Finite Group Databasebeta

← #23771100

Subgroups — #23771100

Order 10112.

472 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#19098485C212yesmaximal, complemented
2#19098483C211yesmaximal, characteristic, complemented
3#19098476C212yesmaximal, complemented
4#19098464C211yesmaximal, characteristic
5#19098446C212yesmaximal, complemented
6#19098441C212yesmaximal
7#19098437C212yesmaximal, complemented
8#19098422C212yesmaximal, complemented
9#400×C79C211yesmaximal, characteristic, complemented
10C22×Dic158C2211yescharacteristic
11C22×D316C2211yescharacteristic
12C22×C4×D79C2212yes—
13C2×C4⋊Dic79C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2212yes—
16C2×(C2×D79)⋊C4C2212yes—
17C2×(C2×D79)⋊C4C2212yes—
18C2×(C2×D79)⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2212yes—
21C2×C4×Dic79C2211yescharacteristic
22C79⋊#95C2212yes—
23C79⋊#95C2211yescharacteristic
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28#95×C79C2211yescharacteristic
29#95×C79C2212yes—
30#95×C79C2212yes—
31C23×D79C2312yes—
32C2×Dic158—42no—
33C2×Dic158—41no—
34C2×D316—41no—
35C2×D316—41no—
36C2×D316Q814yescomplemented
37C22×Dic79C2312yes—
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C2×C4×D79—24no—
41C2×C4×D79—42no—
42C2×C4×D79—42no—
43C4⋊Dic79—24no—
44Dic79⋊C4—42no—
45Dic79⋊C4—42no—
46(C2×D79)⋊C4—24no—
47(C2×D79)⋊C4—42no—
48(C2×D79)⋊C4—42no—
49(C2×D79)⋊C4—42no—
50(C2×D79)⋊C4—42no—
51C4×Dic79—41no—
52C22×C4×C79C2311yescharacteristic
53C22×C4×C79C2312yes—
54C22×C4×C79C2312yes—
55C22×C4×C79C2311yescharacteristic
56C22×C4×C79C2311yescharacteristic
57C4⋊C4×C79—41no—
58C4⋊C4×C79—41no—
59C23×C79C2411yescharacteristic
60C22×D79—22no—
61C22×D79—22no—
62C22×D79—22no—
63C22×D79—22no—
64C22×D79—22no—
65C22×D79—22no—
66C22×D79C2×Q814yes—
67C2×C4×C79—21no—
68C2×C4×C79—21no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—21no—
78C2×C4×C79—21no—
79C2×C4×C79C2×Q812yes—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79#4114yes—
89D316—44no—
90C4×D79—48no—
91Dic158—44no—
92C22×C79C22×Q811yescharacteristic
93C22×C79C2×#4112yes—
94C22×C79H(5,𝔽2)11yescharacteristic
95C22×C79H(5,𝔽2)11yescharacteristic
96C22×C79H(5,𝔽2)12yes—
97C2×D79—24no—
98C2×D79—24no—
99C2×D79—24no—
100C2×D79—42no—
101C2×D79—42no—
102C2×D79—42no—
103C2×D79—42no—
104C4×C79—22no—
105C4×C79—42no—
106C4×C79—42no—
107C4×C79—41no—
108C4×C79—41no—
109Dic79—24no—
110Dic79—42no—
111Dic79—42no—
112C2×C79#53812yes—
113C2×C79#54311yescharacteristic
114C2×C79#55412yes—
115C2×C79#55511yescharacteristic
116C2×C79#56011yescharacteristic
117D79—44no—
118#2784—791nomaximal, Sylow
119C79#278411yescharacteristic, complemented, Sylow
120#400D7911yescharacteristic, complemented
121#396—792no—
122#395—791no—
123#393—792no—
124#390—791no—
125#387—792no—
126#386—792no—
127#385—792no—
128#380—792no—
129C22×Q8—791no—
130C22×D4—791no—
131C23×C4—792no—
132C2×C4⋊C4—792no—
133C2×C4⋊C4—792no—
134C2×C4⋊C4—792no—
135C2×C4⋊C4C2×D7911yescharacteristic
136C2×C4⋊C4C2×D7911yescharacteristic
137C2×C22⋊C4—792no—
138C2×C22⋊C4—792no—
139C2×C22⋊C4—792no—
140C2×C22⋊C4—792no—
141C2×C22⋊C4—792no—
142C2×C42—791no—
143#95—792no—
144#95—791no—
145#95—792no—
146#95—792no—
147#95C2×D7911yescharacteristic
148#95C2×D7912yes—
149#95C2×D7912yes—
150C24—792no—
151C2×Q8—3161no—
152C2×Q8—3162no—
153C2×D4—3161no—
154C2×D4—3161no—
155C2×D4—794no—
156C22×C4—3162no—
157C22×C4—3162no—
158C22×C4—792no—
159C22×C4—792no—
160C22×C4—792no—
161C22×C4—1584no—
162C22×C4C22×D7912yes—
163C22×C4C22×D7912yes—
164C22×C4C22×D7911yescharacteristic
165C22×C4C22×D7911yescharacteristic
166C22×C4C22×D7911yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—3162no—
170C4⋊C4—3162no—
171C4⋊C4—1584no—
172C22⋊C4—3162no—
173C22⋊C4—3162no—
174C22⋊C4—3162no—
175C22⋊C4—3162no—
176C22⋊C4—1584no—
177C42—3161no—
178C23—794no—
179C23—1582no—
180C23—1582no—
181C23—1582no—
182C23—1582no—
183C23—1582no—
184C23—1582no—
185C23C23×D7911yescharacteristic
186Q8—3164no—
187D4—3164no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—3168no—
201C2×C4—794no—
202C2×C4—1582no—
203C2×C4—1582no—
204C2×C4—1582no—
205C2×C4—1582no—
206C2×C4—1582no—
207C2×C4—1582no—
208C2×C4—1582no—
209C2×C4—1582no—
210C2×C4Q8×D7912yes—
211C22—3162no—
212C22—3162no—
213C22—3162no—
214C22—3162no—
215C22—1584no—
216C22—1584no—
217C22—1584no—
218C22C2×Q8×D7911yescharacteristic
219C22#41×D7912yes—
220C22#1457920611yescharacteristic
221C22#1457920711yescharacteristic
222C22#1457920712yes—
223C4—22no—
224C4—42no—
225C4—42no—
226C4—41no—
227C4—41no—
228C4—3162no—
229C4—3162no—
230C4—1584no—
231C2—3164no—
232C2#1909915212yes—
233C2#1909918811yescharacteristic
234C2#1909926912yes—
235C2#1909927511yescharacteristic
236C2#1909930311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC22×D316C22
hypercenter#400D79
hypocenterC79#2784
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. #19098485C2semidirect
2. #19098483C2semidirect
3. #19098476C2semidirect
5. #19098446C2semidirect
7. #19098437C2semidirect
8. #19098422C2semidirect
9. #400×C79C2semidirect
36. C2×D316Q8semidirect
119. C79#2784semidirect
120. #400D79semidirect