Finite Group Databasebeta

← #11774649

Subgroups — #11774649

Order 1152.

576 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#41×C3⋊Dic3C211yesmaximal, characteristic
2#10593805C211yesmaximal, characteristic, complemented
3C4×#3792C211yesmaximal, characteristic, complemented
4Q8⋊#622C212yesmaximal, complemented
5D4⋊#622C212yesmaximal, complemented
6C2×C32×#41C411yescharacteristic
7C2×#3792—21no—
8C2×#3792—21no—
9Q8×C3⋊Dic3C411yescharacteristic
10Q8×C3⋊Dic3C2211yescharacteristic
11D4×C3⋊Dic3—21no—
12D4×C3⋊Dic3—21no—
13D4×C3⋊Dic3C411yescharacteristic
14D4×C3⋊Dic3C2211yescharacteristic
15#64135—21no—
16#64135C411yescharacteristic
17C2×C4×C3⋊Dic3—21no—
18C2×C4×C3⋊Dic3C2211yescharacteristic
19#63779—21no—
20#63777—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23Dic3×#41—62no—
24C32×#41—22no—
25C32×#41—22no—
26C2×C32×Q8C2×C411yescharacteristic
27C2×C32×D4—21no—
28C2×C32×D4C2×C411yescharacteristic
29C22×C32×C4—21no—
30C22×C32×C4C2×C411yescharacteristic
31C22×C3⋊Dic3—21no—
32C22×C3⋊Dic3—21no—
33C22×C3⋊Dic3D411yescharacteristic
34C22×C3⋊Dic3D411yescharacteristic
35#3792—24no—
36#3792—42no—
37C2×#622—22no—
38C2×#622—22no—
39#3757—21no—
40#3757—21no—
41#3757—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C411yescharacteristic
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3C2×C411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3C2311yescharacteristic
53#1489—91nomaximal, Sylow
54C2×C3×#41—22no—
55Q8×Dic3—62no—
56Q8×Dic3—62no—
57D4×Dic3—62no—
58D4×Dic3—62no—
59D4×Dic3—64no—
60D4×Dic3—64no—
61#926—62no—
62#926—64no—
63C2×C4×Dic3—62no—
64C2×C4×Dic3—64no—
65C23×C32—21no—
66C23×C32C22⋊C411yescharacteristic
67C32×Q8—21no—
68C32×Q8M1612yescomplemented
69C32×D4—24no—
70C32×D4—21no—
71C32×D4M1612yescomplemented
72C2×C32×C4—24no—
73C2×C32×C4—21no—
74C2×C32×C4—21no—
75C2×C32×C4—21no—
76C2×C32×C4C22⋊C411yescharacteristic
77C2×C32×C4C22×C411yescharacteristic
78C2×C3⋊Dic3—21no—
79C2×C3⋊Dic3—21no—
80C2×C3⋊Dic3—22no—
81C2×C3⋊Dic3—21no—
82C2×C3⋊Dic3—21no—
83C2×C3⋊Dic3—42no—
84C2×C3⋊Dic3—41no—
85C2×C3⋊Dic3—41no—
86C2×C3⋊Dic3C22⋊C411yescharacteristic
87C2×C3⋊Dic3C22⋊C411yescharacteristic
88C2×C3⋊Dic3C2×D411yescharacteristic
89C2×C3⋊Dic3C2×D411yescharacteristic
90#622—24no—
91#622—42no—
92C4×#41—91no—
93#423—91no—
94C4×M16—91no—
95Q8⋊C8—92no—
96D4⋊C8—92no—
97C3×#41—28no—
98C3×#41—28no—
99C2×C3×Q8—22no—
100C2×C3×D4—24no—
101C2×C3×D4—22no—
102C22×C3×C4—24no—
103C22×C3×C4—22no—
104C22×Dic3—62no—
105C22×Dic3—62no—
106C22×Dic3—64no—
107C22×Dic3—64no—
108#217—64no—
109#217—64no—
110#217—64no—
111C4⋊Dic3—62no—
112C4⋊Dic3—62no—
113C4⋊Dic3—64no—
114C4⋊Dic3—64no—
115C4×Dic3—62no—
116C4×Dic3—62no—
117C4×Dic3—62no—
118C4×Dic3—62no—
119C4×Dic3—64no—
120C4×Dic3—64no—
121C4×Dic3—64no—
122C22×C32—21no—
123C22×C32—22no—
124C22×C32—21no—
125C22×C32—21no—
126C22×C32—41no—
127C22×C32—41no—
128C22×C32C2×C22⋊C411yescharacteristic
129C32×C4—21no—
130C32×C4—22no—
131C32×C4C2×M1611yescharacteristic
132C32×C4C2×M1611yescharacteristic
133C3⋊Dic3—21no—
134C3⋊Dic3—21no—
135C3⋊Dic3—41no—
136C3⋊Dic3—41no—
137C3⋊Dic3#10412yes—
138C3⋊Dic3AGL(1,ℤ/8)11yescharacteristic
139C3⋊Dic3#13711yescharacteristic
140C2×#41#15711yescharacteristic
141C2×M16—181no—
