Finite Group Databasebeta

← C29×#33209 #20328109

Subgroups — C29×#33209 #20328109

Order 7424.

966 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#500C211yesmaximal, characteristic, complemented
2C22×C4×C8×C29C211yesmaximal, characteristic
3C29×#2857C212yesmaximal
4C29×#1990C212yesmaximal, complemented
5C29×#1942C214yesmaximal, complemented
6C29×#1845C211yesmaximal, characteristic, complemented
7C29×#1808C214yesmaximal
8C23×C8×C29C2212yes—
9C2×C29×C4⋊Q8C2212yes—
10C2×C29×C22⋊Q8—22no—
11C22×C42×C29C2211yescharacteristic
12C29×#500—24no—
13C2×C29×#107C2214yes—
14C2×C29×#107C2214yes—
15C2×C4×C8×C29—24no—
16C2×C4×C8×C29C2212yes—
17C2×C4×C8×C29C2211yescharacteristic
18C2×C4×C8×C29C2211yescharacteristic
19C29×#391—22no—
20C29×#389—22no—
21C29×#389C2214yes—
22C29×#384C2212yes—
23C29×#380—22no—
24C29×#380C2214yes—
25C29×#340C2218yes—
26C22×Q8×C29—22no—
27C23×C4×C29D411yescharacteristic
28C23×C4×C29D411yescharacteristic
29C23×C4×C29C2311yescharacteristic
30C22×C8×C29—24no—
31C22×C8×C29—24no—
32C22×C8×C29Q818yescomplemented
33C22×C8×C29C2312yes—
34C22×C8×C29C2312yes—
35C29×C4⋊Q8—24no—
36C29×C4⋊Q8—24no—
37C29×C22⋊Q8—48no—
38C2×C4⋊C4×C29—22no—
39C2×C4⋊C4×C29—24no—
40C2×C4⋊C4×C29—22no—
41C2×C4⋊C4×C29—22no—
42C2×C4⋊C4×C29C2314yes—
43C2×C4⋊C4×C29C2314yes—
44C2×C22⋊C4×C29—24no—
45C2×C42×C29—22no—
46C2×C42×C29—22no—
47C2×C42×C29D411yescharacteristic
48C2×C42×C29D411yescharacteristic
49C2×C42×C29C2311yescharacteristic
50C2×C42×C29C2311yescharacteristic
51C29×#107—28no—
52C29×#107—28no—
53C4×C8×C29—24no—
54C4×C8×C29—22no—
55C4×C8×C29D414yes—
56C29×#95—24no—
57C29×#95—24no—
58C24×C29C2×D411yescharacteristic
59C2×Q8×C29—44no—
60C2×Q8×C29—44no—
61C2×Q8×C29—44no—
62C22×C4×C29—22no—
63C22×C4×C29—22no—
64C22×C4×C29—22no—
65C22×C4×C29—22no—
66C22×C4×C29—21no—
67C22×C4×C29—21no—
68C22×C4×C29—22no—
69C22×C4×C29—24no—
70C22×C4×C29—24no—
71C22×C4×C29D814yes—
72C22×C4×C29Q1614yes—
73C22×C4×C29C2×D411yescharacteristic
74C22×C4×C29C2×D411yescharacteristic
75C22×C4×C29C2×D411yescharacteristic
76C22×C4×C29C2×D411yescharacteristic
77C22×C4×C29C2×D411yescharacteristic
78C22×C4×C29C2×Q814yes—
79C22×C4×C29C2411yescharacteristic
80C2×C8×C29—22no—
81C2×C8×C29—22no—
82C2×C8×C29—216no—
83C2×C8×C29C2×D414yes—
84C2×C8×C29C2×Q814yes—
85C2×C8×C29C2×Q814yes—
86C2×C8×C29#4114yes—
87C4⋊C4×C29—24no—
88C4⋊C4×C29—24no—
89C4⋊C4×C29—28no—
90C4⋊C4×C29—44no—
91C4⋊C4×C29—44no—
92C4⋊C4×C29—48no—
93C4⋊C4×C29—44no—
94C22⋊C4×C29—48no—
95C42×C29—22no—
96C42×C29—22no—
97C42×C29—21no—
98C42×C29—21no—
99C42×C29C2×D412yes—
100C42×C29#4112yes—
101#33209C2911yesmaximal, characteristic, direct product factor, Sylow
102C23×C29—21no—
103C23×C29—21no—
104C23×C29—21no—
105C23×C29—21no—
106C23×C29C4⋊Q812yes—
107C23×C29C2×D812yes—
108C23×C29C2×Q1612yes—
109C23×C29C22×D411yescharacteristic
110Q8×C29—88no—
111C2×C4×C29—21no—
112C2×C4×C29—21no—
113C2×C4×C29—21no—
114C2×C4×C29—21no—
115C2×C4×C29—21no—
