Finite Group Databasebeta

← #23765983

Subgroups — #23765983

Order 10112.

784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×Q8×D79C211yesmaximal, characteristic
2C2×#14579119C211yesmaximal, characteristic
3C2×#14579118C211yesmaximal, characteristic
4#19098470C211yesmaximal, characteristic, complemented
5#19098469C211yesmaximal, characteristic, complemented
6#19098468C211yesmaximal, characteristic, complemented
7#19098467C214yesmaximal, complemented
8#19098425C214yesmaximal
9#391×C79C211yesmaximal, characteristic, complemented
10C22×Dic158C2212yes—
11C22×Dic158C2211yescharacteristic
12C2×Q8×D79—24no—
13C2×Q8×D79—24no—
14C2×Q8×D79C418yescomplemented
15C22×C4×D79C2212yes—
16C22×C4×D79C2211yescharacteristic
17#14579119—24no—
18#14579118—24no—
19C2×C4⋊Dic79C2211yescharacteristic
20C2×Dic79⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×(C2×D79)⋊C4C2212yes—
23C2×C4×Dic79C2212yes—
24C2×C4×Dic79C2211yescharacteristic
25C79⋊#95C2214yes—
26C79⋊#95C2214yes—
27C79⋊#95C2214yes—
28C22×Q8×C79C2211yescharacteristic
29C2×C4⋊C4×C79C2211yescharacteristic
30C2×C42×C79C2211yescharacteristic
31#95×C79C2214yes—
32C23×D79C2311yescharacteristic
33C2×Dic158—24no—
34C2×Dic158—24no—
35C2×Dic158—22no—
36C2×Dic158—22no—
37C2×Dic158C2×C418yes—
38C2×Dic158C2×C414yes—
39Q8×D79—232no—
40C22×Dic79C2312yes—
41C22×Dic79C2312yes—
42C22×Dic79C2312yes—
43C22×Dic79C2311yescharacteristic
44C2×C4×D79—24no—
45C2×C4×D79—24no—
46C2×C4×D79C2×C418yes—
47C2×C4×D79C2×C414yes—
48C2×C4×D79D414yes—
49C2×C4×D79D414yes—
50C4⋊Dic79—22no—
51Dic79⋊C4—24no—
52(C2×D79)⋊C4—24no—
53(C2×D79)⋊C4—24no—
54C4×Dic79—24no—
55C4×Dic79—22no—
56C2×Q8×C79—22no—
57C2×Q8×C79—22no—
58C2×Q8×C79C2×C414yes—
59C22×C4×C79C2312yes—
60C22×C4×C79C2312yes—
61C22×C4×C79C2312yes—
62C22×C4×C79C2311yescharacteristic
63C4⋊C4×C79—22no—
64C42×C79—22no—
65C23×C79C2411yescharacteristic
66C22×D79—22no—
67C22×D79—22no—
68C22×D79C22×C412yes—
69C22×D79C2×D412yes—
70C22×D79C2×D412yes—
71Q8×C79—28no—
72C2×C4×C79—22no—
73C2×C4×C79—22no—
74C2×C4×C79—22no—
75C2×C4×C79—22no—
76C2×C4×C79—22no—
77C2×C4×C79—24no—
78C2×C4×C79—22no—
79C2×C4×C79C22×C414yes—
80C2×C4×C79C22×C412yes—
81C2×C4×C79C2×D412yes—
82C2×C4×C79C2×D412yes—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86C2×Dic79—22no—
87C2×Dic79—22no—
88C2×Dic79—22no—
89C2×Dic79—24no—
90C2×Dic79C22×C414yes—
91C2×Dic79C22×C412yes—
92C2×Dic79C2×D412yes—
93C2×Dic79C2×D412yes—
94C4×D79—216no—
95C4×D79C22⋊C4116yes—
96Dic158—28no—
97Dic158—216no—
98C22×C79C23×C411yescharacteristic
99C22×C79C22×D411yescharacteristic
100C22×C79C22×D411yescharacteristic
101C22×C792−1+412yes—
102C22×C792−1+412yes—
103C2×D79—24no—
104C2×D79—24no—
105C2×D79—22no—
106C2×D79—22no—
107C2×D79C2×C22⋊C414yes—
108C4×C79—24no—
109C4×C79—42no—
110C4×C79—42no—
111C4×C79C2×C22⋊C414yes—
112Dic79—24no—
113Dic79—42no—
114Dic79—42no—
115Dic79C2×C22⋊C414yes—
