#942C2semidirect
94. #3507D3semidirect
792. C3#61348semidirect

Maximal subgroups

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

subgroupindex
C3×#35072
#862812
#837192
#837132
#836962
#836922
#836782
#836682
#834062
#834012
#833302
#832962
#832832
#825592
#825572
C2×#50212
C4×#9422
#613483