Finite Group Databasebeta

← C29×#19314 #20314214

Subgroups — C29×#19314 #20314214

Order 7424.

630 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3165C211yesmaximal, characteristic, complemented
2C29×#3116C211yesmaximal, characteristic
3C29×#3039C211yesmaximal, characteristic
4C29×#2970C211yesmaximal, characteristic
5C29×#1694C212yesmaximal, complemented
6C29×#1692C212yesmaximal, complemented
7C29×#1673C212yesmaximal, complemented
8C29×#1671C212yesmaximal, complemented
9C29×#1569C211yesmaximal, characteristic, complemented
10C29×#1559C211yesmaximal, characteristic, complemented
11C29×#1556C211yesmaximal, characteristic, complemented
12C2×C29×#137—21no—
13C29×#533C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#501—21no—
17C29×#501—21no—
18C29×#500C2212yes—
19C29×#498C2212yes—
20C29×#485—21no—
21C29×#477C2211yescharacteristic
22C29×#476C2211yescharacteristic
23C29×#462—21no—
24C29×#462C2212yes—
25C29×#462C2211yescharacteristic
26C29×#461—21no—
27C29×#461C2212yes—
28C29×#461C2211yescharacteristic
29C29×#452—21no—
30C29×#446C2212yes—
31C29×#441—21no—
32C29×#440—21no—
33C29×#435—22no—
34C8×D4×C29C2212yes—
35C29×#432—21no—
36C29×#432C2211yescharacteristic
37C29×#432C2211yescharacteristic
38C29×#428—22no—
39C29×#423C2211yescharacteristic
40C29×#419—21no—
41C4×M16×C29C2211yescharacteristic
42C2×C29×#97—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#332C2212yes—
49C2×#41×C29D411yescharacteristic
50C22×Q8×C29—21no—
51C29×#137—44no—
52C2×Q16×C29—21no—
53C2×Q16×C29—22no—
54C2×SD16×C29—21no—
55C2×SD16×C29—22no—
56C2×M16×C29—21no—
57C2×M16×C29D412yes—
58C22×C8×C29—22no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8C2312yes—
63C29×C4⋊Q8C2311yescharacteristic
64C29×C4⋊Q8C2311yescharacteristic
65C29×#125—21no—
66C29×C22⋊Q8—21no—
67C29×C22⋊Q8—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29—21no—
70C4×Q8×C29D411yescharacteristic
71C4×Q8×C29C2311yescharacteristic
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C4×D4×C29D411yescharacteristic
75C4×D4×C29C2311yescharacteristic
76C29×#117—21no—
77C29×#117—21no—
78C29×#117D411yescharacteristic
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C42×C29—21no—
82C2×C42×C29C2311yescharacteristic
83C29×#107—22no—
84C29×#107—22no—
85C29×#107—21no—
86C29×#106—22no—
87C29×#106—22no—
88C29×#106—21no—
89C29×C4⋊C8—22no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8C2312yes—
92C29×C4⋊C8C2311yescharacteristic
93C29×C4⋊C8C2311yescharacteristic
94C29×C4⋊C8C2312yes—
95C29×#103—21no—
96C29×#103—21no—
97C29×#103—21no—
98C29×#103—22no—
99C29×#103—22no—
100C29×#102—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—21no—
103C29×C22⋊C8—22no—
104C29×#97—22no—
105C29×#97—21no—
106C29×#97—21no—
107C29×#97D411yescharacteristic
108C29×#97D411yescharacteristic
109C4×C8×C29C2312yes—
110#41×C29—22no—
111#41×C29—41no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—21no—
115C2×Q8×C29—42no—
116C2×Q8×C29—42no—
117C2×Q8×C29—41no—
118C2×Q8×C29C2×D411yescharacteristic
119C2×D4×C29—21no—
120C2×D4×C29C2×D411yescharacteristic
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—41no—
125C22×C4×C29C2×D411yescharacteristic
126C22×C4×C29C2×D411yescharacteristic
127C22×C4×C29#4111yescharacteristic
128Q16×C29—42no—
129Q16×C29—44no—
130SD16×C29—42no—
131SD16×C29—44no—
132M16×C29—24no—
133M16×C29—42no—
134C2×C8×C29—22no—
135C2×C8×C29—22no—
136C2×C8×C29—21no—
137C2×C8×C29—21no—
138C2×C8×C29—44no—
139C2×C8×C29C2×D412yes—
140C2×C8×C29C2×D412yes—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—22no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29C2×D411yescharacteristic
