Finite Group Databasebeta

← #23768304

Subgroups — #23768304

Order 10112.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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×#14579138C212yesmaximal, complemented
2C2×#14579126C211yesmaximal, characteristic, complemented
3C2×D4×Dic79C211yesmaximal, characteristic
4#19098495C211yesmaximal, characteristic, complemented
5#19098493C211yesmaximal, characteristic, complemented
6#19098477C211yesmaximal, characteristic
7#19098457C212yesmaximal, complemented
8#19098456C212yesmaximal, complemented
9#19098427C211yesmaximal, characteristic, complemented
10#19098421C212yesmaximal, complemented
11#394×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C23×Dic79C2212yes—
14#14579138—28no—
15#14579126—24no—
16D4×Dic79—24no—
17C2×C4⋊Dic79C2212yes—
18C2×C4⋊Dic79C2211yescharacteristic
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2212yes—
22C2×Dic79⋊C4C2211yescharacteristic
23C2×C22⋊Dic79C2212yes—
24C2×C22⋊Dic79C2212yes—
25C2×C22⋊Dic79C2212yes—
26C2×C4×Dic79C2211yescharacteristic
27C2×C4×Dic79C2211yescharacteristic
28C2×C4×Dic79C2211yescharacteristic
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C79⋊#95C2211yescharacteristic
33C22×D4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2211yescharacteristic
35C2×C22⋊C4×C79C2212yes—
36C2×C22⋊C4×C79C2212yes—
37#95×C79C2211yescharacteristic
38C2×Dic158—22no—
39C2×Dic158—22no—
40C2×Dic158D414yescomplemented
41C22×Dic79—24no—
42C22×Dic79—24no—
43C22×Dic79—24no—
44C22×Dic79C2312yes—
45C22×Dic79C2311yescharacteristic
46C22×Dic79C2312yes—
47C22×Dic79C2311yescharacteristic
48C22×Dic79C2311yescharacteristic
49C22×Dic79C2311yescharacteristic
50C4⋊Dic79—24no—
51C4⋊Dic79—22no—
52Dic79⋊C4—22no—
53Dic79⋊C4—24no—
54Dic79⋊C4—22no—
55Dic79⋊C4—24no—
56C22⋊Dic79—24no—
57C22⋊Dic79—24no—
58C22⋊Dic79—24no—
59C4×Dic79—22no—
60C4×Dic79—22no—
61C4×Dic79D414yes—
62C24×C79C2312yes—
63C2×D4×C79—24no—
64C2×D4×C79—22no—
65C22×C4×C79C2312yes—
66C22×C4×C79C2311yescharacteristic
67C22×C4×C79C2311yescharacteristic
68C22×C4×C79C2311yescharacteristic
69C4⋊C4×C79—22no—
70C22⋊C4×C79—24no—
71C22⋊C4×C79—24no—
72C23×C79—22no—
73C23×C79—22no—
74C23×C79—22no—
75C23×C79—22no—
76C23×C79—22no—
77C23×C79—22no—
78C23×C79#4114yes—
79C23×C79C2411yescharacteristic
80D4×C79—28no—
81C2×C4×C79—21no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—21no—
85C2×C4×C79—22no—
86C2×C4×C79—22no—
87C2×C4×C79—22no—
88C2×C4×C79—22no—
89C2×C4×C79C2×D412yes—
90C2×C4×C79C2×D412yes—
91C2×Dic79—21no—
92C2×Dic79—21no—
93C2×Dic79—22no—
94C2×Dic79—21no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—22no—
98C2×Dic79—22no—
99C2×Dic79—22no—
100C2×Dic79—22no—
101C2×Dic79—22no—
102C2×Dic79—48no—
103C2×Dic79C2×D412yes—
104C2×Dic79C2×D412yes—
105C2×Dic79C2×D412yes—
106C2×Dic79C2×D412yes—
107C2×Dic79#4112yes—
108Dic158—28no—
109C22×C79—24no—
110C22×C79—24no—
111C22×C79—24no—
112C22×C79—42no—
113C22×C79—42no—
114C22×C79—42no—
115C22×C79—42no—
116C22×C79C22×D411yescharacteristic
117C22×C79C22×D411yescharacteristic
118C22×C79C2×#4111yescharacteristic
119C22×C79C2×#4112yes—
120C22×C792−1+412yes—
121C4×C79—22no—
122C4×C79—22no—
123C4×C79—41no—
124C4×C79—42no—
125Dic79—22no—
