Finite Group Databasebeta

← #23773527

Subgroups — #23773527

Order 10112.

380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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
1#19099115C211yesmaximal, characteristic
2C2×#14579126C211yesmaximal, characteristic
3#19098893C211yesmaximal, characteristic
4#19098847C212yesmaximal, complemented
5#19098772C212yesmaximal, complemented
6#19098721C211yesmaximal, characteristic
7#19098718C211yesmaximal, characteristic
8#19098669C212yesmaximal, complemented
9#19098667C212yesmaximal, complemented
10#19098617C211yesmaximal, characteristic
11#483×C79C211yesmaximal, characteristic
12C22×Dic158C2211yescharacteristic
13C2×Dic316C2212yes—
14C2×#11929614C2212yes—
15#14579160C2211yescharacteristic
16#14579159C2211yescharacteristic
17#14579151—21no—
18#14579140C2211yescharacteristic
19#14579138—21no—
20Q8×Dic79C2211yescharacteristic
21#14579126—21no—
22#14579126—21no—
23#14579126—21no—
24#14579126C2212yes—
25#14579126C2211yescharacteristic
26#14579126C2212yes—
27#14579117—21no—
28C2×Dic79⋊C4—21no—
29C2×C4×Dic79—21no—
30C2×C4×Dic79C2211yescharacteristic
31#14579092C2212yes—
32Dic79⋊C8C2212yes—
33#14579086C2212yes—
34#14579084C2212yes—
35#14579084C2212yes—
36C22⋊(C79⋊C8)C2211yescharacteristic
37#14579071C2212yes—
38C22⋊Q8×C79C2211yescharacteristic
39C2×C4⋊C4×C79C2211yescharacteristic
40#106×C79C2212yes—
41#103×C79C2212yes—
42C22⋊C8×C79C2211yescharacteristic
43C2×Dic158—24no—
44C2×Dic158—21no—
45C2×Dic158—21no—
46C2×Dic158C2311yescharacteristic
47C2×Dic158C2312yes—
48C22×Dic79—21no—
49C22×Dic79D411yescharacteristic
50C22×Dic79D411yescharacteristic
51Dic316—24no—
52#11929614—24no—
53C2×C79⋊C8C2312yes—
54C4⋊Dic79—21no—
55C4⋊Dic79C2311yescharacteristic
56Dic79⋊C4—22no—
57Dic79⋊C4—22no—
58Dic79⋊C4—21no—
59Dic79⋊C4—21no—
60Dic79⋊C4—21no—
61Dic79⋊C4—21no—
62Dic79⋊C4—21no—
63C22⋊Dic79—21no—
64C4×Dic79—22no—
65C4×Dic79—22no—
66C4×Dic79—21no—
67C4×Dic79—21no—
68C4×Dic79D411yescharacteristic
69C4×Dic79D411yescharacteristic
70C4×Dic79C2311yescharacteristic
71C4×Dic79C2311yescharacteristic
72C2×Q8×C79C2311yescharacteristic
73C22×C4×C79—21no—
74C22×C4×C79C2311yescharacteristic
75C2×C8×C79C2312yes—
76C4⋊C4×C79—21no—
77C4⋊C4×C79—21no—
78C4⋊C4×C79C2312yes—
79C4⋊C4×C79C2311yescharacteristic
80C22⋊C4×C79—21no—
81C23×C79C2×D411yescharacteristic
82Q8×C79—22no—
83C2×C4×C79—22no—
84C2×C4×C79—22no—
85C2×C4×C79—21no—
86C2×C4×C79—21no—
87C2×C4×C79—42no—
88C2×C4×C79C2×D411yescharacteristic
89C2×C4×C79C2411yescharacteristic
90C2×Dic79—24no—
91C2×Dic79—22no—
92C2×Dic79—22no—
93C2×Dic79—22no—
94C2×Dic79—21no—
95C2×Dic79—21no—
96C2×Dic79C2×D411yescharacteristic
97C2×Dic79C2×D411yescharacteristic
98C2×Dic79C2×D411yescharacteristic
99C2×Dic79C2×D411yescharacteristic
100Dic158—24no—
101Dic158—22no—
102Dic158—22no—
103Dic158—42no—
104Dic158#4114yes—
105C8×C79—22no—
106C79⋊C8—22no—
107C22×C79—21no—
108C22×C79—21no—
109C22×C79#13712yes—
110C22×C79C22×D411yescharacteristic
