Finite Group Databasebeta

← C29×#19285 #20314185

Subgroups — C29×#19285 #20314185

Order 7424.

636 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3167C211yesmaximal, characteristic
2C29×#3078C211yesmaximal, characteristic, complemented
3C29×#3037C211yesmaximal, characteristic
4C2×C29×#446C211yesmaximal, characteristic, complemented
5C29×#1700C212yesmaximal, complemented
6C29×#1698C212yesmaximal, complemented
7C29×#1692C212yesmaximal, complemented
8C29×#1686C212yesmaximal, complemented
9C29×#1567C211yesmaximal, characteristic, complemented
10C29×#1550C211yesmaximal, characteristic, complemented
11C29×#1547C211yesmaximal, characteristic
12C2×C29×#137—21no—
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C2×C4×Q8×C29C2211yescharacteristic
16C29×#498C2211yescharacteristic
17C29×#492C2211yescharacteristic
18C29×#487C2211yescharacteristic
19C29×#486C2211yescharacteristic
20C29×#479—22no—
21C29×#477C2212yes—
22C29×#475C2212yes—
23C29×#465—21no—
24C29×#465—21no—
25C29×#464—22no—
26C29×#462C2212yes—
27C29×#460C2212yes—
28C29×#446—21no—
29C29×#446—21no—
30C29×#446C2212yes—
31C29×#446C2212yes—
32C4×SD16×C29—21no—
33C4×SD16×C29—21no—
34C29×#428—21no—
35C29×#423C2211yescharacteristic
36C29×#423C2211yescharacteristic
37C2×C29×C4⋊C8—21no—
38C2×C29×C4⋊C8C2211yescharacteristic
39C29×#419—21no—
40C29×#417—21no—
41C2×C29×#97—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#335C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C22×Q8×C29D411yescharacteristic
51C29×#137—44no—
52C2×Q16×C29—22no—
53C2×SD16×C29—22no—
54C2×SD16×C29—21no—
55C2×SD16×C29—21no—
56C2×M16×C29—21no—
57C2×M16×C29—21no—
58C22×C8×C29—21no—
59C22×C8×C29D411yescharacteristic
60C22×C8×C29D411yescharacteristic
61C29×C4⋊Q8C2311yescharacteristic
62C29×C4⋊Q8C2311yescharacteristic
63C29×C4⋊Q8C2311yescharacteristic
64C29×#127C2311yescharacteristic
65C29×#125—21no—
66C29×#124—21no—
67C29×C22⋊Q8—21no—
68C29×C22⋊Q8—21no—
69C29×#121—21no—
70C29×#121—21no—
71C4×Q8×C29—21no—
72C4×Q8×C29—21no—
73C4×Q8×C29—21no—
74C4×Q8×C29—21no—
75C4×Q8×C29D412yes—
76C4×Q8×C29C2312yes—
77C4×D4×C29—21no—
78C4×D4×C29—21no—
79C29×#117—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29D411yescharacteristic
82C2×C42×C29—21no—
83C2×C42×C29C2311yescharacteristic
84C29×#107—22no—
85C29×#106—21no—
86C29×#106—21no—
87C29×#106—22no—
88C29×C4⋊C8—22no—
89C29×C4⋊C8—22no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8—21no—
92C29×C4⋊C8—21no—
93C29×C4⋊C8C2312yes—
94C29×C4⋊C8C2312yes—
95C29×C4⋊C8C2312yes—
96C29×#103—22no—
97C29×#103—22no—
98C29×#103—21no—
99C29×#103—21no—
100C29×#103—22no—
101C29×#102—21no—
102C29×#102—21no—
103C29×#102—22no—
104C29×#97—22no—
105C29×#97—22no—
106C4×C8×C29D411yescharacteristic
107C4×C8×C29D411yescharacteristic
108C4×C8×C29C2311yescharacteristic
109C4×C8×C29C2311yescharacteristic
110#41×C29—42no—
111#41×C29—42no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—22no—
115C2×Q8×C29—21no—
116C2×Q8×C29—21no—
117C2×Q8×C29—21no—
118C2×Q8×C29C2×D412yes—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—41no—
123C22×C4×C29—21no—
124C22×C4×C29—21no—
125C22×C4×C29—41no—
126C22×C4×C29C2×D411yescharacteristic
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29#4111yescharacteristic
129Q16×C29—44no—
130SD16×C29—42no—
131SD16×C29—44no—
132SD16×C29—42no—
133M16×C29—42no—
134M16×C29—42no—
135C2×C8×C29—22no—
136C2×C8×C29—22no—
137C2×C8×C29—22no—
138C2×C8×C29—22no—
139C2×C8×C29—41no—
140C2×C8×C29—42no—
141C2×C8×C29C2×D411yescharacteristic
142C2×C8×C29C2×D411yescharacteristic
143C2×C8×C29C2×D411yescharacteristic
144C2×C8×C29C2×D411yescharacteristic
