Finite Group Databasebeta

← C29×#19334 #20314234

Subgroups — C29×#19334 #20314234

Order 7424.

650 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3235C211yesmaximal, characteristic, complemented
2C29×#3214C211yesmaximal, characteristic
3C29×#3167C211yesmaximal, characteristic, complemented
4C29×#2931C211yesmaximal, characteristic, complemented
5C29×#1691C212yesmaximal, complemented
6C29×#1685C212yesmaximal, complemented
7C29×#1679C212yesmaximal, complemented
8C29×#1677C212yesmaximal, complemented
9C29×#1568C211yesmaximal, characteristic, complemented
10C29×#1559C211yesmaximal, characteristic, complemented
11C29×#1557C211yesmaximal, characteristic, complemented
12C2×C29×#131—21no—
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C29×#532C2211yescharacteristic
16C29×#501—21no—
17C29×#498C2211yescharacteristic
18C29×#496—21no—
19C29×#492C2211yescharacteristic
20C29×#490—21no—
21C29×#489—21no—
22C29×#487C2211yescharacteristic
23C29×#486C2211yescharacteristic
24C29×#482—22no—
25C29×#476C2212yes—
26C29×#474C2212yes—
27C29×#465—21no—
28C29×#465—21no—
29C29×#461C2212yes—
30C29×#459C2212yes—
31C29×#449—22no—
32C4×SD16×C29—21no—
33C4×SD16×C29—21no—
34C29×#436—21no—
35C29×#436C2212yes—
36C8×D4×C29—21no—
37C8×D4×C29C2212yes—
38C29×#432C2211yescharacteristic
39C29×#432C2211yescharacteristic
40C29×#423C2211yescharacteristic
41C29×#408—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29—21no—
51C2×SD16×C29—22no—
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×D8×C29—22no—
55C29×#131—44no—
56C2×M16×C29—21no—
57C2×M16×C29—22no—
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—21no—
86C29×#106—21no—
87C29×#106—22no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8C2312yes—
90C29×C4⋊C8C2312yes—
91C29×C4⋊C8C2312yes—
92C29×#103—21no—
93C29×#103—21no—
94C29×#103—22no—
95C29×#102—22no—
96C29×#102—22no—
97C29×#102—21no—
98C29×#102—21no—
99C29×#102—22no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—22no—
103C29×C22⋊C8—22no—
104C29×#97—21no—
105C29×#97—21no—
106C4×C8×C29D411yescharacteristic
107C4×C8×C29D411yescharacteristic
108C4×C8×C29C2311yescharacteristic
109C4×C8×C29C2311yescharacteristic
110#41×C29—42no—
111#41×C29—42no—
112#41×C29—82no—
113C2×Q8×C29—21no—
114C2×Q8×C29—21no—
115C2×Q8×C29—21no—
116C2×Q8×C29—21no—
117C2×D4×C29—22no—
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—41no—
124C2×D4×C29C2×D412yes—
125C22×C4×C29—22no—
126C22×C4×C29—41no—
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29#4111yescharacteristic
130SD16×C29—42no—
131SD16×C29—42no—
132SD16×C29—82no—
133D8×C29—82no—
134M16×C29—42no—
135M16×C29—44no—
136C2×C8×C29—22no—
137C2×C8×C29—22no—
138C2×C8×C29—22no—
139C2×C8×C29—22no—
140C2×C8×C29—41no—
141C2×C8×C29—44no—
142C2×C8×C29C2×D411yescharacteristic
143C2×C8×C29C2×D411yescharacteristic
144C2×C8×C29C2×D411yescharacteristic
145C2×C8×C29C2×D411yescharacteristic
146C4⋊C4×C29—21no—
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—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29C2×D412yes—
156C22⋊C4×C29—22no—
157C22⋊C4×C29—22no—
158C22⋊C4×C29—41no—
159C22⋊C4×C29—41no—
160C22⋊C4×C29—41no—
161C42×C29—41no—
162C42×C29C2×D411yescharacteristic
163C42×C29C2×D411yescharacteristic
164C42×C29#4111yescharacteristic
165C42×C29C2411yescharacteristic
