Finite Group Databasebeta

← #11909742

Subgroups — #11909742

Order 1152.

3312 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#529C211yesmaximal, characteristic, complemented
2#10596181C214yesmaximal, complemented
3#10596161C212yesmaximal, complemented
4#10596152C212yesmaximal, complemented
5#10596126C214yesmaximal, complemented
6#10596095C212yesmaximal, complemented
7#10596067C212yesmaximal, complemented
8#10596056C211yesmaximal, characteristic, complemented
9Q8×#634C211yesmaximal, characteristic, complemented
10#10596026C212yesmaximal, complemented
11#10596024C211yesmaximal, characteristic, complemented
12#10596023C212yesmaximal, complemented
13#10596014C211yesmaximal, characteristic, complemented
14#10596005C212yesmaximal, complemented
15#10595994C212yesmaximal, complemented
16#10595948C211yesmaximal, characteristic, complemented
17C2×C4×#634C211yesmaximal, characteristic, complemented
18#86128—34nomaximal
19C2×#3830C2214yes—
20C2×#3828C2212yes—
21C2×#3828C2212yes—
22C22×#634C2211yescharacteristic
23C32×#126C2212yes—
24C32×#125C2211yescharacteristic
25C32×#124C2211yescharacteristic
26C32×#123C2212yes—
27C32×C22⋊Q8C2211yescharacteristic
28C32×#121C2211yescharacteristic
29C32×C4×Q8C2211yescharacteristic
30C32×C4×D4C2211yescharacteristic
31C32×C4×D4C2212yes—
32C32×#117C2212yes—
33C2×C32×C42C2211yescharacteristic
34#64156C2212yes—
35Q8×C3⋊Dic3C2212yes—
36#64149C2212yes—
37#64148C2214yes—
38D4×C3⋊Dic3C2212yes—
39#64139C2212yes—
40#64139C2212yes—
41#64139C2212yes—
42C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
43C2×C4⋊(C3⋊Dic3)C2212yes—
44#64133C2212yes—
45C2×#3750C2212yes—
46C2×C4×C3⋊Dic3C2212yes—
47#64107C2214yes—
48#64106C2214yes—
49#64105C2214yes—
50#64105C2214yes—
51#64103C2214yes—
52#64102C2212yes—
53#64102C2212yes—
54#64101C2214yes—
55C4⋊C4×C3⋊D3C2214yes—
56#64099C2212yes—
57#64097C2214yes—
58#64097C2212yes—
59#64095C2214yes—
60#64095C2214yes—
61#64094C2214yes—
62#64094C2214yes—
63#64093C2214yes—
64#64092C2214yes—
65#64090C2214yes—
66#64090C2214yes—
67#64090C2214yes—
68#64087C2214yes—
69#64084C2212yes—
70#64084C2212yes—
71#64083C2211yescharacteristic
72C4×C4⋊(C3⋊D3)C2212yes—
73C4×C4⋊(C3⋊D3)C2212yes—
74C4×C4⋊(C3⋊D3)C2212yes—
75#64078C2211yescharacteristic
76#64078C2212yes—
77C4×#634C2212yes—
78C4×#634C2212yes—
79C4×#634C2211yescharacteristic
80C4×#634C2211yescharacteristic
81C4×#634C2211yescharacteristic
82C4×#634C2211yescharacteristic
83C4×#634C2212yes—
84C3×#529D314yescomplemented
