Finite Group Databasebeta

← #11906038

Subgroups — #11906038

Order 1152.

3087 conjugacy classes of subgroups.

The subgroup lattice has 845 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C2×#64297C211yesmaximal, characteristic, complemented
3#10596287C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5#10595403C214yesmaximal, complemented
6#10595360C212yesmaximal, complemented
7#10595358C214yesmaximal, complemented
8#10595356C212yesmaximal, complemented
9D3×#944C212yesmaximal, complemented
10#10595340C212yesmaximal, complemented
11#10595029C211yesmaximal, characteristic, complemented
12Dic3×#235C211yesmaximal, characteristic, complemented
13#10594885C218yesmaximal, complemented
14#10594855C211yesmaximal, characteristic, complemented
15#87292—31nomaximal
16#86214—31nomaximal
17C22×C32×Q8C2211yescharacteristic
18C2×#3828C2211yescharacteristic
19C3×#1007—28no—
20C2×C3×#239C2212yes—
21C2×C3×#239C2212yes—
22C2×C3×D3×Q8C2212yes—
23C2×C3×D3×Q8C2212yes—
24C2×C3×#235C2211yescharacteristic
25C2×C3×#235C2214yes—
26C2×C3×#235C2211yescharacteristic
27C22×C3×Dic6C2211yescharacteristic
28C2×#3804C2214yes—
29C2×#3799C2212yes—
30C2×#3797C2212yes—
31#64297—28no—
32C2×#3796C2212yes—
33C2×D3×Dic6C2212yes—
34#64156C2212yes—
35#64155C2214yes—
36#64153C2212yes—
37#64138C2214yes—
38#64135C2211yescharacteristic
39C3×#944C2212yes—
40C3×#944C2212yes—
41C3×#944C2214yes—
42C2×C3×Dic3⋊C4C2214yes—
43C2×C3×C4×Dic3C2211yescharacteristic
44#63978C2214yes—
45Dic3×#67C2214yes—
46#63961C2214yes—
47#63911C2211yescharacteristic
48#63904C2218yes—
49C4×#626C2214yes—
50Dic3×D12C2212yes—
51#63888C2218yes—
52#63886C2218yes—
53#63884C2218yes—
54D3×Dic3⋊C4C2218yes—
55C4×D3×Dic3C2212yes—
56#63873C2212yes—
57#63866C2211yescharacteristic
58#63864C2211yescharacteristic
59#63863C2212yes—
60#63860C2211yescharacteristic
61#63856C2214yes—
62#63855C2212yes—
63#63851C2218yes—
64#63850C2218yes—
65Dic3×Dic6C2212yes—
66#63839C2218yes—
67C2×C3×2−1+4—31no—
68C2×#1010—31no—
69C2×#1007—31no—
70C2×#1007D311yescharacteristic, complemented
71C2×C3×C4⋊Q8—31no—
72#5832—32no—
73#5832—31no—
74Dic3×#41—31no—
75#5825—31no—
76#5825—32no—
77#5824—34no—
78#5824—38no—
79#5816—31no—
80#5816—31no—
81#5816—31no—
82#5816—32no—
83#5816—61no—
84Q8×#67—34no—
85C2×#944—32no—
86C2×#944D311yescharacteristic, complemented
87#5727—34no—
88#5726—34no—
89#5725—32no—
90#5724—32no—
91#5724—32no—
92D3×C4⋊Q8—32no—
93#5507—38no—
94#5477—31no—
95C4×#235—31no—
