Finite Group Databasebeta

← #23766671

Subgroups — #23766671

Order 10112.

528 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 159 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×Q8×Dic79C211yesmaximal, characteristic, complemented
2C2×#14579119C211yesmaximal, characteristic
3#19098502C211yesmaximal, characteristic, complemented
4#19098500C211yesmaximal, characteristic
5#19098495C212yesmaximal, complemented
6#19098485C212yesmaximal
7#19098474C211yesmaximal, characteristic
8C4⋊C4×Dic79C212yesmaximal, complemented
9#19098414C211yesmaximal, characteristic, complemented
10#19098410C212yesmaximal
11#395×C79C211yesmaximal, characteristic, complemented
12C22×C4×D79C2211yescharacteristic
13Q8×Dic79—24no—
14#14579119—24no—
15C2×C4⋊Dic79C2212yes—
16C2×C4⋊Dic79C2212yes—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×C4⋊Dic79C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×C4×Dic79C2212yes—
25C2×C4×Dic79C2212yes—
26C2×C4×Dic79C2211yescharacteristic
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2211yescharacteristic
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×Q8×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2212yes—
34C2×C4⋊C4×C79C2211yescharacteristic
35#95×C79C2212yes—
36#95×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C22×Dic79C2312yes—
39C22×Dic79C2311yescharacteristic
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C2×C4×D79—22no—
44C2×C4×D79—22no—
45C2×C4×D79Q814yescomplemented
46C4⋊Dic79—22no—
47C4⋊Dic79—24no—
48C4⋊Dic79—22no—
49C4⋊Dic79—24no—
50Dic79⋊C4—24no—
51(C2×D79)⋊C4—22no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—24no—
54(C2×D79)⋊C4—24no—
55C4×Dic79—22no—
56C4×Dic79—24no—
57C4×Dic79—24no—
58C4×Dic79D414yes—
59C2×Q8×C79—22no—
60C2×Q8×C79—24no—
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2312yes—
65C22×C4×C79C2312yes—
66C4⋊C4×C79—22no—
67C4⋊C4×C79—24no—
68C23×C79C2411yescharacteristic
69C22×D79—21no—
70C22×D79—22no—
71C22×D79—22no—
72C22×D79—21no—
73C22×D79C2×Q812yes—
74Q8×C79—28no—
75C2×C4×C79—22no—
76C2×C4×C79—21no—
77C2×C4×C79—22no—
78C2×C4×C79—21no—
79C2×C4×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79C2×D412yes—
85C2×C4×C79C2×Q812yes—
86C2×C4×C79#4114yes—
87C2×C4×C79#4114yes—
88C2×Dic79—22no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79C2×D412yes—
98C2×Dic79C2×D412yes—
99C2×Dic79C2×Q812yes—
100C2×Dic79#4112yes—
101C4×D79—28no—
102C22×C79C22×D411yescharacteristic
103C22×C79C22×Q811yescharacteristic
104C22×C79C2×#4111yescharacteristic
105C22×C79C2×#4112yes—
106C22×C79C2×#4112yes—
107C2×D79—22no—
108C2×D79—24no—
109C2×D79—41no—
110C2×D79—42no—
111C2×D79—41no—
112C4×C79—22no—
113C4×C79—22no—
114C4×C79—24no—
115C4×C79—24no—
116C4×C79—41no—
117Dic79—22no—
118Dic79—42no—
119Dic79—41no—
120Dic79—42no—
121Dic79C22⋊Q814yes—
122C2×C79C2×C22⋊Q811yescharacteristic
123C2×C79#52511yescharacteristic
