Finite Group Databasebeta

← C29×#60204 #20355104

Subgroups — C29×#60204 #20355104

Order 7424.

2050 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3444C211yesmaximal, characteristic
2C29×#2966C218yesmaximal, complemented
3C29×#2965C214yesmaximal, complemented
4C8×#41×C29C214yesmaximal, complemented
5C29×#2960C212yesmaximal, complemented
6C29×#2931C212yesmaximal, complemented
7C29×#2929C214yesmaximal, complemented
8C29×#2922C212yesmaximal, complemented
9C29×#2920C211yesmaximal, characteristic, complemented
10C4×C29×#131C212yesmaximal, complemented
11C22×C4×C8×C29C211yesmaximal, characteristic, complemented
12C2×C29×#131C2214yes—
13C23×C8×C29C2212yes—
14C29×#533C412yes—
15C29×#533C2211yescharacteristic
16C29×#532C412yes—
17C29×#532C2211yescharacteristic
18C29×#529C414yes—
19C29×#529C414yes—
20C29×#529C2214yes—
21C29×#525C414yes—
22C29×#525C2212yes—
23C4×#41×C29C2214yes—
24C4×#41×C29C2212yes—
25C22×C42×C29C2211yescharacteristic
26C29×#446C2218yescomplemented
27C8×Q8×C29C2218yescomplemented
28C29×#436C2218yescomplemented
29C29×#435C22116yes—
30C8×D4×C29C22116yes—
31C8×D4×C29C2218yescomplemented
32C29×#433C2218yescomplemented
33C29×#432C2214yes—
34C29×#431C2214yes—
35C29×#431C2218yescomplemented
36C29×#424C2214yes—
37C29×#423C2212yes—
38C29×#408C2214yes—
39C29×#407C2212yes—
40C29×#405C2214yes—
41C29×#405C2218yescomplemented
42C4×M16×C29C2212yes—
43C4×M16×C29C2214yescomplemented
44C2×C4×C8×C29C2212yes—
45C2×C4×C8×C29C2212yes—
46C2×C4×C8×C29C2214yes—
47C2×C4×C8×C29C2211yescharacteristic
48C2×C4×C8×C29C2212yes—
49C2×C4×C8×C29C2211yescharacteristic
50C2×C4×C8×C29C2214yescomplemented
51C2×#41×C29C2×C414yes—
52C2×#41×C29C2312yes—
53C23×C4×C29C2×C412yes—
54C23×C4×C29C2311yescharacteristic
55C29×#131—216no—
56C2×M16×C29C2318yes—
57C2×M16×C29C2314yes—
58C22×C8×C29—28no—
59C22×C8×C29C2314yes—
60C22×C8×C29C2318yes—
61C22×C8×C29C2314yes—
62C22×C8×C29C2312yes—
63C22×C8×C29C2312yes—
64C29×C4⋊Q8C2×C412yes—
65C29×C4⋊Q8C2×C411yescharacteristic
66C29×#127C2×C411yescharacteristic
67C29×#126C2×C418yes—
68C29×#125C2×C412yes—
69C29×#125C2×C414yes—
70C29×#124C2×C412yes—
71C29×#124C2×C414yes—
72C29×#123C2×C418yes—
73C29×#123C2×C414yes—
74C29×C22⋊Q8C2×C414yes—
75C29×C22⋊Q8C2×C414yes—
76C29×C22⋊Q8C2×C414yes—
77C29×#121C2×C414yes—
78C29×#121C2×C414yes—
79C29×#121C2×C414yes—
80C29×#120C2×C414yes—
81C4×Q8×C29C2×C414yes—
82C4×Q8×C29C2×C414yes—
83C4×Q8×C29C2314yes—
84C4×D4×C29C2×C418yes—
85C4×D4×C29C2×C418yes—
86C4×D4×C29C2×C414yes—
87C4×D4×C29C2×C414yes—
88C4×D4×C29C2318yes—
89C4×D4×C29C2314yes—
90C29×#117C2×C414yes—
91C29×#117C2×C418yes—
92C29×#117C2314yes—
93C29×#117C2312yes—
94C2×C42×C29C2×C412yes—
