Finite Group Databasebeta

← #11800942

Subgroups — #11800942

Order 1152.

1345 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#627C211yesmaximal, characteristic
2C2×#63838C212yesmaximal
3#10592347C211yesmaximal, characteristic
4C3×#4649C212yesmaximal
5C4×#3724C212yesmaximal
6#10591257C211yesmaximal, characteristic
7Dic3×Dic3⋊C4C214yesmaximal
8#10591239C212yesmaximal
9#73616—32nomaximal
10C22×#627C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C4×C3⋊Dic3C2212yes—
13C2×C3×Dic3⋊C4C2214yes—
14C2×C3×C4×Dic3C2214yes—
15C2×C3×C4×Dic3C2212yes—
16C2×#3724C2212yes—
17C2×#3724C2211yescharacteristic
18C2×Dic3⋊Dic3C2212yes—
19C2×Dic32C2212yes—
20C2×Dic32C2214yes—
21C4×#627C418yescomplemented
22#63838C4116yescomplemented
23C32×#95C2211yescharacteristic
24#63658C2211yescharacteristic
25#63658C2212yes—
26C3×C3⋊#95C2212yes—
27#63579C2214yes—
28C2×#887—34no—
29C2×C4×Dic6—32no—
30C3×C4×C4⋊C4—32no—
31Dic3×C4⋊C4—34no—
32#4932—32no—
33C4×Dic3⋊C4—34no—
34C4×Dic3⋊C4—34no—
35#4649—32no—
36#4649D312yes—
37#4648—32no—
38#4648—32no—
39#4648—61no—
40C22×C32×C4C2312yes—
41C22×C32×C4C2311yescharacteristic
42C22×C3⋊Dic3C2312yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3⋊Dic3C2311yescharacteristic
45C22×C3×Dic3C2312yes—
46C22×C3×Dic3C2314yes—
47C22×C3×Dic3C2312yes—
48C2×#627C2×C418yes—
49C2×#627C2×C414yes—
50C4×C3⋊Dic3C2×C418yes—
51C4×C3⋊Dic3C2×C414yes—
52C3×Dic3⋊C4C2×C4116yes—
53C3×C4×Dic3—44no—
54C3×C4×Dic3C2×C418yes—
55#3724C2×C418yes—
56#3724C2×C414yes—
57Dic3⋊Dic3C2×C418yes—
58Dic32—42no—
59Dic32C2×C4116yes—
60#2276—91noSylow
61C22×Dic6—32no—
62C2×C3×C4⋊C4—34no—
63C2×C3×C42—32no—
64C2×C3×C42—34no—
65C2×C4⋊Dic3—32no—
66C2×Dic3⋊C4—34no—
67C2×Dic3⋊C4—32no—
68C2×Dic3⋊C4—32no—
69C2×Dic3⋊C4C2×D314yes—
70C2×C4×Dic3—32no—
71C2×C4×Dic3—34no—
72C2×C4×Dic3—34no—
73C2×C4×Dic3—34no—
74C2×C4×Dic3—34no—
75C2×C4×Dic3—61no—
76C2×C4×Dic3—62no—
77C2×C4×Dic3C2×D314yes—
78C2×C4×Dic3C2×D312yes—
79#887—332no—
80C4×Dic6—316no—
81C3×#95—21no—
82C3×#95—32no—
83C3×#95C2×D312yes—
84C3⋊#95—32no—
85C3⋊#95—34no—
86C3⋊#95—34no—
87C3⋊#95—34no—
88C3⋊#95—61no—
89C3⋊#95—62no—
90C3⋊#95C2×D312yes—
91C23×C32C2411yescharacteristic
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4C22×C412yes—
96C2×C32×C4C22×C414yes—
97C2×C3⋊Dic3—21no—
98C2×C3⋊Dic3—22no—
99C2×C3⋊Dic3—21no—
100C2×C3⋊Dic3—22no—
101C2×C3⋊Dic3C22×C414yes—
102C2×C3⋊Dic3C22×C412yes—
103C2×C3⋊Dic3C22×C414yes—
