Finite Group Databasebeta

← #11909739

Subgroups — #11909739

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×#559C211yesmaximal, characteristic, complemented
2#10596189C211yesmaximal, characteristic, complemented
3#10596187C211yesmaximal, characteristic, complemented
4#10596153C212yesmaximal, complemented
5#10596152C212yesmaximal, complemented
6#10596151C212yesmaximal, complemented
7#10596148C212yesmaximal, complemented
8#10596133C214yesmaximal, complemented
9#10596126C214yesmaximal, complemented
10#10596051C211yesmaximal, characteristic, complemented
11#10596050C211yesmaximal, characteristic, complemented
12C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
13Q8×#634C211yesmaximal, characteristic, complemented
14#10596022C212yesmaximal, complemented
15#10596019C212yesmaximal, complemented
16#10596017C212yesmaximal, complemented
17#10596010C212yesmaximal, complemented
18#87055—34nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3830C2212yes—
21C2×#3830C2212yes—
22C2×#3828C2214yes—
23C32×#127C2211yescharacteristic
24C32×#124C2212yes—
25C32×#124C2212yes—
26C32×#123C2214yes—
27C32×C4×Q8C2211yescharacteristic
28C32×C4×Q8C2211yescharacteristic
29C32×C4×D4C2212yes—
30C32×C4×D4C2212yes—
31#64156C2211yescharacteristic
32#64155C2212yes—
33#64155C2211yescharacteristic
34Q8×C3⋊Dic3C2212yes—
35Q8×C3⋊Dic3C2211yescharacteristic
36#64149C2212yes—
37#64148C2214yes—
38#64147C2212yes—
39#64147C2212yes—
40#64147C2212yes—
41#64145C2212yes—
42D4×C3⋊Dic3C2212yes—
43D4×C3⋊Dic3C2212yes—
44D4×C3⋊Dic3C2212yes—
45C4×#638C2214yes—
46#64133C2214yes—
47C2×#3750C2214yes—
48#64107C2212yes—
49#64105C2214yes—
50#64104C2211yescharacteristic
51#64103C2212yes—
52C4⋊C4×C3⋊D3C2212yes—
53C4⋊C4×C3⋊D3C2212yes—
54C4⋊C4×C3⋊D3C2211yescharacteristic
55#64099C2211yescharacteristic
56#64097C2214yes—
57#64097C2212yes—
58#64096C2212yes—
59#64096C2211yescharacteristic
60#64095C2214yes—
61#64094C2214yes—
62#64094C2214yes—
63#64093C2214yes—
64#64092C2214yes—
65#64092C2214yes—
66#64090C2214yes—
67#64090C2214yes—
68#64088C2214yes—
69#64087C2214yes—
70#64087C2214yes—
71#64086C2214yes—
72C4×C4⋊(C3⋊D3)C2212yes—
73C4×C4⋊(C3⋊D3)C2212yes—
74C4×C4⋊(C3⋊D3)C2211yescharacteristic
75#64081C2212yes—
76C42×C3⋊D3C2212yes—
77C42×C3⋊D3C2211yescharacteristic
78#64079C2212yes—
79#64078C2212yes—
80#64078C2211yescharacteristic
81C4×#634C2212yes—
82C4×#634C2212yes—
83C4×#634C2211yescharacteristic
84C3×#559D314yescomplemented
85#5718—34no—
86#5716—34no—
87#5682—38no—
88#5681—38no—
89#5680—38no—
90#5677—38no—
91#5662—316no—
92#5655—316no—
93#5580—34no—
94#5579—34no—
95C4×D3×Q8—34no—
96Q8×Dic6—34no—
97#5551—38no—
98#5548—38no—
99#5546—38no—
100#5539—38no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2311yescharacteristic
103C2×C32×D4C2312yes—
104C2×C32×D4C2312yes—
105C2×C32×D4C2312yes—
106C22×C32×C4C2314yes—
107C2×#638C2314yes—
108C2×#638C2314yes—
