Finite Group Databasebeta

← #11774712

Subgroups — #11774712

Order 1152.

550 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 550 conjugacy classes of subgroups — too many to draw. Only its 68 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×Q8×C3⋊D3C211yesmaximal, characteristic
2#10593730C211yesmaximal, characteristic
3C4×#3788C211yesmaximal, characteristic
4Q8⋊#622C212yesmaximal, complemented
5#10590161C212yesmaximal, complemented
6C2×Q8×C3⋊D3C411yescharacteristic
7C2×#3788—21no—
8C32×C4×Q8C411yescharacteristic
9Q8×C3⋊Dic3C2211yescharacteristic
10C4⋊C4×C3⋊D3—21no—
11C4⋊C4×C3⋊D3C411yescharacteristic
12#64096—21no—
13#64096C2211yescharacteristic
14C42×C3⋊D3—21no—
15C42×C3⋊D3C2211yescharacteristic
16C4×#634—21no—
17C4×#634C411yescharacteristic
18#63778—21no—
19#63777—21no—
20#63777—21no—
21C4⋊#622C2212yes—
22C4×#622C2212yes—
23C4×D3×Q8—62no—
24C2×C32×Q8C2×C411yescharacteristic
25Q8×C3⋊D3—22no—
26Q8×C3⋊D3—22no—
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3C2×C411yescharacteristic
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×#634—21no—
33C2×#634C2×C411yescharacteristic
34C2×#622—22no—
35C2×#622—22no—
36#3788—24no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4C2×C411yescharacteristic
39C32×C42—21no—
40C32×C42C2×C411yescharacteristic
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)C2×C411yescharacteristic
43#3750—21no—
44#3750—21no—
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3—21no—
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51C4×C3⋊Dic3C2311yescharacteristic
52#1491—91nomaximal, Sylow
53C2×D3×Q8—62no—
54C3×C4×Q8—22no—
55Q8×Dic3—62no—
56D3×C4⋊C4—62no—
57D3×C4⋊C4—64no—
58#887—62no—
59#887—64no—
60C42×D3—62no—
61C42×D3—64no—
62C4×Dic6—62no—
63C4×Dic6—64no—
64C22×C3⋊D3C22⋊C411yescharacteristic
65C32×Q8—21no—
66C32×Q8M1612yescomplemented
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⋊Dic3—21no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4×C3⋊D3—24no—
78C4×C3⋊D3—21no—
79C4×C3⋊D3—21no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3—22no—
82C4×C3⋊D3—42no—
83#634—24no—
84#634—21no—
85#634M1612yescomplemented
86#622—24no—
87#622—42no—
88C2×C4×Q8—91no—
89#432—91no—
90C4×M16—91no—
91Q8⋊C8—92no—
92Q8⋊C8—92no—
93C2×C3×Q8—22no—
94D3×Q8—68no—
95D3×Q8—68no—
96C2×C4×D3—62no—
97C2×C4×D3—62no—
98C2×C4×D3—62no—
99C2×C4×D3—64no—
100C2×C4×D3—64no—
101C2×Dic6—62no—
102C2×Dic6—64no—
103C3×C4⋊C4—24no—
104C3×C4⋊C4—22no—
105C3×C42—24no—
106C3×C42—22no—
107C4⋊Dic3—62no—
108C4⋊Dic3—64no—
109Dic3⋊C4—64no—
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×C32C2×C22⋊C411yescharacteristic
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3#10412yes—
122C32×C4—22no—
123C32×C4—21no—
124C32×C4—21no—
125C32×C4—41no—
126C32×C4C2×M1611yescharacteristic
127C32×C4C2×M1611yescharacteristic
128C3⋊Dic3—21no—
129C3⋊Dic3—22no—
130C3⋊Dic3—21no—
131C3⋊Dic3—41no—
132C3⋊Dic3#13712yes—
133C22×Q8—91no—
134C2×M16—181no—
135C4×Q8—91no—
136C4×Q8—91no—
137C4×Q8—91no—
138C4×Q8—181no—
139C4×Q8—181no—
140C4×Q8#15711yescharacteristic
141C2×C4⋊C4—91no—
142C2×C4⋊C4—181no—
143C2×C42—91no—
144C2×C42—181no—
145C4⋊C8—92no—
146C22⋊C8—181no—
147#97—181no—
148#97—181no—
149C4×C8—92no—
150C22×D3—62no—
151C3×Q8—24no—
152C3×Q8—24no—
153C2×C3×C4—24no—
154C2×C3×C4—24no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—64no—
162C2×Dic3—64no—
163C4×D3—68no—
164C4×D3—616no—
165C4×D3—64no—
166C4×D3—64no—
167C4×D3—124no—
168C4×D3—128no—
169Dic6—64no—
170Dic6—616no—
171Dic6—64no—
172C2×C32#40711yescharacteristic
173C2×C32#41911yescharacteristic
174C2×C32C2×#10411yescharacteristic
175C3⋊D3—22no—
176C2×Q8—91no—
177C2×Q8—181no—
178C2×Q8—182no—
179C2×Q8—182no—
180C2×Q8C2×#15711yescharacteristic
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4—181no—
185C22×C4—181no—
186M16—184no—
187C2×C8—182no—
188C2×C8—182no—
189C4⋊C4—21no—
190C4⋊C4—91no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—181no—
194C4⋊C4—181no—
195C4⋊C4C2×#15711yescharacteristic
196C42—21no—
197C42—91no—
198C42—91no—
199C42—91no—
200C42—181no—
201C42—181no—
202C42—181no—
203C42C2×#15711yescharacteristic
204C22×C3—22no—
205C2×D3—64no—
206C2×D3—64no—
207C2×D3—64no—
208C3×C4—28no—
209C3×C4—24no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—42no—
213C3×C4—44no—
214Dic3—64no—
215Dic3—64no—
216Dic3—68no—
217Dic3—122no—
218Dic3—124no—
219C32#149111yescharacteristic, complemented, Sylow
220C23—91no—
221Q8—21no—
222Q8—92no—
223Q8—184no—
224Q8—181no—
225Q8#378812yescomplemented
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—182no—
232C2×C4—182no—
233C2×C4—184no—
234C2×C4—181no—
235C2×C4—181no—
236C2×C4—181no—
237C2×C4—181no—
238C2×C4—362no—
239C2×C4C22⋊#15711yescharacteristic
240C2×C4C22⋊#15711yescharacteristic
241C2×C4C22×#15711yescharacteristic
242C8—184no—
243C8—362no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247D3—68no—
248C22—92no—
249C22—181no—
250C22—181no—
251C22C2×C22⋊#15711yescharacteristic
252C4—22no—
253C4—21no—
254C4—21no—
255C4—41no—
256C4—92no—
257C4—181no—
258C4—182no—
259C4—181no—
260C4—361no—
261C4C2×#378811yescharacteristic
262C4#6428311yescharacteristic
263C3—22no—
264C2—182no—
265C2#1059380311yescharacteristic
266C2#1059382911yescharacteristic
267C2#1059383911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC4×Q8#157
hypocenterC32#1491
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
4. Q8⋊#622C2semidirect
5. #10590161C2semidirect
66. C32×Q8M16semidirect
85. #634M16semidirect
219. C32#1491semidirect
225. Q8#3788semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
#105937302
C4×#37882
Q8⋊#6222
#105901612
#14919