85#5710—316no—
86#5690—38no—
87#5681—38no—
88#5655—316no—
89#5624—38no—
90#5596—38no—
91#5585—34no—
92Q8×Dic6—34no—
93#5555—38no—
94#5553—34no—
95#5552—38no—
96#5543—34no—
97#5534—38no—
98#5523—38no—
99#5477—34no—
100C2×C4×Dic6—34no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×D4C2312yes—
103C2×C32×D4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C22×C32×C4C2312yes—
107C22×C32×C4C2311yescharacteristic
108C2×#638C2314yes—
109C2×#638C2314yes—
110C2×#638C2314yes—
111C22×C3⋊Dic3C2312yes—
112C22×C3⋊Dic3C2312yes—
113C22×C3⋊Dic3C2314yes—
114#3830—48no—
115#3828—28no—
116#3828—44no—
117C2×C4⋊(C3⋊D3)C2312yes—
118C2×C4⋊(C3⋊D3)C2312yes—
119C2×C4⋊(C3⋊D3)C2312yes—
120C2×C4×C3⋊D3C2314yes—
121C2×C4×C3⋊D3C2314yes—
122C2×C4×C3⋊D3C2314yes—
123C2×#634—24no—
124C2×#634C2311yescharacteristic
125C2×#634C2312yes—
126C2×#634C2312yes—
127C2×#634C2314yes—
128C2×#634C2311yescharacteristic
129C32×C4⋊C4C2311yescharacteristic
130C32×C4⋊C4C2312yes—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2312yes—
133C32×C4⋊C4C2312yes—
134C32×C4⋊C4C2312yes—
135C32×C22⋊C4C2312yes—
136C32×C22⋊C4C2312yes—
137C32×C22⋊C4C2312yes—
138C32×C22⋊C4C2312yes—
139C32×C22⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141C32×C42C2311yescharacteristic
142C32×C42C2311yescharacteristic
143C32×C42C2311yescharacteristic
144C32×C42C2312yes—
145#3757C2314yes—
146#3752C2314yes—
147#3752C2314yes—
148#3752C2314yes—
149#3752C2314yes—
150#3752C2314yes—
151#3752C2314yes—
152C4⋊(C3⋊Dic3)C2311yescharacteristic
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C4⋊(C3⋊Dic3)C2312yes—
155C4⋊(C3⋊Dic3)C2312yes—
156C4⋊(C3⋊Dic3)C2312yes—
157C4⋊(C3⋊Dic3)C2314yes—
158C4⋊(C3⋊Dic3)C2314yes—
159#3750C2312yes—
160#3750C2312yes—
161#3750C2312yes—
162#3750C2312yes—
163#3750C2314yes—
164#3750C2314yes—
165C4×C3⋊Dic3C2312yes—
166C4×C3⋊Dic3C2312yes—
167C4×C3⋊Dic3C2312yes—
168C4×C3⋊Dic3C2312yes—
169C4×C3⋊Dic3C2314yes—
170#3522—91noSylow
171C2×#237—316no—
172C2×#235—38no—
173C2×#235—38no—
174C22×Dic6—34no—
175C3×#126C2×D318yes—
176C3×#125C2×D314yes—
177C3×#124C2×D314yes—
178C3×#123C2×D318yes—
179C3×C22⋊Q8C2×D314yes—
180C3×#121C2×D314yes—
181C3×C4×Q8C2×D314yes—
182C3×C4×D4C2×D314yes—
183C3×C4×D4C2×D318yes—
184C3×#117C2×D318yes—
185C2×C3×C42C2×D314yes—
186#947—38no—
187Q8×Dic3—38no—
188#940—38no—
189#939—316no—
190D4×Dic3—38no—
191#930—38no—
192#930—38no—
193#930—38no—
194C2×C4⋊Dic3—34no—
195C2×C4⋊Dic3—38no—
196#924—38no—
197C2×Dic3⋊C4—38no—
198C2×C4×Dic3—38no—
199#898—316no—