96C2×C32×Q8—24no—
97C2×C32×Q8C2312yes—
98C2×C32×Q8C2312yes—
99C22×C32×C4C2312yes—
100C22×C32×C4C2311yescharacteristic
101C2×#638C2312yes—
102#3828—24no—
103C2×C4⋊(C3⋊D3)C2311yescharacteristic
104C2×C4×C3⋊D3C2312yes—
105C2×#634C2311yescharacteristic
106C2×C3×#67C2312yes—
107C2×C3×#67C2312yes—
108C22×C3×Dic3C2312yes—
109C22×C3×Dic3C2312yes—
110C3×#239—28no—
111C3×#239—28no—
112C3×D3×Q8—28no—
113C3×D3×Q8—28no—
114C3×#235—24no—
115C3×#235—216no—
116C3×#235D418yescomplemented
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2314yes—
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3C2314yes—
121C2×C3×C4×D3C2314yes—
122C2×C3×C4×D3C2312yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×Dic6—24no—
125C2×C3×Dic6C2312yes—
126C2×C3×Dic6C2312yes—
127C2×C3×Dic6C2314yes—
128C2×C3×Dic6C2311yescharacteristic
129C2×C3×Dic6C2311yescharacteristic
130C2×#627C2314yes—
131C2×#626C2314yes—
132C2×#626C2314yes—
133C2×#624C2314yes—
134#3804—216no—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137#3799—28no—
138#3797—28no—
139#3796—28no—
140D3×Dic6—28no—
141#3757C2312yes—
142#3752C2318yes—
143C4⋊(C3⋊Dic3)C2312yes—
144#3750C2318yes—
145C4×C3⋊Dic3C2312yes—
146C3×Dic3⋊C4C2318yes—
147C3×Dic3⋊C4C2318yes—
148C3×C4×Dic3C2312yes—
149C3×C4×Dic3C2311yescharacteristic
150C3×C4×Dic3C2311yescharacteristic
151#3724C2318yes—
152Dic3⋊Dic3C2314yes—
153Dic3⋊Dic3C2314yes—
154#3722C2314yes—
155(C2×D3)⋊Dic3C2314yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2318yes—
158Dic32C2314yes—
159#3499—91noSylow
160C3×2−1+4—68no—
161C2×C3×#41—32no—
162C2×C3×#41—32no—
163C2×C3×#41—31no—
164C2×C3×#41—34no—
165C2×C3×#41—31no—
166C22×C3×Q8—21no—
167C22×C3×Q8—32no—
168C22×C3×Q8—32no—
169C22×C3×Q8—31no—
170C22×C3×Q8C2×D311yescharacteristic
171C22×C3×Q8C2×D311yescharacteristic
172#1010—68no—
173#1007—28no—
174#1007—68no—
175C2×#239—32no—
176C2×#239—32no—
177C2×#239C2×D312yes—
178C2×#239C2×D312yes—
179C2×D3×Q8—32no—
180C2×D3×Q8—32no—
181C2×D3×Q8—32no—
182C2×D3×Q8C2×D312yes—
183C2×D3×Q8C2×D312yes—
184C2×#237—34no—
185C2×#237—32no—
186C2×#235—31no—
187C2×#235—31no—
188C2×#235—34no—
189C2×#235—32no—
190C2×#235—61no—
191C2×#235C2×D311yescharacteristic
192C2×#235C2×D314yes—
193C2×#235C2×D311yescharacteristic
194C22×Dic6—32no—
195C22×Dic6C2×D311yescharacteristic
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8—34no—
199C2×C3×C4⋊C4—34no—
200C2×C3×C42—31no—
201#947—32no—
202#947—32no—
203#947—32no—
204#947—31no—
205#947—62no—
