Finite Group Databasebeta

← C29×#34485 #20329385

Subgroups — C29×#34485 #20329385

Order 7424.

2340 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#555C211yesmaximal, characteristic
2C29×#2379C214yesmaximal, complemented
3C29×#2369C211yesmaximal, characteristic, complemented
4C29×#2361C214yesmaximal, complemented
5D4×C4⋊C4×C29C212yesmaximal, complemented
6C29×#2346C214yesmaximal, complemented
7C29×#2326C214yesmaximal, complemented
8C29×#2324C214yesmaximal, complemented
9C29×#2317C214yesmaximal, complemented
10C4×C29×C4⋊Q8C211yesmaximal, characteristic, complemented
11C29×#2293C212yesmaximal, complemented
12C29×#555C4116yescomplemented
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C29×#124C2214yes—
15C2×C29×#121C2214yes—
16C2×C4×Q8×C29C2212yes—
17C2×C4×D4×C29C2214yes—
18C2×C4×D4×C29C2214yes—
19C2×C4×D4×C29C2212yes—
20C2×C29×#117C2214yes—
21C2×C29×#117C2214yes—
22C22×C4⋊C4×C29C2214yes—
23C29×#391C2212yes—
24C29×#391C2214yes—
25C29×#390C2212yes—
26C29×#390C2212yes—
27C29×#390C2214yes—
28C29×#389C2212yes—
29C29×#389C2212yes—
30C29×#389C2214yes—
31C29×#389C2214yes—
32C29×#389C2214yes—
33C29×#388C2214yes—
34C29×#388C2214yes—
35C29×#388C2218yes—
36C29×#388C2218yes—
37C29×#386C2218yes—
38C29×#385C2218yes—
39C29×#385C2218yes—
40C29×#385C2218yes—
41C29×#384C2211yescharacteristic
42C29×#384C2214yes—
43C29×#382C2218yes—
44C29×#380C2214yes—
45C4×C4⋊C4×C29C2212yes—
46C4×C4⋊C4×C29C2214yes—
47C4×C4⋊C4×C29C2214yes—
48C4×C22⋊C4×C29C2214yes—
49C29×#376C2214yes—
50C43×C29C2211yescharacteristic
51C22×Q8×C29C2312yes—
52C22×D4×C29C2312yes—
53C22×D4×C29C2314yes—
54C23×C4×C29C2314yes—
55C23×C4×C29C2318yes—
56C29×C4⋊Q8C2×C418yescomplemented
57C29×#124C2×C4132yescomplemented
58C29×#121C2×C4132yescomplemented
59C4×Q8×C29—44no—
60C4×D4×C29—48no—
61C4×D4×C29—48no—
62C4×D4×C29C2×C4116yescomplemented
63C29×#117—48no—
64C29×#117C2×C4132yescomplemented
65C2×C4⋊C4×C29—48no—
66C2×C4⋊C4×C29C2312yes—
67C2×C4⋊C4×C29C2314yes—
68C2×C4⋊C4×C29C2312yes—
69C2×C4⋊C4×C29C2318yes—
70C2×C4⋊C4×C29C2314yes—
71C2×C4⋊C4×C29C2314yes—
72C2×C4⋊C4×C29C2314yes—
73C2×C4⋊C4×C29C2312yes—
74C2×C4⋊C4×C29C2314yes—
75C2×C4⋊C4×C29C2312yes—
76C2×C4⋊C4×C29C2314yes—
77C2×C22⋊C4×C29C2314yes—
78C2×C22⋊C4×C29C2314yes—
79C2×C22⋊C4×C29C2314yes—
80C2×C22⋊C4×C29C2318yes—
81C2×C22⋊C4×C29C2314yes—
82C2×C22⋊C4×C29C2318yes—
83C2×C22⋊C4×C29C2314yes—
84C2×C42×C29C2312yes—
85C2×C42×C29C2314yes—
86C2×C42×C29C2314yes—
87C2×C42×C29C2311yescharacteristic
88C2×C42×C29C2312yes—
89C2×C42×C29C2311yescharacteristic
90C2×C42×C29C2314yes—
91C2×C42×C29C2314yes—
92C2×C42×C29C2311yescharacteristic
93C29×#95C2314yes—
94C29×#95C2318yes—
95C29×#95C2314yes—
96C29×#95C2318yes—
97C29×#95C2318yes—
98C29×#95C2314yes—
99C24×C29C2414yes—
100C2×Q8×C29—42no—
101C2×Q8×C29—42no—
102C2×Q8×C29C22×C418yes—
103C2×D4×C29—24no—
104C2×D4×C29—24no—
105C2×D4×C29—44no—
106C2×D4×C29—44no—
