Finite Group Databasebeta

← #23767859

Subgroups — #23767859

Order 10112.

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

normal subgroups only

This group has 568 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×#14579136C211yesmaximal, characteristic
2C2×#14579119C211yesmaximal, characteristic, complemented
3#19098480C214yesmaximal, complemented
4#19098465C211yesmaximal, characteristic, complemented
5#19098464C211yesmaximal, characteristic, complemented
6#19098453C214yesmaximal, complemented
7#19098428C211yesmaximal, characteristic, complemented
8C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
9#384×C79C211yesmaximal, characteristic, complemented
10C22×D316C2211yescharacteristic
11C22×D316C2212yes—
12C22×C4×D79C2211yescharacteristic
13#14579136—24no—
14#14579119—24no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×(C2×D79)⋊C4C2212yes—
17C2×(C2×D79)⋊C4C2212yes—
18C2×(C2×D79)⋊C4C2214yes—
19C2×(C2×D79)⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2214yes—
21C2×C4×Dic79C2211yescharacteristic
22C2×C4×Dic79C2212yes—
23C79⋊#95C2212yes—
24C79⋊#95C2214yes—
25C2×C4⋊C4×C79C2211yescharacteristic
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2214yes—
28C2×C42×C79C2211yescharacteristic
29C23×D79C2312yes—
30C23×D79C2311yescharacteristic
31C2×D316—24no—
32C2×D316—22no—
33C2×D316—22no—
34C2×D316—22no—
35C2×D316—44no—
36C22×Dic79C2312yes—
37C22×Dic79C2312yes—
38C22×Dic79C2311yescharacteristic
39C2×C4×D79—22no—
40C2×C4×D79—22no—
41C2×C4×D79D414yes—
42C4⋊Dic79—22no—
43(C2×D79)⋊C4—24no—
44(C2×D79)⋊C4—24no—
45(C2×D79)⋊C4—24no—
46(C2×D79)⋊C4—28no—
47(C2×D79)⋊C4—44no—
48C4×Dic79—24no—
49C4×Dic79—22no—
50C22×C4×C79C2312yes—
51C22×C4×C79C2312yes—
52C22×C4×C79C2312yes—
53C22×C4×C79C2311yescharacteristic
54C4⋊C4×C79—22no—
55C4⋊C4×C79—22no—
56C4⋊C4×C79—44no—
57C42×C79—22no—
58C23×C79C2411yescharacteristic
59C22×D79—22no—
60C22×D79—21no—
61C22×D79—21no—
62C22×D79—22no—
63C22×D79—22no—
64C22×D79—24no—
65C22×D79—22no—
66C22×D79—22no—
67C22×D79—24no—
68C22×D79C2×D412yes—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—24no—
74C2×C4×C79—24no—
75C2×C4×C79C2×D412yes—
76C2×C4×C79#4112yes—
77C2×C4×C79#4114yes—
78C2×C4×C79#4112yes—
79C2×Dic79—21no—
80C2×Dic79—21no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—24no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79C2×D412yes—
87D316—48no—
88D316—44no—
89C4×D79—28no—
90C22×C79C22×D411yescharacteristic
91C22×C79C2×#4111yescharacteristic
92C22×C79C2×#4111yescharacteristic
93C22×C79C2×#4112yes—
94C22×C79H(5,𝔽2)12yes—
95C2×D79—22no—
96C2×D79—22no—
97C2×D79—22no—
98C2×D79—42no—
99C2×D79—42no—
100C2×D79—42no—
101C2×D79—42no—
102C2×D79—42no—
103C2×D79—44no—
104C2×D79—44no—
105C4×C79—24no—
106C4×C79—42no—
107C4×C79—42no—
108C4×C79#12314yes—
109Dic79—22no—
110Dic79—42no—
111Dic79—42no—
112C2×C79C2×#12311yescharacteristic
