Finite Group Databasebeta

← C29×#9502 #20304402

Subgroups — C29×#9502 #20304402

Order 7424.

660 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2483C211yesmaximal, characteristic
2C29×#2312C211yesmaximal, characteristic
3C29×#1819C212yesmaximal
4C29×#1819C211yesmaximal, characteristic
5C29×#1304C212yesmaximal
6C22×C22⋊C4×C29C2211yescharacteristic
7C22×C22⋊C4×C29C2211yescharacteristic
8C29×#397—22no—
9C29×#388—24no—
10C29×#385—21no—
11C29×#385C412yescomplemented
12C29×#381—21no—
13C29×#381C412yescomplemented
14C29×#380—21no—
15C29×#379C2212yes—
16C29×#379C2211yescharacteristic
17C29×#379C2212yes—
18C4×C22⋊C4×C29—21no—
19C29×#342—24no—
20C29×#342—22no—
21C25×C29C2311yescharacteristic
22C23×C4×C29C2×C411yescharacteristic
23C23×C4×C29C2×C411yescharacteristic
24C23×C4×C29D411yescharacteristic
25C23×C4×C29D411yescharacteristic
26C2×C4⋊C4×C29—22no—
27C2×C4⋊C4×C29—22no—
28C2×C22⋊C4×C29—22no—
29C2×C22⋊C4×C29—22no—
30C2×C22⋊C4×C29—22no—
31C2×C22⋊C4×C29—21no—
32C2×C22⋊C4×C29—21no—
33C2×C22⋊C4×C29—22no—
34C2×C22⋊C4×C29—21no—
35C2×C22⋊C4×C29—22no—
36C2×C22⋊C4×C29—22no—
37C2×C22⋊C4×C29—22no—
38C2×C22⋊C4×C29—22no—
39C2×C22⋊C4×C29—21no—
40C2×C22⋊C4×C29—22no—
41C2×C22⋊C4×C29C2×C412yes—
42C2×C22⋊C4×C29C2×C412yes—
43C2×C22⋊C4×C29D412yes—
44C2×C22⋊C4×C29D414yes—
45C2×C42×C29—22no—
46C29×#95—22no—
47C29×#95—22no—
48C29×#95—22no—
49C29×#95—22no—
50C29×#95—22no—
51C24×C29—42no—
52C24×C29—42no—
53C24×C29—81no—
54C24×C29C22×C411yescharacteristic
55C24×C29C2×D411yescharacteristic
56C24×C29C2×D411yescharacteristic
57C24×C29C2×D412yes—
58C24×C29#4112yes—
59C22×C4×C29—21no—
60C22×C4×C29—21no—
61C22×C4×C29—21no—
62C22×C4×C29—21no—
63C22×C4×C29—22no—
64C22×C4×C29—21no—
65C22×C4×C29—21no—
66C22×C4×C29—24no—
67C22×C4×C29—22no—
68C22×C4×C29—22no—
69C22×C4×C29—42no—
70C22×C4×C29—42no—
71C22×C4×C29—42no—
72C22×C4×C29—81no—
73C22×C4×C29—81no—
74C22×C4×C29C22⋊C412yes—
75C22×C4×C29C22⋊C412yes—
76C4⋊C4×C29—82no—
77C4⋊C4×C29—82no—
78C22⋊C4×C29—24no—
79C22⋊C4×C29—24no—
80C22⋊C4×C29—44no—
81C22⋊C4×C29—42no—
82C22⋊C4×C29—41no—
83C22⋊C4×C29—42no—
84C22⋊C4×C29—41no—
85C22⋊C4×C29—42no—
86C22⋊C4×C29—44no—
87C22⋊C4×C29—44no—
88C22⋊C4×C29—44no—
89C22⋊C4×C29—82no—
90C22⋊C4×C29—81no—
91C22⋊C4×C29—82no—
92C42×C29—82no—
93#9502C2911yesmaximal, characteristic, direct product factor, Sylow
94C23×C29—22no—
95C23×C29—22no—
96C23×C29—22no—
97C23×C29—22no—
98C23×C29—24no—
99C23×C29—41no—
100C23×C29—41no—
101C23×C29—41no—
102C23×C29—41no—
103C23×C29—42no—
104C23×C29—42no—
105C23×C29—41no—
106C23×C29—42no—
107C23×C29—42no—
108C23×C29—42no—
109C23×C29—88no—
110C23×C29C2×C22⋊C411yescharacteristic
111C23×C29C4×D412yes—
112C23×C29#12011yescharacteristic
113C23×C29#12112yes—
114C23×C29#12311yescharacteristic
115C2×C4×C29—22no—
116C2×C4×C29—22no—
117C2×C4×C29—42no—
118C2×C4×C29—42no—
119C2×C4×C29—42no—
120C2×C4×C29—42no—
121C2×C4×C29—44no—
122C2×C4×C29—42no—
123C2×C4×C29—44no—
124C2×C4×C29—42no—
125C2×C4×C29—42no—
126C2×C4×C29—41no—
127C2×C4×C29—41no—
128C2×C4×C29—42no—
129C2×C4×C29—42no—
130C2×C4×C29—44no—
131C2×C4×C29—81no—
132C2×C4×C29—81no—
133C2×C4×C29—82no—
134C2×C4×C29—82no—
135C2×C4×C29—82no—
136C2×C4×C29—82no—
137C2×C4×C29—82no—
138#2483C2×C2911yescharacteristic
139#2312C2×C2911yescharacteristic
140#1819C2×C2912yes—
141#1819C2×C2911yescharacteristic
142#1304C2×C2912yes—
143C22×C29—21no—
144C22×C29—21no—
145C22×C29—21no—
146C22×C29—21no—
147C22×C29—22no—
