Finite Group Databasebeta

← C29×#19346 #20314246

Subgroups — C29×#19346 #20314246

Order 7424.

582 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3237C211yesmaximal, characteristic, complemented
2C29×#3216C211yesmaximal, characteristic
3C29×#3167C211yesmaximal, characteristic
4C29×#2960C211yesmaximal, characteristic, complemented
5C29×#1692C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1680C212yesmaximal, complemented
8C29×#1678C212yesmaximal, complemented
9C29×#1568C211yesmaximal, characteristic, complemented
10C29×#1559C211yesmaximal, characteristic, complemented
11C29×#1557C211yesmaximal, characteristic
12C29×#533C2211yescharacteristic
13C29×#533C2211yescharacteristic
14C29×#532C2211yescharacteristic
15C29×#501—21no—
16C29×#498C2211yescharacteristic
17C29×#497—21no—
18C29×#492C2211yescharacteristic
19C29×#491—21no—
20C29×#489—21no—
21C29×#487C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#485—22no—
24C29×#477C2212yes—
25C29×#475C2212yes—
26C29×#465—21no—
27C29×#465—21no—
28C29×#462C2212yes—
29C29×#460C2212yes—
30C29×#452—22no—
31C29×#446—21no—
32C29×#446C2212yes—
33C8×Q8×C29—21no—
34C8×Q8×C29C2212yes—
35C4×SD16×C29—21no—
36C4×SD16×C29—21no—
37C29×#432C2211yescharacteristic
38C29×#432C2211yescharacteristic
39C29×#424—21no—
40C29×#423C2211yescharacteristic
41C29×#405—21no—
42C2×C4×C8×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×Q16×C29—22no—
51C2×SD16×C29—22no—
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×M16×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—21no—
83C29×#106—21no—
84C29×#106—22no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—22no—
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—22no—
96C29×#102—21no—
97C29×#102—21no—
98C29×#102—22no—
99C29×C22⋊C8—21no—
100C29×C22⋊C8—21no—
101C29×#97—22no—
102C29×#97—21no—
103C29×#97—21no—
104C4×C8×C29—22no—
105C4×C8×C29D411yescharacteristic
106C4×C8×C29D411yescharacteristic
107C4×C8×C29C2311yescharacteristic
108C4×C8×C29C2311yescharacteristic
109#41×C29—82no—
110C2×Q8×C29—21no—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—21no—
114C2×Q8×C29C2×D412yes—
115C2×D4×C29—21no—
116C2×D4×C29—21no—
117C2×D4×C29—21no—
118C2×D4×C29—41no—
119C22×C4×C29—41no—
120C22×C4×C29C2×D411yescharacteristic
121C22×C4×C29C2×D411yescharacteristic
122C22×C4×C29#4111yescharacteristic
123Q16×C29—82no—
124SD16×C29—42no—
125SD16×C29—42no—
126SD16×C29—82no—
127M16×C29—42no—
128C2×C8×C29—22no—
129C2×C8×C29—22no—
130C2×C8×C29—22no—
131C2×C8×C29—22no—
132C2×C8×C29—41no—
133C2×C8×C29C2×D411yescharacteristic
134C2×C8×C29C2×D411yescharacteristic
135C2×C8×C29C2×D411yescharacteristic
136C2×C8×C29C2×D411yescharacteristic
137C4⋊C4×C29—21no—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—22no—
141C4⋊C4×C29—22no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29C2×D412yes—
151C22⋊C4×C29—22no—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C22⋊C4×C29—41no—
155C42×C29—22no—
156C42×C29—41no—
157C42×C29C2×D411yescharacteristic
158C42×C29C2×D411yescharacteristic
159C42×C29#4111yescharacteristic
160C42×C29C2411yescharacteristic
161#19346C2911yesmaximal, characteristic, direct product factor, Sylow
