Finite Group Databasebeta

← #11909846

Subgroups — #11909846

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×#533C211yesmaximal, characteristic, complemented
2#10596203C211yesmaximal, characteristic, complemented
3#10596198C211yesmaximal, characteristic, complemented
4#10596192C211yesmaximal, characteristic, complemented
5#10596192C211yesmaximal, characteristic, complemented
6#10596167C214yesmaximal, complemented
7#10596113C212yesmaximal, complemented
8#10596103C212yesmaximal, complemented
9#10596095C212yesmaximal
10#10596093C212yesmaximal, complemented
11#10596054C212yesmaximal, complemented
12#10596043C212yesmaximal, complemented
13#10596040C212yesmaximal, complemented
14#10596039C212yesmaximal, complemented
15#10596002C214yesmaximal, complemented
16#10595950C211yesmaximal, characteristic
17C2×C4×#634C211yesmaximal, characteristic, complemented
18#86266—34nomaximal
19C2×Q8×C3⋊D3C2212yes—
20C22×#634C2211yescharacteristic
21C32×C4⋊Q8C2211yescharacteristic
22C32×C4⋊Q8C2211yescharacteristic
23C32×#125C2212yes—
24C32×C22⋊Q8C2212yes—
25C32×C22⋊Q8C2212yes—
26C32×C4×Q8C2212yes—
27C32×C4×Q8C2212yes—
28C32×#117C2212yes—
29C2×C32×C42C2211yescharacteristic
30#64156C2212yes—
31#64155C2212yes—
32Q8×C3⋊Dic3C2212yes—
33Q8×C3⋊Dic3C2212yes—
34Q8×C3⋊Dic3C2212yes—
35#64153C2212yes—
36#64153C2212yes—
37#64139C2211yescharacteristic
38#64138C2212yes—
39C4×#638C2212yes—
40C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
41#64133C2211yescharacteristic
42C2×#3750C2212yes—
43C2×C4×C3⋊Dic3C2212yes—
44#64107C2214yes—
45#64107C2214yes—
46#64107C2214yes—
47#64106C2212yes—
48#64105C2214yes—
49#64105C2214yes—
50#64102C2212yes—
51#64101C2212yes—
52#64101C2214yes—
53#64099C2214yes—
54#64099C2212yes—
55#64099C2212yes—
56#64098C2214yes—
57#64098C2214yes—
58#64098C2214yes—
59#64097C2214yes—
60#64097C2212yes—
61#64096C2212yes—
62#64096C2214yes—
63#64096C2212yes—
64#64095C2214yes—
65#64090C2214yes—
66#64087C2214yes—
67#64086C2214yes—
68#64085C2212yes—
69#64085C2214yes—
70#64084C2211yescharacteristic
71C4×C4⋊(C3⋊D3)C2211yescharacteristic
72#64081C2212yes—
73#64081C2214yes—
74#64079C2211yescharacteristic
75#64079C2214yes—
76C4×#634C2212yes—
77C4×#634C2211yescharacteristic
78C4×#634C2211yescharacteristic
79C4×#634C2211yescharacteristic
80C4×#634C2212yes—
81C4×#634C2211yescharacteristic
82C4×#634C2211yescharacteristic
83C4×#634C2214yes—
84C3×#533D314yescomplemented
85#5732—34no—
86#5727—34no—
87#5721—34no—
88#5721—34no—
89#5696—316no—
90#5642—38no—
91#5632—38no—
92#5624—38no—
93#5622—38no—
94#5583—38no—
95#5572—38no—
96#5569—38no—
97#5568—38no—
98#5531—316no—
99#5479—34no—
100C2×C4×Dic6—34no—
101C2×C32×Q8C2312yes—
102C2×C32×Q8C2312yes—
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C32×C4C2311yescharacteristic
