Finite Group Databasebeta

← #13256827

Subgroups — #13256827

Order 1792.

416 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 121 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#11731787C211yesmaximal, characteristic
2#11728213C212yesmaximal
3#11727333C211yesmaximal, characteristic
4C7×#1296C211yesmaximal, characteristic
5#11725510C212yesmaximal
6C2×#6432C2211yescharacteristic
7C2×C7×C4⋊C8C2212yes—
8C7×#384C2211yescharacteristic
9#89758—22no—
10#89757—22no—
11#89749—22no—
12C2×#6384—22no—
13C4×C4⋊Dic7C2212yes—
14C2×C4×C7⋊C8C2211yescharacteristic
15#89346—22no—
16#89346—22no—
17#10352—71nomaximal, Sylow
18C22×Dic14—21no—
19C22×C7×C8—22no—
20C2×C7×C4⋊C4—22no—
21C2×C7×C4⋊C4D412yes—
22C2×C42×C7C2311yescharacteristic
23C2×C4⋊Dic7—22no—
24C2×C4⋊Dic7—22no—
25C2×C4⋊Dic7D412yes—
26C2×C4⋊Dic7D412yes—
27C2×C4×Dic7—22no—
28C22×C7⋊C8—21no—
29#6432—22no—
30#6432—21no—
31#6432Q812yes—
32C7×C4⋊C8—22no—
33C7×C4⋊C8—22no—
34C7⋊#95—22no—
35C7⋊#95—24no—
36C7⋊#95—22no—
37#6384—44no—
38C4×C7⋊C8—22no—
39#2571—71no—
40#1987—72no—
41#1956—71no—
42#1296D711yescharacteristic
43#1279—72no—
44C22×C4×C7—22no—
45C22×C4×C7C2×D411yescharacteristic
46C22×C4×C7C2×D412yes—
47C22×Dic7—22no—
48C22×Dic7—22no—
49C22×Dic7—41no—
50C2×Dic14—22no—
51C2×Dic14—42no—
52C2×Dic14—42no—
53C2×Dic14—41no—
54C2×C7×C8—42no—
55C2×C7×C8—42no—
56C2×C7×C8—42no—
57C7×C4⋊C4—42no—
58C7×C4⋊C4—42no—
59C7×C4⋊C4—42no—
60C42×C7C2×Q811yescharacteristic
61C42×C7#4112yes—
62C42×C7#4111yescharacteristic
63C4⋊Dic7—24no—
64C4⋊Dic7—22no—
65C4⋊Dic7—22no—
66C4⋊Dic7—22no—
67C4⋊Dic7—22no—
68C4⋊Dic7—42no—
69C4⋊Dic7—82no—
70C4×Dic7—42no—
71C4×Dic7—42no—
72C2×C7⋊C8—22no—
73C2×C7⋊C8—41no—
74C2×C7⋊C8—41no—
75C2×C4⋊Q8—71no—
76C2×C4⋊C8C2×D712yes—
77C2×#103—142no—
78C2×C4×C8—71no—
79#400—142no—
80#389—142no—
81#384C2×D711yescharacteristic
82#382—142no—
83C4×C4⋊C4—72no—
84#340—142no—
85#340—142no—
86C23×C7#12011yescharacteristic
87C2×C4×C7—21no—
88C2×C4×C7—21no—
89C2×C4×C7—44no—
90C2×C4×C7—42no—
91C2×C4×C7C22⋊Q812yes—
92C2×C4×C7C22⋊Q811yescharacteristic
93C2×C4×C7#12411yescharacteristic
94C2×C4×C7#12412yes—
95C2×C4×C7#13512yes—
96C2×C4×C7#13512yes—
97C2×C4×C7#13712yes—
98C2×C4×C7#13712yes—
99C2×Dic7—42no—
100C2×Dic7—42no—
101C2×Dic7—42no—
102C2×Dic7—42no—
103C2×Dic7—42no—
104C2×Dic7—42no—
105C2×Dic7—42no—
106C2×Dic7—81no—
107C2×Dic7—81no—
108Dic14—44no—
109Dic14—82no—
110C7×C8—82no—
111C7⋊C8—42no—
112C22×Q8—141no—
113C22×C8—22no—
114C22×C8—141no—
115C4⋊Q8—72no—
116C4⋊Q8—142no—
117C4⋊Q8—141no—
118C2×C4⋊C4—22no—
119C2×C4⋊C4—72no—
