Finite Group Databasebeta

← #11785128

Subgroups — #11785128

Order 1152.

885 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 885 conjugacy classes of subgroups — too many to draw. Only its 134 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×#64102C211yesmaximal, characteristic
2#10591120C212yesmaximal, complemented
3C2×#63559C212yesmaximal
4C3×#4530C212yesmaximal, complemented
5#68994—32nomaximal
6C22×C4⋊(C3⋊D3)C2211yescharacteristic
7C22×C4×C3⋊D3C412yes—
8C2×C32×C4⋊C4C2211yescharacteristic
9C2×#3752C412yes—
10C2×C4×C3⋊Dic3C2211yescharacteristic
11#64102—22no—
12#64102—22no—
13C2×C3×#208C2214yes—
14#63572—22no—
15#63572—22no—
16#63559—24no—
17C2×#893—32no—
18C2×#893—61no—
19C2×#823—34no—
20#5118—34no—
21C3×#343—32no—
22#4530D312yescomplemented
23C23×C3⋊D3C2×C412yes—
24C22×C32×C4C2×C412yes—
25C22×C32×C4C2311yescharacteristic
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C2×C4⋊(C3⋊D3)—22no—
29C2×C4⋊(C3⋊D3)—22no—
30C2×C4⋊(C3⋊D3)D412yes—
31C2×C4⋊(C3⋊D3)Q812yes—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—22no—
34C2×C4×C3⋊D3—44no—
35C32×C4⋊C4—22no—
36#3752—24no—
37C4×C3⋊Dic3D412yes—
38C4×C3⋊Dic3D412yes—
39C3×#208—24no—
40C3×#208—24no—
41C2×C3×C3⋊C8—24no—
42#1800—91noSylow
43C22×D12—32no—
44C22×D12—61no—
45C22×C4×D3—34no—
46C22×C4×D3—62no—
47C2×C3×M16—34no—
48C2×C3×C4⋊C4—21no—
49C2×C3×C4⋊C4C2×D312yes—
50C2×(C2×D3)⋊C4—34no—
51C2×(C2×D3)⋊C4—62no—
52C2×C4×Dic3—32no—
53C2×C4×Dic3—61no—
54C2×#208C2×D314yes—
55#893—64no—
56#893—64no—
57#893—64no—
58#893—64no—
59#823—68no—
60Dic3⋊C8—64no—
61Dic3⋊C8—64no—
62C23×C32C22×C411yescharacteristic
63C22×C3⋊D3—22no—
64C22×C3⋊D3—22no—
65C22×C3⋊D3—42no—
66C22×C3⋊D3—42no—
67C22×C3⋊D3C4⋊C414yes—
68C2×C32×C4—22no—
69C2×C32×C4—42no—
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2×Q811yescharacteristic
73C2×C32×C4#4112yes—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—41no—
76C2×C3⋊Dic3C22⋊C412yes—
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C22⋊C411yescharacteristic
79C4⋊(C3⋊D3)—24no—
80C4⋊(C3⋊D3)—24no—
81C4×C3⋊D3—44no—
82C4×C3⋊D3—44no—
83C3×C3⋊C8—44no—
84C2×C4×D4—91no—
85#423—92no—
86C2×#100—92no—
87#343—32no—
88C23×D3—34no—
89C23×D3—62no—
90C22×C3×C4—22no—
91C22×C3×C4—21no—
92C22×C3×C4C4×D314yes—
93C22×C3×C4C22×D312yes—
94C22×Dic3—32no—
95C22×Dic3—32no—
96C22×Dic3—61no—
97C22×Dic3—61no—
98C2×D12—34no—
99C2×D12—34no—
100C2×D12—62no—
101C2×D12—62no—
102C2×D12—64no—
103C2×D12—64no—
104C2×D12—64no—
105C2×D12—64no—
106C2×C4×D3—64no—
107C2×C4×D3—64no—
108C2×C4×D3—64no—
109C2×C4×D3—64no—
110C2×C4×D3—128no—
111C2×C4×D3—128no—
112C3×M16—64no—
113C3×M16—64no—
114C2×C3×C8—64no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—24no—
117(C2×D3)⋊C4—68no—
118(C2×D3)⋊C4—68no—
119C4×Dic3—34no—
120C4×Dic3—34no—
121C4×Dic3—62no—
122C4×Dic3—62no—
123#208—24no—
124#208—24no—
125C2×C3⋊C8—24no—
126C22×C32—21no—
127C22×C32—21no—
128C22×C32C2×C22⋊C411yescharacteristic
129C22×C32C2×C4⋊C411yescharacteristic
130C22×C32#11711yescharacteristic
131C2×C3⋊D3—24no—
132C2×C3⋊D3—44no—
133C2×C3⋊D3—42no—
134C2×C3⋊D3—42no—
135C2×C3⋊D3—44no—
136C32×C4—42no—
137C32×C4#12112yes—
138C32×C4C22⋊Q812yes—
139C3⋊Dic3—21no—
140C3⋊Dic3—22no—
141C3⋊Dic3#10012yescomplemented
142C22×D4—91no—
143C23×C4—92no—
144C2×M16—34no—
145C4×D4—182no—
146C4×D4—182no—
147C2×C4⋊C4D3211yescharacteristic
148C2×C22⋊C4—92no—
