Finite Group Databasebeta

← #23776041

Subgroups — #23776041

Order 10112.

370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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#19099291C211yesmaximal, characteristic, complemented
2#19099228C211yesmaximal, characteristic
3#19098915C211yesmaximal, characteristic, complemented
4#19098912C212yesmaximal, complemented
5#19098847C212yesmaximal, complemented
6#19098769C211yesmaximal, characteristic
7#19098767C212yesmaximal
8#19098687C211yesmaximal, characteristic, complemented
9C4×#11929611C211yesmaximal, characteristic
10#19098650C212yesmaximal
11#475×C79C211yesmaximal, characteristic, complemented
12C2×Q8×D79—21no—
13C2×#11929613C2212yes—
14C2×#11929611C2211yescharacteristic
15#14579161C2211yescharacteristic
16#14579160C2212yes—
17#14579159C2212yes—
18#14579153—21no—
19#14579151—22no—
20#14579139—22no—
21#14579137—21no—
22C4×Dic158—21no—
23C4×Dic158C2211yescharacteristic
24#14579126C2212yes—
25C4×D316C2211yescharacteristic
26#14579123C2212yes—
27#14579092C2211yescharacteristic
28Dic79⋊C8C2212yes—
29#14579086C2212yes—
30#14579085C2211yescharacteristic
31#14579084C2212yes—
32#14579084C2212yes—
33#14579081C2211yescharacteristic
34C4×C79⋊C8C2211yescharacteristic
35C8×Dic79C2212yes—
36C4⋊Q8×C79C2211yescharacteristic
37C4×Q8×C79C2211yescharacteristic
38#106×C79C2212yes—
39C4⋊C8×C79C2211yescharacteristic
40#103×C79C2212yes—
41C2×Dic158—22no—
42C2×Dic158D411yescharacteristic
43C2×Dic158C2312yes—
44Q8×D79—44no—
45C2×D316C2311yescharacteristic
46C2×C4×D79—22no—
47C2×C4×D79—21no—
48#11929613—24no—
49#11929611—22no—
50C2×C79⋊C8C2311yescharacteristic
51C2×C79⋊C8C2311yescharacteristic
52C4⋊Dic79—21no—
53C4⋊Dic79—21no—
54C4⋊Dic79D411yescharacteristic
55C4⋊Dic79C2311yescharacteristic
56Dic79⋊C4—22no—
57Dic79⋊C4—22no—
58Dic79⋊C4—22no—
59Dic79⋊C4—22no—
60Dic79⋊C4D412yes—
61(C2×D79)⋊C4—22no—
62(C2×D79)⋊C4—21no—
63C4×Dic79—22no—
64C4×Dic79C2312yes—
65C2×Q8×C79—21no—
66C2×Q8×C79C2311yescharacteristic
67C2×C8×C79C2312yes—
68C4⋊C4×C79—21no—
69C4⋊C4×C79—21no—
70C4⋊C4×C79C2312yes—
71C4⋊C4×C79C2311yescharacteristic
72C42×C79—21no—
73C42×C79C2311yescharacteristic
74C22×D79—21no—
75Q8×C79—21no—
76Q8×C79—21no—
77Q8×C79—42no—
78C2×C4×C79—21no—
79C2×C4×C79—22no—
80C2×C4×C79—21no—
81C2×C4×C79C2×D411yescharacteristic
82C2×C4×C79C2×D411yescharacteristic
83C2×C4×C79C2411yescharacteristic
84C2×Dic79—22no—
85C2×Dic79—21no—
86C2×Dic79C2×D412yes—
87C2×Dic79C2×D412yes—
88D316—21no—
89D316#4112yes—
90C4×D79—42no—
91C4×D79—44no—
92Dic158—22no—
93Dic158—22no—
94Dic158—44no—
95Dic158SD1614yescomplemented
96C8×C79—22no—
97C79⋊C8—21no—
98C79⋊C8—21no—
99C22×C79C22×D411yescharacteristic
100C2×D79—22no—
101C2×D79—41no—
102C2×D79—41no—
103C4×C79—21no—
104C4×C79—41no—
105C4×C79—42no—
106C4×C79—41no—
107C4×C79C2×SD1612yes—
108C4×C79C2×#4111yescharacteristic
109C4×C792−1+411yescharacteristic
110Dic79—22no—
