Finite Group Databasebeta

← #34116103

Subgroups — #34116103

Order 20096.

270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 70 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×#19097858C211yesmaximal, characteristic
2C2×#19097842C211yesmaximal, characteristic, complemented
3#23758280C211yesmaximal, characteristic, complemented
4C2×#19097835C211yesmaximal, characteristic
5#23758143C211yesmaximal, characteristic, complemented
6(C2×#10597845)⋊C8C211yesmaximal, characteristic, complemented
7#23757266C211yesmaximal, characteristic
8#19097858—22no—
9#19097858—22no—
10C2×#14578964C2211yescharacteristic
11C2×#14578964C2211yescharacteristic
12C2×#14578963—21no—
13C2×D157⋊C8C2211yescharacteristic
14C22×#11929441—21no—
15C2×C4×#10597845C2211yescharacteristic
16#19097842—22no—
17#19097838—21no—
18C4⋊#11929441—21no—
19#19097835—22no—
20C2×#14578953C2211yescharacteristic
21C2×C8×D157C2211yescharacteristic
22#19097729C2211yescharacteristic
23#19097696C411yescharacteristic, complemented
24#19097694C411yescharacteristic, complemented
25#19097692C411yescharacteristic, complemented
26#102×C157C411yescharacteristic, complemented
27C22×#10597845—21no—
28#14578964—21no—
29#14578964—21no—
30#14578964—21no—
31#14578964D412yes—
32#14578963—24no—
33D157⋊C8—21no—
34D157⋊C8—21no—
35C2×#11929441—24no—
36C2×#11929441—21no—
37C2×#11929441—21no—
38C2×#11929441D411yescharacteristic
39C2×#11929441D411yescharacteristic
40C4×#10597845—21no—
41C4×#10597845—21no—
42#14578953—21no—
43#14578953—21no—
44#14578953D412yes—
45#14578953Q812yes—
46C2×Dic314C2×C411yescharacteristic
47C2×C22⋊D157—21no—
48C22×Dic157—21no—
49C2×C4×D157C2311yescharacteristic
50C2×#11929434C2×C411yescharacteristic
51C8×D157—21no—
52C8×D157—21no—
53C4⋊Dic157C2×C411yescharacteristic
54#14578931—21no—
55C4×Dic157—21no—
56C2×D4×C157C2×C411yescharacteristic
57C2×C8×C157C2×C411yescharacteristic
58C4⋊C4×C157C2×C411yescharacteristic
59C2×#10597845—22no—
60C2×#10597845—41no—
61C2×#10597845—41no—
62#11929441—21no—
63#11929441—22no—
64#11929441—21no—
65#11929441—41no—
66C22×D157#4111yescharacteristic
67Dic314—21no—
68Dic314C4⋊C412yes—
69C22⋊D157—22no—
70C22⋊D157—22no—
71C2×Dic157—21no—
72C2×Dic157—22no—
73C2×Dic157—22no—
74C2×Dic157—21no—
75C2×Dic157C2×D411yescharacteristic
76C4×D157C2×D411yescharacteristic
77C4×D157C2×D411yescharacteristic
78C4×D157C2×Q811yescharacteristic
79C4×D157#4111yescharacteristic
80#11929434—21no—
81C23×C157—21no—
82D4×C157—21no—
83D4×C157C4⋊C412yes—
84C2×C4×C157—21no—
85C2×C4×C157C22×C411yescharacteristic
86C8×C157—21no—
87C22×C157—22no—
88C22×C157—41no—
89C22×C157—41no—
90C22×C157C4×D411yescharacteristic
91C2×D157—21no—
92C2×D157—21no—
93C2×D157C22⋊Q811yescharacteristic
94C2×D157#12311yescharacteristic
95#10597845—42no—
96C4×C157—41no—
97C4×C157C2×C4⋊C411yescharacteristic
98C4×C157C4×D411yescharacteristic
99Dic157—22no—
100Dic157—41no—
101Dic157#12011yescharacteristic
102Dic157C22⋊Q811yescharacteristic
