Finite Group Databasebeta

← #11909861

Subgroups — #11909861

Order 1152.

2976 conjugacy classes of subgroups.

The subgroup lattice has 633 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#557C211yesmaximal, characteristic, complemented
2#10596202C212yesmaximal, complemented
3#10596199C211yesmaximal, characteristic, complemented
4#10596198C211yesmaximal, characteristic, complemented
5#10596198C212yesmaximal, complemented
6#10596167C214yesmaximal, complemented
7#10596164C214yesmaximal, complemented
8#10596162C212yesmaximal
9#10596156C212yesmaximal, complemented
10#10596055C211yesmaximal, characteristic, complemented
11#10596052C212yesmaximal, complemented
12#10596051C211yesmaximal, characteristic
13#10596049C212yesmaximal, complemented
14#10596043C212yesmaximal, complemented
15C4×Q8×C3⋊D3C211yesmaximal, characteristic, complemented
16#10596039C212yesmaximal, complemented
17#10596038C211yesmaximal, characteristic, complemented
18#87025—34nomaximal
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×Q8×C3⋊D3C2212yes—
21C32×C4⋊Q8C2211yescharacteristic
22C32×C4⋊Q8C2212yes—
23C32×#125C2212yes—
24C32×#125C2214yes—
25C32×C4×Q8C2211yescharacteristic
26C32×C4×Q8C2212yes—
27C32×C4×Q8C2211yescharacteristic
28C32×C4×Q8C2212yes—
29#64156C2211yescharacteristic
30#64155C2212yes—
31#64155C2212yes—
32#64155C2212yes—
33#64155C2211yescharacteristic
34Q8×C3⋊Dic3C2212yes—
35Q8×C3⋊Dic3C2211yescharacteristic
36#64153C2212yes—
37#64107C2214yes—
38#64107C2214yes—
39#64107C2214yes—
40#64107C2212yes—
41#64106C2212yes—
42#64105C2214yes—
43#64105C2214yes—
44#64105C2214yes—
45#64104C2211yescharacteristic
46#64103C2214yes—
47#64103C2212yes—
48#64102C2214yes—
49#64102C2212yes—
50#64101C2214yes—
51#64101C2212yes—
52#64101C2212yes—
53C4⋊C4×C3⋊D3C2212yes—
54C4⋊C4×C3⋊D3C2211yescharacteristic
55#64099C2211yescharacteristic
56#64099C2212yes—
57#64098C2214yes—
58#64098C2214yes—
59#64098C2214yes—
60#64098C2214yes—
61#64097C2214yes—
62#64097C2212yes—
63#64096C2212yes—
64#64096C2214yes—
65#64096C2212yes—
66#64096C2212yes—
67#64096C2211yescharacteristic
68#64085C2214yes—
69#64084C2212yes—
70C4×C4⋊(C3⋊D3)C2212yes—
71C4×C4⋊(C3⋊D3)C2211yescharacteristic
72#64081C2214yes—
73#64081C2214yes—
74#64081C2212yes—
75C42×C3⋊D3C2212yes—
76C42×C3⋊D3C2211yescharacteristic
77#64079C2212yes—
78#64078C2211yescharacteristic
79C4×#634C2212yes—
80C4×#634C2212yes—
81C4×#634C2214yes—
82C4×#634C2211yescharacteristic
83C4×#634C2212yes—
84C3×#557D314yescomplemented
85#5731—38no—
86#5728—34no—
87#5727—34no—
88#5727—38no—
89#5696—316no—
90#5693—316no—
91#5691—38no—
92#5685—38no—
93#5584—34no—
94#5581—38no—
95#5580—34no—
96#5578—38no—
97#5572—38no—
98C4×D3×Q8—34no—
99#5568—38no—
100#5567—34no—
101C2×C32×Q8C2311yescharacteristic
