Finite Group Databasebeta

← #23768306

Subgroups — #23768306

Order 10112.

604 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 147 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×#14579139C212yesmaximal, complemented
2C2×#14579126C211yesmaximal, characteristic, complemented
3C2×#14579123C211yesmaximal, characteristic
4#19098494C211yesmaximal, characteristic, complemented
5#19098481C211yesmaximal, characteristic
6#19098480C211yesmaximal, characteristic
7#19098453C212yesmaximal, complemented
8#19098452C212yesmaximal, complemented
9#19098427C211yesmaximal, characteristic, complemented
10#19098422C212yesmaximal, complemented
11#398×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13C22×D316C2211yescharacteristic
14C22×C4×D79C2212yes—
15#14579139—28no—
16#14579126—24no—
17#14579123—24no—
18C2×Dic79⋊C4C2211yescharacteristic
19C2×Dic79⋊C4C2212yes—
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2211yescharacteristic
22C2×(C2×D79)⋊C4C2212yes—
23C2×(C2×D79)⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2212yes—
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2212yes—
27C2×C4×Dic79C2211yescharacteristic
28C2×C4×Dic79C2211yescharacteristic
29C2×C4×Dic79C2211yescharacteristic
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C79⋊#95C2211yescharacteristic
33C2×C4⋊C4×C79C2212yes—
34C2×C4⋊C4×C79C2211yescharacteristic
35C2×C4⋊C4×C79C2211yescharacteristic
36#95×C79C2212yes—
37#95×C79C2211yescharacteristic
38C23×D79C2312yes—
39C2×Dic158—22no—
40C2×Dic158—22no—
41C2×Dic158D414yescomplemented
42C2×D316—24no—
43C2×D316—22no—
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2311yescharacteristic
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2311yescharacteristic
49C2×C4×D79—24no—
50C2×C4×D79—24no—
51C2×C4×D79—24no—
52Dic79⋊C4—22no—
53Dic79⋊C4—24no—
54Dic79⋊C4—24no—
55Dic79⋊C4—22no—
56(C2×D79)⋊C4—24no—
57(C2×D79)⋊C4—24no—
58(C2×D79)⋊C4—24no—
59(C2×D79)⋊C4—24no—
60(C2×D79)⋊C4—24no—
61C4×Dic79—22no—
62C4×Dic79—22no—
63C4×Dic79D414yes—
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2312yes—
67C22×C4×C79C2311yescharacteristic
68C22×C4×C79C2311yescharacteristic
69C4⋊C4×C79—22no—
70C4⋊C4×C79—22no—
71C4⋊C4×C79—24no—
72C23×C79C2411yescharacteristic
73C22×D79—22no—
74C22×D79—22no—
75C22×D79—22no—
76C22×D79—22no—
77C22×D79—22no—
78C22×D79—22no—
79C22×D79#4114yes—
80C2×C4×C79—21no—
81C2×C4×C79—22no—
82C2×C4×C79—21no—
83C2×C4×C79—21no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79—22no—
90C2×C4×C79—22no—
91C2×C4×C79C2×D412yes—
92C2×C4×C79C2×D412yes—
93C2×Dic79—21no—
94C2×Dic79—21no—
95C2×Dic79—22no—
96C2×Dic79—21no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79C2×D412yes—
102C2×Dic79C2×D412yes—
103C2×Dic79C2×D412yes—
104C2×Dic79C2×D412yes—
105C2×Dic79#4112yes—
106D316—28no—
107C4×D79—48no—
108Dic158—28no—
109C22×C79C22×D411yescharacteristic
110C22×C79C22×D411yescharacteristic
111C22×C79C2×#4111yescharacteristic
112C22×C79C2×#4112yes—
113C22×C792−1+412yes—
114C2×D79—24no—
115C2×D79—24no—
116C2×D79—24no—
117C2×D79—42no—
118C2×D79—42no—
119C2×D79—42no—
120C2×D79—42no—
121C4×C79—22no—
122C4×C79—22no—
123C4×C79—42no—
124C4×C79—41no—
125C4×C79—42no—
126Dic79—22no—