154C4⋊C4×C29C2×D411yescharacteristic
155C22⋊C4×C29—21no—
156C22⋊C4×C29—21no—
157C22⋊C4×C29—21no—
158C22⋊C4×C29—41no—
159C42×C29—21no—
160C42×C29—21no—
161C42×C29—21no—
162C42×C29—41no—
163C42×C29C2×D411yescharacteristic
164C42×C29C2×D411yescharacteristic
165C42×C29#4111yescharacteristic
166C42×C29C2411yescharacteristic
167#19314C2911yesmaximal, characteristic, direct product factor, Sylow
168C23×C29—21no—
169C23×C29#12111yescharacteristic
170Q8×C29—21no—
171Q8×C29—21no—
172Q8×C29—42no—
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—42no—
176Q8×C29—81no—
177Q8×C29—82no—
178D4×C29—21no—
179D4×C29—42no—
180D4×C29AGL(1,ℤ/8)12yes—
181C2×C4×C29—21no—
182C2×C4×C29—22no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—41no—
188C2×C4×C29—42no—
189C2×C4×C29—42no—
190C2×C4×C29—41no—
191C2×C4×C29—41no—
192C2×C4×C29—42no—
193C2×C4×C29—81no—
194C2×C4×C29—82no—
195C2×C4×C29#12111yescharacteristic
196C2×C4×C29#12111yescharacteristic
197C2×C4×C29#12111yescharacteristic
198C2×C4×C29C22×D411yescharacteristic
199C2×C4×C29C22×D411yescharacteristic
200C2×C4×C29C2×#4111yescharacteristic
201C8×C29—22no—
202C8×C29—42no—
203C8×C29—41no—
204C8×C29—42no—
205C8×C29—41no—
206C8×C29#13714yescomplemented
207#3165C2×C2911yescharacteristic, complemented
208#3116C2×C2911yescharacteristic
209#3039C2×C2911yescharacteristic
210#2970C2×C2911yescharacteristic
211#1694C2×C2912yescomplemented
212#1692C2×C2912yescomplemented
213#1673C2×C2912yescomplemented
214#1671C2×C2912yescomplemented
215#1569C2×C2911yescharacteristic, complemented
216#1559C2×C2911yescharacteristic, complemented
217#1556C2×C2911yescharacteristic, complemented
218C22×C29—21no—
219C22×C29—21no—
220C22×C29—22no—
221C22×C29—21no—
222C22×C29—41no—
223C22×C29—41no—
224C22×C29C2×#12111yescharacteristic
225C4×C29—21no—
226C4×C29—21no—
227C4×C29—21no—
228C4×C29—21no—
229C4×C29—41no—
230C4×C29—41no—
231C4×C29—41no—
232C4×C29—82no—
233C4×C29—81no—
234C4×C29—81no—
235C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
236C4×C29C2×#13712yes—
237C4×C29#57511yescharacteristic
238C2×#137—21no—
239#533C22×C2911yescharacteristic
240C2×C4⋊Q8C22×C2911yescharacteristic
241C4×#41C22×C2911yescharacteristic
242#501—21no—
243#501—21no—
244#500C22×C2912yes—
245#498C22×C2912yes—
246#485—21no—
247#477C22×C2911yescharacteristic
248#476C22×C2911yescharacteristic
249#462—21no—
250#462C22×C2911yescharacteristic
251#462C22×C2912yes—
252#461—21no—
253#461C22×C2911yescharacteristic
254#461C22×C2912yes—
255#452—21no—
256#446C22×C2912yes—
257#441—21no—
258#440—21no—
259#435—22no—
260C8×D4C22×C2912yes—
261#432—21no—
262#432C22×C2911yescharacteristic
263#432C22×C2911yescharacteristic
264#428—22no—
265#423C22×C2911yescharacteristic
266#419—21no—
267C4×M16C22×C2911yescharacteristic
268C2×#97—21no—
269#335C22×C2912yes—
270#334C22×C2912yes—
271#333C22×C2912yes—
272#332C22×C2912yes—
273#332C22×C2912yes—
274#332C22×C2912yes—
275C2×C29—41no—
276C2×C29—42no—
277C2×C29#303911yescharacteristic
278C2×C29#305511yescharacteristic
279C2×C29#306911yescharacteristic
280C2×#41D4×C2911yescharacteristic
281C22×Q8—21no—
282#137—44no—
283C2×Q16—22no—
284C2×Q16—21no—
285C2×SD16—22no—
286C2×SD16—21no—
287C2×M16—21no—
288C2×M16D4×C2912yes—
289C22×C8—22no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8—21no—
293C4⋊Q8C23×C2912yes—
294C4⋊Q8C23×C2911yescharacteristic
295C4⋊Q8C23×C2911yescharacteristic
296#125—21no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8D4×C2911yescharacteristic
302C4×Q8C23×C2911yescharacteristic
303C4×D4—21no—
304C4×D4—21no—
305C4×D4D4×C2911yescharacteristic
306C4×D4C23×C2911yescharacteristic
