Finite Group Databasebeta

← C7×#11803 #13189019

Subgroups — C7×#11803 #13189019

Order 1792.

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

normal subgroups only

This group has 478 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
1C2×C7×#398C211yesmaximal, characteristic
2C7×#1821C211yesmaximal, characteristic
3C7×#1463C211yesmaximal, characteristic
4C7×#1346C214yesmaximal, complemented
5C22×C7×C4⋊C4—21no—
6C22×C7×C4⋊C4C411yescharacteristic
7C22×C7×C4⋊C4C2211yescharacteristic
8C7×#407—21no—
9C7×#407—21no—
10C7×#398—21no—
11C7×#398—21no—
12C7×#398C412yes—
13C7×#398C2212yes—
14C2×C7×#95—21no—
15C2×C7×#95C411yescharacteristic
16C7×#343—21no—
17C7×#343C2212yes—
18C7×#324—21no—
19C7×#324C2212yes—
20#11803C711yesmaximal, characteristic, direct product factor, Sylow
21C23×C4×C7—21no—
22C23×C4×C7—21no—
23C23×C4×C7C2×C411yescharacteristic
24C23×C4×C7D411yescharacteristic
25C23×C4×C7D411yescharacteristic
26C2×C7×M16—22no—
27C2×C7×M16—41no—
28C2×C7×C4⋊C4—22no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—22no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4—41no—
33C2×C7×C4⋊C4—41no—
34C2×C7×C4⋊C4—41no—
35C2×C7×C4⋊C4—44no—
36C2×C7×C4⋊C4C2×C412yes—
37C2×C7×C4⋊C4C2×C411yescharacteristic
38C2×C7×C4⋊C4D411yescharacteristic
39C2×C7×C4⋊C4D411yescharacteristic
40C2×C7×C4⋊C4C2311yescharacteristic
41C7×C22⋊C8—22no—
42C7×C22⋊C8—41no—
43C7×C22⋊C8—41no—
44C7×C22⋊C8—41no—
45C7×#95—22no—
46C7×#95—21no—
47C7×#95—22no—
48C7×#95C2×C412yes—
49C2×#398C2×C711yescharacteristic
50#1821C2×C711yescharacteristic
51#1463C2×C711yescharacteristic
52#1346C2×C714yescomplemented
53C24×C7C22⋊C411yescharacteristic
54C22×C4×C7—24no—
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—22no—
61C22×C4×C7—21no—
62C22×C4×C7—22no—
63C22×C4×C7—22no—
64C22×C4×C7—41no—
65C22×C4×C7—42no—
66C22×C4×C7—42no—
67C22×C4×C7—42no—
68C22×C4×C7—42no—
69C22×C4×C7—42no—
70C22×C4×C7—42no—
71C22×C4×C7—41no—
72C22×C4×C7—41no—
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22⋊C411yescharacteristic
75C22×C4×C7C22⋊C411yescharacteristic
76C22×C4×C7C22×C411yescharacteristic
77C22×C4×C7C2×D411yescharacteristic
78C22×C4×C7C2×D411yescharacteristic
79C7×M16—42no—
80C7×M16—42no—
81C7×M16—82no—
82C2×C7×C8—42no—
83C2×C7×C8—42no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—41no—
87C7×C4⋊C4—41no—
88C7×C4⋊C4—42no—
89C7×C4⋊C4—42no—
90C7×C4⋊C4—44no—
91C7×C4⋊C4—44no—
92C22×C4⋊C4—21no—
93C22×C4⋊C4C4×C711yescharacteristic
94C22×C4⋊C4C22×C711yescharacteristic
95#407—21no—
96#407—21no—
97#398—21no—
98#398—21no—
99#398C4×C712yes—
100#398C22×C712yes—
101C2×#95—21no—
102C2×#95C4×C711yescharacteristic
103#343—21no—
104#343C22×C712yes—
105#324—21no—
106#324C22×C712yes—
107C23×C7—22no—
108C23×C7—22no—
109C23×C7—21no—
110C23×C7—21no—
111C23×C7#9911yescharacteristic
112C23×C7#9911yescharacteristic
113C23×C7C2×C22⋊C411yescharacteristic
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—24no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
121C2×C4×C7—21no—
122C2×C4×C7—21no—
123C2×C4×C7—21no—
124C2×C4×C7—42no—
125C2×C4×C7—42no—
126C2×C4×C7—48no—
127C2×C4×C7—42no—
128C2×C4×C7—42no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—41no—
133C2×C4×C7—41no—
134C2×C4×C7—41no—
135C2×C4×C7—41no—
136C2×C4×C7—42no—
137C2×C4×C7—42no—
