Finite Group Databasebeta

← #23771463

Subgroups — #23771463

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×#14579160C211yesmaximal, characteristic, complemented
2C2×#14579154C211yesmaximal, characteristic
3#19098503C211yesmaximal, characteristic, complemented
4#19098501C211yesmaximal, characteristic, complemented
5#19098499C211yesmaximal, characteristic
6#19098496C212yesmaximal, complemented
7#19098491C212yesmaximal
8#19098483C212yesmaximal, complemented
9#19098475C212yesmaximal
10#19098430C211yesmaximal, characteristic, complemented
11#399×C79C211yesmaximal, characteristic
12C22×Dic158C2212yes—
13#14579160—24no—
14#14579154—24no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2212yes—
21C2×C22⋊Dic79C2211yescharacteristic
22C2×C22⋊Dic79C2211yescharacteristic
23C2×C22⋊Dic79C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2212yes—
26C79⋊#95C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2212yes—
34C2×C22⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2212yes—
36#95×C79C2211yescharacteristic
37C2×Dic158—24no—
38C2×Dic158—42no—
39C2×Dic158—42no—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C4⋊Dic79—22no—
47C4⋊Dic79—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—24no—
50Dic79⋊C4—22no—
51Dic79⋊C4—42no—
52C22⋊Dic79—22no—
53C22⋊Dic79—22no—
54C22⋊Dic79—42no—
55C4×Dic79D414yes—
56C24×C79C2311yescharacteristic
57C22×C4×C79C2312yes—
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C4⋊C4×C79—22no—
62C4⋊C4×C79—42no—
63C22⋊C4×C79—22no—
64C22⋊C4×C79—42no—
65C23×C79—21no—
66C23×C79—22no—
67C23×C79—21no—
68C23×C79—22no—
69C23×C79—21no—
70C23×C79C2411yescharacteristic
71C2×C4×C79—22no—
72C2×C4×C79—21no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79C2×D412yes—
81C2×Dic79—22no—
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79—21no—
85C2×Dic79—21no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—21no—
92C2×Dic79—22no—
93C2×Dic79—21no—
94C2×Dic79—22no—
95C2×Dic79C2×D412yes—
96C2×Dic79C2×D412yes—
97Dic158—48no—
98C22×C79—41no—
99C22×C79—41no—
100C22×C79—41no—
101C22×C79—42no—
102C22×C79—42no—
103C22×C79C22×D411yescharacteristic
104C22×C79H(5,𝔽2)12yes—
105C22×C792−1+411yescharacteristic
106C22×C792−1+412yes—
107C22×C792−1+411yescharacteristic
108C4×C79—22no—
109C4×C79—41no—
110C4×C79—42no—
111C4×C79—42no—
112Dic79—22no—
113Dic79—22no—
114Dic79—42no—
115Dic79—41no—
116Dic79—41no—
117Dic79—42no—
118C2×C79—81no—
119C2×C79#53511yescharacteristic
120C2×C79#53611yescharacteristic
121C2×C79#53611yescharacteristic
122C2×C79#56312yes—
123C2×C79#56312yes—
124#2821—791nomaximal, Sylow
125C79#282111yescharacteristic, complemented, Sylow
126C2×C4⋊Q8—791no—
127C2×#126—791no—
128#400—791no—
129#400—791no—
130#399—791no—
131#399D7911yescharacteristic
132#398—792no—
133#397—792no—
134#395—792no—
135#393—792no—
136#383—791no—
137C22×Q8—792no—
138C4⋊Q8—1584no—
139#126—1584no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—791no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4—792no—
145C2×C4⋊C4—791no—
146C2×C4⋊C4C2×D7911yescharacteristic
147C2×C4⋊C4C2×D7912yes—
148C2×C22⋊C4—792no—
149C2×C22⋊C4—791no—
150C2×C22⋊C4—791no—
151C2×C22⋊C4C2×D7911yescharacteristic
152C2×C22⋊C4C2×D7912yes—
153C2×C42—791no—
154#95—792no—
155#95—792no—
156#95—791no—
157#95—792no—
158#95—792no—
159#95—792no—
160#95—792no—
161#95C2×D7911yescharacteristic
162C24C22×D7911yescharacteristic
163C2×Q8—3162no—
164C2×Q8—3162no—
165C2×Q8—1584no—
166C22×C4—791no—
167C22×C4—791no—
168C22×C4—792no—
169C22×C4—791no—
170C22×C4—791no—
171C22×C4—792no—
172C22×C4C22×D7912yes—
173C22×C4C22×D7912yes—
174C22×C4C22×D7911yescharacteristic
175C22×C4C22×D7911yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—3162no—
179C4⋊C4—1582no—
180C4⋊C4—1584no—
181C4⋊C4—1582no—
182C4⋊C4—1582no—
183C4⋊C4—1582no—
184C22⋊C4—22no—
185C22⋊C4—42no—
186C22⋊C4—3162no—
187C22⋊C4—1582no—
188C22⋊C4—1582no—
189C42—794no—
190C23—22no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23—21no—
195C23C23×D7911yescharacteristic
196Q8—3168no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—792no—
207C2×C4—792no—
208C2×C4—1582no—
209C2×C4—1582no—
210C2×C4—1582no—
211C2×C4—1581no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1581no—
215C2×C4—1582no—
216C2×C4—1581no—
217C2×C4—1581no—
218C2×C4—1582no—
219C2×C4—1582no—
220C2×C4—1581no—
221C2×C4—1581no—
222C2×C4D4×D7912yes—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—41no—
227C22—41no—
228C22C2×D4×D7911yescharacteristic
229C22#1457920612yes—
230C22#1457920811yescharacteristic
231C22#1457920812yes—
232C22#1457920911yescharacteristic
233C4—22no—
234C4—42no—
235C4—42no—
236C4—41no—
237C4—3161no—
238C4—3162no—
239C4—3162no—
240C4—3161no—
241C4—1582no—
242C4—1582no—
243C2—81no—
244C2#1909912611yescharacteristic
245C2#1909913511yescharacteristic
246C2#1909913611yescharacteristic
247C2#1909931412yes—
248C2#1909931612yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#399×C79C2
prime radicalC24×C79C23
hypercenter#399D79
hypocenterC79#2821
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14579160C2semidirect
3. #19098503C2semidirect
4. #19098501C2semidirect
6. #19098496C2semidirect
8. #19098483C2semidirect
10. #19098430C2semidirect
125. C79#2821semidirect