Finite Group Databasebeta

← #23771453

Subgroups — #23771453

Order 10112.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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×#14579151C211yesmaximal, characteristic, complemented
2C2×#14579148C211yesmaximal, characteristic
3#19098499C212yesmaximal, complemented
4#19098491C212yesmaximal, complemented
5#19098486C212yesmaximal, complemented
6#19098486C212yesmaximal, complemented
7#19098484C211yesmaximal, characteristic, complemented
8#19098483C211yesmaximal, characteristic, complemented
9#19098477C211yesmaximal, characteristic
10#19098427C211yesmaximal, characteristic, complemented
11#394×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13#14579151—24no—
14#14579148—24no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×C4⋊Dic79C2212yes—
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2212yes—
22C2×Dic79⋊C4C2212yes—
23C2×C22⋊Dic79C2212yes—
24C2×C22⋊Dic79C2212yes—
25C2×C22⋊Dic79C2212yes—
26C2×C22⋊Dic79C2212yes—
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×D4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2212yes—
35C2×C22⋊C4×C79C2212yes—
36#95×C79C2211yescharacteristic
37C2×Dic158—22no—
38C2×Dic158—42no—
39C22×Dic79C2312yes—
40C22×Dic79C2312yes—
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C4⋊Dic79—22no—
46C4⋊Dic79—42no—
47Dic79⋊C4—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—22no—
50Dic79⋊C4—22no—
51Dic79⋊C4—42no—
52Dic79⋊C4—42no—
53C22⋊Dic79—24no—
54C22⋊Dic79—24no—
55C22⋊Dic79—42no—
56C22⋊Dic79—42no—
57C4×Dic79D414yes—
58C24×C79C2312yes—
59C2×D4×C79—22no—
60C2×D4×C79—42no—
61C22×C4×C79C2312yes—
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2311yescharacteristic
65C4⋊C4×C79—22no—
66C22⋊C4×C79—42no—
67C22⋊C4×C79—42no—
68C23×C79—22no—
69C23×C79—22no—
70C23×C79—22no—
71C23×C79—22no—
72C23×C79—22no—
73C23×C79—22no—
74C23×C79—22no—
75C23×C79C2411yescharacteristic
76D4×C79—44no—
77C2×C4×C79—22no—
78C2×C4×C79—21no—
79C2×C4×C79—21no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—22no—
83C2×C4×C79—21no—
84C2×C4×C79—21no—
85C2×C4×C79—22no—
86C2×C4×C79C2×D412yes—
87C2×Dic79—21no—
88C2×Dic79—22no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—21no—
92C2×Dic79—21no—
93C2×Dic79—21no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—21no—
100C2×Dic79—22no—
101C2×Dic79C2×D412yes—
102C2×Dic79C2×D412yes—
103Dic158—44no—
104C22×C79—42no—
105C22×C79—42no—
106C22×C79—42no—
107C22×C79—42no—
108C22×C79—42no—
109C22×C79—42no—
110C22×C79—42no—
111C22×C79C22×D411yescharacteristic
112C22×C79H(5,𝔽2)12yes—
113C22×C79H(5,𝔽2)11yescharacteristic
114C22×C792−1+412yes—
115C22×C792−1+411yescharacteristic
116C4×C79—22no—
117C4×C79—41no—
118C4×C79—41no—
119C4×C79—42no—
120Dic79—22no—
121Dic79—22no—
122Dic79—42no—
123Dic79—41no—
124Dic79—41no—
125Dic79—42no—
126C2×C79—82no—
127C2×C79#53511yescharacteristic
128C2×C79#53611yescharacteristic
129C2×C79#53711yescharacteristic
130C2×C79#56212yes—
131C2×C79#56312yes—
132#2820—791nomaximal, Sylow
133C79#282011yescharacteristic, complemented, Sylow
134C2×#125—791no—
135C2×#124—791no—
136#399—792no—
137#397—792no—
138#396—792no—
139#396—792no—
140#395—791no—
141#395—791no—
142#394—791no—
143#394D7911yescharacteristic
144#382—791no—
145C22×Q8—791no—
146C22×D4C2×D7911yescharacteristic
147#125—1584no—
148#124—1584no—
149C2×C4⋊C4—792no—
150C2×C4⋊C4—792no—
151C2×C4⋊C4—792no—
152C2×C4⋊C4—791no—
153C2×C4⋊C4—791no—
154C2×C4⋊C4—791no—
155C2×C4⋊C4—791no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4C2×D7911yescharacteristic
158C2×C22⋊C4—792no—
159C2×C22⋊C4—792no—
160C2×C22⋊C4—792no—
161C2×C22⋊C4—792no—
162C2×C22⋊C4C2×D7912yes—
163C2×C22⋊C4C2×D7912yes—
164C2×C42—791no—
165#95—791no—
166#95—792no—
167#95—792no—
168#95—792no—
169#95C2×D7911yescharacteristic
170C24C22×D7912yes—
171C2×Q8—3162no—
172C2×Q8—1582no—
173C2×D4—22no—
174C2×D4—42no—
175C22×C4—791no—
176C22×C4—791no—
177C22×C4—792no—
178C22×C4—791no—
179C22×C4—792no—
180C22×C4—791no—
181C22×C4C22×D7912yes—
182C22×C4C22×D7911yescharacteristic
183C22×C4C22×D7911yescharacteristic
184C22×C4C22×D7911yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—3162no—
187C4⋊C4—3162no—
188C4⋊C4—3162no—
189C4⋊C4—1582no—
190C4⋊C4—1582no—
191C4⋊C4—1582no—
192C4⋊C4—1582no—
193C4⋊C4—1582no—
194C22⋊C4—42no—
195C22⋊C4—42no—
196C22⋊C4—3162no—
197C22⋊C4—3162no—
198C22⋊C4—1584no—
199C22⋊C4—1584no—
200C42—794no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23—22no—
208C23C23×D7911yescharacteristic
209Q8—3164no—
210D4—44no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—792no—
221C2×C4—792no—
222C2×C4—1581no—
223C2×C4—1582no—
224C2×C4—1582no—
225C2×C4—1582no—
226C2×C4—1582no—
227C2×C4—1582no—
228C2×C4—1581no—
229C2×C4—1582no—
230C2×C4—1582no—
231C2×C4—1581no—
232C2×C4—1581no—
233C2×C4—1581no—
234C2×C4—1581no—
235C2×C4—1582no—
236C2×C4D4×D7912yes—
237C22—42no—
238C22—42no—
239C22—42no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D7911yescharacteristic
245C22#1457920611yescharacteristic
246C22#1457920612yes—
247C22#1457920811yescharacteristic
248C22#1457920812yes—
249C4—22no—
250C4—41no—
251C4—42no—
252C4—41no—
253C4—3161no—
254C4—3162no—
255C4—3162no—
256C4—3161no—
257C4—1582no—
258C4—1582no—
259C2—82no—
260C2#1909912811yescharacteristic
261C2#1909913311yescharacteristic
262C2#1909914211yescharacteristic
263C2#1909930812yes—
264C2#1909931612yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC22×D4×C79C22
hypercenter#394D79
hypocenterC79#2820
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14579151C2semidirect
3. #19098499C2semidirect
4. #19098491C2semidirect
5. #19098486C2semidirect
6. #19098486C2semidirect
7. #19098484C2semidirect
8. #19098483C2semidirect
10. #19098427C2semidirect
133. C79#2820semidirect