116C2×C4×C29—21no—
117C2×C4×C29—24no—
118C2×C4×C29—24no—
119C2×C4×C29—28no—
120C2×C4×C29—28no—
121C2×C4×C29—44no—
122C2×C4×C29—44no—
123C2×C4×C29—44no—
124C2×C4×C29—44no—
125C2×C4×C29—44no—
126C2×C4×C29—44no—
127C2×C4×C29#12112yes—
128C2×C4×C29#12112yes—
129C2×C4×C29C4⋊Q812yes—
130C2×C4×C29C2×D812yes—
131C2×C4×C29C2×D812yes—
132C2×C4×C29C2×Q1612yes—
133C2×C4×C29C2×Q1612yes—
134C2×C4×C29#13512yes—
135C2×C4×C29#13512yes—
136C2×C4×C29C22×D411yescharacteristic
137C2×C4×C29C22×Q812yes—
138C2×C4×C29C2×#4112yes—
139C2×C4×C29C2×#4111yescharacteristic
140C8×C29—24no—
141C8×C29C22⋊Q818yescomplemented
142C2×#500C2×C2911yescharacteristic, complemented
143C22×C4×C8C2×C2911yescharacteristic
144#2857C2×C2912yes—
145#1990C2×C2912yescomplemented
146#1942C2×C2914yescomplemented
147#1845C2×C2911yescharacteristic, complemented
148#1808C2×C2914yes—
149C22×C29—22no—
150C22×C29—22no—
151C22×C29—22no—
152C22×C29—22no—
153C22×C29—22no—
154C22×C29—22no—
155C22×C29#50014yescomplemented
156C22×C29C2×#12111yescharacteristic
157C22×C29C2×C4⋊Q811yescharacteristic
158C22×C29#53211yescharacteristic
159C22×C29C22×D811yescharacteristic
160C22×C29C22×Q1611yescharacteristic
161C22×C29C2×#13511yescharacteristic
162C22×C29C2×#13511yescharacteristic
163C4×C29—22no—
164C4×C29—22no—
165C4×C29—22no—
166C4×C29—84no—
167C4×C29—84no—
168C4×C29#46614yes—
169C4×C29#46714yes—
170C4×C29C2×C22⋊Q812yes—
171C4×C29#53312yes—
172C23×C8C22×C2912yes—
173C2×C4⋊Q8C22×C2912yes—
174C2×C22⋊Q8—22no—
175C22×C42C22×C2911yescharacteristic
176#500—24no—
177C2×#107C22×C2914yes—
178C2×#107C22×C2914yes—
179C2×C4×C8—24no—
180C2×C4×C8C22×C2912yes—
181C2×C4×C8C22×C2911yescharacteristic
182C2×C4×C8C22×C2911yescharacteristic
183#391—22no—
184#389—22no—
185#389C22×C2914yes—
186#384C22×C2912yes—
187#380—22no—
188#380C22×C2914yes—
189#340C22×C2918yes—
190C2×C29—24no—
191C2×C29#285711yescharacteristic
192C2×C29C2×#46611yescharacteristic
193C2×C29C2×#46711yescharacteristic
194C2×C29C2×#50011yescharacteristic
195C2×C29#316011yescharacteristic
196C2×C29#316911yescharacteristic
197C2×C29#317011yescharacteristic
198C22×Q8—22no—
199C23×C4D4×C2911yescharacteristic
200C23×C4D4×C2911yescharacteristic
201C23×C4C23×C2911yescharacteristic
202C22×C8—24no—
203C22×C8—24no—
204C22×C8Q8×C2918yescomplemented
205C22×C8C23×C2912yes—
206C22×C8C23×C2912yes—
207C4⋊Q8—24no—
208C4⋊Q8—24no—
209C22⋊Q8—48no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—24no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4C23×C2914yes—
215C2×C4⋊C4C23×C2914yes—
216C2×C22⋊C4—24no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42D4×C2911yescharacteristic
220C2×C42D4×C2911yescharacteristic
221C2×C42C23×C2911yescharacteristic
222C2×C42C23×C2911yescharacteristic
223#107—28no—
224#107—28no—
225C4×C8—24no—
226C4×C8—22no—
227C4×C8D4×C2914yes—
228#95—24no—
229#95—24no—
230C29#3320911yescharacteristic, direct product factor, Sylow
231C24C2×D4×C2911yescharacteristic
