Finite Group Databasebeta

← #23769077

Subgroups — #23769077

Order 10112.

540 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14579118C212yesmaximal, complemented
2#19098493C211yesmaximal, characteristic, complemented
3#19098485C212yesmaximal, complemented
4#19098480C211yesmaximal, characteristic
5#19098455C212yesmaximal, complemented
6#19098448C212yesmaximal, complemented
7#19098441C212yesmaximal
8#19098437C212yesmaximal, complemented
9#382×C79C211yesmaximal, characteristic, complemented
10C22×D316C2211yescharacteristic
11C22×C4×D79C2212yes—
12#14579118—28no—
13C2×C4⋊Dic79C2212yes—
14C2×C4⋊Dic79C2211yescharacteristic
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2212yes—
17C2×(C2×D79)⋊C4C2212yes—
18C2×(C2×D79)⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×C4×Dic79C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2211yescharacteristic
26C79⋊#95C2212yes—
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C4⋊C4×C79C2211yescharacteristic
29C2×C42×C79C2211yescharacteristic
30#95×C79C2212yes—
31#95×C79C2212yes—
32C23×D79C2312yes—
33C2×D316—24no—
34C2×D316—41no—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C22×Dic79C2312yes—
38C2×C4×D79—24no—
39C2×C4×D79—24no—
40C2×C4×D79—24no—
41C4⋊Dic79—24no—
42C4⋊Dic79—41no—
43Dic79⋊C4—24no—
44Dic79⋊C4—24no—
45(C2×D79)⋊C4—24no—
46(C2×D79)⋊C4—24no—
47(C2×D79)⋊C4—24no—
48(C2×D79)⋊C4—24no—
49(C2×D79)⋊C4—42no—
50C4×Dic79—24no—
51C22×C4×C79C2311yescharacteristic
52C22×C4×C79C2311yescharacteristic
53C22×C4×C79C2312yes—
54C22×C4×C79C2312yes—
55C22×C4×C79C2311yescharacteristic
56C4⋊C4×C79—41no—
57C4⋊C4×C79—41no—
58C42×C79D414yescomplemented
59C23×C79C2411yescharacteristic
60C22×D79—22no—
61C22×D79—22no—
62C22×D79—22no—
63C22×D79—22no—
64C22×D79—22no—
65C22×D79—22no—
66C22×D79#4114yes—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—21no—
70C2×C4×C79—21no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—21no—
77C2×C4×C79—21no—
78C2×C4×C79C2×D414yes—
79C2×C4×C79C2×D412yes—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79#4114yes—
89D316—44no—
90C4×D79—216no—
91C22×C79C22×D411yescharacteristic
92C22×C79C2×#4112yes—
93C22×C79C2×#4112yes—
94C22×C79H(5,𝔽2)11yescharacteristic
95C22×C792−1+411yescharacteristic
96C2×D79—24no—
97C2×D79—24no—
98C2×D79—24no—
99C2×D79—42no—
100C2×D79—42no—
101C2×D79—42no—
102C2×D79—42no—
103C4×C79—24no—
104C4×C79—22no—
105C4×C79—41no—
106C4×C79—41no—
107C4×C79—42no—
108Dic79—24no—
109Dic79—42no—
110Dic79—42no—
111C2×C79#52512yes—
112C2×C79#53711yescharacteristic
113C2×C79#55111yescharacteristic
114C2×C79#55212yes—
115C2×C79#55511yescharacteristic
116D79—44no—
117#2609—791nomaximal, Sylow
118C79#260911yescharacteristic, complemented, Sylow
119C2×#117—792no—
120#398—791no—
121#396—792no—
122#394—791no—
123#388—792no—
124#387—792no—
125#386—792no—
126#385—792no—
127#382D7911yescharacteristic, complemented
128C22×D4—791no—
129C23×C4—792no—
130#117—1588no—
131C2×C4⋊C4—791no—
132C2×C4⋊C4—792no—
133C2×C4⋊C4—792no—
134C2×C4⋊C4—792no—
135C2×C4⋊C4C2×D7911yescharacteristic
136C2×C4⋊C4C2×D7911yescharacteristic
137C2×C22⋊C4—792no—
138C2×C22⋊C4—792no—
139C2×C22⋊C4—792no—
140C2×C22⋊C4—792no—
141C2×C22⋊C4—792no—
142C2×C42—792no—
143C2×C42C2×D7911yescharacteristic
144#95—791no—
145#95—792no—
146#95—791no—
147#95—792no—
148#95C2×D7912yes—
149#95C2×D7912yes—
150C24—792no—
151C2×D4—3161no—
152C2×D4—1584no—
153C22×C4—792no—
154C22×C4—792no—
155C22×C4—792no—
156C22×C4—1584no—
157C22×C4—1584no—
158C22×C4—1584no—
159C22×C4C22×D7911yescharacteristic
160C22×C4C22×D7911yescharacteristic
161C22×C4C22×D7912yes—
162C22×C4C22×D7912yes—
163C22×C4C22×D7911yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—3161no—
167C4⋊C4—1584no—
168C4⋊C4—1584no—
169C4⋊C4—1584no—
170C22⋊C4—3162no—
171C22⋊C4—1584no—
172C22⋊C4—1584no—
173C22⋊C4—1584no—
174C22⋊C4—1584no—
175C42—1584no—
176C42D31614yescomplemented
177C23—794no—
178C23—1582no—
179C23—1582no—
180C23—1582no—
181C23—1582no—
182C23—1582no—
183C23—1582no—
184C23C23×D7911yescharacteristic
185D4—3164no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—794no—
198C2×C4—15816no—
199C2×C4—1582no—
200C2×C4—1582no—
201C2×C4—1582no—
202C2×C4—1582no—
203C2×C4—1582no—
204C2×C4—1582no—
205C2×C4—1582no—
206C2×C4—1582no—
207C2×C4C2×D31614yes—
208C2×C4C2×D31612yes—
209C22—3162no—
210C22—3162no—
211C22—3162no—
212C22—3162no—
213C22—1584no—
214C22—1584no—
215C22—1584no—
216C22C22×D31611yescharacteristic
217C22#41×D7912yes—
218C22#41×D7912yes—
219C22#1457920611yescharacteristic
220C22#1457920911yescharacteristic
221C4—22no—
222C4—24no—
223C4—41no—
224C4—41no—
225C4—42no—
226C4—3162no—
227C4—3162no—
228C4—1584no—
229C2—3164no—
230C2#1909907512yes—
231C2#1909914411yescharacteristic
232C2#1909924311yescharacteristic
233C2#1909924512yes—
234C2#1909927511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#382×C79C2
prime radicalC22×D316C22
hypercenter#382D79
hypocenterC79#2609
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#14579118C2semidirect
2. #19098493C2semidirect
3. #19098485C2semidirect
5. #19098455C2semidirect
6. #19098448C2semidirect
8. #19098437C2semidirect
9. #382×C79C2semidirect
58. C42×C79D4semidirect
118. C79#2609semidirect
127. #382D79semidirect
176. C42D316semidirect