Finite Group Databasebeta

← #23769556

Subgroups — #23769556

Order 10112.

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

normal subgroups only

This group has 498 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×#14579143C211yesmaximal, characteristic
2C2×#14579137C211yesmaximal, characteristic, complemented
3#19098503C211yesmaximal, characteristic, complemented
4#19098499C211yesmaximal, characteristic, complemented
5#19098492C212yesmaximal, complemented
6#19098482C211yesmaximal, characteristic, complemented
7#19098478C212yesmaximal
8#19098460C212yesmaximal, complemented
9#19098451C212yesmaximal, complemented
10#19098410C211yesmaximal, characteristic, complemented
11#393×C79C211yesmaximal, characteristic, complemented
12C22×C22⋊D79C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14#14579143—24no—
15#14579137—24no—
16C2×C4⋊Dic79C2211yescharacteristic
17C2×C4⋊Dic79C2211yescharacteristic
18C2×Dic79⋊C4C2212yes—
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2211yescharacteristic
21C2×Dic79⋊C4C2212yes—
22C2×C22⋊Dic79C2211yescharacteristic
23C2×C22⋊Dic79C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C2×C4×Dic79C2212yes—
28C79⋊#95C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×Q8×C79C2211yescharacteristic
33C2×C22⋊C4×C79C2211yescharacteristic
34C2×C22⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C2×C22⋊D79—22no—
39C2×C22⋊D79—42no—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2312yes—
42C22×Dic79C2311yescharacteristic
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2312yes—
45C2×C4×D79—42no—
46C2×C4×D79D414yes—
47C4⋊Dic79—22no—
48C4⋊Dic79—22no—
49Dic79⋊C4—24no—
50Dic79⋊C4—24no—
51Dic79⋊C4—22no—
52Dic79⋊C4—42no—
53C22⋊Dic79—22no—
54C22⋊Dic79—24no—
55(C2×D79)⋊C4—24no—
56(C2×D79)⋊C4—24no—
57(C2×D79)⋊C4—22no—
58C4×Dic79—42no—
59C24×C79C2311yescharacteristic
60C2×Q8×C79—22no—
61C2×Q8×C79—42no—
62C22×C4×C79C2312yes—
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C22⋊C4×C79—22no—
67C22⋊C4×C79—42no—
68C23×C79—21no—
69C23×C79—22no—
70C23×C79—22no—
71C23×C79—21no—
72C23×C79—21no—
73C23×C79C2411yescharacteristic
74C22×D79—22no—
75C22×D79—22no—
76C22×D79—21no—
77C22×D79—21no—
78C22×D79C2×D412yes—
79Q8×C79—44no—
80C2×C4×C79—22no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79C2×D412yes—
90C22⋊D79—44no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—21no—
95C2×Dic79—22no—
96C2×Dic79—21no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—21no—
101C2×Dic79—21no—
102C2×Dic79C2×D412yes—
103C2×Dic79#4114yes—
104C4×D79—44no—
105C22×C79—41no—
106C22×C79—41no—
107C22×C79—41no—
108C22×C79—42no—
109C22×C79—42no—
110C22×C79C22×D411yescharacteristic
111C22×C79C2×#4112yes—
112C22×C79H(5,𝔽2)12yes—
113C22×C792−1+411yescharacteristic
114C22×C792−1+411yescharacteristic
115C2×D79—22no—
116C2×D79—22no—
117C2×D79—22no—
118C2×D79—42no—
119C2×D79—42no—
120C4×C79—22no—
121C4×C79—41no—
122C4×C79—42no—
123C4×C79—42no—
124Dic79—22no—
125Dic79—24no—
126Dic79—42no—
127Dic79—41no—
128Dic79—41no—
129C2×C79—81no—
130C2×C79#53211yescharacteristic
