Finite Group Databasebeta

← #11790493

Subgroups — #11790493

Order 1152.

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

normal subgroups only

This group has 302 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
1#10593774C212yesmaximal
2C2×#63769C211yesmaximal, characteristic
3#10593765C211yesmaximal, characteristic
4C3⋊D3×#108C211yesmaximal, characteristic
5#10590188C212yesmaximal
6#64286C2211yescharacteristic
7C2×C4⋊#157C2212yes—
8#64283C2211yescharacteristic
9M16×C3⋊D3C2212yes—
10C2×C8×C3⋊D3C2211yescharacteristic
11#63769—22no—
12#63769—21no—
13#63769—21no—
14#63768—22no—
15#63767—21no—
16C8×#157—21no—
17C32×#108C411yescharacteristic, complemented
18#63649C412yescomplemented
19#63646C411yescharacteristic, complemented
20D3×#108—62no—
21C22×#157—22no—
22C2×C4×C3⋊D3C2311yescharacteristic
23C22⋊#157—21no—
24#3792Q812yes—
25C4⋊#157—22no—
26C4⋊#157—22no—
27C4⋊#157D411yescharacteristic
28C4⋊#157D411yescharacteristic
29C4×#157—21no—
30#3788—21no—
31#3787—21no—
32C32×M16C2×C412yes—
33C2×C32×C8C2×C411yescharacteristic
34#3748C2×C412yes—
35C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
36#3743—22no—
37C8×C3⋊D3—22no—
38C8×C3⋊D3D411yescharacteristic
39C8×C3⋊D3D411yescharacteristic
40C8×C3⋊D3Q811yescharacteristic
41C8×C3⋊D3Q811yescharacteristic
42#1952—91nomaximal, Sylow
43D3×M16—64no—
44C2×D3×C8—62no—
45C3×#108—22no—
46#822—64no—
47#819—62no—
48C22×C3⋊D3#4111yescharacteristic
49C2×#157—21no—
50C2×#157—21no—
51C2×#157—42no—
52C2×#157—82no—
53C2×C32×C4C22×C411yescharacteristic
54C2×C3⋊Dic3C2×Q811yescharacteristic
55C4×C3⋊D3C2×D411yescharacteristic
56C4×C3⋊D3C2×D411yescharacteristic
57C4×C3⋊D3C2×Q811yescharacteristic
58C4×C3⋊D3#4111yescharacteristic
59#622—22no—
60C32×C8—22no—
61C32×C8C4⋊C411yescharacteristic
62C32×C8C4⋊C411yescharacteristic
63C3⋊(C3⋊C8)—22no—
64C3⋊(C3⋊C8)C4⋊C411yescharacteristic
65C3⋊(C3⋊C8)C4⋊C411yescharacteristic
66C2×#108—91no—
67#428—92no—
68C2×#107—91no—
69#405—91no—
70#343—92no—
71C2×C4×D3—62no—
72C3×M16—24no—
73C2×C3×C8—22no—
74#208—64no—
75C2×C3⋊C8—62no—
76ΓL(1,𝔽25)—124no—
77D3×C8—62no—
78D3×C8—62no—
79D3×C8—62no—
80D3×C8—62no—
81D3×C8—124no—
82C22×C32C4×Q811yescharacteristic
83C2×C3⋊D3—21no—
84C2×C3⋊D3—21no—
85C2×C3⋊D3#12111yescharacteristic
86C2×C3⋊D3#12511yescharacteristic
87#157—41no—
88#157—41no—
89#157—82no—
90C32×C4C2×C4⋊C411yescharacteristic
91C32×C4C4×D411yescharacteristic
92C3⋊Dic3C22⋊Q811yescharacteristic
93C3⋊Dic3C4⋊Q811yescharacteristic
94C2×M16—91no—
95C2×M16—92no—
96C22×C8—91no—
97#117—91no—
98C2×C4⋊C4—92no—
99#108—92no—
100#108—91no—
101#108#15711yescharacteristic, complemented
102#107—182no—
103#107—181no—
104#107—181no—
105#106—182no—
106#97—181no—
107C4×C8—181no—
108C22×D3—62no—
109C2×C3×C4—22no—
110C2×Dic3—62no—
111C4×D3—62no—
112C4×D3—62no—
113C4×D3—62no—
114C4×D3—62no—
115C3×C8—22no—
116C3×C8—22no—
117C3×C8—44no—
118C3⋊C8—62no—
119C3⋊C8—62no—
120C3⋊C8—124no—
121C2×C32—21no—
122C2×C32#38911yescharacteristic
123C3⋊D3—21no—
124C3⋊D3#47211yescharacteristic
125C3⋊D3#47311yescharacteristic
126C22×C4—91no—
127C22×C4—182no—
128M16—92no—
129M16—92no—
130M16—182no—
131M16—181no—
132M16C2×#15712yes—
133C2×C8—91no—
134C2×C8—91no—
135C2×C8—91no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—182no—
139C2×C8—181no—
140C2×C8C2×#15711yescharacteristic
141C4⋊C4—91no—
142C4⋊C4—91no—
143C4⋊C4—182no—
144C4⋊C4—182no—
145C22⋊C4—181no—
146C42—181no—
147C22×C3—22no—
148C2×D3—62no—
149C2×D3—62no—
150C2×D3—122no—
151C2×D3—122no—
152C3×C4—22no—
153C3×C4—22no—
154Dic3—62no—
155Dic3—62no—
156C32#195211yescharacteristic, complemented, Sylow
157C23—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—181no—
164C2×C4—181no—
165C2×C4—362no—
166C2×C4—722no—
167C2×C4C22×#15711yescharacteristic
168C8—22no—
169C8—91no—
170C8—91no—
171C8—182no—
172C8—182no—
173C8C4⋊#15711yescharacteristic
174C8C4⋊#15711yescharacteristic
175C2×C3—22no—
176C2×C3—42no—
177D3—62no—
178D3—62no—
179D3—122no—
180C22—91no—
181C22—91no—
182C22—181no—
183C22—181no—
184C22Q8×#15711yescharacteristic
185C4—91no—
186C4—91no—
187C4—361no—
188C4—361no—
189C4—722no—
190C4C2×C4⋊#15711yescharacteristic
191C4D4×#15711yescharacteristic
192C3—22no—
193C2—21no—
194C2—91no—
195C2—91no—
196C2—181no—
197C2#1059375911yescharacteristic
subgroupG/H
centerC2#10593759
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#108C4
socleC2×C32#389
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenter#108#157
hypocenterC32#1952
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
17. C32×#108C4semidirect
18. #63649C4semidirect
19. #63646C4semidirect
101. #108#157semidirect
156. C32#1952semidirect

Maximal subgroups

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

subgroupindex
#105937742
C2×#637692
#105937652
C3⋊D3×#1082
#105901882
#19529