Finite Group Databasebeta

← #11774695

Subgroups — #11774695

Order 1152.

584 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 65 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×C4×#625C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic, complemented
3#10591066C211yesmaximal, characteristic, complemented
4#10590029C214yesmaximal, complemented
5C22×C3×C4×D3—21no—
6C22×#625C411yescharacteristic
7C2×#3792—21no—
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×#3724C411yescharacteristic
10C2×(C2×D3)⋊Dic3—21no—
11C4×#625—21no—
12C4×#625—21no—
13C4×#625C412yes—
14C4×#625C2212yes—
15#63777—21no—
16C4×#622C2212yescomplemented
17C3×#830—21no—
18#63572C2212yescomplemented
19#63555—21no—
20C2×C4×#67—61no—
21#4719—61no—
22C23×C3×D3—21no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3×Dic3—21no—
27C2×C3×C4×D3—22no—
28C2×C3×C4×D3—22no—
29C2×C3×C4×D3—44no—
30C2×#625—21no—
31C2×#625—24no—
32C2×#625C2×C412yes—
33#3792—24no—
34C2×#622—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D411yescharacteristic
37C4×C3⋊Dic3D411yescharacteristic
38C4×C3⋊Dic3C2311yescharacteristic
39C2×C3×C3⋊C8—22no—
40#3724—21no—
41#3724C2×C412yes—
42(C2×D3)⋊Dic3—22no—
43(C2×D3)⋊Dic3—22no—
44#1490—91nomaximal, Sylow
45C23×C3×C4—61no—
46C22×#67—61no—
47C22×C4×D3—21no—
48C2×#217—61no—
49C4×#67—62no—
50C4×#67—62no—
51C4×#67—62no—
52C4×#67—62no—
53C2×(C2×D3)⋊C4—61no—
54C2×Dic3⋊C4—61no—
55C2×C4×Dic3—61no—
56C2×C4×Dic3—61no—
57C3×C22⋊C8—61no—
58#830—21no—
59#815—62no—
60Dic3⋊C8—62no—
61C23×C32C22⋊C411yescharacteristic
62C22×C3×D3—24no—
63C22×C3×D3—22no—
64C22×C3×D3—42no—
65C22×C3×D3—42no—
66C2×C32×C4—22no—
67C2×C32×C4C22⋊C411yescharacteristic
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C22⋊C411yescharacteristic
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22×C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3×Dic3—22no—
76C2×C3×Dic3—42no—
77C3×C4×D3—44no—
78C3×C4×D3—44no—
79#625—24no—
80#625—22no—
81#625M1614yescomplemented
82#622—24no—
83C3×C3⋊C8—42no—
84C2×C4×D4—91no—
85#432—91no—
86C4×M16—91no—
87D4⋊C8—94no—
88C24×C3—61no—
89C23×D3—21no—
90C22×C3×C4—21no—
91C22×C3×C4—21no—
92C22×C3×C4—62no—
93C22×C3×C4—62no—
94C22×C3×C4—61no—
95C22×C3×C4—124no—
96C2×#67—62no—
97C2×#67—62no—
98C2×#67—68no—
99C22×Dic3—21no—
100C22×Dic3—61no—
101C22×Dic3—61no—
102C22×Dic3—61no—
103C22×Dic3—61no—
104C2×C4×D3—22no—
105C2×C4×D3—22no—
106C2×C4×D3—44no—
107C2×C3×C8—62no—
108#217—62no—
109#217—62no—
110(C2×D3)⋊C4—62no—
111(C2×D3)⋊C4—62no—
112Dic3⋊C4—62no—
113Dic3⋊C4—62no—
114C4×Dic3—61no—
115C4×Dic3—61no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C4×Dic3—61no—
120C4×Dic3—61no—
121C4×Dic3—61no—
122C2×C3⋊C8—22no—
123C22×C32—21no—
124C22×C32—21no—
125C22×C32#10412yes—
126C22×C32C2×C22⋊C411yescharacteristic
127C2×C3×D3—24no—
128C2×C3×D3—48no—
129C2×C3×D3—42no—
130C2×C3×D3—42no—
131C32×C4—21no—
132C32×C4AGL(1,ℤ/8)12yes—
133C3⋊Dic3—21no—
134C3⋊Dic3—21no—
135C3⋊Dic3—21no—
136C3⋊Dic3C2×M1612yes—
137C3×Dic3—42no—
138C22×D4—91no—
139C23×C4—61no—
140C2×M16—181no—
141C4×D4—92no—
142C4×D4—92no—
143C4×D4—181no—
144C4×D4—181no—
145C2×C4⋊C4—91no—
