Finite Group Databasebeta

← #23771460

Subgroups — #23771460

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×#14579156C211yesmaximal, characteristic
3#19098505C212yesmaximal, complemented
4#19098498C212yesmaximal
5#19098493C211yesmaximal, characteristic, complemented
6#19098490C211yesmaximal, characteristic
7#19098489C211yesmaximal, characteristic
8#19098483C212yesmaximal, complemented
9#19098476C212yesmaximal
10#19098430C211yesmaximal, characteristic, complemented
11#398×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2212yes—
13#14579160—24no—
14#14579156—24no—
15C2×C4⋊Dic79C2211yescharacteristic
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
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⋊#95C2212yes—
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C2×Dic158—24no—
39C2×Dic158—42no—
40C2×Dic158—42no—
41C22×Dic79C2312yes—
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C22×Dic79C2311yescharacteristic
46C4⋊Dic79—22no—
47C4⋊Dic79—22no—
48Dic79⋊C4—22no—
49Dic79⋊C4—24no—
50Dic79⋊C4—42no—
51(C2×D79)⋊C4—22no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—22no—
54(C2×D79)⋊C4—42no—
55(C2×D79)⋊C4—42no—
56C4×Dic79D414yes—
57C22×C4×C79C2312yes—
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2311yescharacteristic
61C22×C4×C79C2311yescharacteristic
62C4⋊C4×C79—22no—
63C4⋊C4×C79—22no—
64C4⋊C4×C79—42no—
65C23×C79C2411yescharacteristic
66C22×D79—21no—
67C22×D79—21no—
68C22×D79—21no—
69C22×D79—22no—
70C22×D79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—21no—
73C2×C4×C79—21no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—21no—
78C2×C4×C79—22no—
79C2×C4×C79—21no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—22no—
83C2×C4×C79C2×D412yes—
84C2×Dic79—21no—
85C2×Dic79—21no—
86C2×Dic79—22no—
87C2×Dic79—21no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—22no—
95C2×Dic79C2×D412yes—
96C2×Dic79C2×D412yes—
97Dic158—48no—
98C22×C79C22×D411yescharacteristic
99C22×C79H(5,𝔽2)11yescharacteristic
100C22×C79H(5,𝔽2)11yescharacteristic
101C22×C792−1+412yes—
102C22×C792−1+412yes—
103C2×D79—41no—
104C2×D79—41no—
105C2×D79—41no—
106C2×D79—42no—
107C2×D79—42no—
108C4×C79—22no—
109C4×C79—41no—
110C4×C79—42no—
111C4×C79—41no—
112C4×C79—42no—
113Dic79—22no—
114Dic79—22no—
115Dic79—42no—
116Dic79—41no—
117Dic79—42no—
118C2×C79#53511yescharacteristic
119C2×C79#53611yescharacteristic
120C2×C79#53611yescharacteristic
121C2×C79#56312yes—
122C2×C79#56312yes—
123D79—81no—
124#2821—791nomaximal, Sylow
125C79#282111yescharacteristic, complemented, Sylow
126C2×C4⋊Q8—791no—
127C2×#126—791no—
128#400—792no—
129#399—792no—
130#398—791no—
131#398D7911yescharacteristic, complemented
132#397—791no—
133#397—791no—
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⋊C4C2×D7911yescharacteristic
146C2×C4⋊C4C2×D7911yescharacteristic
147C2×C4⋊C4C2×D7912yes—
148C2×C22⋊C4—792no—
149C2×C22⋊C4—792no—
150C2×C22⋊C4—791no—
151C2×C22⋊C4—791no—
152C2×C22⋊C4—791no—
153C2×C42—791no—
154#95—792no—
155#95—791no—
156#95—792no—
157#95—792no—
158#95—792no—
159#95—792no—
160#95C2×D7911yescharacteristic
161#95C2×D7912yes—
162C24—791no—
163C2×Q8—3162no—
164C2×Q8—3162no—
165C2×Q8—1584no—
166C22×C4—791no—
167C22×C4—791no—
168C22×C4—792no—
169C22×C4—791no—
170C22×C4—792no—
171C22×C4C22×D7912yes—
172C22×C4C22×D7911yescharacteristic
173C22×C4C22×D7912yes—
174C22×C4C22×D7911yescharacteristic
175C22×C4C22×D7911yescharacteristic
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—3162no—
180C4⋊C4—1582no—
181C4⋊C4—1584no—
182C4⋊C4—1582no—
183C4⋊C4—1582no—
184C22⋊C4—3162no—
185C22⋊C4—3162no—
186C22⋊C4—1582no—
187C22⋊C4—1582no—
188C22⋊C4—1582no—
189C42—794no—
190C23—1581no—
191C23—1581no—
192C23—1582no—
193C23—1582no—
194C23—1581no—
195C23C23×D7911yescharacteristic
196Q8—3168no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—792no—
210C2×C4—792no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1582no—
217C2×C4—1581no—
218C2×C4—1582no—
219C2×C4—1581no—
220C2×C4—1581no—
221C2×C4—1582no—
222C2×C4D4×D7912yes—
223C22—3161no—
224C22—3162no—
225C22—3162no—
226C22—3161no—
227C22—3161no—
228C22C2×D4×D7911yescharacteristic
229C22#1457920611yescharacteristic
230C22#1457920711yescharacteristic
231C22#1457920812yes—
232C22#1457920912yes—
233C4—22no—
234C4—42no—
235C4—42no—
236C4—41no—
237C4—41no—
238C4—3161no—
239C4—3162no—
240C4—3162no—
241C4—1582no—
242C4—1582no—
243C2—6321no—
244C2#1909912911yescharacteristic
245C2#1909913511yescharacteristic
246C2#1909913811yescharacteristic
247C2#1909931412yes—
248C2#1909931712yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC23×D79C23
hypercenter#398D79
hypocenterC79#2821
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14579160C2semidirect
3. #19098505C2semidirect
5. #19098493C2semidirect
8. #19098483C2semidirect
10. #19098430C2semidirect
11. #398×C79C2semidirect
125. C79#2821semidirect
131. #398D79semidirect