Finite Group Databasebeta

← #34100097

Subgroups — #34100097

Order 20096.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19097819C211yesmaximal, characteristic
2C2×#19097697C212yesmaximal, complemented
3#23757275C212yesmaximal, complemented
4#23757180C211yesmaximal, characteristic, complemented
5C2×#101×C157C211yesmaximal, characteristic, complemented
6#19097819—22no—
7#19097819—24no—
8#19097819C414yescomplemented
9C2×#14578955—22no—
10C2×#14578954—22no—
11C2×#14578954C2212yes—
12C2×Q8×D157—22no—
13C2×C4⋊Dic157C2211yescharacteristic
14C2×C4×Dic157C2211yescharacteristic
15#19097697—24no—
16#19097696—22no—
17#19097693—22no—
18#19097678—22no—
19C22×Q8×C157C2211yescharacteristic
20C2×M16×C157C2212yes—
21#101×C157—22no—
22#14578955—28no—
23#14578955—28no—
24#14578954—28no—
25#14578954—28no—
26#14578954—22no—
27#14578954—22no—
28#14578954C2×C414yes—
29#14578954D414yes—
30C2×Dic314—22no—
31C2×Dic314D412yes—
32Q8×D157—28no—
33Q8×D157—28no—
34C2×D628—22no—
35C2×D628D412yes—
36C2×C22⋊D157—22no—
37C22×Dic157—21no—
38C22×Dic157—21no—
39C2×C4×D157—24no—
40C2×C4×D157—22no—
41C4⋊Dic157—22no—
42C4×Dic157—22no—
43C2×Q8×C157—22no—
44C2×Q8×C157—22no—
45C2×Q8×C157C2×C412yes—
46C2×Q8×C157D412yes—
47C22×C4×C157D412yes—
48C22×C4×C157C2311yescharacteristic
49M16×C157—22no—
50M16×C157—22no—
51C2×C8×C157—22no—
52C22×D157—22no—
53Dic314—28no—
54Dic314—22no—
55Dic314C22⋊C414yes—
56D628—28no—
57D628—22no—
58D628C22⋊C414yes—
59C22⋊D157—24no—
60C22⋊D157—24no—
61C2×Dic157—22no—
62C2×Dic157—22no—
63C2×Dic157—41no—
64C2×Dic157—41no—
65C2×Dic157—42no—
66C2×Dic157—41no—
67C4×D157—216no—
68C4×D157—24no—
69C4×D157—24no—
70C23×C157C2×D411yescharacteristic
71Q8×C157—24no—
72Q8×C157—24no—
73C2×C4×C157—22no—
74C2×C4×C157—22no—
75C2×C4×C157C22⋊C414yes—
76C2×C4×C157C22×C411yescharacteristic
77C2×C4×C157C2×D412yes—
78C2×C4×C157C2×D412yes—
79C2×C4×C157C2×D411yescharacteristic
80C8×C157—42no—
81C22×C157—21no—
82C22×C157—21no—
83C22×C157C2×C22⋊C411yescharacteristic
84C22×C157#12011yescharacteristic
85C22×C157#12011yescharacteristic
86C2×D157—24no—
87C2×D157—42no—
88C2×D157—42no—
89C4×C157—24no—
90C4×C157C2×C22⋊C412yes—
91C4×C157#12012yes—
92Dic157—24no—
93Dic157—42no—
94Dic157—81no—
95C2×C157—21no—
96C2×C157—21no—
97C2×C157#37911yescharacteristic
98C2×C157#45411yescharacteristic
99C2×C157#45611yescharacteristic
100D157—44no—
101C157#179311yescharacteristic, complemented, Sylow
102#1793—1571nomaximal, Sylow
103C2×2−1+4—1571no—
104C2×#104—1572no—
105#417—1572no—
106C2×#101D15711yescharacteristic, complemented
107#391—1571no—
1082−1+4—3144no—
1092−1+4—3142no—
1102−1+4—1574no—
111C2×#41—3142no—
112C2×#41—3142no—
113C2×#41—1572no—
114C22×Q8—3142no—
115C22×Q8C2×D15711yescharacteristic
116C2×M16C2×D15712yes—
117C2×C4⋊C4—1571no—
118C2×C42—1571no—
119#104—3144no—
120#103—3142no—
121#102—3142no—
122#101—22no—
123#95—3142no—
124#41—3148no—
125#41—3148no—
126#41—3148no—
127#41—3142no—
128#41—3142no—
129#41—3148no—
130#41—1574no—
131#41—1574no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—3142no—
135C2×Q8—3148no—
136C2×Q8—3148no—
137C2×Q8—1572no—
138C2×Q8C4×D15712yes—
139C2×Q8C22⋊D15712yes—
140C2×D4—3142no—
141C2×D4—3142no—
142C2×D4—1572no—
143C22×C4—3144no—
144C22×C4—3142no—
145C22×C4—3141no—
146C22×C4—3141no—
147C22×C4D62812yes—
148C22×C4C22×D15711yescharacteristic
149M16—22no—
150M16—22no—
151C2×C8—22no—
152C4⋊C4—3142no—
153C42—3142no—
154C23—3142no—
155C23C2×D62811yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—3148no—
159Q8—3142no—
160Q8—1574no—
161D4—3148no—
162D4—3144no—
163D4—3144no—
164D4—3142no—
165D4—1574no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—31416no—
169C2×C4—3142no—
170C2×C4—3144no—
171C2×C4—3144no—
172C2×C4—3142no—
173C2×C4—6281no—
174C2×C4—6281no—
175C2×C4—6282no—
176C2×C4—6281no—
177C2×C4#1457893114yes—
178C2×C4C2×C4×D15711yescharacteristic
179C2×C4D4×D15712yes—
180C2×C4D4×D15712yes—
181C2×C4C2×C22⋊D15711yescharacteristic
182C8—42no—
183C22—21no—
184C22—21no—
185C22—3144no—
186C22—6282no—
187C22—6282no—
188C22C2×#1457893111yescharacteristic
189C22#1909774111yescharacteristic
190C22#1909774111yescharacteristic
191C4—24no—
192C4—3144no—
193C4—6282no—
194C4—12561no—
195C4C22⋊C4×D15712yes—
196C4#1909773912yes—
197C2—21no—
198C2—21no—
199C2—6284no—
200C2#2375712811yescharacteristic
201C2#2375744811yescharacteristic
202C2#2375745811yescharacteristic
subgroupG/H
centerC22#19097741
commutatorC2×C4×C157C22×C4
FrattiniC22×C4C22×D157
FittingC2×#101×C157C2
socleC22×C157#120
prime radicalC2×#19097819C2
cosocleC22×C4×C157C23
hypercenterC2×#101D157
hypocenterC157#1793
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#19097697C2semidirect
3. #23757275C2semidirect
4. #23757180C2semidirect
5. C2×#101×C157C2semidirect
8. #19097819C4semidirect
101. C157#1793semidirect
106. C2×#101D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190978192
C2×#190976972
#237572752
#237571802
C2×#101×C1572
#1793157