200#897—316no—
201#896—316no—
202#896—316no—
203#894—316no—
204#893—38no—
205#893—38no—
206#892—316no—
207D3×C4⋊C4—316no—
208#890—38no—
209#888—316no—
210#888—38no—
211#886—316no—
212#886—316no—
213#885—316no—
214#885—316no—
215#884—316no—
216#883—316no—
217#67⋊C4—316no—
218#67⋊C4—316no—
219#67⋊C4—316no—
220#878—316no—
221#875—38no—
222#875—38no—
223#874—34no—
224C4×D12—38no—
225C4×D12—38no—
226C4×D12—38no—
227#869—34no—
228#869—38no—
229C4×Dic6—38no—
230C4×Dic6—38no—
231C4×Dic6—34no—
232C4×Dic6—34no—
233C4×Dic6—34no—
234C4×Dic6—34no—
235C4×Dic6—38no—
236C23×C32C2412yes—
237C23×C32C2411yescharacteristic
238C22×C3⋊D3C2414yes—
239C32×Q8—22no—
240C32×D4—24no—
241C32×D4—22no—
242C2×C32×C4—22no—
243C2×C32×C4—22no—
244C2×C32×C4—24no—
245C2×C32×C4—22no—
246C2×C32×C4C2411yescharacteristic
247C2×C32×C4C2412yes—
248C2×C32×C4C2411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C32×C4C2412yes—
251C2×C32×C4C2412yes—
252C2×C32×C4C2411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254C2×C32×C4C2411yescharacteristic
255#638—28no—
256#638—28no—
257#638—44no—
258C2×C3⋊Dic3—24no—
259C2×C3⋊Dic3—24no—
260C2×C3⋊Dic3—44no—
261C2×C3⋊Dic3C2412yes—
262C2×C3⋊Dic3C2412yes—
263C2×C3⋊Dic3C2412yes—
264C2×C3⋊Dic3C2414yes—
265C2×C3⋊Dic3C2412yes—
266C4⋊(C3⋊D3)—24no—
267C4⋊(C3⋊D3)—24no—
268C4⋊(C3⋊D3)—42no—
269C4×C3⋊D3—28no—
270C4×C3⋊D3—44no—
271C4×C3⋊D3—44no—
272#634—22no—
273#634—24no—
274#634—42no—
275#634—44no—
276#634#4114yescomplemented
277#559—92no—
278#559—91no—
279Q82—91no—
280#554—92no—
281#554—91no—
282#550—91no—
283#548—92no—
284#547—94no—
285#547—92no—
286#542—94no—
287#542—92no—
288#532—92no—
289#532—91no—
290#529—92no—
291#529C3⋊D311yescharacteristic, complemented
292#520—92no—
293C2×C4×Q8—91no—
294C2×C3×Q8C22×D314yes—
295C2×C3×D4C22×D314yes—
296C2×C3×D4C22×D318yes—
297C22×C3×C4C22×D314yes—
298C22×C3×C4C22×D314yes—
299C22×C3×C4C22×D318yes—
300C22×C3×C4C22×D314yes—
301C2×#67—316no—
302C2×#67—316no—
303C2×#67—316no—
304C22×Dic3—38no—
305C22×Dic3—38no—
306C22×Dic3—316no—
307#237—1232no—
308#235—632no—
309#235—1216no—
310C2×D12—38no—
311C2×D12—38no—
312C2×D12—38no—
313C2×C4×D3—316no—
314C2×C4×D3—316no—
315C2×C4×D3—316no—
316C2×Dic6—34no—
317C2×Dic6—34no—
318C2×Dic6—38no—
319C2×Dic6—38no—
320C2×Dic6—316no—
321C2×Dic6—616no—
322C3×C4⋊C4C22×D314yes—
323C3×C4⋊C4C22×D318yes—
324C3×C4⋊C4C22×D314yes—
325C3×C4⋊C4C22×D318yes—
326C3×C4⋊C4C22×D318yes—
327C3×C4⋊C4C22×D318yes—
328C3×C22⋊C4C22×D318yes—
329C3×C22⋊C4C22×D318yes—
330C3×C22⋊C4C22×D318yes—
