Finite Group Databasebeta

← #13243097

Subgroups — #13243097

Order 1792.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#11734019C211yesmaximal, characteristic
2#11727438C211yesmaximal, characteristic
3#11726397C212yesmaximal
4C7×#1272C211yesmaximal, characteristic
5#11725283C212yesmaximal
6C2×#6507—21no—
7C7×#391C2211yescharacteristic
8C2×#6409—21no—
9#89755—21no—
10C2×#6381—21no—
11#89707C2211yescharacteristic
12#89700C2212yes—
13#89428—22no—
14#89425—22no—
15C7×#336C2212yes—
16#89346—22no—
17#89346—22no—
18#89319C2211yescharacteristic
19#7829—71nomaximal, Sylow
20C22×C7×Q8D411yescharacteristic
21C22×Dic14—21no—
22C22×C7×C8—22no—
23C2×C7×C4⋊C4D411yescharacteristic
24C2×C42×C7C2311yescharacteristic
25#6507—42no—
26#6507—42no—
27C2×C4⋊Dic7—22no—
28C2×C4⋊Dic7—21no—
29C2×C4⋊Dic7—21no—
30C2×C4⋊Dic7D412yes—
31C2×C4⋊Dic7D412yes—
32C2×Dic7⋊C4—22no—
33C2×Dic7⋊C4—22no—
34C2×C4×Dic7—21no—
35C22×C7⋊C8—21no—
36C7×#95—22no—
37#6409—42no—
38C7⋊#95—21no—
39C7⋊#95—22no—
40C7⋊#95—22no—
41#6381—42no—
42#2734—71no—
43#2100—72no—
44#2095—71no—
45#1272D711yescharacteristic
46#1271—72no—
47C2×C7×Q8—21no—
48C2×C7×Q8—41no—
49C2×C7×Q8—41no—
50C2×C7×Q8SD1612yes—
51C22×C4×C7—21no—
52C22×C4×C7—21no—
53C22×C4×C7C2×D411yescharacteristic
54C22×C4×C7C2×D412yes—
55C22×Dic7—22no—
56C22×Dic7—22no—
57C22×Dic7—41no—
58C2×Dic14—42no—
59C2×Dic14—81no—
60C2×Dic14—81no—
61C2×C7×C8—42no—
62C2×C7×C8—42no—
63C2×C7×C8—42no—
64C7×C4⋊C4—41no—
65C42×C7—41no—
66C4⋊Dic7—22no—
67C4⋊Dic7—42no—
68C4⋊Dic7—41no—
69C4⋊Dic7—44no—
70C4⋊Dic7—41no—
71C4⋊Dic7—81no—
72C4⋊Dic7Q1614yes—
73Dic7⋊C4—44no—
74Dic7⋊C4—42no—
75Dic7⋊C4—42no—
76C4×Dic7—42no—
77C2×C7⋊C8—22no—
78C2×C7⋊C8—41no—
79C2×C7⋊C8—41no—
80C2×C4⋊Q8—141no—
81C2×#107—141no—
82C2×#103—141no—
83#398—141no—
84#395—142no—
85#391C2×D711yescharacteristic
86#389—72no—
87#387—142no—
88#384—71no—
89#340—142no—
90#340—142no—
91#336—71no—
92#336C2×D712yes—
93C23×C7#12011yescharacteristic
94C7×Q8—42no—
95C7×Q8—81no—
96C2×C4×C7—21no—
97C2×C4×C7—22no—
98C2×C4×C7—21no—
99C2×C4×C7—22no—
100C2×C4×C7—22no—
101C2×C4×C7—41no—
102C2×C4×C7—41no—
103C2×C4×C7—41no—
104C2×C4×C7—42no—
105C2×C4×C7C2×SD1611yescharacteristic
106C2×C4×C7C2×Q1612yes—
107C2×C4×C7AGL(1,ℤ/8)11yescharacteristic
108C2×C4×C7#13712yes—
109C2×Dic7—24no—
110C2×Dic7—42no—
111C2×Dic7—42no—
112C2×Dic7—42no—
113C2×Dic7—42no—
114C2×Dic7—42no—
115C2×Dic7—81no—
116C2×Dic7—82no—
117Dic14—84no—
118C7×C8—82no—
119C7⋊C8—42no—
120C22×Q8—141no—
121C22×Q8D2811yescharacteristic
122C22×C8—22no—
123C22×C8—141no—
124C4⋊Q8—282no—
125C4⋊Q8—282no—
