Finite Group Databasebeta

← C29×#19216 #20314116

Subgroups — C29×#19216 #20314116

Order 7424.

592 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3249C211yesmaximal, characteristic, complemented
2C29×#3246C211yesmaximal, characteristic
3C29×#3131C211yesmaximal, characteristic
4C29×#2960C211yesmaximal, characteristic, complemented
5C29×#1704C212yesmaximal, complemented
6C29×#1702C212yesmaximal, complemented
7C29×#1680C212yesmaximal, complemented
8C29×#1678C212yesmaximal, complemented
9C2×C29×#334C211yesmaximal, characteristic, complemented
10C29×#1550C211yesmaximal, characteristic, complemented
11C29×#1547C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C29×#488—21no—
16C29×#488—21no—
17C29×#487C2211yescharacteristic
18C29×#487C2211yescharacteristic
19C29×#486C2211yescharacteristic
20C29×#486C2211yescharacteristic
21C29×#477—21no—
22C29×#477C2212yes—
23C29×#476—21no—
24C29×#475C2212yes—
25C29×#467—22no—
26C29×#465—22no—
27C29×#462—21no—
28C29×#462C2212yes—
29C29×#461—21no—
30C29×#460C2212yes—
31C29×#446—21no—
32C29×#446C2212yes—
33C8×Q8×C29—21no—
34C8×Q8×C29C2212yes—
35C29×#424—21no—
36C29×#423C2211yescharacteristic
37C2×C29×C4⋊C8C2211yescharacteristic
38C2×C29×C4⋊C8C2211yescharacteristic
39C29×#416—21no—
40C29×#416—21no—
41C29×#405—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#334C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×Q16×C29—22no—
51C2×SD16×C29—22no—
52C2×M16×C29—21no—
53C22×C8×C29—21no—
54C22×C8×C29—21no—
55C22×C8×C29D411yescharacteristic
56C22×C8×C29D411yescharacteristic
57C29×C4⋊Q8D411yescharacteristic
58C29×C4⋊Q8D411yescharacteristic
59C29×C4⋊Q8C2311yescharacteristic
60C29×C4⋊Q8C2311yescharacteristic
61C29×C4⋊Q8C2311yescharacteristic
62C29×#127C2311yescharacteristic
63C29×#125—21no—
64C29×#125—21no—
65C29×#124—21no—
66C29×C22⋊Q8—21no—
67C29×C22⋊Q8—21no—
68C29×C22⋊Q8—21no—
69C29×C22⋊Q8D412yes—
70C29×#121—21no—
71C29×#121—21no—
72C4×Q8×C29—21no—
73C4×Q8×C29—21no—
74C4×Q8×C29—21no—
75C4×Q8×C29C2312yes—
76C4×D4×C29—21no—
77C4×D4×C29—21no—
78C29×#117—21no—
79C29×#117—21no—
80C2×C42×C29C2311yescharacteristic
81C29×#107—22no—
82C29×#106—22no—
83C29×C4⋊C8—22no—
84C29×C4⋊C8—22no—
85C29×C4⋊C8—21no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2312yes—
90C29×C4⋊C8C2312yes—
91C29×#103—22no—
92C29×#103—22no—
93C29×#103—21no—
94C29×#103—21no—
95C29×#103—21no—
96C29×#103—21no—
97C29×#103—22no—
98C29×#102—21no—
99C29×#102—21no—
100C29×#102—21no—
101C29×#102—21no—
102C29×#102—22no—
103C29×#97—22no—
104C4×C8×C29—22no—
105C4×C8×C29D411yescharacteristic
106C4×C8×C29D411yescharacteristic
107C4×C8×C29C2311yescharacteristic
108C4×C8×C29C2311yescharacteristic
109#41×C29—42no—
110#41×C29—42no—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—21no—
114C2×Q8×C29—21no—
115C2×Q8×C29C2×D412yes—
116C2×D4×C29—21no—
117C2×D4×C29—21no—
118C2×D4×C29—21no—
119C2×D4×C29—41no—
120C22×C4×C29—41no—
121C22×C4×C29C2×D411yescharacteristic
122C22×C4×C29C2×D411yescharacteristic
123C22×C4×C29#4111yescharacteristic
124Q16×C29—82no—
125SD16×C29—82no—
126M16×C29—42no—
127C2×C8×C29—22no—
128C2×C8×C29—22no—
129C2×C8×C29—22no—
130C2×C8×C29—22no—
131C2×C8×C29—22no—
132C2×C8×C29—81no—
133C2×C8×C29—81no—
134C2×C8×C29C2×D411yescharacteristic
135C2×C8×C29C2×D411yescharacteristic
136C2×C8×C29C2×D411yescharacteristic
137C2×C8×C29C2×D411yescharacteristic
138C4⋊C4×C29—21no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—22no—
142C4⋊C4×C29—22no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29C2×D412yes—