331C3×C22⋊C4C22×D318yes—
332C3×C22⋊C4C22×D318yes—
333C3×C42C22×D314yes—
334C3×C42C22×D314yes—
335C3×C42C22×D314yes—
336C3×C42C22×D314yes—
337C3×C42C22×D318yes—
338#217—316no—
339(C2×D3)⋊C4—316no—
340(C2×D3)⋊C4—316no—
341(C2×D3)⋊C4—316no—
342(C2×D3)⋊C4—316no—
343(C2×D3)⋊C4—316no—
344(C2×D3)⋊C4—316no—
345C4⋊Dic3—34no—
346C4⋊Dic3—34no—
347C4⋊Dic3—38no—
348C4⋊Dic3—38no—
349C4⋊Dic3—38no—
350C4⋊Dic3—316no—
351C4⋊Dic3—316no—
352Dic3⋊C4—38no—
353Dic3⋊C4—38no—
354Dic3⋊C4—38no—
355Dic3⋊C4—38no—
356Dic3⋊C4—316no—
357Dic3⋊C4—316no—
358C4×Dic3—38no—
359C4×Dic3—38no—
360C4×Dic3—38no—
361C4×Dic3—38no—
362C4×Dic3—316no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32H(5,𝔽2)12yes—
369C22×C32C2511yescharacteristic
370C2×C3⋊D3—24no—
371C2×C3⋊D3—24no—
372C2×C3⋊D3—24no—
373C32×C4—21no—
374C32×C4—22no—
375C32×C4—22no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—21no—
379C32×C4—22no—
380C32×C4C2×#4112yes—
381C32×C42−1+412yes—
382C3⋊Dic3—22no—
383C3⋊Dic3—24no—
384C3⋊Dic3—22no—
385C3⋊Dic3—22no—
386C3⋊Dic3C2×#4114yes—
387C2×#41—94no—
388C2×#41—92no—
389C2×#41—92no—
390C22×Q8—91no—
391C4⋊Q8—92no—
392C4⋊Q8—94no—
393C4⋊Q8—91no—
394C4⋊Q8—92no—
395#127—92no—
396#127—91no—
397#126—94no—
398#126C2×C3⋊D312yes—
399#125—92no—
400#125C2×C3⋊D311yescharacteristic
401#124—92no—
402#124—94no—
403#124—94no—
404#124—92no—
405#124—92no—
406#124C2×C3⋊D311yescharacteristic
407#123—94no—
408#123—94no—
409#123—94no—
410#123—94no—
411#123C2×C3⋊D312yes—
412C22⋊Q8—92no—
413C22⋊Q8—94no—
414C22⋊Q8—94no—
415C22⋊Q8—94no—
416C22⋊Q8—94no—
417C22⋊Q8C2×C3⋊D311yescharacteristic
418#121—94no—
419#121—92no—
420#121—92no—
421#121—92no—
422#121—94no—
423#121C2×C3⋊D311yescharacteristic
424C4×Q8—92no—
425C4×Q8—91no—
426C4×Q8—92no—
427C4×Q8—91no—
428C4×Q8—91no—
429C4×Q8—91no—
430C4×Q8—92no—
431C4×Q8—92no—
432C4×Q8C2×C3⋊D311yescharacteristic
433C4×D4—92no—
434C4×D4—92no—
435C4×D4—92no—
436C4×D4—94no—
437C4×D4—94no—
438C4×D4—94no—
439C4×D4—92no—
440C4×D4—92no—
441C4×D4—92no—
442C4×D4C2×C3⋊D312yes—
443C4×D4C2×C3⋊D311yescharacteristic
444#117—94no—
445#117C2×C3⋊D312yes—
446C2×C4⋊C4—92no—
447C2×C4⋊C4—91no—
448C2×C4⋊C4—92no—
449C2×C4⋊C4—94no—
450C2×C42—92no—
451C2×C42C2×C3⋊D311yescharacteristic
452C23×C3C23×D318yes—
453C23×C3C23×D314yes—
454C22×D3—316no—
455C3×Q8—28no—
456C3×D4—216no—
457C3×D4—28no—
458C2×C3×C4—28no—
459C2×C3×C4—28no—
460C2×C3×C4—216no—
461C2×C3×C4—28no—
462C2×C3×C4C23×D314yes—
463C2×C3×C4C23×D318yes—
464C2×C3×C4C23×D314yes—
465C2×C3×C4C23×D314yes—