206#946—34no—
207#946—34no—
208#946—34no—
209#946—38no—
210#946—64no—
211Q8×Dic3—32no—
212#944—32no—
213#944—32no—
214#944—32no—
215#944—32no—
216#944—38no—
217#944—31no—
218#944—62no—
219#944C2×D312yes—
220#944C2×D314yes—
221#944C2×D312yes—
222#940—31no—
223#939—34no—
224#939—38no—
225#936—32no—
226#936—31no—
227#935—34no—
228#935—38no—
229D4×Dic3—34no—
230D4×Dic3—32no—
231#930—34no—
232#929—34no—
233#929—34no—
234#929—34no—
235#929—38no—
236#929—64no—
237C4×#67—34no—
238C4×#67—38no—
239C4×#67—34no—
240#926—31no—
241#926—31no—
242#926—32no—
243#926—61no—
244#924—34no—
245#924—38no—
246C2×Dic3⋊C4—38no—
247C2×Dic3⋊C4C2×D314yes—
248C2×C4×Dic3—32no—
249C2×C4×Dic3C2×D311yescharacteristic
250#896—38no—
251#896—38no—
252#895—38no—
253#894—38no—
254#894—38no—
255#893—38no—
256D3×C4⋊C4—38no—
257#888—38no—
258#875—31no—
259#875—31no—
260#874—31no—
261C4×D12—32no—
262C4×D12—34no—
263#872—32no—
264C42×D3—32no—
265#869—31no—
266C4×Dic6—32no—
267C23×C32C2411yescharacteristic
268C22×C3⋊D3C2412yes—
269C22×C3×D3C2412yes—
270C22×C3×D3C2412yes—
271C32×Q8—24no—
272C32×Q8—24no—
273C2×C32×C4—24no—
274C2×C32×C4C2×D414yes—
275C2×C32×C4C2414yes—
276C2×C32×C4C2411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278#638—24no—
279C2×C3⋊Dic3C2414yes—
280C2×C3⋊Dic3C2412yes—
281C4⋊(C3⋊D3)—22no—
282C4×C3⋊D3—24no—
283#634—22no—
284C3×#67—24no—
285C3×#67C2×D418yes—
286C2×C3×Dic3—24no—
287C2×C3×Dic3—24no—
288C2×C3×Dic3C2412yes—
289C2×C3×Dic3C2414yes—
290C2×C3×Dic3C2412yes—
291C2×C3×Dic3C2412yes—
292C2×C3×Dic3C2412yes—
293C3×D12—28no—
294C3×D12—22no—
295C3×D12C2×D414yes—
296C3×C4×D3—28no—
297C3×C4×D3—24no—
298C3×C4×D3—28no—
299C3×C4×D3C2×D418yes—
300C3×Dic6—24no—
301C3×Dic6—24no—
302C3×Dic6—22no—
303C3×Dic6—28no—
304C3×Dic6C2×D414yes—
305#627—28no—
306#626—28no—
307#626—28no—
308#624—28no—
309D3×Dic3—28no—
310D3×Dic3—28no—
311C2×2−1+4—31no—
312C2×2−1+4—91no—
313D4×Q8—94no—
314#547—98no—
315#547—94no—
316#536—92no—
317#536—92no—
318#536—91no—
319#536—91no—
320#532—91no—
321#532—92no—
322C2×C4⋊Q8—31no—
323C2×C4⋊Q8—92no—
324C4×#41—91no—
325C3×#41—38no—
326C3×#41—616no—
327C3×#41—68no—
328C3×#41—68no—
329C3×#41—64no—
330C2×C3×Q8—24no—
331C2×C3×Q8—24no—
332C2×C3×Q8—22no—
333C2×C3×Q8—22no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×Q8—34no—
337C2×C3×Q8—32no—
338C2×C3×Q8—32no—
339C2×C3×Q8—44no—
340C2×C3×Q8—68no—
341C2×C3×Q8—68no—
342C2×C3×Q8—64no—
343C2×C3×Q8C22×D312yes—
344C2×C3×Q8C22×D312yes—
