Finite Group Databasebeta

← #13241380

Subgroups — #13241380

Order 1792.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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
1#11727393C211yesmaximal, characteristic
2C7×#1393C211yesmaximal, characteristic
3#11725446C211yesmaximal, characteristic
4C2×#6433C411yescharacteristic, complemented
5C2×C7×#99—21no—
6C7×#390C2211yescharacteristic
7C2×#6406—21no—
8#89324—21no—
9#89323—21no—
10#89319C411yescharacteristic, complemented
11#7428—71nomaximal, Sylow
12C22×C7×D4D411yescharacteristic
13C2×C7×C4⋊C4D411yescharacteristic
14C2×C7×C22⋊C4—41no—
15C2×C7×C22⋊C4—41no—
16C2×C42×C7C2×C411yescharacteristic
17C2×C4⋊Dic7—21no—
18C2×Dic7⋊C4—41no—
19C22×C7⋊C8—21no—
20#6433—42no—
21C7×#99—22no—
22C7×#99—41no—
23#6406—42no—
24C22⋊(C7⋊C8)—41no—
25#2025—71no—
26#1393D711yescharacteristic
27#1318—71no—
28C24×C7—21no—
29C2×C7×D4—21no—
30C2×C7×D4—41no—
31C2×C7×D4—41no—
32C2×C7×D4SD1611yescharacteristic
33C2×C7×D4Q1611yescharacteristic
34C22×C4×C7—21no—
35C22×C4×C7—21no—
36C22×C4×C7—81no—
37C22×C4×C7C22⋊C411yescharacteristic
38C22×Dic7—41no—
39C7×C4⋊C4—41no—
40C7×C22⋊C4—42no—
41C7×C22⋊C4—82no—
42C7×C22⋊C4—81no—
43C42×C7—41no—
44C4⋊Dic7—22no—
45C4⋊Dic7—41no—
46Dic7⋊C4—42no—
47Dic7⋊C4—42no—
48C2×C7⋊C8—41no—
49C2×C7⋊C8—41no—
50C2×C7⋊C8—41no—
51C2×C7⋊C8—81no—
52C2×#125—71no—
53C2×#102—141no—
54C2×#99—21no—
55#390C2×D711yescharacteristic
56#340—141no—
57#336—71no—
58#324—141no—
59C23×C7—21no—
60C23×C7—21no—
61C23×C7—41no—
62C23×C7—41no—
63C23×C7—81no—
64C23×C7—81no—
65C23×C7#9911yescharacteristic
66C7×D4—41no—
67C7×D4—41no—
68C7×D4—81no—
69C2×C4×C7—21no—
70C2×C4×C7—21no—
71C2×C4×C7—41no—
72C2×C4×C7—41no—
73C2×C4×C7—41no—
74C2×C4×C7—41no—
75C2×C4×C7—81no—
76C2×C4×C7—82no—
77C2×C4×C7—161no—
78C2×C4×C7—161no—
79C2×C4×C7#10311yescharacteristic
80C2×C4×C7#10411yescharacteristic
81C2×Dic7—42no—
82C2×Dic7—81no—
83C2×Dic7—81no—
84C7⋊C8—81no—
85C7⋊C8—161no—
86C22×D4C22⋊D711yescharacteristic
87C22×C8—141no—
88#125—282no—
89C2×C4⋊C4—141no—
90C2×C4⋊C4—281no—
91C2×C4⋊C4D2811yescharacteristic
92C2×C22⋊C4—41no—
93C2×C22⋊C4—41no—
94C2×C42C4×D711yescharacteristic
95#102—282no—
96#99—22no—
97#99—41no—
98C22⋊C8—281no—
99C22×C7—21no—
100C22×C7—21no—
101C22×C7—41no—
102C22×C7—41no—
103C22×C7—81no—
104C22×C7—81no—
105C22×C7—81no—
106C22×C7—81no—
107C22×C7—161no—
108C22×C7#32811yescharacteristic
109C22×C7AΣL(1,𝔽16)11yescharacteristic
110C22×C7#35411yescharacteristic
111C4×C7—21no—
112C4×C7—21no—
113C4×C7—81no—
114C4×C7—81no—
115C4×C7—162no—
116Dic7—82no—
117C24—21no—
118C2×D4—21no—
119C2×D4—41no—
120C2×D4—41no—
121C2×D4#114211yescharacteristic
122C2×D4#114411yescharacteristic
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—81no—
126C22×C4—281no—
127C22×C4(C2×D7)⋊C411yescharacteristic
128C2×C8—281no—
129C2×C8—281no—
130C2×C8—281no—
131C2×C8—561no—
132C4⋊C4—41no—
133C4⋊C4—142no—
134C4⋊C4—281no—
135C4⋊C4—282no—
136C4⋊C4—282no—
137C22⋊C4—42no—
138C22⋊C4—82no—
139C22⋊C4—81no—
140C42—41no—
141C2×C7—21no—
142C2×C7—21no—
143C2×C7—81no—
144C2×C7—81no—
145C2×C7#135111yescharacteristic
146C2×C7#141211yescharacteristic
147C2×C7#141411yescharacteristic
148C23—21no—
149C23—21no—
150C23—41no—
151C23—41no—
152C23—81no—
153C23—81no—
154C23#638011yescharacteristic
155D4—41no—
156D4—41no—
157D4—81no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—81no—
165C2×C4—82no—
166C2×C4—161no—
167C2×C4—161no—
168C2×C4—282no—
169C2×C4—561no—
170C2×C4—561no—
171C2×C4#637911yescharacteristic
172C2×C4#638411yescharacteristic
173C8—561no—
174C8—1121no—
175C7#742811yescharacteristic, complemented, Sylow
176C22—21no—
177C22—21no—
178C22—41no—
179C22—41no—
180C22—81no—
181C22—81no—
182C22—81no—
183C22—81no—
184C22—161no—
185C22#8924711yescharacteristic
186C22#8926611yescharacteristic
187C22#8926811yescharacteristic
188C4—21no—
189C4—21no—
190C4—81no—
191C4—81no—
192C4—162no—
193C4—562no—
194C2—21no—
195C2—21no—
196C2—81no—
197C2—81no—
198C2#1172529611yescharacteristic
199C2#1172534511yescharacteristic
200C2#1172534911yescharacteristic
subgroupG/H
centerC22#89268
commutatorC2×C42×C7C2×C4
Frattini#390C2×D7
FittingC7×#1393C2
socleC22×C7#354
prime radicalC22×C7×D4D4
cosocleC7×#390C22
hypercenter#1393D7
hypocenterC7#7428
LCSG ▷ C2×C42×C7 ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #390 ◁ #1393

Complements

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

NH ≅ G/Ntype
4. C2×#6433C4semidirect
10. #89319C4semidirect
175. C7#7428semidirect

Maximal subgroups

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

subgroupindex
#117273932
C7×#13932
#117254462
#74287