Finite Group Databasebeta

← C29×#34643 #20329543

Subgroups — C29×#34643 #20329543

Order 7424.

2234 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#529C212yesmaximal, complemented
2C29×#2664C214yesmaximal, complemented
3C29×#2663C214yesmaximal, complemented
4C29×#2662C214yesmaximal, complemented
5C29×#2661C214yesmaximal, complemented
6C29×#2399C211yesmaximal, characteristic, complemented
7C29×#2398C212yesmaximal, complemented
8C29×#2397C211yesmaximal, characteristic, complemented
9C29×#2392C214yesmaximal, complemented
10C29×#2293C214yesmaximal, complemented
11C4×C29×#117C211yesmaximal, characteristic, complemented
12C29×#529—216no—
13C2×C29×#126C2214yes—
14C2×C29×#125C2212yes—
15C2×C29×#124C2212yes—
16C2×C29×#123C2214yes—
17C2×C29×C22⋊Q8C2212yes—
18C2×C29×#121C2212yes—
19C2×C4×Q8×C29C2212yes—
20C2×C4×D4×C29C2214yes—
21C2×C4×D4×C29C2212yes—
22C2×C4×D4×C29C2214yes—
23C2×C29×#117C2214yes—
24C2×C29×#117C2212yes—
25C22×C42×C29C2211yescharacteristic
26C29×#400C2214yes—
27C29×#399C2214yes—
28C29×#398C2214yes—
29C29×#398C2214yes—
30C29×#397C2214yes—
31C29×#397C2214yes—
32C29×#396C2218yes—
33C29×#395C2214yes—
34C29×#394C2218yes—
35C29×#394C2214yes—
36C29×#394C2214yes—
37C29×#393C2214yes—
38C29×#392C2214yes—
39C29×#392C2214yes—
40C29×#390C2218yes—
41C29×#389C2218yes—
42C29×#388C2218yes—
43C29×#388C2218yes—
44C4×C4⋊C4×C29C2214yes—
45C4×C4⋊C4×C29C2214yes—
46C4×C22⋊C4×C29C2214yes—
47C4×C22⋊C4×C29C2218yes—
48C29×#376C2211yescharacteristic
49C29×#376C2211yescharacteristic
50C43×C29C2212yes—
51C22×Q8×C29C2312yes—
52C22×D4×C29C2314yes—
53C22×D4×C29C2312yes—
54C22×D4×C29C2314yes—
55C23×C4×C29C2314yes—
56C23×C4×C29C2311yescharacteristic
57C23×C4×C29C2312yes—
58C29×#126—216no—
59C29×#125—28no—
60C29×#124—28no—
61C29×#123—216no—
62C29×C22⋊Q8—28no—
63C29×#121—28no—
64C4×Q8×C29—28no—
65C4×D4×C29—216no—
66C4×D4×C29—28no—
67C4×D4×C29—216no—
68C29×#117—216no—
69C29×#117—28no—
70C2×C4⋊C4×C29C2314yes—
71C2×C4⋊C4×C29C2314yes—
72C2×C4⋊C4×C29C2314yes—
73C2×C4⋊C4×C29C2312yes—
74C2×C4⋊C4×C29C2314yes—
75C2×C4⋊C4×C29C2314yes—
76C2×C4⋊C4×C29C2312yes—
77C2×C4⋊C4×C29C2314yes—
78C2×C4⋊C4×C29C2318yes—
79C2×C22⋊C4×C29C2314yes—
80C2×C22⋊C4×C29C2314yes—
81C2×C22⋊C4×C29C2314yes—
82C2×C22⋊C4×C29C2314yes—
83C2×C22⋊C4×C29C2314yes—
84C2×C22⋊C4×C29C2314yes—
85C2×C22⋊C4×C29C2318yes—
86C2×C22⋊C4×C29C2318yes—
87C2×C22⋊C4×C29C2318yes—
88C2×C42×C29D418yescomplemented
89C2×C42×C29C2314yes—
90C2×C42×C29C2312yes—
91C2×C42×C29C2318yes—
92C2×C42×C29C2312yes—
93C2×C42×C29C2311yescharacteristic
94C2×C42×C29C2311yescharacteristic
95C2×C42×C29C2312yes—
96C29×#95C2314yes—
97C29×#95C2314yes—
98C29×#95C2318yes—
