Finite Group Databasebeta

← #13247292

Subgroups — #13247292

Order 1792.

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

normal subgroups only

This group has 384 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×#2298C211yesmaximal, characteristic
2#11729326C212yesmaximal
3#11725427C214yesmaximal, complemented
4C2×C7×#117C2211yescharacteristic
5C7×#388—22no—
6C7×#387—22no—
7C4×C7×C4⋊C4C2212yes—
8C4×C7×C22⋊C4C412yes—
9C7×#376C411yescharacteristic
10C43×C7C411yescharacteristic
11#89698C2214yes—
12#89323—22no—
13#89320—22no—
14#8745—71nomaximal, Sylow
15C23×C4×C7C2×C411yescharacteristic
16C7×#117—24no—
17C2×C7×C4⋊C4—22no—
18C2×C7×C4⋊C4D412yes—
19C2×C7×C22⋊C4—22no—
20C2×C7×C22⋊C4D412yes—
21C2×C42×C7—22no—
22C2×C42×C7C2×C411yescharacteristic
23C2×C42×C7C2×C412yes—
24C2×C42×C7C2×C412yes—
25C2×C42×C7C2311yescharacteristic
26C7×#95—22no—
27C7×#95—22no—
28C7×#95—22no—
29C22⋊(C7⋊C8)—24no—
30C4⋊(C7⋊C8)—24no—
31#6377—24no—
32#2298D711yescharacteristic
33#1464—72no—
34#1285—74no—
35C24×C7C22⋊C411yescharacteristic
36C22×C4×C7—22no—
37C22×C4×C7—22no—
38C22×C4×C7—22no—
39C22×C4×C7—42no—
40C22×C4×C7C22⋊C411yescharacteristic
41C22×C4×C7C22⋊C412yes—
42C22×C4×C7C22×C411yescharacteristic
43C22×C4×C7C2×D412yes—
44C7×C4⋊C4—24no—
45C7×C4⋊C4—44no—
46C7×C22⋊C4—24no—
47C7×C22⋊C4—44no—
48C42×C7—22no—
49C42×C7—42no—
50C42×C7—42no—
51C42×C7—44no—
52C42×C7#4114yes—
53C2×C7⋊C8—44no—
54C2×#117C2×D711yescharacteristic
55#432—74no—
56#388—22no—
57#387—22no—
58C4×C4⋊C4C2×D712yes—
59C4×C22⋊C4Dic712yes—
60#376Dic711yescharacteristic
61C43Dic711yescharacteristic
62#324—142no—
63#323—142no—
64C23×C7—21no—
65C23×C7—22no—
66C23×C7—42no—
67C23×C7C2×C22⋊C411yescharacteristic
68C2×C4×C7—22no—
69C2×C4×C7—24no—
70C2×C4×C7—22no—
71C2×C4×C7—21no—
72C2×C4×C7—22no—
73C2×C4×C7—42no—
74C2×C4×C7—44no—
75C2×C4×C7—42no—
76C2×C4×C7—42no—
77C2×C4×C7—42no—
78C2×C4×C7—42no—
79C2×C4×C7—42no—
80C2×C4×C7—42no—
81C2×C4×C7#11712yes—
82C2×C4×C7#12314yes—
83C7⋊C8—84no—
84C23×C4C2×Dic711yescharacteristic
85#117—24no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4C22⋊D712yes—
88C2×C22⋊C4—22no—
89C2×C22⋊C4C22⋊D712yes—
90C2×C42—22no—
91C2×C42C2×Dic711yescharacteristic
92C2×C42C2×Dic712yes—
93C2×C42C2×Dic712yes—
94C2×C42C22×D711yescharacteristic
95C4⋊C8—144no—
96C22⋊C8—144no—
97#97—144no—
98#95—22no—
99#95—22no—
100#95—22no—
101C22×C7—22no—
102C22×C7—41no—
103C22×C7—42no—
104C22×C7—82no—
105C22×C7#38111yescharacteristic
106C22×C7#41312yes—
107C4×C7—22no—
108C4×C7—24no—
109C4×C7—44no—
110C4×C7—41no—
111C4×C7—42no—
112C4×C7—82no—
113C24C22⋊Dic711yescharacteristic
114C22×C4—22no—
115C22×C4—22no—
116C22×C4—22no—
117C22×C4—42no—
118C22×C4C22⋊Dic711yescharacteristic
119C22×C4C22⋊Dic712yes—
120C22×C4C22×Dic711yescharacteristic
121C22×C4C2×C22⋊D712yes—
122C2×C8—284no—
123C4⋊C4—24no—
124C4⋊C4—44no—
125C22⋊C4—24no—
126C22⋊C4—44no—
127C42—22no—
128C42—42no—
129C42—42no—
130C42—44no—
131C42#115714yes—
132C2×C7—22no—
133C2×C7—81no—
134C2×C7#182211yescharacteristic
135C2×C7#182712yes—
136C23—21no—
137C23—22no—
138C23—42no—
139C23C2×C22⋊Dic711yescharacteristic
140C2×C4—22no—
141C2×C4—24no—
142C2×C4—22no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—42no—
146C2×C4—44no—
147C2×C4—42no—
148C2×C4—42no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4#648912yes—
154C2×C4#649214yes—
155C8—564no—
156C7#874511yescharacteristic, complemented, Sylow
157C22—22no—
158C22—41no—
159C22—42no—
160C22—82no—
161C22#8998311yescharacteristic
162C22#9000912yes—
163C4—22no—
164C4—24no—
165C4—44no—
166C4—41no—
167C4—42no—
168C4—82no—
169C2—22no—
170C2—81no—
171C2#1172934311yescharacteristic
172C2#1172939812yes—
subgroupG/H
centerC22#89983
commutatorC22×C4×C7C22×C4
FrattiniC2×C42C22×D7
FittingC7×#2298C2
socleC22×C7#381
prime radicalC24×C7C22⋊C4
cosocleC2×C42×C7C23
hypercenter#2298D7
hypocenterC7#8745
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2298

Complements

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

NH ≅ G/Ntype
3. #11725427C2semidirect
156. C7#8745semidirect

Maximal subgroups

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

subgroupindex
C7×#22982
#117293262
#117254272
#87457