Finite Group Databasebeta

← #23769568

Subgroups — #23769568

Order 10112.

434 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 129 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×#14579154C211yesmaximal, characteristic
2C2×#14579152C211yesmaximal, characteristic, complemented
3#19098503C211yesmaximal, characteristic, complemented
4#19098499C211yesmaximal, characteristic
5#19098497C212yesmaximal, complemented
6#19098494C211yesmaximal, characteristic, complemented
7#19098486C212yesmaximal
8#19098460C212yesmaximal, complemented
9#19098451C212yesmaximal
10#19098414C211yesmaximal, characteristic, complemented
11#397×C79C211yesmaximal, characteristic
12#14579154—24no—
13#14579152—24no—
14C2×C4⋊Dic79C2211yescharacteristic
15C2×C4⋊Dic79C2212yes—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2212yes—
23C2×C22⋊Dic79C2211yescharacteristic
24C2×C22⋊Dic79C2212yes—
25C2×C22⋊Dic79C2211yescharacteristic
26C2×C4×Dic79C2212yes—
27C2×C4×Dic79C2211yescharacteristic
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C22⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C22×Dic79C2311yescharacteristic
38C22×Dic79C2311yescharacteristic
39C22×Dic79C2312yes—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2312yes—
43C4⋊Dic79—24no—
44C4⋊Dic79—22no—
45C4⋊Dic79—22no—
46Dic79⋊C4—24no—
47Dic79⋊C4—22no—
48Dic79⋊C4—24no—
49Dic79⋊C4—24no—
50Dic79⋊C4—22no—
51Dic79⋊C4—42no—
52C22⋊Dic79—22no—
53C22⋊Dic79—22no—
54C22⋊Dic79—24no—
55C4×Dic79—42no—
56C4×Dic79D414yes—
57C24×C79C2311yescharacteristic
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C4⋊C4×C79—22no—
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—22no—
84C2×Dic79—21no—
85C2×Dic79—22no—
86C2×Dic79—21no—
87C2×Dic79—21no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—21no—
92C2×Dic79—22no—
93C2×Dic79—21no—
94C2×Dic79C2×D412yes—
95C2×Dic79C2×D412yes—
96C2×Dic79#4114yes—
97C22×C79—41no—
98C22×C79—41no—
99C22×C79—41no—
100C22×C79—42no—
101C22×C79—42no—
102C22×C79C22×D411yescharacteristic
103C22×C79C2×#4112yes—
104C22×C79H(5,𝔽2)11yescharacteristic
105C22×C792−1+412yes—
106C22×C792−1+411yescharacteristic
107C4×C79—22no—
108C4×C79—41no—
109C4×C79—42no—
110C4×C79—42no—
111Dic79—22no—
112Dic79—22no—
113Dic79—24no—
114Dic79—42no—
115Dic79—41no—
116Dic79—41no—
117C2×C79—81no—
118C2×C79#53211yescharacteristic
119C2×C79#53611yescharacteristic
120C2×C79#53711yescharacteristic
121C2×C79#53912yes—
122C2×C79#54112yes—
123#2664—791nomaximal, Sylow
124C79#266411yescharacteristic, complemented, Sylow
125C2×#126—791no—
126C2×#125—791no—
127#400—791no—
128#399—791no—
129#398—791no—
130#398—792no—
131#397D7911yescharacteristic
132#396—792no—
133#389—792no—
134#388—792no—
135C4×C4⋊C4—791no—
136#126—1584no—
137#125—1584no—
138C2×C4⋊C4—792no—
139C2×C4⋊C4—792no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—791no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4—791no—
145C2×C4⋊C4—792no—
146C2×C4⋊C4—792no—
147C2×C4⋊C4C2×D7911yescharacteristic
148C2×C22⋊C4—791no—
149C2×C22⋊C4—791no—
150C2×C22⋊C4—792no—
151C2×C22⋊C4C2×D7911yescharacteristic
152C2×C22⋊C4C2×D7912yes—
153C2×C42—792no—
154C2×C42—791no—
155#95—791no—
156#95—792no—
157#95—792no—
158#95—792no—
159#95C2×D7911yescharacteristic
160#95C2×D7912yes—
161C24C22×D7911yescharacteristic
162C22×C4—792no—
163C22×C4—791no—
164C22×C4—791no—
165C22×C4—791no—
166C22×C4—792no—
167C22×C4—791no—
168C22×C4C22×D7912yes—
169C22×C4C22×D7912yes—
170C22×C4C22×D7911yescharacteristic
171C22×C4C22×D7911yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—3162no—
174C4⋊C4—1584no—
175C4⋊C4—1584no—
176C4⋊C4—1584no—
177C4⋊C4—1582no—
178C4⋊C4—1584no—
179C4⋊C4—1582no—
180C4⋊C4—1582no—
181C4⋊C4—1582no—
182C22⋊C4—22no—
183C22⋊C4—42no—
184C22⋊C4—1584no—
185C22⋊C4—1582no—
186C22⋊C4—1582no—
187C42—3162no—
188C42—794no—
189C23—22no—
190C23—21no—
191C23—21no—
192C23—22no—
193C23—21no—
194C23C23×D7911yescharacteristic
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—794no—
205C2×C4—792no—
206C2×C4—792no—
207C2×C4—1582no—
208C2×C4—1582no—
209C2×C4—1581no—
210C2×C4—1581no—
211C2×C4—1582no—
212C2×C4—1581no—
213C2×C4—1581no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1581no—
217C2×C4—1582no—
218C2×C4—1581no—
219C2×C4—1582no—
220C2×C4D4×D7912yes—
221C22—41no—
222C22—42no—
223C22—42no—
224C22—41no—
225C22—41no—
226C22C2×D4×D7911yescharacteristic
227C22#41×D7912yes—
228C22#1457920611yescharacteristic
229C22#1457920811yescharacteristic
230C22#1457920812yes—
231C4—22no—
232C4—42no—
233C4—42no—
234C4—41no—
235C4—3161no—
236C4—3162no—
237C4—3161no—
238C4—1582no—
239C4—1584no—
240C4—1582no—
241C2—81no—
242C2#1909911211yescharacteristic
243C2#1909913511yescharacteristic
244C2#1909914211yescharacteristic
245C2#1909915612yes—
246C2#1909917012yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#397×C79C2
prime radicalC24×C79C23
hypercenter#397D79
hypocenterC79#2664
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#14579152C2semidirect
3. #19098503C2semidirect
5. #19098497C2semidirect
6. #19098494C2semidirect
8. #19098460C2semidirect
10. #19098414C2semidirect
124. C79#2664semidirect