Finite Group Databasebeta

← #11790836

Subgroups — #11790836

Order 1152.

834 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 834 conjugacy classes of subgroups — too many to draw. Only its 74 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×#64104C211yesmaximal, characteristic
2#10593812C211yesmaximal, characteristic, complemented
3C4×C22⋊#157C211yesmaximal, characteristic, complemented
4C2×#63774C214yesmaximal, complemented
5C22×C4⋊(C3⋊D3)C411yescharacteristic, complemented
6C22×C4⋊(C3⋊D3)C2212yes—
7C22×C4×C3⋊D3C2211yescharacteristic
8C2×C22⋊#157C2212yes—
9C2×C22⋊#157C2212yes—
10C2×C4⋊#157—21no—
11C2×C4×#157—21no—
12C2×C32×C4⋊C4C411yescharacteristic, complemented
13C2×#3752C412yescomplemented
14#64104—21no—
15#64104—21no—
16#64104—21no—
17#64104—21no—
18#63781—21no—
19#63781—21no—
20#63774—28no—
21C2×#895—62no—
22C23×C3⋊D3C2×C412yes—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—22no—
25C22×#157—22no—
26C22×C32×C4C2×C412yes—
27C22×C32×C4C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C2×C4⋊(C3⋊D3)—22no—
30C2×C4⋊(C3⋊D3)—22no—
31C2×C4⋊(C3⋊D3)—24no—
32C2×C4⋊(C3⋊D3)—24no—
33C2×C4⋊(C3⋊D3)—21no—
34C2×C4⋊(C3⋊D3)—21no—
35C2×C4⋊(C3⋊D3)—42no—
36C2×C4×C3⋊D3—42no—
37C2×C4×C3⋊D3D411yescharacteristic
38C2×C4×C3⋊D3D411yescharacteristic
39C2×C4×C3⋊D3D411yescharacteristic
40C2×C4×C3⋊D3D411yescharacteristic
41C22⋊#157—22no—
42C22⋊#157—24no—
43C22⋊#157D414yescomplemented
44C4⋊#157—42no—
45C4×#157—42no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48#3752—22no—
49#3752—22no—
50#1964—91nomaximal, Sylow
51C22×D12—62no—
52C22×D12—64no—
53C22×C4×D3—62no—
54C2×C3×C4⋊C4—22no—
55C2×(C2×D3)⋊C4—64no—
56#895—64no—
57#895—64no—
58#895—64no—
59#895—64no—
60C23×C32C22×C411yescharacteristic
61C22×C3⋊D3—22no—
62C22×C3⋊D3—24no—
63C22×C3⋊D3—41no—
64C22×C3⋊D3—41no—
65C22×C3⋊D3—42no—
66C22×C3⋊D3—42no—
67C22×C3⋊D3C2×D411yescharacteristic
68C22×C3⋊D3C2×D411yescharacteristic
69C22×C3⋊D3C2×D412yes—
70C22×C3⋊D3#4112yes—
71C2×#157—24no—
72C2×#157—42no—
73C2×#157—42no—
74C2×#157—42no—
75C2×#157—42no—
76C2×#157—42no—
77C2×C32×C4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—24no—
80C2×C32×C4C22⋊C411yescharacteristic
81C2×C32×C4C22⋊C411yescharacteristic
82C2×C3⋊Dic3—41no—
83C2×C3⋊Dic3C22⋊C411yescharacteristic
84C2×C3⋊Dic3C22⋊C411yescharacteristic
85C4⋊(C3⋊D3)—42no—
86C4⋊(C3⋊D3)—44no—
87C4⋊(C3⋊D3)—42no—
88C4⋊(C3⋊D3)—42no—
89C4⋊(C3⋊D3)—42no—
90C4×C3⋊D3—22no—
91C4×C3⋊D3—22no—
92C4×C3⋊D3—41no—
93C4×C3⋊D3—41no—
94C2×#121—91no—
95C2×#99—94no—
96#380—91no—
97C4×C22⋊C4—91no—
98C23×D3—62no—
99C23×D3—64no—
100C22×C3×C4—24no—
101C22×C3×C4—22no—
102C22×Dic3—62no—
103C2×D12—68no—
104C2×D12—68no—
105C2×D12—64no—
106C2×D12—64no—
107C2×D12—128no—
108C2×D12—128no—
109C2×D12—128no—
110C2×C4×D3—62no—
111C2×C4×D3—62no—
112C2×C4×D3—62no—
113C2×C4×D3—62no—
114C2×C4×D3—128no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—24no—
117(C2×D3)⋊C4—68no—
118(C2×D3)⋊C4—68no—
119C22×C32—21no—
120C22×C32—21no—
121C22×C32C2×C22⋊C411yescharacteristic
122C22×C32C4×D412yes—
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3—21no—
127C2×C3⋊D3—42no—
128C2×C3⋊D3—42no—
129C2×C3⋊D3—42no—
130C2×C3⋊D3—42no—
131C2×C3⋊D3—42no—
132C2×C3⋊D3—84no—
133C2×C3⋊D3#12112yes—
134C2×C3⋊D3#12411yescharacteristic
135C2×C3⋊D3#12711yescharacteristic
136#157—44no—
137#157—82no—
138C32×C4—21no—
139C32×C4—42no—
140C32×C4#9912yescomplemented
141C3⋊Dic3—21no—
142C3⋊Dic3—21no—
143C22×D4—92no—
144C22×D4—91no—
145C23×C4—91no—
146#121—181no—
147#121—181no—
148#121—181no—
149#121—181no—
