Finite Group Databasebeta

← #11785297

Subgroups — #11785297

Order 1152.

370 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 79 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
2C2×#63784C212yesmaximal
3#10593545C211yesmaximal, characteristic
4C2×#63744C211yesmaximal, characteristic
5#10590093C212yesmaximal
6C2×Q8×C3⋊D3C2211yescharacteristic
7Q8×#157—22no—
8Q8×#157C414yescomplemented
9C2×C4⋊#157—21no—
10C2×C4⋊#157C2212yes—
11C2×C4⋊#157C2211yescharacteristic
12C2×C4×#157—21no—
13C2×C4×#157C2211yescharacteristic
14C2×#3787C2212yes—
15#63784—24no—
16#63747—21no—
17#63747—21no—
18#63744—22no—
19C22×#157—21no—
20C22×#157—22no—
21C22×#157D411yescharacteristic
22C22×#157D411yescharacteristic
23C2×C32×Q8Q811yescharacteristic
24Q8×C3⋊D3—21no—
25Q8×C3⋊D3—21no—
26Q8×C3⋊D3C2×C412yes—
27Q8×C3⋊D3D412yes—
28C2×C4×C3⋊D3—21no—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×#634—21no—
31C2×#634Q811yescharacteristic
32C2×#622—22no—
33C4⋊#157—24no—
34C4⋊#157—21no—
35C4⋊#157—22no—
36C4⋊#157—22no—
37C4⋊#157C2×C412yes—
38C4×#157—24no—
39C4×#157C2×C412yes—
40C4×#157D412yes—
41#3787—22no—
42#3787—22no—
43#1805—91nomaximal, Sylow
44C2×D3×Q8—121no—
45C22×C3⋊D3C2×D411yescharacteristic
46C2×#157—22no—
47C2×#157—22no—
48C2×#157—22no—
49C2×#157—42no—
50C2×#157—42no—
51C2×#157—42no—
52C2×#157—42no—
53C2×#157C22⋊C412yes—
54C2×#157C22⋊C412yes—
55C32×Q8—21no—
56C32×Q8C4⋊C412yes—
57C2×C32×C4—21no—
58C2×C32×C4C2×Q811yescharacteristic
59C2×C3⋊Dic3—21no—
60C2×C3⋊Dic3#4111yescharacteristic
61C4×C3⋊D3—22no—
62C4×C3⋊D3—22no—
63C4×C3⋊D3C22×C411yescharacteristic
64C4×C3⋊D3C2×D411yescharacteristic
65C4×C3⋊D3C2×D411yescharacteristic
66C4×C3⋊D3#4111yescharacteristic
67#634—21no—
68#634—22no—
69#634—22no—
70#634C4⋊C412yes—
71#622—42no—
72C2×C4×Q8—91no—
73C2×C4⋊C8—91no—
74C2×#103—92no—
75#382—91no—
76#340—92no—
77C2×C3×Q8—41no—
78D3×Q8—122no—
79D3×Q8—122no—
80D3×Q8—122no—
81D3×Q8—122no—
82C2×C4×D3—121no—
83C2×C4×D3—122no—
84C2×Dic6—121no—
85C2×Dic6—122no—
86C22×C32C22⋊Q811yescharacteristic
87C2×C3⋊D3C2×C22⋊C411yescharacteristic
88C2×C3⋊D3#12111yescharacteristic
89C2×C3⋊D3#13512yes—
90C2×C3⋊D3#13712yes—
91#157—22no—
92#157—22no—
93#157—42no—
94#157—82no—
95C32×C4—22no—
96C32×C4C2×C4⋊C411yescharacteristic
97C32×C4C22⋊Q811yescharacteristic
98C3⋊Dic3—22no—
99C3⋊Dic3#11711yescharacteristic
100C3⋊Dic3#12111yescharacteristic
101C22×Q8—91no—
102C22×C8—92no—
103C4×Q8—94no—
104C4×Q8—182no—
105C2×C4⋊C4—91no—
106C2×C4⋊C4—92no—
107C2×C4⋊C4—181no—
108C2×C42—91no—
109C2×C42—181no—
110C4⋊C8—182no—
111#103—184no—
112#95—181no—
113#95—181no—
114C22×D3—121no—
115C3×Q8—42no—
116C3×Q8—42no—
117C2×C3×C4—42no—
118C2×C3×C4—41no—
119C2×Dic3—121no—
120C2×Dic3—122no—
121C4×D3—121no—
122C4×D3—121no—
123C4×D3—121no—
124C4×D3—121no—
125C4×D3—124no—
126C4×D3—124no—
127Dic6—122no—
128Dic6—124no—
129Dic6—124no—
130Dic6—122no—
131C2×C32#38011yescharacteristic
132C2×C32#47912yes—
133C3⋊D3#41611yescharacteristic
134C3⋊D3#41911yescharacteristic
135C3⋊D3#46412yes—
136C2×Q8—92no—
137C2×Q8—92no—
138C2×Q8—91no—
139C2×Q8—181no—
140C2×Q8—181no—
141C2×Q8—181no—
142C2×Q8PSU(3,𝔽2)11yescharacteristic
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—181no—
147C22×C4—181no—
148C22×C4—182no—
149C2×C8—182no—
150C2×C8—182no—
151C2×C8—182no—
152C4⋊C4—92no—
153C4⋊C4—181no—
154C4⋊C4—184no—
155C4⋊C4—182no—
156C4⋊C4—182no—
157C42—92no—
158C42—92no—
159C42—184no—
160C22×C3—41no—
161C2×D3—121no—
162C2×D3—121no—
163C2×D3—122no—
164C2×D3—122no—
165C3×C4—44no—
166C3×C4—41no—
167C3×C4—41no—
168Dic3—121no—
169Dic3—121no—
170Dic3—124no—
171C32#180511yescharacteristic, complemented, Sylow
172C23—91no—
173Q8—21no—
174Q8—92no—
175Q8—182no—
176Q8—182no—
177Q8—181no—
178Q8#377712yes—
179C2×C4—21no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—92no—
186C2×C4—92no—
187C2×C4—182no—
188C2×C4—182no—
189C2×C4—182no—
190C2×C4—182no—
191C2×C4—181no—
192C2×C4—182no—
193C2×C4—362no—
194C2×C4—362no—
195C2×C4—362no—
196C2×C4—362no—
197C2×C4C2×PSU(3,𝔽2)11yescharacteristic
198C8—362no—
199C2×C3—42no—
200C2×C3—41no—
201D3—121no—
202D3—121no—
203D3—122no—
204C22—92no—
205C22—92no—
206C22—91no—
207C22—91no—
208C22C22⋊PSU(3,𝔽2)11yescharacteristic
209C4—22no—
210C4—91no—
211C4—91no—
212C4—182no—
213C4—182no—
214C4—182no—
215C4—362no—
216C4—722no—
217C4C2×#377711yescharacteristic
218C4C22⋊PSU(3,𝔽2)11yescharacteristic
219C3—41no—
220C2—91no—
221C2—91no—
222C2—92no—
223C2#1059356012yes—
224C2#1059356811yescharacteristic
subgroupG/H
centerC22C22⋊PSU(3,𝔽2)
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×PSU(3,𝔽2)
FittingC2×C32×Q8Q8
socleC22×C32C22⋊Q8
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC2×Q8PSU(3,𝔽2)
hypocenterC32#1805
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
171. C32#1805semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#1572
C2×#637842
#105935452
C2×#637442
#105900932
#18059