Finite Group Databasebeta

← #11774696

Subgroups — #11774696

Order 1152.

600 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 61 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
2#10593731C211yesmaximal, characteristic, complemented
3#10590247C211yesmaximal, characteristic, complemented
4#10590030C214yesmaximal, complemented
5C2×#3802C411yescharacteristic
6C2×C4×D32—21no—
7C42×C3⋊D3C2211yescharacteristic
8C3×C4×D12—21no—
9#63921—21no—
10#63902C2212yes—
11C4×#625C412yes—
12#63900C411yescharacteristic
13#63898—21no—
14C2×#3712—21no—
15#63779C2212yescomplemented
16#63778—21no—
17#63777—21no—
18C3×#803—21no—
19#63553C2212yescomplemented
20C4×D3×D4—61no—
21#4707—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—
34C32×C42D411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3C2311yescharacteristic
38C3×(C2×D3)⋊C4—22no—
39C3×C4⋊Dic3—21no—
40C2×C3×C3⋊C8—22no—
41#3724C2×C412yes—
42(C2×D3)⋊Dic3—22no—
43#3712—24no—
44#1490—91nomaximal, Sylow
45C2×D3×D4—61no—
46C22×C4×D3—62no—
47C3×C4×D4—61no—
48D4×Dic3—61no—
49C4×#67—62no—
50C2×ΓL(1,𝔽25)—62no—
51#893—61no—
52D3×C4⋊C4—61no—
53#67⋊C4—62no—
54D3×C22⋊C4—62no—
55C4×D12—21no—
56C42×D3—61no—
57C42×D3—61no—
58C3×#97—61no—
59C8×Dic3—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—42no—
83C3×C3⋊C8—24no—
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—
122ΓL(1,𝔽25)—68no—
123C22×C32C2×C22⋊C411yescharacteristic
124C2×C3⋊D3—21no—
125C2×C3⋊D3—21no—
126C2×C3⋊D3#10412yes—
127C2×C3×D3—24no—
128C2×C3×D3—42no—
129C2×C3×D3—42no—
130D32—48no—
131C32×C4—21no—
132C32×C4—21no—
133C32×C4—21no—
134C3⋊Dic3—21no—
135C3⋊Dic3C2×M1612yes—
136C3⋊Dic3AGL(1,ℤ/8)12yes—
137C3×Dic3—42no—
138C22×D4—91no—
139C23×C4—181no—
140C2×M16—181no—
141C4×D4—61no—
142C4×D4—92no—
143C4×D4—92no—
144C4×D4—181no—
145C2×C4⋊C4—91no—
146C2×C22⋊C4—181no—
147C2×C42—91no—
148C4⋊C8—92no—
149C22⋊C8—181no—
150#97—61no—
151#97—181no—
152C4×C8—92no—
153C23×C3—62no—
154C22×D3—22no—
155C22×D3—61no—
156C22×D3—61no—
157C22×D3—68no—
158C22×D3—124no—
159C22×D3—124no—
160C3×D4—64no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—62no—
168C2×C3×C4—124no—
169#67—64no—
170#67—64no—
171C2×Dic3—22no—
172C2×Dic3—61no—
173C2×Dic3—61no—
174C2×Dic3—61no—
175C2×Dic3—61no—
176C2×Dic3—61no—
177C2×Dic3—61no—
178C2×Dic3—124no—
179D12—24no—
180C4×D3—44no—
181C4×D3—64no—
182C4×D3—64no—
183C4×D3—64no—
184C4×D3—122no—
185C4×D3—122no—
186C4×D3—122no—
187C4×D3—124no—
188C4×D3—124no—
189C3×C8—64no—
190C3⋊C8—24no—
191C2×C32#40711yescharacteristic
192C2×C32#41811yescharacteristic
193C2×C32C2×#10411yescharacteristic
194C3⋊D3—22no—
195C3×D3—44no—
196C24—181no—
197C2×D4—61no—
198C2×D4—92no—
199C2×D4—184no—
200C22×C4—62no—
201C22×C4—91no—
202C22×C4—91no—
203C22×C4—91no—
204C22×C4—181no—
205C22×C4—182no—
206C22×C4—364no—
207M16—184no—
208C2×C8—62no—
209C2×C8—182no—
210C4⋊C4—61no—
211C4⋊C4—92no—
212C22⋊C4—62no—
213C22⋊C4—182no—
214C42—91no—
215C42—91no—
216C42—91no—
217C42GO+(4,𝔽2)11yescharacteristic
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—64no—
221C22×C3—122no—
222C22×C3—122no—
223C2×D3—24no—
224C2×D3—42no—
225C2×D3—42no—
226C2×D3—62no—
227C2×D3—62no—
228C2×D3—62no—
229C2×D3—62no—
230C2×D3—121no—
231C2×D3—121no—
232C2×D3—1216no—
233C3×C4—22no—
234C3×C4—22no—
235C3×C4—22no—
236C3×C4—41no—
237C3×C4—41no—
238C3×C4—41no—
239C3×C4—122no—
240Dic3—42no—
241Dic3—62no—
242Dic3—62no—
243Dic3—62no—
244Dic3—62no—
245Dic3—62no—
246Dic3—121no—
247C32#149011yescharacteristic, complemented, Sylow
248C23—62no—
249C23—91no—
250C23—184no—
251C23—362no—
252C23—362no—
253D4—64no—
254D4—94no—
255D4—182no—
256C2×C4—62no—
257C2×C4—91no—
258C2×C4—91no—
259C2×C4—91no—
260C2×C4—124no—
261C2×C4—182no—
262C2×C4—182no—
263C2×C4—182no—
264C2×C4—364no—
265C2×C4—362no—
266C2×C4D32⋊C411yescharacteristic
267C2×C4D32⋊C411yescharacteristic
268C2×C4C2×GO+(4,𝔽2)11yescharacteristic
269C8—64no—
270C8—362no—
271C2×C3—21no—
272C2×C3—21no—
273C2×C3—21no—
274C2×C3—21no—
275C2×C3—21no—
276C2×C3—21no—
277C2×C3—124no—
278D3—44no—
279D3—64no—
280D3—122no—
281C22—64no—
282C22—92no—
283C22—122no—
284C22—122no—
285C22—181no—
286C22—181no—
287C22—368no—
288C22C2×D32⋊C411yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—92no—
293C4—92no—
294C4—122no—
295C4—181no—
296C3—21no—
297C3—21no—
298C2—124no—
299C2—182no—
300C2#1059330711yescharacteristic
301C2#1059331811yescharacteristic
302C2#1059338011yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
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 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. #10593731C2semidirect
3. #10590247C2semidirect
4. #10590030C2semidirect
15. #63779C22semidirect
19. #63553C22semidirect
79. #625M16semidirect
247. C32#1490semidirect

Maximal subgroups

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

subgroupindex
C4×#38022
#105937312
#105902472
#105900302
#14909