150C2×C4⋊C4—181no—
151C2×C4⋊C4#15711yescharacteristic, complemented
152C2×C22⋊C4—92no—
153C2×C22⋊C4—92no—
154C2×C22⋊C4—92no—
155C2×C42—181no—
156#99—188no—
157#95—181no—
158#95—181no—
159C23×C3—22no—
160C22×D3—62no—
161C22×D3—62no—
162C22×D3—64no—
163C22×D3—64no—
164C22×D3—68no—
165C22×D3—128no—
166C22×D3—124no—
167C22×D3—124no—
168C22×D3—128no—
169C22×D3—128no—
170C2×C3×C4—28no—
171C2×C3×C4—28no—
172C2×C3×C4—22no—
173C2×C3×C4—22no—
174C2×C3×C4—48no—
175C2×Dic3—62no—
176C2×Dic3—62no—
177C2×Dic3—124no—
178D12—128no—
179D12—128no—
180D12—1216no—
181D12—128no—
182D12—128no—
183C4×D3—124no—
184C4×D3—124no—
185C4×D3—124no—
186C4×D3—124no—
187C2×C32—22no—
188C2×C32#39011yescharacteristic
189C2×C32C2×#9911yescharacteristic
190C2×C32#41011yescharacteristic
191C3⋊D3—22no—
192C3⋊D3—21no—
193C3⋊D3—21no—
194C3⋊D3—82no—
195C24—91no—
196C24—92no—
197C2×D4—184no—
198C2×D4—182no—
199C2×D4—182no—
200C2×D4—184no—
201C2×D4—181no—
202C2×D4—181no—
203C2×D4—362no—
204C22×C4—91no—
205C22×C4—91no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—91no—
209C22×C4—182no—
210C22×C4—182no—
211C22×C4—362no—
212C22×C4C2×#15712yes—
213C22×C4C2×#15711yescharacteristic
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—362no—
217C22⋊C4—94no—
218C22⋊C4—182no—
219C22⋊C4—182no—
220C22⋊C4—182no—
221C22⋊C4—184no—
222C42—362no—
223C22×C3—24no—
224C22×C3—24no—
225C22×C3—24no—
226C22×C3—22no—
227C2×D3—64no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—122no—
231C2×D3—122no—
232C2×D3—122no—
233C2×D3—122no—
234C2×D3—128no—
235C2×D3—128no—
236C2×D3—128no—
237C2×D3—128no—
238C2×D3—128no—
239C2×D3—2416no—
240C3×C4—24no—
241C3×C4—24no—
242C3×C4—48no—
243Dic3—122no—
244Dic3—122no—
245C32#196411yescharacteristic, complemented, Sylow
246C23—91no—
247C23—91no—
248C23—92no—
249C23—92no—
250C23—182no—
251C23—184no—
252C23—361no—
253C23—361no—
254C23—362no—
255C23—362no—
256C23C22×#15711yescharacteristic
257D4—362no—
258D4—364no—
259D4—362no—
260D4—362no—
261D4—362no—
262C2×C4—22no—
263C2×C4—24no—
264C2×C4—22no—
265C2×C4—91no—
266C2×C4—91no—
267C2×C4—182no—
268C2×C4—182no—
269C2×C4—184no—
270C2×C4—361no—
271C2×C4—361no—
272C2×C4—361no—
273C2×C4—362no—
274C2×C4—362no—
275C2×C4—362no—
276C2×C4—362no—
277C2×C4—362no—
278C2×C4C22⋊#15711yescharacteristic
279C2×C4C22⋊#15711yescharacteristic
280C2×C3—28no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—22no—
284D3—124no—
285D3—122no—
286D3—122no—
287D3—248no—
288C22—21no—
289C22—21no—
290C22—92no—
291C22—91no—
292C22—91no—
293C22—181no—
294C22—181no—
295C22—181no—
296C22—181no—
297C22—362no—
298C22—362no—
299C22—362no—
300C22—362no—
301C22—362no—
302C22—724no—
303C22D4×#15712yes—
304C22C2×C22⋊#15711yescharacteristic
305C4—21no—
306C4—42no—
307C4—181no—
308C4—181no—
309C4—364no—
310C4—722no—
311C4#6377412yescomplemented
312C3—22no—
313C2—22no—
314C2—182no—
315C2—181no—
316C2—181no—
317C2—722no—
318C2C2×#6377411yescharacteristic
319C2#1059382711yescharacteristic
320C2#1059383211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#64104C2
cosocleC23×C3⋊D3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1964
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. #10593812C2semidirect
3. C4×C22⋊#157C2semidirect
4. C2×#63774C2semidirect
5. C22×C4⋊(C3⋊D3)C4semidirect
12. C2×C32×C4⋊C4C4semidirect
13. C2×#3752C4semidirect
43. C22⋊#157D4semidirect
140. C32×C4#99semidirect
151. C2×C4⋊C4#157semidirect
245. C32#1964semidirect
311. C4#63774semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
#105938122
C4×C22⋊#1572
C2×#637742
#19649