Finite Group Databasebeta

← #13263078

Subgroups — #13263078

Order 1792.

428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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
1C4×C7×C4⋊Q8C211yesmaximal, characteristic
2#11729378C212yesmaximal
3#11725449C212yesmaximal
4#11725441C212yesmaximal
5C2×C7×C4⋊Q8C411yescharacteristic
6C2×C4×C7×Q8C411yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#391C411yescharacteristic
9C7×#391C2211yescharacteristic
10C7×#389—22no—
11C7×#384C2211yescharacteristic
12C4×C7×C4⋊C4—22no—
13C43×C7C411yescharacteristic
14#89697—22no—
15#89323—22no—
16#89323C2214yes—
17#11478—71nomaximal, Sylow
18C22×C7×Q8C2×C411yescharacteristic
19C22×C7×Q8C2×C411yescharacteristic
20C7×C4⋊Q8—22no—
21C7×C4⋊Q8C814yescomplemented
22C4×C7×Q8—41no—
23C4×C7×Q8—41no—
24C4×C7×Q8—41no—
25C4×C7×Q8—41no—
26C2×C7×C4⋊C4—22no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—22no—
29C2×C7×C4⋊C4C2×C411yescharacteristic
30C2×C7×C4⋊C4D412yes—
31C2×C7×C4⋊C4C2311yescharacteristic
32C2×C42×C7—21no—
33C2×C42×C7—21no—
34C2×C42×C7—21no—
35C2×C42×C7C2×C411yescharacteristic
36C2×C42×C7C2×C411yescharacteristic
37C2×C42×C7C2×C411yescharacteristic
38C2×C42×C7D412yes—
39C7×#95—22no—
40C7×#95—22no—
41C22⋊(C7⋊C8)—24no—
42C4⋊(C7⋊C8)—42no—
43C4×C7⋊C8—42no—
44C4×C4⋊Q8D711yescharacteristic
45#1461—72no—
46#1325—72no—
47#1319—72no—
48C2×C7×Q8—21no—
49C2×C7×Q8—41no—
50C2×C7×Q8—41no—
51C2×C7×Q8—41no—
52C2×C7×Q8—41no—
53C2×C7×Q8C2×C812yes—
54C2×C7×Q8C2×C812yes—
55C2×C7×Q8M1612yes—
56C22×C4×C7—21no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7C22⋊C412yes—
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D412yes—
65C7×C4⋊C4—28no—
66C7×C4⋊C4—42no—
67C7×C4⋊C4—41no—
68C7×C4⋊C4—41no—
69C7×C4⋊C4—44no—
70C7×C4⋊C4—42no—
71C42×C7—24no—
72C42×C7—21no—
73C42×C7—21no—
74C42×C7—22no—
75C42×C7—22no—
76C42×C7—21no—
77C42×C7—41no—
78C42×C7—42no—
79C42×C7—41no—
80C42×C7—41no—
81C42×C7C2×C812yes—
82C2×C7⋊C8—44no—
83C2×C4⋊Q8Dic711yescharacteristic
84C2×C4×Q8Dic711yescharacteristic
85C2×C4×Q8C2×D711yescharacteristic
86#431—142no—
87#391Dic711yescharacteristic
88#391C2×D711yescharacteristic
89#389—22no—
90#384C2×D711yescharacteristic
91C4×C4⋊C4—22no—
92C43Dic711yescharacteristic
93#324—74no—
94#324—142no—
95C23×C7C2×C22⋊C411yescharacteristic
96C7×Q8—42no—
97C7×Q8—42no—
98C7×Q8—42no—
99C7×Q8—42no—
100C2×C4×C7—22no—
101C2×C4×C7—22no—
102C2×C4×C7—22no—
103C2×C4×C7—21no—
104C2×C4×C7—22no—
105C2×C4×C7—21no—
106C2×C4×C7—22no—
107C2×C4×C7—22no—
108C2×C4×C7—22no—
109C2×C4×C7—22no—
110C2×C4×C7—22no—
111C2×C4×C7—21no—
112C2×C4×C7—41no—
113C2×C4×C7—41no—
114C2×C4×C7—41no—
115C2×C4×C7—41no—
116C2×C4×C7—41no—
117C2×C4×C7—42no—
118C2×C4×C7—42no—
119C2×C4×C7—41no—
120C2×C4×C7C22⋊C814yes—
121C2×C4×C7#9911yescharacteristic
122C2×C4×C7#9911yescharacteristic
123C2×C4×C7C22×C811yescharacteristic