95C2×C42×C29C2×C412yes—
96C2×C42×C29C2×C412yes—
97C2×C42×C29C2312yes—
98C2×C42×C29C2314yes—
99C2×C42×C29C2312yes—
100C2×C42×C29C2311yescharacteristic
101C2×C42×C29C2311yescharacteristic
102C29×C4⋊C8C2318yes—
103C29×C4⋊C8C23116yes—
104C29×C22⋊C8C2318yes—
105C29×C22⋊C8C23116yes—
106C29×#97C2314yes—
107C29×#97C2318yes—
108C4×C8×C29C2314yes—
109C4×C8×C29C2312yes—
110C4×C8×C29C2312yes—
111C4×C8×C29C2318yes—
112C4×C8×C29C2314yes—
113C4×C8×C29C2314yes—
114C4×C8×C29C2311yescharacteristic
115C4×C8×C29C2312yes—
116C4×C8×C29C2311yescharacteristic
117C24×C29C22×C411yescharacteristic
118#41×C29—216no—
119#41×C29—28no—
120C2×Q8×C29C22×C412yes—
121C2×Q8×C29C22×C414yes—
122C2×D4×C29C22×C414yes—
123C2×D4×C29C22×C412yes—
124C2×D4×C29C22×C418yes—
125C2×D4×C29C22×C414yes—
126C22×C4×C29—28no—
127C22×C4×C29—24no—
128C22×C4×C29C22×C412yes—
129C22×C4×C29C22×C411yescharacteristic
130C22×C4×C29C22×C412yes—
131C22×C4×C29C22×C412yes—
132C22×C4×C29C22×C412yes—
133C22×C4×C29C22×C412yes—
134C22×C4×C29C22×C412yes—
135C22×C4×C29C22×C418yes—
136C22×C4×C29C22×C412yes—
137C22×C4×C29C2412yes—
138C22×C4×C29C2414yes—
139C22×C4×C29C2411yescharacteristic
140M16×C29—28no—
141M16×C29—216no—
142C2×C8×C29—24no—
143C2×C8×C29—28no—
144C2×C8×C29—28no—
145C2×C8×C29—216no—
146C2×C8×C29#4118yescomplemented
147C2×C8×C29C2414yes—
148C2×C8×C29C2418yes—
149C2×C8×C29C2412yes—
150C2×C8×C29C2412yes—
151C4⋊C4×C29C22×C414yes—
152C4⋊C4×C29C22×C418yes—
153C4⋊C4×C29C22×C414yes—
154C4⋊C4×C29C22×C418yes—
155C4⋊C4×C29C22×C414yes—
156C4⋊C4×C29C22×C418yes—
157C22⋊C4×C29C22×C418yes—
158C22⋊C4×C29C22×C418yes—
159C22⋊C4×C29C22×C418yes—
160C22⋊C4×C29C22×C414yes—
161C22⋊C4×C29C22×C418yes—
162C42×C29C22×C412yes—
163C42×C29C22×C412yes—
164C42×C29C22×C412yes—
165C42×C29C22×C412yes—
166C42×C29C22×C411yescharacteristic
167C42×C29C22×C412yes—
168C42×C29C22×C411yescharacteristic
169C42×C29C22×C418yes—
170C42×C29C2411yescharacteristic
171C42×C29C2411yescharacteristic
172C42×C29C2412yes—
173C42×C29C2414yes—
174#60204C2911yesmaximal, characteristic, direct product factor, Sylow
175C23×C29—22no—
176C23×C29—24no—
177C23×C29C23×C414yes—
178C23×C29C23×C411yescharacteristic
179C23×C29C23×C412yes—
180Q8×C29—24no—
181Q8×C29—28no—
182D4×C29—28no—
183D4×C29—216no—
184D4×C29—24no—
185D4×C29—28no—
186C2×C4×C29—22no—
187C2×C4×C29—24no—
188C2×C4×C29—24no—
189C2×C4×C29—24no—
190C2×C4×C29—24no—
191C2×C4×C29—24no—
192C2×C4×C29—24no—
193C2×C4×C29—216no—
194C2×C4×C29—24no—
195C2×C4×C29—28no—
196C2×C4×C29#13118yescomplemented
197C2×C4×C29C23×C412yes—
198C2×C4×C29C23×C412yes—
199C2×C4×C29C23×C412yes—
200C2×C4×C29C23×C414yes—
201C2×C4×C29C23×C418yes—
202C2×C4×C29C23×C411yescharacteristic