126Dic79—22no—
127Dic79—42no—
128Dic79—41no—
129Dic79—42no—
130Dic79#12114yes—
131C2×C79—44no—
132C2×C79C2×#12111yescharacteristic
133C2×C79#52511yescharacteristic
134C2×C79#53611yescharacteristic
135C2×C79#54812yes—
136C2×C79#55212yes—
137#2536—791nomaximal, Sylow
138C79#253611yescharacteristic, complemented, Sylow
139C2×C22⋊Q8—792no—
140C2×C4×Q8—791no—
141C2×C4×D4—791no—
142#398—791no—
143#398—791no—
144#394—791no—
145#394D7911yescharacteristic
146#388—792no—
147#388—792no—
148#382—791no—
149#380—792no—
150C22×Q8—791no—
151C22×D4C2×D7911yescharacteristic
152C23×C4—792no—
153C22⋊Q8—1588no—
154C4×Q8—1584no—
155C4×D4—1584no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4—791no—
158C2×C4⋊C4—791no—
159C2×C4⋊C4—792no—
160C2×C4⋊C4—792no—
161C2×C4⋊C4—792no—
162C2×C4⋊C4C2×D7911yescharacteristic
163C2×C22⋊C4—792no—
164C2×C22⋊C4—792no—
165C2×C22⋊C4—792no—
166C2×C22⋊C4C2×D7912yes—
167C2×C22⋊C4C2×D7912yes—
168C2×C42—791no—
169C2×C42—791no—
170C2×C42—791no—
171#95—792no—
172#95—792no—
173#95—792no—
174#95—791no—
175#95C2×D7911yescharacteristic
176C24C22×D7912yes—
177C2×Q8—794no—
178C2×Q8—1582no—
179C2×Q8—1582no—
180C2×D4—24no—
181C2×D4—22no—
182C22×C4—791no—
183C22×C4—791no—
184C22×C4—791no—
185C22×C4—792no—
186C22×C4—791no—
187C22×C4—792no—
188C22×C4—1584no—
189C22×C4—1584no—
190C22×C4—1584no—
191C22×C4C22×D7912yes—
192C22×C4C22×D7911yescharacteristic
193C22×C4C22×D7911yescharacteristic
194C22×C4C22×D7911yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—1582no—
197C4⋊C4—1584no—
198C4⋊C4—1584no—
199C4⋊C4—1582no—
200C4⋊C4—1584no—
201C4⋊C4—1582no—
202C22⋊C4—24no—
203C22⋊C4—24no—
204C22⋊C4—1584no—
205C22⋊C4—1584no—
206C22⋊C4—1584no—
207C42—794no—
208C42—1582no—
209C42—1582no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23#1192962314yes—
217C23C23×D7911yescharacteristic
218Q8—1588no—
219D4—28no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—3168no—
229C2×C4—792no—
230C2×C4—792no—
231C2×C4—792no—
232C2×C4—792no—
233C2×C4—792no—
234C2×C4—1582no—
235C2×C4—1582no—
236C2×C4—1582no—
237C2×C4—1582no—
238C2×C4—1581no—
239C2×C4—1582no—
240C2×C4—1582no—
241C2×C4—1582no—
242C2×C4—1581no—
243C2×C4—1582no—
244C2×C4—1581no—
245C2×C4D4×D7912yes—
246C2×C4D4×D7912yes—
247C22—24no—
248C22—24no—
249C22—24no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C2×D4×D7911yescharacteristic
255C22C2×D4×D7911yescharacteristic
256C22#41×D7911yescharacteristic
257C22C2×#1192962312yes—
258C22#1457920812yes—
259C4—22no—
260C4—22no—
261C4—42no—
262C4—41no—
263C4—3162no—
264C4—3162no—
265C4—3161no—
266C4—794no—
267C4—1582no—
268C4—1582no—
269C2—44no—
270C2#121×D7911yescharacteristic
271C2#1909906911yescharacteristic
272C2#1909913311yescharacteristic
273C2#1909921912yes—
274C2#1909925012yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#394×C79C2
prime radicalC22×D4×C79C22
hypercenter#394D79
hypocenterC79#2536
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14579138C2semidirect
2. C2×#14579126C2semidirect
4. #19098495C2semidirect
5. #19098493C2semidirect
7. #19098457C2semidirect
8. #19098456C2semidirect
9. #19098427C2semidirect
10. #19098421C2semidirect
40. C2×Dic158D4semidirect
138. C79#2536semidirect