Finite Group Databasebeta

← #23769183

Subgroups — #23769183

Order 10112.

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

normal subgroups only

This group has 526 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×#14579144C211yesmaximal, characteristic
2C22×C4⋊Dic79C211yesmaximal, characteristic, complemented
3#19098503C212yesmaximal, complemented
4#19098500C212yesmaximal, complemented
5#19098495C212yesmaximal, complemented
6#19098490C212yesmaximal, complemented
7#19098440C212yesmaximal
8#19098438C212yesmaximal, complemented
9#381×C79C211yesmaximal, characteristic, complemented
10C22×C22⋊D79C2211yescharacteristic
11C23×Dic79C2212yes—
12#14579144—24no—
13C2×C4⋊Dic79—24no—
14C2×C4⋊Dic79C2212yes—
15C2×C4⋊Dic79C2212yes—
16C2×C4⋊Dic79C2214yes—
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×C22⋊Dic79C2211yescharacteristic
20C2×(C2×D79)⋊C4C2211yescharacteristic
21C2×(C2×D79)⋊C4C2211yescharacteristic
22C2×(C2×D79)⋊C4C2214yes—
23C79⋊#95C2214yes—
24C79⋊#95C2214yes—
25C23×C4×C79C2211yescharacteristic
26C2×C22⋊C4×C79C2212yes—
27#95×C79C2212yes—
28#95×C79C2212yes—
29C23×D79C2311yescharacteristic
30C2×C22⋊D79—22no—
31C2×C22⋊D79—24no—
32C22×Dic79—24no—
33C22×Dic79—44no—
34C22×Dic79C2311yescharacteristic
35C22×Dic79C2311yescharacteristic
36C22×Dic79C2314yes—
37C22×Dic79C2311yescharacteristic
38C4⋊Dic79—24no—
39C4⋊Dic79—24no—
40C4⋊Dic79—44no—
41Dic79⋊C4—22no—
42Dic79⋊C4—22no—
43C22⋊Dic79—22no—
44(C2×D79)⋊C4—22no—
45(C2×D79)⋊C4—22no—
46(C2×D79)⋊C4—44no—
47C24×C79C2311yescharacteristic
48C22×C4×C79—24no—
49C22×C4×C79D414yes—
50C22×C4×C79C2314yes—
51C22×C4×C79C2311yescharacteristic
52C22×C4×C79C2311yescharacteristic
53C22⋊C4×C79—24no—
54C23×C79—22no—
55C23×C79—22no—
56C23×C79C2×D412yes—
57C23×C79#4114yes—
58C23×C79C2411yescharacteristic
59C22×D79—21no—
60C22×D79—22no—
61C22×D79—22no—
62C22×D79—22no—
63C2×C4×C79—28no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—24no—
67C2×C4×C79—24no—
68C2×C4×C79—24no—
69C2×C4×C79C2×D412yes—
70C2×C4×C79C2×D412yes—
71C22⋊D79—44no—
72C2×Dic79—21no—
73C2×Dic79—21no—
74C2×Dic79—21no—
75C2×Dic79—24no—
76C2×Dic79—22no—
77C2×Dic79—24no—
78C2×Dic79—22no—
79C2×Dic79—24no—
80C2×Dic79—22no—
81C2×Dic79—48no—
82C22×C79—22no—
83C22×C79—22no—
84C22×C79—28no—
85C22×C79#12314yes—
86C22×C79C22×D411yescharacteristic
87C22×C79C2×#4112yes—
88C22×C79H(5,𝔽2)12yes—
89C22×C792−1+412yes—
90C2×D79—41no—
91C2×D79—41no—
92C2×D79—41no—
93C2×D79—44no—
94C4×C79—22no—
95C4×C79—22no—
96C4×C79—44no—
97Dic79—41no—
98Dic79—41no—
99Dic79—44no—
100Dic79—41no—
101C2×C79—24no—
102C2×C79C2×#12311yescharacteristic
103C2×C79#53511yescharacteristic
104C2×C79#53611yescharacteristic
105C2×C79#53914yes—
106D79—81no—
107#2623—791nomaximal, Sylow
108C79#262311yescharacteristic, complemented, Sylow
109C2×#123—791no—
110C22×C4⋊C4—791no—
111#400—792no—
112#399—792no—
113#398—792no—
114#397—792no—
115#386—792no—
116#385—792no—
117#381D7911yescharacteristic, complemented
118C22×D4—791no—
119C23×C4—792no—
120C23×C4C2×D7911yescharacteristic
121#123—1584no—
122C2×C4⋊C4—794no—
123C2×C4⋊C4—792no—
124C2×C4⋊C4—792no—
125C2×C4⋊C4—791no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—1584no—
128C2×C22⋊C4—794no—
129C2×C22⋊C4—791no—
130C2×C22⋊C4—791no—
131C2×C22⋊C4—791no—
132C2×C22⋊C4C2×D7912yes—
133#95—794no—
134#95—794no—
135#95C2×D7912yes—
136#95C2×D7912yes—
137C24—791no—
138C24C22×D7911yescharacteristic
139C2×D4—1582no—
140C2×D4—1584no—
141C22×C4—24no—
142C22×C4—3164no—
143C22×C4—791no—
144C22×C4—791no—
145C22×C4—794no—
146C22×C4—791no—
147C22×C4—1584no—
148C22×C4D31614yes—
149C22×C4C22×D7914yes—
150C22×C4C22×D7911yescharacteristic
151C22×C4C22×D7911yescharacteristic
152C4⋊C4—3164no—
153C4⋊C4—1582no—
154C4⋊C4—1582no—
155C4⋊C4—1584no—
156C4⋊C4—1584no—
157C22⋊C4—24no—
158C22⋊C4—3164no—
159C22⋊C4—1582no—
160C22⋊C4—1582no—
161C22⋊C4—1582no—
162C23—22no—
163C23—22no—
164C23—1582no—
165C23—1582no—
166C23—1582no—
167C23—1581no—
168C23C2×D31612yes—
169C23#1192962314yes—
170C23C23×D7911yescharacteristic
171D4—3164no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—28no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—3168no—
179C2×C4—1582no—
180C2×C4—1584no—
181C2×C4—1582no—
182C2×C4—1584no—
183C2×C4—1582no—
184C2×C4—1581no—
185C2×C4—1581no—
186C2×C4—1584no—
187C2×C4—1581no—
188C2×C4C2×D31612yes—
189C2×C4C2×D31612yes—
190C22—22no—
191C22—28no—
192C22—22no—
193C22—3161no—
194C22—3164no—
195C22—3161no—
196C22—3161no—
197C22#1457914514yes—
198C22C22×D31611yescharacteristic
199C22C2×#1192962312yes—
200C22#1457920712yes—
201C22#1457920812yes—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—3161no—
206C4—3161no—
207C4—3164no—
208C4—3161no—
209C2—24no—
210C2—6321no—
211C2C2×#1457914511yescharacteristic
212C2#1909913211yescharacteristic
213C2#1909913911yescharacteristic
214C2#1909915714yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#381×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#381D79
hypocenterC79#2623
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic79C2semidirect
3. #19098503C2semidirect
4. #19098500C2semidirect
5. #19098495C2semidirect
6. #19098490C2semidirect
8. #19098438C2semidirect
9. #381×C79C2semidirect
108. C79#2623semidirect
117. #381D79semidirect