Finite Group Databasebeta

← C29×#8476 #20303376

Subgroups — C29×#8476 #20303376

Order 7424.

678 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 678 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3512C211yesmaximal, characteristic
2C29×#1543C211yesmaximal, characteristic, complemented
3C29×#1536C211yesmaximal, characteristic, complemented
4C29×#1488C212yesmaximal, complemented
5C29×#1470C212yesmaximal, complemented
6C29×#553—22no—
7C29×#553—24no—
8C29×#552—22no—
9C29×#541—21no—
10C29×#540—21no—
11C29×#537C412yes—
12C29×#532C2211yescharacteristic
13C29×#529—22no—
14C2×C29×#125C2211yescharacteristic
15C29×#520C412yes—
16C4×#41×C29C2211yescharacteristic
17C29×#432C2212yes—
18C29×#431C2212yes—
19C29×#333—21no—
20C29×#331—21no—
21C29×#329—22no—
22C29×Q8⋊C8—22no—
23C29×D4⋊C8—22no—
24C29×#324—24no—
25C2×#41×C29C2×C411yescharacteristic
26C2×#41×C29C2×C412yes—
27C29×C4⋊Q8D411yescharacteristic
28C29×#127D411yescharacteristic
29C29×#126—24no—
30C29×#126—24no—
31C29×#125—24no—
32C29×#125—21no—
33C29×#125—21no—
34C29×#125—22no—
35C29×#124D412yes—
36C29×#123—24no—
37C29×#123—24no—
38C29×C22⋊Q8—22no—
39C29×C22⋊Q8—22no—
40C29×#121—24no—
41C29×#121—22no—
42C29×#121—22no—
43C29×#121—24no—
44C29×#121—22no—
45C4×Q8×C29—22no—
46C4×Q8×C29D412yes—
47C4×D4×C29—24no—
48C4×D4×C29—22no—
49C4×D4×C29—24no—
50C4×D4×C29—22no—
51C4×D4×C29—22no—
52C4×D4×C29D412yes—
53C29×#117—24no—
54C29×#117—22no—
55C29×#117—21no—
56C29×#117C2×C411yescharacteristic
57C2×C4⋊C4×C29—22no—
58C2×C4⋊C4×C29C2×C412yes—
59C2×C4⋊C4×C29D414yes—
60C2×C42×C29—21no—
61C2×C42×C29C2311yescharacteristic
62C29×C4⋊C8—22no—
63C29×C4⋊C8—22no—
64C29×C22⋊C8—22no—
65C29×C22⋊C8—22no—
66C29×#97—22no—
67C4×C8×C29—22no—
68#41×C29—42no—
69#41×C29—44no—
70C2×Q8×C29C22⋊C411yescharacteristic
71C2×Q8×C29C22⋊C412yes—
72C2×D4×C29—22no—
73C2×D4×C29—21no—
74C2×D4×C29—24no—
75C2×D4×C29—22no—
76C2×D4×C29C22⋊C411yescharacteristic
77C2×D4×C29C22⋊C412yes—
78C22×C4×C29—24no—
79C22×C4×C29—21no—
80C22×C4×C29—22no—
81C22×C4×C29—22no—
82C22×C4×C29C22⋊C414yes—
83C22×C4×C29C22×C411yescharacteristic
84C22×C4×C29C2×D412yes—
85C2×C8×C29—42no—
86C2×C8×C29—42no—
87C4⋊C4×C29—24no—
88C4⋊C4×C29—24no—
89C4⋊C4×C29—22no—
90C4⋊C4×C29—22no—
91C4⋊C4×C29—24no—
92C4⋊C4×C29—24no—
93C4⋊C4×C29—22no—
94C4⋊C4×C29—22no—
95C4⋊C4×C29C22⋊C412yes—
96C22⋊C4×C29—24no—
97C22⋊C4×C29—24no—
98C22⋊C4×C29—24no—
99C22⋊C4×C29—21no—
100C22⋊C4×C29—22no—
101C22⋊C4×C29—22no—
102C22⋊C4×C29—22no—
103C42×C29—24no—
104C42×C29—21no—
105C42×C29—22no—
106C42×C29C2×D411yescharacteristic
107C42×C29C2×D411yescharacteristic
108C42×C29C2×D412yes—
109#8476C2911yesmaximal, characteristic, direct product factor, Sylow
110C23×C29—22no—
111C23×C29—21no—
112C23×C29C2×C22⋊C411yescharacteristic
113Q8×C29—22no—
114Q8×C29—42no—
115D4×C29—22no—
116D4×C29—42no—
117D4×C29—42no—
118D4×C29—44no—
119D4×C29—82no—
120D4×C29—84no—
121C2×C4×C29—22no—
122C2×C4×C29—22no—
123C2×C4×C29—21no—
124C2×C4×C29—22no—
125C2×C4×C29—24no—
126C2×C4×C29—42no—
127C2×C4×C29—42no—
128C2×C4×C29—44no—
129C2×C4×C29—44no—
130C2×C4×C29—82no—
131C2×C4×C29—84no—
132C2×C4×C29C2×C22⋊C411yescharacteristic
133C2×C4×C29C2×C22⋊C411yescharacteristic
134C2×C4×C29#12012yes—
135C2×C4×C29#12012yes—
136C8×C29—82no—
137C8×C29—82no—
138#3512C2×C2911yescharacteristic
139#1543C2×C2911yescharacteristic, complemented
140#1536C2×C2911yescharacteristic, complemented
141#1488C2×C2912yescomplemented
142#1470C2×C2912yescomplemented
143C22×C29—22no—
144C22×C29—21no—
145C22×C29—42no—
146C22×C29—42no—
147C22×C29—42no—
148C22×C29—41no—
