Finite Group Databasebeta

← C7×#14424 #13191640

Subgroups — C7×#14424 #13191640

Order 1792.

1302 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#387C214yesmaximal
2C2×C7×#384C211yesmaximal, characteristic
3C7×#1445C214yesmaximal
4C7×#1441C212yesmaximal
5C7×#1436C212yesmaximal
6C7×#1434C212yesmaximal
7C22×C7×C4⋊C4C2212yes—
8C22×C7×C4⋊C4C2214yes—
9C22×C7×C4⋊C4C2211yescharacteristic
10C22×C7×C4⋊C4C2211yescharacteristic
11C22×C42×C7C2212yes—
12C22×C42×C7C2211yescharacteristic
13C7×#387—216no—
14C7×#384C418yescomplemented
15C2×C7×#95C2214yes—
16C2×C7×#95C2214yes—
17C2×C7×#95C2214yes—
18C2×C7×#95C2214yes—
19C2×C7×#95C2212yes—
20C2×C7×#95C2212yes—
21C2×C7×#95C2212yes—
22C2×C7×#95C2212yes—
23#14424C711yesmaximal, characteristic, direct product factor, Sylow
24C23×C4×C7C2314yes—
25C23×C4×C7C2312yes—
26C23×C4×C7C2312yes—
27C23×C4×C7C2314yes—
28C23×C4×C7C2312yes—
29C23×C4×C7C2311yescharacteristic
30C2×C7×C4⋊C4—28no—
31C2×C7×C4⋊C4—28no—
32C2×C7×C4⋊C4—28no—
33C2×C7×C4⋊C4—41no—
34C2×C7×C4⋊C4—41no—
35C2×C7×C4⋊C4—41no—
36C2×C7×C4⋊C4—41no—
37C2×C7×C4⋊C4—42no—
38C2×C7×C4⋊C4C2×C4116yes—
39C2×C7×C4⋊C4C2×C414yes—
40C2×C7×C4⋊C4C2×C414yes—
41C2×C42×C7—24no—
42C2×C42×C7—28no—
43C2×C42×C7—42no—
44C2×C42×C7C2×C414yes—
45C7×#95—28no—
46C7×#95—28no—
47C7×#95—28no—
48C7×#95—28no—
49C7×#95—24no—
50C7×#95—42no—
51C7×#95—42no—
52C7×#95D418yes—
53C2×#387C2×C714yes—
54C2×#384C2×C711yescharacteristic
55#1445C2×C714yes—
56#1441C2×C712yes—
57#1436C2×C712yes—
58#1434C2×C712yes—
59C24×C7C2411yescharacteristic
60C22×C4×C7—24no—
61C22×C4×C7—21no—
62C22×C4×C7—21no—
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—24no—
70C22×C4×C7—24no—
71C22×C4×C7—22no—
72C22×C4×C7—22no—
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×C7—24no—
86C22×C4×C7C22×C414yes—
87C22×C4×C7C22×C414yes—
88C22×C4×C7C22×C412yes—
89C22×C4×C7C22×C414yes—
90C22×C4×C7C2×D418yes—
91C22×C4×C7C2×D414yes—
92C22×C4×C7#4114yes—
93C22×C4×C7#4114yes—
94C7×C4⋊C4—232no—
95C7×C4⋊C4—44no—
96C7×C4⋊C4—44no—
97C7×C4⋊C4—48no—
98C42×C7—28no—
99C42×C7—48no—
100C22×C4⋊C4C22×C712yes—
101C22×C4⋊C4C22×C714yes—
102C22×C4⋊C4C22×C711yescharacteristic
103C22×C4⋊C4C22×C711yescharacteristic
104C22×C42C22×C712yes—
105C22×C42C22×C711yescharacteristic
106#387—216no—
107#384C4×C718yescomplemented
108C2×#95C22×C714yes—
109C2×#95C22×C712yes—
110C2×#95C22×C714yes—
111C2×#95C22×C714yes—
112C2×#95C22×C714yes—
113C2×#95C22×C712yes—
114C2×#95C22×C712yes—
115C2×#95C22×C712yes—
116C23×C7C23×C411yescharacteristic
117C23×C7C22×D412yes—
118C23×C7C2×#4112yes—
119C23×C7C2×#4112yes—
120C23×C7H(5,𝔽2)11yescharacteristic
121C23×C7H(5,𝔽2)11yescharacteristic
122C23×C72−1+412yes—
123C23×C72−1+414yes—
124C2×C4×C7—24no—
125C2×C4×C7—22no—
126C2×C4×C7—22no—
127C2×C4×C7—24no—
128C2×C4×C7—24no—
129C2×C4×C7—24no—
130C2×C4×C7—28no—
131C2×C4×C7—28no—
132C2×C4×C7—28no—
133C2×C4×C7—28no—
134C2×C4×C7—24no—
135C2×C4×C7—24no—
136C2×C4×C7—28no—
137C2×C4×C7—28no—
138C2×C4×C7—28no—
139C2×C4×C7—44no—
140C2×C4×C7—44no—
141C2×C4×C7—42no—
142C2×C4×C7—42no—
143C2×C4×C7—44no—
144C2×C4×C7—44no—
145C2×C4×C7—44no—
146C2×C4×C7—42no—
147C2×C4×C7—42no—
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—44no—
155C2×C4×C7—44no—
156C2×C4×C7#11714yes—
157C2×C4×C7C4×D418yes—
158C23×C4C23×C714yes—
159C23×C4C23×C712yes—
160C23×C4C23×C712yes—
