Finite Group Databasebeta

← #11901950

Subgroups — #11901950

Order 1152.

2157 conjugacy classes of subgroups.

The subgroup lattice has 359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C3×#5483C212yesmaximal
3#10595521C212yesmaximal
4C2×#63957C212yesmaximal
5#10594813C214yesmaximal, complemented
6#10594810C214yesmaximal, complemented
7#10594033C218yesmaximal, complemented
8#10594030C218yesmaximal, complemented
9#86571—32nomaximal
10C23×C3⋊Dic3C2211yescharacteristic
11C2×C32×C22⋊C4C2211yescharacteristic
12C2×#3757C2211yescharacteristic
13C2×#3750C2212yes—
14C2×C4×C3⋊Dic3C2212yes—
15#64086C2214yes—
16#64086C2214yes—
17C2×C3×#217C2214yes—
18C3×#924C2218yes—
19C3×#878C22116yes—
20#63982C2218yes—
21C2×#3724C2214yes—
22#63964C22116yes—
23#63957C2214yes—
24#63957C2214yes—
25#63957C2214yes—
26#63957C2214yes—
27C2×Dic32C2214yes—
28#63919C2214yescomplemented
29#63873C2214yescomplemented
30#63870C2218yescomplemented
31#63847C22116yescomplemented
32#63843C2218yescomplemented
33#63839C22116yescomplemented
34#63838C2218yescomplemented
35C3×#543—32no—
36#5623—38no—
37#5623—316no—
38#5622—38no—
39#5622—316no—
40#5483—34no—
41#5483D312yes—
42C2×#877—32no—
43C2×#877—34no—
44C2×#877—61no—
45C24×C32C2311yescharacteristic
46C22×C32×C4C2312yes—
47C22×C3⋊Dic3Q818yescomplemented
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2312yes—
50C22×C3⋊Dic3C2312yes—
51C22×C3⋊Dic3C2311yescharacteristic
52C22×C3⋊Dic3C2311yescharacteristic
53C22×C3×Dic3C2318yes—
54C2×C3×Dic6C2318yes—
55C2×#627C2318yes—
56C32×C22⋊C4C2314yes—
57#3757C2314yes—
58#3750C2318yes—
59C4×C3⋊Dic3C2314yes—
60C4×C3⋊Dic3C2314yes—
61C3×#217C2318yes—
62C3×#217C2318yes—
63C3×C4⋊Dic3C2318yes—
64C3×Dic3⋊C4C23116yes—
65#3724C2318yes—
66#3724C2318yes—
67#3724C2318yes—
68Dic3⋊Dic3C23116yes—
69Dic32C2318yes—
70Dic32C2318yes—
71#3458—91noSylow
72C23×Dic3—32no—
73C23×Dic3—61no—
74C3×C22⋊Q8—38no—
75C3×C22⋊Q8—316no—
76C2×C3×C22⋊C4—21no—
77C2×C3×C22⋊C4—34no—
78C2×C3×C22⋊C4C2×D312yes—
79C2×#217—32no—
80C2×#217—61no—
81C2×#217C2×D314yes—
82Q8×Dic3—38no—
83#944—38no—
84#944—316no—
85#924—316no—
86#924C2×D318yes—
87C2×Dic3⋊C4—34no—
88C2×Dic3⋊C4—38no—
89C2×Dic3⋊C4—62no—
90C2×C4×Dic3—34no—
91C2×C4×Dic3—38no—
92C2×C4×Dic3—62no—
93#889—316no—
94#889—316no—
95#889—316no—
96#888—316no—
97#888—38no—
98#887—38no—
99#887—316no—
100#878—316no—
101#878—316no—
102#878C2×D3116yes—
103#877—38no—
104#877—38no—
105#877—38no—
106#877—38no—
107#877—38no—
108#877—38no—
109#877—64no—
110#877—64no—
111C23×C32—42no—
112C23×C32C2×Q814yes—
113C23×C32C2411yescharacteristic