345C2×C3×Q8C22×D312yes—
346C2×C3×Q8C22×D312yes—
347C2×C3×D4—32no—
348C2×C3×D4—32no—
349C2×C3×D4—31no—
350C2×C3×D4—34no—
351C2×C3×D4—31no—
352C22×C3×C4—21no—
353C22×C3×C4—22no—
354C22×C3×C4—32no—
355C22×C3×C4—32no—
356C22×C3×C4—32no—
357C22×C3×C4—34no—
358C22×C3×C4—34no—
359C22×C3×C4—32no—
360C22×C3×C4C22×D312yes—
361C22×C3×C4C22×D312yes—
362C22×C3×C4C22×D311yescharacteristic
363C22×C3×C4C22×D311yescharacteristic
364C2×#67—32no—
365C2×#67—32no—
366C2×#67—34no—
367C2×#67—34no—
368C2×#67—62no—
369C2×#67C22×D312yes—
370C2×#67C22×D312yes—
371C22×Dic3—34no—
372C22×Dic3—34no—
373C22×Dic3C22×D312yes—
374C22×Dic3C22×D312yes—
375#239—28no—
376#239—28no—
377#239—68no—
378#239—68no—
379D3×Q8—28no—
380D3×Q8—28no—
381D3×Q8—68no—
382D3×Q8—68no—
383D3×Q8—68no—
384#237—68no—
385#237—616no—
386#235—24no—
387#235—216no—
388#235—68no—
389#235—64no—
390#235—64no—
391#235—616no—
392#235—124no—
393#235#6718yescomplemented
394C2×D12—34no—
395C2×D12—34no—
396C2×D12—31no—
397C2×D12—31no—
398C2×D12—61no—
399C2×D12C22×D311yescharacteristic
400C2×D12C22×D314yes—
401C2×D12C22×D311yescharacteristic
402C2×C4×D3—34no—
403C2×C4×D3—34no—
404C2×C4×D3—32no—
405C2×C4×D3—32no—
406C2×C4×D3—34no—
407C2×C4×D3—34no—
408C2×C4×D3—62no—
409C2×C4×D3C22×D312yes—
410C2×C4×D3C22×D314yes—
411C2×C4×D3C22×D314yes—
412C2×C4×D3C22×D312yes—
413C2×Dic6—24no—
414C2×Dic6—31no—
415C2×Dic6—31no—
416C2×Dic6—34no—
417C2×Dic6—34no—
418C2×Dic6—61no—
419C2×Dic6—68no—
420C2×Dic6C22×D311yescharacteristic
421C2×Dic6C22×D314yes—
422C2×Dic6C22×D312yes—
423C2×Dic6C22×D312yes—
424C2×Dic6C22×D311yescharacteristic
425C3×C4⋊C4—38no—
426C3×C4⋊C4—38no—
427C3×C42—32no—
428C3×C42—31no—
429C3×C42—31no—
430#217—32no—
431#217—32no—
432#217—38no—
433#217—34no—
434#217—34no—
435#217—62no—
436(C2×D3)⋊C4—34no—
437(C2×D3)⋊C4—34no—
438(C2×D3)⋊C4—38no—
439(C2×D3)⋊C4—38no—
440(C2×D3)⋊C4—38no—
441(C2×D3)⋊C4—34no—
442(C2×D3)⋊C4—34no—
443(C2×D3)⋊C4—68no—
444C4⋊Dic3—32no—
445C4⋊Dic3—32no—
446C4⋊Dic3—34no—
447C4⋊Dic3—34no—
448C4⋊Dic3—62no—
449Dic3⋊C4—38no—
450Dic3⋊C4—38no—
451Dic3⋊C4—34no—
452Dic3⋊C4—38no—
453Dic3⋊C4—34no—
454Dic3⋊C4—38no—
455Dic3⋊C4—68no—
456Dic3⋊C4C22×D318yes—
457Dic3⋊C4C22×D318yes—
458C4×Dic3—32no—
459C4×Dic3—32no—
460C4×Dic3—34no—
461C4×Dic3—34no—
462C4×Dic3—62no—
463C4×Dic3C22×D311yescharacteristic
464C4×Dic3C22×D311yescharacteristic
465C4×Dic3C22×D312yes—
466C22×C32—22no—
467C22×C32C22×D412yes—
468C22×C32C2511yescharacteristic
469C2×C3⋊D3—22no—
470C2×C3⋊D3—24no—
