Finite Group Databasebeta

← #11783379

Subgroups — #11783379

Order 1152.

1005 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 1005 conjugacy classes of subgroups — too many to draw. Only its 188 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64086C211yesmaximal, characteristic
2C2×#63957C212yesmaximal
3C3×#4526C212yesmaximal
4#10589187C212yesmaximal
5#68951—32nomaximal
6C23×C3⋊Dic3C2211yescharacteristic
7C2×C32×C22⋊C4C2211yescharacteristic
8C2×#3757C2211yescharacteristic
9C2×#3750C412yescomplemented
10C2×C4×C3⋊Dic3C412yescomplemented
11#64086—22no—
12#64086—22no—
13C2×C3×#217C2214yes—
14C2×#3724—22no—
15#63957—24no—
16#63957C418yescomplemented
17C2×Dic32—22no—
18C2×#877—34no—
19C2×#877—32no—
20C2×#877—61no—
21C3×#342—32no—
22#4527—34no—
23#4526D312yes—
24C24×C32C2311yescharacteristic
25C22×C32×C4C2×C412yes—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C414yes—
30C22×C3⋊Dic3D412yes—
31C22×C3⋊Dic3D412yes—
32C22×C3⋊Dic3D412yes—
33C22×C3⋊Dic3Q812yes—
34C22×C3×Dic3—24no—
35C32×C22⋊C4—22no—
36#3757—22no—
37#3750—24no—
38C4×C3⋊Dic3—22no—
39C4×C3⋊Dic3—22no—
40C3×#217—24no—
41C3×#217C2×C418yes—
42#3724—28no—
43Dic32—28no—
44#1740—91noSylow
45C23×Dic3—32no—
46C23×Dic3—61no—
47C2×C3×C22⋊C4—21no—
48C2×C3×C22⋊C4—34no—
49C2×C3×C22⋊C4C2×D312yes—
50C2×#217—32no—
51C2×#217—61no—
52C2×#217C2×D314yes—
53C2×Dic3⋊C4—34no—
54C2×Dic3⋊C4—62no—
55C2×Dic3⋊C4—64no—
56C2×C4×Dic3—34no—
57C2×C4×Dic3—62no—
58C2×C4×Dic3—64no—
59#877—316no—
60#877—68no—
61#877—64no—
62#877—64no—
63#877—64no—
64#877—64no—
65C23×C32—42no—
66C23×C32C22×C411yescharacteristic
67C23×C32C22×C412yes—
68C23×C32C2×D412yes—
69C23×C32C2×D411yescharacteristic
70C23×C32C2×Q811yescharacteristic
71C2×C32×C4—22no—
72C2×C32×C4—42no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—42no—
75C2×C3⋊Dic3C4212yes—
76C2×C3⋊Dic3C4212yes—
77C2×C3⋊Dic3C22⋊C414yes—
78C2×C3⋊Dic3C22⋊C414yes—
79C2×C3⋊Dic3C22⋊C411yescharacteristic
80C2×C3⋊Dic3C22⋊C411yescharacteristic
81C2×C3⋊Dic3C22⋊C412yes—
82C2×C3⋊Dic3C4⋊C412yes—
83C2×C3⋊Dic3C4⋊C412yes—
84C2×C3⋊Dic3C4⋊C414yes—
85C2×C3⋊Dic3C4⋊C414yes—
86C2×C3×Dic3—28no—
87C2×C3×Dic3—48no—
88C2×#117—91no—
89C2×#117—92no—
90#342—32no—
91#342—92no—
92C24×C3—21no—
93C24×C3C22×D312yes—
94C22×C3×C4—22no—
95C22×C3×C4—64no—
96C22×C3×C4C4×D314yes—
97C22×Dic3—24no—
98C22×Dic3—38no—
99C22×Dic3—32no—
100C22×Dic3—32no—
101C22×Dic3—34no—
102C22×Dic3—34no—
103C22×Dic3—34no—
104C22×Dic3—34no—
105C22×Dic3—34no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3—61no—
109C22×Dic3—61no—
110C22×Dic3—64no—
111C22×Dic3—62no—
112C22×Dic3—62no—
113C22×Dic3—62no—
114C3×C22⋊C4—24no—
115C3×C22⋊C4—24no—
116C3×C22⋊C4—38no—
117C3×C22⋊C4—64no—
118#217—24no—
119#217—64no—
120#217—64no—
121#217C4×D318yes—
122Dic3⋊C4—616no—
123Dic3⋊C4—68no—
124Dic3⋊C4—68no—
125C4×Dic3—616no—
126C4×Dic3—64no—
127C4×Dic3—64no—
128C4×Dic3—64no—
129C4×Dic3—64no—
130C22×C32—22no—
131C22×C32—24no—
132C22×C32—42no—
133C22×C32—41no—
134C22×C32—41no—
135C22×C32C2×C4211yescharacteristic
136C22×C32C2×C22⋊C412yes—
137C22×C32C2×C22⋊C411yescharacteristic
138C22×C32C2×C4⋊C412yes—
139C22×C32C2×C4⋊C411yescharacteristic
140C32×C4—42no—
141C3⋊Dic3—42no—
142C3⋊Dic3#9512yes—
143C3⋊Dic3#9514yes—
144C3⋊Dic3#9512yes—
145C3×Dic3—48no—
146C23×C4—91no—
147#117—98no—
148#117—182no—
149#117—182no—
150#117—184no—
151C2×C4⋊C4—92no—
152C2×C4⋊C4—182no—
153C2×C22⋊C4—34no—
154C2×C22⋊C4—91no—
155C2×C22⋊C4D3211yescharacteristic