99C29×#95C2318yes—
100C29×#95C2314yes—
101C29×#95C2314yes—
102C24×C29C2414yes—
103C24×C29C2411yescharacteristic
104C2×Q8×C29—24no—
105C2×Q8×C29—44no—
106C2×D4×C29—28no—
107C2×D4×C29—24no—
108C2×D4×C29—28no—
109C2×D4×C29—48no—
110C2×D4×C29—44no—
111C2×D4×C29—48no—
112C22×C4×C29—24no—
113C22×C4×C29—28no—
114C22×C4×C29—216no—
115C22×C4×C29—44no—
116C22×C4×C29C2×D414yes—
117C22×C4×C29C2×D418yes—
118C22×C4×C29C2414yes—
119C22×C4×C29C2414yes—
120C22×C4×C29C2414yes—
121C22×C4×C29C2414yes—
122C22×C4×C29C2412yes—
123C22×C4×C29C2411yescharacteristic
124C22×C4×C29C2412yes—
125C22×C4×C29C2414yes—
126C22×C4×C29C2411yescharacteristic
127C4⋊C4×C29—28no—
128C4⋊C4×C29—28no—
129C4⋊C4×C29—24no—
130C4⋊C4×C29—28no—
131C4⋊C4×C29—24no—
132C4⋊C4×C29—28no—
133C4⋊C4×C29—28no—
134C4⋊C4×C29—28no—
135C4⋊C4×C29—48no—
136C22⋊C4×C29—28no—
137C22⋊C4×C29—28no—
138C22⋊C4×C29—28no—
139C22⋊C4×C29—28no—
140C22⋊C4×C29—28no—
141C22⋊C4×C29—28no—
142C22⋊C4×C29—216no—
143C22⋊C4×C29—48no—
144C22⋊C4×C29—48no—
145C42×C29—28no—
146C42×C29—24no—
147C42×C29—48no—
148C42×C29C2×D414yes—
149C42×C29C2×D414yes—
150C42×C29C2×D418yes—
151C42×C29#4118yes—
152#34643C2911yesmaximal, characteristic, direct product factor, Sylow
153C23×C29—22no—
154C23×C29—24no—
155C23×C29—24no—
156C23×C29—28no—
157C23×C29—24no—
158C23×C29—28no—
159C23×C29—24no—
160C23×C29C22×D412yes—
161C23×C29C2511yescharacteristic
162Q8×C29—48no—
163D4×C29—48no—
164D4×C29—416no—
165D4×C29—416no—
166C2×C4×C29—22no—
167C2×C4×C29—24no—
168C2×C4×C29—28no—
169C2×C4×C29—24no—
170C2×C4×C29—28no—
171C2×C4×C29—24no—
172C2×C4×C29—24no—
173C2×C4×C29—24no—
174C2×C4×C29—24no—
175C2×C4×C29—28no—
176C2×C4×C29—28no—
177C2×C4×C29—24no—
178C2×C4×C29—28no—
179C2×C4×C29—24no—
180C2×C4×C29—48no—
181C2×C4×C29—416no—
182C2×C4×C29C22×D412yes—
183C2×C4×C29C22×D414yes—
184C2×C4×C29C22×D414yes—
185C2×C4×C29C22×D412yes—
186C2×C4×C29C2×#4118yes—
187C2×C4×C29C2×#4114yes—
188C2×#529C2×C2912yescomplemented
189#2664C2×C2914yescomplemented
190#2663C2×C2914yescomplemented
191#2662C2×C2914yescomplemented
192#2661C2×C2914yescomplemented
193#2399C2×C2911yescharacteristic, complemented
194#2398C2×C2912yescomplemented
195#2397C2×C2911yescharacteristic, complemented
196#2392C2×C2914yescomplemented
197#2293C2×C2914yescomplemented
198C4×#117C2×C2911yescharacteristic, complemented
199C22×C29—22no—
200C22×C29—24no—
201C22×C29—44no—
202C22×C29—44no—
203C22×C29—44no—
204C22×C29—44no—
205C22×C29—48no—
206C22×C29—48no—
207C22×C29C23×D411yescharacteristic
208C22×C29C22×#4112yes—
209C22×C29#58514yes—
210C4×C29—22no—
211C4×C29—24no—
212C4×C29—24no—
213C4×C29—28no—
214C4×C29—44no—
