Finite Group Databasebeta

← #11906035

Subgroups — #11906035

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×#1010C211yesmaximal, characteristic, complemented
2C2×#64298C211yesmaximal, characteristic, complemented
3#10596296C211yesmaximal, characteristic, complemented
4C3×#5832C211yesmaximal, characteristic, complemented
5#10595399C212yesmaximal, complemented
6D3×#944C212yesmaximal, complemented
7#10595152C212yesmaximal, complemented
8#10595151C218yesmaximal, complemented
9#10595147C212yesmaximal, complemented
10Dic3×#235C211yesmaximal, characteristic, complemented
11Dic6×#67C214yesmaximal, complemented
12#10594887C214yesmaximal, complemented
13C2×#63866C211yesmaximal, characteristic, complemented
14#10594855C211yesmaximal, characteristic, complemented
15#87292—31nomaximal
16#86243—31nomaximal
17C2×C32×#41C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C3×#1010—28no—
20C2×C3×D3×Q8C2212yes—
21C2×C3×#237C2212yes—
22C2×C3×#237C2214yes—
23C2×C3×#235C2211yescharacteristic
24C2×C3×#235C2212yes—
25C2×C3×#235C2211yescharacteristic
26C22×C3×Dic6C2211yescharacteristic
27C22×C3×Dic6C2212yes—
28C2×#3805C2214yes—
29#64298—28no—
30C2×#3795C2212yes—
31C2×#3795C2212yes—
32C2×D3×Dic6C2212yes—
33C2×D3×Dic6C2212yes—
34#64153C2212yes—
35#64145C2212yes—
36#64144C2214yes—
37#64135C2211yescharacteristic
38#64133C2214yes—
39C3×#947C2211yescharacteristic
40C3×#944C2211yescharacteristic
41C3×#940C2211yescharacteristic
42C3×#939C2214yes—
43C3×#936C2211yescharacteristic
44C3×C4×#67C2214yes—
45C2×C3×C4×Dic3C2211yescharacteristic
46Dic3×#67C2214yes—
47Dic3×#67C2218yes—
48#63970C2218yes—
49#63969C2218yes—
50C2×Dic3⋊Dic3C2214yes—
51#63964C2218yes—
52#63961C2214yes—
53#63905C2218yes—
54Dic3×D12C2212yes—
55#63887C2218yes—
56D3×Dic3⋊C4C2218yes—
57C4×D3×Dic3C2212yes—
58#63873C2212yes—
59#63866C2212yes—
60#63866C2214yes—
61#63866C2212yes—
62#63863C2212yes—
63#63856C2214yes—
64#63855C2212yes—
65Dic3×Dic6C2212yes—
66#63839C2218yes—
67C2×C3×2−1+4—31no—
68C2×#1010—31no—
69C2×#1010—31no—
70C2×#1010D311yescharacteristic, complemented
71C3×#532—31no—
72#5832—32no—
73#5832D311yescharacteristic, complemented
74Dic3×#41—31no—
75#5825—31no—
76#5825—31no—
77#5825—31no—
78#5825—32no—
79#5825—61no—
80#5824—38no—
81#5824—34no—
82#5816—31no—
83#5816—32no—
84Q8×#67—34no—
85C2×#944—32no—
86C2×#944—31no—
87D3×C4⋊Q8—32no—
88#5716—32no—
89#5675—32no—
90#5675—32no—
