Finite Group Databasebeta

← #11774616

Subgroups — #11774616

Order 1152.

556 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3832C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic, complemented
3#10593727C211yesmaximal, characteristic, complemented
4Q8⋊#622C212yesmaximal, complemented
5#10590160C212yesmaximal, complemented
6C2×#3832C411yescharacteristic
7C32×C4×Q8C411yescharacteristic
8Q8×C3⋊Dic3C2211yescharacteristic
9#64102—21no—
10#64102C2211yescharacteristic
11#64101—21no—
12#64101C411yescharacteristic
13C4×C4⋊(C3⋊D3)—21no—
14C4×C4⋊(C3⋊D3)C411yescharacteristic
15C42×C3⋊D3—21no—
16C42×C3⋊D3C2211yescharacteristic
17#63778—21no—
18#63778—21no—
19#63777—21no—
20C4⋊#622—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23C4×#239—62no—
24C2×C32×Q8C2×C411yescharacteristic
25#3832—22no—
26#3832—22no—
27C2×C4⋊(C3⋊D3)—21no—
28C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3C2×C411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×#622—22no—
36C2×#622—22no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4C2×C411yescharacteristic
39C32×C42—21no—
40C32×C42C2×C411yescharacteristic
41#3752—21no—
42#3752—21no—
43#3752—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)C2×C411yescharacteristic
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51#1488—91nomaximal, Sylow
52C2×#239—62no—
53C3×C4×Q8—22no—
54Q8×Dic3—62no—
55#893—62no—
56#893—64no—
57#892—62no—
58#892—64no—
59C4×D12—62no—
60C4×D12—64no—
61C42×D3—62no—
62C42×D3—64no—
63C22×C3⋊D3—21no—
64C22×C3⋊D3C22⋊C411yescharacteristic
65C32×Q8—21no—
66C32×Q8M1612yes—
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C4⋊(C3⋊D3)—24no—
77C4⋊(C3⋊D3)—21no—
78C4⋊(C3⋊D3)M1612yes—
79C4×C3⋊D3—24no—
80C4×C3⋊D3—21no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—42no—
85C4×C3⋊D3—42no—
86#622—42no—
87#622—42no—
88C4×#41—91no—
89#432—91no—
90#431—91no—
91Q8⋊C8—92no—
92D4⋊C8—92no—
93C2×C3×Q8—22no—
94#239—68no—
95#239—68no—
96C2×D12—62no—
97C2×D12—64no—
98C2×C4×D3—62no—
99C2×C4×D3—62no—
100C2×C4×D3—62no—
101C2×C4×D3—64no—
102C2×C4×D3—64no—
103C2×C4×D3—64no—
104C3×C4⋊C4—24no—
105C3×C4⋊C4—22no—
106C3×C42—24no—
107C3×C42—22no—
108(C2×D3)⋊C4—64no—
109(C2×D3)⋊C4—64no—
110(C2×D3)⋊C4—64no—
111C4⋊Dic3—62no—
112C4⋊Dic3—64no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C4×Dic3—64no—
117C4×Dic3—64no—
118C22×C32C2×C22⋊C411yescharacteristic
119C2×C3⋊D3—21no—
120C2×C3⋊D3—22no—
121C2×C3⋊D3—21no—
122C2×C3⋊D3—21no—
123C2×C3⋊D3—41no—
124C2×C3⋊D3—41no—
125C32×C4—22no—
126C32×C4—21no—
127C32×C4—21no—
128C32×C4—41no—
129C32×C4C2×M1611yescharacteristic
130C32×C4C2×M1611yescharacteristic
131C3⋊Dic3—21no—
132C3⋊Dic3—21no—
133C3⋊Dic3—41no—
134C3⋊Dic3#13512yes—
135C2×#41—91no—
136C4×Q8—91no—
137C4×Q8#15711yescharacteristic
138C4×D4—91no—
139C4×D4—91no—
140C4×D4—181no—
141C4×D4—181no—
142#117—91no—
143#117—181no—
144C2×C42—91no—
145C2×C42—181no—
146C4⋊C8—92no—
147C4⋊C8—181no—
148C22⋊C8—181no—
149C22⋊C8—181no—
150#97—181no—
151C4×C8—92no—
152C22×D3—62no—
153C22×D3—64no—
154C3×Q8—24no—
155C3×Q8—24no—
156C2×C3×C4—24no—
157C2×C3×C4—24no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—22no—
161C2×Dic3—62no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—64no—
165D12—64no—
166D12—616no—
167D12—64no—
168C4×D3—616no—
169C4×D3—64no—
170C4×D3—64no—
171C4×D3—124no—
172C4×D3—128no—
173C4×D3—124no—
174C4×D3—128no—
175C2×C32#40711yescharacteristic
176C2×C32#41611yescharacteristic
177C2×C32#42111yescharacteristic
178C3⋊D3—41no—
179C3⋊D3—42no—
180#41—182no—
181#41—182no—
182C2×Q8C2×#15711yescharacteristic
183C2×D4—91no—
184C2×D4—181no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—181no—
189C22×C4—181no—
190C22×C4—181no—
191C2×C8—182no—
192C2×C8—182no—
193C4⋊C4—21no—
194C4⋊C4—91no—
195C4⋊C4—181no—
196C4⋊C4C2×#15711yescharacteristic
197C22⋊C4—181no—
198C22⋊C4—181no—
199C22⋊C4—181no—
200C42—21no—
201C42—91no—
202C42—91no—
203C42—91no—
204C42—181no—
205C42—181no—
206C42C2×#15711yescharacteristic
207C22×C3—22no—
208C2×D3—68no—
209C2×D3—64no—
210C2×D3—122no—
211C2×D3—122no—
212C2×D3—124no—
213C2×D3—124no—
214C3×C4—28no—
215C3×C4—24no—
216C3×C4—22no—
217C3×C4—22no—
218C3×C4—42no—
219C3×C4—44no—
220Dic3—64no—
221Dic3—64no—
222Dic3—122no—
223Dic3—124no—
224C32#148811yescharacteristic, complemented, Sylow
225C23—91no—
226C23—181no—
227Q8—21no—
228Q8#378812yes—
229D4—92no—
230D4—184no—
231D4—181no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—182no—
238C2×C4—184no—
239C2×C4—181no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—361no—
243C2×C4—362no—
244C2×C4—362no—
245C2×C4C22⋊#15711yescharacteristic
246C2×C4C22⋊#15711yescharacteristic
247C2×C4C22×#15711yescharacteristic
248C8—362no—
249C8—362no—
250C2×C3—22no—
251C2×C3—22no—
252C2×C3—22no—
253D3—124no—
254D3—128no—
255C22—182no—
256C22—181no—
257C22—181no—
258C22—181no—
259C22—361no—
260C22—361no—
261C22C2×C22⋊#15711yescharacteristic
262C4—22no—
263C4—21no—
264C4—21no—
265C4—41no—
266C4—92no—
267C4—181no—
268C4—181no—
269C4—361no—
270C4C2×#378811yescharacteristic
271C4#6428311yescharacteristic
272C3—22no—
273C2—361no—
274C2—362no—
275C2#1059380311yescharacteristic
276C2#1059383111yescharacteristic
277C2#1059384111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3832C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×Q8#157
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10593730C2semidirect
3. #10593727C2semidirect
4. Q8⋊#622C2semidirect
5. #10590160C2semidirect
224. C32#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#38322
#105937302
#105937272
Q8⋊#6222
#105901602
#14889