215C4×C29—44no—
216C4×C29—44no—
217C4×C29—44no—
218C4×C29#53214yes—
219#529—216no—
220C2×#126C22×C2914yes—
221C2×#125C22×C2912yes—
222C2×#124C22×C2912yes—
223C2×#123C22×C2914yes—
224C2×C22⋊Q8C22×C2912yes—
225C2×#121C22×C2912yes—
226C2×C4×Q8C22×C2912yes—
227C2×C4×D4C22×C2914yes—
228C2×C4×D4C22×C2914yes—
229C2×C4×D4C22×C2912yes—
230C2×#117C22×C2912yes—
231C2×#117C22×C2914yes—
232C22×C42C22×C2911yescharacteristic
233#400C22×C2914yes—
234#399C22×C2914yes—
235#398C22×C2914yes—
236#398C22×C2914yes—
237#397C22×C2914yes—
238#397C22×C2914yes—
239#396C22×C2918yes—
240#395C22×C2914yes—
241#394C22×C2918yes—
242#394C22×C2914yes—
243#394C22×C2914yes—
244#393C22×C2914yes—
245#392C22×C2914yes—
246#392C22×C2914yes—
247#390C22×C2918yes—
248#389C22×C2918yes—
249#388C22×C2918yes—
250#388C22×C2918yes—
251C4×C4⋊C4C22×C2914yes—
252C4×C4⋊C4C22×C2914yes—
253C4×C22⋊C4C22×C2918yes—
254C4×C22⋊C4C22×C2914yes—
255#376C22×C2911yescharacteristic
256#376C22×C2911yescharacteristic
257C43C22×C2912yes—
258C2×C29—42no—
259C2×C29—84no—
260C2×C29C2×#53211yescharacteristic
261C2×C29#344912yes—
262C2×C29#345514yes—
263C22×Q8C23×C2912yes—
264C22×D4C23×C2914yes—
265C22×D4C23×C2912yes—
266C22×D4C23×C2914yes—
267C23×C4C23×C2914yes—
268C23×C4C23×C2911yescharacteristic
269C23×C4C23×C2912yes—
270#126—216no—
271#125—28no—
272#124—28no—
273#123—216no—
274C22⋊Q8—28no—
275#121—28no—
276C4×Q8—28no—
277C4×D4—216no—
278C4×D4—28no—
279C4×D4—216no—
280#117—216no—
281#117—28no—
282C2×C4⋊C4C23×C2914yes—
283C2×C4⋊C4C23×C2914yes—
284C2×C4⋊C4C23×C2914yes—
285C2×C4⋊C4C23×C2912yes—
286C2×C4⋊C4C23×C2914yes—
287C2×C4⋊C4C23×C2914yes—
288C2×C4⋊C4C23×C2912yes—
289C2×C4⋊C4C23×C2914yes—
290C2×C4⋊C4C23×C2918yes—
291C2×C22⋊C4C23×C2914yes—
292C2×C22⋊C4C23×C2914yes—
293C2×C22⋊C4C23×C2914yes—
294C2×C22⋊C4C23×C2914yes—
295C2×C22⋊C4C23×C2914yes—
296C2×C22⋊C4C23×C2914yes—
297C2×C22⋊C4C23×C2918yes—
298C2×C22⋊C4C23×C2918yes—
299C2×C22⋊C4C23×C2918yes—
300C2×C42D4×C2918yescomplemented
301C2×C42C23×C2914yes—
302C2×C42C23×C2912yes—
303C2×C42C23×C2918yes—
304C2×C42C23×C2911yescharacteristic
305C2×C42C23×C2911yescharacteristic
306C2×C42C23×C2912yes—
307C2×C42C23×C2912yes—
308#95C23×C2914yes—
309#95C23×C2914yes—
310#95C23×C2918yes—
311#95C23×C2918yes—
312#95C23×C2914yes—
313#95C23×C2914yes—
314C29#3464311yescharacteristic, direct product factor, Sylow
315C24C24×C2914yes—
316C24C24×C2911yescharacteristic
317C2×Q8—24no—
318C2×Q8—44no—
319C2×D4—28no—
320C2×D4—24no—
321C2×D4—28no—
322C2×D4—48no—
323C2×D4—44no—
324C2×D4—48no—
325C22×C4—24no—
326C22×C4—28no—
327C22×C4—216no—
328C22×C4—44no—
329C22×C4C2×D4×C2914yes—
330C22×C4C2×D4×C2918yes—
