Finite Group Databasebeta

← #11791674

Subgroups — #11791674

Order 1152.

306 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 73 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×#64243C211yesmaximal, characteristic
2C4⋊C4×#157C211yesmaximal, characteristic
3C2×#63744C211yesmaximal, characteristic
4#10590163C211yesmaximal, characteristic
5#10590163C211yesmaximal, characteristic
6#10590093C211yesmaximal, characteristic
7#10590093C211yesmaximal, characteristic
8C2×C4⋊#157C2211yescharacteristic
9C2×C4⋊#157C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157—21no—
12C2×C4×#157C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C2×#3777—21no—
16C2×#3777—21no—
17#64243—22no—
18#64243C414yescomplemented
19C4⋊C4×C3⋊D3C2211yescharacteristic
20#63781—21no—
21#63744—22no—
22C22×#157—21no—
23C22×#157—21no—
24C22×#157—21no—
25C22×#157D411yescharacteristic
26C22×#157D411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×#622—21no—
30C2×#622—21no—
31C4⋊#157—21no—
32C4⋊#157—21no—
33C4⋊#157—21no—
34C4⋊#157C2×C412yes—
35C4⋊#157C2×C412yes—
36C4⋊#157Q812yes—
37C4×#157—42no—
38C4×#157C2×C412yes—
39C4×#157D412yes—
40#3787—21no—
41#3787—21no—
42#3787—21no—
43#3787—21no—
44#3777—24no—
45#3777—24no—
46C32×C4⋊C4Q811yescharacteristic
47C4⋊(C3⋊Dic3)Q811yescharacteristic
48#3750—21no—
49#1989—91nomaximal, Sylow
50D3×C4⋊C4—121no—
51C22×C3⋊D3C2×D411yescharacteristic
52C2×#157—21no—
53C2×#157—21no—
54C2×#157—21no—
55C2×#157—21no—
56C2×#157—22no—
57C2×#157—22no—
58C2×#157—22no—
59C2×#157—41no—
60C2×#157—41no—
61C2×#157—41no—
62C2×#157—41no—
63C2×#157—41no—
64C2×#157—41no—
65C2×#157C22⋊C412yes—
66C2×#157C22⋊C412yes—
67C2×C32×C4—21no—
68C2×C32×C4C2×Q811yescharacteristic
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3#4111yescharacteristic
71C4×C3⋊D3—41no—
72C4×C3⋊D3—41no—
73C4×C3⋊D3C22×C411yescharacteristic
74C4×C3⋊D3C2×D411yescharacteristic
75C4×C3⋊D3C2×Q811yescharacteristic
76C4×C3⋊D3#4111yescharacteristic
77#622—41no—
78#622—41no—
79C2×#125—91no—
80C2×C4⋊C8—91no—
81C4×C4⋊C4—91no—
82#340—91no—
83#340—91no—
84#340—91no—
85#340—91no—
86C2×C4×D3—121no—
87C2×C4×D3—122no—
88C3×C4⋊C4—41no—
89C4⋊Dic3—121no—
90Dic3⋊C4—122no—
91C22×C32C22⋊Q811yescharacteristic
92C2×C3⋊D3C2×C22⋊C411yescharacteristic
93C2×C3⋊D3C22⋊Q811yescharacteristic
94C2×C3⋊D3#13511yescharacteristic
95C2×C3⋊D3#13511yescharacteristic
96C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
97C2×C3⋊D3#13711yescharacteristic
98#157—22no—
99#157—22no—
100#157—42no—
101#157—42no—
102#157—42no—
103C32×C4—41no—
104C32×C4C4×Q811yescharacteristic
105C32×C4C4⋊Q811yescharacteristic
106C3⋊Dic3—41no—
107C3⋊Dic3C4×Q811yescharacteristic
108C3⋊Dic3#12411yescharacteristic
109C22×C8—91no—
110C22×C8—91no—
111#125—94no—
112#125—182no—
113C2×C4⋊C4—91no—
