Finite Group Databasebeta

← #23769774

Subgroups — #23769774

Order 10112.

592 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 592 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14579139C212yesmaximal, complemented
2C2×#14579137C212yesmaximal, complemented
3#19098487C212yesmaximal, complemented
4#19098485C212yesmaximal, complemented
5#19098483C211yesmaximal, characteristic, complemented
6#19098464C211yesmaximal, characteristic
7#19098460C212yesmaximal, complemented
8#19098441C212yesmaximal
9#395×C79C211yesmaximal, characteristic, complemented
10C22×Dic158C2211yescharacteristic
11C22×D316C2211yescharacteristic
12C22×C4×D79C2212yes—
13#14579139—28no—
14#14579137—28no—
15C2×C4⋊Dic79C2212yes—
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×C4×Dic79C2211yescharacteristic
26C79⋊#95C2212yes—
27C79⋊#95C2211yescharacteristic
28C22×Q8×C79C2211yescharacteristic
29C2×C4⋊C4×C79C2212yes—
30C2×C4⋊C4×C79C2211yescharacteristic
31#95×C79C2212yes—
32#95×C79C2211yescharacteristic
33C23×D79C2312yes—
34C2×Dic158—24no—
35C2×Dic158—41no—
36C2×D316—41no—
37C2×D316—41no—
38C2×D316Q814yescomplemented
39C22×Dic79C2312yes—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C2×C4×D79—24no—
43C2×C4×D79—24no—
44C2×C4×D79—42no—
45C4⋊Dic79—24no—
46Dic79⋊C4—24no—
47Dic79⋊C4—24no—
48Dic79⋊C4—42no—
49Dic79⋊C4D418yescomplemented
50(C2×D79)⋊C4—24no—
51(C2×D79)⋊C4—24no—
52(C2×D79)⋊C4—24no—
53(C2×D79)⋊C4—24no—
54(C2×D79)⋊C4—42no—
55C4×Dic79—41no—
56C2×Q8×C79—24no—
57C2×Q8×C79—41no—
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2312yes—
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2312yes—
62C22×C4×C79C2311yescharacteristic
63C4⋊C4×C79—24no—
64C4⋊C4×C79—41no—
65C23×C79C2411yescharacteristic
66C22×D79—22no—
67C22×D79—22no—
68C22×D79—22no—
69C22×D79—22no—
70C22×D79—22no—
71C22×D79—22no—
72C22×D79C2×Q814yes—
73Q8×C79—44no—
74C2×C4×C79—22no—
75C2×C4×C79—21no—
76C2×C4×C79—22no—
77C2×C4×C79—21no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—21no—
84C2×C4×C79—22no—
85C2×C4×C79C2×D414yes—
86C2×C4×C79C2×Q812yes—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79C2×D414yes—
95C2×Dic79C2×D414yes—
96D316—44no—
97C4×D79—48no—
98Dic158—44no—
99C22×C79C22×D412yes—
100C22×C79C22×Q811yescharacteristic
101C22×C79H(5,𝔽2)11yescharacteristic
102C22×C79H(5,𝔽2)11yescharacteristic
103C22×C792−1+412yes—
104C2×D79—24no—
105C2×D79—24no—
106C2×D79—24no—
107C2×D79—42no—
108C2×D79—42no—
109C2×D79—42no—
110C2×D79—42no—
111C4×C79—22no—
112C4×C79—24no—
113C4×C79—42no—
114C4×C79—41no—
115C4×C79—41no—
116Dic79—24no—
117Dic79—24no—
118Dic79—42no—
119C2×C79#53712yes—
120C2×C79#54311yescharacteristic
121C2×C79D4211yescharacteristic
122C2×C79D4×Q812yes—
123C2×C79#56311yescharacteristic
124D79—44no—