116C2×C79C22×C22⋊C411yescharacteristic
117C2×C79#51912yes—
118C2×C79#53612yes—
119C2×C79#53611yescharacteristic
120C2×C79#53611yescharacteristic
121D79—24no—
122#2310—791nomaximal, Sylow
123C79#231011yescharacteristic, complemented, Sylow
124C23×Q8—791no—
125C2×#117—791no—
126C2×#117—791no—
127#391—791no—
128#391—791no—
129#391—791no—
130#391—794no—
131#391D7911yescharacteristic, complemented
132#381—794no—
133C22×Q8—798no—
134C22×Q8—792no—
135C22×Q8—791no—
136C22×Q8—1584no—
137C22×Q8—1584no—
138C22×Q8C2×D7911yescharacteristic
139C23×C4—791no—
140C23×C4—792no—
141#117—1584no—
142#117—1584no—
143C2×C4⋊C4—792no—
144C2×C4⋊C4—791no—
145C2×C4⋊C4C2×D7911yescharacteristic
146C2×C22⋊C4—792no—
147C2×C22⋊C4—792no—
148C2×C42—792no—
149C2×C42—791no—
150C2×C42C2×D7911yescharacteristic
151#95—794no—
152#95—794no—
153#95—794no—
154#95C2×D7914yes—
155C24—791no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8—798no—
159C2×Q8—794no—
160C2×Q8—1584no—
161C2×Q8—1584no—
162C2×Q8—15832no—
163C2×Q8—1582no—
164C2×Q8—1582no—
165C2×Q8C4×D7914yes—
166C22×C4—791no—
167C22×C4—794no—
168C22×C4—794no—
169C22×C4—794no—
170C22×C4—792no—
171C22×C4—798no—
172C22×C4—792no—
173C22×C4—792no—
174C22×C4—1584no—
175C22×C4—1584no—
176C22×C4C22×D7912yes—
177C22×C4C22×D7912yes—
178C22×C4C22×D7912yes—
179C22×C4C22×D7911yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—1584no—
182C4⋊C4—1582no—
183C22⋊C4—1584no—
184C22⋊C4—1584no—
185C42—22no—
186C42—1584no—
187C42—1582no—
188C23—792no—
189C23—792no—
190C23—792no—
191C23—1582no—
192C23—1582no—
193C23C23×D7911yescharacteristic
194Q8—28no—
195Q8—15816no—
196Q8—1588no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—792no—
205C2×C4—792no—
206C2×C4—792no—
207C2×C4—7916no—
208C2×C4—794no—
209C2×C4—15816no—
210C2×C4—1582no—
211C2×C4—1582no—
212C2×C4—1584no—
213C2×C4—1582no—
214C2×C4—1582no—
215C2×C4—1582no—
216C2×C4—1582no—
217C2×C4C2×C4×D7914yes—
218C2×C4C2×C4×D7912yes—
219C2×C4D4×D7912yes—
220C2×C4D4×D7912yes—
221C22—794no—
222C22—1584no—
223C22—1582no—
224C22—1584no—
225C22—1582no—
226C22C22×C4×D7911yescharacteristic
227C22C2×D4×D7911yescharacteristic
228C22C2×D4×D7911yescharacteristic
229C22#1457920812yes—
230C22#1457920912yes—
231C4—24no—
232C4—42no—
233C4—42no—
234C4—3162no—
235C4—3162no—
236C4—794no—
237C4—1584no—
238C4C22⋊C4×D7914yes—
239C2—1584no—
240C2C2×C22⋊C4×D7911yescharacteristic
241C2#1909903912yes—
242C2#1909913311yescharacteristic
243C2#1909913612yes—
244C2#1909913811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#391×C79C2
socle, cosocleC23×C79C24
prime radicalC23×D79C23
hypercenter#391D79
hypocenterC79#2310
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
4. #19098470C2semidirect
5. #19098469C2semidirect
6. #19098468C2semidirect
7. #19098467C2semidirect
9. #391×C79C2semidirect
14. C2×Q8×D79C4semidirect
123. C79#2310semidirect
131. #391D79semidirect