Finite Group Databasebeta

← #23771464

Subgroups — #23771464

Order 10112.

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

normal subgroups only

This group has 430 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×#14579159C211yesmaximal, characteristic, complemented
2C2×#14579156C211yesmaximal, characteristic
3#19098504C212yesmaximal, complemented
4#19098498C212yesmaximal
5#19098496C212yesmaximal, complemented
6#19098492C212yesmaximal
7#19098483C211yesmaximal, characteristic, complemented
8#19098476C211yesmaximal, characteristic
9#19098474C211yesmaximal, characteristic
10#19098430C211yesmaximal, characteristic, complemented
11#395×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13#14579159—24no—
14#14579156—24no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C2×(C2×D79)⋊C4C2211yescharacteristic
21C2×(C2×D79)⋊C4C2211yescharacteristic
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×C4×Dic79C2211yescharacteristic
26C79⋊#95C2211yescharacteristic
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×Q8×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C2×Dic158—22no—
39C2×Dic158—42no—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C4⋊Dic79—22no—
46Dic79⋊C4—22no—
47Dic79⋊C4—24no—
48Dic79⋊C4—24no—
49Dic79⋊C4—42no—
50(C2×D79)⋊C4—22no—
51(C2×D79)⋊C4—22no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—42no—
54(C2×D79)⋊C4—42no—
55C4×Dic79D414yes—
56C2×Q8×C79—22no—
57C2×Q8×C79—42no—
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2311yescharacteristic
63C4⋊C4×C79—22no—
64C4⋊C4×C79—42no—
65C23×C79C2411yescharacteristic
66C22×D79—21no—
67C22×D79—22no—
68C22×D79—21no—
69C22×D79—21no—
70C22×D79—22no—
71Q8×C79—44no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—21no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79C2×D412yes—
85C2×Dic79—21no—
86C2×Dic79—21no—
87C2×Dic79—22no—
88C2×Dic79—21no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79C2×D412yes—
97C2×Dic79C2×D412yes—
98Dic158—44no—
99C22×C79C22×D411yescharacteristic
100C22×C79H(5,𝔽2)12yes—
101C22×C792−1+411yescharacteristic
102C22×C792−1+411yescharacteristic
103C22×C792−1+412yes—
104C2×D79—41no—
105C2×D79—41no—
106C2×D79—41no—
107C2×D79—42no—
108C2×D79—42no—
109C4×C79—22no—
110C4×C79—41no—
111C4×C79—42no—
112C4×C79—41no—
113C4×C79—42no—
114Dic79—22no—
115Dic79—22no—
116Dic79—42no—
117Dic79—41no—
118Dic79—42no—
119C2×C79#53511yescharacteristic
120C2×C79#53611yescharacteristic
121C2×C79#53611yescharacteristic
122C2×C79#56312yes—
123C2×C79#56312yes—
124D79—81no—
125#2821—791nomaximal, Sylow
126C79#282111yescharacteristic, complemented, Sylow
127C2×C4⋊Q8—791no—
128C2×#126—791no—
129#400—792no—
130#399—792no—
131#398—792no—
132#397—792no—
133#395—791no—
134#395D7911yescharacteristic, complemented
135#393—791no—
136#393—791no—
137#383—791no—
138C22×Q8—791no—
139C22×Q8C2×D7911yescharacteristic
140C4⋊Q8—1584no—
141#126—1584no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4—791no—
145C2×C4⋊C4—792no—
146C2×C4⋊C4—792no—
147C2×C4⋊C4C2×D7911yescharacteristic
148C2×C4⋊C4C2×D7912yes—
149C2×C22⋊C4—792no—
150C2×C22⋊C4—792no—
151C2×C22⋊C4—791no—
152C2×C22⋊C4—791no—
153C2×C22⋊C4—791no—
154C2×C42—791no—
155#95—791no—
156#95—792no—
157#95—792no—
158#95—792no—
159#95—792no—
160#95—792no—
161#95C2×D7911yescharacteristic
162#95C2×D7912yes—
163C24—791no—
164C2×Q8—22no—
165C2×Q8—42no—
166C2×Q8—3162no—
167C2×Q8—1582no—
168C22×C4—791no—
169C22×C4—791no—
170C22×C4—792no—
171C22×C4—791no—
172C22×C4—792no—
173C22×C4C22×D7912yes—
174C22×C4C22×D7911yescharacteristic
175C22×C4C22×D7912yes—
176C22×C4C22×D7911yescharacteristic
177C22×C4C22×D7911yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—42no—
180C4⋊C4—3162no—
181C4⋊C4—1582no—
182C4⋊C4—1584no—
183C4⋊C4—1584no—
184C4⋊C4—1582no—
185C22⋊C4—3162no—
186C22⋊C4—3162no—
187C22⋊C4—1582no—
188C22⋊C4—1582no—
189C22⋊C4—1582no—
190C42—794no—
191C23—1582no—
192C23—1581no—
193C23—1581no—
194C23—1582no—
195C23—1581no—
196C23C23×D7911yescharacteristic
197Q8—44no—
198Q8—3164no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—792no—
212C2×C4—792no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4—1582no—
219C2×C4—1581no—
220C2×C4—1582no—
221C2×C4—1581no—
222C2×C4—1581no—
223C2×C4—1582no—
224C2×C4D4×D7912yes—
225C22—3161no—
226C22—3161no—
227C22—3162no—
228C22—3162no—
229C22—3161no—
230C22C2×D4×D7911yescharacteristic
231C22#1457920612yes—
232C22#1457920811yescharacteristic
233C22#1457920911yescharacteristic
234C22#1457920912yes—
235C4—22no—
236C4—41no—
237C4—42no—
238C4—42no—
239C4—41no—
240C4—3161no—
241C4—3162no—
242C4—3162no—
243C4—1582no—
244C4—1582no—
245C2—6321no—
246C2#1909912811yescharacteristic
247C2#1909913611yescharacteristic
248C2#1909913811yescharacteristic
249C2#1909931212yes—
250C2#1909931412yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#395×C79C2
prime radicalC23×D79C23
hypercenter#395D79
hypocenterC79#2821
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C2×#14579159C2semidirect
3. #19098504C2semidirect
5. #19098496C2semidirect
7. #19098483C2semidirect
10. #19098430C2semidirect
11. #395×C79C2semidirect
126. C79#2821semidirect
134. #395D79semidirect