Finite Group Databasebeta

← C29×#13964 #20308864

Subgroups — C29×#13964 #20308864

Order 7424.

1342 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#383C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C29C211yesmaximal, characteristic
3C2×C29×#376C211yesmaximal, characteristic
4C29×#1441C214yesmaximal
5C29×#1436C214yesmaximal
6C29×C4⋊#95C212yesmaximal
7C29×#1434C212yesmaximal
8C22×C4⋊C4×C29C2214yes—
9C22×C4⋊C4×C29C2212yes—
10C22×C42×C29C2212yes—
11C22×C42×C29C2211yescharacteristic
12C22×C42×C29C2211yescharacteristic
13C22×C42×C29C2211yescharacteristic
14C29×#383—24no—
15C4×C4⋊C4×C29C418yescomplemented
16C29×#376—24no—
17C2×C29×#95C2212yes—
18C2×C29×#95C2212yes—
19C2×C29×#95C2214yes—
20C2×C29×#95C2214yes—
21C2×C29×#95C2212yes—
22C2×C29×#95C2212yes—
23C2×C29×#95C2212yes—
24C2×C29×#95C2214yes—
25C2×C29×#95C2212yes—
26C23×C4×C29C2314yes—
27C23×C4×C29C2312yes—
28C23×C4×C29C2314yes—
29C23×C4×C29C2311yescharacteristic
30C23×C4×C29C2311yescharacteristic
31C23×C4×C29C2311yescharacteristic
32C23×C4×C29C2312yes—
33C2×C4⋊C4×C29—24no—
34C2×C4⋊C4×C29—24no—
35C2×C4⋊C4×C29—28no—
36C2×C4⋊C4×C29—28no—
37C2×C4⋊C4×C29—44no—
38C2×C4⋊C4×C29C2×C418yes—
39C2×C42×C29—24no—
40C2×C42×C29—28no—
41C2×C42×C29—42no—
42C2×C42×C29—42no—
43C2×C42×C29C2×C414yes—
44C2×C42×C29C2×C414yes—
45C2×C42×C29C2×C414yes—
46C2×C42×C29D414yes—
47C2×C42×C29Q814yes—
48C29×#95—24no—
49C29×#95—24no—
50C29×#95—24no—
51C29×#95—24no—
52C29×#95—24no—
53C29×#95—28no—
54C29×#95—28no—
55C29×#95—44no—
56C29×#95C2×C418yes—
57C24×C29C2411yescharacteristic
58C22×C4×C29—24no—
59C22×C4×C29—22no—
60C22×C4×C29—22no—
61C22×C4×C29—24no—
62C22×C4×C29—22no—
63C22×C4×C29—24no—
64C22×C4×C29—22no—
65C22×C4×C29—24no—
66C22×C4×C29—24no—
67C22×C4×C29—22no—
68C22×C4×C29—22no—
69C22×C4×C29—24no—
70C22×C4×C29—24no—
71C22×C4×C29—24no—
72C22×C4×C29—24no—
73C22×C4×C29—24no—
74C22×C4×C29—24no—
75C22×C4×C29—24no—
76C22×C4×C29—24no—
77C22×C4×C29—24no—
78C22×C4×C29—24no—
79C22×C4×C29—24no—
80C22×C4×C29—24no—
81C22×C4×C29—24no—
82C22×C4×C29C22×C414yes—
83C22×C4×C29C22×C412yes—
84C22×C4×C29C22×C412yes—
85C22×C4×C29C22×C412yes—
86C22×C4×C29C22×C414yes—
87C22×C4×C29C2×D412yes—
88C22×C4×C29C2×D412yes—
89C22×C4×C29C2×D412yes—
90C22×C4×C29C2×Q812yes—
91C22×C4×C29C2×Q812yes—
92C22×C4×C29C2×Q812yes—
93C22×C4×C29#4118yes—
94C22×C4×C29#4114yes—
95C22×C4×C29#4114yes—
96C4⋊C4×C29—216no—
97C4⋊C4×C29—416no—
98C42×C29—216no—
99C42×C29—44no—
100C42×C29—44no—
101C42×C29C4⋊C4116yescomplemented
102#13964C2911yesmaximal, characteristic, direct product factor, Sylow
103C23×C29C23×C411yescharacteristic
104C23×C29C22×D411yescharacteristic
105C23×C29C22×Q811yescharacteristic
106C23×C29C2×#4112yes—
107C23×C29C2×#4112yes—
108C23×C29C2×#4114yes—
