Finite Group Databasebeta

← C29×#11704 #20306604

Subgroups — C29×#11704 #20306604

Order 7424.

504 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3050C211yesmaximal, characteristic
2C29×#2112C211yesmaximal, characteristic, complemented
3C2×C29×#340C211yesmaximal, characteristic, complemented
4C29×#1348C212yesmaximal, complemented
5C29×#1347C212yesmaximal, complemented
6C2×C29×#135C411yescharacteristic, complemented
7C23×C8×C29C2211yescharacteristic
8C29×#525—21no—
9C22×C4⋊C4×C29—21no—
10C2×C29×M32—21no—
11C29×#467C411yescharacteristic, complemented
12C29×#467C2211yescharacteristic
13C29×#466C411yescharacteristic, complemented
14C29×#466C2211yescharacteristic
15C29×#465—21no—
16C29×#465—21no—
17C29×#427C411yescharacteristic, complemented
18C29×#416—21no—
19C29×C22⋊C16—21no—
20C29×C22⋊C16C2212yes—
21C29×#340—21no—
22C29×#340C2212yes—
23C2×#41×C29—21no—
24C23×C4×C29—41no—
25C23×C4×C29D411yescharacteristic
26C29×#135—42no—
27C2×Q16×C29C2×C411yescharacteristic, complemented
28C2×SD16×C29—21no—
29C2×D8×C29C2×C411yescharacteristic, complemented
30C22×C8×C29—42no—
31C22×C8×C29C2×C411yescharacteristic
32C22×C8×C29C2×C411yescharacteristic
33C22×C8×C29D411yescharacteristic
34C22×C8×C29D411yescharacteristic
35C22×C8×C29D411yescharacteristic
36C22×C8×C29C2311yescharacteristic
37C29×#123—41no—
38C29×C22⋊Q8—21no—
39C29×C22⋊Q8—21no—
40C29×#121—21no—
41C29×#121—21no—
42C29×#120—41no—
43C4×D4×C29—41no—
44C4×D4×C29—41no—
45C29×#117—21no—
46C2×C4⋊C4×C29—24no—
47C2×C4⋊C4×C29—22no—
48C2×C4⋊C4×C29—42no—
49C2×C4⋊C4×C29—41no—
50C29×M32—42no—
51C2×C16×C29—22no—
52C29×#107C2×C411yescharacteristic, complemented
53C29×#107C2×C411yescharacteristic, complemented
54C29×#106—21no—
55C29×#103—21no—
56C29×#103—21no—
57C29×#102—21no—
58C29×#102—21no—
59C24×C29D811yescharacteristic
60#41×C29—42no—
61#41×C29—42no—
62C2×Q8×C29—21no—
63C2×D4×C29—21no—
64C2×D4×C29—41no—
65C2×D4×C29—41no—
66C2×D4×C29—41no—
67C22×C4×C29—22no—
68C22×C4×C29—22no—
69C22×C4×C29—44no—
70C22×C4×C29—42no—
71C22×C4×C29—41no—
72C22×C4×C29—82no—
73C22×C4×C29—82no—
74C22×C4×C29C22⋊C411yescharacteristic
75C22×C4×C29C22⋊C411yescharacteristic
76C22×C4×C29D811yescharacteristic
77C22×C4×C29SD1611yescharacteristic
78C22×C4×C29SD1611yescharacteristic
79C22×C4×C29C2×D411yescharacteristic
80Q16×C29—41no—
81SD16×C29—42no—
82D8×C29—41no—
83C2×C8×C29—22no—
84C2×C8×C29—22no—
85C2×C8×C29—41no—
86C2×C8×C29—41no—
87C2×C8×C29—41no—
88C2×C8×C29—41no—
89C2×C8×C29C22⋊C411yescharacteristic
90C2×C8×C29C22⋊C411yescharacteristic
91C2×C8×C29C22×C411yescharacteristic
92C2×C8×C29C2×D411yescharacteristic
93C4⋊C4×C29—24no—
94C4⋊C4×C29—21no—
95C4⋊C4×C29—21no—
96C4⋊C4×C29—44no—
97C4⋊C4×C29—42no—
98C4⋊C4×C29—41no—
99C4⋊C4×C29—41no—
100C22⋊C4×C29—41no—
101C22⋊C4×C29—41no—
102C22⋊C4×C29—41no—
103C22⋊C4×C29—41no—
104C22⋊C4×C29—41no—
105C42×C29—41no—
106C16×C29—42no—
107#11704C2911yesmaximal, characteristic, direct product factor, Sylow
108C23×C29—22no—
109C23×C29—22no—