471C2×C3×D3—24no—
472C2×C3×D3—22no—
473C2×C3×D3—24no—
474C2×C3×D3C22×D414yes—
475C32×C4—24no—
476C32×C4C22×D412yes—
477C32×C4C22×D412yes—
478C3⋊Dic3—22no—
479C3⋊Dic3—24no—
480C3×Dic3—24no—
481C3×Dic3—22no—
482C3×Dic3—22no—
483C3×Dic3C22×D414yes—
484C3×Dic32−1+414yescomplemented
4852−1+4—68no—
4862−1+4—188no—
487C2×#41—32no—
488C2×#41—32no—
489C2×#41—31no—
490C2×#41—31no—
491C2×#41—34no—
492C2×#41—94no—
493C2×#41—92no—
494C2×#41—92no—
495C2×#41—91no—
496C22×Q8—32no—
497C22×Q8—32no—
498C22×Q8—31no—
499C22×Q8—92no—
500C22×Q8—92no—
501C22×Q8D3211yescharacteristic
502C4⋊Q8—32no—
503C4⋊Q8—32no—
504C4⋊Q8—34no—
505C4⋊Q8—91no—
506C4⋊Q8—98no—
507C4⋊Q8—92no—
508C4⋊Q8—92no—
509#127—91no—
510#124—91no—
511#124—91no—
512#124—92no—
513#124—92no—
514#123—98no—
515#123—98no—
516#123—94no—
517#123—94no—
518C22⋊Q8—98no—
519C22⋊Q8—98no—
520C22⋊Q8—94no—
521C22⋊Q8—94no—
522#121—98no—
523#121—94no—
524C4×Q8—92no—
525C4×D4—94no—
526C4×D4—92no—
527C4×D4—98no—
528C4×D4—94no—
529#117—92no—
530#117—91no—
531C2×C4⋊C4—34no—
532C2×C4⋊C4—98no—
533C2×C42—31no—
534C2×C42—92no—
535C23×C3—21no—
536C23×C3—32no—
537C23×C3—32no—
538C23×C3C23×D311yescharacteristic
539C23×C3C23×D311yescharacteristic
540C22×D3—32no—
541C22×D3—32no—
542C22×D3—62no—
543C22×D3C23×D312yes—
544C22×D3C23×D312yes—
545C3×Q8—24no—
546C3×Q8—24no—
547C3×Q8—24no—
548C3×Q8—24no—
549C3×Q8—34no—
550C3×Q8—44no—
551C3×Q8—44no—
552C3×Q8—68no—
553C3×Q8—62no—
554C3×Q8—64no—
555C3×Q8—64no—
556C3×D4—38no—
557C3×D4—34no—
558C3×D4—68no—
559C3×D4—64no—
560C3×D4—62no—
561C2×C3×C4—24no—
562C2×C3×C4—24no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—24no—
566C2×C3×C4—24no—
567C2×C3×C4—32no—
568C2×C3×C4—32no—
569C2×C3×C4—38no—
570C2×C3×C4—32no—
571C2×C3×C4—32no—
572C2×C3×C4—34no—
573C2×C3×C4—44no—
574C2×C3×C4—68no—
575C2×C3×C4—68no—
576C2×C3×C4—64no—
577C2×C3×C4—64no—
578C2×C3×C4—64no—
579C2×C3×C4D3×D414yes—
580C2×C3×C4C2×#6714yes—
581C2×C3×C4C23×D314yes—
582C2×C3×C4C23×D314yes—
583C2×C3×C4C23×D311yescharacteristic
584C2×C3×C4C23×D311yescharacteristic
585C2×C3×C4C23×D311yescharacteristic
586C2×C3×C4C23×D311yescharacteristic
587#67—24no—
588#67—68no—
589#67—64no—
590#67—64no—
591#67—68no—
592#67—124no—
593#67C2×#6718yes—
594C2×Dic3—24no—
595C2×Dic3—24no—
596C2×Dic3—34no—
597C2×Dic3—34no—
598C2×Dic3—32no—
599C2×Dic3—32no—
600C2×Dic3—64no—
601C2×Dic3—62no—
602C2×Dic3—68no—
603C2×Dic3—68no—
604C2×Dic3C23×D312yes—
605C2×Dic3C23×D312yes—
606C2×Dic3C23×D314yes—