102C2×C32×Q8C2312yes—
103C2×C32×Q8C2311yescharacteristic
104Q8×C3⋊D3—24no—
105Q8×C3⋊D3—28no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4⋊(C3⋊D3)C2312yes—
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×C4×C3⋊D3C2312yes—
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×C4×C3⋊D3C2311yescharacteristic
112C2×C4×C3⋊D3C2312yes—
113C2×C4×C3⋊D3C2312yes—
114C2×C4×C3⋊D3C2314yes—
115C2×#634C2312yes—
116C2×#634C2312yes—
117C2×#634C2314yes—
118C2×#634C2311yescharacteristic
119C32×C4⋊C4C2311yescharacteristic
120C32×C4⋊C4C2312yes—
121C32×C4⋊C4C2314yes—
122C32×C4⋊C4C2311yescharacteristic
123C32×C4⋊C4C2312yes—
124C32×C4⋊C4C2314yes—
125C32×C4⋊C4C2312yes—
126C32×C4⋊C4C2314yes—
127C32×C4⋊C4C2312yes—
128C32×C42C2312yes—
129C32×C42C2311yescharacteristic
130C32×C42C2312yes—
131C32×C42C2314yes—
132#3752C2312yes—
133#3752C2312yes—
134#3752C2314yes—
135#3752C2312yes—
136#3752C2314yes—
137#3752C2312yes—
138#3752C2312yes—
139#3752C2314yes—
140#3752C2314yes—
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2312yes—
145C4⋊(C3⋊Dic3)C2314yes—
146C4⋊(C3⋊Dic3)C2312yes—
147C4⋊(C3⋊Dic3)C2312yes—
148#3750C2312yes—
149#3750C2314yes—
150#3750C2312yes—
151#3750C2312yes—
152#3750C2312yes—
153#3750C2314yes—
154#3750C2314yes—
155#3750C2314yes—
156#3750C2312yes—
157#3750C2314yes—
158#3750C2314yes—
159C4×C3⋊Dic3C2311yescharacteristic
160C4×C3⋊Dic3C2312yes—
161C4×C3⋊Dic3C2312yes—
162C4×C3⋊Dic3C2314yes—
163C4×C3⋊Dic3C2314yes—
164C4×C3⋊Dic3C2311yescharacteristic
165C4×C3⋊Dic3C2311yescharacteristic
166C4×C3⋊Dic3C2312yes—
167C4×C3⋊Dic3C2314yes—
168#3523—91noSylow
169C2×D3×Q8—34no—
170C2×D3×Q8—38no—
171C3×C4⋊Q8C2×D314yes—
172C3×C4⋊Q8C2×D318yes—
173C3×#125C2×D318yes—
174C3×#125C2×D3116yes—
175C3×C4×Q8C2×D314yes—
176C3×C4×Q8C2×D318yes—
177C3×C4×Q8C2×D314yes—
178C3×C4×Q8C2×D318yes—
179#947—34no—
180#946—38no—
181#946—38no—
182#946—38no—
183#946—34no—
184Q8×Dic3—38no—
185Q8×Dic3—34no—
186#944—38no—
187#898—316no—
188#898—316no—
189#898—316no—
190#898—38no—
191#897—38no—
192#896—316no—
193#896—316no—
194#896—316no—
195#895—34no—
196#894—316no—
197#894—38no—
198#893—316no—
199#893—38no—
200#892—316no—
201#892—38no—
202#892—38no—
203D3×C4⋊C4—38no—
204D3×C4⋊C4—34no—
205#890—34no—
206#890—38no—
207#889—316no—
208#889—316no—
209#889—316no—
210#889—316no—
211#888—316no—
212#888—38no—
213#887—38no—
214#887—316no—
215#887—38no—
216#887—38no—
217#887—34no—
218#876—316no—
219#875—38no—
220C4×D12—38no—
221C4×D12—34no—
222#872—316no—
223#872—316no—
224#872—38no—
225C42×D3—38no—
226C42×D3—34no—
227#870—38no—
228#869—34no—
229C4×Dic6—38no—
230C4×Dic6—38no—
231C4×Dic6—316no—
232C4×Dic6—34no—
233C4×Dic6—38no—
234C22×C3⋊D3C2412yes—
235C22×C3⋊D3C2411yescharacteristic
236C32×Q8—22no—
237C32×Q8—24no—
