Finite Group Databasebeta

← #13256878

Subgroups — #13256878

Order 1792.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#11727582C212yesmaximal
3#11727306C211yesmaximal, characteristic
4C7×#1295C211yesmaximal, characteristic
5#11725465C212yesmaximal
6C2×#6432C2211yescharacteristic
7C2×C7×#97C2212yes—
8C7×#382C2211yescharacteristic
9#89756—22no—
10C2×#6384—22no—
11#89708C2212yes—
12C2×#6377C2211yescharacteristic
13#89433—22no—
14#89429—22no—
15#89346—22no—
16#89346—22no—
17#10361—71nomaximal, Sylow
18C22×Dic14—21no—
19C22×C7×C8—22no—
20C2×C7×C4⋊C4D412yes—
21C2×C42×C7C2311yescharacteristic
22C2×C4⋊Dic7—22no—
23C2×C4⋊Dic7—22no—
24C2×C4⋊Dic7D412yes—
25C2×C4⋊Dic7D412yes—
26C2×Dic7⋊C4—22no—
27C2×Dic7⋊C4—22no—
28C22×C7⋊C8—21no—
29#6432—22no—
30#6432—21no—
31#6432Q812yes—
32C7×#97—22no—
33C7×#97—22no—
34C7×#95—22no—
35C7⋊#95—22no—
36C7⋊#95—22no—
37C7⋊#95—22no—
38#6384—44no—
39#6377—22no—
40#2845—71no—
41#1993—72no—
42#1960—71no—
43#1295—72no—
44#1295D711yescharacteristic
45C22×C4×C7—22no—
46C22×C4×C7C2×D411yescharacteristic
47C22×C4×C7C2×D412yes—
48C22×Dic7—22no—
49C22×Dic7—22no—
50C22×Dic7—41no—
51C2×Dic14—22no—
52C2×Dic14—42no—
53C2×Dic14—42no—
54C2×Dic14—41no—
55C2×C7×C8—24no—
56C2×C7×C8—42no—
57C2×C7×C8—42no—
58C7×C4⋊C4—42no—
59C42×C7C2×Q811yescharacteristic
60C42×C7#4112yes—
61C42×C7#4111yescharacteristic
62C4⋊Dic7—24no—
63C4⋊Dic7—42no—
64C4⋊Dic7—42no—
65C4⋊Dic7—42no—
66C4⋊Dic7—82no—
67Dic7⋊C4—82no—
68Dic7⋊C4—82no—
69C2×C7⋊C8—22no—
70C2×C7⋊C8—41no—
71C2×C7⋊C8—41no—
72C2×C4⋊Q8—71no—
73C2×#103—142no—
74C2×#97—71no—
75C2×#97C2×D712yes—
76#398—142no—
77#398—142no—
78#398—142no—
79#382—72no—
80#382C2×D711yescharacteristic
81#340—142no—
82#340—142no—
83C23×C7#12011yescharacteristic
84C2×C4×C7—21no—
85C2×C4×C7—21no—
86C2×C4×C7—22no—
87C2×C4×C7—22no—
88C2×C4×C7—42no—
89C2×C4×C7—42no—
90C2×C4×C7—42no—
91C2×C4×C7C22⋊Q812yes—
92C2×C4×C7C22⋊Q811yescharacteristic
93C2×C4×C7#12411yescharacteristic
94C2×C4×C7#12412yes—
95C2×Dic7—42no—
96C2×Dic7—42no—
97C2×Dic7—42no—
98C2×Dic7—42no—
99C2×Dic7—42no—
100C2×Dic7—42no—
101C2×Dic7—42no—
102C2×Dic7—81no—
103C2×Dic7—81no—
104Dic14—44no—
105Dic14—82no—
106C7×C8—44no—
107C7⋊C8—42no—
108C22×Q8—141no—
109C22×C8—22no—
110C22×C8—141no—
111C4⋊Q8—72no—
112C4⋊Q8—142no—
113C4⋊Q8—141no—
114C2×C4⋊C4—72no—
115C2×C4⋊C4—72no—
116C2×C4⋊C4—142no—
117C2×C4⋊C4—142no—
118C2×C4⋊C4—142no—
119C2×C4⋊C4—142no—
120C2×C4⋊C4D2812yes—
121C2×C42C22×D711yescharacteristic
122#103—284no—
123#97—22no—
124#97—22no—
125#97—142no—
126#95—22no—
127#95—142no—
128#95—142no—
129#95—142no—
130C22×C7#39311yescharacteristic
131C22×C7#45311yescharacteristic
132C22×C7#45411yescharacteristic
133C22×C7#45512yes—
134C22×C7#45612yes—
135C4×C7—21no—
136C4×C7—21no—
137C4×C7—22no—
138C4×C7—22no—
139C4×C7—82no—
140Dic7—82no—
141Dic7—82no—
142Dic7—82no—
143C2×Q8—142no—
144C2×Q8—282no—
145C2×Q8—282no—
146C2×Q8—281no—
147C22×C4—22no—
148C22×C4—142no—
149C22×C4—142no—
150C22×C4—281no—
151C22×C4C2×D2811yescharacteristic
152C22×C4D4×D712yes—
153C2×C8—24no—
154C2×C8—42no—
155C2×C8—42no—
156C2×C8—142no—
157C2×C8—281no—
158C2×C8—281no—
159C4⋊C4—42no—
160C4⋊C4—144no—
161C4⋊C4—282no—
162C4⋊C4—282no—
163C4⋊C4—282no—
164C4⋊C4—562no—
165C4⋊C4—562no—
166C4⋊C4—562no—
167C42#115712yes—
168C42#115911yescharacteristic
169C42Q8×D711yescharacteristic
170C2×C7#166112yes—
171C2×C7#166211yescharacteristic
172C2×C7#166311yescharacteristic
173C2×C7#202711yescharacteristic
174C2×C7#202812yes—
175C23#644511yescharacteristic
176Q8—284no—
177Q8—562no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—282no—
186C2×C4—282no—
187C2×C4—282no—
188C2×C4—282no—
189C2×C4—282no—
190C2×C4—282no—
191C2×C4—282no—
192C2×C4—561no—
193C2×C4—561no—
194C2×C4#643811yescharacteristic
195C2×C4#644812yes—
196C2×C4#645912yes—
197C2×C4#646011yescharacteristic
198C8—44no—
199C8—282no—
200C7#1036111yescharacteristic, complemented, Sylow
201C22#8944511yescharacteristic
202C22#8951911yescharacteristic
203C22#8952511yescharacteristic
204C22#8959712yes—
205C22#8959812yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—562no—
212C4—562no—
213C4—562no—
214C2#1172611012yes—
215C2#1172612811yescharacteristic
216C2#1172613111yescharacteristic
217C2#1172652312yes—
218C2#1172674911yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1295C2
socle, prime radicalC23×C7#120
hypercenter#1295D7
hypocenterC7#10361
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
200. C7#10361semidirect

Maximal subgroups

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

subgroupindex
#117316642
#117275822
#117273062
C7×#12952
#117254652
#103617