307#117—21no—
308#117—21no—
309#117D4×C2911yescharacteristic
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C42—21no—
313C2×C42C23×C2911yescharacteristic
314#107—22no—
315#107—22no—
316#107—21no—
317#106—22no—
318#106—22no—
319#106—21no—
320C4⋊C8—22no—
321C4⋊C8—21no—
322C4⋊C8C23×C2912yes—
323C4⋊C8C23×C2911yescharacteristic
324C4⋊C8C23×C2911yescharacteristic
325C4⋊C8C23×C2912yes—
326#103—21no—
327#103—22no—
328#103—22no—
329#103—21no—
330#103—21no—
331#102—21no—
332C22⋊C8—21no—
333C22⋊C8—21no—
334C22⋊C8—22no—
335#97—22no—
336#97—21no—
337#97—21no—
338#97D4×C2911yescharacteristic
339#97D4×C2911yescharacteristic
340C4×C8C23×C2912yes—
341C29#1931411yescharacteristic, direct product factor, Sylow
342#41—22no—
343#41—41no—
344C2×Q8—21no—
345C2×Q8—22no—
346C2×Q8—21no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8—41no—
350C2×Q8C2×D4×C2911yescharacteristic
351C2×D4—21no—
352C2×D4C2×D4×C2911yescharacteristic
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—41no—
357C22×C4C2×D4×C2911yescharacteristic
358C22×C4C2×D4×C2911yescharacteristic
359C22×C4#41×C2911yescharacteristic
360Q16—44no—
361Q16—42no—
362SD16—44no—
363SD16—42no—
364M16—24no—
365M16—42no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—44no—
371C2×C8C2×D4×C2912yes—
372C2×C8C2×D4×C2912yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4C2×D4×C2911yescharacteristic
386C4⋊C4C2×D4×C2911yescharacteristic
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—21no—
390C22⋊C4—41no—
391C42—21no—
392C42—21no—
393C42—21no—
394C42—41no—
395C42C2×D4×C2911yescharacteristic
396C42C2×D4×C2911yescharacteristic
397C42#41×C2911yescharacteristic
398C42C24×C2911yescharacteristic
399C23—21no—
400C23C29×#12111yescharacteristic
401Q8—21no—
402Q8—21no—
403Q8—42no—
404Q8—41no—
405Q8—41no—
406Q8—42no—
407Q8—81no—
408Q8—82no—
409D4—21no—
410D4—42no—
411D4C29×AGL(1,ℤ/8)12yes—
412C2×C4—21no—
413C2×C4—22no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—81no—
425C2×C4—82no—
426C2×C4C29×#12111yescharacteristic
427C2×C4C29×#12111yescharacteristic
428C2×C4C29×#12111yescharacteristic
429C2×C4C22×D4×C2911yescharacteristic
430C2×C4C22×D4×C2911yescharacteristic
431C2×C4C2×#41×C2911yescharacteristic
432C8—22no—
433C8—42no—
434C8—41no—
435C8—42no—
436C8—41no—
437C8C29×#13714yescomplemented
438C22—21no—
439C22—21no—
440C22—22no—
441C22—21no—
442C22—41no—
443C22—41no—
444C22C2×C29×#12111yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—41no—
450C4—41no—
451C4—41no—
452C4—82no—
453C4—81no—
454C4—81no—
455C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
456C4C2×C29×#13712yes—
457C4C29×#57511yescharacteristic
458C2—41no—
459C2—42no—
460C2C29×#303911yescharacteristic
461C2C29×#305511yescharacteristic
462C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×#41×C29D4
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×#3165C2semidirect
5. C29×#1694C2semidirect
6. C29×#1692C2semidirect
7. C29×#1673C2semidirect
8. C29×#1671C2semidirect
9. C29×#1569C2semidirect
10. C29×#1559C2semidirect
11. C29×#1556C2semidirect
167. #19314C29direct (N × H)
206. C8×C29#137semidirect
207. #3165C2×C29semidirect
211. #1694C2×C29semidirect
212. #1692C2×C29semidirect
213. #1673C2×C29semidirect
214. #1671C2×C29semidirect
215. #1569C2×C29semidirect
216. #1559C2×C29semidirect
217. #1556C2×C29semidirect
341. C29#19314direct (N × H)
437. C8C29×#137semidirect

Maximal subgroups

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

subgroupindex
C29×#31652
C29×#31162
C29×#30392
C29×#29702
C29×#16942
C29×#16922
C29×#16732
C29×#16712
C29×#15692
C29×#15592
C29×#15562
#1931429