Finite Group Databasebeta

← #13263462

Subgroups — #13263462

Order 1792.

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

normal subgroups only

This group has 358 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#11739924C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic
3#11729378C211yesmaximal, characteristic
4#11725258C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6432C411yescharacteristic
7C7×#432—21no—
8#90002C412yes—
9#89758—21no—
10#89758—21no—
11#89749C2212yes—
12C4×C4⋊Dic7C411yescharacteristic
13#89701—21no—
14#89701—21no—
15#89697—21no—
16C7×#324—21no—
17C7×#324C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11573—71nomaximal, Sylow
21C22×C7×Q8C2×C411yescharacteristic
22C22×Dic14—21no—
23C4×C7×Q8—41no—
24C4×C7×Q8—41no—
25C2×C7×C4⋊C4D411yescharacteristic
26C2×C7×C4⋊C4D411yescharacteristic
27C2×C7×C4⋊C4C2311yescharacteristic
28C2×C42×C7C2×C411yescharacteristic
29C2×C42×C7D411yescharacteristic
30C2×C42×C7D411yescharacteristic
31C2×C4⋊Dic7—21no—
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7C2×C412yes—
34C2×C4×Dic7C2×C412yes—
35#6432—41no—
36#6432—41no—
37C7×C4⋊C8—41no—
38C7×C22⋊C8—22no—
39C7×#97—41no—
40C7⋊#95—22no—
41C7⋊#95—22no—
42C7⋊#95—21no—
43C7⋊#95—22no—
44C7⋊#95—22no—
45C22⋊(C7⋊C8)—22no—
46C4⋊(C7⋊C8)—41no—
47C4×C7⋊C8—41no—
48#2568—71no—
49#1467D711yescharacteristic
50#1461—71no—
51#1324—74no—
52C2×C7×Q8—22no—
53C2×C7×Q8—22no—
54C2×C7×Q8—41no—
55C22×C4×C7C22⋊C411yescharacteristic
56C22×C4×C7C22⋊C411yescharacteristic
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22×C411yescharacteristic
60C22×C4×C7C2×D411yescharacteristic
61C22×C4×C7C2×D411yescharacteristic
62C22×Dic7—22no—
63C22×Dic7—22no—
64C2×Dic14—44no—
65C2×Dic14—41no—
66C2×Dic14—41no—
67C2×C7×C8—42no—
68C7×C4⋊C4—41no—
69C7×C4⋊C4—41no—
70C7×C4⋊C4—41no—
71C42×C7—21no—
72C42×C7—21no—
73C42×C7—21no—
74C42×C7—21no—
75C42×C7—21no—
76C42×C7—21no—
77C4⋊Dic7—42no—
78C4⋊Dic7—42no—
79C4⋊Dic7—42no—
80C4×Dic7—24no—
81C2×C7⋊C8—42no—
82C2×C4⋊Q8—71no—
83C2×C4×Q8C2×D711yescharacteristic
84#432—21no—
85#431—141no—
86#400—141no—
87#400—141no—
88#391—72no—
89#391—141no—
90#391—141no—
91#382—72no—
92C4×C4⋊C4—71no—
93#324—21no—
94#324—72no—
95#324—141no—
96#324C2×D712yes—
97C23×C7C2×C22⋊C411yescharacteristic
98C7×Q8—44no—
99C2×C4×C7—21no—
100C2×C4×C7—21no—
101C2×C4×C7—21no—
102C2×C4×C7—21no—
103C2×C4×C7—22no—
104C2×C4×C7—21no—
105C2×C4×C7—21no—
106C2×C4×C7—21no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—41no—
111C2×C4×C7—41no—
112C2×C4×C7—41no—
113C2×C4×C7#9911yescharacteristic
114C2×C4×C7#9911yescharacteristic
115C2×C4×C7#10112yes—
116C2×C4×C7#13112yes—
117C2×Dic7—42no—
118C2×Dic7—44no—
119C2×Dic7—42no—
120C2×Dic7—42no—
121C2×Dic7—42no—
122Dic14—82no—