91#5611—38no—
92#5551—34no—
93D4×Dic6—34no—
94C4×#235—31no—
95C2×#869—31no—
96C32×#41—24no—
97C2×C32×Q8C2311yescharacteristic
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2312yes—
100C22×C32×C4C2312yes—
101C22×C32×C4C2311yescharacteristic
102C22×C3⋊Dic3C2312yes—
103C2×#634—24no—
104C2×#634C2312yes—
105C2×#634C2312yes—
106C2×C3×#67C2314yes—
107C2×C3×#67C2312yes—
108C2×C3×#67C2314yes—
109C2×C3×#67C2312yes—
110C22×C3×Dic3C2312yes—
111C22×C3×Dic3C2312yes—
112C22×C3×Dic3C2314yes—
113C3×D3×Q8—28no—
114C3×#237—216no—
115C3×#237—28no—
116C3×#235—24no—
117C3×#235—28no—
118C3×#235D418yescomplemented
119C2×C3×D12C2311yescharacteristic
120C2×C3×D12C2311yescharacteristic
121C2×C3×C4×D3C2312yes—
122C2×C3×C4×D3C2314yes—
123C2×C3×C4×D3C2312yes—
124C2×C3×Dic6—24no—
125C2×C3×Dic6—28no—
126C2×C3×Dic6C2311yescharacteristic
127C2×C3×Dic6C2312yes—
128C2×C3×Dic6C2314yes—
129C2×C3×Dic6C2312yes—
130C2×C3×Dic6C2311yescharacteristic
131C2×#627C2314yes—
132C2×#625C2314yes—
133#3805—216no—
134C2×D3×Dic3C2314yes—
135C2×D3×Dic3C2314yes—
136C2×D3×Dic3C2314yes—
137#3795—28no—
138#3795—28no—
139D3×Dic6—28no—
140D3×Dic6—28no—
141#3757C2318yes—
142#3757C2312yes—
143C4⋊(C3⋊Dic3)C2312yes—
144#3750C2318yes—
145C4×C3⋊Dic3C2312yes—
146C3×#217C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×Dic3⋊C4C2314yes—
149C3×C4×Dic3C2312yes—
150C3×C4×Dic3C2311yescharacteristic
151C3×C4×Dic3C2311yescharacteristic
152#3724C2318yes—
153Dic3⋊Dic3C2318yes—
154Dic3⋊Dic3C2314yes—
155Dic3⋊Dic3C2318yes—
156(C2×D3)⋊Dic3C2314yes—
157(C2×D3)⋊Dic3C2318yes—
158Dic32C2314yes—
159#3499—91noSylow
160C3×2−1+4—68no—
161C2×C3×#41—21no—
162C2×C3×#41—34no—
163C2×C3×#41—32no—
164C2×C3×#41—31no—
165C2×C3×#41—31no—
166C2×C3×#41—32no—
167C2×C3×#41C2×D311yescharacteristic
168C2×C3×#41C2×D311yescharacteristic
169C22×C3×Q8—32no—
170C22×C3×Q8—31no—
171C22×C3×Q8—32no—
172#1010—28no—
173#1010—68no—
174#1010—68no—
175C2×D3×Q8—32no—
176C2×D3×Q8—32no—
177C2×D3×Q8C2×D312yes—
178C2×#237—34no—
179C2×#237—34no—
180C2×#237—32no—
181C2×#237—32no—
182C2×#237C2×D312yes—
183C2×#237C2×D314yes—
184C2×#235—32no—
185C2×#235—32no—
186C2×#235C2×D311yescharacteristic
187C2×#235C2×D312yes—
188C2×#235C2×D311yescharacteristic
189C22×Dic6—31no—
190C22×Dic6—31no—
191C22×Dic6—32no—
192C22×Dic6—32no—
193C22×Dic6—61no—
194C22×Dic6C2×D311yescharacteristic
195C22×Dic6C2×D312yes—
196C3×C4⋊Q8—31no—
197C3×#127—31no—
198C3×#124—31no—