166#19334C2911yesmaximal, characteristic, direct product factor, Sylow
167C23×C29—22no—
168C23×C29—41no—
169C23×C29#12111yescharacteristic
170Q8×C29—42no—
171Q8×C29—41no—
172Q8×C29—41no—
173Q8×C29—42no—
174Q8×C29—81no—
175D4×C29—22no—
176D4×C29—22no—
177D4×C29—42no—
178D4×C29—42no—
179D4×C29—44no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—42no—
183D4×C29—81no—
184D4×C29—82no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—22no—
188C2×C4×C29—22no—
189C2×C4×C29—41no—
190C2×C4×C29—42no—
191C2×C4×C29—42no—
192C2×C4×C29—41no—
193C2×C4×C29—41no—
194C2×C4×C29—41no—
195C2×C4×C29—82no—
196C2×C4×C29#12111yescharacteristic
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29C22×D411yescharacteristic
200C2×C4×C29C22×D411yescharacteristic
201C2×C4×C29C2×#4111yescharacteristic
202C8×C29—21no—
203C8×C29—21no—
204C8×C29—21no—
205C8×C29—42no—
206C8×C29—42no—
207C8×C29—42no—
208C8×C29AGL(1,ℤ/8)12yes—
209#3235C2×C2911yescharacteristic, complemented
210#3214C2×C2911yescharacteristic
211#3167C2×C2911yescharacteristic, complemented
212#2931C2×C2911yescharacteristic, complemented
213#1691C2×C2912yescomplemented
214#1685C2×C2912yescomplemented
215#1679C2×C2912yescomplemented
216#1677C2×C2912yescomplemented
217#1568C2×C2911yescharacteristic, complemented
218#1559C2×C2911yescharacteristic, complemented
219#1557C2×C2911yescharacteristic, complemented
220C22×C29—21no—
221C22×C29—21no—
222C22×C29—21no—
223C22×C29—42no—
224C22×C29—42no—
225C22×C29—42no—
226C22×C29—81no—
227C22×C29—81no—
228C22×C29—81no—
229C22×C29C2×#12111yescharacteristic
230C4×C29—21no—
231C4×C29—21no—
232C4×C29—21no—
233C4×C29—21no—
234C4×C29—42no—
235C4×C29—81no—
236C4×C29—81no—
237C4×C29—81no—
238C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C29#57511yescharacteristic
240C4×C29#57712yes—
241C2×#131—21no—
242#533C22×C2911yescharacteristic
243#532C22×C2911yescharacteristic
244#532C22×C2911yescharacteristic
245#501—21no—
246#498C22×C2911yescharacteristic
247#496—21no—
248#492C22×C2911yescharacteristic
249#490—21no—
250#489—21no—
251#487C22×C2911yescharacteristic
252#486C22×C2911yescharacteristic
253#482—22no—
254#476C22×C2912yes—
255#474C22×C2912yes—
256#465—21no—
257#465—21no—
258#461C22×C2912yes—
259#459C22×C2912yes—
260#449—22no—
261C4×SD16—21no—
262C4×SD16—21no—
263#436—21no—
264#436C22×C2912yes—
265C8×D4—21no—
266C8×D4C22×C2912yes—
267#432C22×C2911yescharacteristic
268#432C22×C2911yescharacteristic
269#423C22×C2911yescharacteristic
270#408—21no—
271C2×C4×C8C22×C2911yescharacteristic
272#335C22×C2912yes—
273#334C22×C2912yes—
274#333C22×C2912yes—
275#332C22×C2912yes—
276#332C22×C2912yes—
277#331C22×C2912yes—
278C2×C29—41no—
279C2×C29—82no—
280C2×C29—161no—
281C2×C29#303611yescharacteristic
282C2×C29#305711yescharacteristic
283C2×C29#306711yescharacteristic
284C2×#41—21no—
285C2×#41—21no—
286C2×SD16—22no—
287C2×SD16—21no—
288C2×SD16—21no—
289C2×D8—22no—
290#131—44no—
291C2×M16—21no—
292C2×M16—22no—
293C22×C8—22no—
294C22×C8D4×C2911yescharacteristic
295C22×C8D4×C2911yescharacteristic
296C4⋊Q8D4×C2911yescharacteristic
297C4⋊Q8C23×C2911yescharacteristic
298C4⋊Q8C23×C2911yescharacteristic
299C4⋊Q8C23×C2911yescharacteristic
300#127D4×C2911yescharacteristic
301#127C23×C2911yescharacteristic
302#125—21no—
303#124—21no—
304#124—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121D4×C2912yes—