107C2×D4×C29C22×C418yes—
108C2×D4×C29C22×C4116yes—
109C22×C4×C29—28no—
110C22×C4×C29—28no—
111C22×C4×C29—48no—
112C22×C4×C29—48no—
113C22×C4×C29—48no—
114C22×C4×C29C22×C4116yes—
115C22×C4×C29C2411yescharacteristic
116C22×C4×C29C2414yes—
117C22×C4×C29C2412yes—
118C22×C4×C29C2414yes—
119C22×C4×C29C2414yes—
120C22×C4×C29C2411yescharacteristic
121C22×C4×C29C2414yes—
122C22×C4×C29C2414yes—
123C22×C4×C29C2411yescharacteristic
124C22×C4×C29C2412yes—
125C4⋊C4×C29—24no—
126C4⋊C4×C29—28no—
127C4⋊C4×C29—24no—
128C4⋊C4×C29—48no—
129C4⋊C4×C29—44no—
130C4⋊C4×C29—44no—
131C4⋊C4×C29—44no—
132C4⋊C4×C29—44no—
133C4⋊C4×C29—42no—
134C4⋊C4×C29C22×C418yes—
135C4⋊C4×C29C22×C4116yes—
136C22⋊C4×C29—28no—
137C22⋊C4×C29—44no—
138C22⋊C4×C29—44no—
139C22⋊C4×C29—44no—
140C22⋊C4×C29—48no—
141C22⋊C4×C29C22×C4132yes—
142C22⋊C4×C29C22×C4116yes—
143C42×C29—24no—
144C42×C29—28no—
145C42×C29—28no—
146C42×C29—22no—
147C42×C29—24no—
148C42×C29—44no—
149C42×C29—41no—
150C42×C29C22×C4116yes—
151C42×C29C22×C414yes—
152#34485C2911yesmaximal, characteristic, direct product factor, Sylow
153C23×C29—24no—
154C23×C29—24no—
155C23×C29—24no—
156C23×C29—24no—
157C23×C29—24no—
158C23×C29—24no—
159C23×C29C23×C418yes—
160C23×C29C2511yescharacteristic
161Q8×C29—48no—
162D4×C29—216no—
163D4×C29—416no—
164C2×C4×C29—24no—
165C2×C4×C29—21no—
166C2×C4×C29—24no—
167C2×C4×C29—22no—
168C2×C4×C29—24no—
169C2×C4×C29—24no—
170C2×C4×C29—21no—
171C2×C4×C29—232no—
172C2×C4×C29—24no—
173C2×C4×C29—22no—
174C2×C4×C29—22no—
175C2×C4×C29—24no—
176C2×C4×C29—21no—
177C2×C4×C29—24no—
178C2×C4×C29—24no—
179C2×C4×C29—28no—
180C2×C4×C29—24no—
181C2×C4×C29—22no—
182C2×C4×C29—24no—
183C2×C4×C29—24no—
184C2×C4×C29—22no—
185C2×C4×C29—816no—
186C2×C4×C29C23×C418yes—
187C2×C4×C29C23×C412yes—
188C2×C4×C29C23×C418yes—
189C2×C4×C29C23×C414yes—
190C2×C4×C29H(5,𝔽2)12yes—
191C2×C4×C29H(5,𝔽2)14yes—
192C2×C4×C292−1+414yes—
193C2×#555C2×C2911yescharacteristic
194#2379C2×C2914yescomplemented
195#2369C2×C2911yescharacteristic, complemented
196#2361C2×C2914yescomplemented
197D4×C4⋊C4C2×C2912yescomplemented
198#2346C2×C2914yescomplemented
199#2326C2×C2914yescomplemented
200#2324C2×C2914yescomplemented
201#2317C2×C2914yescomplemented
202C4×C4⋊Q8C2×C2911yescharacteristic, complemented
203#2293C2×C2912yescomplemented
204C22×C29—28no—
205C22×C29—28no—
206C22×C29—28no—
207C22×C29—44no—
208C22×C29—44no—
209C22×C29—44no—
210C22×C29—44no—
211C22×C29C24×C411yescharacteristic
212C22×C29C2×H(5,𝔽2)12yes—
213C22×C29C2×H(5,𝔽2)11yescharacteristic
214C22×C29C2×2−1+412yes—
215C22×C29#58511yescharacteristic
216C4×C29—28no—
217C4×C29—28no—
218C4×C29—22no—
219C4×C29—22no—
220C4×C29—44no—
221C4×C29—42no—
222C4×C29—41no—
223C4×C29—44no—
224C4×C29—44no—
225C4×C29#52018yes—
226#555C4×C29116yescomplemented
227C2×C4⋊Q8C22×C2911yescharacteristic
228C2×#124C22×C2914yes—
229C2×#121C22×C2914yes—
