Finite Group Databasebeta

← #23769513

Subgroups — #23769513

Order 10112.

524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14579137C211yesmaximal, characteristic
3#19098497C212yesmaximal, complemented
4#19098495C211yesmaximal, characteristic, complemented
5#19098493C211yesmaximal, characteristic, complemented
6#19098483C212yesmaximal, complemented
7#19098482C211yesmaximal, characteristic, complemented
8#19098422C212yesmaximal
9#19098420C212yesmaximal
10#95×D79C211yesmaximal, characteristic
11#395×C79C211yesmaximal, characteristic, complemented
12C22×Dic158C2211yescharacteristic
13C22×C4×D79C2211yescharacteristic
14C22×C4×D79C2212yes—
15#14579139—24no—
16#14579137—24no—
17C2×C4⋊Dic79C2211yescharacteristic
18C2×C4⋊Dic79C2212yes—
19C2×Dic79⋊C4C2211yescharacteristic
20C2×Dic79⋊C4C2212yes—
21C2×Dic79⋊C4C2211yescharacteristic
22C2×Dic79⋊C4C2212yes—
23C2×Dic79⋊C4C2212yes—
24C2×(C2×D79)⋊C4C2211yescharacteristic
25C2×(C2×D79)⋊C4C2212yes—
26C2×(C2×D79)⋊C4C2211yescharacteristic
27C79⋊#95C2211yescharacteristic
28C79⋊#95C2212yes—
29C79⋊#95C2212yes—
30C79⋊#95C2212yes—
31C79⋊#95C2212yes—
32C22×Q8×C79C2211yescharacteristic
33C2×C4⋊C4×C79C2211yescharacteristic
34C2×C4⋊C4×C79C2212yes—
35#95×C79C2211yescharacteristic
36#95×C79C2212yes—
37C23×D79C2311yescharacteristic
38C2×Dic158—22no—
39C2×Dic158—42no—
40C22×Dic79C2311yescharacteristic
41C22×Dic79C2311yescharacteristic
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C22×Dic79C2312yes—
45C2×C4×D79—42no—
46C2×C4×D79—42no—
47C2×C4×D79—42no—
48C2×C4×D79D414yes—
49C2×C4×D79Q818yescomplemented
50C4⋊Dic79—22no—
51C4⋊Dic79—42no—
52Dic79⋊C4—24no—
53Dic79⋊C4—22no—
54Dic79⋊C4—22no—
55Dic79⋊C4—42no—
56Dic79⋊C4—42no—
57(C2×D79)⋊C4—24no—
58(C2×D79)⋊C4—22no—
59(C2×D79)⋊C4—22no—
60C2×Q8×C79—22no—
61C2×Q8×C79—42no—
62C22×C4×C79C2311yescharacteristic
63C22×C4×C79C2311yescharacteristic
64C22×C4×C79C2312yes—
65C22×C4×C79C2311yescharacteristic
66C22×C4×C79C2312yes—
67C4⋊C4×C79—22no—
68C4⋊C4×C79—42no—
69C23×C79C2411yescharacteristic
70C22×D79—22no—
71C22×D79—21no—
72C22×D79—21no—
73C22×D79C2×D412yes—
74C22×D79C2×Q814yes—
75Q8×C79—44no—
76C2×C4×C79—22no—
77C2×C4×C79—22no—
78C2×C4×C79—22no—
79C2×C4×C79—21no—
80C2×C4×C79—22no—
81C2×C4×C79—21no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—22no—
86C2×C4×C79—21no—
87C2×C4×C79C2×D412yes—
88C2×C4×C79C2×Q814yes—
89C2×Dic79—22no—
90C2×Dic79—22no—
91C2×Dic79—22no—
92C2×Dic79—21no—
93C2×Dic79—22no—
94C2×Dic79—21no—
95C2×Dic79—22no—
96C2×Dic79—22no—
97C2×Dic79—21no—
98C2×Dic79—21no—
99C2×Dic79—22no—
100C2×Dic79C2×D412yes—
101C2×Dic79C2×Q814yes—
102C4×D79—44no—
103C4×D79—48no—
104Dic158—44no—
105C22×C79C22×D411yescharacteristic
106C22×C79C22×Q812yes—
107C22×C79H(5,𝔽2)12yes—
108C22×C79H(5,𝔽2)11yescharacteristic
109C22×C792−1+411yescharacteristic
110C2×D79—22no—
111C2×D79—22no—
112C2×D79—24no—
113C2×D79—24no—
114C2×D79C4⋊Q814yes—
115C4×C79—22no—
116C4×C79—24no—
117C4×C79—42no—
118C4×C79—41no—
119C4×C79—41no—
120Dic79—22no—
121Dic79—24no—
122Dic79—41no—