311C4×Q8—21no—
312C4×Q8—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4C23×C2912yes—
317#117—21no—
318C2×C42C23×C2911yescharacteristic
319#107—22no—
320#106—21no—
321#106—21no—
322#106—22no—
323C4⋊C8—21no—
324C4⋊C8C23×C2912yes—
325C4⋊C8C23×C2912yes—
326C4⋊C8C23×C2912yes—
327#103—21no—
328#103—21no—
329#103—22no—
330#102—22no—
331#102—22no—
332#102—21no—
333#102—21no—
334#102—22no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—22no—
338C22⋊C8—22no—
339#97—21no—
340#97—21no—
341C4×C8D4×C2911yescharacteristic
342C4×C8D4×C2911yescharacteristic
343C4×C8C23×C2911yescharacteristic
344C4×C8C23×C2911yescharacteristic
345C29#1933411yescharacteristic, direct product factor, Sylow
346#41—42no—
347#41—42no—
348#41—82no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4C2×D4×C2912yes—
361C22×C4—22no—
362C22×C4—41no—
363C22×C4C2×D4×C2911yescharacteristic
364C22×C4C2×D4×C2911yescharacteristic
365C22×C4#41×C2911yescharacteristic
366SD16—42no—
367SD16—42no—
368SD16—82no—
369D8—82no—
370M16—42no—
371M16—44no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—41no—
377C2×C8—44no—
378C2×C8C2×D4×C2911yescharacteristic
379C2×C8C2×D4×C2911yescharacteristic
380C2×C8C2×D4×C2911yescharacteristic
381C2×C8C2×D4×C2911yescharacteristic
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C2912yes—
392C22⋊C4—22no—
393C22⋊C4—22no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C42—41no—
398C42C2×D4×C2911yescharacteristic
399C42C2×D4×C2911yescharacteristic
400C42#41×C2911yescharacteristic
401C42C24×C2911yescharacteristic
402C23—22no—
403C23—41no—
404C23C29×#12111yescharacteristic
405Q8—42no—
406Q8—41no—
407Q8—41no—
408Q8—42no—
409Q8—81no—
410D4—22no—
411D4—22no—
412D4—42no—
413D4—42no—
414D4—44no—
415D4—41no—
416D4—41no—
417D4—42no—
418D4—81no—
419D4—82no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4C29×#12111yescharacteristic
432C2×C4C29×#12111yescharacteristic
433C2×C4C29×#12111yescharacteristic
434C2×C4C22×D4×C2911yescharacteristic
435C2×C4C22×D4×C2911yescharacteristic
436C2×C4C2×#41×C2911yescharacteristic
437C8—21no—
438C8—21no—
439C8—21no—
440C8—42no—
441C8—42no—
442C8—42no—
443C8C29×AGL(1,ℤ/8)12yes—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22C2×C29×#12111yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
463C4C29×#57511yescharacteristic
464C4C29×#57712yes—
465C2—41no—
466C2—82no—
467C2—161no—
468C2C29×#303611yescharacteristic
469C2C29×#305711yescharacteristic
470C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3214C2
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×#3235C2semidirect
3. C29×#3167C2semidirect
4. C29×#2931C2semidirect
5. C29×#1691C2semidirect
6. C29×#1685C2semidirect
7. C29×#1679C2semidirect
8. C29×#1677C2semidirect
9. C29×#1568C2semidirect
10. C29×#1559C2semidirect
11. C29×#1557C2semidirect
166. #19334C29direct (N × H)
209. #3235C2×C29semidirect
211. #3167C2×C29semidirect
212. #2931C2×C29semidirect
213. #1691C2×C29semidirect
214. #1685C2×C29semidirect
215. #1679C2×C29semidirect
216. #1677C2×C29semidirect
217. #1568C2×C29semidirect
218. #1559C2×C29semidirect
219. #1557C2×C29semidirect
345. C29#19334direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32352
C29×#32142
C29×#31672
C29×#29312
C29×#16912
C29×#16852
C29×#16792
C29×#16772
C29×#15682
C29×#15592
C29×#15572
#1933429