Finite Group Databasebeta

← C7×#11814 #13189030

Subgroups — C7×#11814 #13189030

Order 1792.

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

normal subgroups only

This group has 434 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×#400C211yesmaximal, characteristic
2C7×#1821C211yesmaximal, characteristic
3C7×#1463C211yesmaximal, characteristic
4C7×#1353C214yesmaximal, complemented
5C22×C7×C4⋊C4C411yescharacteristic
6C22×C7×C4⋊C4C2211yescharacteristic
7C7×#407—21no—
8C7×#407—21no—
9C7×#400—21no—
10C7×#400—21no—
11C7×#400C412yes—
12C7×#400C2212yes—
13C2×C7×#95—21no—
14C2×C7×#95—21no—
15C2×C7×#95C411yescharacteristic
16C7×#343—21no—
17C7×#343C2212yes—
18C7×#324—21no—
19C7×#324C2212yes—
20#11814C711yesmaximal, 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—21no—
29C2×C7×C4⋊C4—41no—
30C2×C7×C4⋊C4—41no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4—41no—
33C2×C7×C4⋊C4C2×C412yes—
34C2×C7×C4⋊C4C2×C411yescharacteristic
35C2×C7×C4⋊C4D411yescharacteristic
36C2×C7×C4⋊C4D411yescharacteristic
37C2×C7×C4⋊C4C2311yescharacteristic
38C7×C22⋊C8—22no—
39C7×C22⋊C8—41no—
40C7×C22⋊C8—41no—
41C7×C22⋊C8—41no—
42C7×#95—22no—
43C7×#95—22no—
44C7×#95—21no—
45C7×#95—22no—
46C7×#95—22no—
47C7×#95C2×C412yes—
48C2×#400C2×C711yescharacteristic
49#1821C2×C711yescharacteristic
50#1463C2×C711yescharacteristic
51#1353C2×C714yescomplemented
52C24×C7C22⋊C411yescharacteristic
53C22×C4×C7—21no—
54C22×C4×C7—21no—
55C22×C4×C7—21no—
56C22×C4×C7—21no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—22no—
60C22×C4×C7—22no—
61C22×C4×C7—22no—
62C22×C4×C7—41no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
65C22×C4×C7—42no—
66C22×C4×C7—42no—
67C22×C4×C7—44no—
68C22×C4×C7—42no—
69C22×C4×C7—41no—
70C22×C4×C7—41no—
71C22×C4×C7C22⋊C411yescharacteristic
72C22×C4×C7C22⋊C411yescharacteristic
73C22×C4×C7C22⋊C411yescharacteristic
74C22×C4×C7C22×C411yescharacteristic
75C22×C4×C7C2×D411yescharacteristic
76C22×C4×C7C2×D411yescharacteristic
77C7×M16—42no—
78C7×M16—42no—
79C7×M16—82no—
80C2×C7×C8—42no—
81C2×C7×C8—42no—
82C7×C4⋊C4—41no—
83C7×C4⋊C4—41no—
84C7×C4⋊C4—41no—
85C7×C4⋊C4—41no—
86C7×C4⋊C4—42no—
87C7×C4⋊C4—42no—
88C22×C4⋊C4C4×C711yescharacteristic
89C22×C4⋊C4C22×C711yescharacteristic
90#407—21no—
91#407—21no—
92#400—21no—
93#400—21no—
94#400C4×C712yes—
95#400C22×C712yes—
96C2×#95—21no—
97C2×#95—21no—
98C2×#95C4×C711yescharacteristic
99#343—21no—
100#343C22×C712yes—
101#324—21no—
102#324C22×C712yes—
103C23×C7—22no—
104C23×C7—22no—
105C23×C7—21no—
106C23×C7—21no—
107C23×C7#9911yescharacteristic
108C23×C7#9911yescharacteristic
109C23×C7C2×C22⋊C411yescharacteristic
110C2×C4×C7—21no—
111C2×C4×C7—21no—
112C2×C4×C7—21no—
113C2×C4×C7—21no—
114C2×C4×C7—21no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—42no—
120C2×C4×C7—42no—
121C2×C4×C7—42no—
122C2×C4×C7—42no—
123C2×C4×C7—42no—
124C2×C4×C7—41no—
125C2×C4×C7—41no—
126C2×C4×C7—41no—
127C2×C4×C7—41no—
128C2×C4×C7—42no—
129C2×C4×C7—42no—
130C2×C4×C7—44no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7—81no—
