Finite Group Databasebeta

← #23769171

Subgroups — #23769171

Order 10112.

528 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14579159C211yesmaximal, characteristic, complemented
2C2×#14579141C211yesmaximal, characteristic
3C2×#14579137C211yesmaximal, characteristic
4C2×#14579118C211yesmaximal, characteristic
5#19098497C214yesmaximal, complemented
6#19098492C214yesmaximal
7#19098469C211yesmaximal, characteristic, complemented
8#19098428C211yesmaximal, characteristic, complemented
9#391×C79C211yesmaximal, characteristic, complemented
10C22×Dic158C2211yescharacteristic
11C22×C4×D79C2211yescharacteristic
12#14579159—24no—
13#14579141—24no—
14#14579137—24no—
15#14579118—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×C4⋊Dic79C2212yes—
18C2×Dic79⋊C4C2214yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2214yes—
26C79⋊#95C2214yes—
27C22×Q8×C79C2211yescharacteristic
28C2×C4⋊C4×C79C2211yescharacteristic
29C2×C42×C79C2211yescharacteristic
30#95×C79C2214yes—
31C23×D79C2311yescharacteristic
32C2×Dic158—22no—
33C2×Dic158—22no—
34C2×Dic158—22no—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C22×Dic79C2312yes—
38C22×Dic79C2311yescharacteristic
39C2×C4×D79—22no—
40C2×C4×D79—22no—
41C2×C4×D79D414yes—
42C4⋊Dic79—24no—
43C4⋊Dic79—22no—
44Dic79⋊C4—24no—
45Dic79⋊C4—24no—
46Dic79⋊C4—28no—
47(C2×D79)⋊C4—24no—
48(C2×D79)⋊C4—24no—
49(C2×D79)⋊C4—24no—
50C4×Dic79D414yes—
51C2×Q8×C79—22no—
52C2×Q8×C79—22no—
53C2×Q8×C79—22no—
54C22×C4×C79C2312yes—
55C22×C4×C79C2312yes—
56C22×C4×C79C2312yes—
57C22×C4×C79C2311yescharacteristic
58C4⋊C4×C79—22no—
59C42×C79—22no—
60C23×C79C2411yescharacteristic
61C22×D79—21no—
62C22×D79—21no—
63C22×D79—22no—
64C22×D79—22no—
65C22×D79C2×D412yes—
66Q8×C79—44no—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—24no—
74C2×C4×C79—22no—
75C2×C4×C79C2×D412yes—
76C2×C4×C79C2×D412yes—
77C2×C4×C79#4112yes—
78C2×Dic79—21no—
79C2×Dic79—21no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—24no—
87C2×Dic79C2×D414yes—
88C2×Dic79C2×D412yes—
89C4×D79—28no—
90Dic158—44no—
91C22×C79C22×D411yescharacteristic
92C22×C79C22×D411yescharacteristic
93C22×C79C2×#4111yescharacteristic
94C22×C792−1+412yes—
95C22×C792−1+412yes—
96C2×D79—22no—
97C2×D79—22no—
98C2×D79—22no—
99C2×D79—42no—
100C2×D79—42no—
101C4×C79—42no—
102C4×C79—42no—
103C4×C79—42no—
104C4×C79#12114yes—
105Dic79—22no—
106Dic79—24no—
107Dic79—42no—
108Dic79—42no—
109C2×C79C2×#12111yescharacteristic
110C2×C79#53612yes—
111C2×C79#53611yescharacteristic
112C2×C79#53611yescharacteristic
113C2×C79#54112yes—
114D79—42no—
115#2621—791nomaximal, Sylow
116C79#262111yescharacteristic, complemented, Sylow
117C2×C4⋊Q8—791no—
118C2×C22⋊Q8—791no—
119C2×C22⋊Q8—791no—
120C2×#117—791no—
121#398—794no—
122#397—794no—
123#391—791no—
124#391D7911yescharacteristic, complemented
125#382—791no—
126C22×Q8—791no—
127C22×Q8C2×D7911yescharacteristic
128C23×C4—791no—
129C4⋊Q8—1584no—
130C22⋊Q8—1584no—
131C22⋊Q8—1584no—
132#117—1584no—
133C2×C4⋊C4—792no—
134C2×C4⋊C4—791no—
135C2×C4⋊C4—792no—
136C2×C4⋊C4—792no—
137C2×C4⋊C4—794no—
138C2×C4⋊C4C2×D7911yescharacteristic
139C2×C22⋊C4—792no—
140C2×C22⋊C4—792no—
141C2×C22⋊C4—792no—
142C2×C42—791no—
143C2×C42C2×D7911yescharacteristic
144#95—794no—
145#95—794no—
146#95C2×D7914yes—
147C24—791no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—1582no—
152C2×Q8—1582no—
153C2×Q8—1582no—
154C22×C4—792no—
155C22×C4—791no—
156C22×C4—794no—
157C22×C4—792no—
158C22×C4—792no—
159C22×C4—1582no—
160C22×C4—1582no—
161C22×C4C22×D7912yes—
162C22×C4C22×D7912yes—
163C22×C4C22×D7912yes—
164C22×C4C22×D7911yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—1584no—
167C4⋊C4—1584no—
168C4⋊C4—1588no—
169C4⋊C4—1584no—
170C4⋊C4—1582no—
171C22⋊C4—1584no—
172C22⋊C4—1584no—
173C22⋊C4—1584no—
174C42—22no—
175C42—794no—
176C23—792no—
177C23—1581no—
178C23—1582no—
179C23—1582no—
180C23—1581no—
181C23C23×D7911yescharacteristic
182Q8—44no—
183Q8—3164no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—794no—
193C2×C4—792no—
194C2×C4—1582no—
195C2×C4—1584no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4—1581no—
200C2×C4—1582no—
201C2×C4—1582no—
202C2×C4—1581no—
203C2×C4—1588no—
204C2×C4D4×D7912yes—
205C2×C4D4×D7912yes—
206C2×C4#1192962412yes—
207C22—3162no—
208C22—3162no—
209C22—1582no—
210C22—1582no—
211C22—1582no—
212C22C2×D4×D7911yescharacteristic
213C22C2×D4×D7911yescharacteristic
214C22C2×#1192962411yescharacteristic
215C22#1457920812yes—
216C22#1457920912yes—
217C4—42no—
218C4—42no—
219C4—42no—
220C4—3162no—
221C4—3162no—
222C4—1584no—
223C4—1582no—
224C4#1457913414yes—
225C2—3162no—
226C2C2×#1457913411yescharacteristic
227C2#1909913311yescharacteristic
228C2#1909913612yes—
229C2#1909913811yescharacteristic
230C2#1909917112yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#391×C79C2
prime radicalC23×D79C23
hypercenter#391D79
hypocenterC79#2621
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#14579159C2semidirect
5. #19098497C2semidirect
7. #19098469C2semidirect
8. #19098428C2semidirect
9. #391×C79C2semidirect
116. C79#2621semidirect
124. #391D79semidirect