Finite Group Databasebeta

← #13263464

Subgroups — #13263464

Order 1792.

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

normal subgroups only

This group has 374 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#11739923C211yesmaximal, characteristic
2C7×#1461C211yesmaximal, characteristic
3#11729379C211yesmaximal, characteristic
4#11725259C214yesmaximal
5C2×C4×C7×Q8C2211yescharacteristic
6C2×#6432C411yescharacteristic
7C7×#431—21no—
8#90002C412yes—
9#89751—21no—
10#89751—21no—
11#89748C2212yes—
12C4×C4⋊Dic7C411yescharacteristic
13#89700—21no—
14#89700—21no—
15#89698—21no—
16C7×#324—21no—
17C7×#324C2212yes—
18#89323—21no—
19#89323C2212yes—
20#11574—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×Dic7⋊C4—22no—
35C2×Dic7⋊C4—22no—
36C2×C4×Dic7C2×C412yes—
37#6432—41no—
38#6432—41no—
39C7×C4⋊C8—41no—
40C7×C22⋊C8—22no—
41C4×C7×C8—41no—
42C7⋊#95—22no—
43C7⋊#95—22no—
44C7⋊#95—21no—
45C22⋊(C7⋊C8)—22no—
46C4⋊(C7⋊C8)—41no—
47#6377—41no—
48#2567—71no—
49#1467—71no—
50#1461D711yescharacteristic
51#1325—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—42no—
65C2×Dic14—82no—
66C2×C7×C8—42no—
67C7×C4⋊C4—41no—
68C7×C4⋊C4—41no—
69C7×C4⋊C4—41no—
70C42×C7—21no—
71C42×C7—21no—
72C42×C7—21no—
73C42×C7—21no—
74C42×C7—21no—
75C42×C7—21no—
76C4⋊Dic7—24no—
77C4⋊Dic7—41no—
78C4⋊Dic7—41no—
79C4⋊Dic7—42no—
80Dic7⋊C4—82no—
81Dic7⋊C4—82no—
82C4×Dic7—24no—
83C2×C7⋊C8—42no—
84C2×C4⋊Q8—71no—
85C2×C4×Q8C2×D711yescharacteristic
86#432—141no—
87#431—21no—
88#395—141no—
89#395—141no—
90#391—72no—
91#389—141no—
92#389—141no—
93#384—72no—
94C4×C4⋊C4—71no—
95#324—21no—
96#324—72no—
97#324—141no—
98#324C2×D712yes—
99C23×C7C2×C22⋊C411yescharacteristic
100C7×Q8—44no—
101C2×C4×C7—21no—
102C2×C4×C7—21no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—22no—
106C2×C4×C7—21no—
107C2×C4×C7—21no—
108C2×C4×C7—21no—
109C2×C4×C7—21no—
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—41no—
113C2×C4×C7—41no—
114C2×C4×C7—41no—
115C2×C4×C7#9911yescharacteristic
116C2×C4×C7#9911yescharacteristic
117C2×C4×C7#10112yes—
118C2×C4×C7#13112yes—
119C2×Dic7—24no—
120C2×Dic7—42no—
121C2×Dic7—42no—
122C2×Dic7—42no—
123C2×Dic7—42no—
124C2×Dic7—42no—
125Dic14—84no—
126C7×C8—82no—
127C7⋊C8—82no—
128C22×Q8—141no—
129C22×Q8C4×D711yescharacteristic
130C4⋊Q8—281no—
131C4⋊Q8—281no—
132C4×Q8—41no—
133C4×Q8—41no—
134C2×C4⋊C4—72no—
135C2×C4⋊C4—141no—
136C2×C4⋊C4—141no—
137C2×C4⋊C4—142no—
138C2×C4⋊C4—142no—
139C2×C4⋊C4D2811yescharacteristic
140C2×C4⋊C4C22⋊D711yescharacteristic
141C2×C4⋊C4C22×D711yescharacteristic
142C2×C42—72no—
143C2×C42C4×D711yescharacteristic
144C2×C42D2811yescharacteristic
145C2×C42C22⋊D711yescharacteristic
146C4⋊C8—41no—
147C4⋊C8—281no—
148C22⋊C8—22no—
149C22⋊C8—142no—
150#97—281no—
151C4×C8—41no—
152#95—141no—
153#95—142no—
154#95—142no—
155C22×C7—21no—
156C22×C7—21no—
157C22×C7#40811yescharacteristic
158C22×C7C2×#9911yescharacteristic
159C22×C7C2×#10111yescharacteristic
160C4×C7—21no—
161C4×C7—22no—
162C4×C7—22no—
163C4×C7—41no—
164C4×C7—41no—
165C4×C7—41no—
166C4×C7—41no—
167C4×C7#35612yes—
168Dic7—44no—
169Dic7—82no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—282no—
174C2×Q8—562no—
175C22×C4—142no—
176C22×C4—142no—
177C22×C4(C2×D7)⋊C411yescharacteristic
178C22×C4(C2×D7)⋊C411yescharacteristic
179C22×C4(C2×D7)⋊C411yescharacteristic
180C22×C4(C2×D7)⋊C411yescharacteristic
181C22×C4C2×C4×D711yescharacteristic
182C22×C4C2×D2811yescharacteristic
183C22×C4C2×C22⋊D711yescharacteristic
184C2×C8—42no—
185C2×C8—282no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—144no—
190C4⋊C4—282no—
191C4⋊C4—281no—
192C4⋊C4—281no—
193C4⋊C4—562no—
194C4⋊C4—562no—
195C42—21no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—144no—
202C2×C7—21no—
203C2×C7—21no—
204C2×C7#147211yescharacteristic
205C2×C7#212811yescharacteristic
206C2×C7C2×#35611yescharacteristic
207C23C2×(C2×D7)⋊C411yescharacteristic
208Q8—44no—
209Q8—564no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—144no—
225C2×C4—282no—
226C2×C4—282no—
227C2×C4—282no—
228C2×C4—282no—
229C2×C4—282no—
230C2×C4#638011yescharacteristic
231C2×C4#638011yescharacteristic
232C2×C4#639812yes—
233C2×C4#646412yes—
234C8—82no—
235C8—562no—
236C7#1157411yescharacteristic, complemented, Sylow
237C22—21no—
238C22—21no—
239C22C2×#638011yescharacteristic
240C22#8988211yescharacteristic
241C22C2×#639811yescharacteristic
242C4—21no—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—284no—
250C4—562no—
251C4#8927312yes—
252C2—21no—
253C2—21no—
254C2#1172767711yescharacteristic
255C2#1172781511yescharacteristic
256C2C2×#8927311yescharacteristic
subgroupG/H
centerC22C2×#6380
commutatorC22×C4×C7C22×C4
FrattiniC2×C4⋊C4C22×D7
FittingC7×#1461C2
socleC22×C7C2×#99
prime radicalC23×C7C2×C22⋊C4
cosocleC2×C7×C4⋊C4C23
hypercenter#1461D7
hypocenterC7#11574
LCSG ▷ C22×C4×C7 ▷ C22×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
236. C7#11574semidirect

Maximal subgroups

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

subgroupindex
#117399232
C7×#14612
#117293792
#117252592
#115747