Finite Group Databasebeta

← #23767880

Subgroups — #23767880

Order 10112.

512 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14579139C211yesmaximal, characteristic
2C2×C4⋊C4×D79C211yesmaximal, characteristic
3#19098503C211yesmaximal, characteristic, complemented
4#19098502C211yesmaximal, characteristic, complemented
5#19098501C211yesmaximal, characteristic, complemented
6#19098467C212yesmaximal, complemented
7#19098427C212yesmaximal, complemented
8#19098425C212yesmaximal
9#19098425C212yesmaximal
10#19098410C211yesmaximal, characteristic
11#400×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13C22×C4×D79C2212yes—
14C22×C4×D79C2211yescharacteristic
15#14579139—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×Dic79⋊C4C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C4⋊C4×D79—24no—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2211yescharacteristic
24C2×C4×Dic79C2212yes—
25C79⋊#95C2211yescharacteristic
26C79⋊#95C2212yes—
27C79⋊#95C2212yes—
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C2×C4⋊C4×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34#95×C79C2211yescharacteristic
35#95×C79C2212yes—
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C2×Dic158—22no—
39C2×Dic158—24no—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2312yes—
44C22×Dic79C2311yescharacteristic
45C2×C4×D79—24no—
46C2×C4×D79—24no—
47C2×C4×D79—28no—
48C2×C4×D79D414yes—
49C4⋊Dic79—22no—
50Dic79⋊C4—24no—
51Dic79⋊C4—22no—
52Dic79⋊C4—22no—
53(C2×D79)⋊C4—22no—
54(C2×D79)⋊C4—22no—
55(C2×D79)⋊C4—24no—
56C4×Dic79—24no—
57C22×C4×C79C2311yescharacteristic
58C22×C4×C79C2312yes—
59C22×C4×C79C2311yescharacteristic
60C22×C4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C4⋊C4×C79—22no—
63C4⋊C4×C79—22no—
64C23×C79C2411yescharacteristic
65C22×D79—22no—
66C22×D79—21no—
67C22×D79—21no—
68C22×D79C2×D412yes—
69C22×D79#4114yes—
70C2×C4×C79—22no—
71C2×C4×C79—21no—
72C2×C4×C79—21no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—24no—
77C2×C4×C79—22no—
78C2×C4×C79—21no—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
81C2×C4×C79C2×D412yes—
82C2×Dic79—21no—
83C2×Dic79—21no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—24no—
88C2×Dic79—22no—
89C2×Dic79—21no—
90C2×Dic79—21no—
91C2×Dic79—22no—
92C2×Dic79C2×D412yes—
93C2×Dic79#4114yes—
94C4×D79—28no—
95C4×D79—48no—
96Dic158—44no—
97C22×C79C22×D411yescharacteristic
98C22×C79C2×#4112yes—
99C22×C79C2×#4112yes—
100C22×C792−1+411yescharacteristic
101C22×C792−1+411yescharacteristic
102C2×D79—22no—
103C2×D79—22no—
104C2×D79—24no—
105C2×D79—24no—
106C2×D79#12414yes—
107C4×C79—22no—
108C4×C79—41no—
109C4×C79—42no—
110C4×C79—41no—
111C4×C79—42no—
112Dic79—41no—
113Dic79—42no—
114Dic79—41no—
115Dic79—42no—
116Dic79#12314yes—
117C2×C79C2×#12311yescharacteristic
118C2×C79C2×#12411yescharacteristic
119C2×C79#53611yescharacteristic
120C2×C79#55212yes—
121C2×C79#55212yes—
122D79—24no—
123#2503—791nomaximal, Sylow
124C79#250311yescharacteristic, complemented, Sylow
125C2×C22⋊Q8—791no—
126C22×C4⋊C4—791no—
127#400—791no—
128#400—791no—
129#400—791no—
130#400D7911yescharacteristic, complemented
131#391—792no—
132#382—792no—
133#381—792no—
134#381—792no—
135C4×C22⋊C4—791no—
136C22×Q8—791no—
137C23×C4—791no—
138C23×C4—792no—
139C22⋊Q8—1584no—
140C2×C4⋊C4—792no—
141C2×C4⋊C4—791no—
142C2×C4⋊C4—791no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4—1584no—
145C2×C4⋊C4C2×D7911yescharacteristic
146C2×C4⋊C4C2×D7911yescharacteristic
147C2×C22⋊C4—791no—
148C2×C22⋊C4—791no—
149C2×C22⋊C4—792no—
150C2×C42—792no—
151#95—791no—
152#95—792no—
153#95—792no—
154#95—792no—
155#95—792no—
156#95—792no—
157#95—792no—
158#95C2×D7911yescharacteristic
159#95C2×D7912yes—
160#95C2×D7912yes—
161C24—791no—
162C2×Q8—1582no—
163C2×Q8—1584no—
164C22×C4—791no—
165C22×C4—794no—
166C22×C4—792no—
167C22×C4—791no—
168C22×C4—791no—
169C22×C4—792no—
170C22×C4—1584no—
171C22×C4—1588no—
172C22×C4—1584no—
173C22×C4C22×D7912yes—
174C22×C4C22×D7911yescharacteristic
175C22×C4C22×D7911yescharacteristic
176C22×C4C22×D7912yes—
177C22×C4C22×D7911yescharacteristic
178C4⋊C4—22no—
179C4⋊C4—22no—
180C4⋊C4—1584no—
181C4⋊C4—1582no—
182C4⋊C4—1582no—
183C4⋊C4—1582no—
184C22⋊C4—1584no—
185C22⋊C4—1582no—
186C22⋊C4—1582no—
187C42—1584no—
188C23—794no—
189C23—792no—
190C23—1582no—
191C23—1581no—
192C23—1581no—
193C23C23×D7911yescharacteristic
194Q8—3164no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—24no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—3168no—
207C2×C4—794no—
208C2×C4—792no—
209C2×C4—1588no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1584no—
213C2×C4—1582no—
214C2×C4—1581no—
215C2×C4—1581no—
216C2×C4—1582no—
217C2×C4—1581no—
218C2×C4—1581no—
219C2×C4—1582no—
220C2×C4D4×D7912yes—
221C22—794no—
222C22—1582no—
223C22—1584no—
224C22—1584no—
225C22—1582no—
226C22C2×D4×D7911yescharacteristic
227C22#41×D7912yes—
228C22#41×D7912yes—
229C22#1457920811yescharacteristic
230C22#1457920911yescharacteristic
231C4—22no—
232C4—41no—
233C4—42no—
234C4—41no—
235C4—42no—
236C4—3161no—
237C4—3162no—
238C4—3161no—
239C4—3162no—
240C4—794no—
241C2—1584no—
242C2#123×D7911yescharacteristic
243C2#124×D7911yescharacteristic
244C2#1909913611yescharacteristic
245C2#1909924512yes—
246C2#1909924912yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC23×D79C23
hypercenter#400D79
hypocenterC79#2503
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #19098503C2semidirect
4. #19098502C2semidirect
5. #19098501C2semidirect
6. #19098467C2semidirect
7. #19098427C2semidirect
11. #400×C79C2semidirect
124. C79#2503semidirect
130. #400D79semidirect