162C23×C29—41no—
163C23×C29#12111yescharacteristic
164Q8×C29—22no—
165Q8×C29—22no—
166Q8×C29—42no—
167Q8×C29—41no—
168Q8×C29—41no—
169Q8×C29—42no—
170Q8×C29—81no—
171D4×C29—41no—
172D4×C29—41no—
173D4×C29—42no—
174D4×C29—81no—
175D4×C29—82no—
176C2×C4×C29—21no—
177C2×C4×C29—21no—
178C2×C4×C29—22no—
179C2×C4×C29—22no—
180C2×C4×C29—22no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—82no—
186C2×C4×C29#12111yescharacteristic
187C2×C4×C29#12111yescharacteristic
188C2×C4×C29#12111yescharacteristic
189C2×C4×C29C22×D411yescharacteristic
190C2×C4×C29C22×D411yescharacteristic
191C2×C4×C29C2×#4111yescharacteristic
192C8×C29—21no—
193C8×C29—21no—
194C8×C29—21no—
195C8×C29—42no—
196C8×C29—42no—
197C8×C29—42no—
198C8×C29#13712yes—
199#3237C2×C2911yescharacteristic, complemented
200#3216C2×C2911yescharacteristic
201#3167C2×C2911yescharacteristic
202#2960C2×C2911yescharacteristic, complemented
203#1692C2×C2912yescomplemented
204#1686C2×C2912yescomplemented
205#1680C2×C2912yescomplemented
206#1678C2×C2912yescomplemented
207#1568C2×C2911yescharacteristic, complemented
208#1559C2×C2911yescharacteristic, complemented
209#1557C2×C2911yescharacteristic
210C22×C29—21no—
211C22×C29—21no—
212C22×C29—21no—
213C22×C29—81no—
214C22×C29—81no—
215C22×C29—81no—
216C22×C29C2×#12111yescharacteristic
217C4×C29—21no—
218C4×C29—21no—
219C4×C29—21no—
220C4×C29—21no—
221C4×C29—42no—
222C4×C29—42no—
223C4×C29—81no—
224C4×C29—81no—
225C4×C29—81no—
226C4×C29C2×#13711yescharacteristic
227C4×C29#57511yescharacteristic
228C4×C29#57712yes—
229#533C22×C2911yescharacteristic
230#533C22×C2911yescharacteristic
231#532C22×C2911yescharacteristic
232#501—21no—
233#498C22×C2911yescharacteristic
234#497—21no—
235#492C22×C2911yescharacteristic
236#491—21no—
237#489—21no—
238#487C22×C2911yescharacteristic
239#486C22×C2911yescharacteristic
240#485—22no—
241#477C22×C2912yes—
242#475C22×C2912yes—
243#465—21no—
244#465—21no—
245#462C22×C2912yes—
246#460C22×C2912yes—
247#452—22no—
248#446—21no—
249#446C22×C2912yes—
250C8×Q8—21no—
251C8×Q8C22×C2912yes—
252C4×SD16—21no—
253C4×SD16—21no—
254#432C22×C2911yescharacteristic
255#432C22×C2911yescharacteristic
256#424—21no—
257#423C22×C2911yescharacteristic
258#405—21no—
259C2×C4×C8C22×C2911yescharacteristic
260#335C22×C2912yes—
261#334C22×C2912yes—
262#333C22×C2912yes—
263#332C22×C2912yes—
264#332C22×C2912yes—
265#331C22×C2912yes—
266C2×C29—41no—
267C2×C29—161no—
268C2×C29#303711yescharacteristic
269C2×C29#305711yescharacteristic
270C2×C29#306711yescharacteristic
271C2×#41—21no—
272C2×Q16—22no—
273C2×SD16—22no—
274C2×SD16—21no—
275C2×SD16—21no—
276C2×M16—21no—
277C22×C8D4×C2911yescharacteristic
278C22×C8D4×C2911yescharacteristic
279C4⋊Q8D4×C2911yescharacteristic
280C4⋊Q8D4×C2911yescharacteristic
281C4⋊Q8C23×C2911yescharacteristic
282C4⋊Q8C23×C2911yescharacteristic
283C4⋊Q8C23×C2911yescharacteristic
284#127C23×C2911yescharacteristic
285#125—21no—
286#125—21no—
287#124—21no—
288C22⋊Q8—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C22⋊Q8D4×C2912yes—
292#121—21no—
293#121—21no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8C23×C2912yes—
298C4×D4—21no—
299C4×D4—21no—
300#117—21no—
301#117—21no—
