Finite Group Databasebeta

← #11774694

Subgroups — #11774694

Order 1152.

584 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C4×#3802C211yesmaximal, characteristic
2C4×#3788C211yesmaximal, characteristic, complemented
3#10590299C211yesmaximal, characteristic, complemented
4#10590029C214yesmaximal, complemented
5C2×#3802C411yescharacteristic
6C2×C4×D32—21no—
7C2×#3788—21no—
8C42×C3⋊D3C2211yescharacteristic
9C3×C4×D12—21no—
10#63921—21no—
11#63902C412yes—
12C4×#625C2212yes—
13#63900C411yescharacteristic
14#63898—21no—
15#63777—21no—
16C4×#622C2212yescomplemented
17C3×#803—21no—
18#63572C2212yescomplemented
19#63557—21no—
20C4×D3×D4—61no—
21#4705—61no—
22C22×D32—21no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×C3×D12—21no—
27C2×C3×C4×D3—22no—
28C2×#625C2×C412yes—
29C2×#624—21no—
30C2×D3×Dic3—22no—
31#3802—24no—
32C4×D32—44no—
33C2×#622—22no—
34#3788—24no—
35C32×C42D411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C3×(C2×D3)⋊C4—22no—
40C3×C4⋊Dic3—21no—
41C2×C3×C3⋊C8—22no—
42#3724C2×C412yes—
43(C2×D3)⋊Dic3—22no—
44#1490—91nomaximal, Sylow
45C2×D3×D4—61no—
46C22×C4×D3—62no—
47C3×C4×D4—61no—
48D4×Dic3—61no—
49C4×#67—62no—
50#893—61no—
51D3×C4⋊C4—61no—
52#67⋊C4—62no—
53D3×C22⋊C4—62no—
54C4×D12—21no—
55C42×D3—61no—
56C42×D3—61no—
57C3×#97—61no—
58(C2×D3)⋊C8—62no—
59Dic3⋊C8—62no—
60#803—21no—
61C22×C3⋊D3C22⋊C411yescharacteristic
62C22×C3×D3—22no—
63C2×D32—24no—
64C2×D32—42no—
65C2×D32—42no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3C22⋊C411yescharacteristic
70C2×C3⋊Dic3C22×C411yescharacteristic
71C2×C3⋊Dic3C2×D411yescharacteristic
72C4×C3⋊D3—22no—
73C4×C3⋊D3—22no—
74C4×C3⋊D3—22no—
75C2×C3×Dic3—22no—
76C3×D12—24no—
77C3×C4×D3—44no—
78#625—22no—
79#625M1614yescomplemented
80#624—42no—
81D3×Dic3—44no—
82#622—24no—
83C3×C3⋊C8—42no—
84C2×C4×D4—91no—
85#432—91no—
86C4×M16—91no—
87D4⋊C8—94no—
88C23×D3—62no—
89C2×C3×D4—61no—
90C22×C3×C4—62no—
91C2×#67—62no—
92C22×Dic3—62no—
93D3×D4—68no—
94C2×D12—21no—
95C2×C4×D3—22no—
96C2×C4×D3—61no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—61no—
101C2×C4×D3—61no—
102C2×C4×D3—62no—
103C2×C4×D3—62no—
104C2×C4×D3—128no—
105C2×C3×C8—62no—
106C3×C4⋊C4—61no—
107C3×C22⋊C4—62no—
108C3×C42—21no—
109C3×C42—21no—
110#217—62no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—62no—
113C4⋊Dic3—21no—
114Dic3⋊C4—62no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C2×C3⋊C8—22no—
122C22×C32C2×C22⋊C411yescharacteristic
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C2×C3⋊D3#10412yes—
126C2×C3×D3—24no—
127C2×C3×D3—42no—
128C2×C3×D3—42no—
129D32—48no—
130C32×C4—21no—
131C32×C4—21no—
132C32×C4AGL(1,ℤ/8)12yes—
133C3⋊Dic3—21no—
134C3⋊Dic3—21no—
135C3⋊Dic3C2×M1612yes—
136C3×Dic3—42no—
137C22×D4—91no—
138C23×C4—181no—
139C2×M16—181no—
140C4×D4—61no—
141C4×D4—92no—
142C4×D4—92no—
143C4×D4—181no—
144C2×C4⋊C4—91no—
145C2×C22⋊C4—181no—
146C2×C42—91no—
147C4⋊C8—92no—
