Finite Group Databasebeta

← #23768761

Subgroups — #23768761

Order 10112.

468 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 151 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
2C2×#14579126C211yesmaximal, characteristic
3#19098503C211yesmaximal, characteristic
4#19098502C211yesmaximal, characteristic
5#19098482C211yesmaximal, characteristic
6#19098467C212yesmaximal
7#19098458C212yesmaximal
8#19098450C212yesmaximal
9#19098449C212yesmaximal
10#19098427C211yesmaximal, characteristic
11#395×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13Q8×Dic79—24no—
14#14579126—24no—
15C2×C4⋊Dic79C2212yes—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×C4×Dic79C2211yescharacteristic
22C2×C4×Dic79C2211yescharacteristic
23C2×C4×Dic79C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2211yescharacteristic
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×Q8×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2212yes—
34C2×C4⋊C4×C79C2211yescharacteristic
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C2×Dic158—22no—
38C2×Dic158—22no—
39C2×Dic158Q814yescomplemented
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C4⋊Dic79—24no—
47C4⋊Dic79—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—24no—
50Dic79⋊C4—22no—
51Dic79⋊C4—24no—
52C4×Dic79—22no—
53C4×Dic79—22no—
54C4×Dic79—24no—
55C4×Dic79D414yes—
56C2×Q8×C79—22no—
57C2×Q8×C79—24no—
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2312yes—
63C4⋊C4×C79—22no—
64C4⋊C4×C79—24no—
65C23×C79C2411yescharacteristic
66Q8×C79—28no—
67C2×C4×C79—22no—
68C2×C4×C79—21no—
69C2×C4×C79—21no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—21no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79C2×D412yes—
78C2×C4×C79C2×Q812yes—
79C2×C4×C79#4114yes—
80C2×Dic79—21no—
81C2×Dic79—21no—
82C2×Dic79—22no—
83C2×Dic79—21no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—24no—
89C2×Dic79—22no—
90C2×Dic79C2×D412yes—
91C2×Dic79C2×D412yes—
92C2×Dic79C2×Q812yes—
93C2×Dic79C2×Q812yes—
94C2×Dic79#4112yes—
95Dic158—28no—
96C22×C79C22×D411yescharacteristic
97C22×C79C22×Q811yescharacteristic
98C22×C79C2×#4111yescharacteristic
99C22×C79C2×#4112yes—
100C22×C792−1+412yes—
101C4×C79—22no—
102C4×C79—22no—
103C4×C79—24no—
104C4×C79—41no—
105C4×C79—42no—
106Dic79—22no—
107Dic79—22no—
108Dic79—41no—
109Dic79—42no—
110Dic79—42no—
111Dic79C22⋊Q814yes—
112C2×C79C2×C22⋊Q811yescharacteristic
113C2×C79#52511yescharacteristic
114C2×C79#53611yescharacteristic
115C2×C79#55612yes—
116C2×C79#55712yes—
117#2581—791nomaximal, Sylow
118C79#258111yescharacteristic, complemented, Sylow
119C2×C4×Q8—791no—
120C2×C4×Q8—791no—
121#400—791no—
122#400—791no—
123#395—791no—
124#395D7911yescharacteristic
125#391—792no—
126#389—792no—
127#387—792no—
128#387—792no—
129#382—791no—
130C22×Q8—791no—
131C22×Q8C2×D7911yescharacteristic
132C4×Q8—1584no—
133C4×Q8—1584no—
134C2×C4⋊C4—792no—
135C2×C4⋊C4—791no—
136C2×C4⋊C4—791no—
137C2×C4⋊C4—791no—
138C2×C4⋊C4—792no—
139C2×C4⋊C4—792no—
140C2×C4⋊C4C2×D7911yescharacteristic
141C2×C4⋊C4C2×D7912yes—
142C2×C42—791no—
143C2×C42—791no—
144C2×C42—791no—
145C2×C42—792no—
146#95—792no—
147#95—791no—
148#95—792no—
149#95—792no—
150#95—792no—
151#95—792no—
152#95—792no—
153#95C2×D7911yescharacteristic
154#95C2×D7912yes—
155C2×Q8—22no—
156C2×Q8—24no—
157C2×Q8—794no—
158C2×Q8—1582no—
159C2×Q8—1582no—
160C22×C4—791no—
161C22×C4—791no—
162C22×C4—791no—
163C22×C4—792no—
164C22×C4—792no—
165C22×C4—791no—
166C22×C4C22×D7912yes—
167C22×C4C22×D7911yescharacteristic
168C22×C4C22×D7911yescharacteristic
169C22×C4C22×D7911yescharacteristic
170C22×C4C22×D7912yes—
171C4⋊C4—22no—
172C4⋊C4—24no—
173C4⋊C4—1584no—
174C4⋊C4—1582no—
175C4⋊C4—1584no—
176C4⋊C4—1582no—
177C4⋊C4—1582no—
178C4⋊C4—1584no—
179C42—794no—
180C42—1582no—
181C42—1584no—
182C42—1582no—
183C23C23×D7911yescharacteristic
184Q8—28no—
185Q8—1588no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—792no—
197C2×C4—792no—
198C2×C4—792no—
199C2×C4—792no—
200C2×C4—792no—
201C2×C4—1582no—
202C2×C4—1582no—
203C2×C4—1582no—
204C2×C4—1584no—
205C2×C4—1582no—
206C2×C4—1582no—
207C2×C4—1581no—
208C2×C4—1581no—
209C2×C4—1582no—
210C2×C4—1581no—
211C2×C4D4×D7912yes—
212C2×C4Q8×D7912yes—
213C2×C4#1192962314yes—
214C22C2×D4×D7911yescharacteristic
215C22C2×Q8×D7911yescharacteristic
216C22#41×D7911yescharacteristic
217C22C2×#1192962312yes—
218C22#1457920912yes—
219C4—22no—
220C4—22no—
221C4—24no—
222C4—42no—
223C4—41no—
224C4—3162no—
225C4—3162no—
226C4—3161no—
227C4—794no—
228C4—1582no—
229C4—1582no—
230C2C22⋊Q8×D7911yescharacteristic
231C2#1909906911yescharacteristic
232C2#1909913811yescharacteristic
233C2#1909928412yes—
234C2#1909928812yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#395×C79C2
hypercenter#395D79
hypocenterC79#2581
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
39. C2×Dic158Q8semidirect
118. C79#2581semidirect