Finite Group Databasebeta

← C29×#19201 #20314101

Subgroups — C29×#19201 #20314101

Order 7424.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3246C211yesmaximal, characteristic, complemented
2C29×#3245C211yesmaximal, characteristic
3C29×#3131C211yesmaximal, characteristic, complemented
4C29×#2931C211yesmaximal, characteristic, complemented
5C29×#1699C212yesmaximal, complemented
6C29×#1697C212yesmaximal, complemented
7C29×#1683C212yesmaximal, complemented
8C29×#1681C212yesmaximal, complemented
9C2×C29×#335C211yesmaximal, characteristic, complemented
10C29×#1550C211yesmaximal, characteristic, complemented
11C29×#1547C211yesmaximal, characteristic, complemented
12C2×C29×#131—21no—
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C29×#532C2211yescharacteristic
16C29×#488—21no—
17C29×#488—21no—
18C29×#487C2211yescharacteristic
19C29×#487C2211yescharacteristic
20C29×#486C2211yescharacteristic
21C29×#486C2211yescharacteristic
22C29×#476C2212yes—
23C29×#475—21no—
24C29×#474—21no—
25C29×#474C2212yes—
26C29×#466—22no—
27C29×#465—22no—
28C29×#461C2212yes—
29C29×#460—21no—
30C29×#459—21no—
31C29×#459C2212yes—
32C29×#436—21no—
33C29×#436C2212yes—
34C8×D4×C29—21no—
35C8×D4×C29C2212yes—
36C29×#423C2211yescharacteristic
37C2×C29×C4⋊C8C2211yescharacteristic
38C2×C29×C4⋊C8C2211yescharacteristic
39C29×#416—21no—
40C29×#416—21no—
41C29×#408—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#335C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29—21no—
51C2×SD16×C29—22no—
52C2×D8×C29—22no—
53C29×#131—44no—
54C2×M16×C29—21no—
55C2×M16×C29—22no—
56C22×C8×C29—21no—
57C22×C8×C29—21no—
58C22×C8×C29—22no—
59C22×C8×C29D411yescharacteristic
60C22×C8×C29D411yescharacteristic
61C29×C4⋊Q8D411yescharacteristic
62C29×C4⋊Q8C2311yescharacteristic
63C29×C4⋊Q8C2311yescharacteristic
64C29×C4⋊Q8C2311yescharacteristic
65C29×#127D411yescharacteristic
66C29×#127C2311yescharacteristic
67C29×#125—21no—
68C29×#124—21no—
69C29×#124—21no—
70C29×C22⋊Q8—21no—
71C29×C22⋊Q8—21no—
72C29×#121—21no—
73C29×#121—21no—
74C29×#121—21no—
75C29×#121D412yes—
76C4×Q8×C29—21no—
77C4×Q8×C29—21no—
78C4×D4×C29—21no—
79C4×D4×C29—21no—
80C4×D4×C29—21no—
81C4×D4×C29C2312yes—
82C29×#117—21no—
83C2×C42×C29C2311yescharacteristic
84C29×#107—22no—
85C29×#106—22no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8C2312yes—
90C29×C4⋊C8C2312yes—
91C29×C4⋊C8C2312yes—
92C29×#103—21no—
93C29×#103—21no—
94C29×#103—21no—
95C29×#103—21no—
96C29×#103—22no—
97C29×#102—22no—
98C29×#102—22no—
99C29×#102—21no—
100C29×#102—21no—
101C29×#102—21no—
102C29×#102—21no—
103C29×#102—22no—
104C29×C22⋊C8—22no—
105C29×C22⋊C8—22no—
106C4×C8×C29D411yescharacteristic
107C4×C8×C29D411yescharacteristic
108C4×C8×C29C2311yescharacteristic
109C4×C8×C29C2311yescharacteristic
110#41×C29—42no—
111#41×C29—42no—
112#41×C29—42no—
113#41×C29—42no—
114C2×Q8×C29—21no—
115C2×Q8×C29—21no—
116C2×Q8×C29—21no—
117C2×Q8×C29—21no—
118C2×D4×C29—22no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—21no—
124C2×D4×C29—41no—
125C2×D4×C29C2×D412yes—
126C22×C4×C29—22no—
127C22×C4×C29—41no—
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29#4111yescharacteristic
131SD16×C29—82no—
132D8×C29—82no—
133M16×C29—44no—
134M16×C29—42no—
135C2×C8×C29—22no—
136C2×C8×C29—22no—
137C2×C8×C29—22no—
138C2×C8×C29—22no—
139C2×C8×C29—22no—
140C2×C8×C29—44no—
141C2×C8×C29—81no—
142C2×C8×C29—81no—
143C2×C8×C29C2×D411yescharacteristic
144C2×C8×C29C2×D411yescharacteristic
145C2×C8×C29C2×D411yescharacteristic
146C2×C8×C29C2×D411yescharacteristic
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29C2×D412yes—
157C22⋊C4×C29—22no—
158C22⋊C4×C29—22no—
