Finite Group Databasebeta

← C7×#9452 #13186668

Subgroups — C7×#9452 #13186668

Order 1792.

468 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2983C211yesmaximal, characteristic
2C7×#2546C211yesmaximal, characteristic
3C7×#1558C212yesmaximal
4C7×#1467C211yesmaximal, characteristic
5C7×#1285C212yesmaximal
6C2×C7×C4⋊Q8C412yes—
7C2×C7×C4⋊Q8C2211yescharacteristic
8C2×C4×C7×Q8C2211yescharacteristic
9C7×#446—24no—
10C7×#432—21no—
11C7×#432C2212yes—
12C7×#432C2212yes—
13C7×#431—21no—
14C7×#398—21no—
15C7×#398—21no—
16C7×#391C412yes—
17C7×#389—21no—
18C7×#389—21no—
19C4×C7×C4⋊C4C2211yescharacteristic
20C7×#333—24no—
21C7×#324—21no—
22C7×#324—21no—
23#9452C711yesmaximal, characteristic, direct product factor, Sylow
24C22×C7×Q8C2×C412yes—
25C22×C7×Q8C2×C411yescharacteristic
26C7×C4⋊Q8—22no—
27C7×C4⋊Q8—22no—
28C7×C4⋊Q8—44no—
29C4×C7×Q8—22no—
30C4×C7×Q8—22no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4—21no—
35C2×C7×C4⋊C4—21no—
36C2×C7×C4⋊C4C2×C411yescharacteristic
37C2×C7×C4⋊C4D411yescharacteristic
38C2×C7×C4⋊C4D411yescharacteristic
39C2×C42×C7C2×C412yes—
40C2×C42×C7D411yescharacteristic
41C2×C42×C7D411yescharacteristic
42C2×C42×C7C2311yescharacteristic
43C7×C4⋊C8—22no—
44C7×C4⋊C8—22no—
45C7×C4⋊C8—22no—
46C7×C4⋊C8D414yes—
47C7×C22⋊C8—22no—
48C7×C22⋊C8—22no—
49C7×#97—22no—
50C7×#97—22no—
51C7×#97—22no—
52C4×C7×C8—22no—
53C7×#95—22no—
54C7×#95—22no—
55C7×#95—21no—
56#2983C2×C711yescharacteristic
57#2546C2×C711yescharacteristic
58#1558C2×C712yes—
59#1467C2×C711yescharacteristic
60#1285C2×C712yes—
61C2×C7×Q8—22no—
62C2×C7×Q8—22no—
63C2×C7×Q8—24no—
64C2×C7×Q8—41no—
65C2×C7×Q8—42no—
66C2×C7×Q8—42no—
67C22×C4×C7—22no—
68C22×C4×C7—22no—
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22×C411yescharacteristic
74C22×C4×C7C2×D411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C2×C7×C8—24no—
77C2×C7×C8—42no—
78C7×C4⋊C4—24no—
79C7×C4⋊C4—22no—
80C7×C4⋊C4—22no—
81C7×C4⋊C4—22no—
82C7×C4⋊C4—44no—
83C7×C4⋊C4—44no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—42no—
86C7×C4⋊C4—41no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—21no—
90C42×C7—21no—
91C42×C7—42no—
92C42×C7C2×D412yes—
93C42×C7#4112yes—
94C2×C4⋊Q8C4×C712yes—
95C2×C4⋊Q8C22×C711yescharacteristic
96C2×C4×Q8C22×C711yescharacteristic
97#446—24no—
98#432—21no—
99#432C22×C712yes—
100#432C22×C712yes—
101#431—21no—
102#398—21no—
103#398—21no—
104#391C4×C712yes—
105#389—21no—
106#389—21no—
107C4×C4⋊C4C22×C711yescharacteristic
108#333—24no—
109#324—21no—
110#324—21no—
111C23×C7C2×C22⋊C411yescharacteristic
112C7×Q8—44no—
113C7×Q8—84no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—22no—
119C2×C4×C7—24no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—21no—
125C2×C4×C7—41no—
126C2×C4×C7—42no—
127C2×C4×C7—42no—
128C2×C4×C7—41no—
129C2×C4×C7—41no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7#10012yes—
134C2×C4×C7C4×D412yes—
135C2×C4×C7#12011yescharacteristic
