Finite Group Databasebeta

← C7×#14454 #13191670

Subgroups — C7×#14454 #13191670

Order 1792.

1190 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#384C211yesmaximal, characteristic
2C7×#1441C212yesmaximal
3C7×#1441C214yesmaximal
4C7×#1436C212yesmaximal
5C7×#1436C214yesmaximal
6C7×#1434C212yesmaximal
7C22×C7×C4⋊C4C2212yes—
8C22×C7×C4⋊C4C2211yescharacteristic
9C22×C7×C4⋊C4C2214yes—
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C42×C7C2211yescharacteristic
12C22×C42×C7C2212yes—
13C7×#384C418yescomplemented
14C2×C7×#95C2214yes—
15C2×C7×#95C2214yes—
16C2×C7×#95C2212yes—
17C2×C7×#95C2214yes—
18C2×C7×#95C2212yes—
19C2×C7×#95C2212yes—
20C2×C7×#95C2214yes—
21C2×C7×#95C2212yes—
22#14454C711yesmaximal, characteristic, direct product factor, Sylow
23C23×C4×C7C2314yes—
24C23×C4×C7C2312yes—
25C23×C4×C7C2312yes—
26C23×C4×C7C2314yes—
27C23×C4×C7C2312yes—
28C23×C4×C7C2311yescharacteristic
29C2×C7×C4⋊C4—41no—
30C2×C7×C4⋊C4—44no—
31C2×C7×C4⋊C4—41no—
32C2×C7×C4⋊C4—41no—
33C2×C7×C4⋊C4—44no—
34C2×C7×C4⋊C4—41no—
35C2×C7×C4⋊C4—42no—
36C2×C7×C4⋊C4—44no—
37C2×C7×C4⋊C4C2×C414yes—
38C2×C7×C4⋊C4C2×C414yes—
39C2×C7×C4⋊C4C2×C4116yes—
40C2×C42×C7—24no—
41C2×C42×C7—44no—
42C2×C42×C7—42no—
43C2×C42×C7C2×C414yes—
44C7×#95—28no—
45C7×#95—28no—
46C7×#95—24no—
47C7×#95—42no—
48C7×#95—44no—
49C7×#95—44no—
50C7×#95—42no—
51C7×#95Q818yes—
52C2×#384C2×C711yescharacteristic
53#1441C2×C714yes—
54#1441C2×C712yes—
55#1436C2×C712yes—
56#1436C2×C714yes—
57#1434C2×C712yes—
58C24×C7C2411yescharacteristic
59C22×C4×C7—24no—
60C22×C4×C7—21no—
61C22×C4×C7—21no—
62C22×C4×C7—24no—
63C22×C4×C7—22no—
64C22×C4×C7—24no—
65C22×C4×C7—24no—
66C22×C4×C7—24no—
67C22×C4×C7—24no—
68C22×C4×C7—24no—
69C22×C4×C7—22no—
70C22×C4×C7—22no—
71C22×C4×C7—24no—
72C22×C4×C7—24no—
73C22×C4×C7—22no—
74C22×C4×C7—24no—
75C22×C4×C7—22no—
76C22×C4×C7—24no—
77C22×C4×C7—24no—
78C22×C4×C7—24no—
79C22×C4×C7—24no—
80C22×C4×C7—24no—
81C22×C4×C7—24no—
82C22×C4×C7—24no—
83C22×C4×C7—24no—
84C22×C4×C7—24no—
85C22×C4×C7C22×C414yes—
86C22×C4×C7C22×C414yes—
87C22×C4×C7C22×C412yes—
88C22×C4×C7C22×C414yes—
89C22×C4×C7C2×Q818yes—
90C22×C4×C7C2×Q814yes—
91C22×C4×C7#4114yes—
92C22×C4×C7#4114yes—
93C7×C4⋊C4—44no—
94C7×C4⋊C4—44no—
95C7×C4⋊C4—416no—
96C7×C4⋊C4—48no—
97C42×C7—28no—
98C42×C7—48no—
99C22×C4⋊C4C22×C712yes—
100C22×C4⋊C4C22×C711yescharacteristic
101C22×C4⋊C4C22×C714yes—
102C22×C4⋊C4C22×C711yescharacteristic
103C22×C42C22×C711yescharacteristic
104C22×C42C22×C712yes—
105#384C4×C718yescomplemented
106C2×#95C22×C714yes—
107C2×#95C22×C714yes—
108C2×#95C22×C712yes—
109C2×#95C22×C714yes—
110C2×#95C22×C712yes—
111C2×#95C22×C712yes—
112C2×#95C22×C714yes—
113C2×#95C22×C712yes—
114C23×C7C23×C411yescharacteristic
115C23×C7C22×Q812yes—
116C23×C7C2×#4112yes—
117C23×C7C2×#4112yes—
118C23×C7H(5,𝔽2)11yescharacteristic
119C23×C7H(5,𝔽2)11yescharacteristic
120C23×C7H(5,𝔽2)14yes—
121C23×C72−1+412yes—
122C2×C4×C7—24no—
123C2×C4×C7—22no—
124C2×C4×C7—24no—
125C2×C4×C7—22no—
126C2×C4×C7—24no—
127C2×C4×C7—24no—
128C2×C4×C7—28no—
129C2×C4×C7—28no—
130C2×C4×C7—24no—
131C2×C4×C7—24no—
132C2×C4×C7—28no—
133C2×C4×C7—28no—
134C2×C4×C7—28no—
135C2×C4×C7—28no—
136C2×C4×C7—28no—
137C2×C4×C7—44no—
138C2×C4×C7—44no—
139C2×C4×C7—44no—
140C2×C4×C7—42no—
141C2×C4×C7—44no—
142C2×C4×C7—42no—
143C2×C4×C7—42no—
144C2×C4×C7—44no—
145C2×C4×C7—44no—
146C2×C4×C7—42no—
147C2×C4×C7—44no—
148C2×C4×C7—44no—
149C2×C4×C7—44no—
150C2×C4×C7—44no—
151C2×C4×C7—44no—
152C2×C4×C7—44no—
153C2×C4×C7—44no—
154C2×C4×C7#11714yes—
155C2×C4×C7C4×Q818yes—
156C23×C4C23×C714yes—
157C23×C4C23×C712yes—
