Finite Group Databasebeta

← C2×C7×#2979 #13237443

Subgroups — C2×C7×#2979 #13237443

Order 1792.

2274 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C7×#532C211yesmaximal, characteristic
2C7×#2979C2116yesmaximal, direct product factor
3C2×C7×#436C214yesmaximal, complemented
4C2×C7×C8×D4C214yesmaximal, complemented
5C2×C7×#431C212yesmaximal, complemented
6C2×C7×#408C214yesmaximal, complemented
7C22×C7×#41C2212yes—
8C22×C7×M16C2214yes—
9C23×C7×C8C2214yes—
10C7×#532C418yes—
11C7×#532C2218yes—
12C2×C7×C4⋊Q8C411yescharacteristic
13C2×C7×#127C411yescharacteristic
14C2×C7×#124C412yes—
15C2×C7×#121C414yes—
16C2×C4×C7×D4C2214yes—
17C22×C42×C7C2211yescharacteristic
18C7×#436C22132yescomplemented
19C7×C8×D4C22132yescomplemented
20C7×#431C22116yescomplemented
21C2×C7×C4⋊C8C2212yes—
22C2×C7×C4⋊C8C2212yes—
23C7×#408C22132yescomplemented
24C2×C7×C22⋊C8C2214yes—
25C2×C7×C22⋊C8C2218yes—
26C2×C4×C7×C8C2214yes—
27C2×#2979C711yesmaximal, characteristic, direct product factor, Sylow
28C2×C7×#41—44no—
29C2×C7×#41—44no—
30C2×C7×#41C2×C418yes—
31C2×C7×#41C2318yes—
32C22×C7×Q8C2×C412yes—
33C22×C7×D4C2×C414yes—
34C22×C7×D4C2×C414yes—
35C22×C7×D4C2×C412yes—
36C23×C4×C7C2×C412yes—
37C23×C4×C7C2311yescharacteristic
38C23×C4×C7C2314yes—
39C2×C7×M16—48no—
40C2×C7×M16C23116yes—
41C22×C7×C8—48no—
42C22×C7×C8C2314yes—
43C22×C7×C8C2314yes—
44C22×C7×C8C23116yes—
45C7×C4⋊Q8C2×C418yes—
46C7×#127C2×C418yes—
47C7×#124C2×C4116yes—
48C7×#121C2×C4132yes—
49C4×C7×D4C2×C4116yes—
50C4×C7×D4C23116yes—
51C2×C7×C4⋊C4C2×C414yes—
52C2×C7×C22⋊C4C2×C418yes—
53C2×C42×C7C2×C411yescharacteristic
54C2×C42×C7C2×C411yescharacteristic
55C2×C42×C7C2×C414yes—
56C2×C42×C7C2314yes—
57C2×C42×C7C2312yes—
58C7×C4⋊C8C2318yes—
59C7×C4⋊C8C2318yes—
60C7×C22⋊C8C23116yes—
61C7×C22⋊C8C23132yes—
62C4×C7×C8C23116yes—
63C2×#532C2×C711yescharacteristic
64#2979C2×C7116yesdirect product factor
65C2×#436C2×C714yescomplemented
66C2×C8×D4C2×C714yescomplemented
67C2×#431C2×C712yescomplemented
68C2×#408C2×C714yescomplemented
69C24×C7C22×C414yes—
70C24×C7C22×C411yescharacteristic
71C7×#41—416no—
72C7×#41—48no—
73C7×#41—48no—
74C2×C7×Q8—44no—
75C2×C7×Q8C22×C418yes—
76C2×C7×D4—216no—
77C2×C7×D4—44no—
78C2×C7×D4—48no—
79C2×C7×D4C22×C4116yes—
80C2×C7×D4C22×C4116yes—
81C2×C7×D4C22×C418yes—
82C22×C4×C7—28no—
83C22×C4×C7—28no—
84C22×C4×C7—28no—
85C22×C4×C7—22no—
86C22×C4×C7—22no—
87C22×C4×C7C22×C411yescharacteristic
88C22×C4×C7C22×C412yes—
89C22×C4×C7C22×C412yes—
90C22×C4×C7C22×C418yes—
91C22×C4×C7C22×C414yes—
92C22×C4×C7C22×C418yes—
93C22×C4×C7C22×C412yes—
94C22×C4×C7C2412yes—
95C22×C4×C7C2418yes—
96C22×C4×C7C2411yescharacteristic
97C7×M16—416no—
98C2×C7×C8—28no—
99C2×C7×C8—28no—
100C2×C7×C8—416no—
101C2×C7×C8C2418yes—
102C2×C7×C8C2418yes—
103C7×C4⋊C4C22×C4116yes—
104C7×C22⋊C4C22×C4132yes—