114C2×C4⋊C4—91no—
115C2×C4⋊C4—91no—
116C2×C4⋊C4—91no—
117C2×C4⋊C4—181no—
118C2×C4⋊C4—181no—
119C2×C42—91no—
120C2×C42—181no—
121C4⋊C8—182no—
122#95—181no—
123C22×D3—121no—
124C2×C3×C4—42no—
125C2×C3×C4—41no—
126C2×Dic3—121no—
127C2×Dic3—122no—
128C4×D3—121no—
129C4×D3—121no—
130C4×D3—121no—
131C4×D3—121no—
132C4×D3—242no—
133C4×D3—242no—
134C2×C32#39111yescharacteristic
135C2×C32#47811yescharacteristic
136C2×C32#47911yescharacteristic
137C3⋊D3#41611yescharacteristic
138C3⋊D3#41711yescharacteristic
139C3⋊D3#47811yescharacteristic
140C3⋊D3#47911yescharacteristic
141C22×C4—91no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—181no—
145C22×C4—181no—
146C22×C4—181no—
147C22×C4—181no—
148C2×C8—181no—
149C2×C8—181no—
150C2×C8—181no—
151C2×C8—181no—
152C2×C8—181no—
153C2×C8—181no—
154C4⋊C4—92no—
155C4⋊C4—92no—
156C4⋊C4—92no—
157C4⋊C4—91no—
158C4⋊C4—181no—
159C4⋊C4—181no—
160C4⋊C4—181no—
161C4⋊C4—181no—
162C4⋊C4—184no—
163C4⋊C4—184no—
164C4⋊C4PSU(3,𝔽2)11yescharacteristic
165C42—92no—
166C42—92no—
167C42—362no—
168C22×C3—41no—
169C2×D3—121no—
170C2×D3—121no—
171C2×D3—121no—
172C2×D3—121no—
173C2×D3—121no—
174C2×D3—121no—
175C3×C4—41no—
176C3×C4—41no—
177C3×C4—82no—
178Dic3—121no—
179Dic3—121no—
180Dic3—242no—
181C32#198911yescharacteristic, complemented, Sylow
182C23—91no—
183C2×C4—21no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—92no—
190C2×C4—92no—
191C2×C4—181no—
192C2×C4—181no—
193C2×C4—181no—
194C2×C4—181no—
195C2×C4—182no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4—181no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4—361no—
203C2×C4—361no—
204C2×C4—361no—
205C2×C4—361no—
206C2×C4—361no—
207C2×C4C2×PSU(3,𝔽2)11yescharacteristic
208C8—361no—
209C8—361no—
210C2×C3—41no—
211C2×C3—41no—
212C2×C3—41no—
213D3—121no—
214D3—121no—
215D3—121no—
216D3—121no—
217C22—91no—
218C22—91no—
219C22—91no—
220C22—91no—
221C22—91no—
222C22—91no—
223C22C22⋊PSU(3,𝔽2)11yescharacteristic
224C4—41no—
225C4—91no—
226C4—91no—
227C4—182no—
228C4—182no—
229C4—362no—
230C4—362no—
231C4—362no—
232C4—361no—
233C4C4×PSU(3,𝔽2)11yescharacteristic
234C4C4⋊PSU(3,𝔽2)11yescharacteristic
235C3—41no—
236C2—91no—
237C2—91no—
238C2—91no—
239C2—91no—
240C2#1059355511yescharacteristic
241C2#1059355711yescharacteristic
242C2#1059356011yescharacteristic
subgroupG/H
centerC22C22⋊PSU(3,𝔽2)
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C4⋊C4Q8
socleC22×C32C22⋊Q8
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4PSU(3,𝔽2)
hypocenterC32#1989
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
18. #64243C4semidirect
181. C32#1989semidirect

Maximal subgroups

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

subgroupindex
C2×#642432
C4⋊C4×#1572
C2×#637442
#105901632
#105900932
#19899