145C4⋊C4×C29—22no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—22no—
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—41no—
158C22⋊C4×C29—41no—
159C22⋊C4×C29—41no—
160C42×C29—22no—
161C42×C29—22no—
162C42×C29—41no—
163C42×C29C2×D411yescharacteristic
164C42×C29C2×D411yescharacteristic
165C42×C29#4111yescharacteristic
166C42×C29C2411yescharacteristic
167#19285C2911yesmaximal, characteristic, direct product factor, Sylow
168C23×C29—41no—
169C23×C29#12111yescharacteristic
170Q8×C29—22no—
171Q8×C29—22no—
172Q8×C29—42no—
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—41no—
176Q8×C29—41no—
177Q8×C29—81no—
178D4×C29—41no—
179D4×C29—41no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—81no—
183D4×C29—82no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—22no—
187C2×C4×C29—22no—
188C2×C4×C29—41no—
189C2×C4×C29—42no—
190C2×C4×C29—42no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—41no—
194C2×C4×C29—82no—
195C2×C4×C29#12111yescharacteristic
196C2×C4×C29#12111yescharacteristic
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29AGL(1,ℤ/8)12yes—
199C2×C4×C29#13712yes—
200C2×C4×C29C22×D411yescharacteristic
201C2×C4×C29C22×D411yescharacteristic
202C2×C4×C29C2×#4111yescharacteristic
203C8×C29—21no—
204C8×C29—21no—
205C8×C29—21no—
206C8×C29—42no—
207C8×C29—42no—
208C8×C29—42no—
209C8×C29#13712yescomplemented
210#3167C2×C2911yescharacteristic
211#3078C2×C2911yescharacteristic, complemented
212#3037C2×C2911yescharacteristic
213C2×#446C2×C2911yescharacteristic, complemented
214#1700C2×C2912yescomplemented
215#1698C2×C2912yescomplemented
216#1692C2×C2912yescomplemented
217#1686C2×C2912yescomplemented
218#1567C2×C2911yescharacteristic, complemented
219#1550C2×C2911yescharacteristic, complemented
220#1547C2×C2911yescharacteristic
221C22×C29—21no—
222C22×C29—21no—
223C22×C29—81no—
224C22×C29—81no—
225C22×C29—81no—
226C22×C29#46812yes—
227C22×C29C2×#12111yescharacteristic
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—21no—
231C4×C29—42no—
232C4×C29—42no—
233C4×C29—81no—
234C4×C29—81no—
235C4×C29—81no—
236C4×C29#46812yes—
237C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C29C2×#13711yescharacteristic
239C4×C29C2×#13711yescharacteristic
240C4×C29#57511yescharacteristic
241C2×#137—21no—
242#533C22×C2911yescharacteristic
243#532C22×C2911yescharacteristic
244C2×C4×Q8C22×C2911yescharacteristic
245#498C22×C2911yescharacteristic
246#492C22×C2911yescharacteristic
247#487C22×C2911yescharacteristic
248#486C22×C2911yescharacteristic
249#479—22no—
250#477C22×C2912yes—
251#475C22×C2912yes—
252#465—21no—
253#465—21no—
254#464—22no—
255#462C22×C2912yes—
256#460C22×C2912yes—
257#446—21no—
258#446—21no—
259#446C22×C2912yes—
260#446C22×C2912yes—
261C4×SD16—21no—
262C4×SD16—21no—
263#428—21no—
264#423C22×C2911yescharacteristic
265#423C22×C2911yescharacteristic
266C2×C4⋊C8—21no—
267C2×C4⋊C8C22×C2911yescharacteristic
268#419—21no—
269#417—21no—
270C2×#97—21no—
271C2×C4×C8C22×C2911yescharacteristic
272#335C22×C2912yes—
273#335C22×C2912yes—
274#333C22×C2912yes—
275#332C22×C2912yes—
276#332C22×C2912yes—
277#331C22×C2912yes—
278C2×C29—22no—
279C2×C29—161no—
280C2×C29#303711yescharacteristic
281C2×C29C2×#46811yescharacteristic
282C2×C29#306711yescharacteristic
283C2×#41—21no—
284C22×Q8D4×C2911yescharacteristic
285#137—44no—
286C2×Q16—22no—
287C2×SD16—22no—
288C2×SD16—21no—
289C2×SD16—21no—
290C2×M16—21no—
291C2×M16—21no—
292C22×C8—21no—
293C22×C8D4×C2911yescharacteristic
294C22×C8D4×C2911yescharacteristic
295C4⋊Q8C23×C2911yescharacteristic
296C4⋊Q8C23×C2911yescharacteristic
297C4⋊Q8C23×C2911yescharacteristic
298#127C23×C2911yescharacteristic
299#125—21no—