607C2×Dic3C23×D312yes—
608C2×Dic3C23×D312yes—
609D12—28no—
610D12—22no—
611D12—68no—
612D12—68no—
613D12—62no—
614D12—62no—
615D12—122no—
616D12C2×#6714yes—
617C4×D3—28no—
618C4×D3—24no—
619C4×D3—28no—
620C4×D3—68no—
621C4×D3—68no—
622C4×D3—68no—
623C4×D3—64no—
624C4×D3—64no—
625C4×D3—68no—
626C4×D3—124no—
627C4×D3C2×#6718yes—
628Dic6—24no—
629Dic6—24no—
630Dic6—22no—
631Dic6—28no—
632Dic6—68no—
633Dic6—62no—
634Dic6—62no—
635Dic6—68no—
636Dic6—122no—
637Dic6C2×#6714yes—
638C2×C32—22no—
639C2×C32C23×D411yescharacteristic
640C2×C32C2×2−1+412yes—
641C3⋊D3—42no—
642C3×D3—24no—
643C3×D3—42no—
644#41—38no—
645#41—616no—
646#41—68no—
647#41—68no—
648#41—64no—
649#41—188no—
650#41—1816no—
651#41—188no—
652#41—184no—
653C2×Q8—24no—
654C2×Q8—31no—
655C2×Q8—32no—
656C2×Q8—34no—
657C2×Q8—32no—
658C2×Q8—31no—
659C2×Q8—68no—
660C2×Q8—68no—
661C2×Q8—64no—
662C2×Q8—94no—
663C2×Q8—91no—
664C2×Q8—188no—
665C2×Q8—188no—
666C2×Q8C2×D3212yes—
667C2×Q8C2×D3212yes—
668C2×D4—32no—
669C2×D4—32no—
670C2×D4—31no—
671C2×D4—34no—
672C2×D4—31no—
673C2×D4—94no—
674C2×D4—94no—
675C2×D4—92no—
676C2×D4—91no—
677C22×C4—32no—
678C22×C4—32no—
679C22×C4—32no—
680C22×C4—34no—
681C22×C4—34no—
682C22×C4—32no—
683C22×C4—94no—
684C22×C4—94no—
685C22×C4—94no—
686C22×C4—92no—
687C22×C4C2×D3212yes—
688C22×C4C2×D3211yescharacteristic
689C4⋊C4—38no—
690C4⋊C4—38no—
691C4⋊C4—94no—
692C4⋊C4—98no—
693C4⋊C4—94no—
694C4⋊C4—98no—
695C4⋊C4—92no—
696C22⋊C4—94no—
697C22⋊C4—94no—
698C22⋊C4—94no—
699C22⋊C4—98no—
700C22⋊C4—92no—
701C22⋊C4—98no—
702C42—31no—
703C42—31no—
704C42—32no—
705C42—94no—
706C42—92no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—22no—
710C22×C3—21no—
711C22×C3—34no—
712C22×C3—42no—
713C22×C3—64no—
714C22×C3—62no—
715C22×C3—64no—
716C22×C3C2×D3×D412yes—
717C22×C3C22×#6712yes—
718C22×C3C24×D311yescharacteristic
719C22×C3C24×D311yescharacteristic
720C2×D3—24no—
721C2×D3—24no—
722C2×D3—22no—
723C2×D3—62no—
724C2×D3—64no—
725C2×D3—64no—
726C2×D3—62no—
727C2×D3—122no—
728C2×D3—124no—
729C2×D3C22×#6714yes—
730C3×C4—24no—
731C3×C4—24no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—34no—
735C3×C4—34no—
736C3×C4—44no—
737C3×C4—62no—
738C3×C4—62no—
739C3×C4—64no—
740C3×C4C2×D3×D412yes—
741C3×C4C2×D3×D412yes—
742C3×C4C22×#6712yes—
743C3×C4C22×#6712yes—
744Dic3—24no—
745Dic3—22no—
746Dic3—22no—
747Dic3—62no—
748Dic3—64no—
749Dic3—64no—
750Dic3—62no—
751Dic3—122no—
752Dic3—124no—
753Dic3#100714yescomplemented