109C23×C29H(5,𝔽2)12yes—
110C23×C292−1+412yes—
111C2×C4×C29—24no—
112C2×C4×C29—24no—
113C2×C4×C29—24no—
114C2×C4×C29—22no—
115C2×C4×C29—24no—
116C2×C4×C29—22no—
117C2×C4×C29—24no—
118C2×C4×C29—24no—
119C2×C4×C29—22no—
120C2×C4×C29—22no—
121C2×C4×C29—24no—
122C2×C4×C29—24no—
123C2×C4×C29—24no—
124C2×C4×C29—28no—
125C2×C4×C29—28no—
126C2×C4×C29—24no—
127C2×C4×C29—24no—
128C2×C4×C29—24no—
129C2×C4×C29—28no—
130C2×C4×C29—28no—
131C2×C4×C29—28no—
132C2×C4×C29—44no—
133C2×C4×C29—44no—
134C2×C4×C29—44no—
135C2×C4×C29—44no—
136C2×C4×C29—44no—
137C2×C4×C29—44no—
138C2×C4×C29—44no—
139C2×C4×C29—44no—
140C2×C4×C29—44no—
141C2×C4×C29—44no—
142C2×C4×C29—44no—
143C2×C4×C29—44no—
144C2×C4×C29—44no—
145C2×C4×C29C2×C4⋊C414yes—
146C2×C4×C29C2×C4⋊C414yes—
147C2×C4×C29C2×C4⋊C414yes—
148C2×C4×C29#11718yes—
149C2×#383C2×C2911yescharacteristic
150C2×C4×C4⋊C4C2×C2911yescharacteristic
151C2×#376C2×C2911yescharacteristic
152#1441C2×C2914yes—
153#1436C2×C2914yes—
154C4⋊#95C2×C2912yes—
155#1434C2×C2912yes—
156C22×C29C22×C4⋊C411yescharacteristic
157C22×C29C2×#11712yes—
158C22×C29C4×#4112yes—
159C22×C29#51811yescharacteristic
160C22×C29#51911yescharacteristic
161C22×C29#52512yes—
162C22×C29#53212yes—
163C22×C29#53311yescharacteristic
164C22×C29#53312yes—
165C22×C29#53311yescharacteristic
166C22×C29#53712yes—
167C22×C29#54412yes—
168C22×C29#55114yes—
169C22×C29#55214yes—
170C22×C29#55314yes—
171C22×C29#55614yes—
172C4×C29—24no—
173C4×C29—28no—
174C4×C29—24no—
175C4×C29—24no—
176C4×C29—48no—
177C4×C29—44no—
178C4×C29—84no—
179C22×C4⋊C4C22×C2914yes—
180C22×C4⋊C4C22×C2912yes—
181C22×C42C22×C2912yes—
182C22×C42C22×C2911yescharacteristic
183C22×C42C22×C2911yescharacteristic
184C22×C42C22×C2911yescharacteristic
185#383—24no—
186C4×C4⋊C4C4×C2918yescomplemented
187#376—24no—
188C2×#95C22×C2912yes—
189C2×#95C22×C2912yes—
190C2×#95C22×C2914yes—
191C2×#95C22×C2914yes—
192C2×#95C22×C2912yes—
193C2×#95C22×C2912yes—
194C2×#95C22×C2912yes—
195C2×#95C22×C2914yes—
196C2×#95C22×C2912yes—
197C2×C29#228511yescharacteristic
198C2×C29#229611yescharacteristic
199C2×C29#231611yescharacteristic
200C2×C29#235312yes—
201C2×C29#235612yes—
202C2×C29#260114yes—
203C2×C29#260512yes—
204C2×C29#260612yes—
205C23×C4C23×C2914yes—
206C23×C4C23×C2912yes—
207C23×C4C23×C2914yes—
208C23×C4C23×C2911yescharacteristic
209C23×C4C23×C2911yescharacteristic
210C23×C4C23×C2911yescharacteristic
211C23×C4C23×C2912yes—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—28no—
215C2×C4⋊C4—28no—
216C2×C4⋊C4—44no—
217C2×C4⋊C4C2×C4×C2918yes—
218C2×C42—24no—
219C2×C42—28no—
220C2×C42—42no—
221C2×C42—42no—
222C2×C42C2×C4×C2914yes—
223C2×C42C2×C4×C2914yes—
224C2×C42C2×C4×C2914yes—
225C2×C42D4×C2914yes—
226C2×C42Q8×C2914yes—
227#95—24no—