109C2×#638C2314yes—
110C22×C3⋊Dic3C2314yes—
111C22×C3⋊Dic3C2314yes—
112Q8×C3⋊D3—24no—
113#3830—28no—
114#3830—44no—
115#3828—48no—
116C2×C4⋊(C3⋊D3)C2311yescharacteristic
117C2×C4⋊(C3⋊D3)C2312yes—
118C2×C4×C3⋊D3C2311yescharacteristic
119C2×C4×C3⋊D3C2311yescharacteristic
120C2×C4×C3⋊D3C2312yes—
121C2×C4×C3⋊D3C2312yes—
122C2×C4×C3⋊D3C2311yescharacteristic
123C2×C4×C3⋊D3C2312yes—
124C2×C4×C3⋊D3C2314yes—
125C2×#634C2312yes—
126C2×#634C2314yes—
127C2×#634C2312yes—
128C2×#634C2311yescharacteristic
129C32×C4⋊C4C2311yescharacteristic
130C32×C4⋊C4C2312yes—
131C32×C4⋊C4C2311yescharacteristic
132C32×C4⋊C4C2312yes—
133C32×C22⋊C4C2314yes—
134C32×C22⋊C4C2314yes—
135C32×C22⋊C4C2314yes—
136C32×C42C2311yescharacteristic
137C32×C42C2312yes—
138C32×C42C2312yes—
139#3757C2314yes—
140#3757C2314yes—
141#3757C2314yes—
142#3752C2312yes—
143#3752C2312yes—
144#3752C2312yes—
145#3752C2312yes—
146#3752C2314yes—
147#3752C2312yes—
148C4⋊(C3⋊Dic3)C2312yes—
149C4⋊(C3⋊Dic3)C2311yescharacteristic
150C4⋊(C3⋊Dic3)C2312yes—
151C4⋊(C3⋊Dic3)C2312yes—
152C4⋊(C3⋊Dic3)C2314yes—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C4⋊(C3⋊Dic3)C2312yes—
155#3750C2314yes—
156#3750C2312yes—
157#3750C2312yes—
158#3750C2312yes—
159#3750C2314yes—
160#3750C2314yes—
161#3750C2312yes—
162#3750C2312yes—
163C4×C3⋊Dic3C2312yes—
164C4×C3⋊Dic3C2311yescharacteristic
165C4×C3⋊Dic3C2314yes—
166C4×C3⋊Dic3C2311yescharacteristic
167C4×C3⋊Dic3C2312yes—
168C4×C3⋊Dic3C2312yes—
169C4×C3⋊Dic3C2311yescharacteristic
170#3522—91noSylow
171C2×D3×Q8—34no—
172C2×#237—38no—
173C2×#237—38no—
174C2×#235—316no—
175C3×#127C2×D314yes—
176C3×#124C2×D318yes—
177C3×#124C2×D318yes—
178C3×#123C2×D3116yes—
179C3×C4×Q8C2×D314yes—
180C3×C4×Q8C2×D314yes—
181C3×C4×D4C2×D318yes—
182C3×C4×D4C2×D318yes—
183#947—34no—
184#946—38no—
185#946—34no—
186Q8×Dic3—38no—
187Q8×Dic3—34no—
188#940—38no—
189#939—316no—
190#938—38no—
191#938—38no—
192#938—38no—
193#936—38no—
194D4×Dic3—38no—
195D4×Dic3—38no—
196D4×Dic3—38no—
197C4×#67—316no—
198#924—316no—
199C2×Dic3⋊C4—316no—
200#898—38no—
201#896—316no—
202#895—34no—
203#894—38no—
204D3×C4⋊C4—38no—
205D3×C4⋊C4—38no—
206D3×C4⋊C4—34no—
207#890—34no—
208#888—316no—
209#888—38no—
210#887—38no—
211#887—34no—
212#886—316no—
213#885—316no—
214#885—316no—
215#884—316no—
216#883—316no—
217#883—316no—
218#67⋊C4—316no—
219#67⋊C4—316no—
220#879—316no—
221#878—316no—
222#878—316no—
223#877—316no—
224C4×D12—38no—
225C4×D12—38no—
226C4×D12—34no—
227#872—38no—
228C42×D3—38no—
229C42×D3—34no—
230#870—38no—
231#869—38no—
232#869—34no—
233C4×Dic6—38no—
234C4×Dic6—38no—
235C4×Dic6—34no—
236C23×C32C2414yes—
237C22×C3⋊D3C2412yes—
238C22×C3⋊D3C2411yescharacteristic
239C32×Q8—22no—
240C32×Q8—22no—
241C32×D4—24no—
242C32×D4—24no—
243C32×D4—42no—
244C2×C32×C4—44no—
245C2×C32×C4C2412yes—
246C2×C32×C4C2412yes—
247C2×C32×C4C2412yes—
248C2×C32×C4C2411yescharacteristic