199C3×#124—31no—
200C3×#121—34no—
201C3×C4×D4—34no—
202C2×C3×C42—31no—
203#947—32no—
204#947C2×D311yescharacteristic
205#946—34no—
206#946—38no—
207Q8×Dic3—32no—
208#944—32no—
209#944—32no—
210#944—32no—
211#944—32no—
212#944—38no—
213#944—32no—
214#944—34no—
215#944—32no—
216#944—62no—
217#944C2×D311yescharacteristic
218#940C2×D311yescharacteristic
219#939—38no—
220#939C2×D314yes—
221#938—38no—
222#936—32no—
223#936—32no—
224#936—32no—
225#936—62no—
226#936C2×D311yescharacteristic
227#935—34no—
228#935—34no—
229#935—34no—
230#935—38no—
231#935—64no—
232D4×Dic3—38no—
233D4×Dic3—34no—
234D4×Dic3—32no—
235#929—34no—
236#929—38no—
237C4×#67—34no—
238C4×#67—38no—
239C4×#67C2×D314yes—
240#926—31no—
241#926—31no—
242#926—32no—
243#926—61no—
244C2×C4⋊Dic3—34no—
245#924—34no—
246#924—34no—
247#924—34no—
248#924—38no—
249#924—64no—
250C2×Dic3⋊C4—34no—
251C2×Dic3⋊C4—38no—
252C2×C4×Dic3—32no—
253C2×C4×Dic3C2×D311yescharacteristic
254D3×C4⋊C4—38no—
255#888—38no—
256#883—38no—
257#883—38no—
258#878—38no—
259#878—38no—
260C4×D12—32no—
261#872—32no—
262C42×D3—32no—
263#869—32no—
264#869—32no—
265#869—34no—
266C4×Dic6—32no—
267C23×C32C2412yes—
268C23×C32C2411yescharacteristic
269C22×C3×D3C2412yes—
270C22×C3×D3C2412yes—
271C32×Q8—22no—
272C32×D4—24no—
273C32×D4—22no—
274C2×C32×C4—24no—
275C2×C32×C4C2×D414yes—
276C2×C32×C4C2412yes—
277C2×C32×C4C2411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279C2×C3⋊Dic3—24no—
280C2×C3⋊Dic3C2414yes—
281C2×C3⋊Dic3C2414yes—
282#634—24no—
283#634—24no—
284C3×#67—24no—
285C3×#67—28no—
286C3×#67—28no—
287C3×#67C2×D418yes—
288C2×C3×Dic3—24no—
289C2×C3×Dic3—28no—
290C2×C3×Dic3—24no—
291C2×C3×Dic3C2412yes—
292C2×C3×Dic3C2414yes—
293C2×C3×Dic3C2412yes—
294C2×C3×Dic3C2412yes—
295C2×C3×Dic3C2412yes—
296C3×D12—22no—
297C3×D12C2×D414yes—
298C3×C4×D3—28no—
299C3×C4×D3—24no—
300C3×C4×D3C2×D418yes—
301C3×Dic6—22no—
302C3×Dic6—24no—
303C3×Dic6—24no—
304C3×Dic6—28no—
305C3×Dic6C2×D414yes—
306#627—28no—
307#625—28no—
308D3×Dic3—28no—
309D3×Dic3—28no—
310D3×Dic3—28no—
311C2×2−1+4—31no—
312C2×2−1+4—91no—
313D4×Q8—94no—
314#547—94no—
315#547—98no—
316#536—92no—
317#536—92no—
318#536—91no—
319#536—91no—
320#532—31no—
321#532—92no—
322C2×C4⋊Q8—91no—
323C2×C4⋊Q8—92no—
324C4×#41—91no—
325C3×#41—24no—
326C3×#41—24no—
327C3×#41—38no—
328C3×#41—44no—
329C3×#41—68no—
330C3×#41—68no—
331C3×#41—616no—
332C3×#41—64no—
333C2×C3×Q8—21no—
