Finite Group Databasebeta

← #23766021

Subgroups — #23766021

Order 10112.

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

normal subgroups only

This group has 600 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
1C2×#14579119C211yesmaximal, characteristic
2C2×#14579118C211yesmaximal, characteristic
3C2×C4⋊C4×D79C211yesmaximal, characteristic
4#19098458C214yesmaximal, complemented
5#19098434C214yesmaximal
6#19098432C211yesmaximal, characteristic, complemented
7#19098429C211yesmaximal, characteristic, complemented
8#19098428C211yesmaximal, characteristic, complemented
9#384×C79C211yesmaximal, characteristic, complemented
10C22×C4×D79C2212yes—
11C22×C4×D79C2211yescharacteristic
12#14579119—24no—
13#14579118C418yescomplemented
14C2×C4⋊Dic79C2211yescharacteristic
15C2×C4⋊Dic79C2211yescharacteristic
16C2×Dic79⋊C4C2212yes—
17C2×Dic79⋊C4C2214yes—
18C2×Dic79⋊C4C2212yes—
19C4⋊C4×D79—24no—
20C2×(C2×D79)⋊C4C2212yes—
21C2×(C2×D79)⋊C4C2212yes—
22C2×C4×Dic79C2212yes—
23C2×C4×Dic79C2211yescharacteristic
24C79⋊#95C2214yes—
25C79⋊#95C2214yes—
26C2×C4⋊C4×C79C2211yescharacteristic
27C2×C4⋊C4×C79C2211yescharacteristic
28C2×C4⋊C4×C79C2214yes—
29C2×C42×C79C2211yescharacteristic
30C23×D79C2311yescharacteristic
31C22×Dic79C2312yes—
32C22×Dic79C2312yes—
33C22×Dic79C2312yes—
34C22×Dic79C2311yescharacteristic
35C2×C4×D79—24no—
36C2×C4×D79—44no—
37C2×C4×D79C2×C414yes—
38C2×C4×D79D414yes—
39C2×C4×D79Q814yes—
40C4⋊Dic79—22no—
41C4⋊Dic79—22no—
42Dic79⋊C4—24no—
43Dic79⋊C4—44no—
44Dic79⋊C4C2×C418yescomplemented
45(C2×D79)⋊C4—24no—
46(C2×D79)⋊C4C2×C418yes—
47C4×Dic79—24no—
48C4×Dic79C2×C414yescomplemented
49C22×C4×C79C2312yes—
50C22×C4×C79C2312yes—
51C22×C4×C79C2312yes—
52C22×C4×C79C2311yescharacteristic
53C4⋊C4×C79—22no—
54C4⋊C4×C79—22no—
55C4⋊C4×C79—44no—
56C42×C79C2×C414yescomplemented
57C23×C79C2411yescharacteristic
58C22×D79—22no—
59C22×D79—22no—
60C22×D79C22×C412yes—
61C22×D79C2×D412yes—
62C22×D79C2×Q812yes—
63C2×C4×C79—22no—
64C2×C4×C79—22no—
65C2×C4×C79—22no—
66C2×C4×C79—22no—
67C2×C4×C79—24no—
68C2×C4×C79—24no—
69C2×C4×C79C22×C414yes—
70C2×C4×C79C22×C412yes—
71C2×C4×C79C2×D412yes—
72C2×C4×C79C2×Q812yes—
73C2×Dic79—22no—
74C2×Dic79—22no—
75C2×Dic79—22no—
76C2×Dic79—22no—
77C2×Dic79—24no—
78C2×Dic79—24no—
79C2×Dic79C22×C414yes—
80C2×Dic79C22×C412yes—
81C2×Dic79C2×D412yes—
82C2×Dic79C2×Q812yes—
83C4×D79—48no—
84C4×D79C4⋊C4116yescomplemented
85C22×C79C23×C411yescharacteristic
86C22×C79C22×D411yescharacteristic
87C22×C79C22×Q811yescharacteristic
88C22×C79H(5,𝔽2)12yes—
89C22×C792−1+412yes—
90C2×D79—24no—
91C2×D79—22no—
92C2×D79—22no—
93C2×D79—24no—
94C2×D79C2×C4⋊C414yes—
95C4×C79—24no—
96C4×C79—42no—
97C4×C79—42no—
98C4×C79C2×C4⋊C414yes—
99Dic79—24no—
100Dic79—42no—
101Dic79—42no—
102Dic79C2×C4⋊C414yes—
103C2×C79C22×C4⋊C411yescharacteristic