238C32×Q8—22no—
239C2×C32×C4C2412yes—
240C2×C32×C4C2412yes—
241C2×C32×C4C2411yescharacteristic
242C2×C32×C4C2412yes—
243C2×C32×C4C2414yes—
244C2×C32×C4C2412yes—
245C2×C32×C4C2411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3C2411yescharacteristic
248C2×C3⋊Dic3C2411yescharacteristic
249C2×C3⋊Dic3C2414yes—
250C2×C3⋊Dic3C2412yes—
251C2×C3⋊Dic3C2411yescharacteristic
252C2×C3⋊Dic3C2412yes—
253C2×C3⋊Dic3C2412yes—
254C4⋊(C3⋊D3)—24no—
255C4⋊(C3⋊D3)—22no—
256C4×C3⋊D3—24no—
257C4×C3⋊D3—22no—
258C4×C3⋊D3—22no—
259C4×C3⋊D3—24no—
260C4×C3⋊D3—22no—
261C4×C3⋊D3—24no—
262C4×C3⋊D3—28no—
263#634—24no—
264#634—24no—
265#634—28no—
266#634#4114yes—
267#557—92no—
268#557—91no—
269#557C3⋊D311yescharacteristic, complemented
270#556—92no—
271#556—91no—
272#552—94no—
273#552—92no—
274D4×Q8—92no—
275D4×Q8—91no—
276#541—92no—
277#541—94no—
278#533—91no—
279#533—92no—
280#529—92no—
281#529—91no—
282#519—92no—
283C2×C4×Q8—91no—
284C2×C3×Q8C22×D314yes—
285C2×C3×Q8C22×D318yes—
286C2×C3×Q8C22×D314yes—
287D3×Q8—616no—
288D3×Q8—632no—
289C2×D12—34no—
290C2×D12—38no—
291C2×C4×D3—34no—
292C2×C4×D3—38no—
293C2×C4×D3—34no—
294C2×C4×D3—34no—
295C2×C4×D3—38no—
296C2×C4×D3—38no—
297C2×C4×D3—316no—
298C2×Dic6—34no—
299C2×Dic6—38no—
300C2×Dic6—38no—
301C2×Dic6—316no—
302C3×C4⋊C4C22×D314yes—
303C3×C4⋊C4C22×D318yes—
304C3×C4⋊C4C22×D3116yes—
305C3×C4⋊C4C22×D314yes—
306C3×C4⋊C4C22×D318yes—
307C3×C4⋊C4C22×D3116yes—
308C3×C4⋊C4C22×D318yes—
309C3×C4⋊C4C22×D3116yes—
310C3×C4⋊C4C22×D318yes—
311C3×C42C22×D318yes—
312C3×C42C22×D314yes—
313C3×C42C22×D318yes—
314C3×C42C22×D3116yes—
315(C2×D3)⋊C4—38no—
316(C2×D3)⋊C4—38no—
317(C2×D3)⋊C4—316no—
318(C2×D3)⋊C4—38no—
319(C2×D3)⋊C4—316no—
320(C2×D3)⋊C4—38no—
321(C2×D3)⋊C4—38no—
322(C2×D3)⋊C4—316no—
323(C2×D3)⋊C4—316no—
324C4⋊Dic3—34no—
325C4⋊Dic3—38no—
326C4⋊Dic3—34no—
327C4⋊Dic3—38no—
328C4⋊Dic3—316no—
329C4⋊Dic3—38no—
330C4⋊Dic3—38no—
331Dic3⋊C4—38no—
332Dic3⋊C4—316no—
333Dic3⋊C4—38no—
334Dic3⋊C4—38no—
335Dic3⋊C4—38no—
336Dic3⋊C4—316no—
337Dic3⋊C4—316no—
338Dic3⋊C4—316no—
339Dic3⋊C4—38no—
340Dic3⋊C4—316no—
341Dic3⋊C4—316no—
342C4×Dic3—34no—
343C4×Dic3—38no—
344C4×Dic3—38no—
345C4×Dic3—316no—
346C4×Dic3—316no—
347C4×Dic3—34no—
348C4×Dic3—34no—
349C4×Dic3—38no—
350C4×Dic3—316no—
351C22×C32C2511yescharacteristic
352C2×C3⋊D3—21no—
353C2×C3⋊D3—21no—
354C2×C3⋊D3—22no—
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D32−1+412yes—
358C32×C4—22no—
359C32×C4—24no—
360C32×C4—22no—
361C32×C4—21no—
362C32×C4—22no—
363C32×C4—22no—
364C32×C4C2×#4112yes—
365C32×C42−1+412yes—
366C3⋊Dic3—21no—
367C3⋊Dic3—22no—
368C3⋊Dic3—24no—
369C3⋊Dic3—21no—
370C3⋊Dic3—21no—
371C3⋊Dic3—22no—
372C3⋊Dic3C2×#4114yes—
373C22×Q8—91no—
374C22×Q8—92no—
375C4⋊Q8—92no—
376C4⋊Q8—92no—