203C2×C4×C29C23×C412yes—
204C2×C4×C29C23×C412yes—
205C2×C4×C29C2×#4114yes—
206C2×C4×C29C2511yescharacteristic
207C8×C29—24no—
208C8×C29—28no—
209C8×C29C2×#4114yes—
210C8×C29C2×#4114yes—
211#3444C2×C2911yescharacteristic
212#2966C2×C2918yescomplemented
213#2965C2×C2914yescomplemented
214C8×#41C2×C2914yescomplemented
215#2960C2×C2912yescomplemented
216#2931C2×C2912yescomplemented
217#2929C2×C2914yescomplemented
218#2922C2×C2912yescomplemented
219#2920C2×C2911yescharacteristic, complemented
220C4×#131C2×C2912yescomplemented
221C22×C4×C8C2×C2911yescharacteristic, complemented
222C22×C29—28no—
223C22×C29—22no—
224C22×C29—22no—
225C22×C29—22no—
226C22×C29—24no—
227C22×C29—28no—
228C22×C29C4×#4112yes—
229C22×C29C2×#13114yes—
230C22×C29C24×C411yescharacteristic
231C4×C29—22no—
232C4×C29—24no—
233C4×C29—22no—
234C4×C29—22no—
235C4×C29—28no—
236C4×C29C4×#4112yes—
237C4×C29C2×#13114yes—
238C4×C29C2×#13114yes—
239C4×C29C22×#4112yes—
240C2×#131C22×C2914yes—
241C23×C8C22×C2912yes—
242#533C4×C2912yes—
243#533C22×C2911yescharacteristic
244#532C4×C2912yes—
245#532C22×C2911yescharacteristic
246#529C4×C2914yes—
247#529C4×C2914yes—
248#529C22×C2914yes—
249#525C4×C2914yes—
250#525C22×C2912yes—
251C4×#41C22×C2914yes—
252C4×#41C22×C2912yes—
253C22×C42C22×C2911yescharacteristic
254#446C22×C2918yescomplemented
255C8×Q8C22×C2918yescomplemented
256#436C22×C2918yescomplemented
257#435C22×C29116yes—
258C8×D4C22×C29116yes—
259C8×D4C22×C2918yescomplemented
260#433C22×C2918yescomplemented
261#432C22×C2914yes—
262#431C22×C2914yes—
263#431C22×C2918yescomplemented
264#424C22×C2914yes—
265#423C22×C2912yes—
266#408C22×C2914yes—
267#407C22×C2912yes—
268#405C22×C2914yes—
269#405C22×C2918yescomplemented
270C4×M16C22×C2912yes—
271C4×M16C22×C2914yescomplemented
272C2×C4×C8C22×C2911yescharacteristic
273C2×C4×C8C22×C2911yescharacteristic
274C2×C4×C8C22×C2912yes—
275C2×C4×C8C22×C2912yes—
276C2×C4×C8C22×C2912yes—
277C2×C4×C8C22×C2914yes—
278C2×C4×C8C22×C2914yescomplemented
279C2×C29—22no—
280C2×C29—24no—
281C2×C29—44no—
282C2×C29C2×C4×#4111yescharacteristic
283C2×C29C22×#13112yes—
284C2×#41C2×C4×C2914yes—
285C2×#41C23×C2912yes—
286C23×C4C2×C4×C2912yes—
287C23×C4C23×C2911yescharacteristic
288#131—216no—
289C2×M16C23×C2914yes—
290C2×M16C23×C2918yes—
291C22×C8—28no—
292C22×C8C23×C2912yes—
293C22×C8C23×C2914yes—
294C22×C8C23×C2914yes—
295C22×C8C23×C2918yes—
296C22×C8C23×C2912yes—
297C4⋊Q8C2×C4×C2912yes—
298C4⋊Q8C2×C4×C2911yescharacteristic
299#127C2×C4×C2911yescharacteristic
300#126C2×C4×C2918yes—
301#125C2×C4×C2912yes—
302#125C2×C4×C2914yes—
303#124C2×C4×C2912yes—
304#124C2×C4×C2914yes—
305#123C2×C4×C2918yes—
