Finite Group Databasebeta

← #11707293

Subgroups — #11707293

Order 768.

7406 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3501C211yesmaximal, characteristic, complemented
2#86949C218yesmaximal, complemented
3#86948C214yesmaximal, complemented
4#86926C218yesmaximal, complemented
5#86923C214yesmaximal, complemented
6D3×D4×Q8C214yesmaximal, complemented
7#86747C214yesmaximal, complemented
8#86586C214yesmaximal, complemented
9#86574C218yesmaximal, complemented
10#86281C212yesmaximal, complemented
11#86277C212yesmaximal, complemented
12#85986C214yesmaximal, complemented
13C2×#5632C214yesmaximal, complemented
14#85860C212yesmaximal, complemented
15#85857C212yesmaximal
16C2×D4×Dic6C211yesmaximal, characteristic, complemented
17C4×#1004C211yesmaximal, characteristic
18Q8×H(5,𝔽2)—31nomaximal, Sylow
19C22×D3×Q8C2214yescomplemented
20C2×#1004C2211yescharacteristic
21C23×Dic6C2212yescomplemented
22C3×#554C2214yescomplemented
23C3×#554C2218yescomplemented
24C3×D4×Q8C2214yescomplemented
25C3×#544C2212yescomplemented
26C3×#543C2214yescomplemented
27C3×#533C2212yescomplemented
28C2×C3×C22⋊Q8C2214yescomplemented
29C3×#518C2212yes—
30C2×C3×C4×D4C2211yescharacteristic
31Q8×#67C2218yescomplemented
32C2×#944C2214yescomplemented
33#5798C2211yescharacteristic
34C2×D4×Dic3C2212yes—
35C2×C4×#67C2214yes—
36C2×#924C2212yescomplemented
37#5730C2212yescomplemented
38#5729C2218yescomplemented
39#5728C2214yescomplemented
40#5727C2212yescomplemented
41#5727C2218yescomplemented
42D3×C4⋊Q8C2214yescomplemented
43D3×C4⋊Q8C2218yescomplemented
44#5722C2212yescomplemented
45#5722C2218yescomplemented
46#5721C2212yescomplemented
47#5690C2214yescomplemented
48#5690C2218yescomplemented
49#5689C2218yescomplemented
50#5689C2218yescomplemented
51#5688C2218yescomplemented
52#5685C2214yescomplemented
53#5685C2218yescomplemented
54#5636C2218yescomplemented
55#5636C22116yescomplemented
56#5636C22116yescomplemented
57#5636C22116yescomplemented
58#5635C2214yescomplemented
59#5635C2218yescomplemented
60#5635C22116yescomplemented
61#5634C22116yescomplemented
62#5634C2218yescomplemented
63#5632C2214yescomplemented
64#5632C2218yescomplemented
65#5632C22116yescomplemented
66#5632C22116yescomplemented
67#5632C2218yescomplemented
68#5632C22116yescomplemented
69#5632C2218yescomplemented
70D3×C22⋊Q8C22116yescomplemented
71D3×C22⋊Q8C2218yescomplemented
72#5623C22116yescomplemented
73#5623C2218yescomplemented
74#5622C22116yescomplemented
75#5622C2218yescomplemented
76#5579C2214yescomplemented
77#5578C2218yescomplemented
78#5578C2214yescomplemented
79Q8×D12C2214yescomplemented
80C4×D3×Q8C2214yescomplemented
81#5567C2214yescomplemented
82Q8×Dic6C2214yescomplemented
83#5546C2218yes—
84#5546C2214yes—
85#5545C2218yes—
86#5545C2214yes—
87C4×D3×D4C2218yes—
88C4×D3×D4C2214yes—
89#5543C2218yescomplemented
90#5539C2218yescomplemented
91#5539C2218yescomplemented
92D4×Dic6C2218yescomplemented
93D4×Dic6C2214yescomplemented
94D4×Dic6C2218yescomplemented
95D4×Dic6C2214yescomplemented
96C4×#237C2218yes—