136C2×C4×C7#12112yes—
137C2×C4×C7#12311yescharacteristic
138C7×C8—44no—
139C7×C8—82no—
140C22×Q8C2×C4×C712yes—
141C22×Q8C2×C4×C711yescharacteristic
142C4⋊Q8—22no—
143C4⋊Q8—22no—
144C4⋊Q8—44no—
145C4×Q8—22no—
146C4×Q8—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4C2×C4×C711yescharacteristic
153C2×C4⋊C4C7×D411yescharacteristic
154C2×C4⋊C4C7×D411yescharacteristic
155C2×C42C2×C4×C712yes—
156C2×C42C7×D411yescharacteristic
157C2×C42C7×D411yescharacteristic
158C2×C42C23×C711yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—22no—
162C4⋊C8C7×D414yes—
163C22⋊C8—22no—
164C22⋊C8—22no—
165#97—22no—
166#97—22no—
167#97—22no—
168C4×C8—22no—
169#95—22no—
170#95—22no—
171#95—21no—
172C22×C7—21no—
173C22×C7—21no—
174C22×C7#38611yescharacteristic
175C22×C7C2×#10011yescharacteristic
176C22×C7#41311yescharacteristic
177C4×C7—21no—
178C4×C7—22no—
179C4×C7—22no—
180C4×C7—22no—
181C4×C7—44no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7—41no—
185C4×C7—82no—
186C4×C7#45612yes—
187C2×Q8—22no—
188C2×Q8—22no—
189C2×Q8—24no—
190C2×Q8—41no—
191C2×Q8—42no—
192C2×Q8—42no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4C7×C22⋊C411yescharacteristic
196C22×C4C7×C22⋊C411yescharacteristic
197C22×C4C7×C22⋊C411yescharacteristic
198C22×C4C7×C22⋊C411yescharacteristic
199C22×C4C22×C4×C711yescharacteristic
200C22×C4C2×C7×D411yescharacteristic
201C22×C4C2×C7×D411yescharacteristic
202C2×C8—24no—
203C2×C8—42no—
204C4⋊C4—24no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—44no—
209C4⋊C4—44no—
210C4⋊C4—41no—
211C4⋊C4—42no—
212C4⋊C4—41no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C42C2×C7×D412yes—
219C42C7×#4112yes—
220C2×C7—21no—
221C2×C7—21no—
222C2×C7#188611yescharacteristic
223C2×C7#190011yescharacteristic
224C2×C7#190911yescharacteristic
225C23C2×C7×C22⋊C411yescharacteristic
226Q8—44no—
227Q8—84no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—24no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4C7×#10012yes—
248C2×C4C4×C7×D412yes—
249C2×C4C7×#12011yescharacteristic
250C2×C4C7×#12112yes—
251C2×C4C7×#12311yescharacteristic
252C8—44no—
253C8—82no—
254C7#945211yescharacteristic, direct product factor, Sylow
255C22—21no—
256C22—21no—
257C22C7×#38611yescharacteristic
258C22C2×C7×#10011yescharacteristic
259C22C7×#41311yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4C7×#45612yes—
270C2—21no—
271C2—21no—
272C2C7×#188611yescharacteristic
273C2C7×#190011yescharacteristic
274C2C7×#190911yescharacteristic
subgroupG/H
center, socleC22×C7#386
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C42C23×C7
prime radicalC23×C7C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G

Complements

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

NH ≅ G/Ntype
23. #9452C7direct (N × H)
254. C7#9452direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#29832
C7×#25462
C7×#15582
C7×#14672
C7×#12852
#94527