Finite Group Databasebeta

← #11703835

Subgroups — #11703835

Order 768.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2#87251C212yesmaximal, complemented
3C2×#5791C212yesmaximal, complemented
4#85991C218yesmaximal, complemented
5#85990C214yesmaximal, complemented
6#85989C218yesmaximal, complemented
7#85987C218yesmaximal, complemented
8#85986C214yesmaximal, complemented
9#85985C214yesmaximal, complemented
10#85973C214yesmaximal, complemented
11#85971C214yesmaximal, complemented
12#85970C214yesmaximal, complemented
13#85718C212yesmaximal, complemented
14#85718C214yesmaximal, complemented
15#85697C214yesmaximal, complemented
16#62819—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic, complemented
18C24×C3×C4C2211yescharacteristic
19C2×#1007C2212yescomplemented
20C22×#235C2212yescomplemented
21C2×C3×C22⋊Q8C2214yes—
22C2×C3×C22⋊Q8C2214yescomplemented
23C2×C3×C22⋊Q8C2214yescomplemented
24C2×C3×C22⋊Q8C2214yescomplemented
25C2×C3×C22⋊Q8C2214yescomplemented
26C2×C3×C22⋊Q8C2214yescomplemented
27C22×C3×C4⋊C4C2211yescharacteristic, complemented
28C22×C3×C4⋊C4C2212yescomplemented
29C22×C3×C22⋊C4C2212yes—
30C2×#953C2214yes—
31#5817C2218yescomplemented
32#5817C2218yescomplemented
33#5816C2214yescomplemented
34#5816C2218yescomplemented
35Q8×#67C2218yescomplemented
36Q8×#67C2218yescomplemented
37#5812C2212yescomplemented
38#5791C2214yes—
39#5791C2214yes—
40#5791C2214yes—
41#5791C2214yes—
42#5791C2214yescomplemented
43#5791C2214yescomplemented
44#5791C2214yescomplemented
45#5791C2214yescomplemented
46#5791C2218yescomplemented
47#5791C2218yescomplemented
48C2×#930C2212yes—
49C2×#930C2212yescomplemented
50C2×#929C2214yescomplemented
51C2×C4×#67C2214yes—
52C2×C4×#67C2214yescomplemented
53C2×#926C2212yescomplemented
54C2×#924C2212yes—
55C2×#924C2212yescomplemented
56#5647C22116yescomplemented
57#5646C22116yescomplemented
58#5645C2218yescomplemented
59#5644C2218yescomplemented
60#5643C2218yescomplemented
61#5642C2218yescomplemented
62#5641C2218yescomplemented
63#5640C22116yescomplemented
64#5639C2218yescomplemented
65#5638C22116yescomplemented
66#5637C22116yescomplemented
67#5636C22116yescomplemented
68#5635C2218yescomplemented
69#5634C2218yescomplemented
70#5633C2218yescomplemented
71#5632C2218yescomplemented
72#5631C2218yescomplemented
73#5630C2218yescomplemented
74#5629C2218yescomplemented
75#5628C2218yescomplemented
76#5627C2218yescomplemented
77D3×C22⋊Q8C2218yescomplemented
78#5625C2218yescomplemented
79#5624C2218yescomplemented
80#5623C2218yescomplemented
81#5622C2218yescomplemented
82#5515C2218yescomplemented
83#5515C2218yescomplemented
84#5515C2218yescomplemented
85#5514C2218yescomplemented
86#5514C22116yescomplemented
87#5513C22116yescomplemented
88#5513C2218yescomplemented
89#5511C2218yescomplemented
90#5511C22116yescomplemented
91#5510C2212yescomplemented
92#5510C2214yescomplemented
93#5507C22116yescomplemented
94#5507C2218yescomplemented
95#5504C2214yescomplemented
96#5504C2218yescomplemented
97#5500C2212yescomplemented
98#5500C2214yescomplemented
99#5495C22116yescomplemented
100#5495C22116yescomplemented
