Finite Group Databasebeta

← #13241169

Subgroups — #13241169

Order 1792.

302 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 43 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×#1819C211yesmaximal, characteristic
2#11725428C212yesmaximal
3C22×C7×C22⋊C4C411yescharacteristic
4C7×#379C411yescharacteristic
5C7×#379C2211yescharacteristic
6C7×#342—22no—
7#89320—22no—
8#7349—71nomaximal, Sylow
9C25×C7C2×C411yescharacteristic
10C23×C4×C7—21no—
11C2×C7×C22⋊C4—21no—
12C2×C7×C22⋊C4—21no—
13C2×C7×C22⋊C4—41no—
14C2×C7×C22⋊C4—41no—
15C2×C7×C22⋊C4—41no—
16C2×C7×C22⋊C4—41no—
17C2×C7×C22⋊C4C812yescomplemented
18C2×C7×C22⋊C4D412yes—
19C22⋊(C7⋊C8)—42no—
20#1819D711yescharacteristic
21#1316—72no—
22C24×C7—21no—
23C24×C7—21no—
24C24×C7—42no—
25C24×C7—82no—
26C24×C7C22⋊C411yescharacteristic
27C24×C7C2×C811yescharacteristic
28C24×C7M1611yescharacteristic
29C22×C4×C7—22no—
30C22×C4×C7—22no—
31C22×C4×C7—41no—
32C22×C4×C7—41no—
33C22×C4×C7—41no—
34C22×C4×C7—82no—
35C7×C22⋊C4—41no—
36C7×C22⋊C4—41no—
37C7×C22⋊C4—42no—
38C7×C22⋊C4—42no—
39C7×C22⋊C4—42no—
40C7×C22⋊C4—82no—
41C7×C22⋊C4—82no—
42C2×C7⋊C8—82no—
43C22×C22⋊C4Dic711yescharacteristic
44#379Dic711yescharacteristic
45#379C2×D711yescharacteristic
46#342—22no—
47#323—142no—
48C23×C7—21no—
49C23×C7—22no—
50C23×C7—21no—
51C23×C7—42no—
52C23×C7—41no—
53C23×C7—42no—
54C23×C7—42no—
55C23×C7—42no—
56C23×C7—41no—
57C23×C7—42no—
58C23×C7—81no—
59C23×C7—81no—
60C23×C7—81no—
61C23×C7—81no—
62C23×C7—84no—
63C23×C7—84no—
64C23×C7C22⋊C811yescharacteristic
65C23×C7#9911yescharacteristic
66C23×C7#10011yescharacteristic
67C2×C4×C7—42no—
68C2×C4×C7—42no—
69C2×C4×C7—82no—
70C2×C4×C7—82no—
71C2×C4×C7—82no—
72C2×C4×C7—82no—
73C2×C4×C7—81no—
74C2×C4×C7—82no—
75C7⋊C8—162no—
76C25C2×Dic711yescharacteristic
77C23×C4—21no—
78C2×C22⋊C4—21no—
79C2×C22⋊C4—21no—
80C2×C22⋊C4—41no—
81C2×C22⋊C4—41no—
82C2×C22⋊C4—41no—
83C2×C22⋊C4—41no—
84C2×C22⋊C4C7⋊C812yescomplemented
85C2×C22⋊C4C22⋊D712yes—
86C22⋊C8—282no—
87C22×C7—22no—
88C22×C7—21no—
89C22×C7—21no—
90C22×C7—41no—
91C22×C7—41no—
92C22×C7—41no—
93C22×C7—41no—
94C22×C7—41no—
95C22×C7—41no—
96C22×C7—42no—
97C22×C7—42no—
98C22×C7—41no—
99C22×C7—41no—
100C22×C7—82no—
101C22×C7—84no—
102C22×C7—84no—
103C22×C7—82no—
104C22×C7#32311yescharacteristic
105C22×C7#35212yes—
106C4×C7—82no—
107C4×C7—82no—
108C4×C7—161no—
109C24—21no—
110C24—21no—
111C24—42no—
112C24—82no—
113C24C2×C7⋊C811yescharacteristic
114C24#113611yescharacteristic
115C24C22⋊Dic711yescharacteristic
116C22×C4—22no—
117C22×C4—22no—
118C22×C4—41no—
119C22×C4—41no—
120C22×C4—41no—
121C22×C4—82no—
122C2×C8—562no—
123C22⋊C4—41no—
124C22⋊C4—41no—
125C22⋊C4—42no—
126C22⋊C4—42no—
127C22⋊C4—42no—
128C22⋊C4—82no—
129C22⋊C4—82no—
130C2×C7—21no—
131C2×C7—22no—
132C2×C7—41no—
133C2×C7—42no—
134C2×C7—41no—
135C2×C7—81no—
136C2×C7#131711yescharacteristic
137C23—21no—
138C23—22no—
139C23—21no—
140C23—42no—
141C23—41no—
142C23—42no—
143C23—42no—
144C23—42no—
145C23—41no—
146C23—42no—
147C23—81no—
148C23—81no—
149C23—81no—
150C23—81no—
151C23—84no—
152C23—84no—
153C23C22⋊(C7⋊C8)11yescharacteristic
154C23#640711yescharacteristic
155C23#640811yescharacteristic
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—82no—
159C2×C4—82no—
160C2×C4—82no—
161C2×C4—82no—
162C2×C4—81no—
163C2×C4—82no—
164C8—1122no—
165C7#734911yescharacteristic, complemented, Sylow
166C22—22no—
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—41no—
173C22—41no—
174C22—41no—
175C22—42no—
176C22—42no—
177C22—41no—
178C22—41no—
179C22—82no—
180C22—84no—
181C22—84no—
182C22—82no—
183C22#8932011yescharacteristic
184C22#8933412yes—
185C4—82no—
186C4—82no—
187C4—161no—
188C2—21no—
189C2—22no—
190C2—41no—
191C2—42no—
192C2—41no—
193C2—81no—
194C2#1172543311yescharacteristic
subgroupG/H
centerC2#11725433
commutatorC24×C7C2×C8
Frattini#379C2×D7
FittingC7×#1819C2
socleC2×C7#1317
prime radicalC25×C7C2×C4
cosocleC7×#379C22
hypercenter#1819D7
hypocenterC7#7349
LCSG ▷ C24×C7 ▷ C23×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #379 ◁ #1819

Complements

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

NH ≅ G/Ntype
17. C2×C7×C22⋊C4C8semidirect
84. C2×C22⋊C4C7⋊C8semidirect
165. C7#7349semidirect

Maximal subgroups

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

subgroupindex
C7×#18192
#117254282
#73497