Finite Group Databasebeta

← #23774605

Subgroups — #23774605

Order 10112.

324 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 113 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×#14579152C211yesmaximal, characteristic
3#19098971C212yesmaximal, complemented
4#19098930C212yesmaximal, complemented
5#19098898C211yesmaximal, characteristic
6#19098894C211yesmaximal, characteristic
7#19098891C211yesmaximal, characteristic
8#19098869C212yesmaximal, complemented
9#19098868C212yesmaximal, complemented
10#19098617C211yesmaximal, characteristic
11#484×C79C211yesmaximal, characteristic
12#14579160C2211yescharacteristic
13#14579159C2211yescharacteristic
14#14579152—21no—
15#14579152—21no—
16#14579152C2212yes—
17#14579152C2212yes—
18#14579151—21no—
19#14579140C2211yescharacteristic
20#14579138—21no—
21Q8×Dic79C2211yescharacteristic
22#14579126—21no—
23#14579126C2211yescharacteristic
24#14579117—21no—
25C2×C4⋊Dic79—21no—
26C2×C4⋊Dic79C2211yescharacteristic
27C2×Dic79⋊C4—21no—
28C2×C4×Dic79C2211yescharacteristic
29#14579094C2212yes—
30#14579093C2212yes—
31#14579092C2212yes—
32Dic79⋊C8C2212yes—
33#14579086C2212yes—
34#14579085C2212yes—
35#14579084C2212yes—
36C22⋊(C79⋊C8)C2211yescharacteristic
37#14579071C2212yes—
38C22⋊Q8×C79C2211yescharacteristic
39C2×C4⋊C4×C79C2211yescharacteristic
40#107×C79C2212yes—
41#103×C79C2212yes—
42C22⋊C8×C79C2211yescharacteristic
43C2×Dic158—21no—
44C2×Dic158C2311yescharacteristic
45C22×Dic79—21no—
46C22×Dic79D411yescharacteristic
47C22×Dic79D411yescharacteristic
48C2×C79⋊C8C2312yes—
49C4⋊Dic79—22no—
50C4⋊Dic79—22no—
51C4⋊Dic79—21no—
52C4⋊Dic79—21no—
53C4⋊Dic79C2312yes—
54C4⋊Dic79C2311yescharacteristic
55Dic79⋊C4—22no—
56Dic79⋊C4—22no—
57Dic79⋊C4—21no—
58Dic79⋊C4—21no—
59Dic79⋊C4—21no—
60Dic79⋊C4—21no—
61Dic79⋊C4—21no—
62C22⋊Dic79—21no—
63C4×Dic79—21no—
64C4×Dic79—21no—
65C4×Dic79D411yescharacteristic
66C4×Dic79D411yescharacteristic
67C4×Dic79C2311yescharacteristic
68C4×Dic79C2311yescharacteristic
69C2×Q8×C79C2311yescharacteristic
70C22×C4×C79—21no—
71C22×C4×C79C2311yescharacteristic
72C2×C8×C79C2312yes—
73C4⋊C4×C79—21no—
74C4⋊C4×C79—21no—
75C4⋊C4×C79C2312yes—
76C4⋊C4×C79C2311yescharacteristic
77C22⋊C4×C79—21no—
78C23×C79C2×D411yescharacteristic
79Q8×C79—22no—
80C2×C4×C79—22no—
81C2×C4×C79—21no—
82C2×C4×C79—21no—
83C2×C4×C79—22no—
84C2×C4×C79—42no—
85C2×C4×C79C2×D411yescharacteristic
86C2×C4×C79C2411yescharacteristic
87C2×Dic79—22no—
88C2×Dic79—21no—
89C2×Dic79—21no—
90C2×Dic79—22no—
91C2×Dic79—41no—
92C2×Dic79—42no—
93C2×Dic79C2×D411yescharacteristic
94C2×Dic79C2×D411yescharacteristic
95C2×Dic79C2×D411yescharacteristic
96C2×Dic79C2×D411yescharacteristic
97Dic158—22no—
98Dic158—42no—
99C8×C79—22no—
100C79⋊C8—22no—
101C22×C79—21no—
102C22×C79—21no—
103C22×C79#13712yes—
104C22×C79C22×D411yescharacteristic
105C4×C79—21no—
106C4×C79—41no—
