Finite Group Databasebeta

← #34102089

Subgroups — #34102089

Order 20096.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#23758073C211yesmaximal, characteristic
2#23757716C212yesmaximal, complemented
3#23757531C211yesmaximal, characteristic, complemented
4#23757084C212yesmaximal, complemented
5#349×C157C211yesmaximal, characteristic, complemented
6C2×#14578954—21no—
7#19097804—22no—
8#19097799—22no—
9#19097793—21no—
10#19097793C2212yes—
11C2×Dic628C2211yescharacteristic, complemented
12#19097750—21no—
13Dic1256—22no—
14#19097716—22no—
15#19097703C2211yescharacteristic, complemented
16#19097696—21no—
17C2×M16×C157C2211yescharacteristic
18M32×C157C2212yescomplemented
19#14578954—22no—
20#14578954—22no—
21#14578954—41no—
22#14578954—41no—
23C2×Dic314—21no—
24C2×Dic314—21no—
25C2×D628—21no—
26C2×C22⋊D157—41no—
27C2×C4×D157—41no—
28Dic628—21no—
29Dic628—22no—
30Dic628D412yes—
31#14578943—22no—
32#14578943—22no—
33D1256—21no—
34D1256D412yes—
35C4⋊Dic157—21no—
36#14578933—41no—
37C22⋊Dic157—41no—
38C22×C4×C157D411yescharacteristic
39M16×C157—22no—
40C2×C8×C157D411yescharacteristic
41C2×C8×C157C2311yescharacteristic
42C16×C157—22no—
43C22×D157—41no—
44Dic314—22no—
45Dic314—41no—
46Dic314—41no—
47Dic314—41no—
48D628—22no—
49D628—41no—
50C22⋊D157—42no—
51C22⋊D157—42no—
52C2×Dic157—41no—
53C2×Dic157—41no—
54C2×Dic157—41no—
55C4×D157—42no—
56C4×D157—42no—
57C23×C157D811yescharacteristic
58C2×C4×C157—21no—
59C2×C4×C157—21no—
60C2×C4×C157D811yescharacteristic
61C2×C4×C157C2×D411yescharacteristic
62C8×C157—21no—
63C8×C157C2×D412yes—
64C22×C157—21no—
65C22×C157—41no—
66C22×C157C2×D811yescharacteristic
67C2×D157—42no—
68C2×D157—82no—
69C4×C157—21no—
70C4×C157#12011yescharacteristic
71C4×C157AGL(1,ℤ/8)11yescharacteristic
72Dic157—42no—
73Dic157—81no—
74Dic157—81no—
75C2×C157—21no—
76C2×C157—41no—
77C2×C157#44711yescharacteristic
78D157—82no—
79C157#219111yescharacteristic, complemented, Sylow
80#2191—1571nomaximal, Sylow
81#575—1571no—
82#510—1572no—
83#470—1571no—
84#360—1572no—
85#349D15711yescharacteristic, complemented
86C2×#41—3141no—
87#137—3142no—
88AGL(1,ℤ/8)—3142no—
89#135—3141no—
90#135—1572no—
91C2×Q16—1571no—
92C2×M16C2×D15711yescharacteristic
93C22⋊Q8—3141no—
94Q32—3142no—
95SD32—3142no—
96M32C2×D15712yescomplemented
97#106—1571no—
98#103—3141no—
99#41—3142no—
100#41—3142no—
101#41—6281no—
102#41—6281no—
103C2×Q8—3141no—
104C2×Q8—3141no—
105C2×D4—3141no—
106C2×D4—6281no—
107C22×C4—6281no—
108C22×C4D62811yescharacteristic
109Q16—3141no—
110Q16—3142no—
111Q16—1572no—
112SD16—3142no—
113SD16—3142no—
114D8—3141no—
115D8—1572no—
116M16—22no—
117C2×C8D62811yescharacteristic
118C2×C8C22×D15711yescharacteristic
119C4⋊C4—3141no—
120C4⋊C4—6281no—
121C22⋊C4—6281no—
122C16—22no—
123C23—6281no—
124C23D125611yescharacteristic
125Q8—3142no—
126Q8—6281no—
127Q8—6281no—
128Q8—6281no—
129D4—3142no—
130D4—6281no—
131D4—6282no—
132D4—6282no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—6282no—
136C2×C4—6281no—
137C2×C4—6282no—
138C2×C4—6281no—
139C2×C4—6281no—
140C2×C4D125611yescharacteristic
141C2×C4C2×D62811yescharacteristic
142C8—21no—
143C8D4×D15712yes—
144C22—21no—
145C22—41no—
146C22—6282no—
147C22—12562no—
148C22C2×D125611yescharacteristic
149C4—21no—
150C4—6282no—
151C4—12561no—
152C4—12561no—
153C4#1909774111yescharacteristic
154C4#1909779911yescharacteristic
155C2—21no—
156C2—41no—
157C2—12562no—
158C2#2375740911yescharacteristic
subgroupG/H
centerC2#23757409
commutator, cosocleC2×C8×C157C23
FrattiniC2×C8C22×D157
Fitting#349×C157C2
socleC2×C157#447
prime radical#23758073C2
hypercenter#349D157
hypocenterC157#2191
LCSG ▷ C2×C8×C157 ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #23757716C2semidirect
3. #23757531C2semidirect
4. #23757084C2semidirect
5. #349×C157C2semidirect
11. C2×Dic628C22semidirect
15. #19097703C22semidirect
18. M32×C157C22semidirect
79. C157#2191semidirect
85. #349D157semidirect
96. M32C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237580732
#237577162
#237575312
#237570842
#349×C1572
#2191157