Finite Group Databasebeta

← C2×C29×#2979 #20355127

Subgroups — C2×C29×#2979 #20355127

Order 7424.

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×C29×#532C211yesmaximal, characteristic
2C29×#2979C2116yesmaximal, direct product factor
3C2×C29×#436C214yesmaximal, complemented
4C2×C8×D4×C29C214yesmaximal, complemented
5C2×C29×#431C212yesmaximal, complemented
6C2×C29×#408C214yesmaximal, complemented
7C22×#41×C29C2212yes—
8C22×M16×C29C2214yes—
9C23×C8×C29C2214yes—
10C29×#532C418yes—
11C29×#532C2218yes—
12C2×C29×C4⋊Q8C411yescharacteristic
13C2×C29×#127C411yescharacteristic
14C2×C29×#124C412yes—
15C2×C29×#121C414yes—
16C2×C4×D4×C29C2214yes—
17C22×C42×C29C2211yescharacteristic
18C29×#436C22132yescomplemented
19C8×D4×C29C22132yescomplemented
20C29×#431C22116yescomplemented
21C2×C29×C4⋊C8C2212yes—
22C2×C29×C4⋊C8C2212yes—
23C29×#408C22132yescomplemented
24C2×C29×C22⋊C8C2218yes—
25C2×C29×C22⋊C8C2214yes—
26C2×C4×C8×C29C2214yes—
27C2×#41×C29—44no—
28C2×#41×C29—44no—
29C2×#41×C29C2×C418yes—
30C2×#41×C29C2318yes—
31C22×Q8×C29C2×C412yes—
32C22×D4×C29C2×C414yes—
33C22×D4×C29C2×C414yes—
34C22×D4×C29C2×C412yes—
35C23×C4×C29C2×C412yes—
36C23×C4×C29C2311yescharacteristic
37C23×C4×C29C2314yes—
38C2×M16×C29—48no—
39C2×M16×C29C23116yes—
40C22×C8×C29—48no—
41C22×C8×C29C2314yes—
42C22×C8×C29C2314yes—
43C22×C8×C29C23116yes—
44C29×C4⋊Q8C2×C418yes—
45C29×#127C2×C418yes—
46C29×#124C2×C4116yes—
47C29×#121C2×C4132yes—
48C4×D4×C29C2×C4116yes—
49C4×D4×C29C23116yes—
50C2×C4⋊C4×C29C2×C414yes—
51C2×C22⋊C4×C29C2×C418yes—
52C2×C42×C29C2×C411yescharacteristic
53C2×C42×C29C2×C411yescharacteristic
54C2×C42×C29C2×C414yes—
55C2×C42×C29C2314yes—
56C2×C42×C29C2312yes—
57C29×C4⋊C8C2318yes—
58C29×C4⋊C8C2318yes—
59C29×C22⋊C8C23116yes—
60C29×C22⋊C8C23132yes—
61C4×C8×C29C23116yes—
62C24×C29C22×C414yes—
63C24×C29C22×C411yescharacteristic
64#41×C29—416no—
65#41×C29—48no—
66#41×C29—48no—
67C2×Q8×C29—44no—
68C2×Q8×C29C22×C418yes—
69C2×D4×C29—216no—
70C2×D4×C29—44no—
71C2×D4×C29—48no—
72C2×D4×C29C22×C4116yes—
73C2×D4×C29C22×C4116yes—
74C2×D4×C29C22×C418yes—
75C22×C4×C29—28no—
76C22×C4×C29—28no—
77C22×C4×C29—28no—
78C22×C4×C29—22no—
79C22×C4×C29—22no—
80C22×C4×C29C22×C411yescharacteristic
81C22×C4×C29C22×C412yes—
82C22×C4×C29C22×C412yes—
83C22×C4×C29C22×C418yes—
84C22×C4×C29C22×C414yes—
85C22×C4×C29C22×C418yes—
86C22×C4×C29C22×C412yes—
87C22×C4×C29C2412yes—
88C22×C4×C29C2418yes—
89C22×C4×C29C2411yescharacteristic
90M16×C29—416no—
91C2×C8×C29—28no—
92C2×C8×C29—28no—
93C2×C8×C29—416no—
94C2×C8×C29C2418yes—
95C2×C8×C29C2418yes—
96C4⋊C4×C29C22×C4116yes—
97C22⋊C4×C29C22×C4132yes—
98C42×C29C22×C414yes—
99C42×C29C22×C414yes—
100C42×C29C22×C414yes—
101C42×C29C2414yes—
102C2×#2979C2911yesmaximal, characteristic, direct product factor, Sylow
103C23×C29—22no—
104C23×C29—28no—
105C23×C29—24no—
106C23×C29—216no—
107C23×C29C23×C418yes—