101#5494C2218yescomplemented
102#5494C2218yescomplemented
103#5493C2214yes—
104#5490C22116yescomplemented
105#5490C22116yescomplemented
106#5486C2218yes—
107#5483C2214yes—
108#3541—38no—
109#3538—34no—
110#3536—34no—
111#3535—38no—
112#3520—38no—
113#3505—34no—
114#3501—34no—
115#3495—34no—
116#3492—32no—
117#3492—34no—
118#3490—34no—
119#3489—34no—
120#3486—32no—
121C2×#525—32no—
122C22×C22⋊Q8D311yescharacteristic, complemented
123C25×C3C2311yescharacteristic
124C22×C3×Q8—44no—
125C22×C3×Q8C2312yes—
126C22×C3×Q8C2314yes—
127C22×C3×Q8C2314yes—
128C22×C3×Q8C2312yes—
129C23×C3×C4—44no—
130C23×C3×C4C2312yes—
131C23×C3×C4C2311yescharacteristic
132C23×C3×C4C2312yes—
133C23×C3×C4C2312yes—
134C23×C3×C4C2312yes—
135C23×C3×C4C2312yes—
136C23×C3×C4C2311yescharacteristic
137C23×C3×C4C2312yes—
138C23×C3×C4C2312yes—
139C23×C3×C4C2312yes—
140C22×#67C2314yes—
141C22×#67C2314yes—
142C22×#67C2314yes—
143#1007—48no—
144C2×#239C2318yescomplemented
145C2×D3×Q8C2318yescomplemented
146C2×#235—48no—
147C2×#235C2314yes—
148C2×#235C2314yes—
149C2×#235C2314yes—
150C2×#235C2314yes—
151C2×#235C2318yes—
152C2×#235C2318yes—
153C22×D12C2312yes—
154C22×C4×D3C2314yes—
155C22×Dic6C2312yes—
156C3×C22⋊Q8C2318yes—
157C3×C22⋊Q8C2318yes—
158C3×C22⋊Q8C2318yes—
159C3×C22⋊Q8C2318yes—
160C3×C22⋊Q8C2318yes—
161C3×C22⋊Q8C2318yes—
162C3×C22⋊Q8C2318yes—
163C3×C22⋊Q8C2318yes—
164C2×C3×C4⋊C4C2312yes—
165C2×C3×C4⋊C4C2314yes—
166C2×C3×C4⋊C4C2314yes—
167C2×C3×C4⋊C4C2314yes—
168C2×C3×C4⋊C4C2318yes—
169C2×C3×C4⋊C4C2314yes—
170C2×C3×C4⋊C4C2318yes—
171C2×C3×C4⋊C4C2312yes—
172C2×C3×C22⋊C4C2314yes—
173C2×C3×C22⋊C4C2318yes—
174C2×C3×C22⋊C4C2318yes—
175C2×C3×C22⋊C4C2314yes—
176#953C2318yes—
177#953C2318yes—
178#953C2318yes—
179#953C2318yes—
180C2×#217C2314yes—
181C2×#217C2314yes—
182C2×#217C2314yes—
183#947C2318yescomplemented
184#947C23116yescomplemented
185#946C23116yescomplemented
186#946C2318yescomplemented
187#946C23116yescomplemented
188#946C2318yescomplemented
189Q8×Dic3C2318yescomplemented
190Q8×Dic3C2318yescomplemented
191#944C2318yescomplemented
192#944C23116yescomplemented
193#930C2314yes—
194#930C2314yes—
195#930C2314yes—
196#930C2318yes—
197#930C2318yes—
198#930C2318yes—
199#930C2318yes—
200#930C2314yes—
201#930C2314yes—
202#930C2314yes—
203#930C2314yes—
204#930C2314yes—
205#929C2318yes—
206#929C2318yes—
207#929C23116yes—
208#929C23116yes—
209#929C2318yes—
210#929C2318yes—
211C4×#67C2318yes—
212C4×#67C2318yes—
213C4×#67C2318yes—
214C4×#67C2318yes—
215C4×#67C23116yes—
216C4×#67C23116yes—
217C4×#67C23116yes—
218C4×#67C23116yes—
219C4×#67C2318yes—
220C4×#67C2318yes—
221C4×#67C2318yes—
222C4×#67C2318yes—
223C2×(C2×D3)⋊C4C2314yes—
224C2×(C2×D3)⋊C4C2314yes—
225#926C2314yes—
226#926C2314yes—
227#926C2318yes—
228#926C2318yes—
229#926C2314yes—
230#926C2314yes—
231C2×C4⋊Dic3C2312yes—
232C2×C4⋊Dic3C2312yes—
233#924C2314yes—
234#924C2314yes—
235#924C2318yes—
236#924C2318yes—
237#924C2318yes—
238#924C2318yes—
239#924C2314yes—
240#924C2314yes—
241#924C2314yes—
242#924C2314yes—
243#924C2314yes—
244#924C2314yes—
245C2×Dic3⋊C4C2314yes—
246C2×Dic3⋊C4C2314yes—
