Finite Group Databasebeta

← #23767868

Subgroups — #23767868

Order 10112.

708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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×#14579146C214yesmaximal, complemented
2C2×#14579136C211yesmaximal, characteristic
3C2×C4⋊C4×D79C211yesmaximal, characteristic, complemented
4#19098498C214yesmaximal, complemented
5#19098465C211yesmaximal, characteristic, complemented
6#19098464C211yesmaximal, characteristic, complemented
7#19098432C211yesmaximal, characteristic, complemented
8C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
9#384×C79C211yesmaximal, characteristic, complemented
10C22×D316C2211yescharacteristic
11C22×D316C2212yes—
12C22×C4×D79C2212yes—
13C22×C4×D79C2211yescharacteristic
14#14579146—216no—
15#14579136—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2214yes—
18C2×Dic79⋊C4C2212yes—
19C4⋊C4×D79—24no—
20C2×(C2×D79)⋊C4C2214yes—
21C2×(C2×D79)⋊C4C2214yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2212yes—
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C4⋊C4×C79C2214yes—
29C2×C42×C79C2211yescharacteristic
30C23×D79C2312yes—
31C23×D79C2311yescharacteristic
32C2×D316—24no—
33C2×D316—28no—
34C2×D316—22no—
35C2×D316—22no—
36C2×D316—22no—
37C22×Dic79C2312yes—
38C22×Dic79C2311yescharacteristic
39C22×Dic79C2312yes—
40C2×C4×D79—24no—
41C2×C4×D79—28no—
42C2×C4×D79—22no—
43C2×C4×D79—22no—
44C2×C4×D79D414yes—
45C4⋊Dic79—22no—
46Dic79⋊C4—24no—
47Dic79⋊C4—28no—
48(C2×D79)⋊C4—24no—
49(C2×D79)⋊C4—28no—
50(C2×D79)⋊C4—28no—
51(C2×D79)⋊C4D418yescomplemented
52C4×Dic79—22no—
53C22×C4×C79C2312yes—
54C22×C4×C79C2312yes—
55C22×C4×C79C2312yes—
56C22×C4×C79C2311yescharacteristic
57C4⋊C4×C79—22no—
58C4⋊C4×C79—22no—
59C4⋊C4×C79—28no—
60C42×C79—22no—
61C23×C79C2411yescharacteristic
62C22×D79—21no—
63C22×D79—21no—
64C22×D79—22no—
65C22×D79—24no—
66C22×D79—22no—
67C22×D79—22no—
68C22×D79—22no—
69C22×D79—24no—
70C22×D79C2×D414yes—
71C22×D79C2×D412yes—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79—24no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—24no—
78C2×C4×C79C2×D414yes—
79C2×C4×C79C2×D412yes—
80C2×C4×C79#4112yes—
81C2×C4×C79#4112yes—
82C2×Dic79—22no—
83C2×Dic79—21no—
84C2×Dic79—21no—
85C2×Dic79—22no—
86C2×Dic79—24no—
87C2×Dic79—22no—
88C2×Dic79C2×D414yes—
89C2×Dic79C2×D412yes—
90D316—48no—
91D316—44no—
92C4×D79—28no—
93C4×D79—48no—
94C22×C79C22×D411yescharacteristic
95C22×C79C22×D412yes—
96C22×C79C2×#4111yescharacteristic
97C22×C79C2×#4111yescharacteristic
98C22×C792−1+412yes—
99C2×D79—22no—
100C2×D79—22no—
101C2×D79—24no—
102C2×D79—24no—
103C2×D79—42no—
104C2×D79—42no—
105C2×D79—42no—
106C2×D79—44no—
107C2×D79—44no—
108C2×D79#12714yes—
109C4×C79—24no—
110C4×C79—42no—
111C4×C79—42no—
112C4×C79#12314yescomplemented
113Dic79—22no—
114Dic79—24no—
115Dic79—42no—
116C2×C79C2×#12311yescharacteristic
117C2×C79C2×#12711yescharacteristic
118C2×C79#53611yescharacteristic
119C2×C79#54712yes—