161C23×C4C23×C714yes—
162C23×C4C23×C712yes—
163C23×C4C23×C711yescharacteristic
164C2×C4⋊C4—28no—
165C2×C4⋊C4—28no—
166C2×C4⋊C4—28no—
167C2×C4⋊C4—41no—
168C2×C4⋊C4—41no—
169C2×C4⋊C4—41no—
170C2×C4⋊C4—41no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4C2×C4×C7116yes—
173C2×C4⋊C4C2×C4×C714yes—
174C2×C4⋊C4C2×C4×C714yes—
175C2×C42—24no—
176C2×C42—28no—
177C2×C42—42no—
178C2×C42C2×C4×C714yes—
179#95—28no—
180#95—28no—
181#95—28no—
182#95—28no—
183#95—24no—
184#95—42no—
185#95—42no—
186#95C7×D418yes—
187C22×C7C2×#11711yescharacteristic
188C22×C7C2×C4×D412yes—
189C22×C7#51811yescharacteristic
190C22×C7#51911yescharacteristic
191C22×C7#51912yes—
192C22×C7#53614yes—
193C22×C7#53912yes—
194C22×C7#53912yes—
195C22×C7#54114yes—
196C22×C7D4211yescharacteristic
197C22×C7#54714yes—
198C22×C7#55012yes—
199C22×C7#55214yes—
200C22×C7#55911yescharacteristic
201C22×C7#56312yes—
202C22×C7#56312yes—
203C4×C7—24no—
204C4×C7—28no—
205C4×C7—44no—
206C4×C7—44no—
207C4×C7—48no—
208C4×C7—84no—
209C24C24×C711yescharacteristic
210C22×C4—24no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—24no—
219C22×C4—24no—
220C22×C4—24no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—24no—
225C22×C4—22no—
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×C4—24no—
235C22×C4—24no—
236C22×C4C22×C4×C714yes—
237C22×C4C22×C4×C714yes—
238C22×C4C22×C4×C712yes—
239C22×C4C22×C4×C714yes—
240C22×C4C2×C7×D418yes—
241C22×C4C2×C7×D414yes—
242C22×C4C7×#4114yes—
243C22×C4C7×#4114yes—
244C4⋊C4—232no—
245C4⋊C4—44no—
246C4⋊C4—44no—
247C4⋊C4—48no—
248C42—28no—
249C42—48no—
250C2×C7#231311yescharacteristic
251C2×C7#232712yes—
252C2×C7#234412yes—
253C2×C7#236611yescharacteristic
254C2×C7#238111yescharacteristic
255C2×C7#268012yes—
256C2×C7#272114yes—
257C2×C7#279412yes—
258C23C23×C4×C711yescharacteristic
259C23C22×C7×D412yes—
260C23C2×C7×#4112yes—
261C23C2×C7×#4112yes—
262C23C7×H(5,𝔽2)11yescharacteristic
263C23C7×H(5,𝔽2)11yescharacteristic
264C23C7×2−1+412yes—
265C23C7×2−1+414yes—
266C2×C4—24no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—28no—
273C2×C4—28no—
274C2×C4—28no—
275C2×C4—28no—
276C2×C4—24no—
277C2×C4—24no—
278C2×C4—28no—
279C2×C4—28no—
280C2×C4—28no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4C7×#11714yes—
299C2×C4C4×C7×D418yes—
300C7#1442411yescharacteristic, direct product factor, Sylow
301C22C2×C7×#11711yescharacteristic
302C22C2×C4×C7×D412yes—
303C22C7×#51811yescharacteristic
304C22C7×#51911yescharacteristic
305C22C7×#51912yes—
306C22C7×#53614yes—
307C22C7×#53912yes—
308C22C7×#53912yes—
309C22C7×#54114yes—
310C22C7×D4211yescharacteristic
311C22C7×#54714yes—
312C22C7×#55012yes—
313C22C7×#55214yes—
314C22C7×#55911yescharacteristic
315C22C7×#56312yes—
316C22C7×#56312yes—
317C4—24no—
318C4—28no—
319C4—48no—
320C4—44no—
321C4—44no—
322C4—84no—
323C2C7×#231311yescharacteristic
324C2C7×#232712yes—
325C2C7×#234412yes—
326C2C7×#236611yescharacteristic
327C2C7×#238111yescharacteristic
328C2C7×#268012yes—
329C2C7×#272114yes—
330C2C7×#279412yes—
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
14. C7×#384C4semidirect
23. #14424C7direct (N × H)
107. #384C4×C7semidirect
300. C7#14424direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#3872
C2×C7×#3842
C7×#14452
C7×#14412
C7×#14362
C7×#14342
#144247