97C4×#237C2214yes—
98#5523C2214yes—
99#5522C2214yes—
100#5519C2214yescomplemented
101#5517C2214yescomplemented
102#5511C2218yescomplemented
103#5511C22116yescomplemented
104C2×#897C2214yescomplemented
105C2×#896C2218yescomplemented
106#5504C2212yes—
107C2×#888C2212yescomplemented
108C2×#888C2218yescomplemented
109C2×#887C2214yescomplemented
110#5486C2214yes—
111#5486C2218yes—
112C2×#67⋊C4C2218yes—
113#5483C2218yescomplemented
114C2×#878C2214yescomplemented
115C2×#878C2218yescomplemented
116C4×#235C2212yes—
117C2×#869C2211yescharacteristic, complemented
118C2×C4×Dic6C2211yescharacteristic, complemented
119#3503—38no—
120#3503—34no—
121#3503—34no—
122#3503—32no—
123#3501—34no—
124#3501—38no—
125#3501—38no—
126#3501—34no—
127#3501—32no—
128#3501D311yescharacteristic, complemented
129Q8×#41—34no—
130Q8×#41—32no—
131C2×D4×Q8—34no—
132C2×D4×Q8—34no—
133C2×D4×Q8—31no—
134C4×H(5,𝔽2)—32no—
135C4×H(5,𝔽2)—31no—
136C22×C3×Q8C2314yes—
137C22×C3×D4C2311yescharacteristic
138C23×C3×C4C2312yes—
139C22×#67C2314yes—
140C23×Dic3C2314yes—
141C2×D3×Q8—416no—
142C2×D3×Q8C2314yes—
143C2×D3×Q8C23116yes—
144C2×D3×Q8C2318yes—
145#1004Q8116yescomplemented
146C2×#237C2314yes—
147C2×D3×D4C2314yes—
148C2×#235C2312yes—
149C22×C4×D3C2318yes—
150C22×C4×D3C2314yes—
151C22×Dic6—48no—
152C22×Dic6C2311yescharacteristic
153C22×Dic6C2314yes—
154C22×Dic6C2312yes—
155C22×Dic6C2314yes—
156C22×Dic6C2318yes—
157C22×Dic6C2314yes—
158C22×Dic6C2318yes—
159C3×C4⋊Q8C2312yes—
160C3×C4⋊Q8C2318yes—
161C3×C4⋊Q8C2312yes—
162C3×#125C2318yes—
163C3×#125C2314yes—
164C3×C22⋊Q8C2314yes—
165C3×C22⋊Q8C2318yes—
166C3×C22⋊Q8C2318yes—
167C3×C22⋊Q8C2318yes—
168C3×C22⋊Q8C23116yes—
169C3×C22⋊Q8C23116yes—
170C3×C22⋊Q8C2314yes—
171C3×C4×Q8C2314yes—
172C3×C4×Q8C2314yes—
173C3×C4×D4C2314yes—
174C3×C4×D4C2318yes—
175C3×C4×D4C2314yes—
176C3×C4×D4C2318yes—
177C3×#117C2314yes—
178C2×C3×C4⋊C4C2314yes—
179C2×C3×C4⋊C4C2311yescharacteristic
180C2×C3×C4⋊C4C2318yes—
181C2×C3×C22⋊C4C2312yes—
182C2×C3×C22⋊C4C2318yes—
183C2×C3×C42C2311yescharacteristic
184C2×#217C2314yes—
185C2×#217C2314yes—
186#946C2318yes—
187#946C2318yes—
188#946C23116yes—
189#946C2314yes—
190Q8×Dic3C2318yes—
191Q8×Dic3C2314yes—
192#944C2314yes—
193#944C23116yes—
194#944C2318yes—
195#944C23116yes—
196#944C2318yes—
197D4×Dic3C2318yes—
198D4×Dic3C2314yes—
199D4×Dic3C2318yes—
200D4×Dic3C2314yes—
201C4×#67C2314yes—
202C4×#67C2318yes—
203C4×#67C2318yes—
204C4×#67C2318yes—
205C4×#67C23116yes—
206C4×#67C2314yes—
207C4×#67C23116yes—
208C2×(C2×D3)⋊C4C2318yes—
209C2×(C2×D3)⋊C4C2314yes—
210#926C2312yes—
211C2×C4⋊Dic3C2311yescharacteristic
212C2×C4⋊Dic3C2312yes—
213C2×C4⋊Dic3C2318yes—
214C2×C4⋊Dic3C2312yes—
215#924C23116yes—
216#924C2318yes—
217#924C23116yes—
218#924C2318yes—
219C2×Dic3⋊C4C2312yes—
220C2×Dic3⋊C4C2314yes—
221C2×Dic3⋊C4C2318yes—
222C2×Dic3⋊C4C2318yes—
223C2×Dic3⋊C4C2318yes—
224C2×Dic3⋊C4C2314yes—
225C2×C4×Dic3C2312yes—
226C2×C4×Dic3C2318yes—
227C2×C4×Dic3C2314yes—
228#897C2314yes—
229#897C23116yes—
230#897C2318yes—
231#897C23116yes—
232#897C2318yes—
233#896C2318yes—
