Finite Group Databasebeta

← C7×#11576 #13188792

Subgroups — C7×#11576 #13188792

Order 1792.

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

normal subgroups only

This group has 426 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×#2487C211yesmaximal, characteristic
2C7×#1466C211yesmaximal, characteristic
3C7×#1459C211yesmaximal, characteristic
4C7×#1326C214yesmaximal, complemented
5C2×C4×C7×D4C2211yescharacteristic
6C22×C7×C4⋊C4C411yescharacteristic
7C7×#432—21no—
8C2×C7×C22⋊C8—21no—
9C7×#400—21no—
10C7×#399—21no—
11C7×#389—21no—
12C7×#386C412yes—
13C7×#385C2212yes—
14C7×#380—21no—
15C7×#380C411yescharacteristic
16C7×#324—21no—
17C7×#323—21no—
18C7×#323C2212yes—
19C7×#323C2212yes—
20#11576C711yesmaximal, characteristic, direct product factor, Sylow
21C22×C7×D4C2×C411yescharacteristic
22C23×C4×C7C2×C411yescharacteristic
23C23×C4×C7C2×C412yes—
24C23×C4×C7D411yescharacteristic
25C22×C7×C8—41no—
26C4×C7×D4—41no—
27C4×C7×D4—41no—
28C2×C7×C4⋊C4—21no—
29C2×C7×C4⋊C4—21no—
30C2×C7×C4⋊C4—21no—
31C2×C7×C4⋊C4—22no—
32C2×C7×C4⋊C4—41no—
33C2×C7×C4⋊C4—41no—
34C2×C7×C4⋊C4D411yescharacteristic
35C2×C7×C22⋊C4—22no—
36C2×C7×C22⋊C4C2×C412yes—
37C2×C7×C22⋊C4D411yescharacteristic
38C2×C7×C22⋊C4C2311yescharacteristic
39C2×C42×C7D411yescharacteristic
40C7×C4⋊C8—41no—
41C7×C22⋊C8—22no—
42C7×C22⋊C8—22no—
43C7×C22⋊C8—41no—
44C7×#97—41no—
45C7×#95—21no—
46C7×#95—22no—
47C7×#95—22no—
48#2487C2×C711yescharacteristic
49#1466C2×C711yescharacteristic
50#1459C2×C711yescharacteristic
51#1326C2×C714yescomplemented
52C24×C7C22⋊C411yescharacteristic
53C24×C7C22×C411yescharacteristic
54C2×C7×D4—22no—
55C2×C7×D4—22no—
56C2×C7×D4—41no—
57C22×C4×C7—21no—
58C22×C4×C7—21no—
59C22×C4×C7—21no—
60C22×C4×C7—21no—
61C22×C4×C7—22no—
62C22×C4×C7—22no—
63C22×C4×C7—42no—
64C22×C4×C7—42no—
65C22×C4×C7—42no—
66C22×C4×C7—82no—
67C22×C4×C7C22⋊C411yescharacteristic
68C22×C4×C7C22⋊C411yescharacteristic
69C22×C4×C7C22⋊C411yescharacteristic
70C22×C4×C7C2×D411yescharacteristic
71C22×C4×C7C2×D411yescharacteristic
72C2×C7×C8—42no—
73C2×C7×C8—42no—
74C2×C7×C8—82no—
75C7×C4⋊C4—41no—
76C7×C4⋊C4—42no—
77C7×C4⋊C4—42no—
78C7×C4⋊C4—41no—
79C7×C4⋊C4—41no—
80C7×C4⋊C4—82no—
81C7×C22⋊C4—24no—
82C7×C22⋊C4—41no—
83C7×C22⋊C4—41no—
84C7×C22⋊C4—82no—
85C42×C7—21no—
86C42×C7—21no—
87C2×C4×D4C22×C711yescharacteristic
88C22×C4⋊C4C4×C711yescharacteristic
89#432—21no—
90C2×C22⋊C8—21no—
91#400—21no—
92#399—21no—
93#389—21no—
94#386C4×C712yes—
95#385C22×C712yes—
96#380—21no—
97#380C4×C711yescharacteristic
98#324—21no—
99#323—21no—
100#323C22×C712yes—
101#323C22×C712yes—
102C23×C7—21no—
103C23×C7—21no—
104C23×C7—21no—
105C23×C7—21no—
106C23×C7—41no—
107C23×C7—41no—
108C23×C7—41no—
109C23×C7—41no—
110C23×C7#10112yes—
111C23×C7C2×C22⋊C411yescharacteristic
112C23×C7#13112yes—
113C7×D4—44no—
114C2×C4×C7—22no—
115C2×C4×C7—21no—
116C2×C4×C7—21no—
117C2×C4×C7—21no—
118C2×C4×C7—21no—
119C2×C4×C7—21no—
120C2×C4×C7—21no—
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—42no—
128C2×C4×C7—42no—
129C2×C4×C7—42no—
130C2×C4×C7—42no—
131C2×C4×C7—42no—
132C2×C4×C7—42no—
133C2×C4×C7—81no—
134C2×C4×C7—84no—
135C2×C4×C7#9911yescharacteristic
136C2×C4×C7#9911yescharacteristic
137C7×C8—82no—
