Finite Group Databasebeta

← #34116221

Subgroups — #34116221

Order 20096.

212 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 58 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#23758284C211yesmaximal, characteristic
2#23758266C211yesmaximal, characteristic
3C2×#19097834C211yesmaximal, characteristic
4#23758239C211yesmaximal, characteristic
5#23758152C211yesmaximal, characteristic
6#23758148C211yesmaximal, characteristic
7#101×D157C211yesmaximal, characteristic
8D157⋊M16C2211yescharacteristic
9C2×D157⋊C8C2211yescharacteristic
10#19097850C2211yescharacteristic
11C2×C4⋊#10597845C2211yescharacteristic
12#19097840—21no—
13#19097839—21no—
14#19097834—21no—
15#19097834—21no—
16#19097834—21no—
17#19097834—21no—
18#19097825—21no—
19C8×#10597845—21no—
20C2×Q8×D157C2211yescharacteristic
21M16×D157C2211yescharacteristic
22M16×D157C2211yescharacteristic
23#19097690C411yescharacteristic, complemented
24#19097689C411yescharacteristic, complemented
25#19097689C411yescharacteristic, complemented
26#101×C157C411yescharacteristic, complemented
27C22×#10597845—21no—
28#14578964—21no—
29#14578963—21no—
30D157⋊C8—21no—
31D157⋊C8—21no—
32D157⋊C8D411yescharacteristic
33D157⋊C8D411yescharacteristic
34C2×#11929441—21no—
35C4⋊#10597845—21no—
36C4⋊#10597845—21no—
37C4⋊#10597845D411yescharacteristic
38C4⋊#10597845D411yescharacteristic
39C22⋊#10597845—21no—
40C4×#10597845—21no—
41C2×Dic314—21no—
42C2×Dic314C2×C411yescharacteristic
43Q8×D157—21no—
44Q8×D157—21no—
45Q8×D157—21no—
46Q8×D157—21no—
47C2×C4×D157—21no—
48C2×C4×D157C2311yescharacteristic
49#14578938C2×C411yescharacteristic
50#14578938C2×C411yescharacteristic
51#14578937—21no—
52#14578937—21no—
53C8×D157—21no—
54C8×D157—21no—
55C2×Q8×C157C2×C411yescharacteristic
56M16×C157C2×C411yescharacteristic
57M16×C157C2×C411yescharacteristic
58C2×#10597845—21no—
59C2×#10597845—21no—
60C2×#10597845—41no—
61C2×#10597845—81no—
62#11929441—21no—
63#11929441—21no—
64#11929441—41no—
65C22×D157#4111yescharacteristic
66Dic314—21no—
67Dic314—21no—
68Dic314—41no—
69Dic314—41no—
70C2×Dic157—21no—
71C2×Dic157#4111yescharacteristic
72C4×D157—41no—
73C4×D157—41no—
74C4×D157C2×D411yescharacteristic
75C4×D157C2×D411yescharacteristic
76C4×D157#4111yescharacteristic
77C4×D157#4111yescharacteristic
78#11929434—21no—
79#11929434—21no—
80Q8×C157—21no—
81Q8×C157—21no—
82C2×C4×C157—21no—
83C2×C4×C157C22×C411yescharacteristic
84C8×C157—21no—
85C8×C157—21no—
86C22×C157#11711yescharacteristic
87C2×D157—21no—
88C2×D157—21no—
89C2×D157#12111yescharacteristic
90C2×D157#12611yescharacteristic
91#10597845—41no—
92#10597845—41no—
93#10597845—81no—
94C4×C157—41no—
95C4×C157C4×D411yescharacteristic
96C4×C157C4×D411yescharacteristic
97Dic157—41no—
98Dic157#12311yescharacteristic
99Dic157#12411yescharacteristic
100C2×C157—21no—
101C2×C157#38811yescharacteristic
102D157—21no—
103D157#47111yescharacteristic
104D157#47311yescharacteristic
105C157#193011yescharacteristic, complemented, Sylow
106#1930—1571nomaximal, Sylow
107#428—1571no—
108#419—1571no—
109C2×#103—1571no—
110C2×#101—1571no—
111#405—1571no—
112#343—1571no—
113#341—1571no—
114C22×Q8—1571no—
115C2×M16—1571no—
116C2×M16—1571no—
117C2×M16—1571no—
118C22×C8—1571no—
119#117—1571no—
120C2×C4⋊C4—1571no—
121#107—3141no—
122#106—3141no—
123#103—3141no—
124#103—3141no—
125#103—3141no—
126#103—3141no—
127#101—1571no—
128#101—1571no—
129#101—1571no—
130#101#1059784511yescharacteristic, complemented
131#97—3141no—
132C4×C8—3141no—
133C2×Q8—3141no—
134C2×Q8—3141no—
135C2×Q8—3141no—
136C2×Q8—3141no—
137C2×Q8—3141no—
138C2×Q8—1571no—
139C2×Q8C2×#1059784511yescharacteristic
140C22×C4—3141no—
141C22×C4—3141no—
142C22×C4—1571no—
143M16—3141no—
144M16—3141no—
145M16—3141no—
146M16—3141no—
147M16—1571no—
148M16—1571no—
149M16C2×#1059784511yescharacteristic
150M16C2×#1059784511yescharacteristic
151C2×C8—3141no—
152C2×C8—3141no—
153C2×C8—3141no—
154C2×C8—3141no—
155C2×C8—3141no—
156C2×C8—1571no—
157C2×C8—1571no—
158C4⋊C4—3141no—
159C4⋊C4—3141no—
160C4⋊C4—1571no—
161C4⋊C4—1571no—
162C22⋊C4—3141no—
163C42—3141no—
164C23—1571no—
165Q8—21no—
166Q8—21no—
167Q8—3141no—
168Q8—3141no—
169Q8—6281no—
170Q8—6281no—
171C2×C4—21no—
172C2×C4—3141no—
173C2×C4—3141no—
174C2×C4—3141no—
175C2×C4—6281no—
176C2×C4—6281no—
177C2×C4—6281no—
178C2×C4—1571no—
179C2×C4—1571no—
180C2×C4—1571no—
181C2×C4—1571no—
182C2×C4—1571no—
183C2×C4—12561no—
184C2×C4C22×#1059784511yescharacteristic
185C8—21no—
186C8—21no—
187C8—3141no—
188C8—3141no—
189C8—3141no—
190C8—3141no—
191C8—6281no—
192C22—3141no—
193C22—3141no—
194C22—1571no—
195C22—1571no—
196C22#1909785011yescharacteristic
197C4—41no—
198C4—6281no—
199C4—6281no—
200C4—6281no—
201C4—1571no—
202C4—1571no—
203C4—12561no—
204C4D4×#1059784511yescharacteristic
205C4D4×#1059784511yescharacteristic
206C2—21no—
207C2—3141no—
208C2—1571no—
209C2—1571no—
210C2#2375822311yescharacteristic
subgroupG/H
centerC2#23758223
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#101×C157C4
socleC2×C157#388
prime radicalC22×D157#41
cosocleC2×C4×D157C23
hypercenter#101#10597845
hypocenterC157#1930
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ #101

Complements

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

NH ≅ G/Ntype
23. #19097690C4semidirect
24. #19097689C4semidirect
25. #19097689C4semidirect
26. #101×C157C4semidirect
105. C157#1930semidirect
130. #101#10597845semidirect

Maximal subgroups

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

subgroupindex
#237582842
#237582662
C2×#190978342
#237582392
#237581522
#237581482
#101×D1572
#1930157