234#896C23116yes—
235#896C23116yes—
236#896C23116yes—
237#896C2318yes—
238#896C23116yes—
239#896C2318yes—
240#896C23116yes—
241#893C2314yes—
242#893C2314yes—
243#893C2314yes—
244#892C2314yes—
245#892C2318yes—
246D3×C4⋊C4C2318yes—
247D3×C4⋊C4C23116yes—
248D3×C4⋊C4C2314yes—
249D3×C4⋊C4C2318yes—
250D3×C4⋊C4C2314yes—
251D3×C4⋊C4C2318yes—
252#890C2314yes—
253#890C2318yes—
254#890C2314yes—
255#889C2318yes—
256#889C23116yes—
257#889C23116yes—
258#889C2318yes—
259#889C2318yes—
260#889C23116yes—
261#888C23116yes—
262#888C2318yes—
263#888C23116yes—
264#888C2318yes—
265#888C23116yes—
266#888C2314yes—
267#888C2318yes—
268#888C2314yes—
269#888C2314yes—
270#888C2318yes—
271#888C2318yes—
272#887C2314yes—
273#887C23116yes—
274#887C2318yes—
275#887C2318yes—
276#887C23116yes—
277#887C2314yes—
278#887C2314yes—
279#887C2314yes—
280#67⋊C4C2318yes—
281#67⋊C4C23116yes—
282#67⋊C4C2318yes—
283#67⋊C4C23116yes—
284#67⋊C4C23116yes—
285#67⋊C4C2318yes—
286#67⋊C4C2318yes—
287D3×C22⋊C4C2318yes—
288D3×C22⋊C4C23116yes—
289#878C2318yes—
290#878C23116yes—
291#878C23116yes—
292#878C23116yes—
293#878C23116yes—
294#878C23116yes—
295#878C23116yes—
296#878C23116yes—
297#878C2318yes—
298#877C2318yes—
299#877C23116yes—
300C4×D12C2312yes—
301C4×D12C2318yes—
302C4×D12C2312yes—
303#872C2314yes—
304#872C2318yes—
305C42×D3C2318yes—
306C42×D3C2314yes—
307#870C2318yes—
308#869C2314yes—
309#869C2318yes—
310#869C2314yes—
311C4×Dic6C2312yes—
312C4×Dic6C2314yes—
313C4×Dic6C2318yes—
314C4×Dic6C2318yes—
315C4×Dic6C2318yes—
316C4×Dic6C2312yes—
317C4×Dic6C2312yes—
318C4×Dic6C2312yes—
319C2×H(5,𝔽2)—31no—
320C23×Q8—34no—
321C23×Q8—32no—
322Q82—32no—
323Q82—38no—
324Q82—34no—
325#557—32no—
326#557—38no—
327#557—34no—
328#557—34no—
329#554—32no—
330#554—34no—
331#554—38no—
332#554—34no—
333#554—316no—
334#554—38no—
335#554—316no—
336#554—38no—
337#554—316no—
338#554—316no—
339#554—34no—
340#554—38no—
341#554—38no—
342#554—38no—
343#554—38no—
344#554—316no—
345#554C2×D314yescomplemented
346#554C2×D318yescomplemented
347D4×Q8—38no—
348D4×Q8—32no—
349D4×Q8—38no—
350D4×Q8—38no—
351D4×Q8—34no—
352D4×Q8—38no—
353D4×Q8—38no—
354D4×Q8—316no—
355D4×Q8—316no—
356D4×Q8—316no—
357D4×Q8—34no—
358D4×Q8—34no—
359D4×Q8—38no—
360D4×Q8—38no—
361D4×Q8—34no—
362D4×Q8C2×D314yescomplemented
363#544—38no—
364#544—38no—
365#544—38no—
366#544—316no—
367#544—38no—
368#544—34no—
369#544C2×D312yescomplemented
370#543—38no—
371#543—316no—
372#543—38no—
373#543C2×D314yescomplemented
374#533—34no—
375#533—38no—
376#533—38no—
377#533—316no—
378#533—38no—
379#533—34no—
380#533—34no—
381#533C2×D312yescomplemented
382C2×C4⋊Q8—34no—
383C2×C4⋊Q8—34no—
384C2×C4⋊Q8—38no—
385C2×C4⋊Q8—38no—
386C2×C4⋊Q8—32no—
387C2×C4⋊Q8—31no—
388C2×C22⋊Q8—32no—
389C2×C22⋊Q8—38no—
390C2×C22⋊Q8—316no—
391C2×C22⋊Q8—38no—
392C2×C22⋊Q8—34no—
393C2×C22⋊Q8—38no—
394C2×C22⋊Q8—34no—
395C2×C22⋊Q8C2×D314yescomplemented
396#520—38no—
397#520—34no—
398#520—34no—
399#520—32no—
400#518—31no—
401#518—38no—
402#518—34no—
403#518—38no—
404#518—34no—
405#518C2×D312yes—