300#124—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—21no—
304#121—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8D4×C2912yes—
310C4×Q8C23×C2912yes—
311C4×D4—21no—
312C4×D4—21no—
313#117—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4D4×C2911yescharacteristic
316C2×C42—21no—
317C2×C42C23×C2911yescharacteristic
318#107—22no—
319#106—21no—
320#106—21no—
321#106—22no—
322C4⋊C8—22no—
323C4⋊C8—22no—
324C4⋊C8—21no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8C23×C2912yes—
328C4⋊C8C23×C2912yes—
329C4⋊C8C23×C2912yes—
330#103—22no—
331#103—22no—
332#103—21no—
333#103—21no—
334#103—22no—
335#102—21no—
336#102—21no—
337#102—22no—
338#97—22no—
339#97—22no—
340C4×C8D4×C2911yescharacteristic
341C4×C8D4×C2911yescharacteristic
342C4×C8C23×C2911yescharacteristic
343C4×C8C23×C2911yescharacteristic
344C29#1928511yescharacteristic, direct product factor, Sylow
345#41—42no—
346#41—42no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8C2×D4×C2912yes—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4C2×D4×C2911yescharacteristic
362C22×C4C2×D4×C2911yescharacteristic
363C22×C4#41×C2911yescharacteristic
364Q16—44no—
365SD16—42no—
366SD16—44no—
367SD16—42no—
368M16—42no—
369M16—42no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—42no—
376C2×C8C2×D4×C2911yescharacteristic
377C2×C8C2×D4×C2911yescharacteristic
378C2×C8C2×D4×C2911yescharacteristic
379C2×C8C2×D4×C2911yescharacteristic
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
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—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—22no—
396C42—22no—
397C42—41no—
398C42C2×D4×C2911yescharacteristic
399C42C2×D4×C2911yescharacteristic
400C42#41×C2911yescharacteristic
401C42C24×C2911yescharacteristic
402C23—41no—
403C23C29×#12111yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—42no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—41no—
411Q8—81no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—82no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4C29×#12111yescharacteristic
430C2×C4C29×#12111yescharacteristic
431C2×C4C29×#12111yescharacteristic
432C2×C4C29×AGL(1,ℤ/8)12yes—
433C2×C4C29×#13712yes—
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×#13712yescomplemented
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22C29×#46812yes—
450C22C2×C29×#12111yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—42no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4C29×#46812yes—
460C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
461C4C2×C29×#13711yescharacteristic
462C4C2×C29×#13711yescharacteristic
463C4C29×#57511yescharacteristic
464C2—22no—
465C2—161no—
466C2C29×#303711yescharacteristic
467C2C2×C29×#46811yescharacteristic
468C2C29×#306711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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
2. C29×#3078C2semidirect
4. C2×C29×#446C2semidirect
5. C29×#1700C2semidirect
6. C29×#1698C2semidirect
7. C29×#1692C2semidirect
8. C29×#1686C2semidirect
9. C29×#1567C2semidirect
10. C29×#1550C2semidirect
167. #19285C29direct (N × H)
209. C8×C29#137semidirect
211. #3078C2×C29semidirect
213. C2×#446C2×C29semidirect
214. #1700C2×C29semidirect
215. #1698C2×C29semidirect
216. #1692C2×C29semidirect
217. #1686C2×C29semidirect
218. #1567C2×C29semidirect
219. #1550C2×C29semidirect
344. C29#19285direct (N × H)
443. C8C29×#137semidirect

Maximal subgroups

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

subgroupindex
C29×#31672
C29×#30782
C29×#30372
C2×C29×#4462
C29×#17002
C29×#16982
C29×#16922
C29×#16862
C29×#15672
C29×#15502
C29×#15472
#1928529