232C2×Q8—44no—
233C2×Q8—44no—
234C2×Q8—44no—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4D8×C2914yes—
245C22×C4Q16×C2914yes—
246C22×C4C2×D4×C2911yescharacteristic
247C22×C4C2×D4×C2911yescharacteristic
248C22×C4C2×D4×C2911yescharacteristic
249C22×C4C2×D4×C2911yescharacteristic
250C22×C4C2×D4×C2911yescharacteristic
251C22×C4C2×Q8×C2914yes—
252C22×C4C24×C2911yescharacteristic
253C2×C8—22no—
254C2×C8—22no—
255C2×C8—216no—
256C2×C8C2×D4×C2914yes—
257C2×C8C2×Q8×C2914yes—
258C2×C8C2×Q8×C2914yes—
259C2×C8#41×C2914yes—
260C4⋊C4—24no—
261C4⋊C4—28no—
262C4⋊C4—24no—
263C4⋊C4—44no—
264C4⋊C4—44no—
265C4⋊C4—48no—
266C4⋊C4—44no—
267C22⋊C4—48no—
268C42—22no—
269C42—22no—
270C42—21no—
271C42—21no—
272C42C2×D4×C2912yes—
273C42#41×C2912yes—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23C29×C4⋊Q812yes—
279C23C2×D8×C2912yes—
280C23C2×Q16×C2912yes—
281C23C22×D4×C2911yescharacteristic
282Q8—88no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—28no—
290C2×C4—28no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4C29×#12112yes—
300C2×C4C29×#12112yes—
301C2×C4C29×C4⋊Q812yes—
302C2×C4C2×D8×C2912yes—
303C2×C4C2×D8×C2912yes—
304C2×C4C2×Q16×C2912yes—
305C2×C4C2×Q16×C2912yes—
306C2×C4C29×#13512yes—
307C2×C4C29×#13512yes—
308C2×C4C22×D4×C2911yescharacteristic
309C2×C4C22×Q8×C2912yes—
310C2×C4C2×#41×C2912yes—
311C2×C4C2×#41×C2911yescharacteristic
312C8—24no—
313C8C29×C22⋊Q818yescomplemented
314C22—22no—
315C22—22no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22C29×#50014yescomplemented
321C22C2×C29×#12111yescharacteristic
322C22C2×C29×C4⋊Q811yescharacteristic
323C22C29×#53211yescharacteristic
324C22C22×D8×C2911yescharacteristic
325C22C22×Q16×C2911yescharacteristic
326C22C2×C29×#13511yescharacteristic
327C22C2×C29×#13511yescharacteristic
328C4—22no—
329C4—22no—
330C4—22no—
331C4—84no—
332C4—84no—
333C4C29×#46614yes—
334C4C29×#46714yes—
335C4C2×C29×C22⋊Q812yes—
336C4C29×#53312yes—
337C2—24no—
338C2C29×#285711yescharacteristic
339C2C2×C29×#46611yescharacteristic
340C2C2×C29×#46711yescharacteristic
341C2C2×C29×#50011yescharacteristic
342C2C29×#316011yescharacteristic
343C2C29×#316911yescharacteristic
344C2C29×#317011yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC24×C29C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C22×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#500C2semidirect
4. C29×#1990C2semidirect
5. C29×#1942C2semidirect
6. C29×#1845C2semidirect
32. C22×C8×C29Q8semidirect
101. #33209C29direct (N × H)
141. C8×C29C22⋊Q8semidirect
142. C2×#500C2×C29semidirect
145. #1990C2×C29semidirect
146. #1942C2×C29semidirect
147. #1845C2×C29semidirect
155. C22×C29#500semidirect
204. C22×C8Q8×C29semidirect
230. C29#33209direct (N × H)
313. C8C29×C22⋊Q8semidirect
320. C22C29×#500semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#5002
C22×C4×C8×C292
C29×#28572
C29×#19902
C29×#19422
C29×#18452
C29×#18082
#3320929