Finite Group Databasebeta

← #13263190

Subgroups — #13263190

Order 1792.

510 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C7×#2310C211yesmaximal, characteristic
2#11729326C212yesmaximal
3#11725449C214yesmaximal, complemented
4C23×C7×Q8C411yescharacteristic
5C2×C7×#117C411yescharacteristic
6C2×C7×#117C2211yescharacteristic
7C7×#391—22no—
8C7×#391C412yes—
9C7×#391C2212yes—
10C7×#381—22no—
11#89698—22no—
12#89323C2214yes—
13#89320—22no—
14#11510—71nomaximal, Sylow
15C22×C7×Q8—24no—
16C22×C7×Q8—21no—
17C22×C7×Q8—42no—
18C22×C7×Q8—42no—
19C22×C7×Q8C2×C412yes—
20C23×C4×C7—21no—
21C23×C4×C7C2×C411yescharacteristic
22C7×#117—42no—
23C7×#117—42no—
24C2×C7×C4⋊C4—21no—
25C2×C7×C4⋊C4C2×C411yescharacteristic
26C2×C7×C4⋊C4C2311yescharacteristic
27C2×C7×C22⋊C4—21no—
28C2×C7×C22⋊C4D412yes—
29C2×C42×C7C2×C412yes—
30C2×C42×C7D412yes—
31C7×#95—24no—
32C7×#95—24no—
33C22⋊(C7⋊C8)—24no—
34C4⋊(C7⋊C8)—42no—
35#6377—42no—
36#2310D711yescharacteristic
37#1464—72no—
38#1319—74no—
39C24×C7C22⋊C411yescharacteristic
40C2×C7×Q8—24no—
41C2×C7×Q8—22no—
42C2×C7×Q8—416no—
43C2×C7×Q8—42no—
44C2×C7×Q8—42no—
45C2×C7×Q8—42no—
46C2×C7×Q8—42no—
47C2×C7×Q8M1614yes—
48C22×C4×C7—22no—
49C22×C4×C7—22no—
50C22×C4×C7—22no—
51C22×C4×C7—24no—
52C22×C4×C7—22no—
53C22×C4×C7—22no—
54C22×C4×C7—42no—
55C22×C4×C7—42no—
56C22×C4×C7C22⋊C411yescharacteristic
57C22×C4×C7C22⋊C412yes—
58C22×C4×C7C22×C411yescharacteristic
59C22×C4×C7C2×D412yes—
60C7×C4⋊C4—41no—
61C7×C4⋊C4—41no—
62C7×C4⋊C4—42no—
63C7×C22⋊C4—42no—
64C7×C22⋊C4—42no—
65C42×C7—22no—
66C42×C7—22no—
67C42×C7—42no—
68C2×C7⋊C8—44no—
69C23×Q8Dic711yescharacteristic
70C2×#117Dic711yescharacteristic
71C2×#117C2×D711yescharacteristic
72#432—142no—
73#391—22no—
74#391Dic712yes—
75#391C2×D712yes—
76#381—22no—
77#324—74no—
78#323—142no—
79C23×C7—21no—
80C23×C7—21no—
81C23×C7—41no—
82C23×C7—41no—
83C23×C7#10012yes—
84C23×C7C2×C22⋊C411yescharacteristic
85C7×Q8—44no—
86C7×Q8—48no—
87C7×Q8—44no—
88C2×C4×C7—28no—
89C2×C4×C7—21no—
90C2×C4×C7—21no—
91C2×C4×C7—21no—
92C2×C4×C7—21no—
93C2×C4×C7—24no—
94C2×C4×C7—22no—
95C2×C4×C7—22no—
96C2×C4×C7—48no—
97C2×C4×C7—42no—
98C2×C4×C7—42no—
99C2×C4×C7—42no—
100C2×C4×C7—42no—
101C2×C4×C7—42no—
102C2×C4×C7—42no—
103C2×C4×C7—42no—
104C2×C4×C7#9912yes—
105C2×C4×C7C2×M1612yes—
106C7⋊C8—84no—
107C22×Q8—24no—
108C22×Q8—21no—
109C22×Q8—42no—
110C22×Q8—42no—
111C22×Q8C2×Dic712yes—
112C23×C4—21no—
113C23×C4C2×Dic711yescharacteristic
114#117—42no—
115#117—42no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4C2×Dic711yescharacteristic
118C2×C4⋊C4C22×D711yescharacteristic
119C2×C22⋊C4—21no—
120C2×C22⋊C4C22⋊D712yes—
121C2×C42C2×Dic712yes—
122C2×C42C22⋊D712yes—
123C4⋊C8—282no—
124C22⋊C8—144no—
125#97—282no—
126#95—24no—
127#95—24no—
128C22×C7—21no—
129C22×C7—21no—
130C22×C7—22no—
131C22×C7—42no—
132C22×C7—42no—
133C22×C7—41no—
134C22×C7—41no—
135C22×C7#40711yescharacteristic
136C22×C7C2×#9911yescharacteristic
137C22×C7C2×#10011yescharacteristic
138C4×C7—22no—
139C4×C7—22no—
140C4×C7—42no—
141C4×C7—42no—
142C4×C7—44no—
143C4×C7—82no—
144C24C22⋊Dic711yescharacteristic
145C2×Q8—24no—
146C2×Q8—22no—
147C2×Q8—416no—
148C2×Q8—42no—
149C2×Q8—42no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8#113614yes—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4C22⋊Dic712yes—
162C22×C4C22⋊Dic711yescharacteristic
163C22×C4C22×Dic711yescharacteristic
164C22×C4C2×C22⋊D712yes—
165C2×C8—284no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C22⋊C4—42no—
170C22⋊C4—42no—
171C42—22no—
172C42—22no—
173C42—42no—
174C2×C7—21no—
175C2×C7—21no—
176C2×C7—42no—
177C2×C7#146211yescharacteristic
178C2×C7#212911yescharacteristic
179C2×C7#213511yescharacteristic
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23#640712yes—
185C23C2×C22⋊Dic711yescharacteristic
186Q8—44no—
187Q8—48no—
188Q8—44no—
189C2×C4—28no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—24no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—48no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4#640812yes—
206C2×C4C2×#113612yes—
207C8—564no—
208C7#1151011yescharacteristic, complemented, Sylow
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22#8997911yescharacteristic
217C22C2×#640711yescharacteristic
218C22C2×#640811yescharacteristic
219C4—22no—
220C4—22no—
221C4—44no—
222C4—42no—
223C4—42no—
224C4—82no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2#1172929311yescharacteristic
229C2#1172962511yescharacteristic
230C2#1172962711yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2310C2
socleC22×C7C2×#99
prime radicalC24×C7C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2310D7
hypocenterC7#11510
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2310

Complements

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

NH ≅ G/Ntype
3. #11725449C2semidirect
208. C7#11510semidirect

Maximal subgroups

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

subgroupindex
C7×#23102
#117293262
#117254492
#115107