Finite Group Databasebeta

← C29×#34187 #20329087

Subgroups — C29×#34187 #20329087

Order 7424.

2250 conjugacy classes of subgroups.

The subgroup lattice has 294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C29C211yesmaximal, characteristic
2C29×#2356C218yesmaximal, complemented
3C29×#2355C218yesmaximal, complemented
4C29×#2313C214yesmaximal
5C29×#2310C212yesmaximal
6C29×#2285C212yesmaximal
7C29×#2283C214yesmaximal
8C29×#2274C212yesmaximal
9C23×Q8×C29C2211yescharacteristic
10C2×C4×Q8×C29C4116yescomplemented
11C2×C4×Q8×C29C2214yes—
12C2×C4×Q8×C29C2214yes—
13C2×C29×#117C2214yes—
14C22×C4⋊C4×C29C2211yescharacteristic
15C22×C4⋊C4×C29C2212yes—
16C22×C42×C29C2212yes—
17C22×C42×C29C2211yescharacteristic
18C29×#391C22116yes—
19C29×#387C22132yes—
20C29×#384C2214yes—
21C29×#383C2218yes—
22C29×#382C2218yes—
23C29×#382C2214yes—
24C29×#381C2218yes—
25C29×#380C2214yes—
26C29×#380C2214yes—
27C4×C4⋊C4×C29C22116yes—
28C4×C4⋊C4×C29C2218yes—
29C4×C4⋊C4×C29C2214yes—
30C4×C4⋊C4×C29C2214yes—
31C4×C22⋊C4×C29C2218yes—
32C29×#376C2218yes—
33C22×Q8×C29—28no—
34C22×Q8×C29C2×C418yes—
35C22×Q8×C29C2314yes—
36C23×C4×C29C2311yescharacteristic
37C23×C4×C29C2312yes—
38C23×C4×C29C2312yes—
39C23×C4×C29C2311yescharacteristic
40C23×C4×C29C2311yescharacteristic
41C4×Q8×C29C2×C4132yes—
42C4×Q8×C29C2×C4132yes—
43C29×#117—216no—
44C2×C4⋊C4×C29C2×C4116yes—
45C2×C4⋊C4×C29C2×C418yes—
46C2×C4⋊C4×C29C2318yes—
47C2×C4⋊C4×C29C2318yes—
48C2×C4⋊C4×C29C2318yes—
49C2×C4⋊C4×C29C2314yes—
50C2×C4⋊C4×C29C2318yes—
51C2×C22⋊C4×C29C2318yes—
52C2×C42×C29C2×C4116yes—
53C2×C42×C29C2×C418yes—
54C2×C42×C29C2318yes—
55C2×C42×C29C23116yes—
56C2×C42×C29C2314yes—
57C2×C42×C29C2314yes—
58C2×C42×C29C2312yes—
59C2×C42×C29C2312yes—
60C29×#95C2318yes—
61C29×#95C23116yes—
62C29×#95C23116yes—
63C29×#95C2318yes—
64C29×#95C23116yes—
65C24×C29C2411yescharacteristic
66C2×Q8×C29—232no—
67C2×Q8×C29—28no—
68C2×Q8×C29—28no—
69C2×Q8×C29C22×C4116yes—
70C22×C4×C29—28no—
71C22×C4×C29—24no—
72C22×C4×C29—44no—
73C22×C4×C29—42no—
74C22×C4×C29C22×C414yes—
75C22×C4×C29C22×C418yes—
76C22×C4×C29C22×C418yes—
77C22×C4×C29C22×C414yes—
78C22×C4×C29C22×C414yes—
79C22×C4×C29#4118yes—
80C22×C4×C29C24116yes—
81C22×C4×C29C2414yes—
82C22×C4×C29C2411yescharacteristic
83C22×C4×C29C2412yes—
84C22×C4×C29C2414yes—
85C22×C4×C29C2412yes—
86C22×C4×C29C2411yescharacteristic
87C4⋊C4×C29—216no—
88C4⋊C4×C29—216no—
89C4⋊C4×C29—48no—
90C4⋊C4×C29C22×C4132yes—
91C4⋊C4×C29C22×C4116yes—
92C22⋊C4×C29—216no—
93C42×C29—216no—
94C42×C29—416no—
95C42×C29C22×C4116yes—
96C42×C29C22×C418yes—