105C42×C7C22×C414yes—
106C42×C7C22×C414yes—
107C42×C7C22×C414yes—
108C42×C7C2414yes—
109C22×#41C22×C712yes—
110C22×M16C22×C714yes—
111C23×C8C22×C714yes—
112#532C4×C718yes—
113#532C22×C718yes—
114C2×C4⋊Q8C4×C711yescharacteristic
115C2×#127C4×C711yescharacteristic
116C2×#124C4×C712yes—
117C2×#121C4×C714yes—
118C2×C4×D4C22×C714yes—
119C22×C42C22×C711yescharacteristic
120#436C22×C7132yescomplemented
121C8×D4C22×C7132yescomplemented
122#431C22×C7116yescomplemented
123C2×C4⋊C8C22×C712yes—
124C2×C4⋊C8C22×C712yes—
125#408C22×C7132yescomplemented
126C2×C22⋊C8C22×C714yes—
127C2×C22⋊C8C22×C718yes—
128C2×C4×C8C22×C714yes—
129C23×C7—22no—
130C23×C7—28no—
131C23×C7—24no—
132C23×C7—216no—
133C23×C7C23×C418yes—
134C23×C7C23×C412yes—
135C23×C7C23×C411yescharacteristic
136C7×Q8—48no—
137C7×D4—232no—
138C7×D4—48no—
139C7×D4—416no—
140C2×C4×C7—22no—
141C2×C4×C7—28no—
142C2×C4×C7—24no—
143C2×C4×C7—216no—
144C2×C4×C7—24no—
145C2×C4×C7—216no—
146C2×C4×C7—28no—
147C2×C4×C7—28no—
148C2×C4×C7—22no—
149C2×C4×C7—22no—
150C2×C4×C7#13118yes—
151C2×C4×C7C23×C412yes—
152C2×C4×C7C23×C414yes—
153C2×C4×C7C23×C418yes—
154C2×C4×C7C23×C411yescharacteristic
155C2×C4×C7C23×C414yes—
156C2×C4×C7H(5,𝔽2)12yes—
157C2×C4×C7H(5,𝔽2)12yes—
158C2×C4×C7C2511yescharacteristic
159C7×C8—28no—
160C7×C8—28no—
161C2×#41—44no—
162C2×#41—44no—
163C2×#41C2×C4×C718yes—
164C2×#41C23×C718yes—
165C22×Q8C2×C4×C712yes—
166C22×D4C2×C4×C714yes—
167C22×D4C2×C4×C714yes—
168C22×D4C2×C4×C712yes—
169C23×C4C2×C4×C712yes—
170C23×C4C23×C714yes—
171C23×C4C23×C711yescharacteristic
172C2×M16—48no—
173C2×M16C23×C7116yes—
174C22×C8—48no—
175C22×C8C23×C714yes—
176C22×C8C23×C714yes—
177C22×C8C23×C7116yes—
178C4⋊Q8C2×C4×C718yes—
179#127C2×C4×C718yes—
180#124C2×C4×C7116yes—
181#121C2×C4×C7132yes—
182C4×D4C2×C4×C7116yes—
183C4×D4C23×C7116yes—
184C2×C4⋊C4C2×C4×C714yes—
185C2×C22⋊C4C2×C4×C718yes—
186C2×C42C2×C4×C711yescharacteristic
187C2×C42C2×C4×C711yescharacteristic
188C2×C42C2×C4×C714yes—
189C2×C42C23×C712yes—
190C2×C42C23×C714yes—
191C4⋊C8C23×C718yes—
192C4⋊C8C23×C718yes—
193C22⋊C8C23×C7116yes—
194C22⋊C8C23×C7132yes—
195C4×C8C23×C7116yes—
196C22×C7—22no—
197C22×C7—28no—
198C22×C7—24no—
199C22×C7—216no—
200C22×C7—44no—
201C22×C7—416no—
202C22×C7#51812yes—
203C22×C7C2×#13114yes—
204C22×C7C24×C411yescharacteristic
205C4×C7—22no—
206C4×C7—28no—
207C4×C7—24no—
208C4×C7#51812yes—
209C4×C7C2×#13118yes—
210C4×C7C2×H(5,𝔽2)11yescharacteristic
211C4×C7C2×H(5,𝔽2)11yescharacteristic
212C24C22×C4×C714yes—
213C24C22×C4×C711yescharacteristic
214#41—416no—
215#41—48no—
216#41—48no—
217C2×Q8—44no—
218C2×Q8C22×C4×C718yes—
219C2×D4—216no—
220C2×D4—44no—
221C2×D4—48no—
222C2×D4C22×C4×C7116yes—
223C2×D4C22×C4×C7116yes—
224C2×D4C22×C4×C718yes—
225C22×C4—28no—
226C22×C4—28no—