334C2×C3×Q8—31no—
335C2×C3×Q8—32no—
336C2×C3×Q8—34no—
337C2×C3×Q8—32no—
338C2×C3×Q8—31no—
339C2×C3×Q8—68no—
340C2×C3×Q8—68no—
341C2×C3×Q8—64no—
342C2×C3×Q8C22×D311yescharacteristic
343C2×C3×Q8C22×D311yescharacteristic
344C2×C3×D4—22no—
345C2×C3×D4—21no—
346C2×C3×D4—32no—
347C2×C3×D4—34no—
348C2×C3×D4—34no—
349C2×C3×D4—32no—
350C2×C3×D4—31no—
351C2×C3×D4—31no—
352C2×C3×D4C22×D312yes—
353C2×C3×D4C22×D312yes—
354C2×C3×D4C22×D311yescharacteristic
355C2×C3×D4C22×D311yescharacteristic
356C22×C3×C4—21no—
357C22×C3×C4—22no—
358C22×C3×C4—32no—
359C22×C3×C4—32no—
360C22×C3×C4—34no—
361C22×C3×C4—32no—
362C22×C3×C4—34no—
363C22×C3×C4—32no—
364C22×C3×C4C22×D312yes—
365C22×C3×C4C22×D312yes—
366C22×C3×C4C22×D311yescharacteristic
367C22×C3×C4C22×D311yescharacteristic
368C2×#67—34no—
369C2×#67—34no—
370C2×#67C22×D314yes—
371C2×#67C22×D314yes—
372C2×#67C22×D312yes—
373C2×#67C22×D312yes—
374C22×Dic3—32no—
375C22×Dic3—32no—
376C22×Dic3—34no—
377C22×Dic3—34no—
378C22×Dic3—34no—
379C22×Dic3—62no—
380C22×Dic3C22×D314yes—
381C22×Dic3C22×D312yes—
382C22×Dic3C22×D312yes—
383D3×Q8—28no—
384D3×Q8—68no—
385D3×Q8—68no—
386#237—216no—
387#237—28no—
388#237—68no—
389#237—616no—
390#237—616no—
391#237—68no—
392#235—24no—
393#235—28no—
394#235—68no—
395#235—68no—
396#235#6718yescomplemented
397C2×D12C22×D311yescharacteristic
398C2×D12C22×D311yescharacteristic
399C2×C4×D3—34no—
400C2×C4×D3—34no—
401C2×C4×D3—34no—
402C2×C4×D3C22×D314yes—
403C2×C4×D3C22×D312yes—
404C2×C4×D3C22×D312yes—
405C2×Dic6—24no—
406C2×Dic6—28no—
407C2×Dic6—32no—
408C2×Dic6—32no—
409C2×Dic6—32no—
410C2×Dic6—32no—
411C2×Dic6—34no—
412C2×Dic6—34no—
413C2×Dic6—62no—
414C2×Dic6—62no—
415C2×Dic6—68no—
416C2×Dic6—64no—
417C2×Dic6—64no—
418C2×Dic6—68no—
419C2×Dic6—124no—
420C2×Dic6C22×D312yes—
421C2×Dic6C22×D312yes—
422C2×Dic6C22×D314yes—
423C2×Dic6C22×D311yescharacteristic
424C2×Dic6C22×D311yescharacteristic
425C3×C4⋊C4—34no—
426C3×C22⋊C4—34no—
427C3×C22⋊C4—34no—
428C3×C42—32no—
429C3×C42—31no—
430C3×C42—31no—
431#217—38no—
432#217—38no—
433#217—32no—
434#217—32no—
435#217—38no—
436#217—34no—
437#217—68no—
438#217—62no—
439#217C22×D314yes—
440(C2×D3)⋊C4—34no—
441(C2×D3)⋊C4—38no—
442(C2×D3)⋊C4C22×D314yes—
443C4⋊Dic3—32no—
444C4⋊Dic3—32no—
445C4⋊Dic3—38no—
446C4⋊Dic3—38no—
447C4⋊Dic3—34no—
448C4⋊Dic3—62no—
449Dic3⋊C4—38no—
450Dic3⋊C4—38no—
451Dic3⋊C4—34no—
452Dic3⋊C4—38no—
453Dic3⋊C4—38no—