247C2×C4×Dic3C2314yes—
248#898C23116yescomplemented
249#898C23116yescomplemented
250#898C23116yescomplemented
251#897C2318yescomplemented
252#897C23116yescomplemented
253#896C23116yescomplemented
254#896C23116yescomplemented
255#896C23116yescomplemented
256#895C2318yescomplemented
257#895C23116yescomplemented
258#894C23116yescomplemented
259#894C23116yescomplemented
260#894C23116yescomplemented
261#893C23116yescomplemented
262#893C2318yescomplemented
263#892C23116yescomplemented
264#892C2318yescomplemented
265D3×C4⋊C4C2318yescomplemented
266D3×C4⋊C4C23116yescomplemented
267#890C2318yescomplemented
268#890C23116yescomplemented
269#889C23116yescomplemented
270#889C23116yescomplemented
271#889C23116yescomplemented
272#888C23116yescomplemented
273#888C2318yescomplemented
274#887C2318yescomplemented
275#887C23116yescomplemented
276#886C23116yes—
277#885C23116yes—
278#885C23116yes—
279#884C23116yes—
280#884C23116yes—
281#883C23116yes—
282#883C23116yes—
283#882C23116yes—
284#67⋊C4C23116yes—
285#67⋊C4C23116yes—
286D3×C22⋊C4C23116yes—
287#879C23116yes—
288#879C23116yes—
289#878C23116yes—
290#878C23116yes—
291#877C23116yes—
292C2×2−1+4—32no—
293C22×#41—32no—
294C23×Q8C2×D311yescharacteristic, complemented
295C24×C4C2×D311yescharacteristic
296#563—316no—
297#562—316no—
298#556—38no—
299#554—38no—
300#554—316no—
301#554—38no—
302#554—316no—
303#553—38no—
304#553—316no—
305#552—38no—
306#552—38no—
307#552—316no—
308#552—38no—
309#551—316no—
310#551—316no—
311#551—316no—
312D4×Q8—38no—
313D4×Q8—38no—
314D4×Q8—38no—
315#548—38no—
316#548—38no—
317#548—38no—
318#547—38no—
319#547—316no—
320#547—38no—
321#546—38no—
322#546—316no—
323#546—316no—
324#544—38no—
325#544—32no—
326#544—34no—
327#543—38no—
328#543—34no—
329#542—316no—
330#542—38no—
331#541—38no—
332#539—316no—
333#539—38no—
334#539—38no—
335#539—38no—
336#539—38no—
337#538—38no—
338#538—38no—
339#538—38no—
340#537—38no—
341#537—32no—
342#537—34no—
343#536—34no—
344#536—38no—
345#536—38no—
346#534—34no—
347#533—38no—
348#529—38no—
349#525—34no—
350#525—34no—
351#525—34no—
352#525—34no—
353#525—34no—
354#525—34no—
355#525—34no—
356#525—34no—
357#525—38no—
358#525—38no—
359#525—38no—
360C2×#123—34no—
361C2×C22⋊Q8—32no—
362C2×C22⋊Q8—32no—
363C2×C22⋊Q8—38no—
364C2×C22⋊Q8C2×D314yes—
365C2×C22⋊Q8C2×D314yescomplemented
366C2×C22⋊Q8C2×D314yescomplemented
367C2×C22⋊Q8C2×D314yescomplemented
368C2×C22⋊Q8C2×D314yescomplemented
369C2×C22⋊Q8C2×D314yescomplemented
370C2×#121—32no—
371C2×#121—32no—
372C2×#120—34no—
373#520—34no—
374#520—38no—
375#519—32no—
376#518—38no—
377C2×C4×D4—34no—
378C2×C4×D4—34no—
379C2×#117—32no—
380C22×C4⋊C4C2×D311yescharacteristic, complemented
381C22×C4⋊C4C2×D312yescomplemented
382C22×C22⋊C4C2×D312yes—
383C24×C3—24no—
384C24×C3—42no—
385C24×C3—42no—
386C24×C3C2411yescharacteristic
387C24×C3C2412yes—
388C24×C3C2412yes—
389C24×C3C2411yescharacteristic
390C24×C3C2411yescharacteristic
391C23×D3C2414yes—
392C2×C3×Q8—28no—
393C2×C3×Q8—44no—
394C2×C3×Q8—48no—
395C2×C3×Q8—48no—
396C2×C3×Q8C2418yes—
397C2×C3×Q8C2418yes—
398C22×C3×C4—28no—
399C22×C3×C4—24no—