120C2×C79#54712yes—
121D79—24no—
122D79—82no—
123#2501—791nomaximal, Sylow
124C79#250111yescharacteristic, complemented, Sylow
125C2×#123—794no—
126C2×#121—791no—
127C22×C4⋊C4—791no—
128#399—794no—
129#390—791no—
130#390—791no—
131#384—791no—
132#384D7911yescharacteristic, complemented
133C4×C22⋊C4—791no—
134C22×D4—792no—
135C22×D4—791no—
136C23×C4—791no—
137C23×C4—792no—
138#123—15816no—
139#121—1584no—
140C2×C4⋊C4—791no—
141C2×C4⋊C4—792no—
142C2×C4⋊C4—794no—
143C2×C4⋊C4—1584no—
144C2×C4⋊C4C2×D7911yescharacteristic
145C2×C4⋊C4C2×D7911yescharacteristic
146C2×C4⋊C4C2×D7914yes—
147C2×C22⋊C4—792no—
148C2×C22⋊C4—792no—
149C2×C22⋊C4—794no—
150C2×C22⋊C4—794no—
151C2×C42—791no—
152C2×C42C2×D7911yescharacteristic
153#95—792no—
154C24—791no—
155C24—792no—
156C2×D4—1584no—
157C2×D4—1588no—
158C2×D4—1582no—
159C2×D4—1582no—
160C2×D4—1582no—
161C22×C4—791no—
162C22×C4—792no—
163C22×C4—794no—
164C22×C4—792no—
165C22×C4—1584no—
166C22×C4—1588no—
167C22×C4—1582no—
168C22×C4—1582no—
169C22×C4C22×D7912yes—
170C22×C4C22×D7912yes—
171C22×C4C22×D7912yes—
172C22×C4C22×D7911yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—28no—
176C4⋊C4—1584no—
177C4⋊C4—1588no—
178C4⋊C4—1582no—
179C22⋊C4—798no—
180C22⋊C4—1584no—
181C22⋊C4—1588no—
182C22⋊C4—1588no—
183C42—22no—
184C42—1582no—
185C23—794no—
186C23—792no—
187C23—1582no—
188C23—1582no—
189C23—1584no—
190C23—1584no—
191C23—1582no—
192C23—1581no—
193C23—1581no—
194C23—1582no—
195C23C23×D7911yescharacteristic
196D4—3168no—
197D4—3164no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—3168no—
205C2×C4—794no—
206C2×C4—792no—
207C2×C4—1584no—
208C2×C4—1582no—
209C2×C4—1581no—
210C2×C4—1582no—
211C2×C4—1581no—
212C2×C4—1582no—
213C2×C4—1588no—
214C2×C4D4×D7914yes—
215C2×C4D4×D7912yes—
216C2×C4#1192962412yes—
217C2×C4#1192962512yes—
218C22—3162no—
219C22—3164no—
220C22—3164no—
221C22—3162no—
222C22—3162no—
223C22—794no—
224C22—1582no—
225C22—1584no—
226C22—1584no—
227C22—1582no—
228C22C2×D4×D7911yescharacteristic
229C22C2×D4×D7912yes—
230C22C2×#1192962411yescharacteristic
231C22C2×#1192962511yescharacteristic
232C22#1457920912yes—
233C4—24no—
234C4—42no—
235C4—42no—
236C4—3162no—
237C4—1584no—
238C4—1582no—
239C4#1457914614yescomplemented
240C2—6322no—
241C2—1584no—
242C2C2×#1457914611yescharacteristic
243C2#127×D7911yescharacteristic
244C2#1909913811yescharacteristic
245C2#1909921412yes—
246C2#1909921612yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#384×C79C2
prime radicalC2×#14579136C2
hypercenter#384D79
hypocenterC79#2501
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#14579146C2semidirect
3. C2×C4⋊C4×D79C2semidirect
4. #19098498C2semidirect
5. #19098465C2semidirect
6. #19098464C2semidirect
7. #19098432C2semidirect
8. C4×(C2×D79)⋊C4C2semidirect
9. #384×C79C2semidirect
51. (C2×D79)⋊C4D4semidirect
112. C4×C79#123semidirect
124. C79#2501semidirect
132. #384D79semidirect
239. C4#14579146semidirect