377C4⋊Q8—94no—
378C4⋊Q8—91no—
379C4⋊Q8C2×C3⋊D311yescharacteristic
380C4⋊Q8C2×C3⋊D312yes—
381#126—92no—
382#126—94no—
383#126—94no—
384#126—94no—
385#126—94no—
386#125—91no—
387#125—94no—
388#125—92no—
389#125—94no—
390#125—94no—
391#125—94no—
392#125—92no—
393#125C2×C3⋊D312yes—
394#125C2×C3⋊D314yes—
395#124—91no—
396#124—92no—
397#123—92no—
398#123—94no—
399C22⋊Q8—91no—
400C22⋊Q8—92no—
401C22⋊Q8—92no—
402C22⋊Q8—92no—
403C22⋊Q8—92no—
404C22⋊Q8—94no—
405C22⋊Q8—94no—
406C22⋊Q8—94no—
407#121—91no—
408C4×Q8—91no—
409C4×Q8—92no—
410C4×Q8—91no—
411C4×Q8—92no—
412C4×Q8—94no—
413C4×Q8—92no—
414C4×Q8—92no—
415C4×Q8—91no—
416C4×Q8—92no—
417C4×Q8—94no—
418C4×Q8—92no—
419C4×Q8—92no—
420C4×Q8C2×C3⋊D311yescharacteristic
421C4×Q8C2×C3⋊D312yes—
422C4×Q8C2×C3⋊D311yescharacteristic
423C4×Q8C2×C3⋊D312yes—
424C4×D4—94no—
425C4×D4—92no—
426C4×D4—92no—
427C4×D4—91no—
428#117—94no—
429#117—92no—
430#117—92no—
431#117—92no—
432#117—94no—
433#117—94no—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—91no—
436C2×C42—92no—
437C2×C42—91no—
438C22×D3—34no—
439C22×D3—38no—
440C3×Q8—28no—
441C3×Q8—28no—
442C3×Q8—216no—
443C2×C3×C4C23×D318yes—
444C2×C3×C4C23×D318yes—
445C2×C3×C4C23×D314yes—
446C2×C3×C4C23×D318yes—
447C2×C3×C4C23×D3116yes—
448C2×C3×C4C23×D318yes—
449C2×C3×C4C23×D314yes—
450C2×C3×C4C23×D314yes—
451C2×Dic3—38no—
452C2×Dic3—34no—
453C2×Dic3—34no—
454C2×Dic3—316no—
455C2×Dic3—38no—
456C2×Dic3—34no—
457C2×Dic3—38no—
458D12—616no—
459D12—68no—
460C4×D3—616no—
461C4×D3—632no—
462C4×D3—616no—
463C4×D3—68no—
464C4×D3—68no—
465C4×D3—68no—
466C4×D3—616no—
467Dic6—316no—
468Dic6—616no—
469Dic6—632no—
470Dic6—616no—
471C2×C32C22×#4111yescharacteristic
472C2×C32C2×2−1+411yescharacteristic
473C2×C32C2×2−1+411yescharacteristic
474C3⋊D3—22no—
475C3⋊D3—42no—
476C2×Q8—91no—
477C2×Q8—92no—
478C2×Q8—92no—
479C2×Q8—94no—
480C2×Q8—184no—
481C2×Q8—188no—
482C2×Q8C22×C3⋊D311yescharacteristic
483C2×Q8C22×C3⋊D312yes—
484C2×Q8C22×C3⋊D311yescharacteristic
485C2×D4—92no—
486C2×D4—91no—
487C22×C4—91no—
488C22×C4—91no—
489C22×C4—92no—
490C22×C4—92no—
491C22×C4—91no—
492C22×C4—94no—
493C22×C4—92no—
494C4⋊C4—92no—
495C4⋊C4—92no—
496C4⋊C4—91no—
497C4⋊C4—92no—
498C4⋊C4—92no—
499C4⋊C4—94no—
500C4⋊C4—92no—
501C4⋊C4—92no—
502C4⋊C4—94no—
503C4⋊C4—92no—
504C4⋊C4—94no—
505C4⋊C4—94no—
506C4⋊C4—92no—
507C4⋊C4—91no—
508C4⋊C4—92no—
509C4⋊C4—94no—
510C4⋊C4—94no—
511C4⋊C4—94no—
512C4⋊C4C22×C3⋊D311yescharacteristic
513C4⋊C4C22×C3⋊D312yes—
514C4⋊C4C22×C3⋊D314yes—
515C4⋊C4C22×C3⋊D312yes—
516C4⋊C4C22×C3⋊D312yes—
517C4⋊C4C22×C3⋊D314yes—
518C4⋊C4C22×C3⋊D311yescharacteristic
519C4⋊C4C22×C3⋊D314yes—
520C4⋊C4C22×C3⋊D312yes—
521C22⋊C4—92no—
522C22⋊C4—92no—
523C22⋊C4—94no—
524C22⋊C4—94no—
525C22⋊C4—92no—
526C22⋊C4—94no—