406C4×#41—38no—
407C4×#41—34no—
408C4×#41—34no—
409C4×#41—32no—
410C2×C4×Q8—34no—
411C2×C4×Q8—34no—
412C2×C4×Q8—31no—
413C2×C4×D4—32no—
414C2×C4×D4—34no—
415C2×C4×D4—38no—
416C2×C4×D4—34no—
417C2×C4×D4—38no—
418C2×C4×D4C2×D311yescharacteristic
419C24×C3C2412yes—
420C23×D3C2414yes—
421C2×C3×Q8—48no—
422C2×C3×Q8C2414yes—
423C2×C3×Q8C2418yes—
424C2×C3×Q8C2414yes—
425C2×C3×D4C2×Q818yescomplemented
426C2×C3×D4C2414yes—
427C22×C3×C4—44no—
428C22×C3×C4C2414yes—
429C22×C3×C4C2411yescharacteristic
430C22×C3×C4C2418yes—
431C22×C3×C4C2418yes—
432C22×C3×C4C2411yescharacteristic
433C22×C3×C4C2412yes—
434C22×C3×C4C2414yes—
435C22×C3×C4C2411yescharacteristic
436C2×#67C2×Q8132yescomplemented
437C2×#67C2414yes—
438C2×#67C2418yes—
439C22×Dic3—48no—
440C22×Dic3C2412yes—
441C22×Dic3C2418yes—
442C22×Dic3C2412yes—
443C22×Dic3C2414yes—
444C22×Dic3C2414yes—
445C22×Dic3C2418yes—
446C22×Dic3C2414yes—
447C22×Dic3C2414yes—
448D3×Q8—216no—
449D3×Q8—432no—
450D3×Q8—416no—
451#237C2×Q8132yescomplemented
452D3×D4C2×Q8132yescomplemented
453#235C2×Q8116yescomplemented
454C2×D12C2412yes—
455C2×C4×D3—416no—
456C2×C4×D3—48no—
457C2×C4×D3C2414yes—
458C2×C4×D3C2418yes—
459C2×C4×D3C2414yes—
460C2×C4×D3C2418yes—
461C2×C4×D3C24116yes—
462C2×C4×D3C2418yes—
463C2×C4×D3C2414yes—
464C2×Dic6—24no—
465C2×Dic6—216no—
466C2×Dic6—416no—
467C2×Dic6—48no—
468C2×Dic6—416no—
469C2×Dic6—48no—
470C2×Dic6—44no—
471C2×Dic6C2412yes—
472C2×Dic6C2411yescharacteristic
473C2×Dic6C2418yes—
474C2×Dic6C2414yes—
475C2×Dic6C2418yes—
476C2×Dic6C2418yes—
477C2×Dic6C2414yes—
478C2×Dic6C24116yes—
479C2×Dic6C2418yes—
480C2×Dic6C2412yes—
481C2×Dic6C2411yescharacteristic
482C3×C4⋊C4C2414yes—
483C3×C4⋊C4C2418yes—
484C3×C4⋊C4C2414yes—
485C3×C4⋊C4C2414yes—
486C3×C4⋊C4C24116yes—
487C3×C4⋊C4C2414yes—
488C3×C4⋊C4C2418yes—
489C3×C4⋊C4C2418yes—
490C3×C4⋊C4C2414yes—
491C3×C22⋊C4C24116yes—
492C3×C22⋊C4C2418yes—
493C3×C22⋊C4C2418yes—
494C3×C42C2412yes—
495C3×C42C2412yes—
496C3×C42C2418yes—
497#217C2418yes—
498#217C24116yes—
499#217C2414yes—
500(C2×D3)⋊C4C2414yes—
501(C2×D3)⋊C4C2414yes—
502(C2×D3)⋊C4C2418yes—
503(C2×D3)⋊C4C2418yes—
504(C2×D3)⋊C4C24116yes—
505(C2×D3)⋊C4C2418yes—
506C4⋊Dic3C2412yes—
507C4⋊Dic3C2412yes—
508C4⋊Dic3C2412yes—
509C4⋊Dic3C2418yes—
510C4⋊Dic3C2412yes—
511C4⋊Dic3C2418yes—
512C4⋊Dic3C2418yes—
513C4⋊Dic3C2418yes—
514C4⋊Dic3C24116yes—
515Dic3⋊C4C2414yes—
516Dic3⋊C4C2414yes—
517Dic3⋊C4C2414yes—
518Dic3⋊C4C2414yes—
519Dic3⋊C4C24116yes—
520Dic3⋊C4C2418yes—
521Dic3⋊C4C2418yes—
522Dic3⋊C4C2418yes—
523Dic3⋊C4C2418yes—
524Dic3⋊C4C24116yes—
525Dic3⋊C4C24116yes—
526Dic3⋊C4C2418yes—
527Dic3⋊C4C2418yes—
528Dic3⋊C4C2418yes—
529Dic3⋊C4C24116yes—
530C4×Dic3C2414yes—
531C4×Dic3C2414yes—
532C4×Dic3C2414yes—
533C4×Dic3C2414yes—
534C4×Dic3C2414yes—
535C4×Dic3C24116yes—
536C4×Dic3C2418yes—
537C4×Dic3C2418yes—
538C4×Dic3C2418yes—
539H(5,𝔽2)—316no—
540C2×#41—34no—
541C2×#41—32no—
542C22×Q8—34no—
543C22×Q8—316no—
544C22×Q8—38no—
545C22×Q8—34no—
546C22×Q8—31no—
547C22×Q8—38no—
548C22×Q8—34no—
549C22×Q8—38no—
550C22×Q8—34no—
551C22×Q8—32no—
