Finite Group Databasebeta

← #11785226

Subgroups — #11785226

Order 1152.

470 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 87 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×Q8×#157C211yesmaximal, characteristic
2#10593413C211yesmaximal, characteristic
3C2×#63732C211yesmaximal, characteristic
4#10591552C212yesmaximal
5#10590049C212yesmaximal
6C2×Q8×C3⋊D3C2211yescharacteristic
7Q8×#157—22no—
8Q8×#157C414yescomplemented
9C2×C4⋊#157—21no—
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157—21no—
12C2×C4×#157C2211yescharacteristic
13C2×#3773—21no—
14C2×#3773—21no—
15#63900C2212yes—
16C2×#3710C2212yes—
17#63732—22no—
18C3×#835—22no—
19#63567—22no—
20D3×#103—62no—
21C22×#157—21no—
22C22×#157D411yescharacteristic
23C22×#157D411yescharacteristic
24C2×C32×Q8D411yescharacteristic
25Q8×C3⋊D3—21no—
26Q8×C3⋊D3—21no—
27Q8×C3⋊D3C2×C412yes—
28Q8×C3⋊D3Q812yes—
29C2×C4×C3⋊D3—21no—
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#634—21no—
32C2×#634D411yescharacteristic
33C2×#624—22no—
34C4⋊#157—24no—
35C4⋊#157—21no—
36C4⋊#157C2×C412yes—
37C4×#157—24no—
38C4×#157C2×C412yes—
39C4×#157D412yes—
40#3773—42no—
41#3773—42no—
42C3×C4⋊Dic3—22no—
43C2×C3×C3⋊C8—22no—
44#3724—22no—
45#3710—22no—
46#3710—22no—
47#1803—91nomaximal, Sylow
48C2×D3×Q8—62no—
49C2×D3×C8—62no—
50D3×C4⋊C4—62no—
51C3×#103—62no—
52#835—22no—
53#816—62no—
54#810—62no—
55C22×C3⋊D3C2×D411yescharacteristic
56C2×#157—21no—
57C2×#157—21no—
58C2×#157—22no—
59C2×#157—41no—
60C2×#157—41no—
61C2×#157C22⋊C412yes—
62C2×#157C22⋊C412yes—
63C2×#157SD1612yes—
64C2×#157Q1612yes—
65C32×Q8—21no—
66C32×Q8C4⋊C412yescomplemented
67C2×C32×C4—21no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3#4111yescharacteristic
71C4×C3⋊D3—22no—
72C4×C3⋊D3—22no—
73C4×C3⋊D3C22×C411yescharacteristic
74C4×C3⋊D3C2×D411yescharacteristic
75C4×C3⋊D3C2×Q811yescharacteristic
76C4×C3⋊D3#4111yescharacteristic
77#634—21no—
78#634—22no—
79#634—22no—
80#634C4⋊C412yescomplemented
81C2×C3×Dic3—42no—
82#624—42no—
83#624—42no—
84C3×C3⋊C8—42no—
85C2×C4×Q8—91no—
86C2×C4⋊C8—91no—
87C2×#103—92no—
88#384—91no—
89#340—92no—
90C2×C3×Q8—22no—
91D3×Q8—64no—
92D3×Q8—64no—
93D3×Q8—122no—
94D3×Q8—122no—
95C2×C4×D3—62no—
96C2×C4×D3—122no—
97C2×C4×D3—122no—
98C2×Dic6—62no—
99C2×Dic6—122no—
100C2×C3×C8—62no—
101C3×C4⋊C4—62no—
102C4⋊Dic3—22no—
103Dic3⋊C4—122no—
104C2×C3⋊C8—22no—
105D3×C8—122no—
106D3×C8—122no—
107C22×C32#12111yescharacteristic
108C2×C3⋊D3C2×C22⋊C411yescharacteristic
109C2×C3⋊D3C22⋊Q811yescharacteristic
110C2×C3⋊D3C2×SD1611yescharacteristic
111C2×C3⋊D3C2×Q1611yescharacteristic
112C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
113C2×C3⋊D3#13711yescharacteristic
114#157—22no—
115#157—42no—
116#157#10314yescomplemented
117C32×C4—22no—
118C32×C4C2×C4⋊C411yescharacteristic
119C32×C4#12111yescharacteristic
120C3⋊Dic3—22no—
121C3⋊Dic3#11711yescharacteristic
122C3⋊Dic3C22⋊Q811yescharacteristic
123C3×Dic3—82no—
124C22×Q8—91no—
125C22×C8—92no—
126C4×Q8—94no—