104C2×C79#52012yes—
105C2×C79#53511yescharacteristic
106C2×C79#53611yescharacteristic
107C2×C79#54412yes—
108D79—24no—
109#2317—791nomaximal, Sylow
110C79#231711yescharacteristic, complemented, Sylow
111C2×#117—791no—
112C2×#117—791no—
113C22×C4⋊C4—791no—
114#389—794no—
115#385—794no—
116#384—791no—
117#384D7911yescharacteristic, complemented
118#382—791no—
119#382—791no—
120C23×C4—792no—
121C23×C4—791no—
122#117—798no—
123#117—1584no—
124C2×C4⋊C4—794no—
125C2×C4⋊C4—792no—
126C2×C4⋊C4—791no—
127C2×C4⋊C4—792no—
128C2×C4⋊C4—791no—
129C2×C4⋊C4—1584no—
130C2×C4⋊C4C2×D7911yescharacteristic
131C2×C4⋊C4C2×D7911yescharacteristic
132C2×C4⋊C4C2×D7914yes—
133C2×C22⋊C4—792no—
134C2×C22⋊C4—792no—
135C2×C42—791no—
136C2×C42—792no—
137C2×C42C2×D7911yescharacteristic
138#95—794no—
139#95—794no—
140C24—791no—
141C22×C4—3164no—
142C22×C4—791no—
143C22×C4—794no—
144C22×C4—794no—
145C22×C4—794no—
146C22×C4—792no—
147C22×C4—792no—
148C22×C4—792no—
149C22×C4—1584no—
150C22×C4C22×D7912yes—
151C22×C4C22×D7912yes—
152C22×C4C22×D7912yes—
153C22×C4C22×D7911yescharacteristic
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—44no—
157C4⋊C4—3164no—
158C4⋊C4—798no—
159C4⋊C4—1584no—
160C4⋊C4—1582no—
161C4⋊C4—1582no—
162C22⋊C4—798no—
163C22⋊C4—1584no—
164C42—794no—
165C42—1584no—
166C42C4×D7914yescomplemented
167C23—792no—
168C23—792no—
169C23—792no—
170C23—1582no—
171C23—1582no—
172C23C23×D7911yescharacteristic
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—3168no—
180C2×C4—792no—
181C2×C4—792no—
182C2×C4—792no—
183C2×C4—7916no—
184C2×C4—794no—
185C2×C4—1584no—
186C2×C4—1584no—
187C2×C4—1582no—
188C2×C4—1582no—
189C2×C4—1582no—
190C2×C4—1582no—
191C2×C4C2×C4×D7914yes—
192C2×C4C2×C4×D7912yes—
193C2×C4D4×D7912yes—
194C2×C4Q8×D7912yes—
195C22—794no—
196C22—1582no—
197C22—1584no—
198C22—1584no—
199C22—1582no—
200C22C22×C4×D7911yescharacteristic
201C22C2×D4×D7911yescharacteristic
202C22C2×Q8×D7911yescharacteristic
203C22#1457920612yes—
204C22#1457920912yes—
205C4—24no—
206C4—42no—
207C4—42no—
208C4—3162no—
209C4—3162no—
210C4—794no—
211C4—1584no—
212C4C4⋊C4×D7914yes—
213C2—1584no—
214C2C2×C4⋊C4×D7911yescharacteristic
215C2#1909904412yes—
216C2#1909912611yescharacteristic
217C2#1909913811yescharacteristic
218C2#1909919012yes—
subgroupG/H
center, FrattiniC23C23×D79
commutatorC22×C79C23×C4
Fitting#384×C79C2
socle, cosocleC23×C79C24
prime radicalC23×D79C23
hypercenter#384D79
hypocenterC79#2317
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
4. #19098458C2semidirect
6. #19098432C2semidirect
7. #19098429C2semidirect
8. #19098428C2semidirect
9. #384×C79C2semidirect
13. #14579118C4semidirect
44. Dic79⋊C4C2×C4semidirect
48. C4×Dic79C2×C4semidirect
56. C42×C79C2×C4semidirect
84. C4×D79C4⋊C4semidirect
110. C79#2317semidirect
117. #384D79semidirect
166. C42C4×D79semidirect