123Dic14—82no—
124C7×C8—82no—
125C7⋊C8—82no—
126C22×Q8—141no—
127C22×Q8C4×D711yescharacteristic
128C4⋊Q8—281no—
129C4⋊Q8—281no—
130C4×Q8—41no—
131C4×Q8—41no—
132C2×C4⋊C4—72no—
133C2×C4⋊C4—141no—
134C2×C4⋊C4—141no—
135C2×C4⋊C4D2811yescharacteristic
136C2×C4⋊C4C22⋊D711yescharacteristic
137C2×C4⋊C4C22×D711yescharacteristic
138C2×C42—72no—
139C2×C42C4×D711yescharacteristic
140C2×C42D2811yescharacteristic
141C2×C42C22⋊D711yescharacteristic
142C4⋊C8—41no—
143C4⋊C8—281no—
144C22⋊C8—22no—
145C22⋊C8—142no—
146#97—41no—
147C4×C8—281no—
148#95—141no—
149#95—142no—
150#95—142no—
151#95—142no—
152#95—142no—
153C22×C7—21no—
154C22×C7—21no—
155C22×C7#40811yescharacteristic
156C22×C7C2×#9911yescharacteristic
157C22×C7C2×#10111yescharacteristic
158C4×C7—21no—
159C4×C7—22no—
160C4×C7—22no—
161C4×C7—41no—
162C4×C7—41no—
163C4×C7—41no—
164C4×C7—41no—
165C4×C7#35512yes—
166Dic7—82no—
167Dic7—82no—
168C2×Q8—22no—
169C2×Q8—22no—
170C2×Q8—41no—
171C2×Q8—284no—
172C2×Q8—281no—
173C2×Q8—281no—
174C22×C4—142no—
175C22×C4—142no—
176C22×C4(C2×D7)⋊C411yescharacteristic
177C22×C4(C2×D7)⋊C411yescharacteristic
178C22×C4(C2×D7)⋊C411yescharacteristic
179C22×C4(C2×D7)⋊C411yescharacteristic
180C22×C4C2×C4×D711yescharacteristic
181C22×C4C2×D2811yescharacteristic
182C22×C4C2×C22⋊D711yescharacteristic
183C2×C8—42no—
184C2×C8—282no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—282no—
189C4⋊C4—282no—
190C4⋊C4—282no—
191C42—21no—
192C42—21no—
193C42—21no—
194C42—21no—
195C42—21no—
196C42—21no—
197C42—144no—
198C2×C7—21no—
199C2×C7—21no—
200C2×C7#147211yescharacteristic
201C2×C7#212911yescharacteristic
202C2×C7C2×#35511yescharacteristic
203C23C2×(C2×D7)⋊C411yescharacteristic
204Q8—44no—
205Q8—562no—
206Q8—562no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—282no—
222C2×C4—282no—
223C2×C4—284no—
224C2×C4—282no—
225C2×C4—282no—
226C2×C4#638011yescharacteristic
227C2×C4#638011yescharacteristic
228C2×C4#639812yes—
229C2×C4#647012yes—
230C8—82no—
231C8—562no—
232C7#1157311yescharacteristic, complemented, Sylow
233C22—21no—
234C22—21no—
235C22C2×#638011yescharacteristic
236C22#8990111yescharacteristic
237C22C2×#639811yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—41no—
244C4—41no—
245C4—562no—
246C4—562no—
247C4#8927212yes—
248C2—21no—
249C2—21no—
250C2#1172772611yescharacteristic
251C2#1172781311yescharacteristic
252C2C2×#8927211yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1467C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1467D7
hypocenterC7#11573
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
232. C7#11573semidirect

Maximal subgroups

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

subgroupindex
#117399242
C7×#14672
#117293782
#117252582
#115737