Finite Group Databasebeta

← #11795288

Subgroups — #11795288

Order 1152.

270 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 61 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
1#10593759C211yesmaximal, characteristic
2#10593554C211yesmaximal, characteristic
3C2×#63745C211yesmaximal, characteristic
4C2×#63744C211yesmaximal, characteristic
5#10590163C211yesmaximal, characteristic
6#10590163C211yesmaximal, characteristic
7#10590093C211yesmaximal, characteristic
8C2×C4⋊#157—21no—
9C2×C4⋊#157C2211yescharacteristic
10C2×C4⋊#157C2211yescharacteristic
11C2×C4⋊#157C2211yescharacteristic
12C2×C4×#157C2211yescharacteristic
13C2×#3787C2211yescharacteristic
14C2×#3787C2211yescharacteristic
15C2×#3777—21no—
16C4⋊C4×C3⋊D3C2211yescharacteristic
17#63781—21no—
18#63747—21no—
19#63745—22no—
20#63744—22no—
21C22×#157—21no—
22C22×#157—21no—
23C22×#157—21no—
24C22×#157D411yescharacteristic
25C22×#157D411yescharacteristic
26C2×C4×C3⋊D3—21no—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×#622—21no—
29C2×#622—21no—
30C4⋊#157—21no—
31C4⋊#157—21no—
32C4⋊#157—21no—
33C4⋊#157—21no—
34C4⋊#157—21no—
35C4⋊#157—42no—
36C4⋊#157Q812yes—
37C4×#157—21no—
38C4×#157—21no—
39#3787—21no—
40#3787—21no—
41#3787—21no—
42#3787D412yes—
43#3777—42no—
44C32×C4⋊C4Q811yescharacteristic
45C4⋊(C3⋊Dic3)Q811yescharacteristic
46#3750—21no—
47#2088—91nomaximal, Sylow
48D3×C4⋊C4—121no—
49C22×C3⋊D3C2×D411yescharacteristic
50C2×#157—21no—
51C2×#157—21no—
52C2×#157—21no—
53C2×#157—22no—
54C2×#157—21no—
55C2×#157—21no—
56C2×#157—41no—
57C2×#157—41no—
58C2×#157—41no—
59C2×#157—41no—
60C2×#157—41no—
61C2×#157—41no—
62C2×#157—41no—
63C2×#157—41no—
64C2×#157SD1612yes—
65C2×C32×C4—21no—
66C2×C32×C4C2×Q811yescharacteristic
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3#4111yescharacteristic
69C4×C3⋊D3—41no—
70C4×C3⋊D3—41no—
71C4×C3⋊D3C2×D411yescharacteristic
72C4×C3⋊D3C2×Q811yescharacteristic
73C4×C3⋊D3#4111yescharacteristic
74C4×C3⋊D3#4111yescharacteristic
75#622—22no—
76#622—41no—
77C2×#106—91no—
78C2×C4⋊C8—91no—
79#389—91no—
80#389—91no—
81#340—91no—
82#340—91no—
83#340—91no—
84C2×C4×D3—121no—
85C2×C4×D3—122no—
86C3×C4⋊C4—41no—
87C4⋊Dic3—121no—
88Dic3⋊C4—122no—
89C22×C32C22⋊Q811yescharacteristic
90C2×C3⋊D3#12111yescharacteristic
91C2×C3⋊D3C22⋊Q811yescharacteristic
92C2×C3⋊D3C2×SD1611yescharacteristic
93C2×C3⋊D3#13511yescharacteristic
94C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
95C2×C3⋊D3#13711yescharacteristic
96#157—22no—
97#157—41no—
98#157—42no—
99#157—81no—
100#157—81no—
101C32×C4—41no—
102C32×C4#12511yescharacteristic
103C32×C4C4⋊Q811yescharacteristic
104C3⋊Dic3—41no—
105C3⋊Dic3#12311yescharacteristic
106C3⋊Dic3#12511yescharacteristic
107C22×C8—91no—
108C22×C8—91no—
109C2×C4⋊C4—91no—