149C22×C29—42no—
150C22×C29#37911yescharacteristic
151C4×C29—22no—
152C4×C29—22no—
153C4×C29—21no—
154C4×C29—44no—
155C4×C29—42no—
156C4×C29—41no—
157C4×C29—42no—
158C4×C29#41312yes—
159#553—22no—
160#553—24no—
161#552—22no—
162#541—21no—
163#540—21no—
164#537C4×C2912yes—
165#532C22×C2911yescharacteristic
166#529—22no—
167C2×#125C22×C2911yescharacteristic
168#520C4×C2912yes—
169C4×#41C22×C2911yescharacteristic
170#432C22×C2912yes—
171#431C22×C2912yes—
172#333—21no—
173#331—21no—
174#329—22no—
175Q8⋊C8—22no—
176D4⋊C8—22no—
177#324—24no—
178C2×C29—41no—
179C2×C29—82no—
180C2×C29—81no—
181C2×C29#178511yescharacteristic
182C2×C29#179412yes—
183C2×#41C2×C4×C2911yescharacteristic
184C2×#41C2×C4×C2912yes—
185C4⋊Q8D4×C2911yescharacteristic
186#127D4×C2911yescharacteristic
187#126—24no—
188#126—24no—
189#125—24no—
190#125—21no—
191#125—21no—
192#125—22no—
193#124D4×C2912yes—
194#123—24no—
195#123—24no—
196C22⋊Q8—22no—
197C22⋊Q8—22no—
198#121—24no—
199#121—22no—
200#121—22no—
201#121—24no—
202#121—22no—
203C4×Q8—22no—
204C4×Q8D4×C2912yes—
205C4×D4—24no—
206C4×D4—22no—
207C4×D4—24no—
208C4×D4—22no—
209C4×D4—22no—
210C4×D4D4×C2912yes—
211#117—24no—
212#117—22no—
213#117—21no—
214#117C2×C4×C2911yescharacteristic
215C2×C4⋊C4—22no—
216C2×C4⋊C4C2×C4×C2912yes—
217C2×C4⋊C4D4×C2914yes—
218C2×C42—21no—
219C2×C42C23×C2911yescharacteristic
220C4⋊C8—22no—
221C4⋊C8—22no—
222C22⋊C8—22no—
223C22⋊C8—22no—
224#97—22no—
225C4×C8—22no—
226C29#847611yescharacteristic, direct product factor, Sylow
227#41—42no—
228#41—44no—
229C2×Q8C22⋊C4×C2911yescharacteristic
230C2×Q8C22⋊C4×C2912yes—
231C2×D4—22no—
232C2×D4—21no—
233C2×D4—24no—
234C2×D4—22no—
235C2×D4C22⋊C4×C2911yescharacteristic
236C2×D4C22⋊C4×C2912yes—
237C22×C4—24no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4C22⋊C4×C2914yes—
242C22×C4C22×C4×C2911yescharacteristic
243C22×C4C2×D4×C2912yes—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—24no—
247C4⋊C4—24no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—24no—
251C4⋊C4—24no—
252C4⋊C4—22no—
253C4⋊C4—22no—
254C4⋊C4C22⋊C4×C2912yes—
255C22⋊C4—24no—
256C22⋊C4—24no—
257C22⋊C4—24no—
258C22⋊C4—21no—
259C22⋊C4—22no—
260C22⋊C4—22no—
261C22⋊C4—22no—
262C42—24no—
263C42—21no—
264C42—22no—
265C42C2×D4×C2912yes—
266C42C2×D4×C2911yescharacteristic
267C42C2×D4×C2911yescharacteristic
268C23—21no—
269C23—22no—
270C23C2×C22⋊C4×C2911yescharacteristic
271Q8—22no—
272Q8—42no—
273D4—22no—
274D4—42no—
275D4—42no—
276D4—44no—
277D4—82no—
278D4—84no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—82no—
289C2×C4—84no—
290C2×C4C2×C22⋊C4×C2911yescharacteristic
291C2×C4C2×C22⋊C4×C2911yescharacteristic
292C2×C4C29×#12012yes—
293C2×C4C29×#12012yes—
294C8—82no—
295C8—82no—
296C22—21no—
297C22—22no—
298C22—41no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22C29×#37911yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—42no—
309C4—44no—
310C4—42no—
311C4C29×#41312yes—
312C2—41no—
313C2—81no—
314C2—82no—
315C2C29×#178511yescharacteristic
316C2C29×#179412yes—
subgroupG/H
center, socleC22×C29#379
commutatorC22×C4C22×C4×C29
Frattini, cosocleC2×C42C23×C29
prime radicalC29×#3512C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#1543C2semidirect
3. C29×#1536C2semidirect
4. C29×#1488C2semidirect
5. C29×#1470C2semidirect
109. #8476C29direct (N × H)
139. #1543C2×C29semidirect
140. #1536C2×C29semidirect
141. #1488C2×C29semidirect
142. #1470C2×C29semidirect
226. C29#8476direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35122
C29×#15432
C29×#15362
C29×#14882
C29×#14702
#847629