249C2×C32×C4C2412yes—
250C2×C32×C4C2411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252#638—28no—
253#638—28no—
254#638—44no—
255C2×C3⋊Dic3—28no—
256C2×C3⋊Dic3—44no—
257C2×C3⋊Dic3C2411yescharacteristic
258C2×C3⋊Dic3C2411yescharacteristic
259C2×C3⋊Dic3C2412yes—
260C2×C3⋊Dic3C2411yescharacteristic
261C2×C3⋊Dic3C2414yes—
262C2×C3⋊Dic3C2412yes—
263C2×C3⋊Dic3C2412yes—
264C4⋊(C3⋊D3)—24no—
265C4⋊(C3⋊D3)—22no—
266C4×C3⋊D3—24no—
267C4×C3⋊D3—22no—
268C4×C3⋊D3—24no—
269C4×C3⋊D3—22no—
270C4×C3⋊D3—22no—
271C4×C3⋊D3—24no—
272C4×C3⋊D3—44no—
273#634—24no—
274#634—44no—
275#634—42no—
276#634#4114yescomplemented
277#559—92no—
278#559C3⋊D311yescharacteristic, complemented
279Q82—91no—
280#554—91no—
281#554—92no—
282#550—91no—
283#548—92no—
284#547—94no—
285#547—92no—
286#542—92no—
287#542—94no—
288#532—91no—
289#532—92no—
290#529—92no—
291#529—91no—
292#520—92no—
293C2×C4×Q8—91no—
294C2×C3×Q8C22×D314yes—
295C2×C3×Q8C22×D314yes—
296C2×C3×D4C22×D318yes—
297C2×C3×D4C22×D318yes—
298C2×C3×D4C22×D318yes—
299C22×C3×C4C22×D3116yes—
300C2×#67—316no—
301C2×#67—316no—
302C2×#67—316no—
303C22×Dic3—316no—
304C22×Dic3—316no—
305D3×Q8—616no—
306#237—632no—
307#237—1216no—
308#235—1232no—
309C2×D12—34no—
310C2×D12—38no—
311C2×C4×D3—34no—
312C2×C4×D3—34no—
313C2×C4×D3—38no—
314C2×C4×D3—38no—
315C2×C4×D3—34no—
316C2×C4×D3—38no—
317C2×C4×D3—316no—
318C2×Dic6—34no—
319C2×Dic6—38no—
320C2×Dic6—316no—
321C2×Dic6—38no—
322C3×C4⋊C4C22×D314yes—
323C3×C4⋊C4C22×D318yes—
324C3×C4⋊C4C22×D314yes—
325C3×C4⋊C4C22×D318yes—
326C3×C22⋊C4C22×D3116yes—
327C3×C22⋊C4C22×D3116yes—
328C3×C22⋊C4C22×D3116yes—
329C3×C42C22×D314yes—
330C3×C42C22×D318yes—
331C3×C42C22×D318yes—
332#217—316no—
333#217—316no—
334#217—316no—
335(C2×D3)⋊C4—38no—
336(C2×D3)⋊C4—38no—
337(C2×D3)⋊C4—38no—
338(C2×D3)⋊C4—38no—
339(C2×D3)⋊C4—316no—
340(C2×D3)⋊C4—38no—
341C4⋊Dic3—38no—
342C4⋊Dic3—34no—
343C4⋊Dic3—38no—
344C4⋊Dic3—38no—
345C4⋊Dic3—316no—
346C4⋊Dic3—34no—
347C4⋊Dic3—38no—
348Dic3⋊C4—316no—
349Dic3⋊C4—38no—
350Dic3⋊C4—38no—
351Dic3⋊C4—38no—
352Dic3⋊C4—316no—
353Dic3⋊C4—316no—
354Dic3⋊C4—38no—
355Dic3⋊C4—38no—
356C4×Dic3—38no—
357C4×Dic3—34no—
358C4×Dic3—316no—
359C4×Dic3—34no—
360C4×Dic3—38no—
361C4×Dic3—38no—
362C4×Dic3—34no—
363C22×C32—24no—
364C22×C32—24no—
365C22×C32—24no—
366C22×C32C2511yescharacteristic
367C2×C3⋊D3—21no—
368C2×C3⋊D3—21no—
369C2×C3⋊D3—22no—
370C2×C3⋊D3—22no—
371C2×C3⋊D3—22no—
372C2×C3⋊D3H(5,𝔽2)12yes—
373C32×C4—22no—
374C32×C4—21no—
375C32×C4—22no—
376C32×C4—22no—
377C32×C4—22no—
378C32×C4C2×#4112yes—
379C32×C42−1+412yes—
380C3⋊Dic3—21no—
381C3⋊Dic3—22no—
382C3⋊Dic3—22no—
383C3⋊Dic3—24no—
384C3⋊Dic3—21no—
385C3⋊Dic3—21no—
386C3⋊Dic3C2×#4114yes—
387C2×#41—92no—
388C2×#41—92no—
389C2×#41—94no—
390C22×Q8—91no—
391C4⋊Q8—92no—
392C4⋊Q8—94no—
393C4⋊Q8—91no—
394C4⋊Q8—92no—
395#127—92no—
396#127C2×C3⋊D311yescharacteristic
397#126—92no—