108C23×C29C23×C412yes—
109C23×C29C23×C411yescharacteristic
110Q8×C29—48no—
111D4×C29—232no—
112D4×C29—48no—
113D4×C29—416no—
114C2×C4×C29—22no—
115C2×C4×C29—28no—
116C2×C4×C29—24no—
117C2×C4×C29—216no—
118C2×C4×C29—24no—
119C2×C4×C29—216no—
120C2×C4×C29—28no—
121C2×C4×C29—28no—
122C2×C4×C29—22no—
123C2×C4×C29—22no—
124C2×C4×C29#13118yes—
125C2×C4×C29C23×C412yes—
126C2×C4×C29C23×C414yes—
127C2×C4×C29C23×C418yes—
128C2×C4×C29C23×C411yescharacteristic
129C2×C4×C29C23×C414yes—
130C2×C4×C29H(5,𝔽2)12yes—
131C2×C4×C29H(5,𝔽2)12yes—
132C2×C4×C29C2511yescharacteristic
133C8×C29—28no—
134C8×C29—28no—
135C2×#532C2×C2911yescharacteristic
136#2979C2×C29116yesdirect product factor
137C2×#436C2×C2914yescomplemented
138C2×C8×D4C2×C2914yescomplemented
139C2×#431C2×C2912yescomplemented
140C2×#408C2×C2914yescomplemented
141C22×C29—22no—
142C22×C29—28no—
143C22×C29—24no—
144C22×C29—216no—
145C22×C29—44no—
146C22×C29—416no—
147C22×C29#51812yes—
148C22×C29C2×#13114yes—
149C22×C29C24×C411yescharacteristic
150C4×C29—22no—
151C4×C29—28no—
152C4×C29—24no—
153C4×C29#51812yes—
154C4×C29C2×#13118yes—
155C4×C29C2×H(5,𝔽2)11yescharacteristic
156C4×C29C2×H(5,𝔽2)11yescharacteristic
157C22×#41C22×C2912yes—
158C22×M16C22×C2914yes—
159C23×C8C22×C2914yes—
160#532C4×C2918yes—
161#532C22×C2918yes—
162C2×C4⋊Q8C4×C2911yescharacteristic
163C2×#127C4×C2911yescharacteristic
164C2×#124C4×C2912yes—
165C2×#121C4×C2914yes—
166C2×C4×D4C22×C2914yes—
167C22×C42C22×C2911yescharacteristic
168#436C22×C29132yescomplemented
169C8×D4C22×C29132yescomplemented
170#431C22×C29116yescomplemented
171C2×C4⋊C8C22×C2912yes—
172C2×C4⋊C8C22×C2912yes—
173#408C22×C29132yescomplemented
174C2×C22⋊C8C22×C2914yes—
175C2×C22⋊C8C22×C2918yes—
176C2×C4×C8C22×C2914yes—
177C2×C29—42no—
178C2×C29—48no—
179C2×C29#297914yesdirect product factor
180C2×C29C2×#51811yescharacteristic
181C2×C29C22×#13112yes—
182C2×#41—44no—
183C2×#41—44no—
184C2×#41C2×C4×C2918yes—
185C2×#41C23×C2918yes—
186C22×Q8C2×C4×C2912yes—
187C22×D4C2×C4×C2914yes—
188C22×D4C2×C4×C2914yes—
189C22×D4C2×C4×C2912yes—
190C23×C4C2×C4×C2912yes—
191C23×C4C23×C2914yes—
192C23×C4C23×C2911yescharacteristic
193C2×M16—48no—
194C2×M16C23×C29116yes—
195C22×C8—48no—
196C22×C8C23×C2914yes—
197C22×C8C23×C2914yes—
198C22×C8C23×C29116yes—
199C4⋊Q8C2×C4×C2918yes—
200#127C2×C4×C2918yes—
201#124C2×C4×C29116yes—
202#121C2×C4×C29132yes—
203C4×D4C2×C4×C29116yes—
204C4×D4C23×C29116yes—
205C2×C4⋊C4C2×C4×C2914yes—
206C2×C22⋊C4C2×C4×C2918yes—
207C2×C42C2×C4×C2911yescharacteristic
208C2×C42C2×C4×C2911yescharacteristic
209C2×C42C2×C4×C2914yes—
210C2×C42C23×C2912yes—
211C2×C42C23×C2914yes—
212C4⋊C8C23×C2918yes—
213C4⋊C8C23×C2918yes—
214C22⋊C8C23×C29116yes—
215C22⋊C8C23×C29132yes—
216C4×C8C23×C29116yes—
217C29C2×#297911yescharacteristic, direct product factor, Sylow
218C24C22×C4×C2914yes—
219C24C22×C4×C2911yescharacteristic