149C2×C42—91no—
150C4⋊C8—182no—
151C4⋊C8—182no—
152#100—184no—
153C23×C3—21no—
154C23×C3C2×C4×D312yes—
155C22×D3—38no—
156C22×D3—64no—
157C22×D3—64no—
158C22×D3—64no—
159C22×D3—64no—
160C22×D3—64no—
161C22×D3—124no—
162C22×D3—124no—
163C22×D3—124no—
164C22×D3—124no—
165C2×C3×C4—24no—
166C2×C3×C4—24no—
167C2×C3×C4—21no—
168C2×C3×C4—22no—
169C2×C3×C4—21no—
170C2×C3×C4—22no—
171C2×C3×C4—44no—
172C2×C3×C4—44no—
173C2×C3×C4#23514yes—
174C2×C3×C4D3×D412yes—
175C2×C3×C4D3×D414yes—
176C2×C3×C4D3×Q812yes—
177C2×Dic3—32no—
178C2×Dic3—34no—
179C2×Dic3—32no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—62no—
183C2×Dic3—64no—
184C2×Dic3—64no—
185C2×Dic3—122no—
186C2×Dic3—122no—
187D12—68no—
188D12—68no—
189D12—68no—
190D12—68no—
191C4×D3—128no—
192C4×D3—128no—
193C4×D3—128no—
194C4×D3—128no—
195C3×C8—124no—
196C3⋊C8—44no—
197C2×C32—21no—
198C2×C32—21no—
199C2×C32#38011yescharacteristic
200C2×C32C2×#10011yescharacteristic
201C2×C32#41311yescharacteristic
202C3⋊D3—44no—
203C24—92no—
204C2×D4—92no—
205C2×D4—92no—
206C2×D4—182no—
207C2×D4—182no—
208C22×C4—91no—
209C22×C4—91no—
210C22×C4—182no—
211C22×C4—182no—
212C22×C4—364no—
213C22×C4#62412yes—
214C22×C4C2×D3211yescharacteristic
215M16—64no—
216M16—64no—
217C2×C8—64no—
218C4⋊C4—22no—
219C22⋊C4—184no—
220C42—92no—
221C42—92no—
222C22×C3—22no—
223C22×C3—22no—
224C22×C3—22no—
225C22×C3—22no—
226C22×C3—21no—
227C22×C3—21no—
228C22×C3—21no—
229C22×C3#87212yes—
230C22×C3D3×C22⋊C412yes—
231C22×C3D3×C4⋊C412yes—
232C2×D3—68no—
233C2×D3—68no—
234C2×D3—124no—
235C2×D3—128no—
236C2×D3—128no—
237C2×D3—128no—
238C2×D3—124no—
239C2×D3—124no—
240C2×D3—124no—
241C2×D3—128no—
242C3×C4—22no—
243C3×C4—22no—
244C3×C4—44no—
245C3×C4—44no—
246C3×C4#88414yes—
247C3×C4#89614yes—
248Dic3—34no—
249Dic3—62no—
250Dic3—62no—
251Dic3—62no—
252Dic3—64no—
253Dic3—122no—
254C32#180011yescharacteristic, complemented, Sylow
255C23—94no—
256C23—182no—
257C23—182no—
258C23—362no—
259C23—362no—
260C23C2×#62411yescharacteristic
261D4—184no—
262D4—184no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—91no—
266C2×C4—92no—
267C2×C4—91no—
268C2×C4—182no—
269C2×C4—364no—
270C2×C4—364no—
271C2×C4—361no—
272C2×C4#379711yescharacteristic
273C2×C4#379812yes—
274C2×C4#380211yescharacteristic
275C2×C4#381112yes—
276C8—124no—
277C2×C3—22no—
278C2×C3—22no—
279C2×C3—22no—
280C2×C3—22no—
281C2×C3—21no—
282C2×C3—21no—
283C2×C3—21no—
284C2×C3#466712yes—
285C2×C3D3×#10012yes—
286C2×C3#475112yes—
287D3—128no—
288D3—128no—
289C22—21no—
290C22—21no—
291C22—184no—
292C22—364no—
293C22—364no—
294C22—362no—
295C22—362no—
296C22#6387411yescharacteristic
297C22#6390011yescharacteristic
298C22#6397411yescharacteristic
299C4—42no—
300C4—92no—
301C4—181no—
302C4—182no—
303C4#6386512yes—
304C4#6391212yes—
305C3—21no—
306C3#6899412yescomplemented
307C2—21no—
308C2—21no—
309C2—364no—
310C2#1059135511yescharacteristic
311C2#1059150311yescharacteristic
312C2#1059164011yescharacteristic
subgroupG/H
centerC22#63974
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1800
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10591120C2semidirect
4. C3×#4530C2semidirect
22. #4530D3semidirect
141. C3⋊Dic3#100semidirect
254. C32#1800semidirect
306. C3#68994semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
#105911202
C2×#635592
C3×#45302
#689943