158C23×C4C23×C712yes—
159C23×C4C23×C714yes—
160C23×C4C23×C712yes—
161C23×C4C23×C711yescharacteristic
162C2×C4⋊C4—41no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4—41no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—44no—
170C2×C4⋊C4C2×C4×C714yes—
171C2×C4⋊C4C2×C4×C714yes—
172C2×C4⋊C4C2×C4×C7116yes—
173C2×C42—24no—
174C2×C42—44no—
175C2×C42—42no—
176C2×C42C2×C4×C714yes—
177#95—28no—
178#95—28no—
179#95—24no—
180#95—42no—
181#95—44no—
182#95—44no—
183#95—42no—
184#95C7×Q818yes—
185C22×C7C2×#11711yescharacteristic
186C22×C7C2×C4×Q812yes—
187C22×C7#51811yescharacteristic
188C22×C7#51812yes—
189C22×C7#51911yescharacteristic
190C22×C7#53912yes—
191C22×C7#53912yes—
192C22×C7#54214yes—
193C22×C7#54414yes—
194C22×C7#55314yes—
195C22×C7#55414yes—
196C22×C7#55412yes—
197C22×C7#55511yescharacteristic
198C22×C7Q8211yescharacteristic
199C22×C7#56012yes—
200C22×C7#56012yes—
201C4×C7—24no—
202C4×C7—28no—
203C4×C7—44no—
204C4×C7—44no—
205C4×C7—48no—
206C4×C7—84no—
207C24C24×C711yescharacteristic
208C22×C4—24no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—24no—
212C22×C4—22no—
213C22×C4—24no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—24no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—24no—
224C22×C4—22no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—24no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4C22×C4×C714yes—
235C22×C4C22×C4×C714yes—
236C22×C4C22×C4×C712yes—
237C22×C4C22×C4×C714yes—
238C22×C4C2×C7×Q818yes—
239C22×C4C2×C7×Q814yes—
240C22×C4C7×#4114yes—
241C22×C4C7×#4114yes—
242C4⋊C4—44no—
243C4⋊C4—44no—
244C4⋊C4—416no—
245C4⋊C4—48no—
246C42—28no—
247C42—48no—
248C2×C7#231311yescharacteristic
249C2×C7#233112yes—
250C2×C7#234512yes—
251C2×C7#236911yescharacteristic
252C2×C7#238011yescharacteristic
253C2×C7#279014yes—
254C2×C7#279212yes—
255C2×C7#279512yes—
256C23C23×C4×C711yescharacteristic
257C23C22×C7×Q812yes—
258C23C2×C7×#4112yes—
259C23C2×C7×#4112yes—
260C23C7×H(5,𝔽2)11yescharacteristic
261C23C7×H(5,𝔽2)11yescharacteristic
262C23C7×H(5,𝔽2)14yes—
263C23C7×2−1+412yes—
264C2×C4—24no—
265C2×C4—22no—
266C2×C4—24no—
267C2×C4—22no—
268C2×C4—24no—
269C2×C4—24no—
270C2×C4—28no—
271C2×C4—28no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—28no—
275C2×C4—28no—
276C2×C4—28no—
277C2×C4—28no—
278C2×C4—28no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4C7×#11714yes—
297C2×C4C4×C7×Q818yes—
298C7#1445411yescharacteristic, direct product factor, Sylow
299C22C2×C7×#11711yescharacteristic
300C22C2×C4×C7×Q812yes—
301C22C7×#51811yescharacteristic
302C22C7×#51812yes—
303C22C7×#51911yescharacteristic
304C22C7×#53912yes—
305C22C7×#53912yes—
306C22C7×#54214yes—
307C22C7×#54414yes—
308C22C7×#55314yes—
309C22C7×#55412yes—
310C22C7×#55414yes—
311C22C7×#55511yescharacteristic
312C22C7×Q8211yescharacteristic
313C22C7×#56012yes—
314C22C7×#56012yes—
315C4—24no—
316C4—28no—
317C4—48no—
318C4—44no—
319C4—44no—
320C4—84no—
321C2C7×#231311yescharacteristic
322C2C7×#233112yes—
323C2C7×#234512yes—
324C2C7×#236911yescharacteristic
325C2C7×#238011yescharacteristic
326C2C7×#279014yes—
327C2C7×#279212yes—
328C2C7×#279512yes—
subgroupG/H
center, socle, prime radicalC24×C7C24
commutatorC23C23×C4×C7
Frattini, cosocleC24C24×C7
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C7 ◁ G

Complements

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

NH ≅ G/Ntype
13. C7×#384C4semidirect
22. #14454C7direct (N × H)
105. #384C4×C7semidirect
298. C7#14454direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3842
C7×#14412
C7×#14362
C7×#14342
#144547