Finite Group Databasebeta

← #23768571

Subgroups — #23768571

Order 10112.

564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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, complemented
2C2×D4×Dic79C211yesmaximal, characteristic
3#19098475C214yesmaximal, complemented
4#19098466C211yesmaximal, characteristic
5#19098429C211yesmaximal, characteristic, complemented
6#19098428C211yesmaximal, characteristic, complemented
7#19098421C214yesmaximal, complemented
8C4×Dic79⋊C4C211yesmaximal, characteristic, complemented
9#390×C79C211yesmaximal, characteristic
10C22×Dic158C2212yes—
11C23×Dic79C2212yes—
12#14579160—24no—
13D4×Dic79—24no—
14C2×C4⋊Dic79C2211yescharacteristic
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×C22⋊Dic79C2212yes—
19C2×C22⋊Dic79C2214yes—
20C2×C4×Dic79C2211yescharacteristic
21C2×C4×Dic79C2211yescharacteristic
22C79⋊#95C2212yes—
23C79⋊#95C2214yes—
24C79⋊#95C2214yes—
25C22×D4×C79C2211yescharacteristic
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C22⋊C4×C79C2214yes—
28C2×C42×C79C2211yescharacteristic
29C2×Dic158—24no—
30C2×Dic158—44no—
31C22×Dic79—24no—
32C22×Dic79—28no—
33C22×Dic79C2312yes—
34C22×Dic79C2312yes—
35C22×Dic79C2312yes—
36C22×Dic79C2311yescharacteristic
37C22×Dic79C2311yescharacteristic
38C4⋊Dic79—22no—
39C4⋊Dic79—22no—
40Dic79⋊C4—24no—
41Dic79⋊C4—24no—
42C22⋊Dic79—24no—
43C22⋊Dic79—44no—
44C4×Dic79—22no—
45C4×Dic79D414yes—
46C24×C79C2312yes—
47C2×D4×C79—22no—
48C2×D4×C79—22no—
49C2×D4×C79Q814yescomplemented
50C22×C4×C79C2312yes—
51C22×C4×C79C2312yes—
52C22×C4×C79C2311yescharacteristic
53C4⋊C4×C79—22no—
54C22⋊C4×C79—44no—
55C42×C79—22no—
56C23×C79—22no—
57C23×C79—24no—
58C23×C79—22no—
59C23×C79—24no—
60C23×C79C2×Q814yes—
61C23×C79C2411yescharacteristic
62D4×C79—28no—
63C2×C4×C79—22no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—24no—
67C2×C4×C79—22no—
68C2×C4×C79C2×D412yes—
69C2×C4×C79C2×Q812yes—
70C2×C4×C79#4112yes—
71C2×Dic79—22no—
72C2×Dic79—22no—
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79—24no—
77C2×Dic79—22no—
78C2×Dic79—24no—
79C2×Dic79—48no—
80C2×Dic79C2×D412yes—
81C2×Dic79C2×D412yes—
82C2×Dic79#4114yes—
83Dic158—48no—
84C22×C79—24no—
85C22×C79—28no—
86C22×C79—42no—
87C22×C79—42no—
88C22×C79—44no—
89C22×C79C22×D411yescharacteristic
90C22×C79C22×Q811yescharacteristic
91C22×C79C2×#4112yes—
92C22×C79C2×#4111yescharacteristic
93C22×C79H(5,𝔽2)12yes—
94C4×C79—42no—
95C4×C79—42no—
96C4×C79C22⋊Q814yes—
97Dic79—22no—
98Dic79—42no—
99Dic79—42no—
100Dic79—42no—
101Dic79#12414yes—
102C2×C79—44no—
103C2×C79C2×C22⋊Q811yescharacteristic
104C2×C79C2×#12411yescharacteristic
105C2×C79#53511yescharacteristic
106C2×C79#55412yes—
107C2×C79#55512yes—
108#2563—791nomaximal, Sylow
109C79#256311yescharacteristic, complemented, Sylow
110C2×C4⋊Q8—791no—
111C2×C4×D4—791no—
112#393—794no—
113#390—791no—
114#390D7911yescharacteristic
115#382—791no—
116#382—791no—
117#380—794no—
118C4×C4⋊C4—791no—
119C22×Q8—792no—
120C22×D4C2×D7911yescharacteristic
121C23×C4—792no—
122C4⋊Q8—1584no—
123C4×D4—1584no—
124C2×C4⋊C4—791no—
125C2×C4⋊C4—792no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4C2×D7911yescharacteristic
129C2×C22⋊C4—794no—
130C2×C22⋊C4—792no—
131C2×C22⋊C4C2×D7914yes—
132C2×C42—791no—
133C2×C42—791no—
134C2×C42C2×D7911yescharacteristic
135#95—792no—
136#95—794no—
137#95—794no—
138C24C22×D7912yes—
139C2×Q8—3164no—
140C2×Q8—1584no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4Dic15814yescomplemented
144C22×C4—791no—
145C22×C4—791no—
146C22×C4—792no—
147C22×C4—792no—
148C22×C4—792no—
149C22×C4—1584no—
150C22×C4—1588no—
151C22×C4C22×D7912yes—
152C22×C4C22×D7912yes—
153C22×C4C22×D7911yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—1584no—
156C4⋊C4—1584no—
157C4⋊C4—1582no—
158C4⋊C4—1582no—
159C22⋊C4—44no—
160C22⋊C4—3164no—
161C22⋊C4—1584no—
162C42—22no—
163C42—794no—
164C42—1582no—
165C23—24no—
166C23—22no—
167C23—24no—
168C23—22no—
169C23C2×Dic15814yes—
170C23C23×D7911yescharacteristic
171Q8—3168no—
172D4—28no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—3168no—
179C2×C4—794no—
180C2×C4—792no—
181C2×C4—792no—
182C2×C4—1582no—
183C2×C4—1584no—
184C2×C4—1582no—
185C2×C4—1582no—
186C2×C4—1584no—
187C2×C4—1582no—
188C2×C4—1582no—
189C2×C4—1582no—
190C2×C4D4×D7912yes—
191C2×C4C2×Dic15812yes—
192C2×C4#1192962312yes—
193C22—28no—
194C22—24no—
195C22—44no—
196C22—42no—
197C22—42no—
198C22C2×D4×D7911yescharacteristic
199C22C22×Dic15811yescharacteristic
200C22#41×D7912yes—
201C22C2×#1192962311yescharacteristic
202C22#1457920612yes—
203C4—42no—
204C4—42no—
205C4—3162no—
206C4—3162no—
207C4—3162no—
208C4—794no—
209C4—1582no—
210C4#1457913814yes—
211C2—44no—
212C2C2×#1457913811yescharacteristic
213C2#124×D7911yescharacteristic
214C2#1909912611yescharacteristic
215C2#1909927212yes—
216C2#1909927712yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#390×C79C2
prime radicalC22×D4×C79C22
hypercenter#390D79
hypocenterC79#2563
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14579160C2semidirect
3. #19098475C2semidirect
5. #19098429C2semidirect
6. #19098428C2semidirect
7. #19098421C2semidirect
8. C4×Dic79⋊C4C2semidirect
49. C2×D4×C79Q8semidirect
109. C79#2563semidirect
143. C2×D4Dic158semidirect