110C2×C4⋊C4—91no—
111C2×C4⋊C4—91no—
112C2×C4⋊C4—91no—
113C2×C4⋊C4—181no—
114C2×C4⋊C4—181no—
115C2×C42—91no—
116#106—182no—
117C4⋊C8—182no—
118#95—181no—
119#95—181no—
120C22×D3—121no—
121C2×C3×C4—42no—
122C2×C3×C4—41no—
123C2×Dic3—121no—
124C2×Dic3—122no—
125C4×D3—121no—
126C4×D3—121no—
127C4×D3—121no—
128C4×D3—121no—
129C4×D3—242no—
130C4×D3—242no—
131C2×C32#39811yescharacteristic
132C2×C32#47611yescharacteristic
133C2×C32#47911yescharacteristic
134C3⋊D3#46511yescharacteristic
135C3⋊D3#46811yescharacteristic
136C3⋊D3#47511yescharacteristic
137C3⋊D3#47811yescharacteristic
138C22×C4—91no—
139C22×C4—91no—
140C22×C4—91no—
141C22×C4—181no—
142C22×C4—181no—
143C22×C4—181no—
144C22×C4—181no—
145C2×C8—92no—
146C2×C8—181no—
147C2×C8—181no—
148C2×C8—181no—
149C2×C8—181no—
150C2×C8—181no—
151C4⋊C4—92no—
152C4⋊C4—91no—
153C4⋊C4—181no—
154C4⋊C4—181no—
155C4⋊C4—181no—
156C4⋊C4—181no—
157C4⋊C4—181no—
158C4⋊C4—181no—
159C4⋊C4—362no—
160C4⋊C4—362no—
161C4⋊C4PSU(3,𝔽2)11yescharacteristic
162C42—181no—
163C42—181no—
164C22×C3—41no—
165C2×D3—121no—
166C2×D3—121no—
167C2×D3—121no—
168C2×D3—121no—
169C2×D3—121no—
170C2×D3—121no—
171C3×C4—41no—
172C3×C4—41no—
173C3×C4—82no—
174Dic3—121no—
175Dic3—121no—
176Dic3—242no—
177C32#208811yescharacteristic, complemented, Sylow
178C23—91no—
179C2×C4—21no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—92no—
186C2×C4—181no—
187C2×C4—181no—
188C2×C4—181no—
189C2×C4—182no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4—181no—
193C2×C4—361no—
194C2×C4—361no—
195C2×C4—361no—
196C2×C4—361no—
197C2×C4—361no—
198C2×C4—361no—
199C2×C4—361no—
200C2×C4—361no—
201C2×C4—361no—
202C2×C4—361no—
203C2×C4C2×PSU(3,𝔽2)11yescharacteristic
204C8—182no—
205C8—361no—
206C2×C3—41no—
207C2×C3—41no—
208C2×C3—41no—
209D3—121no—
210D3—121no—
211D3—121no—
212D3—121no—
213C22—91no—
214C22—91no—
215C22—91no—
216C22—91no—
217C22—91no—
218C22—91no—
219C22C22⋊PSU(3,𝔽2)11yescharacteristic
220C4—41no—
221C4—91no—
222C4—91no—
223C4—182no—
224C4—361no—
225C4—362no—
226C4—361no—
227C4—721no—
228C4—721no—
229C4#6424311yescharacteristic
230C4C4⋊PSU(3,𝔽2)11yescharacteristic
231C3—41no—
232C2—91no—
233C2—91no—
234C2—91no—
235C2—91no—
236C2#1059355211yescharacteristic
237C2#1059355911yescharacteristic
238C2#1059356011yescharacteristic
subgroupG/H
centerC22C22⋊PSU(3,𝔽2)
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC32×C4⋊C4Q8
socleC22×C32C22⋊Q8
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C4PSU(3,𝔽2)
hypocenterC32#2088
LCSG ▷ C2×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
177. C32#2088semidirect

Maximal subgroups

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

subgroupindex
#105937592
#105935542
C2×#637452
C2×#637442
#105901632
#105900932
#20889