398#126—94no—
399#125—91no—
400#125—92no—
401#124—91no—
402#124—92no—
403#124—94no—
404#124—94no—
405#124C2×C3⋊D312yes—
406#124C2×C3⋊D312yes—
407#123—92no—
408#123—94no—
409#123—94no—
410#123—94no—
411#123C2×C3⋊D314yes—
412C22⋊Q8—91no—
413C22⋊Q8—92no—
414C22⋊Q8—94no—
415C22⋊Q8—94no—
416C22⋊Q8—94no—
417C22⋊Q8—94no—
418#121—92no—
419#121—92no—
420#121—92no—
421#121—94no—
422#121—91no—
423#121—94no—
424C4×Q8—91no—
425C4×Q8—92no—
426C4×Q8—91no—
427C4×Q8—92no—
428C4×Q8—91no—
429C4×Q8—92no—
430C4×Q8—92no—
431C4×Q8C2×C3⋊D311yescharacteristic
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—91no—
441C4×D4—92no—
442C4×D4C2×C3⋊D312yes—
443C4×D4C2×C3⋊D312yes—
444#117—94no—
445#117—92no—
446C2×C4⋊C4—94no—
447C2×C4⋊C4—92no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—92no—
450C2×C42—91no—
451C2×C42—92no—
452C23×C3C23×D3116yes—
453C22×D3—34no—
454C22×D3—38no—
455C3×Q8—28no—
456C3×Q8—28no—
457C3×D4—216no—
458C3×D4—216no—
459C3×D4—48no—
460C2×C3×C4—416no—
461C2×C3×C4C23×D318yes—
462C2×C3×C4C23×D318yes—
463C2×C3×C4C23×D318yes—
464C2×C3×C4C23×D314yes—
465C2×C3×C4C23×D318yes—
466C2×C3×C4C23×D314yes—
467C2×C3×C4C23×D314yes—
468#67—632no—
469#67—632no—
470#67—1216no—
471C2×Dic3—38no—
472C2×Dic3—34no—
473C2×Dic3—34no—
474C2×Dic3—38no—
475C2×Dic3—34no—
476C2×Dic3—316no—
477C2×Dic3—38no—
478C2×Dic3—632no—
479C2×Dic3—1216no—
480D12—616no—
481D12—68no—
482C4×D3—616no—
483C4×D3—616no—
484C4×D3—68no—
485C4×D3—616no—
486C4×D3—68no—
487C4×D3—68no—
488C4×D3—1216no—
489Dic6—316no—
490Dic6—616no—
491Dic6—1216no—
492Dic6—128no—
493C2×C32—44no—
494C2×C32C22×#4111yescharacteristic
495C2×C32C2×H(5,𝔽2)11yescharacteristic
496C2×C32C2×2−1+411yescharacteristic
497C3⋊D3—22no—
498C3⋊D3—42no—
499#41—188no—
500#41—368no—
501#41—364no—
502C2×Q8—91no—
503C2×Q8—92no—
504C2×Q8—94no—
505C2×Q8—92no—
506C2×Q8—184no—
507C2×Q8C22×C3⋊D311yescharacteristic
508C2×Q8C22×C3⋊D311yescharacteristic
509C2×D4—94no—
510C2×D4—94no—
511C2×D4—94no—
512C2×D4—91no—
513C2×D4—92no—
514C2×D4C22×C3⋊D312yes—
515C2×D4C22×C3⋊D312yes—
516C2×D4C22×C3⋊D312yes—
517C22×C4—94no—
518C22×C4—94no—
519C22×C4—91no—
520C22×C4—91no—
521C22×C4—92no—
522C22×C4—92no—
523C22×C4—91no—
524C22×C4—92no—
525C22×C4—94no—
526C22×C4C22×C3⋊D314yes—
527C4⋊C4—92no—
528C4⋊C4—92no—
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—91no—
538C4⋊C4—92no—
539C4⋊C4—94no—
540C4⋊C4—92no—
541C4⋊C4—94no—
542C4⋊C4C22×C3⋊D311yescharacteristic
543C4⋊C4C22×C3⋊D312yes—
544C4⋊C4C22×C3⋊D311yescharacteristic
545C4⋊C4C22×C3⋊D312yes—
546C22⋊C4—94no—
547C22⋊C4—94no—
548C22⋊C4—94no—
549C22⋊C4—92no—
550C22⋊C4—92no—
551C22⋊C4—92no—
552C22⋊C4—92no—
553C22⋊C4—94no—
554C22⋊C4—92no—
555C22⋊C4C22×C3⋊D314yes—
556C22⋊C4C22×C3⋊D314yes—
557C22⋊C4C22×C3⋊D314yes—
558C42—92no—
559C42—91no—
560C42—91no—
561C42—92no—
562C42—91no—
563C42—92no—
564C42—94no—
565C42C22×C3⋊D312yes—
566C42C22×C3⋊D311yescharacteristic