302C2×C42C23×C2911yescharacteristic
303#107—22no—
304#106—21no—
305#106—21no—
306#106—22no—
307C4⋊C8—22no—
308C4⋊C8—22no—
309C4⋊C8—21no—
310C4⋊C8C23×C2912yes—
311C4⋊C8C23×C2912yes—
312C4⋊C8C23×C2912yes—
313#103—22no—
314#103—22no—
315#103—21no—
316#103—21no—
317#103—22no—
318#102—21no—
319#102—21no—
320#102—22no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323#97—22no—
324#97—21no—
325#97—21no—
326C4×C8—22no—
327C4×C8D4×C2911yescharacteristic
328C4×C8D4×C2911yescharacteristic
329C4×C8C23×C2911yescharacteristic
330C4×C8C23×C2911yescharacteristic
331C29#1934611yescharacteristic, direct product factor, Sylow
332#41—82no—
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—21no—
336C2×Q8—21no—
337C2×Q8C2×D4×C2912yes—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—41no—
342C22×C4—41no—
343C22×C4C2×D4×C2911yescharacteristic
344C22×C4C2×D4×C2911yescharacteristic
345C22×C4#41×C2911yescharacteristic
346Q16—82no—
347SD16—42no—
348SD16—42no—
349SD16—82no—
350M16—42no—
351C2×C8—22no—
352C2×C8—22no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—41no—
356C2×C8C2×D4×C2911yescharacteristic
357C2×C8C2×D4×C2911yescharacteristic
358C2×C8C2×D4×C2911yescharacteristic
359C2×C8C2×D4×C2911yescharacteristic
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4C2×D4×C2912yes—
374C22⋊C4—22no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C42—22no—
379C42—41no—
380C42C2×D4×C2911yescharacteristic
381C42C2×D4×C2911yescharacteristic
382C42#41×C2911yescharacteristic
383C42C24×C2911yescharacteristic
384C23—41no—
385C23C29×#12111yescharacteristic
386Q8—22no—
387Q8—22no—
388Q8—42no—
389Q8—41no—
390Q8—41no—
391Q8—42no—
392Q8—81no—
393D4—41no—
394D4—41no—
395D4—42no—
396D4—81no—
397D4—82no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4C29×#12111yescharacteristic
409C2×C4C29×#12111yescharacteristic
410C2×C4C29×#12111yescharacteristic
411C2×C4C22×D4×C2911yescharacteristic
412C2×C4C22×D4×C2911yescharacteristic
413C2×C4C2×#41×C2911yescharacteristic
414C8—21no—
415C8—21no—
416C8—21no—
417C8—42no—
418C8—42no—
419C8—42no—
420C8C29×#13712yes—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22C2×C29×#12111yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—21no—
432C4—42no—
433C4—42no—
434C4—81no—
435C4—81no—
436C4—81no—
437C4C2×C29×#13711yescharacteristic
438C4C29×#57511yescharacteristic
439C4C29×#57712yes—
440C2—41no—
441C2—161no—
442C2C29×#303711yescharacteristic
443C2C29×#305711yescharacteristic
444C2C29×#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×#3237C2semidirect
4. C29×#2960C2semidirect
5. C29×#1692C2semidirect
6. C29×#1686C2semidirect
7. C29×#1680C2semidirect
8. C29×#1678C2semidirect
9. C29×#1568C2semidirect
10. C29×#1559C2semidirect
161. #19346C29direct (N × H)
199. #3237C2×C29semidirect
202. #2960C2×C29semidirect
203. #1692C2×C29semidirect
204. #1686C2×C29semidirect
205. #1680C2×C29semidirect
206. #1678C2×C29semidirect
207. #1568C2×C29semidirect
208. #1559C2×C29semidirect
331. C29#19346direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32372
C29×#32162
C29×#31672
C29×#29602
C29×#16922
C29×#16862
C29×#16802
C29×#16782
C29×#15682
C29×#15592
C29×#15572
#1934629