Finite Group Databasebeta

← #13256877

Subgroups — #13256877

Order 1792.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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
2C7×#1960C211yesmaximal, characteristic
3#11729542C212yesmaximal
4#11725465C212yesmaximal
5#11725436C211yesmaximal, characteristic
6C2×C7×C4⋊Q8C2211yescharacteristic
7C2×C7×#103—22no—
8C2×C7×#97C2211yescharacteristic
9C7×#382C2211yescharacteristic
10#89756—22no—
11#89708C2212yes—
12C2×#6377C2212yes—
13#89433—22no—
14#89429—22no—
15#89324—22no—
16#89324—22no—
17#10361—71nomaximal, Sylow
18C22×C7×Q8—21no—
19C22×C7×C8—21no—
20C7×C4⋊Q8—22no—
21C7×C4⋊Q8—21no—
22C7×C4⋊Q8Q812yes—
23C2×C7×C4⋊C4—22no—
24C2×C7×C4⋊C4D412yes—
25C2×C42×C7C2311yescharacteristic
26C2×C4⋊Dic7—22no—
27C2×C4⋊Dic7D412yes—
28C2×C4⋊Dic7D412yes—
29C2×Dic7⋊C4—22no—
30C2×Dic7⋊C4—22no—
31C22×C7⋊C8—22no—
32C7×#103—44no—
33C7×#97—22no—
34C7×#95—22no—
35C7⋊#95—22no—
36C7⋊#95—22no—
37C7⋊#95—22no—
38#6377—22no—
39#6377—22no—
40#2845—71no—
41#1993—72no—
42#1960D711yescharacteristic
43#1295—72no—
44#1295—71no—
45C2×C7×Q8—22no—
46C2×C7×Q8—42no—
47C2×C7×Q8—42no—
48C2×C7×Q8—41no—
49C22×C4×C7—22no—
50C22×C4×C7—41no—
51C22×C4×C7C2×D412yes—
52C22×C4×C7C2×D411yescharacteristic
53C22×Dic7—22no—
54C22×Dic7—22no—
55C2×C7×C8—22no—
56C2×C7×C8—41no—
57C2×C7×C8—41no—
58C7×C4⋊C4—24no—
59C7×C4⋊C4—42no—
60C7×C4⋊C4—42no—
61C42×C7C2×Q811yescharacteristic
62C42×C7#4111yescharacteristic
63C42×C7#4112yes—
64C4⋊Dic7—42no—
65C4⋊Dic7—42no—
66C4⋊Dic7—82no—
67Dic7⋊C4—82no—
68Dic7⋊C4—82no—
69C2×C7⋊C8—24no—
70C2×C7⋊C8—42no—
71C2×C7⋊C8—42no—
72C2×C4⋊Q8C2×D711yescharacteristic
73C2×#103—22no—
74C2×#97—72no—
75C2×#97C2×D711yescharacteristic
76#398—142no—
77#398—142no—
78#398—142no—
79#382—72no—
80#382C2×D711yescharacteristic
81#340—142no—
82#340—142no—
83C23×C7#12011yescharacteristic
84C7×Q8—44no—
85C7×Q8—82no—
86C2×C4×C7—21no—
87C2×C4×C7—21no—
88C2×C4×C7—22no—
89C2×C4×C7—22no—
90C2×C4×C7—42no—
91C2×C4×C7—42no—
92C2×C4×C7—42no—
93C2×C4×C7—42no—
94C2×C4×C7—81no—
95C2×C4×C7—81no—
96C2×C4×C7C22⋊Q812yes—
97C2×C4×C7C22⋊Q811yescharacteristic
98C2×C4×C7#12412yes—
99C2×C4×C7#12411yescharacteristic
100C2×Dic7—42no—
101C2×Dic7—42no—
102C2×Dic7—42no—
103C2×Dic7—42no—
104C2×Dic7—42no—
105C2×Dic7—42no—
106C7×C8—42no—
107C7⋊C8—44no—
108C22×Q8—21no—
109C22×C8—21no—
110C22×C8—142no—
111C4⋊Q8—21no—
112C4⋊Q8—22no—
113C4⋊Q8Dic1412yes—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—72no—
116C2×C4⋊C4—72no—
117C2×C4⋊C4—142no—
118C2×C4⋊C4—142no—
119C2×C4⋊C4—142no—
120C2×C4⋊C4C22⋊D712yes—
121C2×C42C22×D711yescharacteristic
122#103—44no—
123#97—22no—
124#97—142no—
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—
140C4×C7—82no—
141Dic7—82no—
142Dic7—82no—
143C2×Q8—22no—
144C2×Q8—42no—
145C2×Q8—42no—
146C2×Q8—41no—
147C22×C4—22no—
148C22×C4—41no—
149C22×C4—142no—
150C22×C4—142no—
151C22×C4D4×D712yes—
152C22×C4C2×C22⋊D711yescharacteristic
153C2×C8—22no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—144no—
157C2×C8—282no—
158C2×C8—282no—
159C4⋊C4—24no—
160C4⋊C4—42no—
161C4⋊C4—42no—
162C4⋊C4—282no—
163C4⋊C4—282no—
164C4⋊C4—562no—
165C4⋊C4—562no—
166C4⋊C4—562no—
167C42C2×Dic1411yescharacteristic
168C42#115711yescharacteristic
169C42#115912yes—
170C2×C7#166112yes—
171C2×C7#166211yescharacteristic
172C2×C7#166311yescharacteristic
173C2×C7#202711yescharacteristic
174C2×C7#202812yes—
175C23#650011yescharacteristic
176Q8—44no—
177Q8—82no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—282no—
189C2×C4—282no—
190C2×C4—282no—
191C2×C4—282no—
192C2×C4—282no—
193C2×C4—282no—
194C2×C4#644112yes—
195C2×C4#644812yes—
196C2×C4#648711yescharacteristic
197C2×C4#649911yescharacteristic
198C8—42no—
199C8—284no—
200C7#1036111yescharacteristic, complemented, Sylow
201C22#8971911yescharacteristic
202C22#8983411yescharacteristic
203C22#8984911yescharacteristic
204C22#8997412yes—
205C22#8997712yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—562no—
213C4—562no—
214C2#1172739711yescharacteristic
215C2#1172808712yes—
216C2#1172900511yescharacteristic
217C2#1172900611yescharacteristic
218C2#1172908512yes—
subgroupG/H
centerC23#6500
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1960C2
socle, prime radicalC23×C7#120
hypercenter#1960D7
hypocenterC7#10361
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

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
C7×#19602
#117295422
#117254652
#117254362
#103617