Finite Group Databasebeta

← #13241379

Subgroups — #13241379

Order 1792.

214 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 37 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#11727290C211yesmaximal, characteristic
2C7×#1317C211yesmaximal, characteristic
3#11725435C211yesmaximal, characteristic
4#90174C411yescharacteristic
5C7×#381C2211yescharacteristic
6#89983—21no—
7#89979—21no—
8C7×#323—21no—
9#89322—21no—
10#89321C411yescharacteristic
11#7427—71nomaximal, Sylow
12C23×C4×C7D411yescharacteristic
13C2×C7×C22⋊C4C2×C411yescharacteristic
14C2×C7×C22⋊C4D411yescharacteristic
15C2×C22⋊Dic7—21no—
16C2×C22⋊Dic7—21no—
17#6487—41no—
18C2×#1136—41no—
19#6441—42no—
20C7×C22⋊C8—41no—
21C7×#95—41no—
22C7⋊#95—42no—
23C22⋊(C7⋊C8)—22no—
24C22⋊(C7⋊C8)—41no—
25#2030—71no—
26#1317D711yescharacteristic
27#1306—71no—
28C24×C7C22⋊C411yescharacteristic
29C22×C4×C7—21no—
30C22×C4×C7—21no—
31C22×C4×C7—21no—
32C22×C4×C7—21no—
33C22×C4×C7—41no—
34C22×C4×C7—41no—
35C22×C4×C7SD1611yescharacteristic
36C22×C4×C7Q1611yescharacteristic
37C22×Dic7—22no—
38C22×Dic7—41no—
39C2×Dic14—41no—
40C2×C7×C8—81no—
41C7×C22⋊C4—41no—
42C7×C22⋊C4—41no—
43C22⋊Dic7—41no—
44C22⋊Dic7—41no—
45C22⋊Dic7—41no—
46C22⋊Dic7—41no—
47C4⋊Dic7—41no—
48Dic7⋊C4—42no—
49#1136—81no—
50#1136—81no—
51C2×C7⋊C8—42no—
52#543—71no—
53#407—141no—
54#381—141no—
55#381C2×D711yescharacteristic
56#342—71no—
57#342—141no—
58#323—21no—
59C23×C7—21no—
60C23×C7—21no—
61C23×C7—81no—
62C23×C7#9911yescharacteristic
63C23×C7#10311yescharacteristic
64C23×C7#10411yescharacteristic
65C2×C4×C7—21no—
66C2×C4×C7—21no—
67C2×C4×C7—41no—
68C2×C4×C7—41no—
69C2×C4×C7—41no—
70C2×C4×C7—41no—
71C2×C4×C7—41no—
72C2×C4×C7—41no—
73C2×C4×C7—81no—
74C2×C4×C7—81no—
75C2×C4×C7—81no—
76C2×Dic7—42no—
77C2×Dic7—82no—
78C2×Dic7—81no—
79C2×Dic7—82no—
80Dic14—161no—
81C7×C8—161no—
82C7⋊C8—82no—
83C23×C4D2811yescharacteristic
84C2×M16—281no—
85C22⋊Q8—282no—
86C22⋊Q8—281no—
87C2×C22⋊C4—141no—
88C2×C22⋊C4—141no—
89C2×C22⋊C4C4×D711yescharacteristic
90C2×C22⋊C4C22⋊D711yescharacteristic
91C22⋊C8—41no—
92C22⋊C8—142no—
93C22⋊C8—281no—
94#95—41no—
95#95—282no—
96C22×C7—21no—
97C22×C7—21no—
98C22×C7—41no—
99C22×C7—41no—
100C22×C7—41no—
101C22×C7—42no—
102C22×C7—81no—
103C22×C7#32811yescharacteristic
104C22×C7AΣL(1,𝔽16)11yescharacteristic
105C22×C7#35411yescharacteristic
106C4×C7—41no—
107C4×C7—41no—
108C4×C7—81no—
109C4×C7—81no—
110Dic7—82no—
111Dic7—161no—
112C24(C2×D7)⋊C411yescharacteristic
113C2×Q8—281no—
114C22×C4—21no—
115C22×C4—21no—
116C22×C4—21no—
117C22×C4—21no—
118C22×C4—41no—
119C22×C4—41no—
120C22×C4—142no—
121C22×C4—281no—
122C22×C4#113211yescharacteristic
123C22×C4Dic2811yescharacteristic
124M16—561no—
125M16—561no—
126C2×C8—81no—
127C2×C8—282no—
128C4⋊C4—282no—
129C4⋊C4—281no—
130C22⋊C4—41no—
131C22⋊C4—41no—
132C22⋊C4—281no—
133C22⋊C4—281no—
134C22⋊C4—281no—
135C22⋊C4—281no—
136C2×C7—21no—
137C2×C7—21no—
138C2×C7—21no—
139C2×C7—41no—
140C2×C7—41no—
141C2×C7#135111yescharacteristic
142C23—21no—
143C23—21no—
144C23—81no—
145C23#638011yescharacteristic
146C23#639011yescharacteristic
147C23#639911yescharacteristic
148Q8—1121no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—81no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—282no—
161C2×C4—562no—
162C2×C4—561no—
163C2×C4—562no—
164C8—161no—
165C8—562no—
166C7#742711yescharacteristic, complemented, Sylow
167C22—21no—
168C22—21no—
169C22—41no—
170C22—41no—
171C22—41no—
172C22—42no—
173C22—81no—
174C22#8926211yescharacteristic
175C22#8926811yescharacteristic
176C22#8927011yescharacteristic
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—562no—
182C4—1121no—
183C2—21no—
184C2—21no—
185C2—21no—
186C2—41no—
187C2—41no—
188C2#1172525511yescharacteristic
subgroupG/H
centerC2#11725255
commutatorC2×C7×C22⋊C4C2×C4
Frattini#381C2×D7
FittingC7×#1317C2
socleC2×C7#1351
prime radicalC24×C7C22⋊C4
cosocleC7×#381C22
hypercenter#1317D7
hypocenterC7#7427
LCSG ▷ C2×C7×C22⋊C4 ▷ C24×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ #381 ◁ #1317

Complements

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

NH ≅ G/Ntype
166. C7#7427semidirect

Maximal subgroups

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

subgroupindex
#117272902
C7×#13172
#117254352
#74277