Finite Group Databasebeta

← #23763378

Subgroups — #23763378

Order 10112.

400 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×C4×Dic79C211yesmaximal, characteristic
2C2×Dic79⋊C8C212yesmaximal, complemented
3C2×C22⋊(C79⋊C8)C211yesmaximal, characteristic
4#19098317C212yesmaximal, complemented
5C2×C22⋊C8×C79C211yesmaximal, characteristic
6C23×Dic79C411yescharacteristic
7C23×Dic79C411yescharacteristic
8C22×C79⋊C8C2212yes—
9C2×C4×Dic79—24no—
10C2×C4×Dic79C411yescharacteristic
11C2×C4×Dic79C411yescharacteristic
12C2×C4×Dic79C2211yescharacteristic
13C2×C4×Dic79C2211yescharacteristic
14Dic79⋊C8—24no—
15C22⋊(C79⋊C8)—22no—
16C23×C4×C79C2211yescharacteristic
17C22×C8×C79C2212yes—
18C22⋊C8×C79—22no—
19C22×Dic79—22no—
20C22×Dic79—22no—
21C22×Dic79—22no—
22C22×Dic79—22no—
23C22×Dic79—22no—
24C22×Dic79C814yescomplemented
25C22×Dic79C2×C411yescharacteristic
26C22×Dic79C2×C411yescharacteristic
27C22×Dic79C2×C411yescharacteristic
28C22×Dic79C2×C411yescharacteristic
29C2×C79⋊C8—22no—
30C2×C79⋊C8—22no—
31C2×C79⋊C8—22no—
32C4×Dic79—22no—
33C4×Dic79—22no—
34C4×Dic79—22no—
35C4×Dic79D414yes—
36C24×C79C2×C411yescharacteristic
37C22×C4×C79—22no—
38C22×C4×C79—22no—
39C22×C4×C79C2×C411yescharacteristic
40C22×C4×C79D412yes—
41C22×C4×C79Q812yes—
42C22×C4×C79C2311yescharacteristic
43C2×C8×C79—22no—
44C2×C8×C79—22no—
45C2×C8×C79—22no—
46C23×C79—21no—
47C23×C79—21no—
48C23×C79—21no—
49C23×C79—21no—
50C23×C79C4⋊C412yes—
51C23×C79C2×C812yes—
52C23×C79M1612yes—
53C23×C79C22×C411yescharacteristic
54C2×C4×C79—21no—
55C2×C4×C79—21no—
56C2×C4×C79—24no—
57C2×C4×C79—24no—
58C2×C4×C79C4⋊C412yes—
59C2×C4×C79C2×D412yes—
60C2×C4×C79C2×D411yescharacteristic
61C2×C4×C79C2×Q811yescharacteristic
62C2×C4×C79#4112yes—
63C2×Dic79—28no—
64C2×Dic79—21no—
65C2×Dic79—21no—
66C2×Dic79—21no—
67C2×Dic79—21no—
68C2×Dic79—21no—
69C2×Dic79—21no—
70C2×Dic79—28no—
71C2×Dic79C22⋊C412yes—
72C2×Dic79C22⋊C412yes—
73C2×Dic79C2×C812yes—
74C2×Dic79C2×C812yes—
75C2×Dic79M1612yes—
76C2×Dic79M1612yes—
77C8×C79—42no—
78C79⋊C8—42no—
79C22×C79—22no—
80C22×C79—22no—
81C22×C79—22no—
82C22×C79—22no—
83C22×C79—22no—
84C22×C79—22no—
85C22×C79C4⋊C814yescomplemented
86C22×C79C2×C22⋊C411yescharacteristic
87C22×C79C2×C4⋊C411yescharacteristic
88C22×C79#11711yescharacteristic
89C22×C79C22×C811yescharacteristic
90C22×C79C2×M1611yescharacteristic
91C22×C79C2×M1611yescharacteristic
92C22×C79C2×M1611yescharacteristic
93C4×C79—22no—
94C4×C79#12112yes—
95C4×C79C22⋊Q812yes—
96Dic79—22no—
97Dic79—22no—
98Dic79—22no—
99Dic79C22⋊C814yescomplemented
100C2×C79—24no—
101C2×C79#38011yescharacteristic
102C2×C79C2×C22⋊C811yescharacteristic
103C2×C79#40711yescharacteristic
104C2×C79C2×C4⋊C811yescharacteristic
105C2×C79#42311yescharacteristic
106C2×C79#43111yescharacteristic
