Finite Group Databasebeta

← #34116104

Subgroups — #34116104

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×#19097859C211yesmaximal, characteristic
2C2×#19097842C211yesmaximal, characteristic, complemented
3#23758280C211yesmaximal, characteristic, complemented
4C2×#19097836C211yesmaximal, characteristic
5#23758143C211yesmaximal, characteristic, complemented
6(C2×#10597845)⋊C8C211yesmaximal, characteristic, complemented
7#23757268C211yesmaximal, characteristic
8#19097859—22no—
9#19097859—22no—
10C2×#14578964—21no—
11C2×#14578964C2211yescharacteristic
12C2×#14578964C2211yescharacteristic
13C2×D157⋊C8—21no—
14C2×D157⋊C8C2211yescharacteristic
15C2×C4×#10597845C2211yescharacteristic
16#19097842—22no—
17#19097838—21no—
18C4⋊#11929441—21no—
19#19097836—22no—
20C2×#14578955C2211yescharacteristic
21C2×C8×D157C2211yescharacteristic
22#19097729C2211yescharacteristic
23#19097695C411yescharacteristic, complemented
24#19097693C411yescharacteristic, complemented
25#19097691C411yescharacteristic, complemented
26#103×C157C411yescharacteristic, complemented
27C22×#10597845—21no—
28#14578964—24no—
29#14578964—21no—
30#14578964—21no—
31#14578964—21no—
32#14578964D412yes—
33D157⋊C8—24no—
34D157⋊C8—21no—
35D157⋊C8—21no—
36C2×#11929441—21no—
37C2×#11929441—21no—
38C2×#11929441D411yescharacteristic
39C2×#11929441D411yescharacteristic
40C4×#10597845—21no—
41C4×#10597845—21no—
42#14578955—21no—
43#14578955—21no—
44#14578955D412yes—
45#14578955Q812yes—
46C2×D628—21no—
47C2×D628C2×C411yescharacteristic
48C2×C4×D157—21no—
49C2×C4×D157C2311yescharacteristic
50C2×#11929434C2×C411yescharacteristic
51C8×D157—21no—
52C8×D157—21no—
53C4⋊Dic157C2×C411yescharacteristic
54#14578931—21no—
55C4×Dic157—21no—
56C2×Q8×C157C2×C411yescharacteristic
57C2×C8×C157C2×C411yescharacteristic
58C4⋊C4×C157C2×C411yescharacteristic
59C2×#10597845—22no—
60C2×#10597845—41no—
61C2×#10597845—41no—
62#11929441—22no—
63#11929441—21no—
64#11929441—21no—
65#11929441—41no—
66C22×D157—21no—
67C22×D157#4111yescharacteristic
68D628—22no—
69D628—22no—
70D628—21no—
71D628C4⋊C412yes—
72C2×Dic157—21no—
73C2×Dic157C2×D411yescharacteristic
74C4×D157—22no—
75C4×D157—22no—
76C4×D157C2×D411yescharacteristic
77C4×D157C2×D411yescharacteristic
78C4×D157C2×Q811yescharacteristic
79C4×D157#4111yescharacteristic
80#11929434—21no—
81Q8×C157—21no—
82Q8×C157C4⋊C412yes—
83C2×C4×C157—21no—
84C2×C4×C157—21no—
85C2×C4×C157C22×C411yescharacteristic
86C8×C157—21no—
87C22×C157C4×D411yescharacteristic
88C2×D157—21no—
89C2×D157—21no—
90C2×D157—22no—
91C2×D157—41no—
92C2×D157—41no—
93C2×D157C22⋊Q811yescharacteristic
94C2×D157#12311yescharacteristic
95#10597845—42no—
96C4×C157—22no—
97C4×C157—41no—
98C4×C157C2×C4⋊C411yescharacteristic
99C4×C157C4×D411yescharacteristic
100Dic157—41no—
101Dic157#12011yescharacteristic
102Dic157C22⋊Q811yescharacteristic
103C2×C157#38511yescharacteristic
104C2×C157#44311yescharacteristic
105C2×C157#44411yescharacteristic
106D157—21no—
107D157—21no—
108D157—42no—
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#1059784511yescharacteristic, complemented
135#102—1571no—
136#102—1571no—
137#41—3141no—
138#41—3141no—
139#41—1572no—
140#41—1572no—
141C2×Q8C2×#1059784511yescharacteristic
142C2×D4—3141no—
143C2×D4—1571no—
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—3141no—
170C23—1571no—
171Q8—21no—
172Q8C4⋊#1059784512yes—
173D4—3142no—
174D4—3142no—
175D4—3141no—
176D4—1572no—
177C2×C4—21no—
178C2×C4—21no—
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—3141no—
198C22—3141no—
199C22—3142no—
200C22—6281no—
201C22—6281no—
202C22—1571no—
203C22—1571no—
204C22D4×#1059784511yescharacteristic
205C4—22no—
206C4—41no—
207C4—6282no—
208C4—6281no—
209C4—1571no—
210C4—1571no—
211C4C2×C4⋊#1059784511yescharacteristic
212C4D4×#1059784511yescharacteristic
213C2—3141no—
214C2—3141no—
215C2—6282no—
216C2#2375822011yescharacteristic
217C2#2375831711yescharacteristic
218C2#2375831811yescharacteristic
subgroupG/H
centerC22D4×#10597845
commutatorC2×C4×C157C22×C4
FrattiniC2×C4C22×#10597845
Fitting#103×C157C4
socleC22×C157C4×D4
prime radicalC2×#14578955C22
cosocleC2×C4×D157C23
hypercenter#103#10597845
hypocenterC157#1866
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

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. #19097695C4semidirect
24. #19097693C4semidirect
25. #19097691C4semidirect
26. #103×C157C4semidirect
109. C157#1866semidirect
134. #103#10597845semidirect

Maximal subgroups

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

subgroupindex
C2×#190978592
C2×#190978422
#237582802
C2×#190978362
#237581432
(C2×#10597845)⋊C82
#237572682
#1866157