230C2×C4×Q8C22×C2912yes—
231C2×C4×D4C22×C2914yes—
232C2×C4×D4C22×C2914yes—
233C2×C4×D4C22×C2912yes—
234C2×#117C22×C2914yes—
235C2×#117C22×C2914yes—
236C22×C4⋊C4C22×C2914yes—
237#391C22×C2912yes—
238#391C22×C2914yes—
239#390C22×C2914yes—
240#390C22×C2912yes—
241#390C22×C2912yes—
242#389C22×C2914yes—
243#389C22×C2912yes—
244#389C22×C2914yes—
245#389C22×C2914yes—
246#389C22×C2912yes—
247#388C22×C2918yes—
248#388C22×C2914yes—
249#388C22×C2918yes—
250#388C22×C2914yes—
251#386C22×C2918yes—
252#385C22×C2918yes—
253#385C22×C2918yes—
254#385C22×C2918yes—
255#384C22×C2911yescharacteristic
256#384C22×C2914yes—
257#382C22×C2918yes—
258#380C22×C2914yes—
259C4×C4⋊C4C22×C2914yes—
260C4×C4⋊C4C22×C2914yes—
261C4×C4⋊C4C22×C2912yes—
262C4×C22⋊C4C22×C2914yes—
263#376C22×C2914yes—
264C43C22×C2911yescharacteristic
265C2×C29—48no—
266C2×C29C2×#52012yes—
267C2×C29C4×H(5,𝔽2)11yescharacteristic
268C2×C29#354411yescharacteristic
269C2×C29#354712yes—
270C2×C29#354911yescharacteristic
271C22×Q8C23×C2912yes—
272C22×D4C23×C2912yes—
273C22×D4C23×C2914yes—
274C23×C4C23×C2914yes—
275C23×C4C23×C2918yes—
276C4⋊Q8C2×C4×C2918yescomplemented
277#124C2×C4×C29132yescomplemented
278#121C2×C4×C29132yescomplemented
279C4×Q8—44no—
280C4×D4—48no—
281C4×D4—48no—
282C4×D4C2×C4×C29116yescomplemented
283#117—48no—
284#117C2×C4×C29132yescomplemented
285C2×C4⋊C4—48no—
286C2×C4⋊C4C23×C2912yes—
287C2×C4⋊C4C23×C2914yes—
288C2×C4⋊C4C23×C2912yes—
289C2×C4⋊C4C23×C2918yes—
290C2×C4⋊C4C23×C2914yes—
291C2×C4⋊C4C23×C2914yes—
292C2×C4⋊C4C23×C2914yes—
293C2×C4⋊C4C23×C2912yes—
294C2×C4⋊C4C23×C2914yes—
295C2×C4⋊C4C23×C2912yes—
296C2×C4⋊C4C23×C2914yes—
297C2×C22⋊C4C23×C2914yes—
298C2×C22⋊C4C23×C2914yes—
299C2×C22⋊C4C23×C2914yes—
300C2×C22⋊C4C23×C2918yes—
301C2×C22⋊C4C23×C2914yes—
302C2×C22⋊C4C23×C2918yes—
303C2×C22⋊C4C23×C2914yes—
304C2×C42C23×C2912yes—
305C2×C42C23×C2914yes—
306C2×C42C23×C2914yes—
307C2×C42C23×C2911yescharacteristic
308C2×C42C23×C2912yes—
309C2×C42C23×C2911yescharacteristic
310C2×C42C23×C2914yes—
311C2×C42C23×C2914yes—
312C2×C42C23×C2911yescharacteristic
313#95C23×C2914yes—
314#95C23×C2918yes—
315#95C23×C2914yes—
316#95C23×C2918yes—
317#95C23×C2918yes—
318#95C23×C2914yes—
319C29#3448511yescharacteristic, direct product factor, Sylow
320C24C24×C2914yes—
321C2×Q8—42no—
322C2×Q8—42no—
323C2×Q8C22×C4×C2918yes—
324C2×D4—24no—
325C2×D4—24no—
326C2×D4—44no—
327C2×D4—44no—
328C2×D4C22×C4×C2918yes—
329C2×D4C22×C4×C29116yes—
330C22×C4—28no—
331C22×C4—28no—
332C22×C4—48no—
333C22×C4—48no—
334C22×C4—48no—
335C22×C4C22×C4×C29116yes—
336C22×C4C24×C2914yes—
337C22×C4C24×C2912yes—
338C22×C4C24×C2914yes—
339C22×C4C24×C2914yes—
340C22×C4C24×C2911yescharacteristic
341C22×C4C24×C2911yescharacteristic
342C22×C4C24×C2914yes—
343C22×C4C24×C2914yes—
344C22×C4C24×C2911yescharacteristic
345C22×C4C24×C2912yes—
346C4⋊C4—24no—
347C4⋊C4—28no—
348C4⋊C4—24no—