754Dic3C22×#6714yes—
755C32#349911yescharacteristic, complemented, Sylow
756C23—32no—
757C23—32no—
758C23—92no—
759C23C22×D3211yescharacteristic
760Q8—24no—
761Q8—24no—
762Q8—34no—
763Q8—68no—
764Q8—62no—
765Q8—64no—
766Q8—64no—
767Q8—188no—
768Q8—182no—
769D4—38no—
770D4—34no—
771D4—68no—
772D4—64no—
773D4—62no—
774D4—188no—
775D4—188no—
776D4—184no—
777D4—182no—
778C2×C4—24no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—38no—
782C2×C4—32no—
783C2×C4—34no—
784C2×C4—32no—
785C2×C4—68no—
786C2×C4—68no—
787C2×C4—64no—
788C2×C4—64no—
789C2×C4—64no—
790C2×C4—94no—
791C2×C4—92no—
792C2×C4—188no—
793C2×C4—188no—
794C2×C4—188no—
795C2×C4—184no—
796C2×C4D3×#6714yes—
797C2×C4C22×D3214yes—
798C2×C4C22×D3211yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C2×C3—22no—
801C2×C3—22no—
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—42no—
805C2×C3—64no—
806C2×C3—122no—
807C2×C3C22×D3×D411yescharacteristic
808C2×C3C2×#100712yes—
809C2×C3D3×2−1+412yes—
810C2×C3C23×#6711yescharacteristic
811D3—24no—
812D3—42no—
813D3—122no—
814D3—122no—
815D3—242no—
816C22—22no—
817C22—34no—
818C22—64no—
819C22—64no—
820C22—62no—
821C22—184no—
822C22—182no—
823C22C2×D3×#6712yes—
824C22C23×D3211yescharacteristic
825C4—24no—
826C4—34no—
827C4—34no—
828C4—62no—
829C4—62no—
830C4—64no—
831C4—184no—
832C4—182no—
833C4C2×D3×#6712yes—
834C4C2×D3×#6712yes—
835C3—21no—
836C3#8621411yescharacteristic, complemented
837C3#8729211yescharacteristic, complemented
838C2—22no—
839C2—64no—
840C2—122no—
841C2—362no—
842C2D3×#100712yes—
843C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC22×C32×Q8C22
hypercenterC22×Q8D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C2×#64297C2semidirect
3. #10596287C2semidirect
4. C2×C3×#944C2semidirect
5. #10595403C2semidirect
6. #10595360C2semidirect
7. #10595358C2semidirect
8. #10595356C2semidirect
9. D3×#944C2semidirect
10. #10595340C2semidirect
11. #10595029C2semidirect
12. Dic3×#235C2semidirect
13. #10594885C2semidirect
14. #10594855C2semidirect
70. C2×#1007D3semidirect
86. C2×#944D3semidirect
116. C3×#235D4semidirect
393. #235#67semidirect
484. C3×Dic32−1+4semidirect
753. Dic3#1007semidirect
755. C32#3499semidirect
836. C3#86214semidirect
837. C3#87292semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C2×#642972
#105962872
C2×C3×#9442
#105954032
#105953602
#105953582
#105953562
D3×#9442
#105953402
#105950292
Dic3×#2352
#105948852
#105948552
#872923
#862143