Finite Group Databasebeta

← #13258307

Subgroups — #13258307

Order 1792.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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#11731664C211yesmaximal, characteristic
2#11727569C212yesmaximal
3#11727302C211yesmaximal, characteristic
4C7×#1295C211yesmaximal, characteristic
5#11725465C212yesmaximal
6C2×C7×#97C2212yes—
7C7×#382C2211yescharacteristic
8#89756—22no—
9#89708C2212yes—
10#89707C2211yescharacteristic
11C2×#6377C2211yescharacteristic
12#89433—22no—
13#89429—22no—
14#89346—22no—
15#89346—22no—
16#89324—22no—
17#10586—71nomaximal, Sylow
18C22×C7×C8—22no—
19C2×C7×C4⋊C4D412yes—
20C2×C42×C7C2311yescharacteristic
21C2×C4⋊Dic7—22no—
22C2×C4⋊Dic7—21no—
23C2×C4⋊Dic7—22no—
24C2×C4⋊Dic7D412yes—
25C2×C4⋊Dic7D412yes—
26C2×Dic7⋊C4—22no—
27C2×Dic7⋊C4—22no—
28C22×C7⋊C8—21no—
29C7×#97—22no—
30C7×#97Q814yes—
31C7×#95—22no—
32C7⋊#95—22no—
33C7⋊#95—22no—
34C7⋊#95—22no—
35#6377—21no—
36#6377Q812yes—
37#2845—71no—
38#1836—72no—
39#1836—71no—
40#1295—72no—
41#1295D711yescharacteristic
42C22×C4×C7—22no—
43C22×C4×C7C2×D411yescharacteristic
44C22×C4×C7C2×D412yes—
45C22×Dic7—22no—
46C22×Dic7—22no—
47C22×Dic7—41no—
48C2×C7×C8—24no—
49C2×C7×C8—42no—
50C2×C7×C8—42no—
51C7×C4⋊C4—42no—
52C42×C7C2×Q812yes—
53C42×C7C2×Q811yescharacteristic
54C42×C7#4111yescharacteristic
55C4⋊Dic7—42no—
56C4⋊Dic7—42no—
57C4⋊Dic7—42no—
58C4⋊Dic7—44no—
59C4⋊Dic7—82no—
60Dic7⋊C4—82no—
61Dic7⋊C4—82no—
62C2×C7⋊C8—22no—
63C2×C7⋊C8—41no—
64C2×C7⋊C8—41no—
65C2×#97—71no—
66C2×#97C2×D712yes—
67#398—142no—
68#398—142no—
69#398—142no—
70#384—71no—
71#382—72no—
72#382C2×D711yescharacteristic
73#340—142no—
74#340—142no—
75#340—142no—
76C23×C7#12011yescharacteristic
77C2×C4×C7—21no—
78C2×C4×C7—22no—
79C2×C4×C7—21no—
80C2×C4×C7—22no—
81C2×C4×C7—42no—
82C2×C4×C7—42no—
83C2×C4×C7—42no—
84C2×C4×C7C22⋊Q812yes—
85C2×C4×C7C22⋊Q811yescharacteristic
86C2×C4×C7C4⋊Q811yescharacteristic
87C2×C4×C7C4⋊Q812yes—
88C2×Dic7—42no—
89C2×Dic7—42no—
90C2×Dic7—42no—
91C2×Dic7—42no—
92C2×Dic7—42no—
93C2×Dic7—42no—
94C2×Dic7—81no—
95C2×Dic7—82no—
96C7×C8—44no—
97C7⋊C8—42no—
98C22×C8—22no—
99C22×C8—141no—
100C2×C4⋊C4—72no—
101C2×C4⋊C4—72no—
102C2×C4⋊C4—141no—
103C2×C4⋊C4—142no—
104C2×C4⋊C4—142no—
105C2×C4⋊C4—142no—
106C2×C4⋊C4—142no—
107C2×C4⋊C4D2812yes—
108C2×C42C22×D711yescharacteristic
109#97—22no—
110#97—72no—
111#97—141no—
112#97Dic1414yes—
113#95—22no—
114#95—142no—
115#95—142no—
116#95—142no—
117C22×C7#39511yescharacteristic
118C22×C7#45411yescharacteristic
119C22×C7#45412yes—
120C22×C7#45511yescharacteristic
121C22×C7#45512yes—
122C4×C7—21no—
123C4×C7—22no—
124C4×C7—21no—
125C4×C7—22no—
126C4×C7—82no—
127Dic7—82no—
128Dic7—82no—
129Dic7—161no—
130C22×C4—22no—
131C22×C4—142no—
132C22×C4—142no—
133C22×C4—281no—
134C22×C4C2×D2811yescharacteristic
135C22×C4D4×D712yes—
136C2×C8—24no—
137C2×C8—42no—
138C2×C8—42no—
139C2×C8—142no—
140C2×C8—281no—
141C2×C8—281no—
142C4⋊C4—42no—
143C4⋊C4—282no—
144C4⋊C4—282no—
145C4⋊C4—282no—
146C4⋊C4—284no—
147C4⋊C4—562no—
148C4⋊C4—562no—
149C4⋊C4—562no—
150C42C2×Dic1412yes—
151C42#115911yescharacteristic
152C42Q8×D711yescharacteristic
153C2×C7#165811yescharacteristic
154C2×C7#166212yes—
155C2×C7#166211yescharacteristic
156C2×C7#206111yescharacteristic
157C2×C7#206112yes—
158C23#644511yescharacteristic
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—282no—
167C2×C4—282no—
168C2×C4—282no—
169C2×C4—282no—
170C2×C4—282no—
171C2×C4—282no—
172C2×C4—561no—
173C2×C4—562no—
174C2×C4#643211yescharacteristic
175C2×C4#644112yes—
176C2×C4#645112yes—
177C2×C4#646011yescharacteristic
178C8—44no—
179C8—282no—
180C7#1058611yescharacteristic, complemented, Sylow
181C22#8942811yescharacteristic
182C22#8951811yescharacteristic
183C22#8952511yescharacteristic
184C22#8959712yes—
185C22#8959912yes—
186C4—21no—
187C4—21no—
188C4—22no—
189C4—22no—
190C4—82no—
191C4—562no—
192C4—562no—
193C4—1121no—
194C2#1172611212yes—
195C2#1172612811yescharacteristic
196C2#1172612911yescharacteristic
197C2#1172649012yes—
198C2#1172673311yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1295C2
socle, prime radicalC23×C7#120
hypercenter#1295D7
hypocenterC7#10586
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
180. C7#10586semidirect

Maximal subgroups

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

subgroupindex
#117316642
#117275692
#117273022
C7×#12952
#117254652
#105867