106C2×#638C2312yes—
107C22×C3⋊Dic3C2312yes—
108C22×C3⋊Dic3C2312yes—
109Q8×C3⋊D3—28no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4×C3⋊D3C2312yes—
112C2×C4×C3⋊D3C2314yes—
113C2×#634—24no—
114C2×#634C2312yes—
115C2×#634C2311yescharacteristic
116C2×#634C2311yescharacteristic
117C2×#634C2314yes—
118C2×#634C2311yescharacteristic
119C32×C4⋊C4C2312yes—
120C32×C4⋊C4C2314yes—
121C32×C4⋊C4C2312yes—
122C32×C4⋊C4C2314yes—
123C32×C4⋊C4C2312yes—
124C32×C4⋊C4C2312yes—
125C32×C22⋊C4C2314yes—
126C32×C42C2311yescharacteristic
127C32×C42C2311yescharacteristic
128C32×C42C2311yescharacteristic
129C32×C42C2311yescharacteristic
130C32×C42C2314yes—
131#3757C2312yes—
132#3752C2312yes—
133#3752C2312yes—
134#3752C2314yes—
135#3752C2312yes—
136#3752C2312yes—
137#3752C2314yes—
138#3752C2314yes—
139C4⋊(C3⋊Dic3)C2312yes—
140C4⋊(C3⋊Dic3)C2311yescharacteristic
141C4⋊(C3⋊Dic3)C2311yescharacteristic
142C4⋊(C3⋊Dic3)C2311yescharacteristic
143C4⋊(C3⋊Dic3)C2314yes—
144C4⋊(C3⋊Dic3)C2311yescharacteristic
145C4⋊(C3⋊Dic3)C2314yes—
146C4⋊(C3⋊Dic3)C2314yes—
147#3750C2312yes—
148#3750C2312yes—
149#3750C2312yes—
150#3750C2312yes—
151#3750C2312yes—
152#3750C2312yes—
153#3750C2312yes—
154#3750C2314yes—
155#3750C2314yes—
156#3750C2312yes—
157#3750C2314yes—
158#3750C2314yes—
159#3750C2314yes—
160C4×C3⋊Dic3C2312yes—
161C4×C3⋊Dic3C2312yes—
162C4×C3⋊Dic3C2312yes—
163C4×C3⋊Dic3C2312yes—
164C4×C3⋊Dic3C2312yes—
165C4×C3⋊Dic3C2314yes—
166C4×C3⋊Dic3C2314yes—
167C4×C3⋊Dic3C2314yes—
168#3523—91noSylow
169C2×D3×Q8—38no—
170C22×Dic6—34no—
171C3×C4⋊Q8C2×D314yes—
172C3×C4⋊Q8C2×D314yes—
173C3×#125C2×D318yes—
174C3×C22⋊Q8C2×D318yes—
175C3×C22⋊Q8C2×D318yes—
176C3×C4×Q8C2×D318yes—
177C3×C4×Q8C2×D318yes—
178C3×#117C2×D318yes—
179C2×C3×C42C2×D314yes—
180#947—38no—
181#946—38no—
182Q8×Dic3—38no—
183Q8×Dic3—38no—
184Q8×Dic3—38no—
185#944—38no—
186#944—38no—
187#930—34no—
188#929—38no—
189C4×#67—38no—
190C2×C4⋊Dic3—34no—
191#924—34no—
192C2×Dic3⋊C4—38no—
193C2×C4×Dic3—38no—
194#898—316no—
195#898—316no—
196#898—316no—
197#897—38no—
198#896—316no—
199#896—316no—
200#893—38no—
201#892—38no—
202#892—316no—
203#890—316no—
204#890—38no—
205#890—38no—
206#889—316no—
207#889—316no—
208#889—316no—
209#888—316no—
210#888—38no—
211#887—38no—
212#887—316no—
213#887—38no—
214#886—316no—
215#67⋊C4—316no—
216#878—316no—
217#877—316no—
218#876—38no—
219#876—316no—
220#875—34no—
221C4×D12—34no—
222#872—38no—
223#872—316no—
224#870—34no—
225#870—316no—
226C4×Dic6—38no—
227C4×Dic6—34no—
228C4×Dic6—34no—
229C4×Dic6—34no—
230C4×Dic6—38no—
231C4×Dic6—34no—
232C4×Dic6—34no—
233C4×Dic6—316no—
234C23×C32C2411yescharacteristic
235C22×C3⋊D3C2412yes—
236C32×Q8—24no—
237C32×Q8—24no—
238C2×C32×C4—22no—
239C2×C32×C4—22no—
