Finite Group Databasebeta

← #23766692

Subgroups — #23766692

Order 10112.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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×#14579126C211yesmaximal, characteristic
2C2×#14579126C211yesmaximal, characteristic
3#19098497C212yesmaximal
4#19098494C211yesmaximal, characteristic
5#19098484C211yesmaximal, characteristic
6#19098483C212yesmaximal
7#19098483C211yesmaximal, characteristic
8C4⋊C4×Dic79C212yesmaximal
9#19098414C212yesmaximal
10#19098408C211yesmaximal, characteristic
11#398×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C22×Dic158C2211yescharacteristic
14#14579126—24no—
15#14579126—24no—
16C2×C4⋊Dic79C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×C4×Dic79C2211yescharacteristic
23C2×C4×Dic79C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C2×C4×Dic79C2211yescharacteristic
26C2×C4×Dic79C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2212yes—
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2211yescharacteristic
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C2×Dic158—22no—
38C2×Dic158—22no—
39C2×Dic158—24no—
40C2×Dic158—22no—
41C2×Dic158—22no—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C4⋊Dic79—24no—
49Dic79⋊C4—24no—
50Dic79⋊C4—22no—
51Dic79⋊C4—24no—
52Dic79⋊C4—24no—
53Dic79⋊C4—22no—
54C4×Dic79—22no—
55C4×Dic79—22no—
56C4×Dic79—24no—
57C4×Dic79D414yes—
58C4×Dic79Q818yescomplemented
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C4⋊C4×C79—22no—
65C4⋊C4×C79—22no—
66C4⋊C4×C79—24no—
67C23×C79C2411yescharacteristic
68C2×C4×C79—21no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—21no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79C2×D412yes—
79C2×C4×C79C2×Q814yes—
80C2×C4×C79#4112yes—
81C2×Dic79—22no—
82C2×Dic79—21no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—21no—
86C2×Dic79—22no—
87C2×Dic79—21no—
88C2×Dic79—21no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79C2×D412yes—
92C2×Dic79C2×D412yes—
93C2×Dic79C2×Q814yes—
94C2×Dic79C2×Q814yes—
95C2×Dic79#4112yes—
96C2×Dic79#4114yes—
97Dic158—28no—
98Dic158—28no—
99C22×C79C22×D411yescharacteristic
100C22×C79C22×Q812yes—
101C22×C79C2×#4112yes—
102C22×C79C2×#4111yescharacteristic
103C22×C79C2×#4111yescharacteristic
104C4×C79—22no—
105C4×C79—22no—
106C4×C79—24no—
107C4×C79—41no—
108C4×C79—42no—
109Dic79—22no—
110Dic79—24no—
111Dic79—22no—
112Dic79—24no—
113Dic79—41no—
114Dic79C4⋊Q814yes—
115C2×C79#52511yescharacteristic
116C2×C79#52511yescharacteristic
117C2×C79C2×C4⋊Q811yescharacteristic
118C2×C79#53312yes—
119C2×C79#53312yes—
120#2399—791nomaximal, Sylow
121C79#239911yescharacteristic, complemented, Sylow
122C2×C4×Q8—791no—
123C2×C4×Q8—791no—
124#398—791no—
125#398—792no—
126#398D7911yescharacteristic
127#395—792no—
128#395—791no—
129#395—791no—
130C4×C4⋊C4—792no—
131C4×C4⋊C4—792no—
132#376—791no—
133C22×Q8—791no—
134C22×Q8—791no—
135C4×Q8—1584no—
136C4×Q8—1584no—
137C2×C4⋊C4—792no—
138C2×C4⋊C4—791no—
139C2×C4⋊C4—791no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—792no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4C2×D7911yescharacteristic
144C2×C4⋊C4C2×D7911yescharacteristic
145C2×C4⋊C4C2×D7912yes—
146C2×C42—791no—
147C2×C42—792no—
148C2×C42—792no—
149C2×C42—791no—
150C2×C42—791no—
151#95—791no—
152#95—792no—
153#95—792no—
154#95—792no—
155#95—792no—
156#95C2×D7911yescharacteristic
157#95C2×D7912yes—
158C2×Q8—1582no—
159C2×Q8—1584no—
160C2×Q8—1582no—
161C2×Q8—1582no—
162C2×Q8—1582no—
163C22×C4—791no—
164C22×C4—792no—
165C22×C4—792no—
166C22×C4—791no—
167C22×C4—791no—
168C22×C4—791no—
169C22×C4C22×D7912yes—
170C22×C4C22×D7911yescharacteristic
171C22×C4C22×D7911yescharacteristic
172C22×C4C22×D7912yes—
173C22×C4C22×D7911yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—1584no—
178C4⋊C4—1584no—
179C4⋊C4—1582no—
180C4⋊C4—1584no—
181C4⋊C4—1584no—
182C4⋊C4—1582no—
183C42—794no—
184C42—798no—
185C42—1582no—
186C42—1582no—
187C42—1584no—
188C23C23×D7911yescharacteristic
189Q8—1588no—
190Q8—1588no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—794no—
202C2×C4—792no—
203C2×C4—794no—
204C2×C4—794no—
205C2×C4—792no—
206C2×C4—792no—
207C2×C4—1582no—
208C2×C4—1581no—
209C2×C4—1582no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1581no—
213C2×C4—1581no—
214C2×C4—1581no—
215C2×C4—1582no—
216C2×C4—1581no—
217C2×C4D4×D7912yes—
218C2×C4Q8×D7914yes—
219C2×C4#1192962312yes—
220C22C2×D4×D7911yescharacteristic
221C22C2×Q8×D7912yes—
222C22#41×D7912yes—
223C22#41×D7911yescharacteristic
224C22C2×#1192962311yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—3161no—
231C4—794no—
232C4—1584no—
233C4—1582no—
234C4—1582no—
235C4—1584no—
236C2#1909907111yescharacteristic
237C2#1909907311yescharacteristic
238C2C4⋊Q8×D7911yescharacteristic
239C2#1909911512yes—
240C2#1909911912yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#398×C79C2
hypercenter#398D79
hypocenterC79#2399
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
58. C4×Dic79Q8semidirect
121. C79#2399semidirect