124C2×C79#52912yes—
125C2×C79#53211yescharacteristic
126C2×C79#53312yes—
127D79—42no—
128#2396—791nomaximal, Sylow
129C79#239611yescharacteristic, complemented, Sylow
130C2×C4×Q8—791no—
131C2×#117—791no—
132#400—791no—
133#399—791no—
134#398—792no—
135#396—792no—
136#395D7911yescharacteristic, complemented
137#393—791no—
138C4×C4⋊C4—792no—
139C4×C4⋊C4—791no—
140C4×C22⋊C4—792no—
141C22×Q8C2×D7911yescharacteristic
142C23×C4—791no—
143C4×Q8—1584no—
144#117—1584no—
145C2×C4⋊C4—791no—
146C2×C4⋊C4—792no—
147C2×C4⋊C4—791no—
148C2×C4⋊C4—792no—
149C2×C4⋊C4—792no—
150C2×C4⋊C4C2×D7911yescharacteristic
151C2×C4⋊C4C2×D7912yes—
152C2×C22⋊C4—791no—
153C2×C22⋊C4—791no—
154C2×C22⋊C4—792no—
155C2×C22⋊C4—792no—
156C2×C42—791no—
157C2×C42—791no—
158C2×C42—792no—
159C2×C42—792no—
160#95—792no—
161#95—792no—
162#95—791no—
163#95—792no—
164#95C2×D7912yes—
165#95C2×D7911yescharacteristic
166C24—791no—
167C2×Q8—22no—
168C2×Q8—24no—
169C22×C4—791no—
170C22×C4—791no—
171C22×C4—794no—
172C22×C4—792no—
173C22×C4—792no—
174C22×C4—791no—
175C22×C4—1582no—
176C22×C4—1582no—
177C22×C4C22×D7911yescharacteristic
178C22×C4C22×D7911yescharacteristic
179C22×C4C22×D7911yescharacteristic
180C22×C4C22×D7912yes—
181C22×C4C22×D7912yes—
182C4⋊C4—22no—
183C4⋊C4—24no—
184C4⋊C4—1582no—
185C4⋊C4—1584no—
186C4⋊C4—1582no—
187C4⋊C4—1584no—
188C4⋊C4—1584no—
189C22⋊C4—1582no—
190C22⋊C4—1582no—
191C22⋊C4—1584no—
192C22⋊C4—1584no—
193C42—794no—
194C42—1584no—
195C42—1582no—
196C42—1584no—
197C23—792no—
198C23—1581no—
199C23—1582no—
200C23—1582no—
201C23—1581no—
202C23C23×D7911yescharacteristic
203Q8—28no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—792no—
214C2×C4—792no—
215C2×C4—792no—
216C2×C4—792no—
217C2×C4—1588no—
218C2×C4—1582no—
219C2×C4—1582no—
220C2×C4—1582no—
221C2×C4—1582no—
222C2×C4—1582no—
223C2×C4—1582no—
224C2×C4—1581no—
225C2×C4—1582no—
226C2×C4—1582no—
227C2×C4D4×D7912yes—
228C2×C4Q8×D7912yes—
229C2×C4#1192962314yes—
230C2×C4#1192962514yes—
231C22—3161no—
232C22—3162no—
233C22—3161no—
234C22—1582no—
235C22—1584no—
236C22C2×D4×D7911yescharacteristic
237C22C2×Q8×D7911yescharacteristic
238C22#41×D7911yescharacteristic
239C22C2×#1192962312yes—
240C22C2×#1192962512yes—
241C4—22no—
242C4—22no—
243C4—24no—
244C4—24no—
245C4—41no—
246C4—3162no—
247C4—3162no—
248C4—3161no—
249C4—794no—
250C4—1582no—
251C2—3162no—
252C2C22⋊Q8×D7911yescharacteristic
253C2#1909906911yescharacteristic
254C2#1909909912yes—
255C2#1909911411yescharacteristic
256C2#1909911812yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#395×C79C2
prime radicalC23×D79C23
hypercenter#395D79
hypocenterC79#2396
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic79C2semidirect
3. #19098502C2semidirect
5. #19098495C2semidirect
8. C4⋊C4×Dic79C2semidirect
9. #19098414C2semidirect
11. #395×C79C2semidirect
45. C2×C4×D79Q8semidirect
129. C79#2396semidirect
136. #395D79semidirect