552C22×Q8—128no—
553C22×Q8—1216no—
554C22×Q8C22×D314yes—
555C22×D4—34no—
556C22×D4—34no—
557C22×D4C22×D311yescharacteristic
558C23×C4—34no—
559C23×C4—38no—
560C23×C4—34no—
561C23×C4C22×D312yes—
562C4⋊Q8—34no—
563C4⋊Q8—38no—
564C4⋊Q8—316no—
565C4⋊Q8—316no—
566C4⋊Q8—38no—
567C4⋊Q8—316no—
568C4⋊Q8—38no—
569C4⋊Q8—34no—
570C4⋊Q8—38no—
571C4⋊Q8—38no—
572C4⋊Q8—316no—
573C4⋊Q8—316no—
574C4⋊Q8—38no—
575C4⋊Q8—38no—
576C4⋊Q8—34no—
577C4⋊Q8—34no—
578C4⋊Q8—34no—
579C4⋊Q8—38no—
580C4⋊Q8—34no—
581C4⋊Q8C22×D312yes—
582C4⋊Q8C22×D318yes—
583C4⋊Q8C22×D312yes—
584#125—316no—
585#125—38no—
586#125—316no—
587#125—38no—
588#125—316no—
589#125—38no—
590#125—38no—
591#125—34no—
592#125—34no—
593#125—38no—
594#125C22×D318yes—
595#125C22×D314yes—
596C22⋊Q8—34no—
597C22⋊Q8—316no—
598C22⋊Q8—38no—
599C22⋊Q8—38no—
600C22⋊Q8—38no—
601C22⋊Q8—38no—
602C22⋊Q8—316no—
603C22⋊Q8—316no—
604C22⋊Q8—38no—
605C22⋊Q8—316no—
606C22⋊Q8—38no—
607C22⋊Q8—38no—
608C22⋊Q8—34no—
609C22⋊Q8—316no—
610C22⋊Q8—316no—
611C22⋊Q8—316no—
612C22⋊Q8—316no—
613C22⋊Q8—316no—
614C22⋊Q8—38no—
615C22⋊Q8—316no—
616C22⋊Q8—38no—
617C22⋊Q8—316no—
618C22⋊Q8—316no—
619C22⋊Q8—38no—
620C22⋊Q8—316no—
621C22⋊Q8—316no—
622C22⋊Q8—316no—
623C22⋊Q8—316no—
624C22⋊Q8—316no—
625C22⋊Q8—38no—
626C22⋊Q8C22×D318yes—
627C22⋊Q8C22×D3116yes—
628C22⋊Q8C22×D314yes—
629C22⋊Q8C22×D318yes—
630C22⋊Q8C22×D318yes—
631C22⋊Q8C22×D3116yes—
632C22⋊Q8C22×D314yes—
633C4×Q8—34no—
634C4×Q8—38no—
635C4×Q8—34no—
636C4×Q8—38no—
637C4×Q8—316no—
638C4×Q8—38no—
639C4×Q8—34no—
640C4×Q8—34no—
641C4×Q8—34no—
642C4×Q8—316no—
643C4×Q8—32no—
644C4×Q8—38no—
645C4×Q8—34no—
646C4×Q8—32no—
647C4×Q8—32no—
648C4×Q8—38no—
649C4×Q8—32no—
650C4×Q8—38no—
651C4×Q8C22×D314yes—
652C4×Q8C22×D314yes—
653C4×D4—38no—
654C4×D4—38no—
655C4×D4—34no—
656C4×D4—34no—
657C4×D4—38no—
658C4×D4—34no—
659C4×D4—38no—
660C4×D4—38no—
661C4×D4—316no—
662C4×D4—316no—
663C4×D4—34no—
664C4×D4—34no—
665C4×D4—34no—
666C4×D4—34no—
667C4×D4—316no—
668C4×D4—38no—
669C4×D4—38no—
670C4×D4—316no—
671C4×D4—316no—
672C4×D4—38no—
673C4×D4—38no—
674C4×D4—32no—
675C4×D4—38no—
676C4×D4—32no—
677C4×D4C22×D314yes—
678C4×D4C22×D318yes—
679C4×D4C22×D314yes—
680C4×D4C22×D318yes—
681#117—32no—
682#117—38no—
683#117—34no—
684#117—38no—
685#117—316no—
686#117—38no—
687#117—34no—
688#117C22×D314yes—
689C2×C4⋊C4—34no—
690C2×C4⋊C4—38no—
691C2×C4⋊C4—32no—
692C2×C4⋊C4—38no—
693C2×C4⋊C4—32no—
694C2×C4⋊C4—31no—
695C2×C4⋊C4—34no—
696C2×C4⋊C4—38no—
697C2×C4⋊C4—38no—
698C2×C4⋊C4—32no—
699C2×C4⋊C4—38no—
700C2×C4⋊C4—34no—
701C2×C4⋊C4—38no—
702C2×C4⋊C4—34no—
703C2×C4⋊C4—38no—
704C2×C4⋊C4—316no—
705C2×C4⋊C4C22×D311yescharacteristic
706C2×C4⋊C4C22×D314yes—
707C2×C4⋊C4C22×D318yes—
708C2×C22⋊C4—34no—
709C2×C22⋊C4—34no—
710C2×C22⋊C4—34no—
711C2×C22⋊C4—38no—
712C2×C22⋊C4—316no—
713C2×C22⋊C4—38no—
714C2×C22⋊C4C22×D318yes—
715C2×C22⋊C4C22×D312yes—
716C2×C42—38no—
717C2×C42—34no—
718C2×C42—32no—
719C2×C42—38no—
720C2×C42—34no—
721C2×C42C22×D311yescharacteristic
722C23×C3—42no—
723C23×C3—42no—
724C23×C3C22×Q818yescomplemented
725C23×C3C2514yes—