146C2×C22⋊C4—181no—
147C2×C42—91no—
148C4⋊C8—92no—
149C22⋊C8—61no—
150#97—181no—
151#97—181no—
152C4×C8—92no—
153C23×C3—21no—
154C23×C3—21no—
155C23×C3—62no—
156C23×C3—64no—
157C23×C3—122no—
158C23×C3—122no—
159C22×D3—22no—
160C22×D3—24no—
161C22×D3—42no—
162C22×D3—42no—
163C2×C3×C4—24no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—42no—
169C2×C3×C4—62no—
170C2×C3×C4—124no—
171C2×C3×C4—124no—
172C2×C3×C4—122no—
173#67—64no—
174#67—64no—
175#67—68no—
176C2×Dic3—22no—
177C2×Dic3—42no—
178C2×Dic3—61no—
179C2×Dic3—61no—
180C2×Dic3—61no—
181C2×Dic3—61no—
182C2×Dic3—61no—
183C2×Dic3—61no—
184C2×Dic3—61no—
185C2×Dic3—61no—
186C2×Dic3—64no—
187C2×Dic3—122no—
188C2×Dic3—122no—
189C2×Dic3—122no—
190C4×D3—44no—
191C4×D3—44no—
192C3×C8—122no—
193C3⋊C8—42no—
194C2×C32—22no—
195C2×C32#40711yescharacteristic
196C2×C32#41811yescharacteristic
197C2×C32C2×#10411yescharacteristic
198C3×D3—44no—
199C24—61no—
200C2×D4—92no—
201C2×D4—181no—
202C2×D4—184no—
203C22×C4—61no—
204C22×C4—62no—
205C22×C4—62no—
206C22×C4—91no—
207C22×C4—91no—
208C22×C4—124no—
209C22×C4GO+(4,𝔽2)11yescharacteristic
210M16—184no—
211C2×C8—62no—
212C2×C8—182no—
213C4⋊C4—92no—
214C4⋊C4—181no—
215C22⋊C4—182no—
216C22⋊C4—182no—
217C42—91no—
218C42—91no—
219C42—91no—
220C42—91no—
221C22×C3—22no—
222C22×C3—22no—
223C22×C3—21no—
224C22×C3—21no—
225C22×C3—22no—
226C22×C3—22no—
227C22×C3—41no—
228C22×C3—41no—
229C22×C3—64no—
230C22×C3—122no—
231C22×C3—128no—
232C22×C3—122no—
233C2×D3—24no—
234C2×D3—42no—
235C2×D3—48no—
236C2×D3—42no—
237C3×C4—22no—
238C3×C4—22no—
239C3×C4—22no—
240C3×C4—41no—
241C3×C4—122no—
242Dic3—42no—
243Dic3—62no—
244Dic3—62no—
245Dic3—62no—
246Dic3—121no—
247Dic3—121no—
248Dic3—121no—
249Dic3—121no—
250Dic3—121no—
251C32#149011yescharacteristic, complemented, Sylow
252C23—64no—
253C23—62no—
254C23—122no—
255C23—122no—
256C23D32⋊C411yescharacteristic
257D4—94no—
258D4—182no—
259D4—184no—
260C2×C4—22no—
261C2×C4—62no—
262C2×C4—91no—
263C2×C4—91no—
264C2×C4—91no—
265C2×C4—91no—
266C2×C4—124no—
267C2×C4—122no—
268C2×C4—124no—
269C2×C4—182no—
270C2×C4—182no—
271C2×C4D32⋊C411yescharacteristic
272C2×C4C2×GO+(4,𝔽2)11yescharacteristic
273C8—122no—
274C8—184no—
275C2×C3—24no—
276C2×C3—21no—
277C2×C3—21no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3—21no—
282C2×C3—42no—
283C2×C3—124no—
284D3—44no—
285C22—21no—
286C22—21no—
287C22—64no—
288C22—128no—
289C22—122no—
290C22—122no—
291C22#6373112yes—
292C22C2×D32⋊C411yescharacteristic
293C4—21no—
294C4—92no—
295C4—122no—
296C4—181no—
297C4—181no—
298C4—181no—
299C4#6423612yes—
300C3—21no—
301C3—21no—
302C2—22no—
303C2—124no—
304C2#1059330711yescharacteristic
305C2C2×#6373111yescharacteristic
306C2#1059349311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC22×#625C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1490
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C4×#3792C2semidirect
3. #10591066C2semidirect
4. #10590029C2semidirect
16. C4×#622C22semidirect
18. #63572C22semidirect
81. #625M16semidirect
251. C32#1490semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6252
C4×#37922
#105910662
#105900292
#14909