466C2×C3×C4C23×D318yes—
467C2×C3×C4C23×D318yes—
468C2×C3×C4C23×D314yes—
469C2×C3×C4C23×D314yes—
470C2×C3×C4C23×D314yes—
471#67—632no—
472#67—632no—
473#67—1216no—
474C2×Dic3—38no—
475C2×Dic3—38no—
476C2×Dic3—38no—
477C2×Dic3—38no—
478C2×Dic3—316no—
479C2×Dic3—616no—
480C2×Dic3—616no—
481C2×Dic3—1216no—
482D12—616no—
483D12—616no—
484D12—128no—
485C4×D3—632no—
486C4×D3—1216no—
487C4×D3—1216no—
488Dic6—316no—
489Dic6—616no—
490Dic6—68no—
491Dic6—128no—
492Dic6—1216no—
493C2×C32—22no—
494C2×C32—42no—
495C2×C32C22×#4111yescharacteristic
496C2×C32C2×H(5,𝔽2)11yescharacteristic
497C2×C32C2×2−1+411yescharacteristic
498C3⋊D3—44no—
499#41—188no—
500#41—364no—
501#41—368no—
502C2×Q8—91no—
503C2×Q8—92no—
504C2×Q8—91no—
505C2×Q8—94no—
506C2×Q8—92no—
507C2×Q8—184no—
508C2×Q8C22×C3⋊D311yescharacteristic
509C2×D4—94no—
510C2×D4—94no—
511C2×D4—94no—
512C2×D4—92no—
513C2×D4—92no—
514C2×D4—92no—
515C2×D4C22×C3⋊D311yescharacteristic
516C2×D4C22×C3⋊D312yes—
517C22×C4—92no—
518C22×C4—92no—
519C22×C4—94no—
520C22×C4—94no—
521C22×C4—94no—
522C22×C4—94no—
523C22×C4C22×C3⋊D311yescharacteristic
524C22×C4C22×C3⋊D311yescharacteristic
525C22×C4C22×C3⋊D311yescharacteristic
526C22×C4C22×C3⋊D312yes—
527C4⋊C4—92no—
528C4⋊C4—91no—
529C4⋊C4—94no—
530C4⋊C4—94no—
531C4⋊C4—92no—
532C4⋊C4—92no—
533C4⋊C4—91no—
534C4⋊C4—92no—
535C4⋊C4—92no—
536C4⋊C4—92no—
537C4⋊C4—92no—
538C4⋊C4—94no—
539C4⋊C4—94no—
540C4⋊C4C22×C3⋊D312yes—
541C4⋊C4C22×C3⋊D312yes—
542C4⋊C4C22×C3⋊D311yescharacteristic
543C4⋊C4C22×C3⋊D311yescharacteristic
544C4⋊C4C22×C3⋊D312yes—
545C4⋊C4C22×C3⋊D312yes—
546C22⋊C4—94no—
547C22⋊C4—94no—
548C22⋊C4—94no—
549C22⋊C4—94no—
550C22⋊C4—94no—
551C22⋊C4—94no—
552C22⋊C4—94no—
553C22⋊C4C22×C3⋊D312yes—
554C22⋊C4C22×C3⋊D312yes—
555C22⋊C4C22×C3⋊D312yes—
556C22⋊C4C22×C3⋊D312yes—
557C22⋊C4C22×C3⋊D312yes—
558C42—92no—
559C42—92no—
560C42—92no—
561C42—92no—
562C42—94no—
563C42C22×C3⋊D311yescharacteristic
564C42C22×C3⋊D311yescharacteristic
565C42C22×C3⋊D311yescharacteristic
566C42C22×C3⋊D311yescharacteristic
567C42C22×C3⋊D312yes—
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—28no—
571C22×C3—28no—
572C22×C3—28no—
573C22×C3#100918yes—
574C22×C3C24×D314yes—
575C2×D3—616no—
576C2×D3—616no—
577C2×D3—616no—
578C3×C4—24no—
579C3×C4—28no—
580C3×C4—28no—
581C3×C4—24no—
582C3×C4—24no—
583C3×C4—24no—
584C3×C4—28no—
585C3×C4D3×#4118yes—
586C3×C4#101018yes—
587Dic3—316no—
588Dic3—68no—
589Dic3—616no—
590Dic3—68no—
591Dic3—68no—
592C32#352211yescharacteristic, complemented, Sylow