726C23×C3C2511yescharacteristic
727C22×D3—44no—
728C22×D3—44no—
729C22×D3C22×Q8116yescomplemented
730C22×D3C2514yes—
731C3×Q8—28no—
732C3×Q8—48no—
733C3×Q8—44no—
734C3×D4C22×Q8116yescomplemented
735C2×C3×C4—22no—
736C2×C3×C4—28no—
737C2×C3×C4—44no—
738C2×C3×C4—42no—
739C2×C3×C4—48no—
740C2×C3×C4—48no—
741C2×C3×C4—41no—
742C2×C3×C4C22×Q814yescomplemented
743C2×C3×C4C2518yes—
744C2×C3×C4C2512yes—
745C2×C3×C4C2514yes—
746C2×C3×C4C2518yes—
747C2×C3×C4C2511yescharacteristic
748C2×C3×C4C2512yes—
749C2×C3×C4C2511yescharacteristic
750#67C22×Q8116yescomplemented
751#67C22×Q8132yescomplemented
752C2×Dic3—216no—
753C2×Dic3—24no—
754C2×Dic3—44no—
755C2×Dic3—44no—
756C2×Dic3—48no—
757C2×Dic3—42no—
758C2×Dic3—44no—
759C2×Dic3C22×Q8116yescomplemented
760C2×Dic3C2514yes—
761C2×Dic3C2514yes—
762C2×Dic3C2512yes—
763C2×Dic3C2518yes—
764C2×Dic3C2514yes—
765C2×Dic3C2514yes—
766C2×Dic3C2512yes—
767D12C22×Q818yescomplemented
768C4×D3—28no—
769C4×D3—216no—
770C4×D3—48no—
771C4×D3—416no—
772C4×D3—48no—
773C4×D3—44no—
774C4×D3C22×Q8116yescomplemented
775Dic6—22no—
776Dic6—28no—
777Dic6—24no—
778Dic6—216no—
779Dic6—216no—
780Dic6—44no—
781Dic6—48no—
782Dic6—416no—
783Dic6—48no—
784Dic6C22×Q818yescomplemented
785Dic6H(5,𝔽2)14yescomplemented
786C24—34no—
787C24C23×D312yes—
788#41—332no—
789#41—316no—
790C2×Q8—32no—
791C2×Q8—31no—
792C2×Q8—38no—
793C2×Q8—38no—
794C2×Q8—32no—
795C2×Q8—34no—
796C2×Q8—31no—
797C2×Q8—38no—
798C2×Q8—38no—
799C2×Q8—316no—
800C2×Q8—34no—
801C2×Q8—48no—
802C2×Q8—64no—
803C2×Q8—616no—
804C2×Q8—616no—
805C2×Q8—124no—
806C2×Q8—128no—
807C2×Q8—1216no—
808C2×Q8—128no—
809C2×Q8—1216no—
810C2×Q8—1216no—
811C2×Q8—1232no—
812C2×Q8C23×D314yes—
813C2×Q8C23×D314yes—
814C2×Q8C23×D318yes—
815C2×D4—332no—
816C2×D4—38no—
817C2×D4—34no—
818C2×D4—332no—
819C2×D4—32no—
820C2×D4D3×Q818yescomplemented
821C2×D4C23×D314yes—
822C22×C4—34no—
823C22×C4—34no—
824C22×C4—38no—
825C22×C4—32no—
826C22×C4—34no—
827C22×C4—32no—
828C22×C4—34no—
829C22×C4—38no—
830C22×C4—34no—
831C22×C4—38no—
832C22×C4—34no—
833C22×C4—38no—
834C22×C4—34no—
835C22×C4—38no—
836C22×C4—316no—
837C22×C4—44no—
838C22×C4—128no—
839C22×C4—1216no—
840C22×C4—128no—
841C22×C4C23×D314yes—
842C22×C4C23×D311yescharacteristic
843C22×C4C23×D318yes—
844C22×C4C23×D311yescharacteristic
845C22×C4C23×D314yes—
846C22×C4C23×D312yes—
847C22×C4C23×D318yes—
848C22×C4C23×D311yescharacteristic
849C4⋊C4—38no—
850C4⋊C4—34no—
851C4⋊C4—32no—
852C4⋊C4—38no—
853C4⋊C4—38no—
854C4⋊C4—316no—
855C4⋊C4—34no—
856C4⋊C4—38no—
857C4⋊C4—32no—
858C4⋊C4—316no—
859C4⋊C4—38no—
860C4⋊C4—316no—
861C4⋊C4—38no—
862C4⋊C4—38no—
863C4⋊C4—316no—
864C4⋊C4—38no—
865C4⋊C4—316no—
866C4⋊C4—38no—
867C4⋊C4—34no—
868C4⋊C4—38no—
869C4⋊C4—32no—
870C4⋊C4—38no—
871C4⋊C4—34no—
872C4⋊C4—32no—
873C4⋊C4C23×D314yes—
874C4⋊C4C23×D314yes—
875C4⋊C4C23×D314yes—
876C4⋊C4C23×D314yes—
877C4⋊C4C23×D3116yes—
878C4⋊C4C23×D318yes—
879C4⋊C4C23×D318yes—
880C4⋊C4C23×D318yes—
881C4⋊C4C23×D314yes—
882C22⋊C4—316no—
883C22⋊C4—38no—
884C22⋊C4—34no—
885C22⋊C4—38no—
886C22⋊C4—38no—
