Finite Group Databasebeta

← C7×#11574 #13188790

Subgroups — C7×#11574 #13188790

Order 1792.

374 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2567C211yesmaximal, characteristic
2C7×#1467C211yesmaximal, characteristic
3C7×#1461C211yesmaximal, characteristic
4C7×#1325C214yesmaximal
5C2×C7×C4⋊Q8C411yescharacteristic
6C2×C4×C7×Q8C2211yescharacteristic
7C7×#432—21no—
8C7×#431—21no—
9C7×#395—21no—
10C7×#395—21no—
11C7×#391C412yes—
12C7×#389—21no—
13C7×#389—21no—
14C7×#384C2212yes—
15C4×C7×C4⋊C4C411yescharacteristic
16C7×#324—21no—
17C7×#324—21no—
18C7×#324C2212yes—
19C7×#324C2212yes—
20#11574C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×Q8—21no—
22C22×C7×Q8C2×C411yescharacteristic
23C7×C4⋊Q8—41no—
24C7×C4⋊Q8—41no—
25C4×C7×Q8—41no—
26C4×C7×Q8—41no—
27C2×C7×C4⋊C4—21no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—22no—
30C2×C7×C4⋊C4—22no—
31C2×C7×C4⋊C4C2×C412yes—
32C2×C7×C4⋊C4D411yescharacteristic
33C2×C7×C4⋊C4D411yescharacteristic
34C2×C7×C4⋊C4C2311yescharacteristic
35C2×C42×C7C2×C412yes—
36C2×C42×C7C2×C411yescharacteristic
37C2×C42×C7D411yescharacteristic
38C2×C42×C7D411yescharacteristic
39C7×C4⋊C8—41no—
40C7×C4⋊C8—41no—
41C7×C22⋊C8—22no—
42C7×C22⋊C8—22no—
43C7×#97—41no—
44C4×C7×C8—41no—
45C7×#95—21no—
46C7×#95—22no—
47C7×#95—22no—
48#2567C2×C711yescharacteristic
49#1467C2×C711yescharacteristic
50#1461C2×C711yescharacteristic
51#1325C2×C714yes—
52C2×C7×Q8—22no—
53C2×C7×Q8—22no—
54C2×C7×Q8—41no—
55C2×C7×Q8—42no—
56C2×C7×Q8—82no—
57C22×C4×C7—22no—
58C22×C4×C7—22no—
59C22×C4×C7C22⋊C411yescharacteristic
60C22×C4×C7C22⋊C411yescharacteristic
61C22×C4×C7C22⋊C411yescharacteristic
62C22×C4×C7C22⋊C411yescharacteristic
63C22×C4×C7C22×C411yescharacteristic
64C22×C4×C7C2×D411yescharacteristic
65C22×C4×C7C2×D411yescharacteristic
66C2×C7×C8—42no—
67C2×C7×C8—42no—
68C7×C4⋊C4—24no—
69C7×C4⋊C4—41no—
70C7×C4⋊C4—41no—
71C7×C4⋊C4—41no—
72C7×C4⋊C4—42no—
73C7×C4⋊C4—41no—
74C7×C4⋊C4—41no—
75C7×C4⋊C4—82no—
76C7×C4⋊C4—82no—
77C42×C7—21no—
78C42×C7—21no—
79C42×C7—21no—
80C42×C7—21no—
81C42×C7—21no—
82C42×C7—21no—
83C42×C7—24no—
84C2×C4⋊Q8C4×C711yescharacteristic
85C2×C4×Q8C22×C711yescharacteristic
86#432—21no—
87#431—21no—
88#395—21no—
89#395—21no—
90#391C4×C712yes—
91#389—21no—
92#389—21no—
93#384C22×C712yes—
94C4×C4⋊C4C4×C711yescharacteristic
95#324—21no—
96#324—21no—
97#324C22×C712yes—
98#324C22×C712yes—
99C23×C7C2×C22⋊C411yescharacteristic
100C7×Q8—44no—
101C7×Q8—84no—
102C2×C4×C7—21no—
103C2×C4×C7—21no—
104C2×C4×C7—21no—
105C2×C4×C7—21no—
106C2×C4×C7—22no—
107C2×C4×C7—24no—
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—42no—
115C2×C4×C7—42no—
116C2×C4×C7—41no—
117C2×C4×C7—41no—
118C2×C4×C7—41no—
119C2×C4×C7—42no—
120C2×C4×C7—42no—
121C2×C4×C7—42no—
122C2×C4×C7#9911yescharacteristic
123C2×C4×C7#9911yescharacteristic
124C2×C4×C7#10112yes—
125C2×C4×C7#13112yes—
126C7×C8—82no—
127C7×C8—82no—
128C22×Q8—21no—
129C22×Q8C2×C4×C711yescharacteristic
130C4⋊Q8—41no—
131C4⋊Q8—41no—
132C4×Q8—41no—
133C4×Q8—41no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4C2×C4×C712yes—
139C2×C4⋊C4C7×D411yescharacteristic
140C2×C4⋊C4C7×D411yescharacteristic
141C2×C4⋊C4C23×C711yescharacteristic
142C2×C42C2×C4×C712yes—
143C2×C42C2×C4×C711yescharacteristic
144C2×C42C7×D411yescharacteristic
145C2×C42C7×D411yescharacteristic
146C4⋊C8—41no—
147C4⋊C8—41no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150#97—41no—
151C4×C8—41no—
152#95—21no—
153#95—22no—
154#95—22no—
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—44no—
164C4×C7—41no—
165C4×C7—41no—
166C4×C7—41no—
167C4×C7—41no—
168C4×C7—82no—
169C4×C7#35612yes—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—42no—
174C2×Q8—82no—
175C22×C4—22no—
176C22×C4—22no—
177C22×C4C7×C22⋊C411yescharacteristic
178C22×C4C7×C22⋊C411yescharacteristic
179C22×C4C7×C22⋊C411yescharacteristic
180C22×C4C7×C22⋊C411yescharacteristic
181C22×C4C22×C4×C711yescharacteristic
182C22×C4C2×C7×D411yescharacteristic
183C22×C4C2×C7×D411yescharacteristic
184C2×C8—42no—
185C2×C8—42no—
186C4⋊C4—24no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—82no—
194C4⋊C4—82no—
195C42—21no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—21no—
201C42—24no—
202C2×C7—21no—
203C2×C7—21no—
204C2×C7#147211yescharacteristic
205C2×C7#212811yescharacteristic
206C2×C7C2×#35611yescharacteristic
207C23C2×C7×C22⋊C411yescharacteristic
208Q8—44no—
209Q8—84no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4C7×#9911yescharacteristic
231C2×C4C7×#9911yescharacteristic
232C2×C4C7×#10112yes—
233C2×C4C7×#13112yes—
234C8—82no—
235C8—82no—
236C7#1157411yescharacteristic, direct product factor, Sylow
237C22—21no—
238C22—21no—
239C22C7×#40811yescharacteristic
240C22C2×C7×#9911yescharacteristic
241C22C2×C7×#10111yescharacteristic
242C4—22no—
243C4—22no—
244C4—21no—
245C4—44no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—82no—
251C4C7×#35612yes—
252C2—21no—
253C2—21no—
254C2C7×#147211yescharacteristic
255C2C7×#212811yescharacteristic
256C2C2×C7×#35611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C4⋊C4C23×C7
prime radicalC23×C7C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×Q8 ◁ G

Complements

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

NH ≅ G/Ntype
20. #11574C7direct (N × H)
236. C7#11574direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#25672
C7×#14672
C7×#14612
C7×#13252
#115747