120C2×C4⋊C4—72no—
121C2×C4⋊C4—142no—
122C2×C4⋊C4—142no—
123C2×C4⋊C4D2812yes—
124C2×C42—142no—
125C2×C42C22×D711yescharacteristic
126C4⋊C8—22no—
127C4⋊C8—22no—
128#103—284no—
129C4×C8—142no—
130#95—142no—
131#95—144no—
132#95—142no—
133C22×C7#39311yescharacteristic
134C22×C7#45212yes—
135C22×C7#45212yes—
136C22×C7#45311yescharacteristic
137C22×C7#45411yescharacteristic
138C4×C7—21no—
139C4×C7—21no—
140C4×C7—82no—
141C4×C7#47912yes—
142C4×C7#47912yes—
143C4×C7#48812yes—
144C4×C7#49112yes—
145Dic7—82no—
146Dic7—82no—
147Dic7—82no—
148C2×Q8—142no—
149C2×Q8—282no—
150C2×Q8—282no—
151C2×Q8—281no—
152C22×C4—22no—
153C22×C4—142no—
154C22×C4—142no—
155C22×C4—281no—
156C22×C4C2×D2811yescharacteristic
157C22×C4D4×D712yes—
158C2×C8—42no—
159C2×C8—42no—
160C2×C8—42no—
161C2×C8—142no—
162C2×C8—281no—
163C2×C8—281no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—144no—
168C4⋊C4—142no—
169C4⋊C4—142no—
170C4⋊C4—142no—
171C4⋊C4—142no—
172C4⋊C4—282no—
173C4⋊C4—562no—
174C42—282no—
175C42—282no—
176C42#115712yes—
177C42#115911yescharacteristic
178C42Q8×D711yescharacteristic
179C2×C7#163011yescharacteristic
180C2×C7#163411yescharacteristic
181C2×C7#163812yes—
182C2×C7#202612yes—
183C2×C7#202711yescharacteristic
184C23#644511yescharacteristic
185Q8—284no—
186Q8—562no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—44no—
191C2×C4—282no—
192C2×C4—282no—
193C2×C4—282no—
194C2×C4—282no—
195C2×C4—282no—
196C2×C4—282no—
197C2×C4—282no—
198C2×C4—561no—
199C2×C4—561no—
200C2×C4#643811yescharacteristic
201C2×C4#644812yes—
202C2×C4#645912yes—
203C2×C4#646011yescharacteristic
204C2×C4#647512yes—
205C2×C4#647812yes—
206C2×C4#647912yes—
207C2×C4#648112yes—
208C8—82no—
209C8—282no—
210C7#1035211yescharacteristic, complemented, Sylow
211C22#8944511yescharacteristic
212C22#8951911yescharacteristic
213C22#8952511yescharacteristic
214C22#8955512yes—
215C22#8958212yes—
216C4—21no—
217C4—21no—
218C4—82no—
219C4—562no—
220C4—562no—
221C4—562no—
222C4#8954012yes—
223C4#8956912yes—
224C4#8962912yes—
225C4#8964912yes—
226C2#1172615811yescharacteristic
227C2#1172618912yes—
228C2#1172624711yescharacteristic
229C2#1172666512yes—
230C2#1172674911yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1296C2
socle, prime radicalC23×C7#120
hypercenter#1296D7
hypocenterC7#10352
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
210. C7#10352semidirect

Maximal subgroups

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

subgroupindex
#117317872
#117282132
#117273332
C7×#12962
#117255102
#103527