127C4×Q8—182no—
128C2×C4⋊C4—92no—
129C2×C4⋊C4—91no—
130C2×C4⋊C4—181no—
131C2×C4⋊C4—181no—
132C2×C4⋊C4—181no—
133C2×C42—91no—
134C2×C42—181no—
135C4⋊C8—182no—
136#103—62no—
137#103—182no—
138C22×D3—62no—
139C3×Q8—24no—
140C3×Q8—42no—
141C2×C3×C4—22no—
142C2×C3×C4—42no—
143C2×C3×C4—122no—
144C2×Dic3—42no—
145C2×Dic3—62no—
146C2×Dic3—122no—
147C4×D3—62no—
148C4×D3—62no—
149C4×D3—62no—
150C4×D3—62no—
151C4×D3—124no—
152C4×D3—124no—
153C4×D3—242no—
154C4×D3—242no—
155Dic6—64no—
156Dic6—124no—
157Dic6—124no—
158Dic6—122no—
159C3×C8—122no—
160C3⋊C8—42no—
161C2×C32#38011yescharacteristic
162C2×C32#46011yescharacteristic
163C2×C32#46211yescharacteristic
164C3⋊D3C2×#10311yescharacteristic
165C3⋊D3#41711yescharacteristic
166C3⋊D3#47511yescharacteristic
167C3⋊D3#47711yescharacteristic
168C2×Q8—92no—
169C2×Q8—92no—
170C2×Q8—91no—
171C2×Q8—181no—
172C2×Q8—181no—
173C2×Q8—181no—
174C2×Q8GO+(4,𝔽2)11yescharacteristic
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—91no—
178C22×C4—181no—
179C22×C4—182no—
180C22×C4—181no—
181C2×C8—62no—
182C2×C8—182no—
183C2×C8—182no—
184C4⋊C4—62no—
185C4⋊C4—92no—
186C4⋊C4—182no—
187C4⋊C4—181no—
188C4⋊C4—184no—
189C4⋊C4—362no—
190C4⋊C4—362no—
191C42—92no—
192C42—92no—
193C42—184no—
194C22×C3—22no—
195C2×D3—62no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—62no—
199C2×D3—62no—
200C2×D3—62no—
201C3×C4—22no—
202C3×C4—22no—
203C3×C4—44no—
204C3×C4—242no—
205Dic3—62no—
206Dic3—62no—
207Dic3—82no—
208Dic3—124no—
209C32#180311yescharacteristic, complemented, Sylow
210C23—91no—
211Q8—21no—
212Q8—92no—
213Q8—182no—
214Q8—182no—
215Q8—181no—
216Q8#377312yescomplemented
217C2×C4—21no—
218C2×C4—92no—
219C2×C4—92no—
220C2×C4—92no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—91no—
225C2×C4—91no—
226C2×C4—92no—
227C2×C4—122no—
228C2×C4—182no—
229C2×C4—182no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4—181no—
233C2×C4—182no—
234C2×C4—362no—
235C2×C4—362no—
236C2×C4—361no—
237C2×C4—361no—
238C2×C4C2×GO+(4,𝔽2)11yescharacteristic
239C8—122no—
240C2×C3—22no—
241C2×C3—22no—
242C2×C3—22no—
243D3—62no—
244D3—62no—
245D3—62no—
246D3—62no—
247C22—91no—
248C22—91no—
249C22—91no—
250C22—91no—
251C22—91no—
252C22—91no—
253C22#6424211yescharacteristic
254C4—22no—
255C4—94no—
256C4—91no—
257C4—91no—
258C4—182no—
259C4—182no—
260C4—242no—
261C4—362no—
262C4C2×#377311yescharacteristic
263C4#6424211yescharacteristic
264C3—22no—
265C2—91no—
266C2—91no—
267C2—91no—
268C2—91no—
269C2#1059347611yescharacteristic
270C2#1059347711yescharacteristic
271C2#1059351611yescharacteristic
subgroupG/H
centerC22#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×Q8GO+(4,𝔽2)
hypocenterC32#1803
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
8. Q8×#157C4semidirect
66. C32×Q8C4⋊C4semidirect
80. #634C4⋊C4semidirect
116. #157#103semidirect
209. C32#1803semidirect
216. Q8#3773semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#1572
#105934132
C2×#637322
#105915522
#105900492
#18039