306#123C2×C4×C2914yes—
307C22⋊Q8C2×C4×C2914yes—
308C22⋊Q8C2×C4×C2914yes—
309C22⋊Q8C2×C4×C2914yes—
310#121C2×C4×C2914yes—
311#121C2×C4×C2914yes—
312#121C2×C4×C2914yes—
313#120C2×C4×C2914yes—
314C4×Q8C2×C4×C2914yes—
315C4×Q8C2×C4×C2914yes—
316C4×Q8C23×C2914yes—
317C4×D4C2×C4×C2918yes—
318C4×D4C2×C4×C2918yes—
319C4×D4C2×C4×C2914yes—
320C4×D4C2×C4×C2914yes—
321C4×D4C23×C2918yes—
322C4×D4C23×C2914yes—
323#117C2×C4×C2914yes—
324#117C2×C4×C2918yes—
325#117C23×C2912yes—
326#117C23×C2914yes—
327C2×C42C2×C4×C2912yes—
328C2×C42C2×C4×C2912yes—
329C2×C42C2×C4×C2912yes—
330C2×C42C23×C2914yes—
331C2×C42C23×C2911yescharacteristic
332C2×C42C23×C2912yes—
333C2×C42C23×C2912yes—
334C2×C42C23×C2911yescharacteristic
335C4⋊C8C23×C2918yes—
336C4⋊C8C23×C29116yes—
337C22⋊C8C23×C2918yes—
338C22⋊C8C23×C29116yes—
339#97C23×C2914yes—
340#97C23×C2918yes—
341C4×C8C23×C2911yescharacteristic
342C4×C8C23×C2911yescharacteristic
343C4×C8C23×C2912yes—
344C4×C8C23×C2912yes—
345C4×C8C23×C2912yes—
346C4×C8C23×C2914yes—
347C4×C8C23×C2914yes—
348C4×C8C23×C2914yes—
349C4×C8C23×C2918yes—
350C29#6020411yescharacteristic, direct product factor, Sylow
351C24C22×C4×C2911yescharacteristic
352#41—216no—
353#41—28no—
354C2×Q8C22×C4×C2912yes—
355C2×Q8C22×C4×C2914yes—
356C2×D4C22×C4×C2914yes—
357C2×D4C22×C4×C2912yes—
358C2×D4C22×C4×C2918yes—
359C2×D4C22×C4×C2914yes—
360C22×C4—28no—
361C22×C4—24no—
362C22×C4C22×C4×C2912yes—
363C22×C4C22×C4×C2911yescharacteristic
364C22×C4C22×C4×C2912yes—
365C22×C4C22×C4×C2912yes—
366C22×C4C22×C4×C2912yes—
367C22×C4C22×C4×C2912yes—
368C22×C4C22×C4×C2912yes—
369C22×C4C22×C4×C2918yes—
370C22×C4C22×C4×C2912yes—
371C22×C4C24×C2912yes—
372C22×C4C24×C2914yes—
373C22×C4C24×C2911yescharacteristic
374M16—28no—
375M16—216no—
376C2×C8—24no—
377C2×C8—28no—
378C2×C8—28no—
379C2×C8—216no—
380C2×C8#41×C2918yescomplemented
381C2×C8C24×C2914yes—
382C2×C8C24×C2918yes—
383C2×C8C24×C2912yes—
384C2×C8C24×C2912yes—
385C4⋊C4C22×C4×C2914yes—
386C4⋊C4C22×C4×C2918yes—
387C4⋊C4C22×C4×C2914yes—
388C4⋊C4C22×C4×C2918yes—
389C4⋊C4C22×C4×C2914yes—
390C4⋊C4C22×C4×C2918yes—
391C22⋊C4C22×C4×C2918yes—
392C22⋊C4C22×C4×C2918yes—
393C22⋊C4C22×C4×C2918yes—
394C22⋊C4C22×C4×C2914yes—
395C22⋊C4C22×C4×C2918yes—
396C42C22×C4×C2912yes—
397C42C22×C4×C2912yes—
398C42C22×C4×C2912yes—
399C42C22×C4×C2912yes—
400C42C22×C4×C2911yescharacteristic
401C42C22×C4×C2912yes—
402C42C22×C4×C2911yescharacteristic
403C42C22×C4×C2918yes—
404C42C24×C2911yescharacteristic
405C42C24×C2911yescharacteristic
406C42C24×C2912yes—
407C42C24×C2914yes—
408C23—22no—
409C23—24no—
410C23C23×C4×C2914yes—
411C23C23×C4×C2911yescharacteristic
412C23C23×C4×C2912yes—
