Finite Group Databasebeta

← #23769523

Subgroups — #23769523

Order 10112.

448 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14579160C211yesmaximal, characteristic
2C2×#14579151C211yesmaximal, characteristic
3#19098495C211yesmaximal, characteristic
4#19098494C211yesmaximal, characteristic
5#19098493C211yesmaximal, characteristic
6#19098484C212yesmaximal
7#19098483C212yesmaximal
8#19098432C212yesmaximal
9#19098427C212yesmaximal
10#19098408C211yesmaximal, characteristic
11#398×C79C211yesmaximal, characteristic
12C22×Dic158C2212yes—
13#14579160—24no—
14#14579151—24no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×C4⋊Dic79C2211yescharacteristic
17C2×C4⋊Dic79C2212yes—
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2211yescharacteristic
23C2×Dic79⋊C4C2212yes—
24C2×Dic79⋊C4C2212yes—
25C2×C4×Dic79C2211yescharacteristic
26C2×C4×Dic79C2212yes—
27C79⋊#95C2212yes—
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C2×Dic158—24no—
38C2×Dic158—42no—
39C2×Dic158—42no—
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C4⋊Dic79—22no—
47C4⋊Dic79—22no—
48C4⋊Dic79—42no—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51Dic79⋊C4—22no—
52Dic79⋊C4—24no—
53Dic79⋊C4—22no—
54Dic79⋊C4—42no—
55Dic79⋊C4—42no—
56C4×Dic79D414yes—
57C4×Dic79Q818yescomplemented
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2312yes—
63C4⋊C4×C79—22no—
64C4⋊C4×C79—22no—
65C4⋊C4×C79—42no—
66C23×C79C2411yescharacteristic
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—21no—
71C2×C4×C79—21no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—21no—
77C2×C4×C79—22no—
78C2×C4×C79C2×D412yes—
79C2×C4×C79C2×Q814yes—
80C2×Dic79—22no—
81C2×Dic79—21no—
82C2×Dic79—21no—
83C2×Dic79—22no—
84C2×Dic79—21no—
85C2×Dic79—21no—
86C2×Dic79—22no—
87C2×Dic79—21no—
88C2×Dic79—22no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79C2×D412yes—
93C2×Dic79C2×D412yes—
94C2×Dic79C2×Q814yes—
95C2×Dic79C2×Q814yes—
96Dic158—48no—
97C22×C79C22×D411yescharacteristic
98C22×C79C22×Q812yes—
99C22×C79H(5,𝔽2)11yescharacteristic
100C22×C79H(5,𝔽2)11yescharacteristic
101C22×C792−1+412yes—
102C4×C79—22no—
103C4×C79—24no—
104C4×C79—41no—
105C4×C79—42no—
106C4×C79—41no—
107Dic79—22no—
108Dic79—24no—
109Dic79—42no—
110Dic79—41no—
111Dic79—41no—
112Dic79C4⋊Q814yes—
113C2×C79C2×C4⋊Q811yescharacteristic
114C2×C79#53511yescharacteristic
115C2×C79#53611yescharacteristic
116C2×C79#54412yes—
117C2×C79#54412yes—
118#2660—791nomaximal, Sylow
119C79#266011yescharacteristic, complemented, Sylow
120C2×C4⋊Q8—791no—
121C2×#125—791no—
122#398—791no—
123#398—791no—
124#398—791no—
125#398D7911yescharacteristic
126#395—792no—
127#395—792no—
128#384—792no—
129#382—792no—
130#376—791no—
131C22×Q8—792no—
132C4⋊Q8—1584no—
133#125—1584no—
134C2×C4⋊C4—792no—
135C2×C4⋊C4—792no—
136C2×C4⋊C4—792no—
137C2×C4⋊C4—791no—
138C2×C4⋊C4—791no—
139C2×C4⋊C4—791no—
140C2×C4⋊C4—791no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4C2×D7911yescharacteristic
145C2×C4⋊C4C2×D7911yescharacteristic
146C2×C4⋊C4C2×D7912yes—
147C2×C42—791no—
148C2×C42—792no—
149#95—792no—
150#95—791no—
151#95—792no—
152#95—792no—
153#95—792no—
154#95C2×D7911yescharacteristic
155#95C2×D7912yes—
156C2×Q8—3162no—
157C2×Q8—3162no—
158C2×Q8—1584no—
159C22×C4—791no—
160C22×C4—792no—
161C22×C4—791no—
162C22×C4—791no—
163C22×C4—792no—
164C22×C4—791no—
165C22×C4C22×D7911yescharacteristic
166C22×C4C22×D7912yes—
167C22×C4C22×D7911yescharacteristic
168C22×C4C22×D7911yescharacteristic
169C22×C4C22×D7912yes—
170C4⋊C4—22no—
171C4⋊C4—22no—
172C4⋊C4—42no—
173C4⋊C4—3162no—
174C4⋊C4—3162no—
175C4⋊C4—3162no—
176C4⋊C4—1582no—
177C4⋊C4—1582no—
178C4⋊C4—1582no—
179C4⋊C4—1584no—
180C4⋊C4—1582no—
181C4⋊C4—1582no—
182C4⋊C4—1582no—
183C42—794no—
184C42—798no—
185C23C23×D7911yescharacteristic
186Q8—3168no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—794no—
199C2×C4—792no—
200C2×C4—794no—
201C2×C4—792no—
202C2×C4—1581no—
203C2×C4—1582no—
204C2×C4—1581no—
205C2×C4—1582no—
206C2×C4—1582no—
207C2×C4—1581no—
208C2×C4—1581no—
209C2×C4—1582no—
210C2×C4—1581no—
211C2×C4—1582no—
212C2×C4—1581no—
213C2×C4—1582no—
214C2×C4D4×D7912yes—
215C2×C4Q8×D7914yes—
216C22C2×D4×D7911yescharacteristic
217C22C2×Q8×D7912yes—
218C22#1457920611yescharacteristic
219C22#1457920711yescharacteristic
220C22#1457920812yes—
221C4—24no—
222C4—22no—
223C4—42no—
224C4—41no—
225C4—41no—
226C4—3162no—
227C4—3161no—
228C4—3161no—
229C4—794no—
230C4—1584no—
231C4—1582no—
232C2C4⋊Q8×D7911yescharacteristic
233C2#1909912911yescharacteristic
234C2#1909913511yescharacteristic
235C2#1909919212yes—
236C2#1909919312yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#398×C79C2
hypercenter#398D79
hypocenterC79#2660
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
57. C4×Dic79Q8semidirect
119. C79#2660semidirect