127Dic79—22no—
128Dic79—41no—
129Dic79—42no—
130Dic79#12114yes—
131C2×C79C2×#12111yescharacteristic
132C2×C79#52511yescharacteristic
133C2×C79#53611yescharacteristic
134C2×C79#54812yes—
135C2×C79#55212yes—
136D79—44no—
137#2536—791nomaximal, Sylow
138C79#253611yescharacteristic, complemented, Sylow
139C2×C22⋊Q8—792no—
140C2×C4×Q8—791no—
141C2×C4×D4—791no—
142#398—791no—
143#398D7911yescharacteristic, complemented
144#394—791no—
145#394—791no—
146#388—792no—
147#388—792no—
148#382—791no—
149#380—792no—
150C22×Q8—791no—
151C22×D4—791no—
152C23×C4—792no—
153C22⋊Q8—1588no—
154C4×Q8—1584no—
155C4×D4—1584no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4—791no—
158C2×C4⋊C4—792no—
159C2×C4⋊C4—792no—
160C2×C4⋊C4C2×D7911yescharacteristic
161C2×C4⋊C4C2×D7911yescharacteristic
162C2×C4⋊C4C2×D7912yes—
163C2×C22⋊C4—792no—
164C2×C22⋊C4—792no—
165C2×C22⋊C4—792no—
166C2×C22⋊C4—792no—
167C2×C22⋊C4—792no—
168C2×C42—791no—
169C2×C42—791no—
170C2×C42—791no—
171#95—792no—
172#95—792no—
173#95—791no—
174#95C2×D7912yes—
175#95C2×D7911yescharacteristic
176C24—792no—
177C2×Q8—794no—
178C2×Q8—1582no—
179C2×Q8—1582no—
180C2×D4—1584no—
181C2×D4—1582no—
182C22×C4—791no—
183C22×C4—791no—
184C22×C4—791no—
185C22×C4—792no—
186C22×C4—791no—
187C22×C4—1584no—
188C22×C4—1584no—
189C22×C4—1584no—
190C22×C4C22×D7912yes—
191C22×C4C22×D7912yes—
192C22×C4C22×D7911yescharacteristic
193C22×C4C22×D7911yescharacteristic
194C22×C4C22×D7911yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—1582no—
199C4⋊C4—1584no—
200C4⋊C4—1584no—
201C4⋊C4—1582no—
202C22⋊C4—1584no—
203C22⋊C4—1584no—
204C22⋊C4—1584no—
205C22⋊C4—1584no—
206C22⋊C4—1584no—
207C42—794no—
208C42—1582no—
209C42—1582no—
210C23—794no—
211C23—1582no—
212C23—1582no—
213C23—1582no—
214C23—1582no—
215C23—1582no—
216C23—1582no—
217C23C23×D7911yescharacteristic
218Q8—1588no—
219D4—1588no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—3168no—
232C2×C4—792no—
233C2×C4—792no—
234C2×C4—792no—
235C2×C4—792no—
236C2×C4—792no—
237C2×C4—1582no—
238C2×C4—1582no—
239C2×C4—1582no—
240C2×C4—1581no—
241C2×C4—1582no—
242C2×C4—1581no—
243C2×C4—1582no—
244C2×C4—1581no—
245C2×C4D4×D7912yes—
246C2×C4D4×D7912yes—
247C22—3162no—
248C22—3162no—
249C22—3162no—
250C22—3162no—
251C22—1584no—
252C22—1584no—
253C22—1584no—
254C22C2×D4×D7911yescharacteristic
255C22C2×D4×D7911yescharacteristic
256C22#41×D7912yes—
257C22#41×D7911yescharacteristic
258C22#1457920912yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—42no—
263C4—41no—
264C4—3162no—
265C4—3161no—
266C4—794no—
267C4—1582no—
268C4—1582no—
269C2—3164no—
270C2#121×D7911yescharacteristic
271C2#1909907111yescharacteristic
272C2#1909913811yescharacteristic
273C2#1909922312yes—
274C2#1909924512yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#398×C79C2
prime radicalC22×D316C22
hypercenter#398D79
hypocenterC79#2536
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#14579139C2semidirect
2. C2×#14579126C2semidirect
4. #19098494C2semidirect
7. #19098453C2semidirect
8. #19098452C2semidirect
9. #19098427C2semidirect
10. #19098422C2semidirect
11. #398×C79C2semidirect
41. C2×Dic158D4semidirect
138. C79#2536semidirect
143. #398D79semidirect