400C22×C3×C4—44no—
401C22×C3×C4—44no—
402C22×C3×C4—44no—
403C22×C3×C4—44no—
404C22×C3×C4—42no—
405C22×C3×C4—44no—
406C22×C3×C4—44no—
407C22×C3×C4—44no—
408C22×C3×C4C2412yes—
409C22×C3×C4C2412yes—
410C22×C3×C4C2412yes—
411C22×C3×C4C2412yes—
412C22×C3×C4C2412yes—
413C22×C3×C4C2412yes—
414C22×C3×C4C2414yes—
415C22×C3×C4C2414yes—
416C22×C3×C4C2412yes—
417C22×C3×C4C2411yescharacteristic
418C22×C3×C4C2412yes—
419C22×C3×C4C2412yes—
420C22×C3×C4C2411yescharacteristic
421C22×C3×C4C2414yes—
422C22×C3×C4C2414yes—
423C22×C3×C4C2414yes—
424C22×C3×C4C2414yes—
425C22×C3×C4C2412yes—
426C22×C3×C4C2412yes—
427C22×C3×C4C2411yescharacteristic
428C22×C3×C4C2412yes—
429C22×C3×C4C2411yescharacteristic
430C2×#67—216no—
431C2×#67—48no—
432C2×#67—48no—
433C2×#67C2418yes—
434C2×#67C2418yes—
435C2×#67C2418yes—
436C2×#67C2418yes—
437C2×#67C2418yes—
438C2×#67C2418yes—
439C22×Dic3C2414yes—
440C22×Dic3C2414yes—
441C22×Dic3C2414yes—
442#239—416no—
443D3×Q8—416no—
444#235—216no—
445#235—48no—
446#235—48no—
447#235—48no—
448#235—416no—
449#235—416no—
450C2×D12—44no—
451C2×D12C2414yes—
452C2×D12C2418yes—
453C2×D12C2418yes—
454C2×D12C2414yes—
455C2×C4×D3—48no—
456C2×C4×D3C2418yes—
457C2×C4×D3C24116yes—
458C2×C4×D3C24116yes—
459C2×C4×D3C2418yes—
460C2×Dic6—44no—
461C2×Dic6C2414yes—
462C2×Dic6C2418yes—
463C2×Dic6C2418yes—
464C2×Dic6C2414yes—
465C3×C4⋊C4C2418yes—
466C3×C4⋊C4C24116yes—
467C3×C4⋊C4C24116yes—
468C3×C4⋊C4C2418yes—
469C3×C22⋊C4C24116yes—
470C3×C22⋊C4C24116yes—
471#217C2418yes—
472#217C2418yes—
473#217C2418yes—
474#217C2418yes—
475#217C2418yes—
476#217C2418yes—
477(C2×D3)⋊C4C24116yes—
478(C2×D3)⋊C4C24116yes—
479(C2×D3)⋊C4C24116yes—
480(C2×D3)⋊C4C24116yes—
481(C2×D3)⋊C4C2418yes—
482(C2×D3)⋊C4C2418yes—
483(C2×D3)⋊C4C2418yes—
484(C2×D3)⋊C4C2418yes—
485C4⋊Dic3C2418yes—
486C4⋊Dic3C2418yes—
487C4⋊Dic3C2418yes—
488C4⋊Dic3C2418yes—
489C4⋊Dic3C2414yes—
490C4⋊Dic3C2414yes—
491C4⋊Dic3C2414yes—
492C4⋊Dic3C2414yes—
493Dic3⋊C4C24116yes—
494Dic3⋊C4C24116yes—
495Dic3⋊C4C24116yes—
496Dic3⋊C4C24116yes—
497Dic3⋊C4C2418yes—
498Dic3⋊C4C2418yes—
499Dic3⋊C4C2418yes—
500Dic3⋊C4C2418yes—
501C4×Dic3C24116yes—
502C4×Dic3C24116yes—
503C4×Dic3C2418yes—
504C4×Dic3C2418yes—
505C25C22×D311yescharacteristic
5062−1+4—128no—
507C2×#41—38no—
508C2×#41—34no—
509C2×#41—38no—
510C2×#41—34no—
511C2×#41—34no—
512C2×#41—34no—
513C2×#41—38no—
514C2×#41—128no—
515C22×Q8—38no—
516C22×Q8—32no—
517C22×Q8—44no—
518C22×Q8C22×D312yes—
519C22×Q8C22×D314yes—
520C22×Q8C22×D312yes—
521C22×Q8C22×D314yes—
522C22×D4—34no—
523C22×D4—34no—
524C22×D4—34no—
525C22×D4—32no—
526C23×C4—34no—
527C23×C4—44no—
528C23×C4C22×D311yescharacteristic
529C23×C4C22×D312yes—
530C23×C4C22×D312yes—
531C23×C4C22×D312yes—
532C23×C4C22×D311yescharacteristic
533C23×C4C22×D312yes—
534C23×C4C22×D312yes—
535C23×C4C22×D312yes—
536C23×C4C22×D312yes—
537C23×C4C22×D312yes—
538C4⋊Q8—38no—
539C4⋊Q8—316no—
540C4⋊Q8—38no—
541C4⋊Q8—316no—
542#126—316no—
543#126—316no—
544#126—316no—
545#126—316no—
546#126—316no—
547#125—38no—
548#125—316no—
549#125—316no—
550#125—316no—
551#125—316no—
552#124—38no—
553#124—316no—
554#124—316no—
