Finite Group Databasebeta

← #23768397

Subgroups — #23768397

Order 10112.

604 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14579159C211yesmaximal, characteristic, complemented
2C2×#14579150C211yesmaximal, characteristic
3C2×#14579149C211yesmaximal, characteristic
4C2×#14579123C211yesmaximal, characteristic
5#19098492C214yesmaximal, complemented
6#19098468C211yesmaximal, characteristic, complemented
7#19098422C214yesmaximal, complemented
8C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
9#391×C79C211yesmaximal, characteristic, complemented
10C22×Dic158C2211yescharacteristic
11C22×D316C2211yescharacteristic
12C22×C4×D79C2212yes—
13#14579159—24no—
14#14579150—24no—
15#14579149—24no—
16#14579123—24no—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2214yes—
21C2×(C2×D79)⋊C4C2214yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×C4×Dic79C2211yescharacteristic
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2214yes—
27C22×Q8×C79C2211yescharacteristic
28C2×C4⋊C4×C79C2211yescharacteristic
29C2×C42×C79C2211yescharacteristic
30#95×C79C2214yes—
31C23×D79C2312yes—
32C2×Dic158—22no—
33C2×Dic158—22no—
34C2×Dic158—22no—
35C2×D316—22no—
36C2×D316—22no—
37C2×D316D414yes—
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2311yescharacteristic
42C2×C4×D79—24no—
43C2×C4×D79—28no—
44Dic79⋊C4—24no—
45Dic79⋊C4—24no—
46Dic79⋊C4—24no—
47(C2×D79)⋊C4—24no—
48(C2×D79)⋊C4—28no—
49(C2×D79)⋊C4—28no—
50C4×Dic79—22no—
51C4×Dic79D414yes—
52C2×Q8×C79—22no—
53C2×Q8×C79—22no—
54C2×Q8×C79—22no—
55C22×C4×C79C2312yes—
56C22×C4×C79C2312yes—
57C22×C4×C79C2312yes—
58C22×C4×C79C2311yescharacteristic
59C4⋊C4×C79—22no—
60C42×C79—22no—
61C23×C79C2411yescharacteristic
62C22×D79—22no—
63C22×D79—24no—
64C22×D79—22no—
65C22×D79—24no—
66C22×D79C2×D414yes—
67Q8×C79—44no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—24no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79C2×D412yes—
77C2×C4×C79C2×D412yes—
78C2×C4×C79#4112yes—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79C2×D412yes—
87C2×Dic79C2×D412yes—
88C2×Dic79#4114yes—
89D316—28no—
90C4×D79—48no—
91Dic158—44no—
92C22×C79C22×D411yescharacteristic
93C22×C79C22×D411yescharacteristic
94C22×C79C2×#4112yes—
95C22×C79C2×#4111yescharacteristic
96C22×C792−1+412yes—
97C2×D79—24no—
98C2×D79—28no—
99C2×D79—42no—
100C2×D79—42no—
101C2×D79—44no—
102C4×C79—42no—
103C4×C79—42no—
104C4×C79—42no—
105C4×C79#12114yes—
106Dic79—22no—
107Dic79—42no—
108Dic79—42no—
109Dic79#12414yescomplemented
110C2×C79C2×#12111yescharacteristic
111C2×C79C2×#12411yescharacteristic
112C2×C79#53611yescharacteristic
113C2×C79#54712yes—
114C2×C79#55612yes—
115D79—44no—
116#2547—791nomaximal, Sylow
117C79#254711yescharacteristic, complemented, Sylow
118C2×C4⋊Q8—791no—
119C2×#124—791no—
120C2×#124—791no—
121C2×C4×D4—791no—
122#397—794no—
123#391—791no—
124#391D7911yescharacteristic, complemented
125#380—794no—
126C4×C4⋊C4—791no—
127C22×Q8—791no—
128C22×Q8C2×D7911yescharacteristic
129C22×D4—791no—
130C23×C4—792no—
131C4⋊Q8—1584no—
132#124—1584no—
133#124—1584no—
134C4×D4—1584no—
135C2×C4⋊C4—792no—
136C2×C4⋊C4—792no—
137C2×C4⋊C4—792no—
138C2×C4⋊C4C2×D7911yescharacteristic
139C2×C22⋊C4—792no—
140C2×C22⋊C4—794no—
141C2×C22⋊C4—794no—
142C2×C42—791no—
143C2×C42—791no—
144C2×C42C2×D7911yescharacteristic
145#95—792no—
146#95—794no—
147#95C2×D7914yes—
148C24—792no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—22no—
152C2×Q8—1582no—
153C2×Q8—1582no—
154C2×Q8—1582no—
155C2×D4—794no—
156C2×D4—1582no—
157C2×D4—1582no—
158C22×C4—791no—
159C22×C4—791no—
160C22×C4—792no—
161C22×C4—792no—
162C22×C4—1584no—
163C22×C4—1588no—
164C22×C4C22×D7912yes—
165C22×C4C22×D7912yes—
166C22×C4C22×D7912yes—
167C22×C4C22×D7911yescharacteristic
168C4⋊C4—22no—
169C4⋊C4—1584no—
170C4⋊C4—1584no—
171C4⋊C4—1584no—
172C22⋊C4—1584no—
173C22⋊C4—1588no—
174C22⋊C4—1588no—
175C42—22no—
176C42—794no—
177C42—1582no—
178C23—794no—
179C23—1584no—
180C23—1582no—
181C23—1584no—
182C23—1582no—
183C23C23×D7911yescharacteristic
184Q8—44no—
185Q8—3164no—
186D4—1588no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—3168no—
196C2×C4—794no—
197C2×C4—792no—
198C2×C4—792no—
199C2×C4—1582no—
200C2×C4—1582no—
201C2×C4—1582no—
202C2×C4—1582no—
203C2×C4—1582no—
204C2×C4—1582no—
205C2×C4—1582no—
206C2×C4D4×D7912yes—
207C2×C4D4×D7912yes—
208C2×C4#1192962412yes—
209C22—3162no—
210C22—3164no—
211C22—3162no—
212C22—1588no—
213C22—1584no—
214C22C2×D4×D7911yescharacteristic
215C22C2×D4×D7911yescharacteristic
216C22#41×D7912yes—
217C22C2×#1192962411yescharacteristic
218C22#1457920912yes—
219C4—42no—
220C4—42no—
221C4—42no—
222C4—3162no—
223C4—3162no—
224C4—794no—
225C4—1582no—
226C4#1457913414yes—
227C2—3164no—
228C2C2×#1457913411yescharacteristic
229C2#124×D7911yescharacteristic
230C2#1909913811yescharacteristic
231C2#1909921512yes—
232C2#1909928512yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#391×C79C2
prime radicalC22×D316C22
hypercenter#391D79
hypocenterC79#2547
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#14579159C2semidirect
5. #19098492C2semidirect
6. #19098468C2semidirect
7. #19098422C2semidirect
8. C4×Dic79⋊C4C2semidirect
9. #391×C79C2semidirect
109. Dic79#124semidirect
117. C79#2547semidirect
124. #391D79semidirect