138C2×C4×C7—42no—
139C2×C4×C7—81no—
140C2×C4×C7—82no—
141C2×C4×C7—82no—
142C2×C4×C7AGL(1,ℤ/8)12yes—
143C7×C8—82no—
144C7×C8—82no—
145C23×C4—21no—
146C23×C4—21no—
147C23×C4C2×C4×C711yescharacteristic
148C23×C4C7×D411yescharacteristic
149C23×C4C7×D411yescharacteristic
150C2×M16—22no—
151C2×M16—41no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—41no—
156C2×C4⋊C4—41no—
157C2×C4⋊C4—41no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—44no—
160C2×C4⋊C4C2×C4×C712yes—
161C2×C4⋊C4C2×C4×C711yescharacteristic
162C2×C4⋊C4C7×D411yescharacteristic
163C2×C4⋊C4C7×D411yescharacteristic
164C2×C4⋊C4C23×C711yescharacteristic
165C22⋊C8—22no—
166C22⋊C8—41no—
167C22⋊C8—41no—
168C22⋊C8—41no—
169#95—22no—
170#95—21no—
171#95—22no—
172#95C2×C4×C712yes—
173C22×C7—24no—
174C22×C7—24no—
175C22×C7—21no—
176C22×C7—21no—
177C22×C7—21no—
178C22×C7—21no—
179C22×C7—21no—
180C22×C7—21no—
181C22×C7#35212yes—
182C22×C7#35612yes—
183C22×C7C2×#9911yescharacteristic
184C22×C7#41811yescharacteristic
185C22×C7#42111yescharacteristic
186C4×C7—22no—
187C4×C7—44no—
188C4×C7—41no—
189C4×C7—41no—
190C4×C7—41no—
191C4×C7—41no—
192C4×C7—41no—
193C4×C7—82no—
194C24C7×C22⋊C411yescharacteristic
195C22×C4—24no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—22no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—41no—
206C22×C4—42no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—42no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4C7×C22⋊C411yescharacteristic
215C22×C4C7×C22⋊C411yescharacteristic
216C22×C4C7×C22⋊C411yescharacteristic
217C22×C4C22×C4×C711yescharacteristic
218C22×C4C2×C7×D411yescharacteristic
219C22×C4C2×C7×D411yescharacteristic
220M16—42no—
221M16—42no—
222M16—82no—
223C2×C8—42no—
224C2×C8—42no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—44no—
232C4⋊C4—44no—
233C2×C7—21no—
234C2×C7—22no—
235C2×C7—22no—
236C2×C7—21no—
237C2×C7#151011yescharacteristic
238C2×C7C2×#35211yescharacteristic
239C2×C7C2×#35611yescharacteristic
240C23—22no—
241C23—22no—
242C23—21no—
243C23—21no—
244C23C7×#9911yescharacteristic
245C23C7×#9911yescharacteristic
246C23C2×C7×C22⋊C411yescharacteristic
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—24no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—48no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—81no—
273C2×C4—82no—
274C2×C4—82no—
275C2×C4C7×AGL(1,ℤ/8)12yes—
276C8—82no—
277C8—82no—
278C7#1180311yescharacteristic, direct product factor, Sylow
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C7×#35212yes—
288C22C7×#35612yes—
289C22C2×C7×#9911yescharacteristic
290C22C7×#41811yescharacteristic
291C22C7×#42111yescharacteristic
292C4—22no—
293C4—44no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C2—21no—
301C2—22no—
302C2—22no—
303C2—21no—
304C2C7×#151011yescharacteristic
305C2C2×C7×#35211yescharacteristic
306C2C2×C7×#35611yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC22×C4C22×C4×C7
Frattini, cosocleC2×C4⋊C4C23×C7
prime radicalC24×C7C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C24×C7 ◁ C22×C7×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1346C2semidirect
20. #11803C7direct (N × H)
52. #1346C2×C7semidirect
278. C7#11803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3982
C7×#18212
C7×#14632
C7×#13462
#118037