887C22⋊C4—34no—
888C22⋊C4—38no—
889C22⋊C4—316no—
890C22⋊C4—34no—
891C22⋊C4C23×D3116yes—
892C22⋊C4C23×D318yes—
893C22⋊C4C23×D318yes—
894C42—38no—
895C42—34no—
896C42—34no—
897C42—38no—
898C42—38no—
899C42—316no—
900C42—34no—
901C42—34no—
902C42—34no—
903C42C23×D312yes—
904C42C23×D318yes—
905C42C23×D312yes—
906C22×C3—21no—
907C22×C3—24no—
908C22×C3—21no—
909C22×C3—24no—
910C22×C3—48no—
911C22×C3C23×Q818yes—
912C22×C3C23×Q812yes—
913C22×C3C2611yescharacteristic
914C2×D3—24no—
915C2×D3—24no—
916C2×D3—416no—
917C2×D3C23×Q818yes—
918C3×C4—21no—
919C3×C4—24no—
920C3×C4—28no—
921C3×C4—28no—
922C3×C4—22no—
923C3×C4C23×Q814yes—
924C3×C4C2×H(5,𝔽2)12yes—
925Dic3—24no—
926Dic3—28no—
927Dic3—22no—
928Dic3—24no—
929Dic3—24no—
930Dic3C23×Q818yes—
931Dic3C2×H(5,𝔽2)14yes—
932C23—34no—
933C23—316no—
934C23—42no—
935C23—42no—
936C23—124no—
937C23—124no—
938C23C2×D3×Q818yescomplemented
939C23C24×D314yes—
940C23C24×D311yescharacteristic
941Q8—28no—
942Q8—38no—
943Q8—34no—
944Q8—48no—
945Q8—44no—
946Q8—64no—
947Q8—616no—
948Q8—616no—
949Q8—62no—
950Q8—68no—
951Q8—124no—
952Q8—128no—
953Q8—1216no—
954Q8—128no—
955D4—332no—
956D4—316no—
957D4—38no—
958D4C2×D3×Q8116yescomplemented
959C2×C4—22no—
960C2×C4—28no—
961C2×C4—316no—
962C2×C4—34no—
963C2×C4—32no—
964C2×C4—316no—
965C2×C4—34no—
966C2×C4—34no—
967C2×C4—34no—
968C2×C4—38no—
969C2×C4—32no—
970C2×C4—44no—
971C2×C4—42no—
972C2×C4—48no—
973C2×C4—48no—
974C2×C4—41no—
975C2×C4—616no—
976C2×C4—616no—
977C2×C4—64no—
978C2×C4—68no—
979C2×C4—128no—
980C2×C4—1216no—
981C2×C4—128no—
982C2×C4—124no—
983C2×C4—124no—
984C2×C4—128no—
985C2×C4—124no—
986C2×C4—124no—
987C2×C4—122no—
988C2×C4C2×D3×Q814yescomplemented
989C2×C4C24×D318yes—
990C2×C4C24×D312yes—
991C2×C4C24×D314yes—
992C2×C4C24×D318yes—
993C2×C4C24×D311yescharacteristic
994C2×C4C24×D312yes—
995C2×C4C24×D311yescharacteristic
996C2×C3—28no—
997C2×C3—22no—
998C2×C3C24×Q811yescharacteristic
999C2×C3C22×H(5,𝔽2)11yescharacteristic
1000C2×C32−1+611yescharacteristic
1001D3—28no—
1002C22—24no—
1003C22—21no—
1004C22—24no—
1005C22—21no—
1006C22—38no—
1007C22—48no—
1008C22—64no—
1009C22—64no—
1010C22—1216no—
1011C22C22×D3×Q818yes—
1012C22C22×D3×Q812yes—
1013C22C25×D311yescharacteristic
1014C4—21no—
1015C4—24no—
1016C4—28no—
1017C4—28no—
1018C4—22no—
1019C4—38no—
1020C4—34no—
1021C4—68no—
1022C4—62no—
1023C4—64no—
1024C4—64no—
1025C4—64no—
1026C4C22×D3×Q814yes—
1027C4D3×H(5,𝔽2)12yes—
1028C3Q8×H(5,𝔽2)11yescharacteristic, complemented, Sylow
1029C2—22no—
1030C2—28no—
1031C2—68no—
1032C2C23×D3×Q811yescharacteristic
1033C2C2×D3×H(5,𝔽2)11yescharacteristic
1034C2#8757211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC3×#3501C2
prime radicalC2×#1004C22
hypercenter#3501D3
hypocenterC3Q8×H(5,𝔽2)
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. C3×#3501C2semidirect
2. #86949C2semidirect
3. #86948C2semidirect
4. #86926C2semidirect
5. #86923C2semidirect
6. D3×D4×Q8C2semidirect
7. #86747C2semidirect
8. #86586C2semidirect
9. #86574C2semidirect
10. #86281C2semidirect
11. #86277C2semidirect