97C42×C29C22×C4116yes—
98C42×C29C22×C418yes—
99#34187C2911yesmaximal, characteristic, direct product factor, Sylow
100C23×C29—22no—
101C23×C29—22no—
102C23×C29C23×C412yes—
103C23×C29C2×#4114yes—
104C23×C29C2511yescharacteristic
105Q8×C29—232no—
106C2×C4×C29—216no—
107C2×C4×C29—28no—
108C2×C4×C29—22no—
109C2×C4×C29—28no—
110C2×C4×C29—24no—
111C2×C4×C29—28no—
112C2×C4×C29—216no—
113C2×C4×C29—216no—
114C2×C4×C29—216no—
115C2×C4×C29—48no—
116C2×C4×C29—44no—
117C2×C4×C29#117116yes—
118C2×C4×C29C23×C412yes—
119C2×C4×C29C23×C418yes—
120C2×C4×C29C23×C414yes—
121C2×C4×C29C23×C418yes—
122C2×C4×C29C23×C414yes—
123C2×C4×C29C23×C412yes—
124C2×C4×C29C2×#4114yes—
125C2×C4×C29C2×#4114yes—
126C2×C4×C292−1+414yes—
127C22×C4×Q8C2×C2911yescharacteristic
128#2356C2×C2918yescomplemented
129#2355C2×C2918yescomplemented
130#2313C2×C2914yes—
131#2310C2×C2912yes—
132#2285C2×C2912yes—
133#2283C2×C2914yes—
134#2274C2×C2912yes—
135C22×C29—22no—
136C22×C29—22no—
137C22×C29—28no—
138C22×C29C2×#11714yes—
139C22×C29C24×C411yescharacteristic
140C22×C29C22×#4112yes—
141C22×C29C2×2−1+412yes—
142C22×C29#58512yes—
143C4×C29—28no—
144C4×C29—22no—
145C4×C29—28no—
146C4×C29—24no—
147C4×C29—416no—
148C4×C29C2×#11718yes—
149C4×C29#51914yes—
150C23×Q8C22×C2911yescharacteristic
151C2×C4×Q8C4×C29116yescomplemented
152C2×C4×Q8C22×C2914yes—
153C2×C4×Q8C22×C2914yes—
154C2×#117C22×C2914yes—
155C22×C4⋊C4C22×C2912yes—
156C22×C4⋊C4C22×C2911yescharacteristic
157C22×C42C22×C2912yes—
158C22×C42C22×C2911yescharacteristic
159#391C22×C29116yes—
160#387C22×C29132yes—
161#384C22×C2914yes—
162#383C22×C2918yes—
163#382C22×C2918yes—
164#382C22×C2914yes—
165#381C22×C2918yes—
166#380C22×C2914yes—
167#380C22×C2914yes—
168C4×C4⋊C4C22×C2918yes—
169C4×C4⋊C4C22×C2914yes—
170C4×C4⋊C4C22×C29116yes—
171C4×C4⋊C4C22×C2914yes—
172C4×C22⋊C4C22×C2918yes—
173#376C22×C2918yes—
174C2×C29—24no—
175C2×C29C22×#11711yescharacteristic
176C2×C29C2×#51911yescharacteristic
177C2×C29#342811yescharacteristic
178C2×C29#350714yes—
179C22×Q8—28no—
180C22×Q8C2×C4×C2918yes—
181C22×Q8C23×C2914yes—
182C23×C4C23×C2912yes—
183C23×C4C23×C2911yescharacteristic
184C23×C4C23×C2912yes—
185C23×C4C23×C2911yescharacteristic
186C23×C4C23×C2911yescharacteristic
187C4×Q8C2×C4×C29132yes—
188C4×Q8C2×C4×C29132yes—
189#117—216no—
190C2×C4⋊C4C2×C4×C29116yes—
191C2×C4⋊C4C2×C4×C2918yes—
192C2×C4⋊C4C23×C2918yes—
193C2×C4⋊C4C23×C2918yes—
194C2×C4⋊C4C23×C2918yes—
195C2×C4⋊C4C23×C2914yes—
196C2×C4⋊C4C23×C2918yes—
197C2×C22⋊C4C23×C2918yes—
198C2×C42C2×C4×C29116yes—
199C2×C42C2×C4×C2918yes—