138C7×C8—82no—
139C22×D4C2×C4×C711yescharacteristic
140C23×C4C2×C4×C711yescharacteristic
141C23×C4C2×C4×C712yes—
142C23×C4C7×D411yescharacteristic
143C22×C8—41no—
144C4×D4—41no—
145C4×D4—41no—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4C7×D411yescharacteristic
153C2×C22⋊C4—22no—
154C2×C22⋊C4C2×C4×C712yes—
155C2×C22⋊C4C7×D411yescharacteristic
156C2×C22⋊C4C23×C711yescharacteristic
157C2×C42C7×D411yescharacteristic
158C4⋊C8—41no—
159C22⋊C8—22no—
160C22⋊C8—22no—
161C22⋊C8—41no—
162#97—41no—
163#95—21no—
164#95—22no—
165#95—22no—
166C22×C7—21no—
167C22×C7—21no—
168C22×C7—22no—
169C22×C7—22no—
170C22×C7—42no—
171C22×C7—42no—
172C22×C7—42no—
173C22×C7—41no—
174C22×C7—41no—
175C22×C7—41no—
176C22×C7—41no—
177C22×C7—81no—
178C22×C7#40811yescharacteristic
179C22×C7C2×#9911yescharacteristic
180C22×C7C2×#10111yescharacteristic
181C4×C7—21no—
182C4×C7—41no—
183C4×C7—41no—
184C4×C7—41no—
185C4×C7—41no—
186C4×C7—82no—
187C4×C7—82no—
188C4×C7#35212yes—
189C24C7×C22⋊C411yescharacteristic
190C24C22×C4×C711yescharacteristic
191C2×D4—22no—
192C2×D4—22no—
193C2×D4—41no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—82no—
204C22×C4C7×C22⋊C411yescharacteristic
205C22×C4C7×C22⋊C411yescharacteristic
206C22×C4C7×C22⋊C411yescharacteristic
207C22×C4C2×C7×D411yescharacteristic
208C22×C4C2×C7×D411yescharacteristic
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—82no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—82no—
218C22⋊C4—24no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—82no—
222C42—21no—
223C42—21no—
224C2×C7—21no—
225C2×C7—21no—
226C2×C7—42no—
227C2×C7—42no—
228C2×C7#147211yescharacteristic
229C2×C7C2×#35211yescharacteristic
230C2×C7#212211yescharacteristic
231C23—21no—
232C23—21no—
233C23—21no—
234C23—21no—
235C23—41no—
236C23—41no—
237C23—41no—
238C23—41no—
239C23C7×#10112yes—
240C23C2×C7×C22⋊C411yescharacteristic
241C23C7×#13112yes—
242D4—44no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—81no—
263C2×C4—84no—
264C2×C4C7×#9911yescharacteristic
265C2×C4C7×#9911yescharacteristic
266C8—82no—
267C8—82no—
268C7#1157611yescharacteristic, direct product factor, Sylow
269C22—21no—
270C22—21no—
271C22—22no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—42no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22—81no—
281C22C7×#40811yescharacteristic
282C22C2×C7×#9911yescharacteristic
283C22C2×C7×#10111yescharacteristic
284C4—21no—
285C4—41no—
286C4—41no—
287C4—41no—
288C4—41no—
289C4—82no—
290C4—82no—
291C4C7×#35212yes—
292C2—21no—
293C2—21no—
294C2—42no—
295C2—42no—
296C2C7×#147211yescharacteristic
297C2C2×C7×#35211yescharacteristic
298C2C7×#212211yescharacteristic
subgroupG/H
center, socleC22×C7C2×#99
commutatorC24C22×C4×C7
Frattini, cosocleC2×C22⋊C4C23×C7
prime radicalC22×C7×D4C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C7 ◁ C22×C4×C7 ◁ C2×C4×C7×D4 ◁ G

Complements

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

NH ≅ G/Ntype
4. C7×#1326C2semidirect
20. #11576C7direct (N × H)
51. #1326C2×C7semidirect
268. C7#11576direct (N × H)

Maximal subgroups

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

subgroupindex
C7×#24872
C7×#14662
C7×#14592
C7×#13262
#115767