148C22×C29—21no—
149C22×C29—22no—
150C22×C29—22no—
151C22×C29—22no—
152C22×C29—21no—
153C22×C29—22no—
154C22×C29—22no—
155C22×C29—21no—
156C22×C29—44no—
157C22×C29—44no—
158C22×C29—84no—
159C22×C29—82no—
160C22×C29—84no—
161C22×C29#38611yescharacteristic
162C22×C29#41012yes—
163C22×C29#45812yes—
164C4×C29—42no—
165C4×C29—42no—
166C4×C29—84no—
167C4×C29—82no—
168C4×C29—81no—
169C4×C29—81no—
170C4×C29—162no—
171C22×C22⋊C4C22×C2911yescharacteristic
172C22×C22⋊C4C22×C2911yescharacteristic
173#397—22no—
174#388—24no—
175#385—21no—
176#385C4×C2912yescomplemented
177#381—21no—
178#381C4×C2912yescomplemented
179#380—21no—
180#379C22×C2912yes—
181#379C22×C2911yescharacteristic
182#379C22×C2912yes—
183C4×C22⋊C4—21no—
184#342—24no—
185#342—22no—
186C2×C29—22no—
187C2×C29—22no—
188C2×C29—42no—
189C2×C29—41no—
190C2×C29—42no—
191C2×C29#189011yescharacteristic
192C2×C29#189911yescharacteristic
193C2×C29#191311yescharacteristic
194C25C23×C2911yescharacteristic
195C23×C4C2×C4×C2911yescharacteristic
196C23×C4C2×C4×C2911yescharacteristic
197C23×C4D4×C2911yescharacteristic
198C23×C4D4×C2911yescharacteristic
199C2×C4⋊C4—22no—
200C2×C4⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—22no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4C2×C4×C2912yes—
215C2×C22⋊C4C2×C4×C2912yes—
216C2×C22⋊C4D4×C2912yes—
217C2×C22⋊C4D4×C2914yes—
218C2×C42—22no—
219#95—22no—
220#95—22no—
221#95—22no—
222#95—22no—
223#95—22no—
224C29#950211yescharacteristic, direct product factor, Sylow
225C24—42no—
226C24—42no—
227C24—81no—
228C24C22×C4×C2911yescharacteristic
229C24C2×D4×C2911yescharacteristic
230C24C2×D4×C2911yescharacteristic
231C24C2×D4×C2912yes—
232C24#41×C2912yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4C22⋊C4×C2912yes—
249C22×C4C22⋊C4×C2912yes—
250C4⋊C4—82no—
251C4⋊C4—82no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—42no—
255C22⋊C4—44no—
256C22⋊C4—41no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—44no—
261C22⋊C4—44no—
262C22⋊C4—44no—
263C22⋊C4—82no—
264C22⋊C4—81no—
265C22⋊C4—82no—
266C42—82no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—24no—
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—42no—
277C23—42no—
278C23—41no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—88no—
283C23C2×C22⋊C4×C2911yescharacteristic
284C23C4×D4×C2912yes—
285C23C29×#12011yescharacteristic
286C23C29×#12112yes—
287C23C29×#12311yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—21no—
320C22—22no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—44no—
325C22—44no—
326C22—84no—
327C22—82no—
328C22—84no—
329C22C29×#38611yescharacteristic
330C22C29×#41012yes—
331C22C29×#45812yes—
332C4—42no—
333C4—42no—
334C4—84no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—162no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—42no—
343C2—41no—
344C2C29×#189011yescharacteristic
345C2C29×#189911yescharacteristic
346C2C29×#191311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC24C22×C4×C29
Frattini, cosocleC25C23×C29
prime radicalC25×C29C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C25×C29 ◁ G

Complements

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

NH ≅ G/Ntype
11. C29×#385C4semidirect
13. C29×#381C4semidirect
93. #9502C29direct (N × H)
176. #385C4×C29semidirect
178. #381C4×C29semidirect
224. C29#9502direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24832
C29×#23122
C29×#18192
C29×#13042
#950229