240C2×C32×C4—22no—
241C2×C32×C4C2411yescharacteristic
242C2×C32×C4C2414yes—
243C2×C32×C4C2414yes—
244C2×C32×C4C2411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—24no—
250C2×C3⋊Dic3—24no—
251C2×C3⋊Dic3—24no—
252C2×C3⋊Dic3C2412yes—
253C2×C3⋊Dic3C2412yes—
254C2×C3⋊Dic3C2412yes—
255C2×C3⋊Dic3C2412yes—
256C2×C3⋊Dic3C2412yes—
257C2×C3⋊Dic3C2412yes—
258C2×C3⋊Dic3C2412yes—
259C4⋊(C3⋊D3)—22no—
260C4×C3⋊D3—24no—
261C4×C3⋊D3—28no—
262#634—22no—
263#634—22no—
264#634—24no—
265#634—28no—
266#634#4114yes—
267#557—91no—
268#557—91no—
269#557—92no—
270#556—91no—
271#556—92no—
272#552—92no—
273#552—94no—
274D4×Q8—91no—
275D4×Q8—92no—
276#541—94no—
277#541—92no—
278#533—92no—
279#533C3⋊D311yescharacteristic, complemented
280#529—92no—
281#529—91no—
282#519—92no—
283C2×C4×Q8—91no—
284C2×C3×Q8C22×D318yes—
285C2×C3×Q8C22×D318yes—
286C22×C3×C4C22×D314yes—
287C22×C3×C4C22×D314yes—
288C22×C3×C4C22×D314yes—
289C2×#67—38no—
290C22×Dic3—38no—
291C22×Dic3—38no—
292D3×Q8—632no—
293C2×D12—34no—
294C2×C4×D3—38no—
295C2×C4×D3—316no—
296C2×Dic6—34no—
297C2×Dic6—38no—
298C2×Dic6—34no—
299C2×Dic6—34no—
300C2×Dic6—316no—
301C2×Dic6—616no—
302C3×C4⋊C4C22×D318yes—
303C3×C4⋊C4C22×D3116yes—
304C3×C4⋊C4C22×D318yes—
305C3×C4⋊C4C22×D3116yes—
306C3×C4⋊C4C22×D318yes—
307C3×C4⋊C4C22×D318yes—
308C3×C22⋊C4C22×D3116yes—
309C3×C42C22×D314yes—
310C3×C42C22×D314yes—
311C3×C42C22×D314yes—
312C3×C42C22×D314yes—
313C3×C42C22×D3116yes—
314#217—38no—
315(C2×D3)⋊C4—38no—
316(C2×D3)⋊C4—38no—
317(C2×D3)⋊C4—316no—
318(C2×D3)⋊C4—38no—
319(C2×D3)⋊C4—38no—
320(C2×D3)⋊C4—316no—
321(C2×D3)⋊C4—316no—
322C4⋊Dic3—38no—
323C4⋊Dic3—34no—
324C4⋊Dic3—34no—
325C4⋊Dic3—34no—
326C4⋊Dic3—316no—
327C4⋊Dic3—34no—
328C4⋊Dic3—316no—
329C4⋊Dic3—316no—
330Dic3⋊C4—38no—
331Dic3⋊C4—38no—
332Dic3⋊C4—38no—
333Dic3⋊C4—38no—
334Dic3⋊C4—38no—
335Dic3⋊C4—38no—
336Dic3⋊C4—38no—
337Dic3⋊C4—316no—
338Dic3⋊C4—316no—
339Dic3⋊C4—38no—
340Dic3⋊C4—316no—
341Dic3⋊C4—316no—
342Dic3⋊C4—316no—
343C4×Dic3—38no—
344C4×Dic3—38no—
345C4×Dic3—38no—
346C4×Dic3—38no—
347C4×Dic3—38no—
348C4×Dic3—316no—
349C4×Dic3—316no—
350C4×Dic3—316no—
351C22×C32—21no—
352C22×C32—21no—
353C22×C322−1+412yes—
354C22×C32C2511yescharacteristic
355C2×C3⋊D3—22no—
356C2×C3⋊D3—22no—
357C2×C3⋊D3—22no—
358C32×C4—21no—
359C32×C4—24no—
360C32×C4—21no—
361C32×C4—21no—
362C32×C4—21no—
363C32×C4—24no—
364C32×C4C2×#4112yes—
365C32×C42−1+412yes—
366C3⋊Dic3—22no—
367C3⋊Dic3—22no—
368C3⋊Dic3—22no—
369C3⋊Dic3—22no—
370C3⋊Dic3—22no—
371C3⋊Dic3—22no—
372C3⋊Dic3C2×#4114yes—
373C22×Q8—92no—
374C22×Q8—91no—
375C4⋊Q8—92no—
376C4⋊Q8—92no—
377C4⋊Q8—92no—
378C4⋊Q8—94no—
379C4⋊Q8C2×C3⋊D311yescharacteristic
380C4⋊Q8C2×C3⋊D311yescharacteristic
381#126—94no—
382#126—94no—
383#126—94no—
384#126—92no—
385#126—94no—