111Dic79—42no—
112Dic79—41no—
113Dic79C2×SD1614yes—
114C2×C79#54811yescharacteristic
115C2×C79C22×SD1611yescharacteristic
116C2×C79#57811yescharacteristic
117D79—42no—
118#3359—791nomaximal, Sylow
119C79#335911yescharacteristic, complemented, Sylow
120#557—791no—
121D4×Q8—791no—
122#487—791no—
123#487—792no—
124#475—792no—
125#475D7911yescharacteristic, complemented
126#461—791no—
127#461—792no—
128C8×Q8—791no—
129C4×SD16—791no—
130C4×SD16—792no—
131C22×Q8—1581no—
132C2×SD16—791no—
133C2×SD16—792no—
134C4⋊Q8—792no—
135C4⋊Q8—792no—
136C4⋊Q8—791no—
137C4⋊Q8C2×D7911yescharacteristic
138#125—1581no—
139#125—1582no—
140C22⋊Q8—1582no—
141C22⋊Q8—1581no—
142C4×Q8—791no—
143C4×Q8—792no—
144C4×Q8—1581no—
145C4×Q8C2×D7911yescharacteristic
146C4×D4—792no—
147C4×D4—791no—
148#106—791no—
149#106C2×D7912yes—
150C4⋊C8—792no—
151C4⋊C8C2×D7911yescharacteristic
152#103—791no—
153#103—792no—
154#103—792no—
155#103—792no—
156#103C2×D7912yes—
157#102—791no—
158C4×C8—792no—
159C4×C8—791no—
160C2×Q8—21no—
161C2×Q8—3164no—
162C2×Q8—791no—
163C2×Q8—792no—
164C2×Q8—1582no—
165C2×Q8C22×D7911yescharacteristic
166C2×D4—791no—
167C22×C4—1582no—
168C22×C4—1581no—
169SD16—1584no—
170SD16—1582no—
171C2×C8—791no—
172C2×C8—791no—
173C2×C8C22×D7912yes—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—792no—
177C4⋊C4—791no—
178C4⋊C4—791no—
179C4⋊C4—1582no—
180C4⋊C4—1582no—
181C4⋊C4—1582no—
182C4⋊C4—1582no—
183C4⋊C4—1581no—
184C4⋊C4—1581no—
185C4⋊C4C22×D7911yescharacteristic
186C4⋊C4C22×D7912yes—
187C22⋊C4—1582no—
188C22⋊C4—1581no—
189C42—21no—
190C42—792no—
191C42—1582no—
192C42C22×D7911yescharacteristic
193C23—1581no—
194Q8—21no—
195Q8—21no—
196Q8—42no—
197Q8—3164no—
198Q8—794no—
199Q8—1582no—
200Q8—1582no—
201D4—792no—
202D4—1581no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—3164no—
207C2×C4—3162no—
208C2×C4—792no—
209C2×C4—792no—
210C2×C4—1582no—
211C2×C4—1581no—
212C2×C4D4×D7911yescharacteristic
213C2×C4D4×D7911yescharacteristic
214C2×C4C23×D7911yescharacteristic
215C8—22no—
216C8—1581no—
217C8—1581no—
218C22—3161no—
219C22—3161no—
220C22—1582no—
221C22C2×D4×D7911yescharacteristic
222C4—21no—
223C4—41no—
224C4—42no—
225C4—41no—
226C4—3162no—
227C4—3161no—
228C4—794no—
229C4—1582no—
230C4SD16×D7912yes—
231C4#41×D7911yescharacteristic
232C4#1457920911yescharacteristic
233C2—3162no—
234C2#1909922311yescharacteristic
235C2C2×SD16×D7911yescharacteristic
236C2#1909937911yescharacteristic
subgroupG/H
centerC22C2×D4×D79
commutator, cosocleC2×C4×C79C24
FrattiniC2×C4C23×D79
Fitting#475×C79C2
socleC22×C79C22×D4
prime radicalC2×D316C23
hypercenter#475D79
hypocenterC79#3359
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #19099291C2semidirect
3. #19098915C2semidirect
4. #19098912C2semidirect
5. #19098847C2semidirect
8. #19098687C2semidirect
11. #475×C79C2semidirect
95. Dic158SD16semidirect
119. C79#3359semidirect
125. #475D79semidirect