331C22×C4C24×C2914yes—
332C22×C4C24×C2914yes—
333C22×C4C24×C2914yes—
334C22×C4C24×C2914yes—
335C22×C4C24×C2912yes—
336C22×C4C24×C2912yes—
337C22×C4C24×C2911yescharacteristic
338C22×C4C24×C2914yes—
339C22×C4C24×C2911yescharacteristic
340C4⋊C4—28no—
341C4⋊C4—28no—
342C4⋊C4—24no—
343C4⋊C4—28no—
344C4⋊C4—24no—
345C4⋊C4—28no—
346C4⋊C4—28no—
347C4⋊C4—28no—
348C4⋊C4—48no—
349C22⋊C4—28no—
350C22⋊C4—28no—
351C22⋊C4—28no—
352C22⋊C4—28no—
353C22⋊C4—28no—
354C22⋊C4—28no—
355C22⋊C4—216no—
356C22⋊C4—48no—
357C22⋊C4—48no—
358C42—28no—
359C42—24no—
360C42—48no—
361C42C2×D4×C2914yes—
362C42C2×D4×C2914yes—
363C42C2×D4×C2918yes—
364C42#41×C2918yes—
365C23—22no—
366C23—24no—
367C23—24no—
368C23—28no—
369C23—24no—
370C23—28no—
371C23—24no—
372C23C22×D4×C2912yes—
373C23C25×C2911yescharacteristic
374Q8—48no—
375D4—48no—
376D4—416no—
377D4—416no—
378C2×C4—22no—
379C2×C4—24no—
380C2×C4—28no—
381C2×C4—24no—
382C2×C4—28no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—28no—
388C2×C4—28no—
389C2×C4—24no—
390C2×C4—28no—
391C2×C4—24no—
392C2×C4—48no—
393C2×C4—416no—
394C2×C4C22×D4×C2912yes—
395C2×C4C22×D4×C2914yes—
396C2×C4C22×D4×C2914yes—
397C2×C4C22×D4×C2912yes—
398C2×C4C2×#41×C2918yes—
399C2×C4C2×#41×C2914yes—
400C22—22no—
401C22—24no—
402C22—44no—
403C22—44no—
404C22—44no—
405C22—44no—
406C22—48no—
407C22—48no—
408C22C23×D4×C2911yescharacteristic
409C22C22×#41×C2912yes—
410C22C29×#58514yes—
411C4—22no—
412C4—24no—
413C4—24no—
414C4—28no—
415C4—44no—
416C4—44no—
417C4—44no—
418C4—44no—
419C4C29×#53214yes—
420C2—42no—
421C2—84no—
422C2C2×C29×#53211yescharacteristic
423C2C29×#344912yes—
424C2C29×#345514yes—
subgroupG/H
centerC22×C4×C29C24
commutator, Frattini, cosocleC23C25×C29
socleC23×C29C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#529C2semidirect
2. C29×#2664C2semidirect
3. C29×#2663C2semidirect
4. C29×#2662C2semidirect
5. C29×#2661C2semidirect
6. C29×#2399C2semidirect
7. C29×#2398C2semidirect
8. C29×#2397C2semidirect
9. C29×#2392C2semidirect
10. C29×#2293C2semidirect
11. C4×C29×#117C2semidirect
88. C2×C42×C29D4semidirect
152. #34643C29direct (N × H)
188. C2×#529C2×C29semidirect
189. #2664C2×C29semidirect
190. #2663C2×C29semidirect
191. #2662C2×C29semidirect
192. #2661C2×C29semidirect
193. #2399C2×C29semidirect
194. #2398C2×C29semidirect
195. #2397C2×C29semidirect
196. #2392C2×C29semidirect
197. #2293C2×C29semidirect
198. C4×#117C2×C29semidirect
300. C2×C42D4×C29semidirect
314. C29#34643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5292
C29×#26642
C29×#26632
C29×#26622
C29×#26612
C29×#23992
C29×#23982
C29×#23972
C29×#23922
C29×#22932
C4×C29×#1172
#3464329