Finite Group Databasebeta

← #13263292

Subgroups — #13263292

Order 1792.

376 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C7×#2327C211yesmaximal, characteristic
2#11729379C212yesmaximal
3#11725449C212yesmaximal
4#11725438C212yesmaximal
5C2×C7×C4⋊Q8C411yescharacteristic
6C2×C4×C7×Q8C411yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#391C411yescharacteristic
9C7×#391C2211yescharacteristic
10C7×#387—22no—
11C7×#387—22no—
12C7×#382C2211yescharacteristic
13C7×#376C411yescharacteristic
14#89698—22no—
15#89323—22no—
16#89323C2214yes—
17#11536—71nomaximal, Sylow
18C22×C7×Q8C2×C411yescharacteristic
19C22×C7×Q8C2×C411yescharacteristic
20C7×C4⋊Q8—22no—
21C7×C4⋊Q8—22no—
22C4×C7×Q8—42no—
23C4×C7×Q8—42no—
24C2×C7×C4⋊C4—22no—
25C2×C7×C4⋊C4—21no—
26C2×C7×C4⋊C4C2×C411yescharacteristic
27C2×C7×C4⋊C4D412yes—
28C2×C7×C4⋊C4C2311yescharacteristic
29C2×C42×C7—21no—
30C2×C42×C7C2×C411yescharacteristic
31C2×C42×C7C2×C411yescharacteristic
32C2×C42×C7C2×C411yescharacteristic
33C2×C42×C7D412yes—
34C7×#95—21no—
35C7×#95—21no—
36C7×#95—22no—
37C7×#95—22no—
38C7×#95—22no—
39C22⋊(C7⋊C8)—24no—
40C4⋊(C7⋊C8)—42no—
41#6377—42no—
42#2327D711yescharacteristic
43#1467—72no—
44#1324—72no—
45#1319—72no—
46C2×C7×Q8—21no—
47C2×C7×Q8—21no—
48C2×C7×Q8—21no—
49C2×C7×Q8—41no—
50C2×C7×Q8—41no—
51C2×C7×Q8—41no—
52C2×C7×Q8—41no—
53C2×C7×Q8M1612yes—
54C22×C4×C7—21no—
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7—21no—
58C22×C4×C7C22⋊C412yes—
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22×C411yescharacteristic
62C22×C4×C7C2×D412yes—
63C7×C4⋊C4—28no—
64C7×C4⋊C4—42no—
65C7×C4⋊C4—41no—
66C7×C4⋊C4—41no—
67C7×C4⋊C4—42no—
68C42×C7—22no—
69C42×C7—22no—
70C42×C7—22no—
71C42×C7—21no—
72C42×C7—41no—
73C42×C7—42no—
74C42×C7M1612yes—
75C2×C7⋊C8—44no—
76C2×C4⋊Q8Dic711yescharacteristic
77C2×C4×Q8Dic711yescharacteristic
78C2×C4×Q8C2×D711yescharacteristic
79#432—142no—
80#391Dic711yescharacteristic
81#391C2×D711yescharacteristic
82#387—22no—
83#387—22no—
84#382C2×D711yescharacteristic
85#376Dic711yescharacteristic
86#324—74no—
87#324—142no—
88C23×C7C2×C22⋊C411yescharacteristic
89C7×Q8—42no—
90C7×Q8—42no—
91C7×Q8—42no—
92C7×Q8—42no—
93C2×C4×C7—21no—
94C2×C4×C7—21no—
95C2×C4×C7—22no—
96C2×C4×C7—22no—
97C2×C4×C7—22no—
98C2×C4×C7—22no—
99C2×C4×C7—21no—
100C2×C4×C7—22no—
101C2×C4×C7—22no—
102C2×C4×C7—41no—
103C2×C4×C7—41no—
104C2×C4×C7—41no—
105C2×C4×C7—41no—
106C2×C4×C7—41no—
107C2×C4×C7—41no—
108C2×C4×C7—42no—
109C2×C4×C7—41no—
110C2×C4×C7—41no—
111C2×C4×C7—42no—
112C2×C4×C7—41no—
113C2×C4×C7—41no—
114C2×C4×C7#9912yes—
115C2×C4×C7C2×M1611yescharacteristic
116C2×C4×C7C2×M1611yescharacteristic
117C7⋊C8—84no—
118C22×Q8C2×Dic711yescharacteristic
119C22×Q8C2×Dic711yescharacteristic
120C4⋊Q8—22no—
121C4⋊Q8—22no—
122C4×Q8—42no—
123C4×Q8—42no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—21no—
126C2×C4⋊C4C2×Dic711yescharacteristic
127C2×C4⋊C4C22⋊D712yes—
128C2×C4⋊C4C22×D711yescharacteristic
129C2×C42—21no—
130C2×C42C2×Dic711yescharacteristic
131C2×C42C2×Dic711yescharacteristic
132C2×C42C2×Dic711yescharacteristic
133C2×C42C22⋊D712yes—
134C4⋊C8—282no—
135C22⋊C8—144no—
136#97—282no—
137#95—21no—
138#95—22no—
139#95—21no—
140#95—22no—
141#95—22no—
142C22×C7—21no—
143C22×C7—21no—
144C22×C7#40711yescharacteristic
145C22×C7C2×#9911yescharacteristic
146C22×C7#41311yescharacteristic
147C4×C7—22no—
148C4×C7—21no—
149C4×C7—21no—
150C4×C7—42no—
151C4×C7—42no—
152C4×C7—41no—
153C4×C7—42no—
154C4×C7—42no—
155C4×C7—81no—
156C4×C7—81no—
157C2×Q8—21no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8#113612yes—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4C22⋊Dic712yes—
170C22×C4C22⋊Dic711yescharacteristic
171C22×C4C22⋊Dic711yescharacteristic
172C22×C4C22×Dic711yescharacteristic
173C22×C4C2×C22⋊D712yes—
174C2×C8—284no—
175C4⋊C4—28no—
176C4⋊C4—42no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C42—22no—
181C42—22no—
182C42—22no—
183C42—21no—
184C42—41no—
185C42—42no—
186C42#113612yes—
187C2×C7—21no—
188C2×C7—21no—
189C2×C7#146511yescharacteristic
190C2×C7#212911yescharacteristic
191C2×C7#213311yescharacteristic
192C23C2×C22⋊Dic711yescharacteristic
193Q8—42no—
194Q8—42no—
195Q8—42no—
196Q8—42no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4#640812yes—
219C2×C4C2×#113611yescharacteristic
220C2×C4C2×#113611yescharacteristic
221C8—564no—
222C7#1153611yescharacteristic, complemented, Sylow
223C22—21no—
224C22—21no—
225C22#8997911yescharacteristic
226C22C2×#640811yescharacteristic
227C22#9000911yescharacteristic
228C4—21no—
229C4—21no—
230C4—22no—
231C4—42no—
232C4—42no—
233C4—42no—
234C4—42no—
235C4—41no—
236C4—81no—
237C4—81no—
238C2—21no—
239C2—21no—
240C2#1172935611yescharacteristic
241C2#1172962511yescharacteristic
242C2#1172962611yescharacteristic
subgroupG/H
centerC22C2×#6408
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#2327C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#2327D7
hypocenterC7#11536
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2327

Complements

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

NH ≅ G/Ntype
222. C7#11536semidirect

Maximal subgroups

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

subgroupindex
C7×#23272
#117293792
#117254492
#117254382
#115367