220#41—416no—
221#41—48no—
222#41—48no—
223C2×Q8—44no—
224C2×Q8C22×C4×C2918yes—
225C2×D4—216no—
226C2×D4—44no—
227C2×D4—48no—
228C2×D4C22×C4×C29116yes—
229C2×D4C22×C4×C29116yes—
230C2×D4C22×C4×C2918yes—
231C22×C4—28no—
232C22×C4—28no—
233C22×C4—28no—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4C22×C4×C2911yescharacteristic
237C22×C4C22×C4×C2912yes—
238C22×C4C22×C4×C2912yes—
239C22×C4C22×C4×C2918yes—
240C22×C4C22×C4×C2914yes—
241C22×C4C22×C4×C2918yes—
242C22×C4C22×C4×C2912yes—
243C22×C4C24×C2912yes—
244C22×C4C24×C2918yes—
245C22×C4C24×C2911yescharacteristic
246M16—416no—
247C2×C8—28no—
248C2×C8—28no—
249C2×C8—416no—
250C2×C8C24×C2918yes—
251C2×C8C24×C2918yes—
252C4⋊C4C22×C4×C29116yes—
253C22⋊C4C22×C4×C29132yes—
254C42C22×C4×C2914yes—
255C42C22×C4×C2914yes—
256C42C22×C4×C2914yes—
257C42C24×C2914yes—
258C23—22no—
259C23—28no—
260C23—24no—
261C23—216no—
262C23C23×C4×C2918yes—
263C23C23×C4×C2912yes—
264C23C23×C4×C2911yescharacteristic
265Q8—48no—
266D4—232no—
267D4—48no—
268D4—416no—
269C2×C4—22no—
270C2×C4—28no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—216no—
274C2×C4—216no—
275C2×C4—28no—
276C2×C4—28no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4C29×#13118yes—
280C2×C4C23×C4×C2912yes—
281C2×C4C23×C4×C2914yes—
282C2×C4C23×C4×C2918yes—
283C2×C4C23×C4×C2911yescharacteristic
284C2×C4C23×C4×C2914yes—
285C2×C4C29×H(5,𝔽2)12yes—
286C2×C4C29×H(5,𝔽2)12yes—
287C2×C4C25×C2911yescharacteristic
288C8—28no—
289C8—28no—
290C22—24no—
291C22—216no—
292C22—22no—
293C22—28no—
294C22—44no—
295C22—416no—
296C22C29×#51812yes—
297C22C2×C29×#13114yes—
298C22C24×C4×C2911yescharacteristic
299C4—24no—
300C4—22no—
301C4—28no—
302C4C29×#51812yes—
303C4C2×C29×#13118yes—
304C4C2×C29×H(5,𝔽2)11yescharacteristic
305C4C2×C29×H(5,𝔽2)11yescharacteristic
306C2—42no—
307C2—48no—
308C2C29×#297914yesdirect product factor
309C2C2×C29×#51811yescharacteristic
310C2C22×C29×#13112yes—
subgroupG/H
centerC22×C4×C29C24
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC23×C29C23×C4
prime radicalC2×C29×#532C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2979C2direct (N × H)
3. C2×C29×#436C2semidirect
4. C2×C8×D4×C29C2semidirect
5. C2×C29×#431C2semidirect
6. C2×C29×#408C2semidirect
18. C29×#436C22semidirect
19. C8×D4×C29C22semidirect
20. C29×#431C22semidirect
23. C29×#408C22semidirect
102. C2×#2979C29direct (N × H)
136. #2979C2×C29direct (N × H)
137. C2×#436C2×C29semidirect
138. C2×C8×D4C2×C29semidirect
139. C2×#431C2×C29semidirect
140. C2×#408C2×C29semidirect
168. #436C22×C29semidirect
169. C8×D4C22×C29semidirect
170. #431C22×C29semidirect
173. #408C22×C29semidirect
179. C2×C29#2979direct (N × H)
217. C29C2×#2979direct (N × H)
308. C2C29×#2979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5322
C29×#29792
C2×C29×#4362
C2×C8×D4×C292
C2×C29×#4312
C2×C29×#4082
C2×#297929