104C2×C3⋊Dic3C22×C412yes—
105C2×C3×Dic3—24no—
106C2×C3×Dic3—22no—
107C2×C3×Dic3—22no—
108C2×C3×Dic3—24no—
109C2×C3×Dic3C22×C418yes—
110C2×C3×Dic3C22×C414yes—
111C2×C3×Dic3C22×C418yes—
112C2×C3×Dic3C22×C414yes—
113#627C42116yescomplemented
114C2×C4×Q8—91no—
115C2×C4×Q8—92no—
116C4×C4⋊C4—32no—
117C4×C4⋊C4—91no—
118C4×C4⋊C4—92no—
119C4×C4⋊C4—94no—
120#376—92no—
121#376—91no—
122C22×C3×C4—21no—
123C22×C3×C4—22no—
124C22×C3×C4—32no—
125C22×C3×C4—32no—
126C22×C3×C4—34no—
127C22×C3×C4C22×D312yes—
128C22×C3×C4C22×D314yes—
129C22×Dic3—32no—
130C22×Dic3—34no—
131C22×Dic3—32no—
132C22×Dic3—61no—
133C22×Dic3—62no—
134C22×Dic3—61no—
135C22×Dic3C22×D312yes—
136C22×Dic3C22×D314yes—
137C22×Dic3C22×D312yes—
138C2×Dic6—38no—
139C2×Dic6—316no—
140C3×C4⋊C4—316no—
141C3×C42—38no—
142C3×C42—124no—
143C4⋊Dic3—38no—
144Dic3⋊C4—38no—
145Dic3⋊C4—38no—
146Dic3⋊C4—316no—
147Dic3⋊C4C4×D3116yes—
148C4×Dic3—38no—
149C4×Dic3—316no—
150C4×Dic3—316no—
151C4×Dic3—316no—
152C4×Dic3—44no—
153C4×Dic3—68no—
154C4×Dic3—64no—
155C4×Dic3—124no—
156C4×Dic3C4×D318yes—
157C22×C32C23×C411yescharacteristic
158C22×C32C23×C412yes—
159C22×C32H(5,𝔽2)11yescharacteristic
160C22×C322−1+411yescharacteristic
161C22×C322−1+412yes—
162C32×C4—22no—
163C32×C4—24no—
164C3⋊Dic3—24no—
165C3⋊Dic3—22no—
166C3⋊Dic3C2×C4214yes—
167C3×Dic3—24no—
168C3×Dic3—28no—
169C3×Dic3C2×C4218yes—
170C22×Q8—91no—
171C4×Q8—98no—
172C4×Q8—916no—
173C2×C4⋊C4—34no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—91no—
176C2×C4⋊C4—92no—
177C2×C42—32no—
178C2×C42—34no—
179C2×C42—94no—
180C2×C42—92no—
181C2×C42—91no—
182C2×C42—92no—
183#95—32no—
184#95—94no—
185#95—91no—
186#95—92no—
187#95D3211yescharacteristic
188C23×C3—21no—
189C23×C3C23×D312yes—
190C2×C3×C4—24no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4—22no—
194C2×C3×C4—24no—
195C2×C3×C4—38no—
196C2×C3×C4—34no—
197C2×C3×C4—38no—
198C2×C3×C4—34no—
199C2×C3×C4—42no—
200C2×C3×C4—42no—
201C2×C3×C4—42no—
202C2×C3×C4—64no—
203C2×C3×C4—62no—
204C2×C3×C4—62no—
205C2×C3×C4—64no—
206C2×C3×C4C2×C4×D314yes—
207C2×C3×C4C2×C4×D318yes—
208C2×Dic3—22no—
209C2×Dic3—24no—
210C2×Dic3—22no—
211C2×Dic3—24no—
212C2×Dic3—34no—
213C2×Dic3—38no—
214C2×Dic3—38no—
215C2×Dic3—34no—
216C2×Dic3—64no—
217C2×Dic3—62no—
218C2×Dic3—64no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—64no—
223C2×Dic3—64no—
224C2×Dic3—122no—
225C2×Dic3—121no—
226C2×Dic3—122no—
227C2×Dic3—121no—
