Finite Group Databasebeta

← #23771074

Subgroups — #23771074

Order 10112.

448 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 121 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#19098504C212yesmaximal, complemented
2#19098502C211yesmaximal, characteristic, complemented
3#19098492C212yesmaximal, complemented
4#19098480C211yesmaximal, characteristic
5#19098454C212yesmaximal, complemented
6#19098441C212yesmaximal
7#19098437C212yesmaximal, complemented
8#19098434C212yesmaximal, complemented
9#382×C79C211yesmaximal, characteristic, complemented
10C22×D316C2211yescharacteristic
11C22×C4×D79C2212yes—
12C2×C4⋊Dic79C2211yescharacteristic
13C2×Dic79⋊C4C2212yes—
14C2×Dic79⋊C4C2212yes—
15C2×(C2×D79)⋊C4C2212yes—
16C2×(C2×D79)⋊C4C2212yes—
17C2×(C2×D79)⋊C4C2212yes—
18C2×(C2×D79)⋊C4C2212yes—
19C2×(C2×D79)⋊C4C2212yes—
20C79⋊#95C2212yes—
21C79⋊#95C2212yes—
22C79⋊#95C2212yes—
23C79⋊#95C2212yes—
24C79⋊#95C2211yescharacteristic
25C79⋊#95C2211yescharacteristic
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C42×C79C2211yescharacteristic
29#95×C79C2212yes—
30#95×C79C2212yes—
31C23×D79C2312yes—
32C2×D316—24no—
33C2×D316—41no—
34C22×Dic79C2312yes—
35C22×Dic79C2312yes—
36C22×Dic79C2312yes—
37C2×C4×D79—42no—
38C2×C4×D79—42no—
39C2×C4×D79—42no—
40C4⋊Dic79—41no—
41Dic79⋊C4—42no—
42Dic79⋊C4—42no—
43(C2×D79)⋊C4—24no—
44(C2×D79)⋊C4—24no—
45(C2×D79)⋊C4—24no—
46(C2×D79)⋊C4—42no—
47(C2×D79)⋊C4—42no—
48C22×C4×C79C2312yes—
49C22×C4×C79C2311yescharacteristic
50C22×C4×C79C2311yescharacteristic
51C22×C4×C79C2312yes—
52C22×C4×C79C2311yescharacteristic
53C4⋊C4×C79—41no—
54C4⋊C4×C79—41no—
55C42×C79—22no—
56C23×C79C2411yescharacteristic
57C22×D79—22no—
58C22×D79—22no—
59C22×D79—22no—
60C22×D79—22no—
61C22×D79—22no—
62C22×D79—22no—
63C22×D79#4114yes—
64C2×C4×C79—21no—
65C2×C4×C79—21no—
66C2×C4×C79—22no—
67C2×C4×C79—22no—
68C2×C4×C79—22no—
69C2×C4×C79—22no—
70C2×C4×C79—22no—
71C2×C4×C79—22no—
72C2×C4×C79—22no—
73C2×C4×C79—21no—
74C2×C4×C79—22no—
75C2×C4×C79—21no—
76C2×C4×C79#4112yes—
77C2×Dic79—22no—
78C2×Dic79—22no—
79C2×Dic79—22no—
80C2×Dic79—22no—
81C2×Dic79—22no—
82C2×Dic79—22no—
83C2×Dic79—22no—
84C2×Dic79—22no—
85C2×Dic79—22no—
86D316—44no—
87C4×D79—48no—
88C22×C79C2×#4112yes—
89C22×C79C2×#4111yescharacteristic
90C22×C79H(5,𝔽2)11yescharacteristic
91C22×C79H(5,𝔽2)12yes—
92C22×C792−1+411yescharacteristic
93C2×D79—24no—
94C2×D79—24no—
95C2×D79—24no—
96C2×D79—42no—
97C2×D79—42no—
98C2×D79—42no—
99C2×D79—42no—
100C4×C79—22no—
101C4×C79—41no—
102C4×C79—41no—
103C4×C79—42no—
104C4×C79—42no—
105Dic79—42no—
106Dic79—42no—
107Dic79—42no—
108C2×C79#53911yescharacteristic
109C2×C79#53912yes—
