Finite Group Databasebeta

← #11864655

Subgroups — #11864655

Order 1152.

2136 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×C32×#135C211yesmaximal, characteristic, complemented
3#10596304C211yesmaximal, characteristic, complemented
4C2×#64160C211yesmaximal, characteristic, complemented
5#10592931C211yesmaximal, characteristic, complemented
6#10592885C212yesmaximal, complemented
7#10592872C212yesmaximal, complemented
8#10592869C212yesmaximal, complemented
9#10592857C212yesmaximal, complemented
10#10592809C211yesmaximal, characteristic, complemented
11C2×#63643C211yesmaximal, characteristic, complemented
12#83913—34nomaximal
13C2×C32×#41C2211yescharacteristic
14C2×C32×#41C2211yescharacteristic
15#64367—24no—
16#64367—24no—
17C2×Q8×C3⋊D3C2212yes—
18C2×#3830—22no—
19C2×#3830C2212yes—
20C2×#3828—21no—
21C2×#3828C2211yescharacteristic
22C22×#634—21no—
23C22×#634C2211yescharacteristic
24C32×#135—24no—
25C2×C32×Q16C2211yescharacteristic
26C2×C32×SD16C2211yescharacteristic
27C2×C32×SD16C2211yescharacteristic
28C2×C32×D8C2211yescharacteristic
29C22×C32×C8C2211yescharacteristic
30#64160—24no—
31#64155C2212yes—
32C2×#3756C2212yes—
33#64148—22no—
34#64147C2212yes—
35C2×#3754C2212yes—
36#64139—21no—
37C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
38#64133—21no—
39C2×#3748C2211yescharacteristic
40#63662C2212yes—
41#63659C2212yes—
42#63647C2212yes—
43#63647C2212yes—
44#63643C2212yes—
45#63643C2212yes—
46C2×#1010—34no—
47C2×C3×#135D314yescomplemented
48#5833—34no—
49C2×#951—34no—
50#5232—34no—
51#5186—38no—
52#5173—38no—
53#5170—38no—
54#5158—38no—
55#5110—34no—
56C2×#816—34no—
57C32×#41—22no—
58C32×#41—22no—
59C32×#41—22no—
60C32×#41D414yescomplemented
61C2×C32×Q8C2311yescharacteristic
62C2×C32×Q8C2311yescharacteristic
63C2×C32×D4—21no—
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
66C2×C32×D4C2311yescharacteristic
67C22×C32×C4—21no—
68C22×C32×C4—21no—
69C22×C32×C4C2311yescharacteristic
70C2×#638—22no—
71C2×#638—22no—
72C2×#638D412yes—
73C22×C3⋊Dic3—21no—
74C22×C3⋊Dic3—22no—
75C22×C3⋊Dic3—21no—
76Q8×C3⋊D3—24no—
77Q8×C3⋊D3—24no—
78#3830—216no—
79#3830—24no—
80#3830—24no—
81#3828—28no—
82#3828—22no—
83#3828—22no—
84C2×C4⋊(C3⋊D3)D411yescharacteristic
85C2×C4×C3⋊D3—22no—
86C2×C4×C3⋊D3C2312yes—
87C2×#634—28no—
88C2×#634—21no—
89C2×#634—22no—
90C2×#634—22no—
91C2×#634D411yescharacteristic
92C2×#634D414yescomplemented
93C2×#634C2312yes—
94C32×Q16—22no—
95C32×SD16—22no—
96C32×SD16—22no—
97C32×D8—22no—
98C2×C32×C8—22no—
99C2×C32×C8C2311yescharacteristic
100C2×C32×C8C2311yescharacteristic
101#3757—22no—
102#3756—24no—
103#3754—24no—
104#3752—22no—
105C4⋊(C3⋊Dic3)—21no—
106C4⋊(C3⋊Dic3)C2312yes—
107#3750—22no—
108#3748—22no—
109C2×C3⋊(C3⋊C8)C2312yes—