159C22⋊C4×C29—41no—
160C22⋊C4×C29—41no—
161C22⋊C4×C29—41no—
162C42×C29—41no—
163C42×C29C2×D411yescharacteristic
164C42×C29C2×D411yescharacteristic
165C42×C29#4111yescharacteristic
166C42×C29C2411yescharacteristic
167#19201C2911yesmaximal, characteristic, direct product factor, Sylow
168C23×C29—22no—
169C23×C29—41no—
170C23×C29#12111yescharacteristic
171Q8×C29—42no—
172Q8×C29—41no—
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—41no—
176Q8×C29—81no—
177D4×C29—22no—
178D4×C29—22no—
179D4×C29—42no—
180D4×C29—44no—
181D4×C29—41no—
182D4×C29—41no—
183D4×C29—41no—
184D4×C29—41no—
185D4×C29—42no—
186D4×C29—81no—
187D4×C29—82no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—22no—
191C2×C4×C29—41no—
192C2×C4×C29—42no—
193C2×C4×C29—42no—
194C2×C4×C29—41no—
195C2×C4×C29—41no—
196C2×C4×C29—41no—
197C2×C4×C29—82no—
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29#12111yescharacteristic
201C2×C4×C29#13512yes—
202C2×C4×C29AGL(1,ℤ/8)12yes—
203C2×C4×C29C22×D411yescharacteristic
204C2×C4×C29C22×D411yescharacteristic
205C2×C4×C29C2×#4111yescharacteristic
206C8×C29—21no—
207C8×C29—21no—
208C8×C29—21no—
209C8×C29—21no—
210C8×C29—42no—
211C8×C29—42no—
212C8×C29—42no—
213#3246C2×C2911yescharacteristic, complemented
214#3245C2×C2911yescharacteristic
215#3131C2×C2911yescharacteristic, complemented
216#2931C2×C2911yescharacteristic, complemented
217#1699C2×C2912yescomplemented
218#1697C2×C2912yescomplemented
219#1683C2×C2912yescomplemented
220#1681C2×C2912yescomplemented
221C2×#335C2×C2911yescharacteristic, complemented
222#1550C2×C2911yescharacteristic, complemented
223#1547C2×C2911yescharacteristic, complemented
224C22×C29—21no—
225C22×C29—21no—
226C22×C29—42no—
227C22×C29—42no—
228C22×C29—42no—
229C22×C29—81no—
230C22×C29—81no—
231C22×C29—81no—
232C22×C29#46312yes—
233C22×C29C2×#12111yescharacteristic
234C4×C29—21no—
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—42no—
238C4×C29—81no—
239C4×C29—81no—
240C4×C29—81no—
241C4×C29#46312yes—
242C4×C29C2×#13511yescharacteristic
243C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C29#57611yescharacteristic
245C4×C29#57811yescharacteristic
246C2×#131—21no—
247#533C22×C2911yescharacteristic
248#532C22×C2911yescharacteristic
249#532C22×C2911yescharacteristic
250#488—21no—
251#488—21no—
252#487C22×C2911yescharacteristic
253#487C22×C2911yescharacteristic
254#486C22×C2911yescharacteristic
255#486C22×C2911yescharacteristic
256#476C22×C2912yes—
257#475—21no—
258#474—21no—
259#474C22×C2912yes—
260#466—22no—
261#465—22no—
262#461C22×C2912yes—
263#460—21no—
264#459—21no—
265#459C22×C2912yes—
266#436—21no—
267#436C22×C2912yes—
268C8×D4—21no—
269C8×D4C22×C2912yes—
270#423C22×C2911yescharacteristic
271C2×C4⋊C8C22×C2911yescharacteristic
272C2×C4⋊C8C22×C2911yescharacteristic
273#416—21no—
274#416—21no—
275#408—21no—
276C2×C4×C8C22×C2911yescharacteristic
277#335C22×C2912yes—
278#335C22×C2912yes—
279#333C22×C2912yes—
280#332C22×C2912yes—
281#332C22×C2912yes—
282#331C22×C2912yes—
283C2×C29—22no—
284C2×C29—82no—
285C2×C29—161no—
286C2×C29C2×#46311yescharacteristic
287C2×C29#306111yescharacteristic
288C2×C29#306711yescharacteristic
289C2×#41—21no—
290C2×#41—21no—
291C2×SD16—22no—
292C2×D8—22no—
293#131—44no—
294C2×M16—21no—
295C2×M16—22no—
296C22×C8—21no—
297C22×C8—21no—
298C22×C8—22no—
299C22×C8D4×C2911yescharacteristic
300C22×C8D4×C2911yescharacteristic
301C4⋊Q8D4×C2911yescharacteristic
302C4⋊Q8C23×C2911yescharacteristic
303C4⋊Q8C23×C2911yescharacteristic
304C4⋊Q8C23×C2911yescharacteristic
305#127D4×C2911yescharacteristic
306#127C23×C2911yescharacteristic
307#125—21no—
308#124—21no—
309#124—21no—
