Finite Group Databasebeta

← #23769067

Subgroups — #23769067

Order 10112.

428 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 145 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#19098486C212yesmaximal
2#19098486C212yesmaximal
3#19098461C212yesmaximal, complemented
4#19098460C212yesmaximal, complemented
5#19098450C212yesmaximal, complemented
6#19098447C212yesmaximal, complemented
7#19098426C211yesmaximal, characteristic
8C4×C22⋊Dic79C211yesmaximal, characteristic
9C4×C22⋊C4×C79C211yesmaximal, characteristic
10C2×C4⋊Dic79C2212yes—
11C2×C4⋊Dic79C2212yes—
12C2×Dic79⋊C4C2212yes—
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×Dic79⋊C4C2212yes—
16C2×C22⋊Dic79C2212yes—
17C2×C22⋊Dic79C2211yescharacteristic
18C2×C22⋊Dic79C2211yescharacteristic
19C2×C4×Dic79C2211yescharacteristic
20C2×C4×Dic79C2211yescharacteristic
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2212yes—
24C79⋊#95C2212yes—
25C79⋊#95C2212yes—
26C23×C4×C79C2211yescharacteristic
27C2×C22⋊C4×C79C2212yes—
28C2×C42×C79C2211yescharacteristic
29C2×C42×C79C2211yescharacteristic
30#95×C79C2212yes—
31C22×Dic79C2312yes—
32C22×Dic79C2312yes—
33C22×Dic79C2312yes—
34C22×Dic79C2312yes—
35C4⋊Dic79—24no—
36C4⋊Dic79—42no—
37Dic79⋊C4—24no—
38Dic79⋊C4—24no—
39Dic79⋊C4—24no—
40Dic79⋊C4—42no—
41C22⋊Dic79—24no—
42C22⋊Dic79—41no—
43C22⋊Dic79—41no—
44C4×Dic79—41no—
45C4×Dic79—41no—
46C24×C79C2311yescharacteristic
47C22×C4×C79—41no—
48C22×C4×C79—41no—
49C22×C4×C79Q814yes—
50C22×C4×C79C2312yes—
51C22×C4×C79C2311yescharacteristic
52C22×C4×C79C2311yescharacteristic
53C22×C4×C79C2312yes—
54C22⋊C4×C79—24no—
55C42×C79—41no—
56C42×C79—41no—
57C23×C79—22no—
58C23×C79—22no—
59C23×C79—21no—
60C23×C79—21no—
61C23×C79C2×Q812yes—
62C23×C79C2411yescharacteristic
63C2×C4×C79—22no—
64C2×C4×C79—21no—
65C2×C4×C79—21no—
66C2×C4×C79—22no—
67C2×C4×C79—21no—
68C2×C4×C79—21no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—44no—
73C2×C4×C79C2×Q812yes—
74C2×C4×C79C2×Q812yes—
75C2×C4×C79#4114yes—
76C2×Dic79—22no—
77C2×Dic79—22no—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79#4114yes—
88C22×C79—22no—
89C22×C79—22no—
90C22×C79—22no—
91C22×C79—42no—
92C22×C79—42no—
93C22×C79C22×Q811yescharacteristic
94C22×C79C2×#4112yes—
95C22×C79C2×#4112yes—
96C22×C79H(5,𝔽2)11yescharacteristic
97C22×C79H(5,𝔽2)11yescharacteristic
98C4×C79—22no—
99C4×C79—22no—
100C4×C79—24no—
101C4×C79—42no—
102Dic79—24no—
103Dic79—42no—
104Dic79—42no—
105Dic79—42no—
106C2×C79—42no—
107C2×C79#53311yescharacteristic
108C2×C79#53311yescharacteristic
109C2×C79#54311yescharacteristic
110C2×C79#55312yes—
111C2×C79#55312yes—
112#2608—791nomaximal, Sylow
113C79#260811yescharacteristic, complemented, Sylow
114#396—792no—
115#396—792no—
116#389—792no—
117#389—792no—
118#387—792no—
119#387—792no—
120#381—791no—
121C4×C22⋊C4—791no—
122C4×C22⋊C4D7911yescharacteristic
123C23×C4C2×D7911yescharacteristic
124C2×C4⋊C4—792no—
125C2×C4⋊C4—792no—
126C2×C4⋊C4—792no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—792no—
129C2×C4⋊C4—792no—
130C2×C22⋊C4—791no—
131C2×C22⋊C4—791no—
132C2×C22⋊C4—792no—
133C2×C22⋊C4C2×D7912yes—
134C2×C42—791no—
135C2×C42—791no—
136C2×C42C2×D7911yescharacteristic
137C2×C42C2×D7911yescharacteristic
138#95—792no—
139#95—792no—
140#95—792no—
141#95—792no—
142#95—792no—
143#95C2×D7912yes—
144C24C22×D7911yescharacteristic
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—792no—
148C22×C4—792no—
149C22×C4—792no—
150C22×C4—792no—
151C22×C4Dic15814yes—
152C22×C4C22×D7912yes—
153C22×C4C22×D7911yescharacteristic
154C22×C4C22×D7911yescharacteristic
155C22×C4C22×D7912yes—
156C4⋊C4—3162no—
157C4⋊C4—3162no—
158C4⋊C4—1584no—
159C4⋊C4—1584no—
160C4⋊C4—1584no—
161C4⋊C4—1584no—
162C22⋊C4—24no—
163C22⋊C4—3161no—
164C22⋊C4—3161no—
165C22⋊C4—1584no—
166C42—41no—
167C42—41no—
168C42—3161no—
169C42—3161no—
170C23—22no—
171C23—22no—
172C23—21no—
173C23—21no—
174C23C2×Dic15812yes—
175C23C23×D7911yescharacteristic
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—44no—
186C2×C4—794no—
187C2×C4—1582no—
188C2×C4—1582no—
189C2×C4—1582no—
190C2×C4—1582no—
191C2×C4—1582no—
192C2×C4—1582no—
193C2×C4—1582no—
194C2×C4—1582no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4C2×Dic15812yes—
199C2×C4C2×Dic15812yes—
200C2×C4#1192962414yes—
201C22—22no—
202C22—22no—
203C22—22no—
204C22—42no—
205C22—42no—
206C22C22×Dic15811yescharacteristic
207C22#41×D7912yes—
208C22C2×#1192962412yes—
209C22#1457920611yescharacteristic
210C22#1457920611yescharacteristic
211C4—22no—
212C4—22no—
213C4—24no—
214C4—42no—
215C4—3162no—
216C4—3162no—
217C4—3162no—
218C4—1584no—
219C2—42no—
220C2#1909911611yescharacteristic
221C2#1909912011yescharacteristic
222C2#1909918911yescharacteristic
223C2#1909926212yes—
224C2#1909926312yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC4×C22⋊C4×C79C2
prime radicalC24×C79C23
hypercenterC4×C22⋊C4D79
hypocenterC79#2608
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #19098461C2semidirect
4. #19098460C2semidirect
5. #19098450C2semidirect
6. #19098447C2semidirect
113. C79#2608semidirect