Finite Group Databasebeta

← #34101167

Subgroups — #34101167

Order 20096.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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×#19097804C211yesmaximal, characteristic, complemented
2#23757840C211yesmaximal, characteristic
3C2×#19097758C211yesmaximal, characteristic, complemented
4C2×#19097697C211yesmaximal, characteristic, complemented
5#23757283C211yesmaximal, characteristic, complemented
6#23757034C211yesmaximal, characteristic, complemented
7C2×#100×C157C211yesmaximal, characteristic, complemented
8C2×#14578954C2211yescharacteristic
9C22×Dic314C2211yescharacteristic
10#19097804—22no—
11#19097804—22no—
12C2×Dic628—21no—
13C2×#14578943—21no—
14#19097767—21no—
15#19097758—22no—
16#19097758—21no—
17#19097758—22no—
18#19097742—22no—
19#19097740—22no—
20#19097730C2211yescharacteristic
21C2×C22⋊Dic157—22no—
22C2×C4×Dic157C2211yescharacteristic
23#19097697—22no—
24#19097696—22no—
25C22×D4×C157C2211yescharacteristic
26C2×M16×C157C2211yescharacteristic
27C2×M16×C157C2211yescharacteristic
28#100×C157—22no—
29#14578954—21no—
30#14578954—21no—
31#14578954—21no—
32#14578954—21no—
33C2×Dic314—21no—
34C2×Dic314—21no—
35C2×Dic314—21no—
36C2×Dic314—21no—
37C2×Dic314—21no—
38C2×Dic314D411yescharacteristic
39C2×Dic314D412yescomplemented
40C2×D628D411yescharacteristic
41C2×C22⋊D157—24no—
42C2×C22⋊D157—21no—
43C22×Dic157—21no—
44C22×Dic157—21no—
45C2×C4×D157—21no—
46Dic628—24no—
47#14578943—24no—
48C4⋊Dic157D412yes—
49C22⋊Dic157—28no—
50C22⋊Dic157—24no—
51C22⋊Dic157—21no—
52C4×Dic157—21no—
53C4×Dic157—21no—
54C4×Dic157D412yescomplemented
55C24×C157D412yes—
56C2×D4×C157—21no—
57C2×D4×C157—21no—
58C2×D4×C157—21no—
59C2×D4×C157—21no—
60C2×D4×C157—21no—
61C2×D4×C157—21no—
62C22×C4×C157C2311yescharacteristic
63M16×C157—21no—
64M16×C157—21no—
65M16×C157—21no—
66M16×C157D412yescomplemented
67C2×C8×C157—21no—
68C2×C8×C157—21no—
69C22×D157—21no—
70Dic314—21no—
71Dic314—22no—
72Dic314—22no—
73Dic314—21no—
74Dic314—41no—
75Dic314—41no—
76D628—21no—
77D628—21no—
78C22⋊D157—41no—
79C22⋊D157—41no—
80C22⋊D157—84no—
81C2×Dic157—21no—
82C2×Dic157—22no—
83C2×Dic157—22no—
84C2×Dic157—22no—
85C2×Dic157—42no—
86C2×Dic157—41no—
87C2×Dic157—41no—
88C4×D157—41no—
89C4×D157—41no—
90C23×C157—22no—
91C23×C157—22no—
92C23×C157—22no—
93C23×C157—44no—
94C23×C157C2×D411yescharacteristic
95D4×C157—41no—
96D4×C157—41no—
97D4×C157—41no—
98D4×C157—41no—
99C2×C4×C157C2×D411yescharacteristic
100C2×C4×C157C2×D411yescharacteristic
101C2×C4×C157C2×D411yescharacteristic
102C2×C4×C157C2×D411yescharacteristic
103C2×C4×C157C2×D411yescharacteristic
104C2×C4×C157#4111yescharacteristic
105C8×C157—22no—
106C8×C157—41no—
107C22×C157—22no—
108C22×C157—44no—
109C22×C157—42no—
110C22×C157—44no—
111C22×C157—82no—
112C22×C157#12011yescharacteristic
113C22×C157#12011yescharacteristic
114C22×C157#12111yescharacteristic
115C2×D157—41no—
116C2×D157—42no—
117C4×C157#12011yescharacteristic
118C4×C157#12111yescharacteristic
119C4×C157#12111yescharacteristic
120C4×C157#12711yescharacteristic
121Dic157—42no—
122Dic157—41no—
123Dic157—42no—
124Dic157—42no—
125C2×C157—21no—
126C2×C157—21no—
127C2×C157—82no—
128C2×C157#39211yescharacteristic
129C2×C157#45512yes—