228#95—24no—
229#95—24no—
230#95—24no—
231#95—24no—
232#95—28no—
233#95—28no—
234#95—44no—
235#95C2×C4×C2918yes—
236C29#1396411yescharacteristic, direct product factor, Sylow
237C24C24×C2911yescharacteristic
238C22×C4—24no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—24no—
242C22×C4—22no—
243C22×C4—24no—
244C22×C4—22no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—24no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—24no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4C22×C4×C2914yes—
263C22×C4C22×C4×C2912yes—
264C22×C4C22×C4×C2912yes—
265C22×C4C22×C4×C2912yes—
266C22×C4C22×C4×C2914yes—
267C22×C4C2×D4×C2912yes—
268C22×C4C2×D4×C2912yes—
269C22×C4C2×D4×C2912yes—
270C22×C4C2×Q8×C2912yes—
271C22×C4C2×Q8×C2912yes—
272C22×C4C2×Q8×C2912yes—
273C22×C4#41×C2918yes—
274C22×C4#41×C2914yes—
275C22×C4#41×C2914yes—
276C4⋊C4—216no—
277C4⋊C4—416no—
278C42—216no—
279C42—44no—
280C42—44no—
281C42C4⋊C4×C29116yescomplemented
282C23C23×C4×C2911yescharacteristic
283C23C22×D4×C2911yescharacteristic
284C23C22×Q8×C2911yescharacteristic
285C23C2×#41×C2912yes—
286C23C2×#41×C2912yes—
287C23C2×#41×C2914yes—
288C23C29×H(5,𝔽2)12yes—
289C23C29×2−1+412yes—
290C2×C4—24no—
291C2×C4—24no—
292C2×C4—24no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—24no—
301C2×C4—24no—
302C2×C4—24no—
303C2×C4—28no—
304C2×C4—28no—
305C2×C4—24no—
306C2×C4—24no—
307C2×C4—24no—
308C2×C4—28no—
309C2×C4—28no—
310C2×C4—28no—
311C2×C4—44no—
312C2×C4—44no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4C2×C4⋊C4×C2914yes—
325C2×C4C2×C4⋊C4×C2914yes—
326C2×C4C2×C4⋊C4×C2914yes—
327C2×C4C29×#11718yes—
328C22C22×C4⋊C4×C2911yescharacteristic
329C22C2×C29×#11712yes—
330C22C4×#41×C2912yes—
331C22C29×#51811yescharacteristic
332C22C29×#51911yescharacteristic
333C22C29×#52512yes—
334C22C29×#53212yes—
335C22C29×#53311yescharacteristic
336C22C29×#53311yescharacteristic
337C22C29×#53312yes—
338C22C29×#53712yes—
339C22C29×#54412yes—
340C22C29×#55114yes—
341C22C29×#55214yes—
342C22C29×#55314yes—
343C22C29×#55614yes—
344C4—24no—
345C4—24no—
346C4—24no—
347C4—28no—
348C4—48no—
349C4—44no—
350C4—84no—
351C2C29×#228511yescharacteristic
352C2C29×#229611yescharacteristic
353C2C29×#231611yescharacteristic
354C2C29×#235312yes—
355C2C29×#235612yes—
356C2C29×#260114yes—
357C2C29×#260512yes—
358C2C29×#260612yes—
subgroupG/H
center, socle, prime radicalC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
15. C4×C4⋊C4×C29C4semidirect
101. C42×C29C4⋊C4semidirect
102. #13964C29direct (N × H)
186. C4×C4⋊C4C4×C29semidirect
236. C29#13964direct (N × H)
281. C42C4⋊C4×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#3832
C2×C4×C4⋊C4×C292
C2×C29×#3762
C29×#14412
C29×#14362
C29×C4⋊#952
C29×#14342
#1396429