Finite Group Databasebeta

← #11790528

Subgroups — #11790528

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×#63770C211yesmaximal, 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#63770—22no—
13#63770—21no—
14#63770—21no—
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#3788D412yes—
30#3787—21no—
31C32×M16C2×C412yes—
32C2×C32×C8C2×C411yescharacteristic
33#3748C2×C412yes—
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35#3743—22no—
36C8×C3⋊D3—22no—
37C8×C3⋊D3D411yescharacteristic
38C8×C3⋊D3D411yescharacteristic
39C8×C3⋊D3Q811yescharacteristic
40C8×C3⋊D3Q811yescharacteristic
41#1953—91nomaximal, Sylow
42D3×M16—64no—
43C2×D3×C8—62no—
44C3×#108—22no—
45#822—64no—
46#819—62no—
47C22×C3⋊D3C2×Q811yescharacteristic
48C2×#157—22no—
49C2×C32×C4C22×C411yescharacteristic
50C2×C3⋊Dic3#4111yescharacteristic
51C4×C3⋊D3C2×D411yescharacteristic
52C4×C3⋊D3C2×D411yescharacteristic
53C4×C3⋊D3C2×Q811yescharacteristic
54C4×C3⋊D3#4111yescharacteristic
55#622—22no—
56#622—42no—
57C32×C8—22no—
58C32×C8C4⋊C411yescharacteristic
59C32×C8C4⋊C411yescharacteristic
60C3⋊(C3⋊C8)—22no—
61C3⋊(C3⋊C8)C4⋊C411yescharacteristic
62C3⋊(C3⋊C8)C4⋊C411yescharacteristic
63#430—92no—
64C2×#108—91no—
65C2×#108—91no—
66#405—91no—
67#344—92no—
68C2×C4×D3—62no—
69C3×M16—24no—
70C2×C3×C8—22no—
71#208—64no—
72C2×C3⋊C8—62no—
73ΓL(1,𝔽25)—124no—
74D3×C8—62no—
75D3×C8—62no—
76D3×C8—62no—
77D3×C8—62no—
78D3×C8—124no—
79C22×C32C4×Q811yescharacteristic
80C2×C3⋊D3—41no—
81C2×C3⋊D3C22⋊Q811yescharacteristic
82C2×C3⋊D3C4⋊Q811yescharacteristic
83#157—42no—
84C32×C4C2×C4⋊C411yescharacteristic
85C32×C4C4×D411yescharacteristic
86C3⋊Dic3#12111yescharacteristic
87C3⋊Dic3#12511yescharacteristic
88C2×M16—91no—
89C2×M16—92no—
90C2×M16—92no—
91C22×C8—91no—
92#117—91no—
93#108—92no—
94#108—91no—
95#108—181no—
96#108—181no—
97#108—182no—
98#108—182no—
99#108#15711yescharacteristic, complemented
100#97—181no—
101C4×C8—181no—
102C22×D3—62no—
103C2×C3×C4—22no—
104C2×Dic3—62no—
105C4×D3—62no—
106C4×D3—62no—
107C4×D3—62no—
108C4×D3—62no—
109C3×C8—22no—
110C3×C8—22no—
111C3×C8—44no—
112C3⋊C8—62no—
113C3⋊C8—62no—
114C3⋊C8—124no—
115C2×C32—21no—
116C2×C32#38911yescharacteristic
117C3⋊D3—21no—
118C3⋊D3—21no—
119C22×C4—91no—
120M16—92no—
121M16—92no—
122M16—182no—
123M16—181no—
124M16—182no—
125M16—182no—
126M16C2×#15712yes—
127C2×C8—91no—
128C2×C8—91no—
129C2×C8—91no—
130C2×C8—91no—
131C2×C8—91no—
132C2×C8—182no—
133C2×C8—181no—
134C2×C8—182no—
135C2×C8C2×#15711yescharacteristic
136C4⋊C4—181no—
137C22⋊C4—92no—
138C42—181no—
139C22×C3—22no—
140C2×D3—62no—
141C2×D3—62no—
142C2×D3—124no—
143C3×C4—22no—
144C3×C4—22no—
145Dic3—62no—
146Dic3—62no—
147C32#195311yescharacteristic, complemented, Sylow
148C23—91no—
149C2×C4—91no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4—91no—
153C2×C4—91no—
154C2×C4—182no—
155C2×C4C22×#15711yescharacteristic
156C8—22no—
157C8—91no—
158C8—91no—
159C8—182no—
160C8—182no—
161C8—362no—
162C8C4⋊#15711yescharacteristic
163C8C4⋊#15711yescharacteristic
164C2×C3—22no—
165C2×C3—42no—
166D3—64no—
167D3—122no—
168C22—91no—
169C22—91no—
170C22—361no—
171C22Q8×#15711yescharacteristic
172C4—91no—
173C4—91no—
174C4—362no—
175C4C2×C4⋊#15711yescharacteristic
176C4D4×#15711yescharacteristic
177C3—22no—
178C2—21no—
179C2—181no—
180C2—181no—
181C2#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
99. #108#157semidirect
147. C32#1953semidirect

Maximal subgroups

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

subgroupindex
#105937762
C2×#637702
#105937652
C3⋊D3×#1082
#105901912
#19539