110C2×C79#55111yescharacteristic
111C2×C79#55312yes—
112C2×C79H(3,𝔽4)11yescharacteristic
113D79—44no—
114#2782—791nomaximal, Sylow
115C79#278211yescharacteristic, complemented, Sylow
116#400—791no—
117#400—792no—
118#397—792no—
119#394—791no—
120#388—792no—
121#386—792no—
122#385—792no—
123#385—792no—
124#382D7911yescharacteristic, complemented
125C22×D4—791no—
126C23×C4—792no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—791no—
129C2×C4⋊C4—792no—
130C2×C4⋊C4C2×D7911yescharacteristic
131C2×C4⋊C4C2×D7911yescharacteristic
132C2×C22⋊C4—792no—
133C2×C22⋊C4—792no—
134C2×C22⋊C4—792no—
135C2×C22⋊C4—792no—
136C2×C22⋊C4—792no—
137C2×C42C2×D7911yescharacteristic
138#95—792no—
139#95—792no—
140#95—792no—
141#95—792no—
142#95—791no—
143#95—791no—
144#95C2×D7912yes—
145#95C2×D7912yes—
146C24—792no—
147C2×D4—3161no—
148C2×D4—1584no—
149C22×C4—3162no—
150C22×C4—3162no—
151C22×C4—3162no—
152C22×C4—792no—
153C22×C4—792no—
154C22×C4—792no—
155C22×C4C22×D7911yescharacteristic
156C22×C4C22×D7912yes—
157C22×C4C22×D7911yescharacteristic
158C22×C4C22×D7912yes—
159C22×C4C22×D7911yescharacteristic
160C4⋊C4—41no—
161C4⋊C4—41no—
162C4⋊C4—3162no—
163C4⋊C4—3162no—
164C4⋊C4—3161no—
165C22⋊C4—3162no—
166C22⋊C4—3162no—
167C22⋊C4—1584no—
168C22⋊C4—1584no—
169C22⋊C4—1584no—
170C42—22no—
171C23—794no—
172C23—1582no—
173C23—1582no—
174C23—1582no—
175C23—1582no—
176C23—1582no—
177C23—1582no—
178C23C23×D7911yescharacteristic
179D4—3164no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—3168no—
193C2×C4—1582no—
194C2×C4—1582no—
195C2×C4—1582no—
196C2×C4—1582no—
197C2×C4—1582no—
198C2×C4—1582no—
199C2×C4—1582no—
200C2×C4—1582no—
201C2×C4—1582no—
202C2×C4#1192962412yes—
203C22—3162no—
204C22—3162no—
205C22—3162no—
206C22—3162no—
207C22—1584no—
208C22—1584no—
209C22—1584no—
210C22#41×D7912yes—
211C22C2×#1192962411yescharacteristic
212C22#1457920611yescharacteristic
213C22#1457920712yes—
214C22#1457920911yescharacteristic
215C4—22no—
216C4—41no—
217C4—41no—
218C4—42no—
219C4—42no—
220C4—3162no—
221C4—3162no—
222C4—3162no—
223C2—3164no—
224C2#1909916011yescharacteristic
225C2#1909916112yes—
226C2#1909924311yescharacteristic
227C2#1909925712yes—
228C2#1909930511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D79
commutator, socle, cosocleC23×C79C24
Fitting#382×C79C2
prime radicalC22×D316C22
hypercenter#382D79
hypocenterC79#2782
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. #19098504C2semidirect
2. #19098502C2semidirect
3. #19098492C2semidirect
5. #19098454C2semidirect
7. #19098437C2semidirect
8. #19098434C2semidirect
9. #382×C79C2semidirect
115. C79#2782semidirect
124. #382D79semidirect