152C22⋊C4×C29—22no—
153C22⋊C4×C29—41no—
154C22⋊C4×C29—41no—
155C22⋊C4×C29—41no—
156C42×C29—22no—
157C42×C29—41no—
158C42×C29C2×D411yescharacteristic
159C42×C29C2×D411yescharacteristic
160C42×C29#4111yescharacteristic
161C42×C29C2411yescharacteristic
162#19216C2911yesmaximal, characteristic, direct product factor, Sylow
163C23×C29—41no—
164C23×C29#12111yescharacteristic
165Q8×C29—22no—
166Q8×C29—22no—
167Q8×C29—42no—
168Q8×C29—41no—
169Q8×C29—41no—
170Q8×C29—41no—
171Q8×C29—41no—
172Q8×C29—81no—
173D4×C29—41no—
174D4×C29—41no—
175D4×C29—41no—
176D4×C29—41no—
177D4×C29—81no—
178D4×C29—82no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—22no—
182C2×C4×C29—22no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—82no—
188C2×C4×C29#12111yescharacteristic
189C2×C4×C29#12111yescharacteristic
190C2×C4×C29#12111yescharacteristic
191C2×C4×C29#13512yes—
192C2×C4×C29#13712yes—
193C2×C4×C29C22×D411yescharacteristic
194C2×C4×C29C22×D411yescharacteristic
195C2×C4×C29C2×#4111yescharacteristic
196C8×C29—21no—
197C8×C29—21no—
198C8×C29—21no—
199C8×C29—21no—
200C8×C29—42no—
201C8×C29—42no—
202C8×C29—42no—
203#3249C2×C2911yescharacteristic, complemented
204#3246C2×C2911yescharacteristic
205#3131C2×C2911yescharacteristic
206#2960C2×C2911yescharacteristic, complemented
207#1704C2×C2912yescomplemented
208#1702C2×C2912yescomplemented
209#1680C2×C2912yescomplemented
210#1678C2×C2912yescomplemented
211C2×#334C2×C2911yescharacteristic, complemented
212#1550C2×C2911yescharacteristic, complemented
213#1547C2×C2911yescharacteristic
214C22×C29—21no—
215C22×C29—21no—
216C22×C29—81no—
217C22×C29—81no—
218C22×C29—81no—
219C22×C29#46412yes—
220C22×C29C2×#12111yescharacteristic
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—42no—
225C4×C29—42no—
226C4×C29—81no—
227C4×C29—81no—
228C4×C29—81no—
229C4×C29#46412yes—
230C4×C29C2×#13511yescharacteristic
231C4×C29C2×#13711yescharacteristic
232C4×C29#57711yescharacteristic
233C4×C29#57711yescharacteristic
234#533C22×C2911yescharacteristic
235#533C22×C2911yescharacteristic
236#532C22×C2911yescharacteristic
237#488—21no—
238#488—21no—
239#487C22×C2911yescharacteristic
240#487C22×C2911yescharacteristic
241#486C22×C2911yescharacteristic
242#486C22×C2911yescharacteristic
243#477—21no—
244#477C22×C2912yes—
245#476—21no—
246#475C22×C2912yes—
247#467—22no—
248#465—22no—
249#462—21no—
250#462C22×C2912yes—
251#461—21no—
252#460C22×C2912yes—
253#446—21no—
254#446C22×C2912yes—
255C8×Q8—21no—
256C8×Q8C22×C2912yes—
257#424—21no—
258#423C22×C2911yescharacteristic
259C2×C4⋊C8C22×C2911yescharacteristic
260C2×C4⋊C8C22×C2911yescharacteristic
261#416—21no—
262#416—21no—
263#405—21no—
264C2×C4×C8C22×C2911yescharacteristic
265#334C22×C2912yes—
266#334C22×C2912yes—
267#333C22×C2912yes—
268#332C22×C2912yes—
269#332C22×C2912yes—
270#331C22×C2912yes—
271C2×C29—22no—
272C2×C29—161no—
273C2×C29C2×#46411yescharacteristic
274C2×C29#306011yescharacteristic
275C2×C29#306711yescharacteristic
276C2×#41—21no—
277C2×Q16—22no—
278C2×SD16—22no—
279C2×M16—21no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8D4×C2911yescharacteristic
283C22×C8D4×C2911yescharacteristic
284C4⋊Q8D4×C2911yescharacteristic
285C4⋊Q8D4×C2911yescharacteristic
286C4⋊Q8C23×C2911yescharacteristic
287C4⋊Q8C23×C2911yescharacteristic
288C4⋊Q8C23×C2911yescharacteristic
289#127C23×C2911yescharacteristic
290#125—21no—
291#125—21no—
292#124—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8D4×C2912yes—