555#124—316no—
556#123—38no—
557#123—38no—
558#123—38no—
559#123—38no—
560#123—316no—
561#123—316no—
562#123—316no—
563#123—316no—
564#123—316no—
565#123—316no—
566#123—316no—
567#123—316no—
568C22⋊Q8—38no—
569C22⋊Q8—38no—
570C22⋊Q8—316no—
571C22⋊Q8—316no—
572C22⋊Q8—34no—
573C22⋊Q8—34no—
574C22⋊Q8—34no—
575C22⋊Q8—34no—
576C22⋊Q8—34no—
577C22⋊Q8—34no—
578C22⋊Q8—34no—
579C22⋊Q8—34no—
580C22⋊Q8—38no—
581C22⋊Q8—38no—
582C22⋊Q8—38no—
583C22⋊Q8—38no—
584C22⋊Q8—38no—
585C22⋊Q8—316no—
586C22⋊Q8—316no—
587C22⋊Q8—316no—
588C22⋊Q8—316no—
589C22⋊Q8—316no—
590C22⋊Q8—316no—
591C22⋊Q8C22×D318yes—
592C22⋊Q8C22×D318yes—
593C22⋊Q8C22×D318yes—
594C22⋊Q8C22×D318yes—
595C22⋊Q8C22×D318yes—
596C22⋊Q8C22×D318yes—
597C22⋊Q8C22×D318yes—
598C22⋊Q8C22×D318yes—
599#121—34no—
600#121—34no—
601#121—34no—
602#121—34no—
603#121—34no—
604#121—34no—
605#121—34no—
606#121—34no—
607#121—38no—
608#121—38no—
609#121—38no—
610#121—38no—
611#121—38no—
612#121—316no—
613#121—316no—
614#121—316no—
615#120—38no—
616#120—38no—
617#120—38no—
618#120—38no—
619#120—316no—
620C4×Q8—38no—
621C4×Q8—38no—
622C4×Q8—38no—
623C4×Q8—316no—
624C4×D4—38no—
625C4×D4—38no—
626C4×D4—38no—
627C4×D4—38no—
628C4×D4—38no—
629C4×D4—38no—
630C4×D4—38no—
631C4×D4—38no—
632C4×D4—316no—
633C4×D4—316no—
634C4×D4—316no—
635C4×D4—316no—
636C4×D4—316no—
637C4×D4—38no—
638C4×D4—316no—
639C4×D4—316no—
640#117—34no—
641#117—34no—
642#117—34no—
643#117—34no—
644#117—38no—
645#117—38no—
646#117—38no—
647#117—316no—
648#117—316no—
649C2×C4⋊C4—32no—
650C2×C4⋊C4—32no—
651C2×C4⋊C4—34no—
652C2×C4⋊C4—34no—
653C2×C4⋊C4—38no—
654C2×C4⋊C4—316no—
655C2×C4⋊C4C22×D312yes—
656C2×C4⋊C4C22×D314yes—
657C2×C4⋊C4C22×D314yes—
658C2×C4⋊C4C22×D318yes—
659C2×C4⋊C4C22×D314yes—
660C2×C4⋊C4C22×D312yes—
661C2×C4⋊C4C22×D314yes—
662C2×C4⋊C4C22×D318yes—
663C2×C22⋊C4—34no—
664C2×C22⋊C4—34no—
665C2×C22⋊C4—34no—
666C2×C22⋊C4—34no—
667C2×C22⋊C4—34no—
668C2×C22⋊C4—316no—
669C2×C22⋊C4C22×D314yes—
670C2×C22⋊C4C22×D314yes—
671C2×C22⋊C4C22×D318yes—
672C2×C22⋊C4C22×D318yes—
673C2×C42—34no—
674C23×C3—22no—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—24no—
678C23×C3—24no—
679C23×C3—24no—
680C23×C3—22no—
681C23×C3—24no—
682C23×C3—41no—
683C23×C3—42no—
684C23×C3—41no—
685C23×C3—41no—
686C23×C3—42no—
687C23×C3—41no—
688C23×C3—416no—
689C23×C32−1+414yescomplemented
690C23×C3C2512yes—
691C23×C3C2511yescharacteristic
692C23×C3C2511yescharacteristic
693C23×C3C2512yes—
694C23×C3C2511yescharacteristic
695C22×D3—28no—
696C22×D3—44no—
697C22×D3—44no—
698C22×D3C2518yes—
699C3×Q8—216no—
700C3×Q8—48no—
701C2×C3×C4—24no—
702C2×C3×C4—28no—
703C2×C3×C4—22no—
704C2×C3×C4—28no—
705C2×C3×C4—24no—
706C2×C3×C4—24no—
707C2×C3×C4—24no—
708C2×C3×C4—24no—
709C2×C3×C4—24no—
710C2×C3×C4—24no—
711C2×C3×C4—41no—
712C2×C3×C4—42no—
713C2×C3×C4—42no—
714C2×C3×C4—42no—
715C2×C3×C4—41no—
716C2×C3×C4—42no—
717C2×C3×C4—42no—
718C2×C3×C4—44no—
719C2×C3×C4—44no—
720C2×C3×C4—44no—
721C2×C3×C4—44no—
722C2×C3×C4H(5,𝔽2)14yes—
723C2×C3×C4C2512yes—
724C2×C3×C4C2518yes—
725C2×C3×C4C2518yes—
726C2×C3×C4C2512yes—
727C2×C3×C4C2512yes—
728C2×C3×C4C2512yes—
729#67—216no—