130D157—81no—
131C157#200411yescharacteristic, complemented, Sylow
132#2004—1571nomaximal, Sylow
133C2×#137—1571no—
134#535—1571no—
135C2×#124—1571no—
136C2×#104—1571no—
137#419—1571no—
138C2×#100D15711yescharacteristic, complemented
139#339—1571no—
140C2×#41—1571no—
141C22×Q8—1571no—
142C22×D4C2×D15711yescharacteristic
143#137—3142no—
144#137—3142no—
145C2×Q16—3141no—
146C2×SD16—3141no—
147C2×M16C2×D15711yescharacteristic
148C2×M16C2×D15711yescharacteristic
149#127—3141no—
150#124—3142no—
151#124—3141no—
152#124—3142no—
153#121—3142no—
154#120—3142no—
155#117—1571no—
156C2×C22⋊C4—3142no—
157C2×C42—1571no—
158#104—3142no—
159#103—3142no—
160#100—22no—
161C24D62812yes—
162#41—3141no—
163#41—3141no—
164#41—3141no—
165#41—3141no—
166C2×Q8—3141no—
167C2×Q8—3141no—
168C2×Q8—3141no—
169C2×Q8—3141no—
170C2×Q8—3141no—
171C2×Q8—1571no—
172C2×Q8—1572no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—3141no—
180C2×D4—3144no—
181C2×D4—1571no—
182C22×C4—3141no—
183C22×C4—3141no—
184C22×C4—3141no—
185C22×C4C22×D15711yescharacteristic
186Q16—3144no—
187SD16—3144no—
188M16—21no—
189M16—21no—
190M16—21no—
191M16C22⋊D15712yescomplemented
192C2×C8—21no—
193C2×C8—21no—
194C4⋊C4—1572no—
195C22⋊C4—3148no—
196C22⋊C4—3144no—
197C22⋊C4—3141no—
198C42—3141no—
199C42—3141no—
200C42—1572no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—44no—
205C23—3141no—
206C23C2×D62811yescharacteristic
207Q8—3142no—
208Q8—3141no—
209Q8—3142no—
210Q8—3141no—
211Q8—6281no—
212Q8—6281no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—3141no—
218D4—3141no—
219D4—6281no—
220D4—6281no—
221D4—12564no—
222C2×C4—3142no—
223C2×C4—3142no—
224C2×C4—3142no—
225C2×C4—3141no—
226C2×C4—6282no—
227C2×C4—6281no—
228C2×C4—6281no—
229C2×C4—6281no—
230C2×C4—6281no—
231C2×C4D4×D15711yescharacteristic
232C2×C4D4×D15711yescharacteristic
233C2×C4D4×D15711yescharacteristic
234C2×C4D4×D15711yescharacteristic
235C2×C4C2×C22⋊D15711yescharacteristic
236C2×C4#1457895411yescharacteristic
237C8—22no—
238C8—41no—
239C22—22no—
240C22—44no—
241C22—42no—
242C22—44no—
243C22—82no—
244C22—6281no—
245C22—6282no—
246C22#1909774111yescharacteristic
247C22#1909774111yescharacteristic
248C22#1909774511yescharacteristic
249C4—6282no—
250C4—6281no—
251C4—6282no—
252C4—6282no—
253C4#1909773911yescharacteristic
254C4#1909774411yescharacteristic
255C4#1909774411yescharacteristic
256C4#1909776711yescharacteristic
257C2—21no—
258C2—21no—
259C2—82no—
260C2—12561no—
261C2#2375718211yescharacteristic
262C2#2375745312yes—
subgroupG/H
centerC22#19097741
commutator, cosocleC22×C4×C157C23
FrattiniC22×C4C22×D157
FittingC2×#100×C157C2
socleC22×C157#120
prime radical#23757840C2
hypercenterC2×#100D157
hypocenterC157#2004
LCSG ▷ C22×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
1. C2×#19097804C2semidirect
3. C2×#19097758C2semidirect
4. C2×#19097697C2semidirect
5. #23757283C2semidirect
6. #23757034C2semidirect
7. C2×#100×C157C2semidirect
39. C2×Dic314D4semidirect
54. C4×Dic157D4semidirect
66. M16×C157D4semidirect
131. C157#2004semidirect
138. C2×#100D157semidirect
191. M16C22⋊D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190978042
#237578402
C2×#190977582
C2×#190976972
#237572832
#237570342
C2×#100×C1572
#2004157