Finite Group Databasebeta

← C7×#9454 #13186670

Subgroups — C7×#9454 #13186670

Order 1792.

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

normal subgroups only

This group has 448 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×#2567C211yesmaximal, characteristic
3C7×#1556C212yesmaximal
4C7×#1467C211yesmaximal, characteristic
5C7×#1285C212yesmaximal
6C2×C7×C4⋊Q8C2211yescharacteristic
7C2×C4×C7×Q8C2211yescharacteristic
8C7×#446—24no—
9C7×#432—21no—
10C7×#432C2212yes—
11C7×#432C2212yes—
12C7×#431—21no—
13C7×#395—21no—
14C7×#395—21no—
15C7×#391C412yes—
16C7×#389—21no—
17C7×#389—21no—
18C7×#384C412yes—
19C4×C7×C4⋊C4C2211yescharacteristic
20C7×#332—24no—
21C7×#324—21no—
22C7×#324—21no—
23#9454C711yesmaximal, characteristic, direct product factor, Sylow
24C22×C7×Q8—21no—
25C22×C7×Q8C2×C411yescharacteristic
26C7×C4⋊Q8—22no—
27C7×C4⋊Q8—22no—
28C4×C7×Q8—22no—
29C4×C7×Q8—22no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—21no—
32C2×C7×C4⋊C4—22no—
33C2×C7×C4⋊C4—22no—
34C2×C7×C4⋊C4C2×C412yes—
35C2×C7×C4⋊C4C2×C411yescharacteristic
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C7×C4⋊C4D411yescharacteristic
38C2×C42×C7C2×C412yes—
39C2×C42×C7D411yescharacteristic
40C2×C42×C7D411yescharacteristic
41C2×C42×C7C2311yescharacteristic
42C7×C4⋊C8—22no—
43C7×C4⋊C8—22no—
44C7×C4⋊C8—22no—
45C7×C4⋊C8D414yes—
46C7×C22⋊C8—22no—
47C7×C22⋊C8—22no—
48C7×#97—22no—
49C7×#97—22no—
50C7×#97—22no—
51C4×C7×C8—22no—
52C7×#95—22no—
53C7×#95—22no—
54C7×#95—21no—
55#2983C2×C711yescharacteristic
56#2567C2×C711yescharacteristic
57#1556C2×C712yes—
58#1467C2×C711yescharacteristic
59#1285C2×C712yes—
60C2×C7×Q8—22no—
61C2×C7×Q8—22no—
62C2×C7×Q8—41no—
63C2×C7×Q8—42no—
64C2×C7×Q8—82no—
65C22×C4×C7—22no—
66C22×C4×C7—22no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C22⋊C411yescharacteristic
71C22×C4×C7C22×C411yescharacteristic
72C22×C4×C7C2×D411yescharacteristic
73C22×C4×C7C2×D411yescharacteristic
74C2×C7×C8—24no—
75C2×C7×C8—42no—
76C7×C4⋊C4—24no—
77C7×C4⋊C4—22no—
78C7×C4⋊C4—22no—
79C7×C4⋊C4—22no—
80C7×C4⋊C4—24no—
81C7×C4⋊C4—41no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—82no—
84C7×C4⋊C4—82no—
85C42×C7—21no—
86C42×C7—21no—
87C42×C7—21no—
88C42×C7—21no—
89C42×C7—42no—
90C42×C7C2×D412yes—
91C42×C7#4112yes—
92C2×C4⋊Q8C22×C711yescharacteristic
93C2×C4×Q8C22×C711yescharacteristic
94#446—24no—
95#432—21no—
96#432C22×C712yes—
97#432C22×C712yes—
98#431—21no—
99#395—21no—
100#395—21no—
101#391C4×C712yes—
102#389—21no—
103#389—21no—
104#384C4×C712yes—
105C4×C4⋊C4C22×C711yescharacteristic
106#332—24no—
107#324—21no—
108#324—21no—
109C23×C7C2×C22⋊C411yescharacteristic
110C7×Q8—44no—
111C7×Q8—84no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—22no—
117C2×C4×C7—24no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—41no—
124C2×C4×C7—42no—
125C2×C4×C7—42no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—42no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7#10112yes—
132C2×C4×C7C4×D412yes—
133C2×C4×C7#12011yescharacteristic
134C2×C4×C7#12112yes—
135C2×C4×C7#12311yescharacteristic
136C7×C8—44no—
137C7×C8—82no—
138C22×Q8—21no—
139C22×Q8C2×C4×C711yescharacteristic
140C4⋊Q8—22no—
141C4⋊Q8—22no—
142C4×Q8—22no—
143C4×Q8—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4C2×C4×C712yes—
149C2×C4⋊C4C2×C4×C711yescharacteristic
150C2×C4⋊C4C7×D411yescharacteristic
151C2×C4⋊C4C7×D411yescharacteristic
152C2×C42C2×C4×C712yes—
153C2×C42C7×D411yescharacteristic
154C2×C42C7×D411yescharacteristic
155C2×C42C23×C711yescharacteristic
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—22no—
159C4⋊C8C7×D414yes—
160C22⋊C8—22no—
161C22⋊C8—22no—
162#97—22no—
163#97—22no—
164#97—22no—
165C4×C8—22no—
166#95—22no—
167#95—22no—
168#95—21no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7#38611yescharacteristic
172C22×C7C2×#10111yescharacteristic
173C22×C7#41311yescharacteristic
174C4×C7—21no—
175C4×C7—22no—
176C4×C7—22no—
177C4×C7—22no—
178C4×C7—44no—
179C4×C7—41no—
180C4×C7—41no—
181C4×C7—41no—
182C4×C7—82no—
183C4×C7#45612yes—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8—41no—
187C2×Q8—42no—
188C2×Q8—82no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C7×C22⋊C411yescharacteristic
192C22×C4C7×C22⋊C411yescharacteristic
193C22×C4C7×C22⋊C411yescharacteristic
194C22×C4C7×C22⋊C411yescharacteristic
195C22×C4C22×C4×C711yescharacteristic
196C22×C4C2×C7×D411yescharacteristic
197C22×C4C2×C7×D411yescharacteristic
198C2×C8—24no—
199C2×C8—42no—
200C4⋊C4—24no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—24no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—82no—
208C4⋊C4—82no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C42—42no—
214C42C2×C7×D412yes—
215C42C7×#4112yes—
216C2×C7—21no—
217C2×C7—21no—
218C2×C7#188611yescharacteristic
219C2×C7#190111yescharacteristic
220C2×C7#191011yescharacteristic
221C23C2×C7×C22⋊C411yescharacteristic
222Q8—44no—
223Q8—84no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4C7×#10112yes—
244C2×C4C4×C7×D412yes—
245C2×C4C7×#12011yescharacteristic
246C2×C4C7×#12112yes—
247C2×C4C7×#12311yescharacteristic
248C8—44no—
249C8—82no—
250C7#945411yescharacteristic, direct product factor, Sylow
251C22—21no—
252C22—21no—
253C22C7×#38611yescharacteristic
254C22C2×C7×#10111yescharacteristic
255C22C7×#41311yescharacteristic
256C4—21no—
257C4—22no—
258C4—22no—
259C4—22no—
260C4—44no—
261C4—41no—
262C4—41no—
263C4—41no—
264C4—82no—
265C4C7×#45612yes—
266C2—21no—
267C2—21no—
268C2C7×#188611yescharacteristic
269C2C7×#190111yescharacteristic
270C2C7×#191011yescharacteristic
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. #9454C7direct (N × H)
250. C7#9454direct (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×#25672
C7×#15562
C7×#14672
C7×#12852
#94547