228C2×Dic3C2×C4×D318yes—
229C2×Dic3C2×C4×D314yes—
230C2×Dic3C2×C4×D318yes—
231C2×Dic3C2×C4×D314yes—
232Dic6—332no—
233C2×C32C22×C4211yescharacteristic
234C2×C32#51911yescharacteristic
235C2×C32#51912yes—
236C2×C32#52011yescharacteristic
237C2×C32#52012yes—
238C2×Q8—94no—
239C2×Q8—98no—
240C22×C4—32no—
241C22×C4—34no—
242C22×C4—32no—
243C22×C4—91no—
244C22×C4—92no—
245C22×C4—91no—
246C22×C4C2×D3211yescharacteristic
247C22×C4C2×D3212yes—
248C4⋊C4—316no—
249C4⋊C4—94no—
250C4⋊C4—98no—
251C4⋊C4—98no—
252C42—38no—
253C42—916no—
254C42—98no—
255C42—94no—
256C42—124no—
257C42—362no—
258C22×C3—22no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3C22×C4×D312yes—
264C22×C3C22×C4×D314yes—
265C22×C3#100412yes—
266C22×C3#100712yes—
267C22×C3#101014yes—
268C3×C4—24no—
269C3×C4—28no—
270C3×C4—38no—
271C3×C4—44no—
272C3×C4—42no—
273C3×C4—64no—
274C3×C4—68no—
275Dic3—24no—
276Dic3—28no—
277Dic3—38no—
278Dic3—64no—
279Dic3—64no—
280Dic3—68no—
281Dic3—124no—
282Dic3—122no—
283Dic3C42×D318yes—
284C32#227611yescharacteristic, complemented, Sylow
285C23C22×D3211yescharacteristic
286Q8—916no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—34no—
291C2×C4—38no—
292C2×C4—34no—
293C2×C4—38no—
294C2×C4—64no—
295C2×C4—62no—
296C2×C4—64no—
297C2×C4—62no—
298C2×C4—94no—
299C2×C4—92no—
300C2×C4—94no—
301C2×C4—92no—
302C2×C4—182no—
303C2×C4—181no—
304C2×C4—182no—
305C2×C4—181no—
306C2×C4C4×D3212yes—
307C2×C4C4×D3214yes—
308C2×C3—22no—
309C2×C3—22no—
310C2×C3—21no—
311C2×C3—21no—
312C2×C3—21no—
313C2×C3C2×C42×D312yes—
314C2×C3#550412yes—
315C2×C3#551612yes—
316C2×C3#554614yes—
317C2×C3#557214yes—
318C22C2×C4×D3212yes—
319C22C2×C4×D3211yescharacteristic
320C22#6430912yes—
321C22#6431311yescharacteristic
322C22#6431611yescharacteristic
323C4—24no—
324C4—22no—
325C4—38no—
326C4—68no—
327C4—64no—
328C4—94no—
329C4—184no—
330C4—182no—
331C3—21no—
332C3#7361612yescomplemented
333C2C42×D3211yescharacteristic
334C2#1059405112yes—
335C2#1059424511yescharacteristic
336C2#1059434712yes—
337C2#1059450911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2276
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
21. C4×#627C4semidirect
22. #63838C4semidirect
113. #627C42semidirect
284. C32#2276semidirect
332. C3#73616semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6272
C2×#638382
#105923472
C3×#46492
C4×#37242
#105912572
Dic3×Dic3⋊C42
#105912392
#736163