107C2×C79#43211yescharacteristic
108#1797—791nomaximal, Sylow
109C79#179711yescharacteristic, complemented, Sylow
110C22×C42—791no—
111C2×C4⋊C8—792no—
112C2×C22⋊C8—791no—
113C2×C22⋊C8D7911yescharacteristic
114#336—792no—
115C23×C4—791no—
116C23×C4—791no—
117C23×C4C2×D7911yescharacteristic
118C22×C8—792no—
119C22×C8C2×D7912yes—
120C2×C42—791no—
121C2×C42—791no—
122C2×C42—791no—
123C2×C42—791no—
124C2×C42—1584no—
125C4⋊C8—1584no—
126C22⋊C8—22no—
127C22⋊C8—1582no—
128C24C4×D7911yescharacteristic
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—791no—
132C22×C4—794no—
133C22×C4—791no—
134C22×C4—791no—
135C22×C4—791no—
136C22×C4—1582no—
137C22×C4—1582no—
138C22×C4—1582no—
139C22×C4—1582no—
140C22×C4—1582no—
141C22×C4Dic15812yes—
142C22×C4C4×D7911yescharacteristic
143C22×C4C22⋊D7912yes—
144C22×C4C22×D7911yescharacteristic
145C2×C8—22no—
146C2×C8—22no—
147C2×C8—22no—
148C2×C8—1582no—
149C2×C8—1582no—
150C2×C8—1582no—
151C42—794no—
152C42—1582no—
153C42—1582no—
154C42—1582no—
155C23—21no—
156C23—21no—
157C23—21no—
158C23—21no—
159C23Dic79⋊C412yes—
160C23C8×D7912yes—
161C23#1192960712yes—
162C23C2×C4×D7911yescharacteristic
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—24no—
166C2×C4—24no—
167C2×C4—792no—
168C2×C4—792no—
169C2×C4—792no—
170C2×C4—792no—
171C2×C4—792no—
172C2×C4—792no—
173C2×C4—1588no—
174C2×C4—1588no—
175C2×C4—1581no—
176C2×C4—1581no—
177C2×C4—1581no—
178C2×C4—1581no—
179C2×C4—1581no—
180C2×C4—1581no—
181C2×C4Dic79⋊C412yes—
182C2×C4D4×D7912yes—
183C2×C4C2×C22⋊D7911yescharacteristic
184C2×C4C2×Dic15811yescharacteristic
185C2×C4#1192962312yes—
186C8—42no—
187C8—3162no—
188C22—22no—
189C22—22no—
190C22—22no—
191C22—22no—
192C22—22no—
193C22—22no—
194C22Dic79⋊C814yescomplemented
195C22C22⋊C4×D7911yescharacteristic
196C22C2×Dic79⋊C411yescharacteristic
197C22#1457911711yescharacteristic
198C22C2×C8×D7911yescharacteristic
199C22M16×D7911yescharacteristic
200C22M16×D7911yescharacteristic
201C22C2×#1192960711yescharacteristic
202C4—22no—
203C4—794no—
204C4—1582no—
205C4—1582no—
206C4—1582no—
207C4#1457913312yes—
208C4#1457913812yes—
209C2—24no—
210C2#1909842111yescharacteristic
211C2C22⋊C8×D7911yescharacteristic
212C2#1909852511yescharacteristic
213C2C2×Dic79⋊C811yescharacteristic
214C2#1909858611yescharacteristic
215C2#1909861311yescharacteristic
216C2#1909861711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D79
commutatorC22×C79C22×C8
FittingC2×C22⋊C8×C79C2
socleC23×C79C22×C4
prime radicalC24×C79C2×C4
cosocleC22×C4×C79C23
hypercenterC2×C22⋊C8D79
hypocenterC79#1797
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic79⋊C8C2semidirect
4. #19098317C2semidirect
24. C22×Dic79C8semidirect
85. C22×C79C4⋊C8semidirect
99. Dic79C22⋊C8semidirect
109. C79#1797semidirect
194. C22Dic79⋊C8semidirect