454Dic3⋊C4—38no—
455Dic3⋊C4—38no—
456Dic3⋊C4—68no—
457Dic3⋊C4C22×D314yes—
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×C32—22no—
468C22×C32—24no—
469C22×C32C22×D412yes—
470C22×C32C2511yescharacteristic
471C2×C3×D3—24no—
472C2×C3×D3—22no—
473C2×C3×D3—24no—
474C2×C3×D3C22×D414yes—
475C32×C4—22no—
476C32×C4C22×D412yes—
477C32×C4C22×D412yes—
478C3⋊Dic3—24no—
479C3⋊Dic3—24no—
480C3×Dic3—22no—
481C3×Dic3—24no—
482C3×Dic3—22no—
483C3×Dic3C22×D414yes—
484C3×Dic32−1+414yescomplemented
4852−1+4—68no—
4862−1+4—188no—
487C2×#41—32no—
488C2×#41—34no—
489C2×#41—31no—
490C2×#41—31no—
491C2×#41—32no—
492C2×#41—92no—
493C2×#41—92no—
494C2×#41—94no—
495C2×#41D3211yescharacteristic
496C22×Q8—32no—
497C22×Q8—31no—
498C22×Q8—32no—
499C22×Q8—92no—
500C22×Q8—92no—
501C22×Q8—91no—
502C4⋊Q8—31no—
503C4⋊Q8—92no—
504C4⋊Q8—92no—
505C4⋊Q8—94no—
506C4⋊Q8—98no—
507C4⋊Q8—92no—
508C4⋊Q8—92no—
509#127—31no—
510#124—31no—
511#124—31no—
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—34no—
523#121—98no—
524C4×Q8—92no—
525C4×D4—34no—
526C4×D4—92no—
527C4×D4—94no—
528C4×D4—98no—
529#117—92no—
530#117—91no—
531C2×C4⋊C4—98no—
532C2×C4⋊C4—94no—
533C2×C42—31no—
534C2×C42—92no—
535C23×C3—21no—
536C23×C3—22no—
537C23×C3—32no—
538C23×C3—32no—
539C23×C3C23×D312yes—
540C23×C3C23×D312yes—
541C23×C3C23×D311yescharacteristic
542C23×C3C23×D311yescharacteristic
543C22×D3C23×D312yes—
544C22×D3C23×D312yes—
545C3×Q8—22no—
546C3×Q8—22no—
547C3×Q8—34no—
548C3×Q8—42no—
549C3×Q8—68no—
550C3×Q8—64no—
551C3×Q8—64no—
552C3×Q8—62no—
553C3×D4—24no—
554C3×D4—24no—
555C3×D4—22no—
556C3×D4—22no—
557C3×D4—38no—
558C3×D4—34no—
559C3×D4—42no—
560C3×D4—44no—
561C3×D4—68no—
562C3×D4—68no—
563C3×D4—64no—
564C3×D4—62no—
565C2×C3×C4—24no—
566C2×C3×C4—24no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—22no—
570C2×C3×C4—24no—
571C2×C3×C4—32no—
572C2×C3×C4—32no—
573C2×C3×C4—38no—
574C2×C3×C4—34no—
575C2×C3×C4—32no—
576C2×C3×C4—32no—
577C2×C3×C4—44no—
578C2×C3×C4—68no—
579C2×C3×C4—64no—
580C2×C3×C4—68no—
581C2×C3×C4—64no—
582C2×C3×C4—64no—
583C2×C3×C4D3×D414yes—
584C2×C3×C4C2×#6714yes—
585C2×C3×C4C23×D312yes—
586C2×C3×C4C23×D312yes—
587C2×C3×C4C23×D311yescharacteristic
588C2×C3×C4C23×D311yescharacteristic
589C2×C3×C4C23×D311yescharacteristic
590C2×C3×C4C23×D311yescharacteristic
591#67—24no—
592#67—28no—
593#67—28no—
594#67—68no—
595#67—68no—
596#67C2×#6718yes—
597C2×Dic3—24no—
598C2×Dic3—24no—