200C2×C42C23×C2918yes—
201C2×C42C23×C29116yes—
202C2×C42C23×C2914yes—
203C2×C42C23×C2912yes—
204C2×C42C23×C2914yes—
205C2×C42C23×C2912yes—
206#95C23×C2918yes—
207#95C23×C29116yes—
208#95C23×C29116yes—
209#95C23×C2918yes—
210#95C23×C29116yes—
211C29#3418711yescharacteristic, direct product factor, Sylow
212C24C24×C2911yescharacteristic
213C2×Q8—232no—
214C2×Q8—28no—
215C2×Q8—28no—
216C2×Q8C22×C4×C29116yes—
217C22×C4—28no—
218C22×C4—24no—
219C22×C4—44no—
220C22×C4—42no—
221C22×C4C22×C4×C2914yes—
222C22×C4C22×C4×C2918yes—
223C22×C4C22×C4×C2918yes—
224C22×C4C22×C4×C2914yes—
225C22×C4C22×C4×C2914yes—
226C22×C4#41×C2918yes—
227C22×C4C24×C29116yes—
228C22×C4C24×C2911yescharacteristic
229C22×C4C24×C2914yes—
230C22×C4C24×C2914yes—
231C22×C4C24×C2912yes—
232C22×C4C24×C2912yes—
233C22×C4C24×C2911yescharacteristic
234C4⋊C4—216no—
235C4⋊C4—216no—
236C4⋊C4—48no—
237C4⋊C4C22×C4×C29132yes—
238C4⋊C4C22×C4×C29116yes—
239C22⋊C4—216no—
240C42—216no—
241C42—416no—
242C42C22×C4×C29116yes—
243C42C22×C4×C2918yes—
244C42C22×C4×C29116yes—
245C42C22×C4×C2918yes—
246C23—22no—
247C23—22no—
248C23C23×C4×C2912yes—
249C23C2×#41×C2914yes—
250C23C25×C2911yescharacteristic
251Q8—232no—
252C2×C4—216no—
253C2×C4—28no—
254C2×C4—22no—
255C2×C4—28no—
256C2×C4—24no—
257C2×C4—28no—
258C2×C4—216no—
259C2×C4—216no—
260C2×C4—216no—
261C2×C4—48no—
262C2×C4—44no—
263C2×C4C29×#117116yes—
264C2×C4C23×C4×C2912yes—
265C2×C4C23×C4×C2918yes—
266C2×C4C23×C4×C2914yes—
267C2×C4C23×C4×C2918yes—
268C2×C4C23×C4×C2914yes—
269C2×C4C23×C4×C2912yes—
270C2×C4C2×#41×C2914yes—
271C2×C4C2×#41×C2914yes—
272C2×C4C29×2−1+414yes—
273C22—28no—
274C22—22no—
275C22—22no—
276C22C2×C29×#11714yes—
277C22C24×C4×C2911yescharacteristic
278C22C22×#41×C2912yes—
279C22C2×C29×2−1+412yes—
280C22C29×#58512yes—
281C4—28no—
282C4—22no—
283C4—28no—
284C4—24no—
285C4—416no—
286C4C2×C29×#11718yes—
287C4C29×#51914yes—
288C2—24no—
289C2C22×C29×#11711yescharacteristic
290C2C2×C29×#51911yescharacteristic
291C2C29×#342811yescharacteristic
292C2C29×#350714yes—
subgroupG/H
center, socleC23×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC23C25×C29
prime radicalC24×C29C24
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2356C2semidirect
3. C29×#2355C2semidirect
10. C2×C4×Q8×C29C4semidirect
99. #34187C29direct (N × H)
128. #2356C2×C29semidirect
129. #2355C2×C29semidirect
151. C2×C4×Q8C4×C29semidirect
211. C29#34187direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C292
C29×#23562
C29×#23552
C29×#23132
C29×#23102
C29×#22852
C29×#22832
C29×#22742
#3418729