148C22⋊C8—181no—
149#97—61no—
150#97—181no—
151C4×C8—92no—
152C23×C3—62no—
153C22×D3—22no—
154C22×D3—61no—
155C22×D3—61no—
156C22×D3—68no—
157C22×D3—124no—
158C22×D3—124no—
159C3×D4—64no—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—62no—
167C2×C3×C4—124no—
168#67—64no—
169#67—64no—
170C2×Dic3—22no—
171C2×Dic3—61no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—124no—
178D12—24no—
179C4×D3—44no—
180C4×D3—64no—
181C4×D3—64no—
182C4×D3—122no—
183C4×D3—122no—
184C4×D3—122no—
185C4×D3—122no—
186C4×D3—124no—
187C4×D3—124no—
188C3×C8—122no—
189C3⋊C8—42no—
190C2×C32#40711yescharacteristic
191C2×C32#41811yescharacteristic
192C2×C32C2×#10411yescharacteristic
193C3⋊D3—22no—
194C3×D3—44no—
195C24—181no—
196C2×D4—61no—
197C2×D4—92no—
198C2×D4—184no—
199C22×C4—62no—
200C22×C4—91no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—181no—
204C22×C4—182no—
205C22×C4—364no—
206M16—184no—
207C2×C8—62no—
208C2×C8—182no—
209C4⋊C4—61no—
210C4⋊C4—92no—
211C22⋊C4—62no—
212C22⋊C4—182no—
213C42—91no—
214C42—91no—
215C42—91no—
216C42GO+(4,𝔽2)11yescharacteristic
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—64no—
220C22×C3—122no—
221C22×C3—122no—
222C2×D3—24no—
223C2×D3—42no—
224C2×D3—42no—
225C2×D3—62no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—121no—
230C2×D3—121no—
231C2×D3—1216no—
232C3×C4—22no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—41no—
236C3×C4—41no—
237C3×C4—41no—
238C3×C4—122no—
239Dic3—42no—
240Dic3—62no—
241Dic3—62no—
242Dic3—62no—
243Dic3—121no—
244Dic3—121no—
245Dic3—121no—
246C32#149011yescharacteristic, complemented, Sylow
247C23—62no—
248C23—91no—
249C23—184no—
250C23—362no—
251C23—362no—
252D4—64no—
253D4—94no—
254D4—182no—
255C2×C4—62no—
256C2×C4—91no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—124no—
260C2×C4—182no—
261C2×C4—182no—
262C2×C4—182no—
263C2×C4—362no—
264C2×C4—364no—
265C2×C4D32⋊C411yescharacteristic
266C2×C4D32⋊C411yescharacteristic
267C2×C4C2×GO+(4,𝔽2)11yescharacteristic
268C8—122no—
269C8—184no—
270C2×C3—21no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—124no—
277D3—44no—
278D3—64no—
279D3—122no—
280C22—64no—
281C22—92no—
282C22—122no—
283C22—122no—
284C22—181no—
285C22—181no—
286C22—368no—
287C22C2×D32⋊C411yescharacteristic
288C4—21no—
289C4—21no—
290C4—92no—
291C4—122no—
292C4—181no—
293C4—181no—
294C4#6422412yes—
295C3—21no—
296C3—21no—
297C2—124no—
298C2—182no—
299C2#1059330711yescharacteristic
300C2#1059332511yescharacteristic
301C2#1059336311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3802C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1490
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4×#3788C2semidirect
3. #10590299C2semidirect
4. #10590029C2semidirect
16. C4×#622C22semidirect
18. #63572C22semidirect
79. #625M16semidirect
246. C32#1490semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
C4×#37882
#105902992
#105900292
#14909