111C4×C79—21no—
112C4×C79—41no—
113C4×C79—42no—
114C4×C79—41no—
115C4×C79C2×#4112yes—
116Dic79—24no—
117Dic79—21no—
118Dic79—21no—
119Dic79—21no—
120Dic79—41no—
121Dic79—41no—
122Dic79#13712yes—
123C2×C79—22no—
124C2×C79#52511yescharacteristic
125C2×C79C2×#13711yescharacteristic
126C2×C79C2×#13711yescharacteristic
127#3113—791nomaximal, Sylow
128C79#311311yescharacteristic, complemented, Sylow
129#533—791no—
130C2×C4×Q8—791no—
131#483—791no—
132#483D7911yescharacteristic
133#475—792no—
134#462—792no—
135#451—791no—
136#451—791no—
137#441—792no—
138#441—792no—
139#432—791no—
140C22×Q8—791no—
141C2×Q16—792no—
142C2×Q16—792no—
143C4⋊Q8—791no—
144C4⋊Q8—791no—
145#125—1581no—
146C22⋊Q8—791no—
147C22⋊Q8—1581no—
148C22⋊Q8C2×D7911yescharacteristic
149C4×Q8—791no—
150C4×Q8—792no—
151C4×Q8—792no—
152C4×Q8—791no—
153C4×Q8—1581no—
154C4×Q8—1581no—
155C4×Q8—1581no—
156#117—1581no—
157C2×C4⋊C4—1581no—
158C2×C4⋊C4C2×D7911yescharacteristic
159C2×C42—791no—
160C2×C42—1581no—
161#106—792no—
162#106C2×D7912yes—
163C4⋊C8—792no—
164#103—792no—
165#103—792no—
166#103—792no—
167#103C2×D7912yes—
168C22⋊C8—791no—
169C22⋊C8C2×D7911yescharacteristic
170#97—792no—
171C2×Q8—792no—
172C2×Q8—791no—
173C2×Q8—1581no—
174C2×Q8—1584no—
175C2×Q8—1581no—
176C2×Q8C22×D7911yescharacteristic
177C22×C4—21no—
178C22×C4—791no—
179C22×C4—791no—
180C22×C4—1581no—
181C22×C4C22×D7911yescharacteristic
182Q16—1584no—
183Q16—1584no—
184C2×C8—792no—
185C2×C8C22×D7912yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—791no—
189C4⋊C4—1582no—
190C4⋊C4—1582no—
191C4⋊C4—1581no—
192C4⋊C4—1581no—
193C4⋊C4—1581no—
194C4⋊C4—1581no—
195C4⋊C4—1581no—
196C4⋊C4—1581no—
197C4⋊C4C22×D7911yescharacteristic
198C4⋊C4C22×D7912yes—
199C22⋊C4—21no—
200C22⋊C4—1581no—
201C42—791no—
202C42—791no—
203C42—791no—
204C42—791no—
205C42—1582no—
206C42—1582no—
207C42—1581no—
208C42—1581no—
209C23D4×D7911yescharacteristic
210Q8—22no—
211Q8—3162no—
212Q8—794no—
213Q8—1584no—
214Q8—1582no—
215Q8—1582no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—791no—
222C2×C4—791no—
223C2×C4—791no—
224C2×C4—791no—
225C2×C4—1581no—
226C2×C4—1581no—
227C2×C4—1582no—
228C2×C4—1584no—
229C2×C4—1582no—
230C2×C4—1582no—
231C2×C4D4×D7911yescharacteristic
232C2×C4C23×D7911yescharacteristic
233C8—22no—
234C8—1582no—
235C22—21no—
236C22—21no—
237C22#1457919012yes—
238C22C2×D4×D7911yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—42no—
243C4—3161no—
244C4—3161no—
245C4—792no—
246C4—1584no—
247C4—1581no—
248C4—1581no—
249C4—1581no—
250C4#41×D7912yes—
251C2—22no—
252C2#1909907111yescharacteristic
253C2#137×D7911yescharacteristic
254C2C2×#1457919011yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#483×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#483D79
hypocenterC79#3113
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
4. #19098847C2semidirect
5. #19098772C2semidirect
8. #19098669C2semidirect
9. #19098667C2semidirect
128. C79#3113semidirect