134C2×C4×C7—84no—
135C2×C4×C7—82no—
136C2×C4×C7—82no—
137C2×C4×C7#13712yes—
138C7×C8—82no—
139C7×C8—82no—
140C23×C4—21no—
141C23×C4—21no—
142C23×C4C2×C4×C711yescharacteristic
143C23×C4C7×D411yescharacteristic
144C23×C4C7×D411yescharacteristic
145C2×M16—22no—
146C2×M16—41no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—41no—
149C2×C4⋊C4—41no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C2×C4×C712yes—
153C2×C4⋊C4C2×C4×C711yescharacteristic
154C2×C4⋊C4C7×D411yescharacteristic
155C2×C4⋊C4C7×D411yescharacteristic
156C2×C4⋊C4C23×C711yescharacteristic
157C22⋊C8—22no—
158C22⋊C8—41no—
159C22⋊C8—41no—
160C22⋊C8—41no—
161#95—22no—
162#95—22no—
163#95—21no—
164#95—22no—
165#95—22no—
166#95C2×C4×C712yes—
167C22×C7—24no—
168C22×C7—24no—
169C22×C7—21no—
170C22×C7—21no—
171C22×C7—21no—
172C22×C7—21no—
173C22×C7—21no—
174C22×C7—21no—
175C22×C7#35212yes—
176C22×C7#35512yes—
177C22×C7C2×#9911yescharacteristic
178C22×C7#41911yescharacteristic
179C22×C7#42111yescharacteristic
180C4×C7—22no—
181C4×C7—41no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7—41no—
185C4×C7—41no—
186C4×C7—82no—
187C4×C7—82no—
188C24C7×C22⋊C411yescharacteristic
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4—42no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—44no—
204C22×C4—42no—
205C22×C4—41no—
206C22×C4—41no—
207C22×C4C7×C22⋊C411yescharacteristic
208C22×C4C7×C22⋊C411yescharacteristic
209C22×C4C7×C22⋊C411yescharacteristic
210C22×C4C22×C4×C711yescharacteristic
211C22×C4C2×C7×D411yescharacteristic
212C22×C4C2×C7×D411yescharacteristic
213M16—42no—
214M16—42no—
215M16—82no—
216C2×C8—42no—
217C2×C8—42no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C2×C7—21no—
225C2×C7—22no—
226C2×C7—22no—
227C2×C7—21no—
228C2×C7#151111yescharacteristic
229C2×C7C2×#35211yescharacteristic
230C2×C7C2×#35511yescharacteristic
231C23—22no—
232C23—22no—
233C23—21no—
234C23—21no—
235C23C7×#9911yescharacteristic
236C23C7×#9911yescharacteristic
237C23C2×C7×C22⋊C411yescharacteristic
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—44no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—81no—
262C2×C4—84no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4C7×#13712yes—
266C8—82no—
267C8—82no—
268C7#1181411yescharacteristic, direct product factor, Sylow
269C22—24no—
270C22—24no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22C7×#35212yes—
278C22C7×#35512yes—
279C22C2×C7×#9911yescharacteristic
280C22C7×#41911yescharacteristic
281C22C7×#42111yescharacteristic
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—82no—
289C4—82no—
290C2—21no—
291C2—22no—
292C2—22no—
293C2—21no—
294C2C7×#151111yescharacteristic
295C2C2×C7×#35211yescharacteristic
296C2C2×C7×#35511yescharacteristic
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×#1353C2semidirect
20. #11814C7direct (N × H)
51. #1353C2×C7semidirect
268. C7#11814direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#4002
C7×#18212
C7×#14632
C7×#13532
#118147