110C23×C29—21no—
111C23×C29—21no—
112C23×C29—41no—
113C23×C29#10211yescharacteristic
114C23×C29#10211yescharacteristic
115C23×C29C2×D811yescharacteristic
116Q8×C29—41no—
117Q8×C29—41no—
118D4×C29—41no—
119D4×C29—41no—
120D4×C29—82no—
121D4×C29—82no—
122D4×C29—81no—
123D4×C29—81no—
124C2×C4×C29—22no—
125C2×C4×C29—22no—
126C2×C4×C29—22no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—44no—
132C2×C4×C29—41no—
133C2×C4×C29—41no—
134C2×C4×C29—41no—
135C2×C4×C29—88no—
136C2×C4×C29—82no—
137C2×C4×C29—82no—
138C2×C4×C29—82no—
139C2×C4×C29#9912yes—
140C2×C4×C29#10211yescharacteristic
141C2×C4×C29#10211yescharacteristic
142C2×C4×C29#10412yes—
143C2×C4×C29C2×C22⋊C411yescharacteristic
144C2×C4×C29C2×SD1611yescharacteristic
145C8×C29—21no—
146C8×C29—21no—
147C8×C29—21no—
148C8×C29—21no—
149#3050C2×C2911yescharacteristic
150#2112C2×C2911yescharacteristic, complemented
151C2×#340C2×C2911yescharacteristic, complemented
152#1348C2×C2912yescomplemented
153#1347C2×C2912yescomplemented
154C22×C29—24no—
155C22×C29—24no—
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—81no—
163C22×C29—81no—
164C22×C29—81no—
165C22×C29#32712yes—
166C22×C29#36012yes—
167C22×C29C2×#10211yescharacteristic
168C22×C29#50911yescharacteristic
169C22×C29#51011yescharacteristic
170C4×C29—21no—
171C4×C29—21no—
172C4×C29—84no—
173C4×C29—81no—
174C4×C29—81no—
175C4×C29—81no—
176C4×C29#32712yes—
177C4×C29C2×#9911yescharacteristic
178C4×C29C2×#10411yescharacteristic
179C2×#135C4×C2911yescharacteristic, complemented
180C23×C8C22×C2911yescharacteristic
181#525—21no—
182C22×C4⋊C4—21no—
183C2×M32—21no—
184#467C4×C2911yescharacteristic, complemented
185#467C22×C2911yescharacteristic
186#466C4×C2911yescharacteristic, complemented
187#466C22×C2911yescharacteristic
188#465—21no—
189#465—21no—
190#427C4×C2911yescharacteristic, complemented
191#416—21no—
192C22⋊C16—21no—
193C22⋊C16C22×C2912yes—
194#340—21no—
195#340C22×C2912yes—
196C2×C29—21no—
197C2×C29—22no—
198C2×C29—22no—
199C2×C29—21no—
200C2×C29—161no—
201C2×C29C2×#32711yescharacteristic
202C2×C29#213911yescharacteristic
203C2×C29C2×#36011yescharacteristic
204C2×#41—21no—
205C23×C4—41no—
206C23×C4D4×C2911yescharacteristic
207#135—42no—
208C2×Q16C2×C4×C2911yescharacteristic, complemented
209C2×SD16—21no—
210C2×D8C2×C4×C2911yescharacteristic, complemented
211C22×C8—42no—
212C22×C8C2×C4×C2911yescharacteristic
213C22×C8C2×C4×C2911yescharacteristic
214C22×C8D4×C2911yescharacteristic
215C22×C8D4×C2911yescharacteristic
216C22×C8D4×C2911yescharacteristic
217C22×C8C23×C2911yescharacteristic
218#123—41no—
219C22⋊Q8—21no—
220C22⋊Q8—21no—
221#121—21no—
222#121—21no—
223#120—41no—
224C4×D4—41no—
225C4×D4—41no—
226#117—21no—
227C2×C4⋊C4—24no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—42no—
230C2×C4⋊C4—41no—
231M32—42no—
232C2×C16—22no—
233#107C2×C4×C2911yescharacteristic, complemented
234#107C2×C4×C2911yescharacteristic, complemented
235#106—21no—
236#103—21no—
237#103—21no—
