Finite Group Databasebeta

← #23769201

Subgroups — #23769201

Order 10112.

464 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14579119C211yesmaximal, characteristic
3#19098501C211yesmaximal, characteristic, complemented
4#19098495C211yesmaximal, characteristic, complemented
5#19098493C211yesmaximal, characteristic, complemented
6#19098492C212yesmaximal
7#19098490C212yesmaximal
8#19098467C212yesmaximal, complemented
9#19098460C212yesmaximal, complemented
10#19098422C211yesmaximal, characteristic
11#400×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14#14579139—24no—
15#14579119—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×C4⋊Dic79C2212yes—
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2211yescharacteristic
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2212yes—
26C2×C4×Dic79C2212yes—
27C79⋊#95C2211yescharacteristic
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×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2311yescharacteristic
45C2×C4×D79—24no—
46C2×C4×D79D414yes—
47C4⋊Dic79—22no—
48C4⋊Dic79—42no—
49Dic79⋊C4—22no—
50Dic79⋊C4—24no—
51Dic79⋊C4—22no—
52Dic79⋊C4—42no—
53(C2×D79)⋊C4—24no—
54(C2×D79)⋊C4—22no—
55(C2×D79)⋊C4—22no—
56(C2×D79)⋊C4—42no—
57C4×Dic79—24no—
58C22×C4×C79C2311yescharacteristic
59C22×C4×C79C2312yes—
60C22×C4×C79C2312yes—
61C22×C4×C79C2311yescharacteristic
62C22×C4×C79C2311yescharacteristic
63C4⋊C4×C79—22no—
64C4⋊C4×C79—22no—
65C23×C79C2411yescharacteristic
66C22×D79—22no—
67C22×D79—21no—
68C22×D79—22no—
69C22×D79—21no—
70C22×D79C2×D412yes—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—21no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—21no—
79C2×C4×C79—24no—
80C2×C4×C79—22no—
81C2×C4×C79—21no—
82C2×C4×C79C2×D412yes—
83C2×Dic79—22no—
84C2×Dic79—21no—
85C2×Dic79—21no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—22no—
90C2×Dic79—21no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—21no—
94C2×Dic79C2×D412yes—
95C2×Dic79#4114yes—
96C4×D79—28no—
97Dic158—44no—
98C22×C79C22×D411yescharacteristic
99C22×C79C2×#4112yes—
100C22×C79H(5,𝔽2)11yescharacteristic
101C22×C792−1+412yes—
102C22×C792−1+411yescharacteristic
103C2×D79—22no—
104C2×D79—22no—
105C2×D79—22no—
106C2×D79—42no—
107C2×D79—42no—
108C4×C79—22no—
109C4×C79—41no—
110C4×C79—42no—
111C4×C79—41no—
112C4×C79—42no—
113Dic79—41no—
114Dic79—42no—
115Dic79—41no—
116Dic79—42no—
117Dic79#12314yes—
118C2×C79C2×#12311yescharacteristic
119C2×C79#53611yescharacteristic
120C2×C79#53711yescharacteristic
121C2×C79#54112yes—
122C2×C79#54212yes—
123D79—42no—
124#2625—791nomaximal, Sylow
125C79#262511yescharacteristic, complemented, Sylow
126C2×C22⋊Q8—791no—
127C2×#117—791no—
128#400—791no—
129#400D7911yescharacteristic, complemented
130#398—791no—
131#398—791no—
132#397—792no—
133#397—792no—
134#391—792no—
135#389—792no—
136#380—791no—
137C22×Q8—791no—
138C23×C4—791no—
139C22⋊Q8—1584no—
140#117—1584no—
141C2×C4⋊C4—792no—
142C2×C4⋊C4—792no—
143C2×C4⋊C4—791no—
144C2×C4⋊C4—791no—
145C2×C4⋊C4—791no—
146C2×C4⋊C4—792no—
147C2×C4⋊C4C2×D7911yescharacteristic
148C2×C4⋊C4C2×D7911yescharacteristic
149C2×C22⋊C4—792no—
150C2×C22⋊C4—792no—
151C2×C22⋊C4—791no—
152C2×C22⋊C4—791no—
153C2×C42—792no—
154#95—791no—
155#95—792no—
156#95—792no—
157#95—792no—
158#95—792no—
159#95C2×D7911yescharacteristic
160#95C2×D7912yes—
161#95C2×D7912yes—
162C24—791no—
163C2×Q8—1582no—
164C2×Q8—1584no—
165C22×C4—791no—
166C22×C4—794no—
167C22×C4—792no—
168C22×C4—791no—
169C22×C4—792no—
170C22×C4—791no—
171C22×C4—1584no—
172C22×C4C22×D7912yes—
173C22×C4C22×D7911yescharacteristic
174C22×C4C22×D7912yes—
175C22×C4C22×D7911yescharacteristic
176C22×C4C22×D7911yescharacteristic
177C4⋊C4—22no—
178C4⋊C4—22no—
179C4⋊C4—3162no—
180C4⋊C4—3162no—
181C4⋊C4—1584no—
182C4⋊C4—1582no—
183C4⋊C4—1582no—
184C4⋊C4—1582no—
185C22⋊C4—3162no—
186C22⋊C4—1584no—
187C22⋊C4—1582no—
188C22⋊C4—1582no—
189C42—1584no—
190C23—792no—
191C23—1582no—
192C23—1581no—
193C23—1582no—
194C23—1581no—
195C23C23×D7911yescharacteristic
196Q8—3164no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—794no—
209C2×C4—792no—
210C2×C4—1588no—
211C2×C4—1582no—
212C2×C4—1582no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1581no—
216C2×C4—1582no—
217C2×C4—1582no—
218C2×C4—1581no—
219C2×C4—1582no—
220C2×C4—1581no—
221C2×C4—1581no—
222C2×C4D4×D7912yes—
223C22—3162no—
224C22—3162no—
225C22—1582no—
226C22—1582no—
227C22—1582no—
228C22C2×D4×D7911yescharacteristic
229C22#41×D7912yes—
230C22#1457920711yescharacteristic
231C22#1457920812yes—
232C22#1457920911yescharacteristic
233C4—22no—
234C4—41no—
235C4—42no—
236C4—41no—
237C4—42no—
238C4—3162no—
239C4—3161no—
240C4—3162no—
241C4—3161no—
242C4—794no—
243C2—3162no—
244C2#123×D7911yescharacteristic
245C2#1909913311yescharacteristic
246C2#1909914311yescharacteristic
247C2#1909917212yes—
248C2#1909917912yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#400×C79C2
prime radicalC23×D79C23
hypercenter#400D79
hypocenterC79#2625
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #19098501C2semidirect
4. #19098495C2semidirect
5. #19098493C2semidirect
8. #19098467C2semidirect
9. #19098460C2semidirect
11. #400×C79C2semidirect
125. C79#2625semidirect
129. #400D79semidirect