567C42C22×C3⋊D312yes—
568C22×C3—216no—
569C22×C3—216no—
570C22×C3—216no—
571C22×C3C24×D314yes—
572C2×D3—38no—
573C2×D3—64no—
574C2×D3—64no—
575C2×D3—68no—
576C2×D3—68no—
577C2×D3—68no—
578C3×C4—28no—
579C3×C4—28no—
580C3×C4—24no—
581C3×C4—28no—
582C3×C4—28no—
583C3×C4D3×#4118yes—
584C3×C4#101018yes—
585Dic3—316no—
586Dic3—64no—
587Dic3—68no—
588Dic3—64no—
589Dic3—68no—
590Dic3—616no—
591Dic3—64no—
592C32#352211yescharacteristic, complemented, Sylow
593C23—91no—
594C23—92no—
595C23C23×C3⋊D314yes—
596Q8—22no—
597Q8—22no—
598Q8—94no—
599Q8—184no—
600Q8—364no—
601Q8—362no—
602D4—24no—
603D4—24no—
604D4—42no—
605D4—184no—
606D4—188no—
607D4—188no—
608D4—182no—
609D4—364no—
610C2×C4—44no—
611C2×C4—92no—
612C2×C4—91no—
613C2×C4—91no—
614C2×C4—91no—
615C2×C4—92no—
616C2×C4—94no—
617C2×C4—92no—
618C2×C4—184no—
619C2×C4—184no—
620C2×C4—182no—
621C2×C4—188no—
622C2×C4—182no—
623C2×C4—184no—
624C2×C4—182no—
625C2×C4—364no—
626C2×C4—364no—
627C2×C4C23×C3⋊D312yes—
628C2×C4C23×C3⋊D312yes—
629C2×C4C23×C3⋊D311yescharacteristic
630C2×C4C23×C3⋊D312yes—
631C2×C4C23×C3⋊D312yes—
632C2×C4C23×C3⋊D311yescharacteristic
633C2×C4C23×C3⋊D311yescharacteristic
634C2×C3—416no—
635C2×C3C2×D3×#4114yes—
636C2×C3C2×#101014yes—
637C2×C3D3×H(5,𝔽2)14yes—
638D3—68no—
639D3—128no—
640C22—24no—
641C22—24no—
642C22—24no—
643C22—92no—
644C22—181no—
645C22—181no—
646C22—182no—
647C22—182no—
648C22—182no—
649C22C24×C3⋊D311yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—22no—
654C4—21no—
655C4—94no—
656C4—182no—
657C4—181no—
658C4—181no—
659C4—181no—
660C4—182no—
661C4—184no—
662C4#41×C3⋊D312yes—
663C4#6436712yes—
664C3#8705514yescomplemented
665C2—44no—
666C2—182no—
667C2—362no—
668C2C2×#41×C3⋊D311yescharacteristic
669C2C2×#6436711yescharacteristic
670C2C3⋊D3×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#559C2
hypercenter#559C3⋊D3
hypocenterC32#3522
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #559

Complements

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

NH ≅ G/Ntype
1. C32×#559C2semidirect
2. #10596189C2semidirect
3. #10596187C2semidirect
4. #10596153C2semidirect
5. #10596152C2semidirect
6. #10596151C2semidirect
7. #10596148C2semidirect
8. #10596133C2semidirect
9. #10596126C2semidirect
10. #10596051C2semidirect
11. #10596050C2semidirect
12. C4×Q8×C3⋊D3C2semidirect
13. Q8×#634C2semidirect
14. #10596022C2semidirect
15. #10596019C2semidirect
16. #10596017C2semidirect
17. #10596010C2semidirect
84. C3×#559D3semidirect
276. #634#41semidirect
278. #559C3⋊D3semidirect
592. C32#3522semidirect
664. C3#87055semidirect

Maximal subgroups

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

subgroupindex
C32×#5592
#105961892
#105961872
#105961532
#105961522
#105961512
#105961482
#105961332
#105961262
#105960512
#105960502
C4×Q8×C3⋊D32
Q8×#6342
#105960222
#105960192
#105960172
#105960102
#870553