Finite Group Databasebeta

← #13263193

Subgroups — #13263193

Order 1792.

490 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 107 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×C7×#382C211yesmaximal, characteristic
2#11729306C212yesmaximal
3#11725438C214yesmaximal, complemented
4C22×C7×C4⋊C4C411yescharacteristic
5C22×C7×C4⋊C4C2211yescharacteristic
6C22×C42×C7C411yescharacteristic
7C7×#382—22no—
8C7×#382C412yes—
9C7×#382C2212yes—
10C2×C7×#95—22no—
11#89979—22no—
12#89323—22no—
13#89323C2214yes—
14#11511—71nomaximal, Sylow
15C23×C4×C7—21no—
16C23×C4×C7—21no—
17C23×C4×C7C2×C411yescharacteristic
18C23×C4×C7D412yes—
19C2×C7×C4⋊C4—21no—
20C2×C7×C4⋊C4—41no—
21C2×C7×C4⋊C4—41no—
22C2×C7×C4⋊C4—41no—
23C2×C7×C4⋊C4—41no—
24C2×C7×C4⋊C4C2×C412yes—
25C2×C7×C4⋊C4C2×C411yescharacteristic
26C2×C7×C4⋊C4D412yes—
27C2×C7×C4⋊C4C2311yescharacteristic
28C2×C42×C7—21no—
29C2×C42×C7—24no—
30C2×C42×C7C2×C412yes—
31C2×#1136—42no—
32C7×#95—24no—
33C7×#95—24no—
34C22⋊(C7⋊C8)—24no—
35C22⋊(C7⋊C8)—42no—
36C2×#382D711yescharacteristic
37#1463—72no—
38#1324—74no—
39C24×C7C22⋊C411yescharacteristic
40C22×C4×C7—21no—
41C22×C4×C7—21no—
42C22×C4×C7—22no—
43C22×C4×C7—22no—
44C22×C4×C7—24no—
45C22×C4×C7—22no—
46C22×C4×C7—22no—
47C22×C4×C7—22no—
48C22×C4×C7—22no—
49C22×C4×C7—42no—
50C22×C4×C7—42no—
51C22×C4×C7—44no—
52C22×C4×C7—44no—
53C22×C4×C7—41no—
54C22×C4×C7—41no—
55C22×C4×C7C22⋊C411yescharacteristic
56C22×C4×C7C22⋊C412yes—
57C22×C4×C7C22×C411yescharacteristic
58C22×C4×C7C2×D412yes—
59C7×C4⋊C4—41no—
60C7×C4⋊C4—42no—
61C7×C4⋊C4—41no—
62C7×C4⋊C4—42no—
63C7×C4⋊C4—42no—
64C42×C7—24no—
65C42×C7—22no—
66C42×C7M1614yescomplemented
67#1136—84no—
68C2×C7⋊C8—44no—
69C22×C4⋊C4Dic711yescharacteristic
70C22×C4⋊C4C2×D711yescharacteristic
71C22×C42Dic711yescharacteristic
72#407—142no—
73#382—22no—
74#382Dic712yes—
75#382C2×D712yes—
76C2×#95—22no—
77#324—74no—
78#324—142no—
79C23×C7—22no—
80C23×C7—22no—
81C23×C7—21no—
82C23×C7—21no—
83C23×C7#9911yescharacteristic
84C23×C7#9911yescharacteristic
85C23×C7C2×C22⋊C411yescharacteristic
86C2×C4×C7—24no—
87C2×C4×C7—24no—
88C2×C4×C7—21no—
89C2×C4×C7—21no—
90C2×C4×C7—21no—
91C2×C4×C7—21no—
92C2×C4×C7—24no—
93C2×C4×C7—22no—
94C2×C4×C7—22no—
95C2×C4×C7—48no—
96C2×C4×C7—42no—
97C2×C4×C7—42no—
98C2×C4×C7—44no—
99C2×C4×C7—42no—
100C2×C4×C7—42no—
101C2×C4×C7—44no—
102C2×C4×C7—42no—
103C2×C4×C7—82no—
104C2×C4×C7—82no—
105C2×C4×C7—82no—
106C2×C4×C7#10112yes—
107C2×C4×C7C2×M1612yes—
108C7⋊C8—84no—
109C23×C4—21no—
110C23×C4—21no—
111C23×C4C2×Dic711yescharacteristic
112C23×C4C22⋊D712yes—
113C2×M16—282no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4C2×Dic712yes—
120C2×C4⋊C4C2×Dic711yescharacteristic
121C2×C4⋊C4C22⋊D712yes—
122C2×C4⋊C4C22×D711yescharacteristic
123C2×C42—21no—
124C2×C42—24no—
125C2×C42C2×Dic712yes—
126C22⋊C8—144no—
127C22⋊C8—282no—
128#95—24no—
129#95—24no—
130C22×C7—24no—
131C22×C7—24no—
132C22×C7—21no—
133C22×C7—21no—
134C22×C7—21no—
135C22×C7—21no—
136C22×C7—21no—
137C22×C7—21no—
138C22×C7#35412yes—
139C22×C7#35512yes—
140C22×C7#40711yescharacteristic
141C22×C7C2×#9911yescharacteristic
142C22×C7C2×#10111yescharacteristic
143C4×C7—22no—
144C4×C7—22no—
145C4×C7—44no—
146C4×C7—42no—
147C4×C7—42no—
148C4×C7—82no—
149C24C22⋊Dic711yescharacteristic
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—24no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—44no—
162C22×C4—44no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4C22⋊Dic711yescharacteristic
166C22×C4C22⋊Dic712yes—
167C22×C4C22×Dic711yescharacteristic
168C22×C4C2×C22⋊D712yes—
169M16—564no—
170C2×C8—284no—
171C4⋊C4—41no—
172C4⋊C4—42no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C42—24no—
177C42—22no—
178C42#113614yescomplemented
179C2×C7—21no—
180C2×C7—22no—
181C2×C7—22no—
182C2×C7—21no—
183C2×C7#146311yescharacteristic
184C2×C7C2×#35411yescharacteristic
185C2×C7C2×#35511yescharacteristic
186C23—21no—
187C23—21no—
188C23—22no—
189C23—22no—
190C23#640811yescharacteristic
191C23#640811yescharacteristic
192C23C2×C22⋊Dic711yescharacteristic
193C2×C4—24no—
194C2×C4—24no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—24no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—48no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—42no—
210C2×C4—82no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4#641012yes—
214C2×C4C2×#113612yes—
215C8—564no—
216C7#1151111yescharacteristic, complemented, Sylow
217C22—24no—
218C22—24no—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22#8933612yes—
226C22#8933712yes—
227C22#8997911yescharacteristic
228C22C2×#640811yescharacteristic
229C22C2×#641011yescharacteristic
230C4—22no—
231C4—22no—
232C4—44no—
233C4—42no—
234C4—42no—
235C4—82no—
236C2—21no—
237C2—21no—
238C2—22no—
239C2—22no—
240C2#1172930611yescharacteristic
241C2C2×#8933611yescharacteristic
242C2C2×#8933711yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC2×C7×#382C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenterC2×#382D7
hypocenterC7#11511
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
3. #11725438C2semidirect
66. C42×C7M16semidirect
178. C42#1136semidirect
216. C7#11511semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C7×#3822
#117293062
#117254382
#115117