527C22⋊C4—92no—
528C22⋊C4—94no—
529C22⋊C4—92no—
530C42—92no—
531C42—91no—
532C42—92no—
533C42—91no—
534C42—92no—
535C42—91no—
536C42—94no—
537C42—94no—
538C42—94no—
539C42C22×C3⋊D311yescharacteristic
540C42C22×C3⋊D312yes—
541C42C22×C3⋊D314yes—
542C42C22×C3⋊D312yes—
543C22×C3C24×D314yes—
544C2×D3—38no—
545C2×D3—64no—
546C2×D3—64no—
547C2×D3—68no—
548C2×D3—68no—
549C2×D3—68no—
550C3×C4—28no—
551C3×C4—28no—
552C3×C4—216no—
553C3×C4—28no—
554C3×C4—24no—
555C3×C4—28no—
556C3×C4#100718yes—
557C3×C4D3×#4118yes—
558Dic3—316no—
559Dic3—616no—
560Dic3—64no—
561Dic3—64no—
562Dic3—68no—
563Dic3—64no—
564Dic3—68no—
565C32#352311yescharacteristic, complemented, Sylow
566C23—91no—
567C23—92no—
568Q8—22no—
569Q8—22no—
570Q8—24no—
571Q8—94no—
572Q8—184no—
573Q8—188no—
574Q8—184no—
575D4—184no—
576D4—182no—
577C2×C4—92no—
578C2×C4—91no—
579C2×C4—91no—
580C2×C4—94no—
581C2×C4—92no—
582C2×C4—91no—
583C2×C4—92no—
584C2×C4—184no—
585C2×C4—188no—
586C2×C4—184no—
587C2×C4—182no—
588C2×C4—182no—
589C2×C4—182no—
590C2×C4—184no—
591C2×C4C23×C3⋊D312yes—
592C2×C4C23×C3⋊D312yes—
593C2×C4C23×C3⋊D311yescharacteristic
594C2×C4C23×C3⋊D312yes—
595C2×C4C23×C3⋊D314yes—
596C2×C4C23×C3⋊D312yes—
597C2×C4C23×C3⋊D311yescharacteristic
598C2×C4C23×C3⋊D311yescharacteristic
599C2×C3C2×#100714yes—
600C2×C3C2×D3×#4114yes—
601C2×C3D3×2−1+414yes—
602D3—68no—
603D3—128no—
604C22—92no—
605C22—181no—
606C22—181no—
607C22—182no—
608C22—182no—
609C22—182no—
610C22C24×C3⋊D311yescharacteristic
611C4—22no—
612C4—22no—
613C4—24no—
614C4—22no—
615C4—21no—
616C4—22no—
617C4—94no—
618C4—181no—
619C4—184no—
620C4—181no—
621C4—182no—
622C4—181no—
623C4—182no—
624C4#6436412yes—
625C4#41×C3⋊D312yes—
626C3#8702514yescomplemented
627C2—182no—
628C2—362no—
629C2C2×#6436411yescharacteristic
630C2C2×#41×C3⋊D311yescharacteristic
631C2C3⋊D3×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#557C2
prime radical#64104C22
hypercenter#557C3⋊D3
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. C32×#557C2semidirect
2. #10596202C2semidirect
3. #10596199C2semidirect
4. #10596198C2semidirect
5. #10596198C2semidirect
6. #10596167C2semidirect
7. #10596164C2semidirect
9. #10596156C2semidirect
10. #10596055C2semidirect
11. #10596052C2semidirect
13. #10596049C2semidirect
14. #10596043C2semidirect
15. C4×Q8×C3⋊D3C2semidirect
16. #10596039C2semidirect
17. #10596038C2semidirect
84. C3×#557D3semidirect
269. #557C3⋊D3semidirect
565. C32#3523semidirect
626. C3#87025semidirect

Maximal subgroups

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

subgroupindex
C32×#5572
#105962022
#105961992
#105961982
#105961672
#105961642
#105961622
#105961562
#105960552
#105960522
#105960512
#105960492
#105960432
C4×Q8×C3⋊D32
#105960392
#105960382
#870253