Finite Group Databasebeta

← C101×#20302 #38802453

Subgroups — C101×#20302 #38802453

Order 25856.

690 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 198 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
1C101×#3325C214yesmaximal, complemented
2C101×#1709C211yesmaximal, characteristic, complemented
3C101×#1697C214yesmaximal, complemented
4C101×#1634C212yesmaximal, complemented
5C101×#1619C212yesmaximal, complemented
6C101×#1589C212yesmaximal, complemented
7#555×C101C2212yes—
8D42×C101C2212yescomplemented
9#494×C101C2211yescharacteristic, complemented
10#493×C101C2211yescharacteristic
11#486×C101C2214yescomplemented
12#482×C101—24no—
13#476×C101C2214yescomplemented
14#469×C101—24no—
15#459×C101C2214yes—
16#447×C101—24no—
17C4×D8×C101C2212yes—
18#436×C101C2214yescomplemented
19#418×C101—24no—
20#335×C101C2212yescomplemented
21#333×C101C2212yescomplemented
22#331×C101C2212yescomplemented
23D4⋊C8×C101C2214yescomplemented
24C82×C101C2211yescharacteristic, complemented
25C22×D4×C101—24no—
26C2×Q16×C101—41no—
27C2×D8×C101—24no—
28C2×D8×C101—41no—
29C2×D8×C101D412yes—
30C2×M16×C101—24no—
31C4⋊Q8×C101C2312yes—
32#127×C101C2312yes—
33#124×C101—42no—
34#121×C101—24no—
35#121×C101—24no—
36#120×C101—42no—
37C4×D4×C101C2314yes—
38#117×C101—24no—
39#107×C101D412yes—
40#106×C101—24no—
41C4⋊C8×C101C2314yes—
42#102×C101—24no—
43#102×C101—24no—
44#102×C101—24no—
45#102×C101—24no—
46#102×C101D414yes—
47C22⋊C8×C101—24no—
48C4×C8×C101C2311yescharacteristic
49C4×C8×C101C2312yes—
50C24×C101—42no—
51C2×Q8×C101—22no—
52C2×D4×C101—24no—
53C2×D4×C101—22no—
54C2×D4×C101—44no—
55C2×D4×C101—48no—
56C2×D4×C101—42no—
57C2×D4×C101—84no—
58C2×D4×C101C2×D414yes—
59C22×C4×C101—24no—
60Q16×C101—82no—
61D8×C101—42no—
62D8×C101—82no—
63D8×C101—84no—
64M16×C101—84no—
65C2×C8×C101—21no—
66C2×C8×C101—24no—
67C2×C8×C101C2×D412yes—
68C2×C8×C101C2×D412yes—
69C4⋊C4×C101—24no—
70C4⋊C4×C101C2×D414yes—
71C22⋊C4×C101—24no—
72C22⋊C4×C101—42no—
73C22⋊C4×C101—44no—
74C42×C101—42no—
75C42×C101C2411yescharacteristic
76C23×C101—24no—
77C23×C101—42no—
78C23×C101—88no—
79C23×C101—162no—
80Q8×C101—82no—
81D4×C101—24no—
82D4×C101—24no—
83D4×C101—44no—
84D4×C101—44no—
85D4×C101—82no—
86D4×C101—88no—
87D4×C101—162no—
88C2×C4×C101—24no—
89C2×C4×C101—44no—
90C2×C4×C101—44no—
91C2×C4×C101—42no—
92C2×C4×C101C22×D412yes—
93C2×C4×C101H(5,𝔽2)11yescharacteristic
94C8×C101—22no—
95C8×C101—22no—
96C8×C101—22no—
97C8×C101—44no—
98C22×C101—44no—
99C22×C101—44no—
100C22×C101—44no—
101C22×C101—84no—
102C22×C101—82no—
103C22×C101—168no—
104C22×C101D4211yescharacteristic
105C4×C101—21no—
106C4×C101—44no—
107C4×C101—82no—
108C4×C101#57512yes—
109C4×C101#57612yes—
110#20302C10111yesmaximal, characteristic, direct product factor, Sylow
111C2×C101—84no—
112C2×C101—162no—
113C2×C101#327312yes—
114C2×C101#329211yescharacteristic
115#3325C2×C10114yescomplemented
116#1709C2×C10111yescharacteristic, complemented
117#1697C2×C10114yescomplemented
118#1634C2×C10112yescomplemented
119#1619C2×C10112yescomplemented
120#1589C2×C10112yescomplemented
121C101#2030211yescharacteristic, direct product factor, Sylow