114C23×C32C2412yes—
115C2×C32×C4—42no—
116C2×C32×C4C2414yes—
117C2×C3⋊Dic3—42no—
118C2×C3⋊Dic3C2×Q818yes—
119C2×C3⋊Dic3C2×Q818yes—
120C2×C3⋊Dic3C2×Q814yes—
121C2×C3⋊Dic3C2×Q814yes—
122C2×C3⋊Dic3C2414yes—
123C2×C3⋊Dic3C2411yescharacteristic
124C2×C3⋊Dic3C2412yes—
125C2×C3⋊Dic3C2411yescharacteristic
126C2×C3×Dic3—48no—
127C2×C3×Dic3C24116yes—
128C3×Dic6—48no—
129#627—48no—
130#544—98no—
131#544—94no—
132#543—32no—
133#543—92no—
134#533—98no—
135#533—94no—
136C2×#117—92no—
137C2×#117—91no—
138C24×C3—21no—
139C24×C3C22×D312yes—
140C2×C3×Q8—38no—
141C22×C3×C4—22no—
142C22×C3×C4—38no—
143C22×C3×C4C22×D314yes—
144C22×Dic3—316no—
145C22×Dic3—34no—
146C22×Dic3—32no—
147C22×Dic3—34no—
148C22×Dic3—32no—
149C22×Dic3—34no—
150C22×Dic3—62no—
151C22×Dic3—62no—
152C22×Dic3—61no—
153C22×Dic3—61no—
154C22×Dic3—68no—
155C22×Dic3—62no—
156C22×Dic3C22×D318yes—
157C2×Dic6—316no—
158C2×Dic6C22×D318yes—
159C3×C4⋊C4—316no—
160C3×C4⋊C4—38no—
161C3×C22⋊C4—24no—
162C3×C22⋊C4—38no—
163C3×C22⋊C4—38no—
164C3×C22⋊C4C22×D318yes—
165#217—38no—
166#217—64no—
167#217C22×D318yes—
168#217C22×D318yes—
169C4⋊Dic3—316no—
170C4⋊Dic3C22×D318yes—
171Dic3⋊C4—316no—
172Dic3⋊C4—316no—
173Dic3⋊C4—316no—
174Dic3⋊C4—316no—
175Dic3⋊C4—316no—
176Dic3⋊C4—68no—
177Dic3⋊C4C22×D3116yes—
178C4×Dic3—38no—
179C4×Dic3—38no—
180C4×Dic3—316no—
181C4×Dic3—316no—
182C4×Dic3—64no—
183C4×Dic3—64no—
184C22×C32—22no—
185C22×C32—24no—
186C22×C32—44no—
187C22×C32C22×Q812yes—
188C22×C32C22×Q814yes—
189C22×C32C2511yescharacteristic
190C32×C4—24no—
191C3⋊Dic3—24no—
192C3⋊Dic3C22×Q812yes—
193C3⋊Dic3C22×Q814yes—
194C3⋊Dic3C22×Q812yes—
195C3×Dic3—216no—
196C23×C4—91no—
197C4⋊Q8—94no—
198C4⋊Q8—916no—
199C4⋊Q8—94no—
200#125—916no—
201#125—98no—
202C22⋊Q8—38no—
203C22⋊Q8—316no—
204C22⋊Q8—98no—
205C22⋊Q8—916no—
206C4×Q8—98no—
207C4×Q8—98no—
208#117—94no—
209#117—94no—
210#117—94no—
211#117—94no—
212#117—94no—
213#117—94no—
214C2×C4⋊C4—94no—
215C2×C4⋊C4—92no—
216C2×C22⋊C4—34no—
217C2×C22⋊C4—91no—
218C2×C22⋊C4D3211yescharacteristic
219C2×C42—94no—
220C2×C42—92no—
221C23×C3—21no—
222C23×C3—22no—
223C23×C3—24no—
224C23×C3—44no—
225C23×C3—44no—
226C23×C3D3×Q818yes—
227C23×C3C23×D314yes—
228C23×C3C23×D312yes—
229C3×Q8—128no—
230C2×C3×C4—24no—
231C2×C3×C4—316no—
232C2×C3×C4—44no—
233C2×C3×C4—44no—
234C2×C3×C4—128no—
235C2×C3×C4C23×D318yes—
236C2×Dic3—316no—
237C2×Dic3—38no—
238C2×Dic3—316no—
239C2×Dic3—38no—
240C2×Dic3—32no—
241C2×Dic3—34no—
242C2×Dic3—32no—
243C2×Dic3—38no—
244C2×Dic3—48no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—68no—