110#3013—91noSylow
111C2×C3×#41C2×D314yes—
112C2×C3×#41C2×D314yes—
113#1010—616no—
114#1010—616no—
115C2×D3×Q8—38no—
116C2×#237—38no—
117C2×#237—68no—
118C2×#235—34no—
119C2×#235—64no—
120C22×Dic6—34no—
121C22×Dic6—64no—
122C3×#135—216no—
123C2×C3×Q16C2×D314yes—
124C2×C3×SD16C2×D314yes—
125C2×C3×SD16C2×D314yes—
126C2×C3×D8C2×D314yes—
127C22×C3×C8C2×D314yes—
128#951—616no—
129#946—38no—
130C2×#216—38no—
131#939—68no—
132#938—38no—
133C2×#214—38no—
134#930—64no—
135C2×C4⋊Dic3—34no—
136#924—64no—
137C2×#208—34no—
138#835—38no—
139#832—38no—
140(C2×D3)⋊C8—38no—
141(C2×D3)⋊C8—38no—
142#816—38no—
143#816—38no—
144C23×C32—21no—
145C23×C32—21no—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3C2×D412yes—
148C32×Q8—21no—
149C32×Q8—21no—
150C32×Q8—21no—
151C32×Q8C2×D412yes—
152C32×D4—24no—
153C32×D4—21no—
154C32×D4—21no—
155C32×D4—21no—
156C32×D4—42no—
157C32×D4C2×D412yes—
158C2×C32×C4—21no—
159C2×C32×C4—24no—
160C2×C32×C4—21no—
161C2×C32×C4—42no—
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2411yescharacteristic
166#638—28no—
167#638—24no—
168#638—82no—
169C2×C3⋊Dic3—28no—
170C2×C3⋊Dic3—24no—
171C2×C3⋊Dic3—22no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—81no—
174C2×C3⋊Dic3C2×D412yes—
175C4⋊(C3⋊D3)—22no—
176C4×C3⋊D3—28no—
177C4×C3⋊D3—22no—
178C4×C3⋊D3—22no—
179#634—28no—
180#634—22no—
181#634—24no—
182#634—22no—
183#634C2×D414yes—
184C32×C8—21no—
185C32×C8—21no—
186C3⋊(C3⋊C8)—22no—
187C2×2−1+4—91no—
188C2×#137—91no—
189C2×#135C3⋊D311yescharacteristic, complemented
190#537—91no—
191#452—92no—
192#451—92no—
193#449—92no—
194#448—92no—
195#417—91no—
196C2×#103—91no—
197#408—91no—
198C3×#41—28no—
199C3×#41—28no—
200C3×#41—28no—
201C3×#41#67116yescomplemented
202C2×C3×Q8C22×D314yes—
203C2×C3×Q8C22×D314yes—
204C2×C3×D4—24no—
205C2×C3×D4—24no—
206C2×C3×D4C22×D314yes—
207C2×C3×D4C22×D314yes—
208C22×C3×C4—24no—
209C22×C3×C4—24no—
210C22×C3×C4C22×D314yes—
211C2×#67—38no—
212C2×#67—68no—
213C2×#67—68no—
214C22×Dic3—68no—
215C22×Dic3—64no—
216C22×Dic3—64no—
217D3×Q8—616no—
218D3×Q8—616no—
219#237—616no—
220#237—664no—
221#237—616no—
222#235—632no—
223#235—68no—
224#235—68no—
225C2×D12—34no—
226C2×C4×D3—38no—
227C2×C4×D3—68no—
228C2×Dic6—316no—
229C2×Dic6—38no—
230C2×Dic6—34no—
231C2×Dic6—68no—
232C2×Dic6—632no—
233C2×Dic6—64no—
234C2×Dic6—68no—
235C3×Q16—28no—
236C3×SD16—28no—
237C3×SD16—28no—
238C3×D8—28no—
239C2×C3×C8—28no—
240C2×C3×C8C22×D314yes—
241C2×C3×C8C22×D314yes—
242#217—68no—
243#216—616no—
244#214—616no—
245(C2×D3)⋊C4—68no—
246C4⋊Dic3—38no—
247C4⋊Dic3—64no—
248Dic3⋊C4—68no—
249#208—68no—
250C2×C3⋊C8—38no—
251C22×C32—21no—
252C22×C32—21no—
253C22×C32—22no—
254C22×C32—41no—
255C22×C32—41no—
256C22×C32—41no—