593C23—94no—
594C23C23×C3⋊D312yes—
595C23C23×C3⋊D311yescharacteristic
596Q8—22no—
597Q8—94no—
598Q8—184no—
599Q8—182no—
600Q8—362no—
601Q8—364no—
602D4—24no—
603D4—22no—
604D4—188no—
605D4—188no—
606D4—184no—
607D4—184no—
608D4—362no—
609D4—364no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—92no—
615C2×C4—92no—
616C2×C4—92no—
617C2×C4—92no—
618C2×C4—94no—
619C2×C4—188no—
620C2×C4—184no—
621C2×C4—184no—
622C2×C4—364no—
623C2×C4—364no—
624C2×C4—364no—
625C2×C4C23×C3⋊D311yescharacteristic
626C2×C4C23×C3⋊D312yes—
627C2×C4C23×C3⋊D311yescharacteristic
628C2×C4C23×C3⋊D311yescharacteristic
629C2×C4C23×C3⋊D311yescharacteristic
630C2×C4C23×C3⋊D312yes—
631C2×C4C23×C3⋊D312yes—
632C2×C4C23×C3⋊D311yescharacteristic
633C2×C4C23×C3⋊D311yescharacteristic
634C2×C3—28no—
635C2×C3—48no—
636C2×C3C2×D3×#4114yes—
637C2×C3C2×#100914yes—
638C2×C3C2×#101014yes—
639D3—1216no—
640C22—21no—
641C22—21no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—184no—
646C22—184no—
647C22—184no—
648C22#6436612yes—
649C22C24×C3⋊D311yescharacteristic
650C4—22no—
651C4—21no—
652C4—21no—
653C4—21no—
654C4—22no—
655C4—21no—
656C4—22no—
657C4—94no—
658C4—182no—
659C4—182no—
660C4—182no—
661C4—184no—
662C4#41×C3⋊D312yes—
663C4#6436712yes—
664C3#8612814yescomplemented
665C2—22no—
666C2—42no—
667C2—364no—
668C2C2×#41×C3⋊D311yescharacteristic
669C2C2×#6436611yescharacteristic
670C2C2×#6436711yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#529C2
hypercenter#529C3⋊D3
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #529

Complements

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

NH ≅ G/Ntype
1. C32×#529C2semidirect
2. #10596181C2semidirect
3. #10596161C2semidirect
4. #10596152C2semidirect
5. #10596126C2semidirect
6. #10596095C2semidirect
7. #10596067C2semidirect
8. #10596056C2semidirect
9. Q8×#634C2semidirect
10. #10596026C2semidirect
11. #10596024C2semidirect
12. #10596023C2semidirect
13. #10596014C2semidirect
14. #10596005C2semidirect
15. #10595994C2semidirect
16. #10595948C2semidirect
17. C2×C4×#634C2semidirect
84. C3×#529D3semidirect
276. #634#41semidirect
291. #529C3⋊D3semidirect
592. C32#3522semidirect
664. C3#86128semidirect

Maximal subgroups

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

subgroupindex
C32×#5292
#105961812
#105961612
#105961522
#105961262
#105960952
#105960672
#105960562
Q8×#6342
#105960262
#105960242
#105960232
#105960142
#105960052
#105959942
#105959482
C2×C4×#6342
#861283