310C22⋊Q8—21no—
311C22⋊Q8—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121D4×C2912yes—
316C4×Q8—21no—
317C4×Q8—21no—
318C4×D4—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4C23×C2912yes—
322#117—21no—
323C2×C42C23×C2911yescharacteristic
324#107—22no—
325#106—22no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8—21no—
329C4⋊C8C23×C2912yes—
330C4⋊C8C23×C2912yes—
331C4⋊C8C23×C2912yes—
332#103—21no—
333#103—21no—
334#103—21no—
335#103—21no—
336#103—22no—
337#102—22no—
338#102—22no—
339#102—21no—
340#102—21no—
341#102—21no—
342#102—21no—
343#102—22no—
344C22⋊C8—22no—
345C22⋊C8—22no—
346C4×C8D4×C2911yescharacteristic
347C4×C8D4×C2911yescharacteristic
348C4×C8C23×C2911yescharacteristic
349C4×C8C23×C2911yescharacteristic
350C29#1920111yescharacteristic, direct product factor, Sylow
351#41—42no—
352#41—42no—
353#41—42no—
354#41—42no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4C2×D4×C2912yes—
367C22×C4—22no—
368C22×C4—41no—
369C22×C4C2×D4×C2911yescharacteristic
370C22×C4C2×D4×C2911yescharacteristic
371C22×C4#41×C2911yescharacteristic
372SD16—82no—
373D8—82no—
374M16—44no—
375M16—42no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—44no—
382C2×C8—81no—
383C2×C8—81no—
384C2×C8C2×D4×C2911yescharacteristic
385C2×C8C2×D4×C2911yescharacteristic
386C2×C8C2×D4×C2911yescharacteristic
387C2×C8C2×D4×C2911yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4C2×D4×C2912yes—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C42—41no—
404C42C2×D4×C2911yescharacteristic
405C42C2×D4×C2911yescharacteristic
406C42#41×C2911yescharacteristic
407C42C24×C2911yescharacteristic
408C23—22no—
409C23—41no—
410C23C29×#12111yescharacteristic
411Q8—42no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—41no—
416Q8—81no—
417D4—22no—
418D4—22no—
419D4—42no—
420D4—44no—
421D4—42no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—81no—
427D4—82no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—82no—
438C2×C4C29×#12111yescharacteristic
439C2×C4C29×#12111yescharacteristic
440C2×C4C29×#12111yescharacteristic
441C2×C4C29×#13512yes—
442C2×C4C29×AGL(1,ℤ/8)12yes—
443C2×C4C22×D4×C2911yescharacteristic
444C2×C4C22×D4×C2911yescharacteristic
445C2×C4C2×#41×C2911yescharacteristic
446C8—21no—
447C8—21no—
448C8—21no—
449C8—21no—
450C8—42no—
451C8—42no—
452C8—42no—
453C22—21no—
454C22—21no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22C29×#46312yes—
462C22C2×C29×#12111yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4C29×#46312yes—
471C4C2×C29×#13511yescharacteristic
472C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
473C4C29×#57611yescharacteristic
474C4C29×#57811yescharacteristic
475C2—22no—
476C2—82no—
477C2—161no—
478C2C2×C29×#46311yescharacteristic
479C2C29×#306111yescharacteristic
480C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3245C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3246C2semidirect
3. C29×#3131C2semidirect
4. C29×#2931C2semidirect
5. C29×#1699C2semidirect
6. C29×#1697C2semidirect
7. C29×#1683C2semidirect
8. C29×#1681C2semidirect
9. C2×C29×#335C2semidirect
10. C29×#1550C2semidirect
11. C29×#1547C2semidirect
167. #19201C29direct (N × H)
213. #3246C2×C29semidirect
215. #3131C2×C29semidirect
216. #2931C2×C29semidirect
217. #1699C2×C29semidirect
218. #1697C2×C29semidirect
219. #1683C2×C29semidirect
220. #1681C2×C29semidirect
221. C2×#335C2×C29semidirect
222. #1550C2×C29semidirect
223. #1547C2×C29semidirect
350. C29#19201direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32462
C29×#32452
C29×#31312
C29×#29312
C29×#16992
C29×#16972
C29×#16832
C29×#16812
C2×C29×#3352
C29×#15502
C29×#15472
#1920129