599C2×Dic3—28no—
600C2×Dic3—34no—
601C2×Dic3—34no—
602C2×Dic3—34no—
603C2×Dic3—34no—
604C2×Dic3—64no—
605C2×Dic3—64no—
606C2×Dic3—68no—
607C2×Dic3—64no—
608C2×Dic3—64no—
609C2×Dic3—68no—
610C2×Dic3—68no—
611C2×Dic3—124no—
612C2×Dic3C23×D312yes—
613C2×Dic3C23×D312yes—
614C2×Dic3C23×D314yes—
615C2×Dic3C23×D312yes—
616C2×Dic3C23×D312yes—
617D12—22no—
618D12C2×#6714yes—
619C4×D3—28no—
620C4×D3—24no—
621C4×D3—68no—
622C4×D3—68no—
623C4×D3—68no—
624C4×D3C2×#6718yes—
625Dic6—22no—
626Dic6—24no—
627Dic6—24no—
628Dic6—28no—
629Dic6—68no—
630Dic6—64no—
631Dic6—64no—
632Dic6—64no—
633Dic6—64no—
634Dic6—68no—
635Dic6—124no—
636Dic6—124no—
637Dic6C2×#6714yes—
638C2×C32—22no—
639C2×C32—42no—
640C2×C32C23×D411yescharacteristic
641C2×C32C2×2−1+412yes—
642C3×D3—24no—
643C3×D3—42no—
644#41—24no—
645#41—38no—
646#41—68no—
647#41—68no—
648#41—616no—
649#41—64no—
650#41—188no—
651#41—188no—
652#41—1816no—
653C2×Q8—31no—
654C2×Q8—34no—
655C2×Q8—32no—
656C2×Q8—31no—
657C2×Q8—32no—
658C2×Q8—68no—
659C2×Q8—68no—
660C2×Q8—64no—
661C2×Q8—94no—
662C2×Q8—92no—
663C2×Q8—92no—
664C2×Q8—188no—
665C2×Q8—188no—
666C2×Q8—184no—
667C2×Q8C2×D3211yescharacteristic
668C2×D4—32no—
669C2×D4—34no—
670C2×D4—32no—
671C2×D4—34no—
672C2×D4—31no—
673C2×D4—31no—
674C2×D4—94no—
675C2×D4C2×D3212yes—
676C2×D4C2×D3211yescharacteristic
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—34no—
690C4⋊C4—98no—
691C4⋊C4—98no—
692C4⋊C4—98no—
693C4⋊C4—94no—
694C4⋊C4—98no—
695C4⋊C4—92no—
696C22⋊C4—34no—
697C22⋊C4—34no—
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—24no—
711C22×C3—24no—
712C22×C3—22no—
713C22×C3—22no—
714C22×C3—21no—
715C22×C3—34no—
716C22×C3—42no—
717C22×C3—42no—
718C22×C3—44no—
719C22×C3—64no—
720C22×C3—64no—
721C22×C3—62no—
722C22×C3C2×D3×D412yes—
723C22×C3C22×#6712yes—
724C22×C3C24×D311yescharacteristic
725C22×C3C24×D311yescharacteristic
726C2×D3—24no—
727C2×D3—22no—
728C2×D3—24no—
729C2×D3C22×#6714yes—
730C3×C4—22no—
731C3×C4—22no—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—34no—
735C3×C4—34no—
736C3×C4—42no—
737C3×C4—64no—
738C3×C4—62no—
739C3×C4—62no—
740C3×C4C2×D3×D412yes—
741C3×C4C2×D3×D412yes—
742C3×C4C22×#6712yes—
743C3×C4C22×#6712yes—
744Dic3—22no—
745Dic3—22no—
746Dic3—24no—
747Dic3—64no—
748Dic3—64no—
749Dic3—64no—
750Dic3—64no—
751Dic3—124no—
752Dic3—124no—
753Dic3#101014yescomplemented
754Dic3C22×#6714yes—
