Finite Group Databasebeta

← #11774615

Subgroups — #11774615

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×#3830C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic, complemented
3#10593727C211yesmaximal, characteristic, complemented
4D4⋊#622C212yesmaximal, complemented
5#10590161C212yesmaximal, complemented
6C2×#3830C411yescharacteristic
7C32×C4×D4C411yescharacteristic
8D4×C3⋊Dic3C2211yescharacteristic
9C4×#638—21no—
10C2×C4×C3⋊Dic3—21no—
11#64101C411yescharacteristic
12#64096C2211yescharacteristic
13#64090—21no—
14#64086—21no—
15C42×C3⋊D3C2211yescharacteristic
16C4×#634C411yescharacteristic
17#63778—21no—
18#63778—21no—
19#63777—21no—
20C4⋊#622—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23C4×#237—62no—
24C2×C32×D4C2×C411yescharacteristic
25C22×C32×C4—21no—
26C2×#638—21no—
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3—21no—
29#3830—22no—
30#3830—22no—
31C2×C4×C3⋊D3C2×C411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3D411yescharacteristic
34C2×#634C2×C411yescharacteristic
35C2×#622—22no—
36C2×#622—22no—
37C32×C4⋊C4C2×C411yescharacteristic
38C32×C22⋊C4—21no—
39C32×C42C2×C411yescharacteristic
40#3757—21no—
41#3752—21no—
42C4⋊(C3⋊Dic3)C2×C411yescharacteristic
43#3750—21no—
44#3750—21no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51#1488—91nomaximal, Sylow
52C2×#237—62no—
53C3×C4×D4—22no—
54D4×Dic3—62no—
55C4×#67—64no—
56C2×C4×Dic3—64no—
57#892—62no—
58#887—62no—
59#67⋊C4—64no—
60#877—64no—
61C42×D3—62no—
62C4×Dic6—62no—
63C23×C32—21no—
64C22×C3⋊D3C22⋊C411yescharacteristic
65C32×D4—21no—
66C32×D4M1612yes—
67C2×C32×C4—21no—
68C2×C32×C4—42no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72#638—24no—
73C2×C3⋊Dic3—24no—
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—42no—
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C2×C3⋊Dic3C2×D411yescharacteristic
80C4×C3⋊D3—21no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—41no—
84#634—21no—
85#634M1612yes—
86#622—42no—
87#622—42no—
88C4×#41—91no—
89#432—91no—
90#431—91no—
91Q8⋊C8—92no—
92D4⋊C8—92no—
93C2×C3×D4—22no—
94C22×C3×C4—24no—
95C2×#67—64no—
96C22×Dic3—64no—
97C22×Dic3—64no—
98#237—68no—
99#237—68no—
100C2×C4×D3—62no—
101C2×C4×D3—62no—
102C2×C4×D3—62no—
103C2×Dic6—62no—
104C3×C4⋊C4—22no—
105C3×C22⋊C4—24no—
106C3×C42—22no—
107#217—64no—
108(C2×D3)⋊C4—64no—
109C4⋊Dic3—62no—
110Dic3⋊C4—64no—
111Dic3⋊C4—64no—
112C4×Dic3—62no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—64no—
116C4×Dic3—64no—
117C4×Dic3—64no—
118C22×C32—22no—
119C22×C32—41no—
120C22×C32—41no—
121C22×C32C2×C22⋊C411yescharacteristic
122C2×C3⋊D3—21no—
123C2×C3⋊D3—21no—
124C2×C3⋊D3—21no—
125C32×C4—21no—
126C32×C4—21no—
127C32×C4—41no—
128C32×C4C2×M1611yescharacteristic
129C32×C4C2×M1611yescharacteristic
130C3⋊Dic3—22no—
131C3⋊Dic3—21no—
132C3⋊Dic3—21no—
133C3⋊Dic3—41no—
134C3⋊Dic3#13512yes—
135C2×#41—91no—
136C4×Q8—91no—
137C4×Q8—91no—
138C4×D4—91no—
139C4×D4—181no—
140C4×D4—181no—
141C4×D4#15711yescharacteristic
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—
152C23×C3—24no—
153C22×D3—62no—
154C3×D4—24no—
155C3×D4—24no—
156C2×C3×C4—24no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—22no—
160C2×C3×C4—48no—
161#67—616no—
162C2×Dic3—62no—
163C2×Dic3—62no—
164C2×Dic3—62no—
165C2×Dic3—64no—
166C2×Dic3—616no—
167C2×Dic3—64no—
168C2×Dic3—128no—
169C4×D3—64no—
170C4×D3—64no—
171C4×D3—124no—
172C4×D3—124no—
173Dic6—64no—
174Dic6—64no—
175C2×C32—42no—
176C2×C32#40711yescharacteristic
177C2×C32#41611yescharacteristic
178C2×C32#42111yescharacteristic
179C3⋊D3—41no—
180#41—182no—
181#41—182no—
182C2×Q8—91no—
183C2×D4—181no—
184C2×D4C2×#15711yescharacteristic
185C22×C4—21no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—91no—
189C22×C4—181no—
190C22×C4—181no—
191C2×C8—182no—
192C2×C8—182no—
193C4⋊C4—91no—
194C4⋊C4—181no—
195C4⋊C4—181no—
196C4⋊C4C2×#15711yescharacteristic
197C22⋊C4—21no—
198C22⋊C4—181no—
199C22⋊C4—181no—
200C42—91no—
201C42—91no—
202C42—91no—
203C42—181no—
204C42—181no—
205C42—181no—
206C42C2×#15711yescharacteristic
207C22×C3—28no—
208C22×C3—22no—
209C22×C3—44no—
210C22×C3—44no—
211C2×D3—64no—
212C2×D3—122no—
213C2×D3—122no—
214C3×C4—24no—
215C3×C4—22no—
216C3×C4—22no—
217C3×C4—42no—
218C3×C4—44no—
219Dic3—64no—
220Dic3—68no—
221Dic3—64no—
222Dic3—122no—
223Dic3—124no—
224C32#148811yescharacteristic, complemented, Sylow
225C23—21no—
226C23—91no—
227Q8—92no—
228Q8—181no—
229D4—21no—
230D4—184no—
231D4#378812yes—
232C2×C4—21no—
233C2×C4—42no—
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—181no—
243C2×C4—361no—
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—
253C2×C3—48no—
254D3—124no—
255C22—22no—
256C22—41no—
257C22—41no—
258C22—181no—
259C22—181no—
260C22—181no—
261C22C2×C22⋊#15711yescharacteristic
262C4—21no—
263C4—21no—
264C4—41no—
265C4—92no—
266C4—181no—
267C4—182no—
268C4—181no—
269C4—361no—
270C4C2×#378811yescharacteristic
271C4#6428311yescharacteristic
272C3—22no—
273C2—42no—
274C2—361no—
275C2#1059380311yescharacteristic
276C2#1059381611yescharacteristic
277C2#1059384111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×D4C4
socleC22×C32C2×C22⋊C4
prime radicalC2×#3830C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×D4#157
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10593730C2semidirect
3. #10593727C2semidirect
4. D4⋊#622C2semidirect
5. #10590161C2semidirect
224. C32#1488semidirect

Maximal subgroups

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

subgroupindex
C4×#38302
#105937302
#105937272
D4⋊#6222
#105901612
#14889