413Q8—24no—
414Q8—28no—
415D4—28no—
416D4—216no—
417D4—24no—
418D4—28no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—24no—
426C2×C4—216no—
427C2×C4—24no—
428C2×C4—28no—
429C2×C4C29×#13118yescomplemented
430C2×C4C23×C4×C2912yes—
431C2×C4C23×C4×C2912yes—
432C2×C4C23×C4×C2912yes—
433C2×C4C23×C4×C2914yes—
434C2×C4C23×C4×C2918yes—
435C2×C4C23×C4×C2911yescharacteristic
436C2×C4C23×C4×C2912yes—
437C2×C4C23×C4×C2912yes—
438C2×C4C2×#41×C2914yes—
439C2×C4C25×C2911yescharacteristic
440C8—24no—
441C8—28no—
442C8C2×#41×C2914yes—
443C8C2×#41×C2914yes—
444C22—28no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—28no—
449C22—24no—
450C22C4×#41×C2912yes—
451C22C2×C29×#13114yes—
452C22C24×C4×C2911yescharacteristic
453C4—22no—
454C4—22no—
455C4—28no—
456C4—22no—
457C4—24no—
458C4C4×#41×C2912yes—
459C4C2×C29×#13114yes—
460C4C2×C29×#13114yes—
461C4C22×#41×C2912yes—
462C2—22no—
463C2—24no—
464C2—44no—
465C2C2×C4×#41×C2911yescharacteristic
466C2C22×C29×#13112yes—
subgroupG/H
centerC4×C8×C29C23
commutatorC22C24×C4×C29
Frattini, cosocleC2×C4C25×C29
socleC22×C29C24×C4
prime radicalC29×#3444C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C4×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2966C2semidirect
3. C29×#2965C2semidirect
4. C8×#41×C29C2semidirect
5. C29×#2960C2semidirect
6. C29×#2931C2semidirect
7. C29×#2929C2semidirect
8. C29×#2922C2semidirect
9. C29×#2920C2semidirect
10. C4×C29×#131C2semidirect
11. C22×C4×C8×C29C2semidirect
26. C29×#446C22semidirect
27. C8×Q8×C29C22semidirect
28. C29×#436C22semidirect
31. C8×D4×C29C22semidirect
32. C29×#433C22semidirect
35. C29×#431C22semidirect
41. C29×#405C22semidirect
43. C4×M16×C29C22semidirect
50. C2×C4×C8×C29C22semidirect
146. C2×C8×C29#41semidirect
174. #60204C29direct (N × H)
196. C2×C4×C29#131semidirect
212. #2966C2×C29semidirect
213. #2965C2×C29semidirect
214. C8×#41C2×C29semidirect
215. #2960C2×C29semidirect
216. #2931C2×C29semidirect
217. #2929C2×C29semidirect
218. #2922C2×C29semidirect
219. #2920C2×C29semidirect
220. C4×#131C2×C29semidirect
221. C22×C4×C8C2×C29semidirect
254. #446C22×C29semidirect
255. C8×Q8C22×C29semidirect
256. #436C22×C29semidirect
259. C8×D4C22×C29semidirect
260. #433C22×C29semidirect
263. #431C22×C29semidirect
269. #405C22×C29semidirect
271. C4×M16C22×C29semidirect
278. C2×C4×C8C22×C29semidirect
350. C29#60204direct (N × H)
380. C2×C8#41×C29semidirect
429. C2×C4C29×#131semidirect

Maximal subgroups

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

subgroupindex
C29×#34442
C29×#29662
C29×#29652
C8×#41×C292
C29×#29602
C29×#29312
C29×#29292
C29×#29222
C29×#29202
C4×C29×#1312
C22×C4×C8×C292
#6020429