156C2×C42—92no—
157C2×C42—182no—
158C23×C3—21no—
159C23×C3—22no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—22no—
163C23×C3—44no—
164C23×C3—44no—
165C23×C3C2×C4×D314yes—
166C23×C3C2×C4×D312yes—
167C23×C3D3×D412yes—
168C23×C3D3×D414yes—
169C23×C3D3×Q812yes—
170C2×C3×C4—24no—
171C2×C3×C4—24no—
172C2×C3×C4—44no—
173C2×C3×C4—44no—
174C2×C3×C4—68no—
175C2×C3×C4—128no—
176C2×Dic3—28no—
177C2×Dic3—34no—
178C2×Dic3—34no—
179C2×Dic3—38no—
180C2×Dic3—32no—
181C2×Dic3—32no—
182C2×Dic3—38no—
183C2×Dic3—34no—
184C2×Dic3—38no—
185C2×Dic3—38no—
186C2×Dic3—34no—
187C2×Dic3—34no—
188C2×Dic3—48no—
189C2×Dic3—62no—
190C2×Dic3—62no—
191C2×Dic3—61no—
192C2×Dic3—61no—
193C2×Dic3—62no—
194C2×Dic3—64no—
195C2×Dic3—64no—
196C2×Dic3—64no—
197C2×Dic3—64no—
198C2×Dic3—62no—
199C2×Dic3—62no—
200C2×Dic3—64no—
201C2×Dic3—64no—
202C2×Dic3—124no—
203C2×Dic3—124no—
204C2×C32—21no—
205C2×C32—21no—
206C2×C32—22no—
207C2×C32—22no—
208C2×C32C2×#9511yescharacteristic
209C2×C32#41012yes—
210C24C2×D3211yescharacteristic
211C22×C4—64no—
212C22×C4—92no—
213C22×C4—94no—
214C22×C4—92no—
215C22×C4—91no—
216C22×C4—91no—
217C22×C4—92no—
218C22×C4—92no—
219C22×C4—92no—
220C22×C4#62412yes—
221C4⋊C4—184no—
222C4⋊C4—188no—
223C22⋊C4—22no—
224C22⋊C4—38no—
225C22⋊C4—64no—
226C22⋊C4—182no—
227C42—182no—
228C42—182no—
229C42—188no—
230C22×C3—24no—
231C22×C3—28no—
232C22×C3—24no—
233C22×C3—21no—
234C22×C3—22no—
235C22×C3—21no—
236C22×C3—22no—
237C22×C3—21no—
238C22×C3—44no—
239C22×C3—44no—
240C22×C3—42no—
241C22×C3—42no—
242C22×C3—42no—
243C22×C3—44no—
244C22×C3—42no—
245C22×C3C42×D312yes—
246C22×C3D3×C22⋊C414yes—
247C22×C3D3×C22⋊C412yes—
248C22×C3D3×C4⋊C414yes—
249C22×C3D3×C4⋊C412yes—
250C3×C4—44no—
251C3×C4—44no—
252C3×C4—128no—
253Dic3—34no—
254Dic3—38no—
255Dic3—34no—
256Dic3—48no—
257Dic3—62no—
258Dic3—62no—
259Dic3—64no—
260Dic3—124no—
261Dic3—124no—
262C32#174011yescharacteristic, complemented, Sylow
263C23—42no—
264C23#379711yescharacteristic
265C23C4×D3212yes—
266C23#380211yescharacteristic
267C23C2×#62411yescharacteristic
268C23#381112yes—
269C2×C4—22no—
270C2×C4—42no—
271C2×C4—68no—
272C2×C4—92no—
273C2×C4—92no—
274C2×C4—94no—
275C2×C4—94no—
276C2×C4—92no—
277C2×C4—92no—
278C2×C4—94no—
279C2×C4—94no—
280C2×C4—91no—
281C2×C4—91no—
282C2×C4—92no—
283C2×C4—128no—
284C2×C4—182no—
285C2×C4—362no—
286C2×C3—22no—
287C2×C3—22no—
288C2×C3—24no—
289C2×C3—22no—
290C2×C3—24no—
291C2×C3—22no—
292C2×C3—22no—
293C2×C3—21no—
294C2×C3—42no—
295C2×C3—42no—
296C2×C3D3×#9512yes—
297C2×C3#474014yes—
298C22—22no—
299C22—24no—
300C22—41no—
301C22—42no—
302C22—41no—
303C22C4×#62411yescharacteristic
304C22#6388312yes—
305C22#6390011yescharacteristic
306C22#6392112yes—
307C22#6397411yescharacteristic
308C4—42no—
309C4—92no—
310C4—94no—
311C4—92no—
312C4—128no—
313C4—362no—
314C3—21no—
315C3#6895112yescomplemented
316C2—22no—
317C2—21no—
318C2—22no—
319C2—21no—
320C2#1059137011yescharacteristic
321C2#1059152912yes—
subgroupG/H
centerC22#63974
commutatorC22×C32C2×C42
FrattiniC24C2×D32
FittingC2×C32×C22⋊C4C22
socleC22×C32C2×C22⋊C4
prime radical, cosocleC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#1740
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
9. C2×#3750C4semidirect
10. C2×C4×C3⋊Dic3C4semidirect
16. #63957C4semidirect
262. C32#1740semidirect
315. C3#68951semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×#639572
C3×#45262
#105891872
#689513