Finite Group Databasebeta

← #23768425

Subgroups — #23768425

Order 10112.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14579160C212yesmaximal
2C2×#14579159C212yesmaximal
3#19098484C212yesmaximal
4#19098483C211yesmaximal, characteristic
5#19098460C212yesmaximal
6#19098458C212yesmaximal
7#19098432C211yesmaximal, characteristic
8#19098414C212yesmaximal
9#395×C79C211yesmaximal, characteristic
10C22×Dic158C2211yescharacteristic
11C22×Dic158C2212yes—
12#14579160—28no—
13#14579159—28no—
14C2×C4⋊Dic79C2212yes—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2212yes—
22C2×C4×Dic79C2212yes—
23C2×C4×Dic79C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2211yescharacteristic
27C79⋊#95C2212yes—
28C22×Q8×C79C2211yescharacteristic
29C2×C4⋊C4×C79C2212yes—
30C2×C4⋊C4×C79C2211yescharacteristic
31#95×C79C2212yes—
32#95×C79C2211yescharacteristic
33C2×Dic158—24no—
34C2×Dic158—24no—
35C2×Dic158—24no—
36C2×Dic158—42no—
37C2×Dic158—41no—
38C22×Dic79C2312yes—
39C22×Dic79C2312yes—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C4⋊Dic79—24no—
43C4⋊Dic79—41no—
44Dic79⋊C4—24no—
45Dic79⋊C4—24no—
46Dic79⋊C4—24no—
47Dic79⋊C4—24no—
48Dic79⋊C4D418yes—
49Dic79⋊C4Q818yescomplemented
50C4×Dic79—24no—
51C4×Dic79—24no—
52C4×Dic79Q814yescomplemented
53C2×Q8×C79—24no—
54C2×Q8×C79—41no—
55C22×C4×C79C2311yescharacteristic
56C22×C4×C79C2311yescharacteristic
57C22×C4×C79C2312yes—
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2312yes—
60C4⋊C4×C79—24no—
61C4⋊C4×C79—41no—
62C23×C79C2411yescharacteristic
63Q8×C79—44no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—21no—
67C2×C4×C79—22no—
68C2×C4×C79—21no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—21no—
73C2×C4×C79—21no—
74C2×C4×C79C2×D414yes—
75C2×C4×C79C2×Q812yes—
76C2×C4×C79C2×Q814yes—
77C2×Dic79—22no—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79C2×D414yes—
85C2×Dic79C2×D414yes—
86C2×Dic79C2×Q814yes—
87C2×Dic79C2×Q814yes—
88C2×Dic79C2×Q814yes—
89Dic158—44no—
90Dic158—48no—
91C22×C79C22×D412yes—
92C22×C79C22×Q811yescharacteristic
93C22×C79C22×Q812yes—
94C22×C79H(5,𝔽2)11yescharacteristic
95C22×C792−1+411yescharacteristic
96C4×C79—22no—
97C4×C79—24no—
98C4×C79—24no—
99C4×C79—41no—
100C4×C79—41no—
101Dic79—24no—
102Dic79—24no—
103Dic79—42no—
104Dic79C4⋊Q818yescomplemented
105C2×C79C2×C4⋊Q812yes—
106C2×C79#54411yescharacteristic
107C2×C79D4211yescharacteristic
108C2×C79D4×Q812yes—
109C2×C79Q8211yescharacteristic
110#2551—791nomaximal, Sylow
111C79#255111yescharacteristic, complemented, Sylow
112C2×C4⋊Q8—792no—
113C2×C4⋊Q8—792no—
114#395—791no—
115#395—792no—
116#395D7911yescharacteristic
117#389—792no—
118#389—792no—
119#384—791no—
120C4×C4⋊C4—792no—
121C22×Q8—791no—
122C22×Q8—792no—
123C22×Q8C2×D7911yescharacteristic
124C4⋊Q8—1588no—
125C4⋊Q8—1588no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—792no—
129C2×C4⋊C4—792no—
130C2×C4⋊C4—792no—
131C2×C4⋊C4—792no—
132C2×C4⋊C4—792no—
133C2×C4⋊C4—792no—
134C2×C4⋊C4C2×D7912yes—
135C2×C4⋊C4C2×D7911yescharacteristic
136C2×C42—791no—
137C2×C42—792no—
138C2×C42—792no—
139#95—792no—
140#95—791no—
141#95—792no—
142#95C2×D7912yes—
143#95C2×D7911yescharacteristic
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—3162no—
147C2×Q8—3161no—
148C2×Q8—1584no—
149C2×Q8—1584no—
150C2×Q8—1584no—
151C22×C4—792no—
152C22×C4—792no—
153C22×C4—792no—
154C22×C4—792no—
155C22×C4C22×D7911yescharacteristic
156C22×C4C22×D7911yescharacteristic
157C22×C4C22×D7912yes—
158C22×C4C22×D7911yescharacteristic
159C22×C4C22×D7912yes—
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—3161no—
163C4⋊C4—798no—
164C4⋊C4—798no—
165C4⋊C4—1584no—
166C4⋊C4—1584no—
167C4⋊C4—1584no—
168C4⋊C4—1584no—
169C4⋊C4—1584no—
170C42—794no—
171C42—1584no—
172C42—1584no—
173C23C23×D7911yescharacteristic
174Q8—44no—
175Q8—3168no—
176Q8—3164no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—794no—
188C2×C4—794no—
189C2×C4—794no—
190C2×C4—794no—
191C2×C4—794no—
192C2×C4—1582no—
193C2×C4—1582no—
194C2×C4—1582no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4D4×D7914yes—
200C2×C4Q8×D7912yes—
201C2×C4Q8×D7914yes—
202C22C2×D4×D7912yes—
203C22C2×Q8×D7911yescharacteristic
204C22C2×Q8×D7912yes—
205C22#1457920611yescharacteristic
206C22#1457920811yescharacteristic
207C4—22no—
208C4—24no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—3162no—
213C4—798no—
214C4—1584no—
215C4—1584no—
216C2C4⋊Q8×D7912yes—
217C2#1909919211yescharacteristic
218C2#1909919511yescharacteristic
219C2#1909922612yes—
220C2#1909929311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, prime radical, cosocleC23×C79C24
Fitting#395×C79C2
hypercenter#395D79
hypocenterC79#2551
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
49. Dic79⋊C4Q8semidirect
52. C4×Dic79Q8semidirect
104. Dic79C4⋊Q8semidirect
111. C79#2551semidirect