107C4×C79—42no—
108C4×C79—41no—
109C4×C792−1+412yes—
110Dic79—21no—
111Dic79—21no—
112Dic79—21no—
113Dic79—21no—
114Dic79—41no—
115Dic79—42no—
116Dic79—41no—
117C2×C79—22no—
118C2×C79#53611yescharacteristic
119C2×C79C2×#13711yescharacteristic
120C2×C79#57511yescharacteristic
121#3236—791nomaximal, Sylow
122C79#323611yescharacteristic, complemented, Sylow
123#533—791no—
124C2×#125—791no—
125#501—792no—
126#491—792no—
127#484—791no—
128#484D7911yescharacteristic
129#483—791no—
130#483—791no—
131#479—792no—
132#479—792no—
133#432—791no—
134C4⋊Q8—791no—
135C4⋊Q8—791no—
136#125—792no—
137#125—792no—
138#125—1581no—
139#125—1581no—
140#125—1581no—
141C22⋊Q8—791no—
142C22⋊Q8—1581no—
143C22⋊Q8C2×D7911yescharacteristic
144C4×Q8—791no—
145C4×Q8—791no—
146C4×Q8—1581no—
147#117—1581no—
148C2×C4⋊C4—791no—
149C2×C4⋊C4—1581no—
150C2×C4⋊C4—1581no—
151C2×C4⋊C4C2×D7911yescharacteristic
152C2×C42—791no—
153#107—792no—
154#107C2×D7912yes—
155#106—792no—
156#106—792no—
157C4⋊C8—792no—
158#103—792no—
159#103—792no—
160#103—792no—
161#103C2×D7912yes—
162C22⋊C8—791no—
163C22⋊C8C2×D7911yescharacteristic
164#97—792no—
165C2×Q8—791no—
166C2×Q8—1581no—
167C2×Q8C22×D7911yescharacteristic
168C22×C4—21no—
169C22×C4—791no—
170C22×C4—791no—
171C22×C4—1581no—
172C22×C4C22×D7911yescharacteristic
173C2×C8—792no—
174C2×C8C22×D7912yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—792no—
178C4⋊C4—791no—
179C4⋊C4—1582no—
180C4⋊C4—1582no—
181C4⋊C4—1581no—
182C4⋊C4—1581no—
183C4⋊C4—1581no—
184C4⋊C4—1581no—
185C4⋊C4—1582no—
186C4⋊C4—1582no—
187C4⋊C4—1581no—
188C4⋊C4—1581no—
189C4⋊C4—1581no—
190C4⋊C4C22×D7912yes—
191C4⋊C4C22×D7911yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—1581no—
194C42—791no—
195C42—791no—
196C42—791no—
197C42—791no—
198C42—1581no—
199C42—1581no—
200C23D4×D7911yescharacteristic
201Q8—22no—
202Q8—3162no—
203Q8—1582no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—3162no—
210C2×C4—3161no—
211C2×C4—791no—
212C2×C4—791no—
213C2×C4—791no—
214C2×C4—791no—
215C2×C4—1581no—
216C2×C4—1581no—
217C2×C4—1582no—
218C2×C4—1582no—
219C2×C4D4×D7911yescharacteristic
220C2×C4C23×D7911yescharacteristic
221C8—22no—
222C8—1582no—
223C22—21no—
224C22—21no—
225C22#1457919312yes—
226C22C2×D4×D7911yescharacteristic
227C4—21no—
228C4—42no—
229C4—41no—
230C4—41no—
231C4—3162no—
232C4—3161no—
233C4—3161no—
234C4—1581no—
235C4—1581no—
236C4—1581no—
237C4—1581no—
238C4#1457920812yes—
239C2—22no—
240C2#1909913511yescharacteristic
241C2C2×#1457919311yescharacteristic
242C2#1909935911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#484×C79C2
socleC22×C79C22×D4
prime radicalC23×C79C2×D4
hypercenter#484D79
hypocenterC79#3236
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #19098971C2semidirect
4. #19098930C2semidirect
8. #19098869C2semidirect
9. #19098868C2semidirect
122. C79#3236semidirect