Finite Group Databasebeta

← #13256090

Subgroups — #13256090

Order 1792.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#11736716C212yesmaximal
2#11735924C211yesmaximal, characteristic
3#11728547C212yesmaximal
4#11727576C211yesmaximal, characteristic
5C7×#1281C211yesmaximal, characteristic
6#90161C2212yes—
7C2×#6432C2211yescharacteristic
8C7×#431C2212yes—
9C2×C7×#97C2211yescharacteristic
10#89878—22no—
11C2×#6390—22no—
12#89708C2211yescharacteristic
13#89623—24no—
14#89493—24no—
15#89474—22no—
16#89474—22no—
17#89453—22no—
18#89452—22no—
19#89262—24no—
20#10227—71nomaximal, Sylow
21C22×Dic14—21no—
22C22×C7×C8D412yes—
23C2×C42×C7C2311yescharacteristic
24#6489—22no—
25C2×C4⋊Dic7—22no—
26C2×C4⋊Dic7—21no—
27#6487—22no—
28#6487—22no—
29#6433—22no—
30#6432—22no—
31#6432—21no—
32#6432D412yes—
33#6432D412yes—
34#6432D412yes—
35C4×Dic14—22no—
36C4×Dic14—22no—
37C7×C4⋊C8—22no—
38C7×C22⋊C8D414yes—
39C7×#97—22no—
40C4×C7×C8—22no—
41C7⋊#95—22no—
42#6392—24no—
43#6391—22no—
44#6391—22no—
45#6391—28no—
46#6390—28no—
47#6390—44no—
48#3229—72no—
49#3162—71no—
50#1960—71no—
51#1518—72no—
52#1281D711yescharacteristic
53C22×C4×C7C2×D412yes—
54C22×C4×C7C2×D411yescharacteristic
55C22×Dic7—41no—
56C22×Dic7—41no—
57C2×Dic14—22no—
58C2×Dic14—22no—
59C2×Dic14—22no—
60C2×Dic14—42no—
61C2×Dic14—42no—
62C2×Dic14—41no—
63C2×C7×C8—22no—
64C2×C7×C8—22no—
65C2×C7×C8—24no—
66C2×C7×C8SD1614yes—
67C42×C7C2×D412yes—
68C42×C7C2×D411yescharacteristic
69C42×C7#4111yescharacteristic
70C22⋊Dic7—42no—
71C4⋊Dic7—22no—
72C4⋊Dic7—24no—
73C4⋊Dic7—22no—
74C4⋊Dic7—22no—
75C4⋊Dic7—22no—
76C4⋊Dic7—42no—
77C4⋊Dic7—42no—
78Dic7⋊C4—42no—
79Dic7⋊C4—42no—
80C4×Dic7—42no—
81#533—72no—
82C2×C4⋊Q8—71no—
83#501—142no—
84#501—142no—
85#498—142no—
86#487—142no—
87#483—144no—
88#475—144no—
89#431C2×D712yes—
90#427—142no—
91C2×#103—142no—
92C2×#97C2×D711yescharacteristic
93#382—71no—
94#328—144no—
95C23×C7#12711yescharacteristic
96C2×C4×C7—42no—
97C2×C4×C7#12012yes—
98C2×C4×C7#12011yescharacteristic
99C2×C4×C7#12112yes—
100C2×C4×C7#12111yescharacteristic
101C2×C4×C7C2×SD1612yes—
102C2×C4×C7#13712yes—
103C2×Dic7—42no—
104C2×Dic7—42no—
105C2×Dic7—42no—
106C2×Dic7—81no—
107C2×Dic7—81no—
108C2×Dic7—82no—
109C2×Dic7—81no—
110Dic14—44no—
111Dic14—44no—
112Dic14—82no—
113Dic14—82no—
114C7×C8—24no—
115C7×C8—44no—
116C22×Q8—141no—
117C22×C8D2812yes—
118C4⋊Q8—72no—
119C4⋊Q8—72no—
120C4⋊Q8—72no—
121C4⋊Q8—142no—
122C4⋊Q8—141no—
123#125—142no—
124C22⋊Q8—142no—
125C22⋊Q8—142no—
126C4×Q8—142no—
127C4×Q8—142no—
128#117—142no—
129C2×C4⋊C4—142no—
130C2×C4⋊C4—141no—
131C2×C42C22×D711yescharacteristic
132#107—144no—
133#106—142no—
134#106—142no—
135#106—148no—
136C4⋊C8—22no—
137#103—148no—
138#103—284no—
139C22⋊C8D2814yes—
140#97—22no—
141C4×C8—22no—
142#95—142no—
143C22×C7—22no—
144C22×C7#39211yescharacteristic
145C22×C7#49211yescharacteristic
146C22×C7#49711yescharacteristic
147C4×C7—22no—
148C4×C7—22no—
149C4×C7#44812yes—
150C4×C7#46112yes—
151Dic7—82no—
152Dic7—82no—
153Dic7—82no—
154Dic7—161no—
155C2×Q8—142no—
156C2×Q8—142no—
157C2×Q8—142no—
158C2×Q8—281no—
159C2×Q8—282no—
160C2×Q8—282no—
161C22×C4—281no—
162C22×C4—281no—
163C22×C4C2×D2812yes—
164C22×C4C2×D2811yescharacteristic
165C2×C8—22no—
166C2×C8—22no—
167C2×C8—24no—
168C2×C8#113214yes—
169C4⋊C4—144no—
170C4⋊C4—142no—
171C4⋊C4—142no—
172C4⋊C4—142no—
173C4⋊C4—142no—
174C4⋊C4—282no—
175C4⋊C4—282no—
176C4⋊C4—282no—
177C4⋊C4—282no—
178C22⋊C4—282no—
179C42—282no—
180C42D4×D712yes—
181C42D4×D711yescharacteristic
182C42#116111yescharacteristic
183C2×C7—21no—
184C2×C7—21no—
185C2×C7#200912yes—
186C2×C7#201311yescharacteristic
187C23#643711yescharacteristic
188Q8—284no—
189Q8—284no—
190Q8—562no—
191Q8—562no—
192C2×C4—42no—
193C2×C4—282no—
194C2×C4—282no—
195C2×C4—282no—
196C2×C4—561no—
197C2×C4—561no—
198C2×C4—562no—
199C2×C4—561no—
200C2×C4#644512yes—
201C2×C4#644511yescharacteristic
202C2×C4#645812yes—
203C2×C4#645811yescharacteristic
204C2×C4C2×#113212yes—
205C2×C4#647212yes—
206C8—24no—
207C8—44no—
208C7#1022711yescharacteristic, complemented, Sylow
209C22—22no—
210C22#8944311yescharacteristic
211C22#8946511yescharacteristic
212C22#8948711yescharacteristic
213C4—22no—
214C4—22no—
215C4—562no—
216C4—562no—
217C4—562no—
218C4—1121no—
219C4#8951012yes—
220C4#8961312yes—
221C2—21no—
222C2—21no—
223C2#1172644111yescharacteristic
224C2#1172678512yes—
subgroupG/H
centerC22#89443
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1281C2
socleC22×C7#392
prime radicalC23×C7#127
hypercenter#1281D7
hypocenterC7#10227
LCSG ▷ C2×C42×C7 ▷ C22×C7 ▷ C7
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

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

NH ≅ G/Ntype
208. C7#10227semidirect

Maximal subgroups

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

subgroupindex
#117367162
#117359242
#117285472
#117275762
C7×#12812
#102277