Finite Group Databasebeta

← #23769282

Subgroups — #23769282

Order 10112.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14579152C211yesmaximal, characteristic
2C2×#14579126C211yesmaximal, characteristic
3#19098505C212yesmaximal
4#19098501C211yesmaximal, characteristic
5#19098495C211yesmaximal, characteristic
6#19098493C211yesmaximal, characteristic
7#19098484C212yesmaximal
8#19098446C212yesmaximal
9#19098445C212yesmaximal
10#19098430C211yesmaximal, characteristic
11#400×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13#14579152—24no—
14#14579126—24no—
15C2×C4⋊Dic79C2212yes—
16C2×C4⋊Dic79C2212yes—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×C4×Dic79C2211yescharacteristic
23C2×C4×Dic79C2211yescharacteristic
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34#95×C79C2211yescharacteristic
35#95×C79C2212yes—
36#95×C79C2212yes—
37C2×Dic158—22no—
38C2×Dic158—22no—
39C2×Dic158—22no—
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C4⋊Dic79—24no—
47C4⋊Dic79—24no—
48C4⋊Dic79—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—24no—
51Dic79⋊C4—22no—
52Dic79⋊C4—24no—
53C4×Dic79—22no—
54C4×Dic79—22no—
55C4×Dic79D414yes—
56C22×C4×C79C2312yes—
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C4⋊C4×C79—22no—
62C4⋊C4×C79—22no—
63C23×C79C2411yescharacteristic
64C2×C4×C79—21no—
65C2×C4×C79—21no—
66C2×C4×C79—22no—
67C2×C4×C79—21no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—24no—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79C2×D412yes—
75C2×C4×C79#4112yes—
76C2×Dic79—21no—
77C2×Dic79—21no—
78C2×Dic79—21no—
79C2×Dic79—21no—
80C2×Dic79—22no—
81C2×Dic79—21no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79C2×D412yes—
90C2×Dic79C2×D412yes—
91C2×Dic79#4112yes—
92Dic158—28no—
93C22×C79C22×D411yescharacteristic
94C22×C79C2×#4111yescharacteristic
95C22×C79C2×#4111yescharacteristic
96C22×C792−1+412yes—
97C22×C792−1+412yes—
98C4×C79—22no—
99C4×C79—22no—
100C4×C79—42no—
101C4×C79—41no—
102C4×C79—42no—
103Dic79—22no—
104Dic79—22no—
105Dic79—22no—
106Dic79—42no—
107Dic79—41no—
108Dic79—42no—
109C2×C79#52511yescharacteristic
110C2×C79#53611yescharacteristic
111C2×C79#53611yescharacteristic
112C2×C79#54112yes—
113C2×C79#54112yes—
114#2634—791nomaximal, Sylow
115C79#263411yescharacteristic, complemented, Sylow
116C2×#125—791no—
117C2×C4×Q8—791no—
118#400—791no—
119#400—792no—
120#400D7911yescharacteristic
121#398—791no—
122#398—791no—
123#395—792no—
124#387—792no—
125#387—792no—
126#383—791no—
127C22×Q8—791no—
128#125—1584no—
129C4×Q8—1584no—
130C2×C4⋊C4—791no—
131C2×C4⋊C4—791no—
132C2×C4⋊C4—792no—
133C2×C4⋊C4—792no—
134C2×C4⋊C4—791no—
135C2×C4⋊C4—792no—
136C2×C4⋊C4—792no—
137C2×C4⋊C4C2×D7911yescharacteristic
138C2×C4⋊C4C2×D7911yescharacteristic
139C2×C42—791no—
140C2×C42—791no—
141C2×C42—791no—
142#95—792no—
143#95—792no—
144#95—791no—
145#95—792no—
146#95—792no—
147#95—792no—
148#95—792no—
149#95C2×D7911yescharacteristic
150#95C2×D7912yes—
151#95C2×D7912yes—
152C2×Q8—1582no—
153C2×Q8—1582no—
154C2×Q8—1582no—
155C22×C4—791no—
156C22×C4—791no—
157C22×C4—791no—
158C22×C4—792no—
159C22×C4—791no—
160C22×C4—792no—
161C22×C4C22×D7912yes—
162C22×C4C22×D7911yescharacteristic
163C22×C4C22×D7912yes—
164C22×C4C22×D7911yescharacteristic
165C22×C4C22×D7911yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—1582no—
169C4⋊C4—1584no—
170C4⋊C4—1584no—
171C4⋊C4—1584no—
172C4⋊C4—1582no—
173C4⋊C4—1582no—
174C4⋊C4—1584no—
175C42—794no—
176C42—1582no—
177C42—1582no—
178C23C23×D7911yescharacteristic
179Q8—1588no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—792no—
191C2×C4—792no—
192C2×C4—792no—
193C2×C4—1582no—
194C2×C4—1582no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4—1581no—
200C2×C4—1582no—
201C2×C4—1581no—
202C2×C4—1581no—
203C2×C4—1581no—
204C2×C4—1582no—
205C2×C4—1581no—
206C2×C4D4×D7912yes—
207C2×C4#1192962512yes—
208C22C2×D4×D7911yescharacteristic
209C22#41×D7911yescharacteristic
210C22C2×#1192962511yescharacteristic
211C22#1457920812yes—
212C22#1457920812yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—42no—
217C4—41no—
218C4—3162no—
219C4—3162no—
220C4—3161no—
221C4—1582no—
222C4—1582no—
223C4—1582no—
224C2#1909907611yescharacteristic
225C2#1909913311yescharacteristic
226C2#1909913511yescharacteristic
227C2#1909917012yes—
228C2#1909917612yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#400×C79C2
hypercenter#400D79
hypocenterC79#2634
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
115. C79#2634semidirect