126C2×C4⋊C4—72no—
127C2×C4⋊C4—72no—
128C2×C4⋊C4—142no—
129C2×C4⋊C4—142no—
130C2×C4⋊C4—141no—
131C2×C4⋊C4—142no—
132C2×C4⋊C4—141no—
133C2×C4⋊C4D2811yescharacteristic
134C2×C42—141no—
135C2×C42C22×D711yescharacteristic
136#107—282no—
137#103—282no—
138#95—22no—
139#95—141no—
140#95—142no—
141#95—142no—
142C22×C7#45011yescharacteristic
143C22×C7#45112yes—
144C22×C7#45311yescharacteristic
145C22×C7#45412yes—
146C22×C7#45811yescharacteristic
147C4×C7—21no—
148C4×C7—21no—
149C4×C7—22no—
150C4×C7—22no—
151C4×C7—42no—
152C4×C7—81no—
153Dic7—44no—
154Dic7—82no—
155Dic7—161no—
156C2×Q8—21no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—282no—
160C2×Q8—561no—
161C2×Q8—561no—
162C2×Q8#113212yes—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—142no—
166C22×C4—142no—
167C22×C4—281no—
168C22×C4C2×D2811yescharacteristic
169C22×C4D4×D712yes—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—142no—
174C2×C8—281no—
175C2×C8—281no—
176C4⋊C4—41no—
177C4⋊C4—74no—
178C4⋊C4—142no—
179C4⋊C4—282no—
180C4⋊C4—284no—
181C4⋊C4—281no—
182C4⋊C4—281no—
183C4⋊C4—284no—
184C4⋊C4—282no—
185C4⋊C4—282no—
186C4⋊C4—561no—
187C42—41no—
188C42—282no—
189C2×C7#161311yescharacteristic
190C2×C7#161712yes—
191C2×C7#163311yescharacteristic
192C2×C7#163712yes—
193C2×C7#165711yescharacteristic
194C23#644511yescharacteristic
195Q8—42no—
196Q8—81no—
197Q8—564no—
198C2×C4—22no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—144no—
208C2×C4—282no—
209C2×C4—282no—
210C2×C4—282no—
211C2×C4—282no—
212C2×C4—282no—
213C2×C4—561no—
214C2×C4—562no—
215C2×C4C2×#113211yescharacteristic
216C2×C4#647111yescharacteristic
217C2×C4#647812yes—
218C2×C4D7×Q1612yes—
219C8—82no—
220C8—282no—
221C7#782911yescharacteristic, complemented, Sylow
222C22#8950311yescharacteristic
223C22#8951411yescharacteristic
224C22#8951911yescharacteristic
225C22#8958012yes—
226C22#8959912yes—
227C4—22no—
228C4—22no—
229C4—21no—
230C4—21no—
231C4—42no—
232C4—81no—
233C4—284no—
234C4—562no—
235C4—1121no—
236C2#1172586611yescharacteristic
237C2#1172602312yes—
238C2#1172608512yes—
239C2#1172610811yescharacteristic
240C2#1172625911yescharacteristic
subgroupG/H
centerC23#6445
commutator, cosocleC2×C42×C7C23
FrattiniC2×C42C22×D7
FittingC7×#1272C2
socle, prime radicalC23×C7#120
hypercenter#1272D7
hypocenterC7#7829
LCSG ▷ C2×C42×C7 ▷ C23×C7 ▷ C7
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
221. C7#7829semidirect

Maximal subgroups

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

subgroupindex
#117340192
#117274382
#117263972
C7×#12722
#117252832
#78297