227C22×C4—28no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4C22×C4×C711yescharacteristic
231C22×C4C22×C4×C712yes—
232C22×C4C22×C4×C712yes—
233C22×C4C22×C4×C718yes—
234C22×C4C22×C4×C714yes—
235C22×C4C22×C4×C718yes—
236C22×C4C22×C4×C712yes—
237C22×C4C24×C712yes—
238C22×C4C24×C718yes—
239C22×C4C24×C711yescharacteristic
240M16—416no—
241C2×C8—28no—
242C2×C8—28no—
243C2×C8—416no—
244C2×C8C24×C718yes—
245C2×C8C24×C718yes—
246C4⋊C4C22×C4×C7116yes—
247C22⋊C4C22×C4×C7132yes—
248C42C22×C4×C714yes—
249C42C22×C4×C714yes—
250C42C22×C4×C714yes—
251C42C24×C714yes—
252C2×C7—42no—
253C2×C7—48no—
254C2×C7#297914yesdirect product factor
255C2×C7C2×#51811yescharacteristic
256C2×C7C22×#13112yes—
257C23—22no—
258C23—28no—
259C23—24no—
260C23—216no—
261C23C23×C4×C718yes—
262C23C23×C4×C712yes—
263C23C23×C4×C711yescharacteristic
264Q8—48no—
265D4—232no—
266D4—48no—
267D4—416no—
268C2×C4—22no—
269C2×C4—28no—
270C2×C4—24no—
271C2×C4—28no—
272C2×C4—28no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—216no—
276C2×C4—24no—
277C2×C4—216no—
278C2×C4C7×#13118yes—
279C2×C4C23×C4×C712yes—
280C2×C4C23×C4×C714yes—
281C2×C4C23×C4×C718yes—
282C2×C4C23×C4×C711yescharacteristic
283C2×C4C23×C4×C714yes—
284C2×C4C7×H(5,𝔽2)12yes—
285C2×C4C7×H(5,𝔽2)12yes—
286C2×C4C25×C711yescharacteristic
287C8—28no—
288C8—28no—
289C7C2×#297911yescharacteristic, direct product factor, Sylow
290C22—24no—
291C22—216no—
292C22—22no—
293C22—28no—
294C22—44no—
295C22—416no—
296C22C7×#51812yes—
297C22C2×C7×#13114yes—
298C22C24×C4×C711yescharacteristic
299C4—24no—
300C4—22no—
301C4—28no—
302C4C7×#51812yes—
303C4C2×C7×#13118yes—
304C4C2×C7×H(5,𝔽2)11yescharacteristic
305C4C2×C7×H(5,𝔽2)11yescharacteristic
306C2—42no—
307C2—48no—
308C2C7×#297914yesdirect product factor
309C2C2×C7×#51811yescharacteristic
310C2C22×C7×#13112yes—
subgroupG/H
centerC22×C4×C7C24
commutatorC22C24×C4×C7
Frattini, cosocleC2×C4C25×C7
socleC23×C7C23×C4
prime radicalC2×C7×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C7 ◁ G

Complements

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

NH ≅ G/Ntype
2. C7×#2979C2direct (N × H)
3. C2×C7×#436C2semidirect
4. C2×C7×C8×D4C2semidirect
5. C2×C7×#431C2semidirect
6. C2×C7×#408C2semidirect
18. C7×#436C22semidirect
19. C7×C8×D4C22semidirect
20. C7×#431C22semidirect
23. C7×#408C22semidirect
27. C2×#2979C7direct (N × H)
64. #2979C2×C7direct (N × H)
65. C2×#436C2×C7semidirect
66. C2×C8×D4C2×C7semidirect
67. C2×#431C2×C7semidirect
68. C2×#408C2×C7semidirect
120. #436C22×C7semidirect
121. C8×D4C22×C7semidirect
122. #431C22×C7semidirect
125. #408C22×C7semidirect
254. C2×C7#2979direct (N × H)
289. C7C2×#2979direct (N × H)
308. C2C7×#2979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C7×#5322
C7×#29792
C2×C7×#4362
C2×C7×C8×D42
C2×C7×#4312
C2×C7×#4082
C2×#29797