238#102—21no—
239#102—21no—
240C29#1170411yescharacteristic, direct product factor, Sylow
241C24D8×C2911yescharacteristic
242#41—42no—
243#41—42no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—41no—
254C22×C4—82no—
255C22×C4—82no—
256C22×C4C22⋊C4×C2911yescharacteristic
257C22×C4C22⋊C4×C2911yescharacteristic
258C22×C4D8×C2911yescharacteristic
259C22×C4SD16×C2911yescharacteristic
260C22×C4SD16×C2911yescharacteristic
261C22×C4C2×D4×C2911yescharacteristic
262Q16—41no—
263SD16—42no—
264D8—41no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8C22⋊C4×C2911yescharacteristic
272C2×C8C22⋊C4×C2911yescharacteristic
273C2×C8C22×C4×C2911yescharacteristic
274C2×C8C2×D4×C2911yescharacteristic
275C4⋊C4—24no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—44no—
279C4⋊C4—42no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—41no—
288C16—42no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—41no—
294C23C29×#10211yescharacteristic
295C23C29×#10211yescharacteristic
296C23C2×D8×C2911yescharacteristic
297Q8—41no—
298Q8—41no—
299D4—41no—
300D4—41no—
301D4—81no—
302D4—81no—
303D4—82no—
304D4—82no—
305C2×C4—22no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—44no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—88no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—82no—
320C2×C4C29×#9912yes—
321C2×C4C29×#10211yescharacteristic
322C2×C4C29×#10211yescharacteristic
323C2×C4C29×#10412yes—
324C2×C4C2×C22⋊C4×C2911yescharacteristic
325C2×C4C2×SD16×C2911yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22C29×#32712yes—
342C22C29×#36012yes—
343C22C2×C29×#10211yescharacteristic
344C22C29×#50911yescharacteristic
345C22C29×#51011yescharacteristic
346C4—21no—
347C4—21no—
348C4—84no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4C29×#32712yes—
353C4C2×C29×#9911yescharacteristic
354C4C2×C29×#10411yescharacteristic
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—161no—
360C2C2×C29×#32711yescharacteristic
361C2C29×#213911yescharacteristic
362C2C2×C29×#36011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#102
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2112C2semidirect
3. C2×C29×#340C2semidirect
4. C29×#1348C2semidirect
5. C29×#1347C2semidirect
6. C2×C29×#135C4semidirect
11. C29×#467C4semidirect
13. C29×#466C4semidirect
17. C29×#427C4semidirect
27. C2×Q16×C29C2×C4semidirect
29. C2×D8×C29C2×C4semidirect
52. C29×#107C2×C4semidirect
53. C29×#107C2×C4semidirect
107. #11704C29direct (N × H)
150. #2112C2×C29semidirect
151. C2×#340C2×C29semidirect
152. #1348C2×C29semidirect
153. #1347C2×C29semidirect
179. C2×#135C4×C29semidirect
184. #467C4×C29semidirect
186. #466C4×C29semidirect
190. #427C4×C29semidirect
208. C2×Q16C2×C4×C29semidirect
210. C2×D8C2×C4×C29semidirect
233. #107C2×C4×C29semidirect
234. #107C2×C4×C29semidirect
240. C29#11704direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30502
C29×#21122
C2×C29×#3402
C29×#13482
C29×#13472
#1170429