131C2×C79#53411yescharacteristic
132C2×C79#53611yescharacteristic
133C2×C79#53912yes—
134C2×C79#54212yes—
135D79—42no—
136#2663—791nomaximal, Sylow
137C79#266311yescharacteristic, complemented, Sylow
138C2×#123—791no—
139C2×C22⋊Q8—791no—
140#400—791no—
141#399—791no—
142#397—792no—
143#395—791no—
144#394—792no—
145#393D7911yescharacteristic, complemented
146#389—792no—
147#388—792no—
148C4×C22⋊C4—791no—
149C22×Q8C2×D7911yescharacteristic
150C22×D4—791no—
151C23×C4—791no—
152#123—1584no—
153C22⋊Q8—1584no—
154C2×C4⋊C4—792no—
155C2×C4⋊C4—792no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4—791no—
158C2×C4⋊C4—791no—
159C2×C4⋊C4—792no—
160C2×C22⋊C4—791no—
161C2×C22⋊C4—792no—
162C2×C22⋊C4—792no—
163C2×C22⋊C4—791no—
164C2×C22⋊C4—792no—
165C2×C22⋊C4C2×D7911yescharacteristic
166C2×C22⋊C4C2×D7912yes—
167C2×C42—792no—
168#95—791no—
169#95—792no—
170#95—792no—
171#95—792no—
172#95C2×D7911yescharacteristic
173#95C2×D7912yes—
174C24—791no—
175C24C22×D7911yescharacteristic
176C2×Q8—22no—
177C2×Q8—42no—
178C2×D4—3162no—
179C2×D4—1582no—
180C22×C4—3162no—
181C22×C4—794no—
182C22×C4—792no—
183C22×C4—791no—
184C22×C4—791no—
185C22×C4—792no—
186C22×C4—791no—
187C22×C4C22×D7912yes—
188C22×C4C22×D7912yes—
189C22×C4C22×D7911yescharacteristic
190C22×C4C22×D7911yescharacteristic
191C4⋊C4—3162no—
192C4⋊C4—1584no—
193C4⋊C4—1584no—
194C4⋊C4—1582no—
195C4⋊C4—1582no—
196C4⋊C4—1582no—
197C22⋊C4—22no—
198C22⋊C4—42no—
199C22⋊C4—1584no—
200C22⋊C4—1584no—
201C22⋊C4—1582no—
202C22⋊C4—1584no—
203C22⋊C4—1582no—
204C42—3162no—
205C23—22no—
206C23—22no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—792no—
211C23—1582no—
212C23—1582no—
213C23—1581no—
214C23—1581no—
215C23C23×D7911yescharacteristic
216Q8—44no—
217D4—3164no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—3164no—
228C2×C4—794no—
229C2×C4—792no—
230C2×C4—1582no—
231C2×C4—1582no—
232C2×C4—1582no—
233C2×C4—1581no—
234C2×C4—1581no—
235C2×C4—1581no—
236C2×C4—1582no—
237C2×C4—1581no—
238C2×C4—1582no—
239C2×C4—1582no—
240C2×C4—1582no—
241C2×C4D4×D7912yes—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—41no—
246C22—41no—
247C22—3162no—
248C22—3162no—
249C22—1582no—
250C22—1582no—
251C22—1582no—
252C22C2×D4×D7911yescharacteristic
253C22#41×D7912yes—
254C22#1457920612yes—
255C22#1457920811yescharacteristic
256C22#1457920911yescharacteristic
257C4—22no—
258C4—42no—
259C4—41no—
260C4—42no—
261C4—3161no—
262C4—3162no—
263C4—3161no—
264C4—1584no—
265C4—1582no—
266C2—81no—
267C2—3162no—
268C2#1909911211yescharacteristic
269C2#1909912311yescharacteristic
270C2#1909913611yescharacteristic
271C2#1909915912yes—
272C2#1909917712yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#393×C79C2
prime radicalC22×C22⋊D79C22
hypercenter#393D79
hypocenterC79#2663
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
2. C2×#14579137C2semidirect
3. #19098503C2semidirect
4. #19098499C2semidirect
5. #19098492C2semidirect
6. #19098482C2semidirect
8. #19098460C2semidirect
9. #19098451C2semidirect
10. #19098410C2semidirect
11. #393×C79C2semidirect
137. C79#2663semidirect
145. #393D79semidirect