122#555C22×C10112yes—
123D42C22×C10112yescomplemented
124#494C22×C10111yescharacteristic, complemented
125#493C22×C10111yescharacteristic
126#486C22×C10114yescomplemented
127#482—24no—
128#476C22×C10114yescomplemented
129#469—24no—
130#459C22×C10114yes—
131#447—24no—
132C4×D8C22×C10112yes—
133#436C22×C10114yescomplemented
134#418—24no—
135#335C22×C10112yescomplemented
136#333C22×C10112yescomplemented
137#331C22×C10112yescomplemented
138D4⋊C8C22×C10114yescomplemented
139C82C22×C10111yescharacteristic, complemented
140C22×D4—24no—
141C2×Q16—41no—
142C2×D8—24no—
143C2×D8—41no—
144C2×D8D4×C10112yes—
145C2×M16—24no—
146C4⋊Q8C23×C10112yes—
147#127C23×C10112yes—
148#124—42no—
149#121—24no—
150#121—24no—
151#120—42no—
152C4×D4C23×C10114yes—
153#117—24no—
154#107D4×C10112yes—
155#106—24no—
156C4⋊C8C23×C10114yes—
157#102—24no—
158#102—24no—
159#102—24no—
160#102—24no—
161#102D4×C10114yes—
162C22⋊C8—24no—
163C4×C8C23×C10111yescharacteristic
164C4×C8C23×C10112yes—
165C24—42no—
166C2×Q8—22no—
167C2×D4—24no—
168C2×D4—22no—
169C2×D4—44no—
170C2×D4—48no—
171C2×D4—42no—
172C2×D4—84no—
173C2×D4C2×D4×C10114yes—
174C22×C4—24no—
175Q16—82no—
176D8—42no—
177D8—82no—
178D8—84no—
179M16—84no—
180C2×C8—21no—
181C2×C8—24no—
182C2×C8C2×D4×C10112yes—
183C2×C8C2×D4×C10112yes—
184C4⋊C4—24no—
185C4⋊C4C2×D4×C10114yes—
186C22⋊C4—24no—
187C22⋊C4—42no—
188C22⋊C4—44no—
189C42—42no—
190C42C24×C10111yescharacteristic
191C23—24no—
192C23—42no—
193C23—88no—
194C23—162no—
195Q8—82no—
196D4—24no—
197D4—24no—
198D4—44no—
199D4—44no—
200D4—82no—
201D4—88no—
202D4—162no—
203C2×C4—24no—
204C2×C4—44no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4C22×D4×C10112yes—
208C2×C4H(5,𝔽2)×C10111yescharacteristic
209C8—22no—
210C8—22no—
211C8—22no—
212C8—44no—
213C22—44no—
214C22—44no—
215C22—44no—
216C22—84no—
217C22—82no—
218C22—168no—
219C22D42×C10111yescharacteristic
220C4—21no—
221C4—44no—
222C4—82no—
223C4#575×C10112yes—
224C4#576×C10112yes—
225C2—84no—
226C2—162no—
227C2C101×#327312yes—
228C2C101×#329211yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3325C2semidirect
2. C101×#1709C2semidirect
3. C101×#1697C2semidirect
4. C101×#1634C2semidirect
5. C101×#1619C2semidirect
6. C101×#1589C2semidirect
8. D42×C101C22semidirect
9. #494×C101C22semidirect
11. #486×C101C22semidirect
13. #476×C101C22semidirect
18. #436×C101C22semidirect
20. #335×C101C22semidirect
21. #333×C101C22semidirect
22. #331×C101C22semidirect
23. D4⋊C8×C101C22semidirect
24. C82×C101C22semidirect
110. #20302C101direct (N × H)
115. #3325C2×C101semidirect
116. #1709C2×C101semidirect
117. #1697C2×C101semidirect
118. #1634C2×C101semidirect
119. #1619C2×C101semidirect
120. #1589C2×C101semidirect
121. C101#20302direct (N × H)
123. D42C22×C101semidirect
124. #494C22×C101semidirect
126. #486C22×C101semidirect
128. #476C22×C101semidirect
133. #436C22×C101semidirect
135. #335C22×C101semidirect
136. #333C22×C101semidirect
137. #331C22×C101semidirect
138. D4⋊C8C22×C101semidirect
139. C82C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33252
C101×#17092
C101×#16972
C101×#16342
C101×#16192
C101×#15892
#20302101