12. #85986C2semidirect
13. C2×#5632C2semidirect
14. #85860C2semidirect
16. C2×D4×Dic6C2semidirect
19. C22×D3×Q8C22semidirect
21. C23×Dic6C22semidirect
22. C3×#554C22semidirect
23. C3×#554C22semidirect
24. C3×D4×Q8C22semidirect
25. C3×#544C22semidirect
26. C3×#543C22semidirect
27. C3×#533C22semidirect
28. C2×C3×C22⋊Q8C22semidirect
31. Q8×#67C22semidirect
32. C2×#944C22semidirect
36. C2×#924C22semidirect
37. #5730C22semidirect
38. #5729C22semidirect
39. #5728C22semidirect
40. #5727C22semidirect
41. #5727C22semidirect
42. D3×C4⋊Q8C22semidirect
43. D3×C4⋊Q8C22semidirect
44. #5722C22semidirect
45. #5722C22semidirect
46. #5721C22semidirect
47. #5690C22semidirect
48. #5690C22semidirect
49. #5689C22semidirect
50. #5689C22semidirect
51. #5688C22semidirect
52. #5685C22semidirect
53. #5685C22semidirect
54. #5636C22semidirect
55. #5636C22semidirect
56. #5636C22semidirect
57. #5636C22semidirect
58. #5635C22semidirect
59. #5635C22semidirect
60. #5635C22semidirect
61. #5634C22semidirect
62. #5634C22semidirect
63. #5632C22semidirect
64. #5632C22semidirect
65. #5632C22semidirect
66. #5632C22semidirect
67. #5632C22semidirect
68. #5632C22semidirect
69. #5632C22semidirect
70. D3×C22⋊Q8C22semidirect
71. D3×C22⋊Q8C22semidirect
72. #5623C22semidirect
73. #5623C22semidirect
74. #5622C22semidirect
75. #5622C22semidirect
76. #5579C22semidirect
77. #5578C22semidirect
78. #5578C22semidirect
79. Q8×D12C22semidirect
80. C4×D3×Q8C22semidirect
81. #5567C22semidirect
82. Q8×Dic6C22semidirect
89. #5543C22semidirect
90. #5539C22semidirect
91. #5539C22semidirect
92. D4×Dic6C22semidirect
93. D4×Dic6C22semidirect
94. D4×Dic6C22semidirect
95. D4×Dic6C22semidirect
100. #5519C22semidirect
101. #5517C22semidirect
102. #5511C22semidirect
103. #5511C22semidirect
104. C2×#897C22semidirect
105. C2×#896C22semidirect
107. C2×#888C22semidirect
108. C2×#888C22semidirect
109. C2×#887C22semidirect
113. #5483C22semidirect
114. C2×#878C22semidirect
115. C2×#878C22semidirect
117. C2×#869C22semidirect
118. C2×C4×Dic6C22semidirect
128. #3501D3semidirect
145. #1004Q8semidirect
345. #554C2×D3semidirect
346. #554C2×D3semidirect
362. D4×Q8C2×D3semidirect
369. #544C2×D3semidirect
373. #543C2×D3semidirect
381. #533C2×D3semidirect
395. C2×C22⋊Q8C2×D3semidirect
425. C2×C3×D4C2×Q8semidirect
436. C2×#67C2×Q8semidirect
451. #237C2×Q8semidirect
452. D3×D4C2×Q8semidirect
453. #235C2×Q8semidirect
724. C23×C3C22×Q8semidirect
729. C22×D3C22×Q8semidirect
734. C3×D4C22×Q8semidirect
742. C2×C3×C4C22×Q8semidirect
750. #67C22×Q8semidirect
751. #67C22×Q8semidirect
759. C2×Dic3C22×Q8semidirect
767. D12C22×Q8semidirect
774. C4×D3C22×Q8semidirect
784. Dic6C22×Q8semidirect
785. Dic6H(5,𝔽2)semidirect
820. C2×D4D3×Q8semidirect
938. C23C2×D3×Q8semidirect
958. D4C2×D3×Q8semidirect
988. C2×C4C2×D3×Q8semidirect
1028. C3Q8×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C3×#35012
#869492
#869482
#869262
#869232
D3×D4×Q82
#867472
#865862
#865742
#862812
#862772
#859862
C2×#56322
#858602
#858572
C2×D4×Dic62
C4×#10042
Q8×H(5,𝔽2)3