124C2×C4×C7C2×M1611yescharacteristic
125C7⋊C8—84no—
126C22×Q8C2×Dic711yescharacteristic
127C22×Q8C2×Dic711yescharacteristic
128C4⋊Q8—22no—
129C4⋊Q8C7⋊C814yescomplemented
130C4×Q8—41no—
131C4×Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4C2×Dic711yescharacteristic
138C2×C4⋊C4C22⋊D712yes—
139C2×C4⋊C4C22×D711yescharacteristic
140C2×C42—21no—
141C2×C42—21no—
142C2×C42—21no—
143C2×C42C2×Dic711yescharacteristic
144C2×C42C2×Dic711yescharacteristic
145C2×C42C2×Dic711yescharacteristic
146C2×C42C22⋊D712yes—
147C4⋊C8—282no—
148C22⋊C8—144no—
149C4×C8—282no—
150#95—22no—
151#95—22no—
152C22×C7—21no—
153C22×C7—21no—
154C22×C7C2×C22⋊C811yescharacteristic
155C22×C7C2×#9911yescharacteristic
156C22×C7#41311yescharacteristic
157C4×C7—24no—
158C4×C7—21no—
159C4×C7—24no—
160C4×C7—21no—
161C4×C7—21no—
162C4×C7—42no—
163C4×C7—42no—
164C4×C7—41no—
165C4×C7—42no—
166C4×C7—81no—
167C4×C7#35612yes—
168C2×Q8—21no—
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8C2×C7⋊C812yes—
174C2×Q8C2×C7⋊C812yes—
175C2×Q8#113612yes—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4C22⋊Dic712yes—
181C22×C4C22⋊Dic711yescharacteristic
182C22×C4C22⋊Dic711yescharacteristic
183C22×C4C22×Dic711yescharacteristic
184C22×C4C2×C22⋊D712yes—
185C2×C8—284no—
186C4⋊C4—28no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—44no—
192C42—24no—
193C42—22no—
194C42—21no—
195C42—22no—
196C42—21no—
197C42—21no—
198C42—41no—
199C42—42no—
200C42—41no—
201C42—41no—
202C42C2×C7⋊C812yes—
203C2×C7—21no—
204C2×C7—21no—
205C2×C7#145911yescharacteristic
206C2×C7#212611yescharacteristic
207C2×C7C2×#35611yescharacteristic
208C23C2×C22⋊Dic711yescharacteristic
209Q8—42no—
210Q8—42no—
211Q8—42no—
212Q8—42no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4C22⋊(C7⋊C8)14yes—
234C2×C4#640811yescharacteristic
235C2×C4#640811yescharacteristic
236C2×C4C22×C7⋊C811yescharacteristic
237C2×C4C2×#113611yescharacteristic
238C8—564no—
239C7#1147811yescharacteristic, complemented, Sylow
240C22—21no—
241C22—21no—
242C22C2×C22⋊(C7⋊C8)11yescharacteristic
243C22C2×#640811yescharacteristic
244C22#9000911yescharacteristic
245C4—24no—
246C4—21no—
247C4—24no—
248C4—21no—
249C4—21no—
250C4—42no—
251C4—42no—
252C4—41no—
253C4—42no—
254C4—81no—
255C4#8934312yes—
256C2—21no—
257C2—21no—
258C2#1172935411yescharacteristic
259C2C2×#8934311yescharacteristic
260C2#1172957311yescharacteristic
subgroupG/H
centerC2×C4#6408
commutatorC2×C4×C7C22×C8
FrattiniC2×C4⋊C4C22×D7
FittingC4×C7×C4⋊Q8C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenterC4×C4⋊Q8D7
hypocenterC7#11478
LCSG ▷ C2×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
21. C7×C4⋊Q8C8semidirect
129. C4⋊Q8C7⋊C8semidirect
239. C7#11478semidirect

Maximal subgroups

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

subgroupindex
C4×C7×C4⋊Q82
#117293782
#117254492
#117254412
#114787