297#121—21no—
298#121—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8C23×C2912yes—
303C4×D4—21no—
304C4×D4—21no—
305#117—21no—
306#117—21no—
307C2×C42C23×C2911yescharacteristic
308#107—22no—
309#106—22no—
310C4⋊C8—22no—
311C4⋊C8—22no—
312C4⋊C8—21no—
313C4⋊C8—21no—
314C4⋊C8—21no—
315C4⋊C8C23×C2912yes—
316C4⋊C8C23×C2912yes—
317C4⋊C8C23×C2912yes—
318#103—22no—
319#103—22no—
320#103—21no—
321#103—21no—
322#103—21no—
323#103—21no—
324#103—22no—
325#102—21no—
326#102—21no—
327#102—21no—
328#102—21no—
329#102—22no—
330#97—22no—
331C4×C8—22no—
332C4×C8D4×C2911yescharacteristic
333C4×C8D4×C2911yescharacteristic
334C4×C8C23×C2911yescharacteristic
335C4×C8C23×C2911yescharacteristic
336C29#1921611yescharacteristic, direct product factor, Sylow
337#41—42no—
338#41—42no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8C2×D4×C2912yes—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—41no—
348C22×C4—41no—
349C22×C4C2×D4×C2911yescharacteristic
350C22×C4C2×D4×C2911yescharacteristic
351C22×C4#41×C2911yescharacteristic
352Q16—82no—
353SD16—82no—
354M16—42no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—22no—
360C2×C8—81no—
361C2×C8—81no—
362C2×C8C2×D4×C2911yescharacteristic
363C2×C8C2×D4×C2911yescharacteristic
364C2×C8C2×D4×C2911yescharacteristic
365C2×C8C2×D4×C2911yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4C2×D4×C2912yes—
380C22⋊C4—22no—
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C42—22no—
385C42—41no—
386C42C2×D4×C2911yescharacteristic
387C42C2×D4×C2911yescharacteristic
388C42#41×C2911yescharacteristic
389C42C24×C2911yescharacteristic
390C23—41no—
391C23C29×#12111yescharacteristic
392Q8—22no—
393Q8—22no—
394Q8—42no—
395Q8—41no—
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—81no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—41no—
404D4—81no—
405D4—82no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4C29×#12111yescharacteristic
416C2×C4C29×#12111yescharacteristic
417C2×C4C29×#12111yescharacteristic
418C2×C4C29×#13512yes—
419C2×C4C29×#13712yes—
420C2×C4C22×D4×C2911yescharacteristic
421C2×C4C22×D4×C2911yescharacteristic
422C2×C4C2×#41×C2911yescharacteristic
423C8—21no—
424C8—21no—
425C8—21no—
426C8—21no—
427C8—42no—
428C8—42no—
429C8—42no—
430C22—21no—
431C22—21no—
432C22—81no—
433C22—81no—
434C22—81no—
435C22C29×#46412yes—
436C22C2×C29×#12111yescharacteristic
437C4—21no—
438C4—21no—
439C4—21no—
440C4—42no—
441C4—42no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4C29×#46412yes—
446C4C2×C29×#13511yescharacteristic
447C4C2×C29×#13711yescharacteristic
448C4C29×#57711yescharacteristic
449C4C29×#57711yescharacteristic
450C2—22no—
451C2—161no—
452C2C2×C29×#46411yescharacteristic
453C2C29×#306011yescharacteristic
454C2C29×#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
1. C29×#3249C2semidirect
4. C29×#2960C2semidirect
5. C29×#1704C2semidirect
6. C29×#1702C2semidirect
7. C29×#1680C2semidirect
8. C29×#1678C2semidirect
9. C2×C29×#334C2semidirect
10. C29×#1550C2semidirect
162. #19216C29direct (N × H)
203. #3249C2×C29semidirect
206. #2960C2×C29semidirect
207. #1704C2×C29semidirect
208. #1702C2×C29semidirect
209. #1680C2×C29semidirect
210. #1678C2×C29semidirect
211. C2×#334C2×C29semidirect
212. #1550C2×C29semidirect
336. C29#19216direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32492
C29×#32462
C29×#31312
C29×#29602
C29×#17042
C29×#17022
C29×#16802
C29×#16782
C2×C29×#3342
C29×#15502
C29×#15472
#1921629