125#2683—791nomaximal, Sylow
126C79#268311yescharacteristic, complemented, Sylow
127C2×C22⋊Q8—792no—
128C2×C22⋊Q8—792no—
129#396—792no—
130#396—792no—
131#395—791no—
132#395D7911yescharacteristic, complemented
133#390—791no—
134#389—792no—
135#386—792no—
136C22×Q8—791no—
137C22×Q8C2×D7911yescharacteristic
138C22×D4—791no—
139C23×C4—792no—
140C22⋊Q8—1588no—
141C22⋊Q8—1588no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4—792no—
144C2×C4⋊C4—792no—
145C2×C4⋊C4—792no—
146C2×C4⋊C4—792no—
147C2×C4⋊C4C2×D7912yes—
148C2×C4⋊C4C2×D7911yescharacteristic
149C2×C22⋊C4—792no—
150C2×C22⋊C4—792no—
151C2×C22⋊C4—792no—
152C2×C22⋊C4—792no—
153C2×C22⋊C4—792no—
154C2×C42—791no—
155#95—792no—
156#95—791no—
157#95C2×D7912yes—
158#95C2×D7911yescharacteristic
159C24—792no—
160C2×Q8—24no—
161C2×Q8—41no—
162C2×Q8—3161no—
163C2×Q8—1584no—
164C2×D4—3161no—
165C2×D4—3161no—
166C2×D4—794no—
167C22×C4—3162no—
168C22×C4—792no—
169C22×C4—792no—
170C22×C4—792no—
171C22×C4—1584no—
172C22×C4—1584no—
173C22×C4C22×D7911yescharacteristic
174C22×C4C22×D7912yes—
175C22×C4C22×D7911yescharacteristic
176C22×C4C22×D7912yes—
177C22×C4C22×D7911yescharacteristic
178C4⋊C4—24no—
179C4⋊C4—41no—
180C4⋊C4—3162no—
181C4⋊C4—798no—
182C4⋊C4—1584no—
183C4⋊C4—1584no—
184C4⋊C4—1584no—
185C22⋊C4—3162no—
186C22⋊C4—1584no—
187C22⋊C4—1584no—
188C22⋊C4—1584no—
189C22⋊C4—1584no—
190C42—3161no—
191C23—794no—
192C23—1582no—
193C23—1582no—
194C23—1582no—
195C23—1582no—
196C23—1582no—
197C23—1582no—
198C23C23×D7911yescharacteristic
199Q8—44no—
200Q8—3164no—
201D4—3164no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—3168no—
214C2×C4—794no—
215C2×C4—794no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4—1582no—
219C2×C4—1582no—
220C2×C4—1582no—
221C2×C4—1582no—
222C2×C4—1582no—
223C2×C4D4×D7914yes—
224C2×C4Q8×D7912yes—
225C22—3162no—
226C22—3162no—
227C22—3162no—
228C22—3162no—
229C22—1584no—
230C22—1584no—
231C22—1584no—
232C22C2×D4×D7912yes—
233C22C2×Q8×D7911yescharacteristic
234C22#1457920611yescharacteristic
235C22#1457920711yescharacteristic
236C22#1457920912yes—
237C4—22no—
238C4—24no—
239C4—42no—
240C4—41no—
241C4—41no—
242C4—3162no—
243C4—1584no—
244C4—1584no—
245C2—3164no—
246C2#1909914312yes—
247C2#1909918811yescharacteristic
248C2#1909919511yescharacteristic
249C2#1909922812yes—
250C2#1909931211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#395×C79C2
prime radicalC22×D316C22
hypercenter#395D79
hypocenterC79#2683
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14579139C2semidirect
2. C2×#14579137C2semidirect
3. #19098487C2semidirect
4. #19098485C2semidirect
5. #19098483C2semidirect
7. #19098460C2semidirect
9. #395×C79C2semidirect
38. C2×D316Q8semidirect
49. Dic79⋊C4D4semidirect
126. C79#2683semidirect
132. #395D79semidirect