123Dic79—41no—
124Dic79—42no—
125C2×C79C2×C4⋊Q811yescharacteristic
126C2×C79#53411yescharacteristic
127C2×C79#53711yescharacteristic
128C2×C79#54312yes—
129C2×C79#54412yes—
130D79—24no—
131#2659—791nomaximal, Sylow
132C79#265911yescharacteristic, complemented, Sylow
133C2×C22⋊Q8—791no—
134C2×C22⋊Q8—791no—
135#398—791no—
136#398—791no—
137#398—792no—
138#395—791no—
139#395—792no—
140#395D7911yescharacteristic, complemented
141#380—792no—
142#380—792no—
143C2×#95—791no—
144C22×Q8—791no—
145C22×Q8C2×D7911yescharacteristic
146C23×C4—791no—
147C23×C4—792no—
148C22⋊Q8—1584no—
149C22⋊Q8—1584no—
150C2×C4⋊C4—792no—
151C2×C4⋊C4—792no—
152C2×C4⋊C4—792no—
153C2×C4⋊C4—792no—
154C2×C4⋊C4—791no—
155C2×C4⋊C4—791no—
156C2×C4⋊C4—791no—
157C2×C4⋊C4C2×D7911yescharacteristic
158C2×C4⋊C4C2×D7912yes—
159C2×C22⋊C4—791no—
160C2×C22⋊C4—792no—
161C2×C22⋊C4—791no—
162#95—791no—
163#95—792no—
164#95—792no—
165#95—792no—
166#95—792no—
167#95C2×D7911yescharacteristic
168#95C2×D7912yes—
169C24—791no—
170C2×Q8—22no—
171C2×Q8—42no—
172C2×Q8—3162no—
173C2×Q8—1582no—
174C22×C4—3162no—
175C22×C4—3162no—
176C22×C4—3162no—
177C22×C4—794no—
178C22×C4—798no—
179C22×C4—792no—
180C22×C4—791no—
181C22×C4—792no—
182C22×C4—791no—
183C22×C4—791no—
184C22×C4C22×D7911yescharacteristic
185C22×C4C22×D7912yes—
186C22×C4C22×D7911yescharacteristic
187C22×C4C22×D7911yescharacteristic
188C22×C4C22×D7912yes—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—3162no—
192C4⋊C4—3162no—
193C4⋊C4—3162no—
194C4⋊C4—1582no—
195C4⋊C4—1584no—
196C4⋊C4—1582no—
197C4⋊C4—1582no—
198C22⋊C4—1582no—
199C22⋊C4—1582no—
200C22⋊C4—1584no—
201C23—794no—
202C23—792no—
203C23—1582no—
204C23—1581no—
205C23—1581no—
206C23C23×D7911yescharacteristic
207Q8—44no—
208Q8—3164no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—3168no—
221C2×C4—3164no—
222C2×C4—794no—
223C2×C4—792no—
224C2×C4—1582no—
225C2×C4—1582no—
226C2×C4—1581no—
227C2×C4—1582no—
228C2×C4—1581no—
229C2×C4—1581no—
230C2×C4—1582no—
231C2×C4—1581no—
232C2×C4—1582no—
233C2×C4—1582no—
234C2×C4—1582no—
235C2×C4D4×D7912yes—
236C2×C4Q8×D7914yes—
237C22—794no—
238C22—1582no—
239C22—1584no—
240C22—1584no—
241C22—1582no—
242C22C2×D4×D7911yescharacteristic
243C22C2×Q8×D7912yes—
244C22#1457920612yes—
245C22#1457920711yescharacteristic
246C22#1457920911yescharacteristic
247C4—24no—
248C4—22no—
249C4—41no—
250C4—42no—
251C4—41no—
252C4—3162no—
253C4—3161no—
254C4—3161no—
255C4—1584no—
256C4—1582no—
257C2—1584no—
258C2C4⋊Q8×D7911yescharacteristic
259C2#1909912311yescharacteristic
260C2#1909914311yescharacteristic
261C2#1909918812yes—
262C2#1909919012yes—
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#395×C79C2
prime radicalC23×D79C23
hypercenter#395D79
hypocenterC79#2659
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
3. #19098497C2semidirect
4. #19098495C2semidirect
5. #19098493C2semidirect
6. #19098483C2semidirect
7. #19098482C2semidirect
11. #395×C79C2semidirect
49. C2×C4×D79Q8semidirect
132. C79#2659semidirect
140. #395D79semidirect