730#67—216no—
731#67—216no—
732#67—216no—
733#67—48no—
734#67—48no—
735C2×Dic3—28no—
736C2×Dic3—44no—
737C2×Dic3—44no—
738C2×Dic3C2518yes—
739C2×Dic3C2518yes—
740C2×Dic3C2518yes—
741D12—28no—
742D12—44no—
743D12—48no—
744D12—48no—
745C4×D3—216no—
746C4×D3—48no—
747C4×D3—416no—
748C4×D3—416no—
749Dic6—28no—
750Dic6—44no—
751Dic6—48no—
752Dic6—48no—
753C24—24no—
754C24—34no—
755C24—42no—
756C24—42no—
757C24C23×D311yescharacteristic
758C24C23×D312yes—
759C24C23×D312yes—
760C24C23×D311yescharacteristic
761C24C23×D311yescharacteristic
762#41—616no—
763#41—128no—
764#41—128no—
765#41—1216no—
766#41—1216no—
767#41—128no—
768#41—1216no—
769C2×Q8—28no—
770C2×Q8—34no—
771C2×Q8—38no—
772C2×Q8—34no—
773C2×Q8—38no—
774C2×Q8—44no—
775C2×Q8—48no—
776C2×Q8—48no—
777C2×Q8—124no—
778C2×Q8—1216no—
779C2×Q8C23×D318yes—
780C2×Q8C23×D318yes—
781C2×D4—38no—
782C2×D4—38no—
783C2×D4—38no—
784C2×D4—38no—
785C2×D4—38no—
786C2×D4—38no—
787C2×D4—34no—
788C2×D4—38no—
789C2×D4—38no—
790C2×D4—34no—
791C2×D4—616no—
792C2×D4—124no—
793C2×D4—128no—
794C2×D4—128no—
795C22×C4—24no—
796C22×C4—28no—
797C22×C4—34no—
798C22×C4—34no—
799C22×C4—34no—
800C22×C4—38no—
801C22×C4—316no—
802C22×C4—316no—
803C22×C4—38no—
804C22×C4—44no—
805C22×C4—44no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4—44no—
809C22×C4—42no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—128no—
813C22×C4C23×D312yes—
814C22×C4C23×D314yes—
815C22×C4C23×D314yes—
816C22×C4C23×D312yes—
817C22×C4C23×D312yes—
818C22×C4C23×D312yes—
819C22×C4C23×D312yes—
820C22×C4C23×D311yescharacteristic
821C22×C4C23×D312yes—
822C22×C4C23×D312yes—
823C22×C4C23×D312yes—
824C22×C4C23×D312yes—
825C22×C4C23×D314yes—
826C22×C4C23×D314yes—
827C22×C4C23×D314yes—
828C22×C4C23×D314yes—
829C22×C4C23×D311yescharacteristic
830C22×C4C23×D312yes—
831C22×C4C23×D311yescharacteristic
832C22×C4C23×D312yes—
833C22×C4C23×D312yes—
834C22×C4C23×D311yescharacteristic
835C4⋊C4—34no—
836C4⋊C4—38no—
837C4⋊C4—38no—
838C4⋊C4—34no—
839C4⋊C4—34no—
840C4⋊C4—34no—
841C4⋊C4—38no—
842C4⋊C4—38no—
843C4⋊C4—38no—
844C4⋊C4—316no—
845C4⋊C4—316no—
846C4⋊C4—38no—
847C4⋊C4—316no—
848C4⋊C4—316no—
849C4⋊C4—38no—
850C4⋊C4—38no—
851C4⋊C4C23×D318yes—
852C4⋊C4C23×D3116yes—
853C4⋊C4C23×D3116yes—
854C4⋊C4C23×D318yes—
855C22⋊C4—38no—
856C22⋊C4—38no—
857C22⋊C4—38no—
858C22⋊C4—38no—
859C22⋊C4—38no—
860C22⋊C4—38no—
861C22⋊C4—38no—
862C22⋊C4—38no—
863C22⋊C4—316no—
864C22⋊C4—316no—
865C22⋊C4—38no—
866C22⋊C4—38no—
867C22⋊C4—316no—
868C22⋊C4—316no—
869C22⋊C4C23×D3116yes—
870C22⋊C4C23×D3116yes—
871C42—38no—
872C42—38no—
873C42—316no—
874C42—316no—
875C22×C3—28no—
876C22×C3—22no—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—21no—
880C22×C3—21no—
881C22×C3—22no—
882C22×C3—21no—
883C22×C3—21no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—44no—
888C22×C3—48no—
889C22×C3—48no—
890C22×C3—44no—
891C22×C3C2×H(5,𝔽2)12yes—
892C22×C3C2×2−1+414yes—
893C22×C3C2×2−1+412yes—
894C22×C3#58512yes—
895C22×C3C2611yescharacteristic
896C2×D3—28no—
897C2×D3—28no—
898C2×D3—28no—
899C2×D3—88no—
900C3×C4—22no—
901C3×C4—28no—
902C3×C4—22no—
903C3×C4—22no—