386#125—92no—
387#125—94no—
388#125—94no—
389#125—94no—
390#125—94no—
391#125—92no—
392#125—91no—
393#125—94no—
394#125C2×C3⋊D312yes—
395#124—92no—
396#124—91no—
397#123—92no—
398#123—94no—
399C22⋊Q8—92no—
400C22⋊Q8—91no—
401C22⋊Q8—94no—
402C22⋊Q8—94no—
403C22⋊Q8—92no—
404C22⋊Q8—94no—
405C22⋊Q8C2×C3⋊D312yes—
406C22⋊Q8C2×C3⋊D312yes—
407#121—91no—
408C4×Q8—92no—
409C4×Q8—92no—
410C4×Q8—92no—
411C4×Q8—94no—
412C4×Q8—92no—
413C4×Q8—92no—
414C4×Q8—91no—
415C4×Q8—92no—
416C4×Q8—91no—
417C4×Q8—91no—
418C4×Q8—92no—
419C4×Q8—91no—
420C4×Q8—94no—
421C4×Q8—91no—
422C4×Q8C2×C3⋊D312yes—
423C4×Q8C2×C3⋊D312yes—
424C4×D4—92no—
425C4×D4—92no—
426C4×D4—94no—
427C4×D4—91no—
428#117—94no—
429#117—92no—
430#117—94no—
431#117—92no—
432#117—94no—
433#117C2×C3⋊D312yes—
434C2×C4⋊C4—92no—
435C2×C4⋊C4—91no—
436C2×C42—92no—
437C2×C42C2×C3⋊D311yescharacteristic
438C23×C3C23×D314yes—
439C22×D3—38no—
440C3×Q8—216no—
441C3×Q8—216no—
442C2×C3×C4—28no—
443C2×C3×C4—28no—
444C2×C3×C4—28no—
445C2×C3×C4C23×D314yes—
446C2×C3×C4C23×D3116yes—
447C2×C3×C4C23×D3116yes—
448C2×C3×C4C23×D314yes—
449C2×C3×C4C23×D314yes—
450C2×C3×C4C23×D314yes—
451C2×C3×C4C23×D314yes—
452C2×C3×C4C23×D314yes—
453#67—616no—
454C2×Dic3—38no—
455C2×Dic3—38no—
456C2×Dic3—38no—
457C2×Dic3—38no—
458C2×Dic3—38no—
459C2×Dic3—38no—
460C2×Dic3—38no—
461C2×Dic3—616no—
462C2×Dic3—616no—
463D12—68no—
464C4×D3—632no—
465C4×D3—616no—
466Dic6—316no—
467Dic6—616no—
468Dic6—632no—
469Dic6—68no—
470Dic6—68no—
471C2×C32—22no—
472C2×C32C22×#4111yescharacteristic
473C2×C32C2×2−1+411yescharacteristic
474C2×C32C2×2−1+411yescharacteristic
475C3⋊D3—42no—
476C2×Q8—91no—
477C2×Q8—91no—
478C2×Q8—94no—
479C2×Q8—92no—
480C2×Q8—91no—
481C2×Q8—184no—
482C2×Q8—188no—
483C2×Q8C22×C3⋊D312yes—
484C2×Q8C22×C3⋊D312yes—
485C2×D4—92no—
486C2×D4—91no—
487C22×C4—92no—
488C22×C4—92no—
489C22×C4—94no—
490C22×C4—92no—
491C22×C4C22×C3⋊D311yescharacteristic
492C22×C4C22×C3⋊D311yescharacteristic
493C22×C4C22×C3⋊D311yescharacteristic
494C4⋊C4—92no—
495C4⋊C4—91no—
496C4⋊C4—92no—
497C4⋊C4—91no—
498C4⋊C4—92no—
499C4⋊C4—92no—
500C4⋊C4—92no—
501C4⋊C4—94no—
502C4⋊C4—92no—
503C4⋊C4—92no—
504C4⋊C4—94no—
505C4⋊C4—94no—
506C4⋊C4—94no—
507C4⋊C4—91no—
508C4⋊C4—94no—
509C4⋊C4—92no—
510C4⋊C4—91no—
511C4⋊C4—94no—
512C4⋊C4—94no—
513C4⋊C4—92no—
514C4⋊C4—94no—
515C4⋊C4C22×C3⋊D312yes—
516C4⋊C4C22×C3⋊D314yes—
517C4⋊C4C22×C3⋊D312yes—
518C4⋊C4C22×C3⋊D312yes—
519C4⋊C4C22×C3⋊D312yes—
520C4⋊C4C22×C3⋊D314yes—
521C22⋊C4—92no—
522C22⋊C4—92no—
523C22⋊C4—94no—
524C22⋊C4—92no—
525C22⋊C4—94no—
526C22⋊C4—92no—
527C22⋊C4—92no—
528C22⋊C4—94no—
529C22⋊C4C22×C3⋊D314yes—
530C42—92no—
531C42—92no—
532C42—92no—
533C42—92no—
534C42—94no—
535C42—94no—
536C42—94no—
537C42—92no—
538C42C22×C3⋊D311yescharacteristic