248C2×Dic3—68no—
249C2×Dic3—61no—
250C2×Dic3—61no—
251C2×Dic3—62no—
252C2×Dic3—64no—
253C2×Dic3—124no—
254C2×Dic3—124no—
255C2×Dic3C23×D3116yes—
256Dic6—48no—
257Dic6—1216no—
258C2×C32—22no—
259C2×C32—24no—
260C2×C32C23×Q811yescharacteristic
261C2×C32#58512yes—
262C24C2×D3211yescharacteristic
263C2×Q8—38no—
264C2×Q8—98no—
265C22×C4—38no—
266C22×C4—91no—
267C22×C4—92no—
268C22×C4—91no—
269C22×C4—92no—
270C22×C4—98no—
271C22×C4—92no—
272C22×C4C2×D3212yes—
273C4⋊C4—316no—
274C4⋊C4—38no—
275C4⋊C4—98no—
276C4⋊C4—98no—
277C4⋊C4—98no—
278C4⋊C4—916no—
279C4⋊C4—98no—
280C22⋊C4—38no—
281C22⋊C4—38no—
282C22⋊C4—94no—
283C22⋊C4C2×D3214yes—
284C42—98no—
285C42—98no—
286C42—94no—
287C42—94no—
288C22×C3—24no—
289C22×C3—28no—
290C22×C3—24no—
291C22×C3—22no—
292C22×C3—24no—
293C22×C3—21no—
294C22×C3—44no—
295C22×C3—48no—
296C22×C3—48no—
297C22×C3C2×D3×Q818yes—
298C22×C3C2×D3×Q814yes—
299C22×C3C24×D312yes—
300C3×C4—28no—
301C3×C4—44no—
302C3×C4—616no—
303Dic3—216no—
304Dic3—34no—
305Dic3—38no—
306Dic3—34no—
307Dic3—62no—
308Dic3—62no—
309Dic3—64no—
310Dic3—68no—
311Dic3—124no—
312C32#345811yescharacteristic, complemented, Sylow
313C23—42no—
314C23#379714yes—
315C23C22×D3211yescharacteristic
316C23C22×D3212yes—
317Q8—128no—
318Q8—368no—
319C2×C4—316no—
320C2×C4—42no—
321C2×C4—94no—
322C2×C4—98no—
323C2×C4—94no—
324C2×C4—98no—
325C2×C4—91no—
326C2×C4—92no—
327C2×C4—91no—
328C2×C4—94no—
329C2×C4—128no—
330C2×C4—362no—
331C2×C4C22×D3214yes—
332C2×C3—24no—
333C2×C3—24no—
334C2×C3—28no—
335C2×C3—21no—
336C2×C3—22no—
337C2×C3—44no—
338C2×C3C22×D3×Q812yes—
339C2×C3#596614yes—
340C22—22no—
341C22—24no—
342C22—44no—
343C22C2×#379712yes—
344C22C2×#379714yes—
345C22C23×D3211yescharacteristic
346C4—24no—
347C4—616no—
348C4—92no—
349C4—94no—
350C4—92no—
351C4—184no—
352C3—21no—
353C3#8657112yescomplemented
354C2—22no—
355C2—24no—
356C2C22×#379711yescharacteristic
357C2#1059667912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C22⋊C4C22
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#3458
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
5. #10594813C2semidirect
6. #10594810C2semidirect
7. #10594033C2semidirect
8. #10594030C2semidirect
28. #63919C22semidirect
29. #63873C22semidirect
30. #63870C22semidirect
31. #63847C22semidirect
32. #63843C22semidirect
33. #63839C22semidirect
34. #63838C22semidirect
47. C22×C3⋊Dic3Q8semidirect
312. C32#3458semidirect
353. C3#86571semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C3×#54832
#105955212
C2×#639572
#105948132
#105948102
#105940332
#105940302
#865713