904C3×C4—28no—
905C3×C4C2×H(5,𝔽2)14yes—
906Dic3—28no—
907Dic3—28no—
908Dic3—28no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—24no—
913C23—24no—
914C23—24no—
915C23—22no—
916C23—24no—
917C23—38no—
918C23—41no—
919C23—42no—
920C23—41no—
921C23—41no—
922C23—42no—
923C23—41no—
924C23—416no—
925C23—68no—
926C23—124no—
927C23—124no—
928C23#100714yescomplemented
929C23C24×D312yes—
930C23C24×D311yescharacteristic
931C23C24×D311yescharacteristic
932C23C24×D312yes—
933C23C24×D311yescharacteristic
934Q8—216no—
935Q8—48no—
936Q8—68no—
937Q8—128no—
938Q8—124no—
939Q8—128no—
940D4—616no—
941D4—616no—
942D4—616no—
943D4—616no—
944D4—68no—
945D4—124no—
946D4—128no—
947D4—128no—
948D4—128no—
949D4—128no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—28no—
953C2×C4—28no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—24no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—38no—
961C2×C4—38no—
962C2×C4—38no—
963C2×C4—41no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—41no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—44no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—44no—
974C2×C4—68no—
975C2×C4—616no—
976C2×C4—128no—
977C2×C4—1216no—
978C2×C4—1216no—
979C2×C4—124no—
980C2×C4—124no—
981C2×C4#100414yes—
982C2×C4C24×D312yes—
983C2×C4C24×D318yes—
984C2×C4C24×D318yes—
985C2×C4C24×D312yes—
986C2×C4C24×D312yes—
987C2×C4C24×D312yes—
988C2×C3—24no—
989C2×C3—22no—
990C2×C3—22no—
991C2×C3—22no—
992C2×C3—42no—
993C2×C3C22×H(5,𝔽2)11yescharacteristic
994C2×C3C22×2−1+411yescharacteristic
995C2×C3C2×#58511yescharacteristic
996D3—48no—
997C22—28no—
998C22—21no—
999C22—21no—
1000C22—22no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—22no—
1006C22—22no—
1007C22—22no—
1008C22—22no—
1009C22—44no—
1010C22—48no—
1011C22—48no—
1012C22—44no—
1013C22—68no—
1014C22—68no—
1015C22—68no—
1016C22—248no—
1017C22C2×#100412yes—
1018C22C2×#100714yes—
1019C22C2×#100712yes—
1020C22#596412yes—
1021C22C25×D311yescharacteristic
1022C4—22no—
1023C4—22no—
1024C4—22no—
1025C4—28no—
1026C4—28no—
1027C4—68no—
1028C4—68no—
1029C4—68no—
1030C4C2×#100414yes—
1031C3#6281911yescharacteristic, complemented, Sylow
1032C2—22no—
1033C2—22no—
1034C2—22no—
1035C2—24no—
1036C2—42no—
1037C2—128no—
1038C2C22×#100411yescharacteristic
1039C2C22×#100711yescharacteristic
1040C2C2×#596411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D3
commutator, socle, cosocleC22×C3C26
FittingC22×C3×C22⋊Q8C2
hypercenterC22×C22⋊Q8D3
hypocenterC3#62819
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. #87251C2semidirect
3. C2×#5791C2semidirect
4. #85991C2semidirect
5. #85990C2semidirect
6. #85989C2semidirect
7. #85987C2semidirect
8. #85986C2semidirect
9. #85985C2semidirect
10. #85973C2semidirect
11. #85971C2semidirect
12. #85970C2semidirect
13. #85718C2semidirect
14. #85718C2semidirect
15. #85697C2semidirect
17. C23×C3×Q8C22semidirect
19. C2×#1007C22semidirect
20. C22×#235C22semidirect
22. C2×C3×C22⋊Q8C22semidirect
23. C2×C3×C22⋊Q8C22semidirect
24. C2×C3×C22⋊Q8C22semidirect
25. C2×C3×C22⋊Q8C22semidirect
26. C2×C3×C22⋊Q8C22semidirect