755C32#349911yescharacteristic, complemented, Sylow
756C23—32no—
757C23—32no—
758C23C22×D3212yes—
759C23C22×D3211yescharacteristic
760Q8—22no—
761Q8—34no—
762Q8—68no—
763Q8—64no—
764Q8—64no—
765Q8—62no—
766Q8—188no—
767Q8—184no—
768Q8—184no—
769D4—24no—
770D4—22no—
771D4—38no—
772D4—34no—
773D4—68no—
774D4—68no—
775D4—64no—
776D4—62no—
777D4—188no—
778C2×C4—24no—
779C2×C4—32no—
780C2×C4—32no—
781C2×C4—38no—
782C2×C4—32no—
783C2×C4—32no—
784C2×C4—34no—
785C2×C4—68no—
786C2×C4—68no—
787C2×C4—64no—
788C2×C4—64no—
789C2×C4—64no—
790C2×C4—94no—
791C2×C4—94no—
792C2×C4—188no—
793C2×C4—188no—
794C2×C4—188no—
795C2×C4—184no—
796C2×C4D3×#6714yes—
797C2×C4C22×D3212yes—
798C2×C4C22×D3211yescharacteristic
799C2×C4C22×D3211yescharacteristic
800C2×C3—22no—
801C2×C3—22no—
802C2×C3—22no—
803C2×C3—21no—
804C2×C3—42no—
805C2×C3—42no—
806C2×C3—42no—
807C2×C3—64no—
808C2×C3—82no—
809C2×C3—122no—
810C2×C3C22×D3×D411yescharacteristic
811C2×C3C2×#101012yes—
812C2×C3D3×2−1+412yes—
813C2×C3C23×#6711yescharacteristic
814D3—24no—
815D3—42no—
816C22—22no—
817C22—24no—
818C22—22no—
819C22—34no—
820C22—64no—
821C22—64no—
822C22—62no—
823C22C2×D3×#6712yes—
824C22C23×D3211yescharacteristic
825C4—22no—
826C4—34no—
827C4—34no—
828C4—62no—
829C4—64no—
830C4—62no—
831C4—184no—
832C4—184no—
833C4C2×D3×#6712yes—
834C4C2×D3×#6712yes—
835C3—21no—
836C3#8624311yescharacteristic, complemented
837C3#8729211yescharacteristic, complemented
838C2—22no—
839C2—42no—
840C2—64no—
841C2—122no—
842C2D3×#101012yes—
843C2C22×D3×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×#41C22
hypercenterC2×#41D32
hypocenterC32#3499
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C2×#64298C2semidirect
3. #10596296C2semidirect
4. C3×#5832C2semidirect
5. #10595399C2semidirect
6. D3×#944C2semidirect
7. #10595152C2semidirect
8. #10595151C2semidirect
9. #10595147C2semidirect
10. Dic3×#235C2semidirect
11. Dic6×#67C2semidirect
12. #10594887C2semidirect
13. C2×#63866C2semidirect
14. #10594855C2semidirect
70. C2×#1010D3semidirect
73. #5832D3semidirect
118. C3×#235D4semidirect
396. #235#67semidirect
484. C3×Dic32−1+4semidirect
753. Dic3#1010semidirect
755. C32#3499semidirect
836. C3#86243semidirect
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×#10102
C2×#642982
#105962962
C3×#58322
#105953992
D3×#9442
#105951522
#105951512
#105951472
Dic3×#2352
Dic6×#672
#105948872
C2×#638662
#105948552
#872923
#862433