Finite Group Databasebeta

← #11790529

Subgroups — #11790529

Order 1152.

290 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 66 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#10593776C212yesmaximal
2C2×#63771C211yesmaximal, characteristic
3#10593765C211yesmaximal, characteristic
4C3⋊D3×#108C211yesmaximal, characteristic
5#10590191C212yesmaximal
6#64286C2211yescharacteristic
7#64283C2211yescharacteristic
8C2×#3788C2212yes—
9M16×C3⋊D3C2212yes—
10C2×C8×C3⋊D3C2211yescharacteristic
11#63771—22no—
12#63771—21no—
13#63771—21no—
14#63770—22no—
15#63767—21no—
16C8×#157—21no—
17C32×#108C411yescharacteristic, complemented
18#63649C412yescomplemented
19#63646C411yescharacteristic, complemented
20D3×#108—62no—
21C2×C4×C3⋊D3C2311yescharacteristic
22C22⋊#157Q812yes—
23#3792—21no—
24C2×#622—22no—
25C4⋊#157—21no—
26C4×#157—21no—
27#3788—22no—
28#3788—22no—
29#3788D411yescharacteristic
30#3788D411yescharacteristic
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#1953—91nomaximal, Sylow
43D3×M16—64no—
44C2×D3×C8—62no—
45C3×#108—22no—
46#822—64no—
47#819—62no—
48C22×C3⋊D3C2×Q811yescharacteristic
49C2×#157—22no—
50C2×C32×C4C22×C411yescharacteristic
51C2×C3⋊Dic3#4111yescharacteristic
52C4×C3⋊D3C2×D411yescharacteristic
53C4×C3⋊D3C2×D411yescharacteristic
54C4×C3⋊D3C2×Q811yescharacteristic
55C4×C3⋊D3#4111yescharacteristic
56#622—21no—
57#622—21no—
58#622—42no—
59C32×C8—22no—
60C32×C8C4⋊C411yescharacteristic
61C32×C8C4⋊C411yescharacteristic
62C3⋊(C3⋊C8)—22no—
63C3⋊(C3⋊C8)C4⋊C411yescharacteristic
64C3⋊(C3⋊C8)C4⋊C411yescharacteristic
65#430—92no—
66C2×#108—91no—
67C2×#108—91no—
68#405—91no—
69#344—92no—
70C2×C4×D3—62no—
71C3×M16—24no—
72C2×C3×C8—22no—
73#208—64no—
74C2×C3⋊C8—62no—
75ΓL(1,𝔽25)—124no—
76D3×C8—62no—
77D3×C8—62no—
78D3×C8—62no—
79D3×C8—62no—
80D3×C8—124no—
81C22×C32C4×Q811yescharacteristic
82C2×C3⋊D3—41no—
83C2×C3⋊D3C22⋊Q811yescharacteristic
84C2×C3⋊D3C4⋊Q811yescharacteristic
85#157—42no—
86C32×C4C2×C4⋊C411yescharacteristic
87C32×C4C4×D411yescharacteristic
88C3⋊Dic3#12111yescharacteristic
89C3⋊Dic3#12511yescharacteristic
90C2×M16—91no—
91C2×M16—92no—
92C2×M16—92no—
93C22×C8—91no—
94#117—91no—
95#108—92no—
96#108—91no—
97#108—181no—
98#108—181no—
99#108—182no—
100#108—182no—
101#108#15711yescharacteristic, complemented
102#97—181no—
103C4×C8—181no—
104C22×D3—62no—
105C2×C3×C4—22no—
106C2×Dic3—62no—
107C4×D3—62no—
108C4×D3—62no—
109C4×D3—62no—
110C4×D3—62no—
111C3×C8—22no—
112C3×C8—22no—
113C3×C8—44no—
114C3⋊C8—62no—
115C3⋊C8—62no—
116C3⋊C8—124no—
117C2×C32—21no—
118C2×C32#38911yescharacteristic
119C3⋊D3—21no—
120C3⋊D3—21no—
121C22×C4—91no—
122M16—91no—
123M16—91no—
124M16—92no—
125M16—182no—
126M16—181no—
127M16—182no—
128M16—182no—
129M16C2×#15712yes—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—91no—
133C2×C8—91no—
134C2×C8—91no—
135C2×C8—182no—
136C2×C8—181no—
137C2×C8—182no—
138C2×C8C2×#15711yescharacteristic
139C4⋊C4—181no—
140C22⋊C4—92no—
141C42—181no—
142C22×C3—22no—
143C2×D3—62no—
144C2×D3—62no—
145C2×D3—124no—
146C3×C4—22no—
147C3×C4—22no—
148Dic3—62no—
149Dic3—62no—
150C32#195311yescharacteristic, complemented, Sylow
151C23—91no—
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—91no—
157C2×C4—182no—
158C2×C4C22×#15711yescharacteristic
159C8—22no—
160C8—91no—
161C8—91no—
162C8—181no—
163C8—181no—
164C8—182no—
165C8—362no—
166C8C4⋊#15711yescharacteristic
167C8C4⋊#15711yescharacteristic
168C2×C3—22no—
169C2×C3—42no—
170D3—64no—
171D3—122no—
172C22—91no—
173C22—91no—
174C22—361no—
175C22Q8×#15711yescharacteristic
176C4—91no—
177C4—91no—
178C4—362no—
179C4C2×C4⋊#15711yescharacteristic
180C4D4×#15711yescharacteristic
181C3—22no—
182C2—21no—
183C2—181no—
184C2—181no—
185C2#1059375911yescharacteristic
subgroupG/H
centerC2#10593759
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#108C4
socleC2×C32#389
prime radicalC22×C3⋊D3C2×Q8
cosocleC2×C4×C3⋊D3C23
hypercenter#108#157
hypocenterC32#1953
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
150. C32#1953semidirect

Maximal subgroups

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

subgroupindex
#105937762
C2×#637712
#105937652
C3⋊D3×#1082
#105901912
#19539