257C22×C32—41no—
258C22×C32—41no—
259C22×C32#12012yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—22no—
262C2×C3⋊D3—22no—
263C2×C3⋊D3—22no—
264C32×C4—22no—
265C32×C4—41no—
266C32×C4#12012yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C22×D411yescharacteristic
269C3⋊Dic3—22no—
270C3⋊Dic3—24no—
271C3⋊Dic3—42no—
2722−1+4—184no—
2732−1+4—184no—
274C2×#41—91no—
275C2×#41—92no—
276C2×#41—181no—
277C2×#41—182no—
278C2×#41C2×C3⋊D311yescharacteristic
279C2×#41C2×C3⋊D311yescharacteristic
280C22×Q8—92no—
281C22×Q8—91no—
282C22×Q8—181no—
283#137—184no—
284#135—24no—
285C2×Q16—92no—
286C2×Q16C2×C3⋊D311yescharacteristic
287C2×SD16—92no—
288C2×SD16C2×C3⋊D311yescharacteristic
289C2×SD16C2×C3⋊D311yescharacteristic
290C2×D8C2×C3⋊D311yescharacteristic
291C2×M16—91no—
292C22×C8C2×C3⋊D311yescharacteristic
293C22⋊Q8—92no—
294C22⋊Q8—181no—
295#121—92no—
296#121—181no—
297#121—182no—
298C2×C4⋊C4—91no—
299#103—92no—
300#103—92no—
301#103—92no—
302#102—92no—
303C22⋊C8—92no—
304C22⋊C8—92no—
305C23×C3—24no—
306C23×C3—24no—
307C23×C3D3×D414yes—
308C22×D3—38no—
309C3×Q8—24no—
310C3×Q8—24no—
311C3×Q8—24no—
312C3×Q8C2×#6718yes—
313C3×D4—216no—
314C3×D4—24no—
315C3×D4—24no—
316C3×D4—24no—
317C3×D4—48no—
318C3×D4C2×#6718yes—
319C2×C3×C4—24no—
320C2×C3×C4—216no—
321C2×C3×C4—24no—
322C2×C3×C4—48no—
323C2×C3×C4D3×D414yes—
324C2×C3×C4D3×D418yes—
325C2×C3×C4C2×#6718yes—
326C2×C3×C4C23×D314yes—
327#67—632no—
328#67—616no—
329#67—248no—
330C2×Dic3—38no—
331C2×Dic3—632no—
332C2×Dic3—616no—
333C2×Dic3—68no—
334C2×Dic3—68no—
335C2×Dic3—244no—
336D12—68no—
337C4×D3—632no—
338C4×D3—68no—
339C4×D3—68no—
340Dic6—316no—
341Dic6—632no—
342Dic6—616no—
343Dic6—68no—
344Dic6—68no—
345C3×C8—24no—
346C3×C8—24no—
347C3⋊C8—68no—
348C2×C32—22no—
349C2×C32—42no—
350C2×C32—81no—
351C2×C32C2×#12011yescharacteristic
352C2×C32#57711yescharacteristic
353C2×C32#57811yescharacteristic
354C3⋊D3—42no—
355#41—22no—
356#41—22no—
357#41—22no—
358#41—188no—
359#41—184no—
360#41—1816no—
361#41—184no—
362#41—182no—
363#41—182no—
364#41#63814yescomplemented
365C2×Q8—91no—
366C2×Q8—92no—
367C2×Q8—94no—
368C2×Q8—182no—
369C2×Q8—188no—
370C2×Q8—184no—
371C2×Q8—184no—
372C2×Q8—181no—
373C2×Q8—182no—
374C2×Q8C22×C3⋊D311yescharacteristic
375C2×Q8C22×C3⋊D311yescharacteristic
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—92no—
379C2×D4—91no—
380C2×D4—182no—
381C2×D4—182no—
382C2×D4C22×C3⋊D311yescharacteristic
383C2×D4C22×C3⋊D311yescharacteristic
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—92no—
387C22×C4—182no—
388C22×C4—182no—
389C22×C4—181no—
390C22×C4—181no—
391C22×C4C22×C3⋊D311yescharacteristic
392Q16—22no—
393Q16—184no—
394SD16—22no—
395SD16—22no—
396SD16—184no—
397D8—22no—
398M16—182no—
