Finite Group Databasebeta

← #23769561

Subgroups — #23769561

Order 10112.

434 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 137 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×#14579155C211yesmaximal, characteristic
2#19098501C211yesmaximal, characteristic, complemented
3#19098498C211yesmaximal, characteristic
4#19098496C212yesmaximal, complemented
5#19098494C211yesmaximal, characteristic, complemented
6#19098489C211yesmaximal, characteristic
7#19098485C212yesmaximal
8#19098458C212yesmaximal, complemented
9#19098453C212yesmaximal
10C4×C4⋊Dic79C211yesmaximal, characteristic, complemented
11C2×#125×C79C211yesmaximal, characteristic, complemented
12#14579155—24no—
13C2×C4⋊Dic79C2212yes—
14C2×Dic79⋊C4C2211yescharacteristic
15C2×Dic79⋊C4C2212yes—
16C2×Dic79⋊C4C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2211yescharacteristic
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2211yescharacteristic
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2212yes—
24C2×C4×Dic79C2212yes—
25C79⋊#95C2211yescharacteristic
26C79⋊#95C2211yescharacteristic
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31#125×C79—24no—
32C2×C4⋊C4×C79C2212yes—
33C2×C4⋊C4×C79C2212yes—
34C2×C4⋊C4×C79C2211yescharacteristic
35C2×C4⋊C4×C79C2211yescharacteristic
36C2×C42×C79C2211yescharacteristic
37C23×D79C2311yescharacteristic
38C22×Dic79C2312yes—
39C22×Dic79C2311yescharacteristic
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2312yes—
43C4⋊Dic79—24no—
44Dic79⋊C4—24no—
45Dic79⋊C4—22no—
46Dic79⋊C4—22no—
47Dic79⋊C4—22no—
48Dic79⋊C4—42no—
49(C2×D79)⋊C4—24no—
50(C2×D79)⋊C4—22no—
51(C2×D79)⋊C4—22no—
52(C2×D79)⋊C4—22no—
53(C2×D79)⋊C4—42no—
54C4×Dic79—42no—
55C22×C4×C79C2312yes—
56C22×C4×C79C2312yes—
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2311yescharacteristic
60C4⋊C4×C79—24no—
61C4⋊C4×C79—24no—
62C4⋊C4×C79—22no—
63C4⋊C4×C79—22no—
64C42×C79D414yes—
65C23×C79C2411yescharacteristic
66C22×D79—21no—
67C22×D79—22no—
68C22×D79—21no—
69C22×D79—21no—
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—22no—
78C2×C4×C79—22no—
79C2×C4×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79C2×D412yes—
82C2×C4×C79C2×D412yes—
83C2×C4×C79C2×D412yes—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—21no—
87C2×Dic79—21no—
88C2×Dic79—21no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—21no—
93C2×Dic79—21no—
94C2×Dic79—22no—
95C2×Dic79—22no—
96C2×Dic79#4114yes—
97C22×C79C22×D411yescharacteristic
98C22×C79C2×#4112yes—
99C22×C79H(5,𝔽2)11yescharacteristic
100C22×C792−1+411yescharacteristic
101C22×C792−1+412yes—
102C2×D79—41no—
103C2×D79—41no—
104C2×D79—41no—
105C2×D79—42no—
106C2×D79—42no—
107C4×C79—22no—
108C4×C79—22no—
109C4×C79—22no—
110C4×C79—42no—
111C4×C79—42no—
112Dic79—24no—
113Dic79—41no—
114Dic79—41no—
115Dic79—41no—
116Dic79—42no—
117C2×C79#53211yescharacteristic
118C2×C79#53611yescharacteristic
119C2×C79#53711yescharacteristic
120C2×C79#53912yes—
121C2×C79#54112yes—
122D79—81no—
123#2664—791nomaximal, Sylow
124C79#266411yescharacteristic, complemented, Sylow
125C2×#126—791no—
126C2×#125D7911yescharacteristic, complemented
127#400—791no—
128#399—791no—
129#398—791no—
130#398—792no—
131#397—791no—
132#396—792no—
133#389—792no—
134#388—792no—
135C4×C4⋊C4—791no—
136#126—1584no—
137#125—24no—
138C2×C4⋊C4—792no—
139C2×C4⋊C4—791no—
140C2×C4⋊C4—791no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4—792no—
144C2×C4⋊C4C2×D7912yes—
145C2×C4⋊C4C2×D7912yes—
146C2×C4⋊C4C2×D7911yescharacteristic
147C2×C4⋊C4C2×D7911yescharacteristic
148C2×C22⋊C4—792no—
149C2×C22⋊C4—791no—
150C2×C22⋊C4—791no—
151C2×C22⋊C4—791no—
152C2×C22⋊C4—792no—
153C2×C42—792no—
154C2×C42C2×D7911yescharacteristic
155#95—791no—
156#95—791no—
157#95—792no—
158#95—792no—
159#95—792no—
160#95—792no—
161C24—791no—
162C22×C4—792no—
163C22×C4—792no—
164C22×C4—791no—
165C22×C4—791no—
166C22×C4—791no—
167C22×C4C22×D7912yes—
168C22×C4C22×D7912yes—
169C22×C4C22×D7911yescharacteristic
170C22×C4C22×D7911yescharacteristic
171C22×C4C22×D7911yescharacteristic
172C4⋊C4—24no—
173C4⋊C4—24no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—3162no—
177C4⋊C4—1584no—
178C4⋊C4—1584no—
179C4⋊C4—1582no—
180C4⋊C4—1582no—
181C4⋊C4—1582no—
182C22⋊C4—3162no—
183C22⋊C4—1584no—
184C22⋊C4—1582no—
185C22⋊C4—1582no—
186C22⋊C4—1582no—
187C42—3162no—
188C42C22⋊D7914yes—
189C23—1582no—
190C23—1581no—
191C23—1581no—
192C23—1582no—
193C23—1581no—
194C23C23×D7911yescharacteristic
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—794no—
206C2×C4—1582no—
207C2×C4—1582no—
208C2×C4—1582no—
209C2×C4—1581no—
210C2×C4—1581no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1581no—
214C2×C4—1581no—
215C2×C4—1581no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4C2×C22⋊D7912yes—
219C2×C4C2×C22⋊D7912yes—
220C2×C4C2×C22⋊D7912yes—
221C22—3161no—
222C22—3161no—
223C22—3162no—
224C22—3162no—
225C22—3161no—
226C22C22×C22⋊D7911yescharacteristic
227C22#41×D7912yes—
228C22#1457920711yescharacteristic
229C22#1457920811yescharacteristic
230C22#1457920912yes—
231C4—22no—
232C4—22no—
233C4—22no—
234C4—42no—
235C4—42no—
236C4—3161no—
237C4—3161no—
238C4—3162no—
239C4—3161no—
240C4—1584no—
241C2—6321no—
242C2#1909910911yescharacteristic
243C2#1909913711yescharacteristic
244C2#1909914111yescharacteristic
245C2#1909916112yes—
246C2#1909917212yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
FittingC2×#125×C79C2
prime radicalC23×D79C23
hypercenterC2×#125D79
hypocenterC79#2664
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #19098501C2semidirect
4. #19098496C2semidirect
5. #19098494C2semidirect
8. #19098458C2semidirect
10. C4×C4⋊Dic79C2semidirect
11. C2×#125×C79C2semidirect
124. C79#2664semidirect
126. C2×#125D79semidirect