349C4⋊C4—48no—
350C4⋊C4—44no—
351C4⋊C4—44no—
352C4⋊C4—44no—
353C4⋊C4—44no—
354C4⋊C4—42no—
355C4⋊C4C22×C4×C2918yes—
356C4⋊C4C22×C4×C29116yes—
357C22⋊C4—28no—
358C22⋊C4—44no—
359C22⋊C4—44no—
360C22⋊C4—48no—
361C22⋊C4—44no—
362C22⋊C4C22×C4×C29132yes—
363C22⋊C4C22×C4×C29116yes—
364C42—24no—
365C42—28no—
366C42—28no—
367C42—22no—
368C42—24no—
369C42—44no—
370C42—41no—
371C42C22×C4×C29116yes—
372C42C22×C4×C2914yes—
373C23—24no—
374C23—24no—
375C23—24no—
376C23—24no—
377C23—24no—
378C23—24no—
379C23C23×C4×C2918yes—
380C23C25×C2911yescharacteristic
381Q8—48no—
382D4—216no—
383D4—416no—
384C2×C4—24no—
385C2×C4—21no—
386C2×C4—24no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—21no—
391C2×C4—232no—
392C2×C4—24no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—28no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—816no—
406C2×C4C23×C4×C2918yes—
407C2×C4C23×C4×C2912yes—
408C2×C4C23×C4×C2918yes—
409C2×C4C23×C4×C2914yes—
410C2×C4C29×H(5,𝔽2)12yes—
411C2×C4C29×H(5,𝔽2)14yes—
412C2×C4C29×2−1+414yes—
413C22—28no—
414C22—28no—
415C22—28no—
416C22—44no—
417C22—44no—
418C22—44no—
419C22—44no—
420C22C24×C4×C2911yescharacteristic
421C22C2×C29×H(5,𝔽2)11yescharacteristic
422C22C2×C29×H(5,𝔽2)12yes—
423C22C2×C29×2−1+412yes—
424C22C29×#58511yescharacteristic
425C4—22no—
426C4—28no—
427C4—28no—
428C4—22no—
429C4—44no—
430C4—42no—
431C4—44no—
432C4—44no—
433C4—41no—
434C4C29×#52018yes—
435C2—48no—
436C2C2×C29×#52012yes—
437C2C4×C29×H(5,𝔽2)11yescharacteristic
438C2C29×#354411yescharacteristic
439C2C29×#354712yes—
440C2C29×#354911yescharacteristic
subgroupG/H
center, socleC23×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC23C25×C29
prime radicalC2×C29×#555C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2379C2semidirect
3. C29×#2369C2semidirect
4. C29×#2361C2semidirect
5. D4×C4⋊C4×C29C2semidirect
6. C29×#2346C2semidirect
7. C29×#2326C2semidirect
8. C29×#2324C2semidirect
9. C29×#2317C2semidirect
10. C4×C29×C4⋊Q8C2semidirect
11. C29×#2293C2semidirect
12. C29×#555C4semidirect
56. C29×C4⋊Q8C2×C4semidirect
57. C29×#124C2×C4semidirect
58. C29×#121C2×C4semidirect
62. C4×D4×C29C2×C4semidirect
64. C29×#117C2×C4semidirect
152. #34485C29direct (N × H)
194. #2379C2×C29semidirect
195. #2369C2×C29semidirect
196. #2361C2×C29semidirect
197. D4×C4⋊C4C2×C29semidirect
198. #2346C2×C29semidirect
199. #2326C2×C29semidirect
200. #2324C2×C29semidirect
201. #2317C2×C29semidirect
202. C4×C4⋊Q8C2×C29semidirect
203. #2293C2×C29semidirect
226. #555C4×C29semidirect
276. C4⋊Q8C2×C4×C29semidirect
277. #124C2×C4×C29semidirect
278. #121C2×C4×C29semidirect
282. C4×D4C2×C4×C29semidirect
284. #117C2×C4×C29semidirect
319. C29#34485direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5552
C29×#23792
C29×#23692
C29×#23612
D4×C4⋊C4×C292
C29×#23462
C29×#23262
C29×#23242
C29×#23172
C4×C29×C4⋊Q82
C29×#22932
#3448529