399C2×C8—22no—
400C2×C8—92no—
401C2×C8C22×C3⋊D311yescharacteristic
402C2×C8C22×C3⋊D311yescharacteristic
403C4⋊C4—92no—
404C4⋊C4—182no—
405C4⋊C4—181no—
406C22⋊C4—182no—
407C22⋊C4—182no—
408C22×C3—24no—
409C22×C3—24no—
410C22×C3—28no—
411C22×C3—44no—
412C22×C3—44no—
413C22×C3—44no—
414C22×C3—44no—
415C22×C3—44no—
416C22×C3#93718yes—
417C22×C3C2×D3×D414yes—
418C2×D3—68no—
419C2×D3—68no—
420C2×D3—68no—
421C3×C4—28no—
422C3×C4—44no—
423C3×C4#93718yes—
424C3×C4C2×D3×D414yes—
425C3×C4C22×#6714yes—
426Dic3—616no—
427Dic3—68no—
428Dic3—128no—
429C32#301311yescharacteristic, complemented, Sylow
430C23—21no—
431C23—21no—
432C23—92no—
433C23D4×C3⋊D311yescharacteristic
434Q8—21no—
435Q8—21no—
436Q8—21no—
437Q8—94no—
438Q8—188no—
439Q8—182no—
440Q8—182no—
441Q8—184no—
442Q8C2×#63812yes—
443D4—24no—
444D4—21no—
445D4—21no—
446D4—21no—
447D4—42no—
448D4—188no—
449D4—184no—
450D4—182no—
451D4—722no—
452D4C2×#63812yes—
453C2×C4—21no—
454C2×C4—24no—
455C2×C4—21no—
456C2×C4—42no—
457C2×C4—92no—
458C2×C4—188no—
459C2×C4—188no—
460C2×C4—182no—
461C2×C4—184no—
462C2×C4—182no—
463C2×C4—182no—
464C2×C4—182no—
465C2×C4—721no—
466C2×C4D4×C3⋊D312yes—
467C2×C4D4×C3⋊D311yescharacteristic
468C2×C4C2×#63812yes—
469C2×C4C23×C3⋊D311yescharacteristic
470C8—21no—
471C8—21no—
472C8—182no—
473C2×C3—28no—
474C2×C3—48no—
475C2×C3—84no—
476C2×C3#577014yes—
477C2×C3#577114yes—
478C2×C3C2×#93714yes—
479D3—128no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—182no—
489C22—182no—
490C22—182no—
491C22#6414612yes—
492C22C2×D4×C3⋊D311yescharacteristic
493C4—22no—
494C4—41no—
495C4—182no—
496C4—184no—
497C4—362no—
498C4#6414612yes—
499C4C2×D4×C3⋊D311yescharacteristic
500C4C22×#63811yescharacteristic
501C3#8391314yescomplemented
502C2—22no—
503C2—42no—
504C2—81no—
505C2—362no—
506C2#1059624111yescharacteristic
507C2#1059624211yescharacteristic
508C2C2×#6414611yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#135C2
socleC22×C32C22×D4
hypercenterC2×#135C3⋊D3
hypocenterC32#3013
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×C32×#135C2semidirect
3. #10596304C2semidirect
4. C2×#64160C2semidirect
5. #10592931C2semidirect
6. #10592885C2semidirect
7. #10592872C2semidirect
8. #10592869C2semidirect
9. #10592857C2semidirect
10. #10592809C2semidirect
11. C2×#63643C2semidirect
47. C2×C3×#135D3semidirect
60. C32×#41D4semidirect
92. C2×#634D4semidirect
189. C2×#135C3⋊D3semidirect
201. C3×#41#67semidirect
364. #41#638semidirect
429. C32#3013semidirect
501. C3#83913semidirect

Maximal subgroups

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

subgroupindex
C2×#643672
C2×C32×#1352
#105963042
C2×#641602
#105929312
#105928852
#105928722
#105928692
#105928572
#105928092
C2×#636432
#839133