27. C22×C3×C4⋊C4C22semidirect
28. C22×C3×C4⋊C4C22semidirect
31. #5817C22semidirect
32. #5817C22semidirect
33. #5816C22semidirect
34. #5816C22semidirect
35. Q8×#67C22semidirect
36. Q8×#67C22semidirect
37. #5812C22semidirect
42. #5791C22semidirect
43. #5791C22semidirect
44. #5791C22semidirect
45. #5791C22semidirect
46. #5791C22semidirect
47. #5791C22semidirect
49. C2×#930C22semidirect
50. C2×#929C22semidirect
52. C2×C4×#67C22semidirect
53. C2×#926C22semidirect
55. C2×#924C22semidirect
56. #5647C22semidirect
57. #5646C22semidirect
58. #5645C22semidirect
59. #5644C22semidirect
60. #5643C22semidirect
61. #5642C22semidirect
62. #5641C22semidirect
63. #5640C22semidirect
64. #5639C22semidirect
65. #5638C22semidirect
66. #5637C22semidirect
67. #5636C22semidirect
68. #5635C22semidirect
69. #5634C22semidirect
70. #5633C22semidirect
71. #5632C22semidirect
72. #5631C22semidirect
73. #5630C22semidirect
74. #5629C22semidirect
75. #5628C22semidirect
76. #5627C22semidirect
77. D3×C22⋊Q8C22semidirect
78. #5625C22semidirect
79. #5624C22semidirect
80. #5623C22semidirect
81. #5622C22semidirect
82. #5515C22semidirect
83. #5515C22semidirect
84. #5515C22semidirect
85. #5514C22semidirect
86. #5514C22semidirect
87. #5513C22semidirect
88. #5513C22semidirect
89. #5511C22semidirect
90. #5511C22semidirect
91. #5510C22semidirect
92. #5510C22semidirect
93. #5507C22semidirect
94. #5507C22semidirect
95. #5504C22semidirect
96. #5504C22semidirect
97. #5500C22semidirect
98. #5500C22semidirect
99. #5495C22semidirect
100. #5495C22semidirect
101. #5494C22semidirect
102. #5494C22semidirect
104. #5490C22semidirect
105. #5490C22semidirect
122. C22×C22⋊Q8D3semidirect
144. C2×#239C23semidirect
145. C2×D3×Q8C23semidirect
183. #947C23semidirect
184. #947C23semidirect
185. #946C23semidirect
186. #946C23semidirect
187. #946C23semidirect
188. #946C23semidirect
189. Q8×Dic3C23semidirect
190. Q8×Dic3C23semidirect
191. #944C23semidirect
192. #944C23semidirect
248. #898C23semidirect
249. #898C23semidirect
250. #898C23semidirect
251. #897C23semidirect
252. #897C23semidirect
253. #896C23semidirect
254. #896C23semidirect
255. #896C23semidirect
256. #895C23semidirect
257. #895C23semidirect
258. #894C23semidirect
259. #894C23semidirect
260. #894C23semidirect
261. #893C23semidirect
262. #893C23semidirect
263. #892C23semidirect
264. #892C23semidirect
265. D3×C4⋊C4C23semidirect
266. D3×C4⋊C4C23semidirect
267. #890C23semidirect
268. #890C23semidirect
269. #889C23semidirect
270. #889C23semidirect
271. #889C23semidirect
272. #888C23semidirect
273. #888C23semidirect
274. #887C23semidirect
275. #887C23semidirect
294. C23×Q8C2×D3semidirect
365. C2×C22⋊Q8C2×D3semidirect
366. C2×C22⋊Q8C2×D3semidirect
367. C2×C22⋊Q8C2×D3semidirect
368. C2×C22⋊Q8C2×D3semidirect
369. C2×C22⋊Q8C2×D3semidirect
380. C22×C4⋊C4C2×D3semidirect
381. C22×C4⋊C4C2×D3semidirect
689. C23×C32−1+4semidirect
928. C23#1007semidirect
1031. C3#62819semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
#872512
C2×#57912
#859912
#859902
#859892
#859872
#859862
#859852
#859732
#859712
#859702
#857182
#856972
#628193