Finite Group Databasebeta

← #13263440

Subgroups — #13263440

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#11739920C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic
3#11729378C211yesmaximal, characteristic
4#11725261C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6507C412yes—
7C2×#6432C411yescharacteristic
8C7×#432—21no—
9#89755—21no—
10#89755—21no—
11#89746C2212yes—
12C4×C4⋊Dic7C411yescharacteristic
13#89700—21no—
14#89700—21no—
15#89697—21no—
16C7×#324—21no—
17C7×#324C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11568—71nomaximal, Sylow
21C22×C7×Q8C2×C411yescharacteristic
22C22×Dic14C2×C412yes—
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
31#6507—44no—
32C2×C4⋊Dic7—21no—
33C2×C4⋊Dic7—21no—
34C2×C4⋊Dic7—21no—
35C2×Dic7⋊C4—22no—
36C2×Dic7⋊C4—22no—
37C2×C4×Dic7C2×C412yes—
38#6432—41no—
39#6432—41no—
40C7×C4⋊C8—41no—
41C7×C22⋊C8—22no—
42C7×#97—41no—
43C7⋊#95—21no—
44C7⋊#95—22no—
45C7⋊#95—22no—
46C22⋊(C7⋊C8)—22no—
47C4⋊(C7⋊C8)—41no—
48C4×C7⋊C8—41no—
49#2546—71no—
50#1467D711yescharacteristic
51#1461—71no—
52#1319—74no—
53C2×C7×Q8—22no—
54C2×C7×Q8—22no—
55C2×C7×Q8—41no—
56C22×C4×C7C22⋊C411yescharacteristic
57C22×C4×C7C22⋊C411yescharacteristic
58C22×C4×C7C22⋊C411yescharacteristic
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22×C411yescharacteristic
61C22×C4×C7C2×D411yescharacteristic
62C22×C4×C7C2×D411yescharacteristic
63C22×Dic7—22no—
64C22×Dic7—22no—
65C2×Dic14—24no—
66C2×Dic14—42no—
67C2×Dic14—42no—
68C2×C7×C8—42no—
69C7×C4⋊C4—41no—
70C7×C4⋊C4—41no—
71C7×C4⋊C4—41no—
72C42×C7—21no—
73C42×C7—21no—
74C42×C7—21no—
75C42×C7—21no—
76C42×C7—21no—
77C42×C7—21no—
78C4⋊Dic7—24no—
79C4⋊Dic7—42no—
80C4⋊Dic7—41no—
81C4⋊Dic7—41no—
82Dic7⋊C4—44no—
83Dic7⋊C4—44no—
84C4×Dic7—42no—
85C2×C7⋊C8—42no—
86C2×C4⋊Q8—72no—
87C2×C4⋊Q8—71no—
88C2×C4×Q8C2×D711yescharacteristic
89#432—21no—
90#431—141no—
91#398—141no—
92#398—141no—
93#391—72no—
94#389—141no—
95#389—141no—
96C4×C4⋊C4—71no—
97#324—21no—
98#324—72no—
99#324—141no—
100#324C2×D712yes—
101C23×C7C2×C22⋊C411yescharacteristic
102C7×Q8—44no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—21no—
106C2×C4×C7—21no—
107C2×C4×C7—22no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—41no—
115C2×C4×C7—41no—
116C2×C4×C7—41no—
117C2×C4×C7#9911yescharacteristic
118C2×C4×C7#9911yescharacteristic
119C2×C4×C7#10012yes—
120C2×C4×C7#13112yes—
121C2×Dic7—24no—
122C2×Dic7—42no—
123C2×Dic7—42no—
124C2×Dic7—42no—
125C2×Dic7—42no—
126C2×Dic7—42no—
127Dic14—84no—
128C7×C8—82no—
129C7⋊C8—82no—
130C22×Q8—72no—
131C22×Q8C4×D711yescharacteristic
132C4⋊Q8—281no—
133C4⋊Q8—281no—
134C4⋊Q8—284no—
135C4×Q8—41no—
136C4×Q8—41no—
137C2×C4⋊C4—141no—
138C2×C4⋊C4—142no—
139C2×C4⋊C4—142no—
140C2×C4⋊C4—141no—
141C2×C4⋊C4—141no—
142C2×C4⋊C4D2811yescharacteristic
143C2×C4⋊C4C22⋊D711yescharacteristic
144C2×C4⋊C4C22×D711yescharacteristic
145C2×C42—72no—
146C2×C42C4×D711yescharacteristic
147C2×C42D2811yescharacteristic
148C2×C42C22⋊D711yescharacteristic
149C4⋊C8—41no—
150C4⋊C8—281no—
151C22⋊C8—22no—
152C22⋊C8—142no—
153#97—41no—
154C4×C8—281no—
155#95—141no—
156#95—142no—
157#95—142no—
158C22×C7—21no—
159C22×C7—21no—
160C22×C7#40811yescharacteristic
161C22×C7C2×#9911yescharacteristic
162C22×C7C2×#10011yescharacteristic
163C4×C7—21no—
164C4×C7—22no—
165C4×C7—22no—
166C4×C7—41no—
167C4×C7—41no—
168C4×C7—41no—
169C4×C7—41no—
170C4×C7#35612yes—
171Dic7—44no—
172Dic7—82no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—41no—
176C2×Q8—144no—
177C2×Q8—282no—
178C2×Q8—282no—
179C22×C4—142no—
180C22×C4—142no—
181C22×C4(C2×D7)⋊C411yescharacteristic
182C22×C4(C2×D7)⋊C411yescharacteristic
183C22×C4(C2×D7)⋊C411yescharacteristic
184C22×C4(C2×D7)⋊C411yescharacteristic
185C22×C4C2×C4×D711yescharacteristic
186C22×C4C2×D2811yescharacteristic
187C22×C4C2×C22⋊D711yescharacteristic
188C2×C8—42no—
189C2×C8—282no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—144no—
194C4⋊C4—284no—
195C4⋊C4—282no—
196C4⋊C4—281no—
197C4⋊C4—281no—
198C4⋊C4—284no—
199C42—21no—
200C42—21no—
201C42—21no—
202C42—21no—
203C42—21no—
204C42—21no—
205C42—282no—
206C2×C7—21no—
207C2×C7—21no—
208C2×C7#147111yescharacteristic
209C2×C7#212911yescharacteristic
210C2×C7C2×#35611yescharacteristic
211C23C2×(C2×D7)⋊C411yescharacteristic
212Q8—44no—
213Q8—564no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—144no—
229C2×C4—282no—
230C2×C4—282no—
231C2×C4—282no—
232C2×C4—282no—
233C2×C4—282no—
234C2×C4#638011yescharacteristic
235C2×C4#638011yescharacteristic
236C2×C4#639712yes—
237C2×C4#647012yes—
238C8—82no—
239C8—562no—
240C7#1156811yescharacteristic, complemented, Sylow
241C22—21no—
242C22—21no—
243C22C2×#638011yescharacteristic
244C22#8990111yescharacteristic
245C22C2×#639711yescharacteristic
246C4—21no—
247C4—22no—
248C4—22no—
249C4—41no—
250C4—41no—
251C4—41no—
252C4—41no—
253C4—284no—
254C4—562no—
255C4#8927312yes—
256C2—21no—
257C2—21no—
258C2#1172772411yescharacteristic
259C2#1172781311yescharacteristic
260C2C2×#8927311yescharacteristic
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#11568
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
240. C7#11568semidirect

Maximal subgroups

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

subgroupindex
#117399202
C7×#14672
#117293782
#117252612
#115687