113C2×C79#53211yescharacteristic
114C2×C79#53511yescharacteristic
115C2×C79#55312yes—
116C2×C79#55512yes—
117D79—42no—
118D79—82no—
119#2500—791nomaximal, Sylow
120C79#250011yescharacteristic, complemented, Sylow
121C2×#121—791no—
122C2×#117—791no—
123#394—794no—
124#390—791no—
125#390—791no—
126#388—794no—
127#384D7911yescharacteristic, complemented
128#382—791no—
129C4×C22⋊C4—791no—
130C22×D4—792no—
131C22×D4—791no—
132C23×C4—791no—
133#121—1584no—
134#117—1584no—
135C2×C4⋊C4—791no—
136C2×C4⋊C4C2×D7911yescharacteristic
137C2×C4⋊C4C2×D7911yescharacteristic
138C2×C4⋊C4C2×D7914yes—
139C2×C22⋊C4—794no—
140C2×C22⋊C4—792no—
141C2×C22⋊C4—792no—
142C2×C22⋊C4—792no—
143C2×C22⋊C4—794no—
144C2×C42—792no—
145C2×C42—791no—
146C2×C42C2×D7911yescharacteristic
147#95—792no—
148#95—794no—
149C24—791no—
150C24—792no—
151C2×D4—3164no—
152C2×D4—1584no—
153C2×D4—1582no—
154C2×D4—1582no—
155C2×D4—1582no—
156C22×C4—791no—
157C22×C4—794no—
158C22×C4—792no—
159C22×C4—792no—
160C22×C4—1582no—
161C22×C4—1582no—
162C22×C4C22×D7912yes—
163C22×C4C22×D7912yes—
164C22×C4C22×D7912yes—
165C22×C4C22×D7911yescharacteristic
166C4⋊C4—22no—
167C4⋊C4—22no—
168C4⋊C4—44no—
169C4⋊C4—1582no—
170C22⋊C4—3164no—
171C22⋊C4—1584no—
172C22⋊C4—1584no—
173C22⋊C4—1588no—
174C22⋊C4—1584no—
175C42—22no—
176C42—1584no—
177C42—1582no—
178C23—792no—
179C23—1582no—
180C23—1584no—
181C23—1582no—
182C23—1584no—
183C23—1582no—
184C23—1581no—
185C23—1582no—
186C23—1581no—
187C23—1582no—
188C23C23×D7911yescharacteristic
189D4—3168no—
190D4—3164no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—792no—
198C2×C4—1582no—
199C2×C4—1582no—
200C2×C4—1584no—
201C2×C4—1582no—
202C2×C4—1582no—
203C2×C4—1581no—
204C2×C4—1581no—
205C2×C4—1588no—
206C2×C4D4×D7912yes—
207C2×C4#1192962412yes—
208C2×C4#1192962514yes—
209C2×C4#1192962512yes—
210C22—3162no—
211C22—3162no—
212C22—3164no—
213C22—3164no—
214C22—3162no—
215C22—3162no—
216C22—3162no—
217C22—1582no—
218C22—1582no—
219C22—1582no—
220C22C2×D4×D7911yescharacteristic
221C22C2×#1192962411yescharacteristic
222C22C2×#1192962512yes—
223C22C2×#1192962511yescharacteristic
224C22#1457920612yes—
225C4—24no—
226C4—42no—
227C4—42no—
228C4—3162no—
229C4—3162no—
230C4—1582no—
231C4#1457914614yes—
232C2—3162no—
233C2—6322no—
234C2C2×#1457914611yescharacteristic
235C2#1909911411yescharacteristic
236C2#1909912611yescharacteristic
237C2#1909926112yes—
238C2#1909927912yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#384×C79C2
prime radicalC2×#14579136C2
hypercenter#384D79
hypocenterC79#2500
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#14579119C2semidirect
3. #19098480C2semidirect
4. #19098465C2semidirect
5. #19098464C2semidirect
6. #19098453C2semidirect
7. #19098428C2semidirect
8. C4×(C2×D79)⋊C4C2semidirect
9. #384×C79C2semidirect
120. C79#2500semidirect
127. #384D79semidirect