539C42C22×C3⋊D311yescharacteristic
540C42C22×C3⋊D311yescharacteristic
541C42C22×C3⋊D311yescharacteristic
542C42C22×C3⋊D314yes—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3#100718yes—
546C22×C3C24×D314yes—
547C2×D3—68no—
548C2×D3—68no—
549C2×D3—68no—
550C3×C4—24no—
551C3×C4—24no—
552C3×C4—24no—
553C3×C4—216no—
554C3×C4—24no—
555C3×C4—216no—
556C3×C4D3×#4118yes—
557C3×C4#101018yes—
558Dic3—316no—
559Dic3—68no—
560Dic3—68no—
561Dic3—68no—
562Dic3—68no—
563Dic3—68no—
564Dic3—68no—
565C32#352311yescharacteristic, complemented, Sylow
566C23—92no—
567C23C23×C3⋊D311yescharacteristic
568Q8—24no—
569Q8—24no—
570Q8—94no—
571Q8—184no—
572Q8—188no—
573Q8—182no—
574Q8—182no—
575D4—184no—
576D4—182no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—92no—
581C2×C4—92no—
582C2×C4—92no—
583C2×C4—92no—
584C2×C4—92no—
585C2×C4—92no—
586C2×C4—92no—
587C2×C4—188no—
588C2×C4—184no—
589C2×C4—184no—
590C2×C4—184no—
591C2×C4C23×C3⋊D311yescharacteristic
592C2×C4C23×C3⋊D314yes—
593C2×C4C23×C3⋊D314yes—
594C2×C4C23×C3⋊D311yescharacteristic
595C2×C4C23×C3⋊D311yescharacteristic
596C2×C4C23×C3⋊D311yescharacteristic
597C2×C4C23×C3⋊D311yescharacteristic
598C2×C4C23×C3⋊D311yescharacteristic
599C2×C3—28no—
600C2×C3C2×#100714yes—
601C2×C3C2×D3×#4114yes—
602C2×C3C2×#101014yes—
603D3—128no—
604C22—21no—
605C22—21no—
606C22—182no—
607C22—182no—
608C22—182no—
609C22#6436412yes—
610C22C24×C3⋊D311yescharacteristic
611C4—21no—
612C4—21no—
613C4—21no—
614C4—24no—
615C4—21no—
616C4—24no—
617C4—94no—
618C4—182no—
619C4—182no—
620C4—182no—
621C4—182no—
622C4—182no—
623C4—182no—
624C4#41×C3⋊D312yes—
625C4#6436712yes—
626C3#8626614yescomplemented
627C2—22no—
628C2—362no—
629C2C2×#6436411yescharacteristic
630C2C2×#41×C3⋊D311yescharacteristic
631C2C2×#6436711yescharacteristic
subgroupG/H
center, FrattiniC22C24×C3⋊D3
commutator, socle, cosocleC22×C32C25
FittingC32×#533C2
prime radical#64139C22
hypercenter#533C3⋊D3
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C32×#533C2semidirect
2. #10596203C2semidirect
3. #10596198C2semidirect
4. #10596192C2semidirect
5. #10596192C2semidirect
6. #10596167C2semidirect
7. #10596113C2semidirect
8. #10596103C2semidirect
10. #10596093C2semidirect
11. #10596054C2semidirect
12. #10596043C2semidirect
13. #10596040C2semidirect
14. #10596039C2semidirect
15. #10596002C2semidirect
17. C2×C4×#634C2semidirect
84. C3×#533D3semidirect
279. #533C3⋊D3semidirect
565. C32#3523semidirect
626. C3#86266semidirect

Maximal subgroups

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

subgroupindex
C32×#5332
#105962032
#105961982
#105961922
#105961672
#105961132
#105961032
#105960952
#105960932
#105960542
#105960432
#105960402
#105960392
#105960022
#105959502
C2×C4×#6342
#862663