103C2×C157—42no—
104C2×C157#38511yescharacteristic
105C2×C157#44311yescharacteristic
106C2×C157#44411yescharacteristic
107D157—21no—
108D157—21no—
109C157#186611yescharacteristic, complemented, Sylow
110#1866—1571nomaximal, Sylow
111C2×#131—1571no—
112C2×#108—1571no—
113#424—1571no—
114C2×#104—1571no—
115#416—1571no—
116#339—1571no—
117#336—1571no—
118C2×#41—1571no—
119#131—3142no—
120#131—3142no—
121C2×M16—3141no—
122C2×M16—1571no—
123C2×M16—1571no—
124C22×C8—3141no—
125C22×C8—1571no—
126C22×C8—1571no—
127#117—1571no—
128C2×C42—1571no—
129#108—3142no—
130C4⋊C8—3141no—
131C4⋊C8—3141no—
132#104—3142no—
133#103—1571no—
134#103—1571no—
135#102—1571no—
136#102#1059784511yescharacteristic, complemented
137#41—3141no—
138#41—3141no—
139#41—1572no—
140#41—1572no—
141C2×Q8—1571no—
142C2×D4—3141no—
143C2×D4C2×#1059784511yescharacteristic
144C22×C4—3141no—
145C22×C4—3141no—
146C22×C4—1571no—
147M16—3144no—
148M16—3141no—
149M16—3141no—
150M16—3141no—
151M16—1572no—
152C2×C8—3141no—
153C2×C8—3141no—
154C2×C8—3144no—
155C2×C8—3141no—
156C2×C8—3141no—
157C2×C8—3141no—
158C2×C8—3141no—
159C2×C8—1571no—
160C2×C8—1571no—
161C2×C8—1571no—
162C2×C8C2×#1059784511yescharacteristic
163C4⋊C4—1571no—
164C4⋊C4C2×#1059784511yescharacteristic
165C22⋊C4—3141no—
166C42—3141no—
167C42—3141no—
168C42—3141no—
169C23—21no—
170C23—1571no—
171Q8—3141no—
172Q8—1572no—
173D4—21no—
174D4—3142no—
175D4—3142no—
176D4C4⋊#1059784512yes—
177C2×C4—21no—
178C2×C4—3141no—
179C2×C4—3142no—
180C2×C4—3142no—
181C2×C4—3142no—
182C2×C4—3141no—
183C2×C4—6281no—
184C2×C4—6281no—
185C2×C4—1571no—
186C2×C4—1571no—
187C2×C4—1571no—
188C2×C4—1571no—
189C2×C4—1571no—
190C2×C4C22×#1059784511yescharacteristic
191C8—21no—
192C8—3141no—
193C8—3142no—
194C8—3141no—
195C8—3141no—
196C8—6281no—
197C22—22no—
198C22—41no—
199C22—41no—
200C22—3141no—
201C22—3141no—
202C22—1571no—
203C22—1571no—
204C22D4×#1059784511yescharacteristic
205C4—41no—
206C4—3142no—
207C4—6282no—
208C4—6281no—
209C4—1571no—
210C4—1571no—
211C4C2×C4⋊#1059784511yescharacteristic
212C4D4×#1059784511yescharacteristic
213C2—42no—
214C2—3141no—
215C2—3141no—
216C2#2375822011yescharacteristic
217C2#2375831511yescharacteristic
218C2#2375831811yescharacteristic
subgroupG/H
centerC22D4×#10597845
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#102×C157C4
socleC22×C157C4×D4
prime radicalC2×#14578953C22
cosocleC2×C4×D157C23
hypercenter#102#10597845
hypocenterC157#1866
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#19097842C2semidirect
3. #23758280C2semidirect
5. #23758143C2semidirect
6. (C2×#10597845)⋊C8C2semidirect
23. #19097696C4semidirect
24. #19097694C4semidirect
25. #19097692C4semidirect
26. #102×C157C4semidirect
109. C157#1866semidirect
136. #102#10597845semidirect

Maximal subgroups

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

subgroupindex
C2×#190978582
C2×#190978422
#237582802
C2×#190978352
#237581432
(C2×#10597845)⋊C82
#237572662
#1866157