142C2×M16—181no—
143C4×Q8—91no—
144C4×Q8—91no—
145C4×D4—91no—
146C4×D4—91no—
147C4×D4—181no—
148C4×D4—181no—
149#117—91no—
150#117—181no—
151C2×C42—91no—
152C2×C42—181no—
153C4⋊C8—92no—
154C4⋊C8—181no—
155#97—181no—
156C4×C8—92no—
157C23×C3—24no—
158C23×C3—22no—
159C3×Q8—24no—
160C3×Q8—24no—
161C3×D4—216no—
162C3×D4—24no—
163C3×D4—24no—
164C2×C3×C4—24no—
165C2×C3×C4—216no—
166C2×C3×C4—24no—
167C2×C3×C4—24no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—62no—
173C2×Dic3—62no—
174C2×Dic3—64no—
175C2×Dic3—64no—
176C2×Dic3—124no—
177C2×Dic3—122no—
178C2×Dic3—122no—
179C2×Dic3—128no—
180C2×Dic3—124no—
181C2×Dic3—124no—
182C2×C32—41no—
183C2×C32—42no—
184C2×C32#40711yescharacteristic
185C2×C32#41711yescharacteristic
186C2×C32C2×#10411yescharacteristic
187#41—22no—
188#41—22no—
189C2×Q8C2×#15711yescharacteristic
190C2×D4—21no—
191C2×D4C2×#15711yescharacteristic
192C22×C4—21no—
193C22×C4—91no—
194C22×C4—91no—
195C22×C4—181no—
196C22×C4—181no—
197C22×C4C2×#15711yescharacteristic
198M16—184no—
199M16—362no—
200C2×C8—182no—
201C2×C8—182no—
202C4⋊C4—91no—
203C4⋊C4—91no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C22⋊C4—181no—
207C22⋊C4—181no—
208C22⋊C4—181no—
209C42—91no—
210C42—91no—
211C42—91no—
212C42—91no—
213C42—181no—
214C42—181no—
215C42—181no—
216C22×C3—24no—
217C22×C3—28no—
218C22×C3—22no—
219C22×C3—42no—
220C22×C3—42no—
221C22×C3—44no—
222C22×C3—44no—
223C3×C4—24no—
224C3×C4—28no—
225C3×C4—22no—
226C3×C4—22no—
227Dic3—64no—
228Dic3—62no—
229Dic3—62no—
230Dic3—122no—
231Dic3—122no—
232Dic3—124no—
233Dic3—124no—
234C32#148911yescharacteristic, complemented, Sylow
235C23—21no—
236C23C22⋊#15711yescharacteristic
237Q8—21no—
238Q8#379212yescomplemented
239D4—24no—
240D4—21no—
241D4#379212yescomplemented
242C2×C4—24no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—91no—
247C2×C4—91no—
248C2×C4—91no—
249C2×C4—91no—
250C2×C4—182no—
251C2×C4—181no—
252C2×C4—181no—
253C2×C4—181no—
254C2×C4—181no—
255C2×C4—362no—
256C2×C4—361no—
257C2×C4—361no—
258C2×C4C22⋊#15711yescharacteristic
259C2×C4C22×#15711yescharacteristic
260C8—184no—
261C8—362no—
262C2×C3—22no—
263C2×C3—22no—
264C2×C3—22no—
265C2×C3—44no—
266C2×C3—48no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—22no—
271C22—41no—
272C22—41no—
273C22C2×C22⋊#15711yescharacteristic
274C4—21no—
275C4—22no—
276C4—92no—
277C4—91no—
278C4—91no—
279C4—181no—
280C4—181no—
281C4—361no—
282C4—361no—
283C4C2×#379211yescharacteristic
284C4C2×#379211yescharacteristic
285C3—22no—
286C2—41no—
287C2—42no—
288C2#1059383911yescharacteristic
289C2#1059384011yescharacteristic
290C2#1059384511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
Fitting, prime radicalC2×C32×#41C4
socleC22×C32C2×C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×#41#157
hypocenterC32#1489
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10593805C2semidirect
3. C4×#3792C2semidirect
4. Q8⋊#622C2semidirect
5. D4⋊#622C2semidirect
68. C32×Q8M16semidirect
71. C32×D4M16semidirect
234. C32#1489semidirect
238. Q8#3792semidirect
241. D4#3792semidirect

Maximal subgroups

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

subgroupindex
#41×C3⋊Dic32
#105938052
C4×#37922
Q8⋊#6222
D4⋊#6222
#14899