Finite Group Databasebeta

← C29×#9264 #20304164

Subgroups — C29×#9264 #20304164

Order 7424.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3188C211yesmaximal, characteristic
2C29×#2977C211yesmaximal, characteristic, complemented
3C29×#1504C211yesmaximal, characteristic, complemented
4C2×C29×#327C211yesmaximal, characteristic, complemented
5C29×#1471C211yesmaximal, characteristic, complemented
6C29×#1298C211yesmaximal, characteristic, complemented
7C29×#1280C211yesmaximal, characteristic, complemented
8C29×#525C2211yescharacteristic
9C2×C29×#121C2211yescharacteristic
10C29×#484C411yescharacteristic, complemented
11C29×#482—21no—
12C29×#481C411yescharacteristic, complemented
13C29×#466—21no—
14C29×#465—21no—
15C29×#450C411yescharacteristic, complemented
16C29×#449—21no—
17C29×#447C411yescharacteristic, complemented
18C29×#435—21no—
19C29×#435—21no—
20C8×D4×C29—21no—
21C8×D4×C29—21no—
22C29×#433—21no—
23C29×#408—21no—
24C29×#407C2211yescharacteristic
25C2×C29×C22⋊C8C2211yescharacteristic
26C2×C29×C22⋊C8C2211yescharacteristic
27C2×C29×C22⋊C8C2211yescharacteristic
28C2×C29×#95C2211yescharacteristic
29C29×#328—21no—
30C29×#327—21no—
31C29×#327—21no—
32C29×#327—21no—
33C29×#323—21no—
34C29×#323—21no—
35C2×#41×C29D411yescharacteristic
36C22×D4×C29—21no—
37C22×D4×C29C2×C411yescharacteristic
38C23×C4×C29—21no—
39C23×C4×C29C2311yescharacteristic
40C2×SD16×C29—21no—
41C2×D8×C29—21no—
42C2×M16×C29—21no—
43C2×M16×C29—21no—
44C22×C8×C29—21no—
45C22×C8×C29—21no—
46C22×C8×C29—21no—
47C22×C8×C29—21no—
48C29×#123—21no—
49C29×C22⋊Q8C2×C411yescharacteristic
50C29×C22⋊Q8D411yescharacteristic
51C29×#121—21no—
52C29×#121—21no—
53C29×#121—21no—
54C29×#121—21no—
55C29×#121C2×C411yescharacteristic
56C29×#121D411yescharacteristic
57C29×#120—21no—
58C4×D4×C29—21no—
59C4×D4×C29—21no—
60C29×#117D411yescharacteristic
61C2×C4⋊C4×C29C2×C411yescharacteristic
62C2×C22⋊C4×C29—21no—
63C29×#107—21no—
64C29×#106—21no—
65C29×C4⋊C8—21no—
66C29×C4⋊C8—21no—
67C29×#103—21no—
68C29×#102—21no—
69C29×#102—21no—
70C29×#102—21no—
71C29×C22⋊C8—21no—
72C29×C22⋊C8—21no—
73C29×C22⋊C8—21no—
74C29×C22⋊C8—21no—
75C29×C22⋊C8—21no—
76C29×C22⋊C8—21no—
77C29×C22⋊C8—21no—
78C29×C22⋊C8C2×C411yescharacteristic
79C29×C22⋊C8C2×C411yescharacteristic
80C29×C22⋊C8D411yescharacteristic
81C29×C22⋊C8D411yescharacteristic
82C29×C22⋊C8D411yescharacteristic
83C29×C22⋊C8D411yescharacteristic
84C29×#97—21no—
85C4×C8×C29—21no—
86C29×#95—21no—
87C29×#95—21no—
88C24×C29—21no—
89C24×C29#4111yescharacteristic
90#41×C29—81no—
91C2×Q8×C29C22⋊C411yescharacteristic
92C2×D4×C29—21no—
93C2×D4×C29—21no—
94C2×D4×C29—21no—
95C2×D4×C29—21no—
96C2×D4×C29—21no—
97C2×D4×C29—41no—
98C2×D4×C29—41no—
99C2×D4×C29—81no—
100C2×D4×C29—81no—
101C2×D4×C29—81no—
102C2×D4×C29C22⋊C411yescharacteristic
103C22×C4×C29—21no—
104C22×C4×C29—22no—
105C22×C4×C29—21no—
106C22×C4×C29—41no—
107C22×C4×C29—41no—
108C22×C4×C29—81no—
109C22×C4×C29—81no—
110C22×C4×C29—81no—
111C22×C4×C29C22×C411yescharacteristic
112C22×C4×C29C2×D411yescharacteristic
113C22×C4×C29C2×D411yescharacteristic
114C22×C4×C29C2×D411yescharacteristic
115C22×C4×C29C2×D411yescharacteristic
116C22×C4×C29#4111yescharacteristic
117SD16×C29—81no—
118D8×C29—81no—
119M16×C29—81no—
120M16×C29—81no—
121C2×C8×C29—21no—
122C2×C8×C29—21no—
123C2×C8×C29—21no—
124C2×C8×C29—21no—
125C2×C8×C29—21no—
126C2×C8×C29—21no—
127C2×C8×C29—41no—
128C2×C8×C29—81no—
129C2×C8×C29—81no—
130C2×C8×C29—81no—
131C2×C8×C29—81no—
132C4⋊C4×C29—21no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
136C4⋊C4×C29C22⋊C411yescharacteristic
137C4⋊C4×C29C22⋊C411yescharacteristic
138C22⋊C4×C29—21no—
139C22⋊C4×C29—21no—
140C22⋊C4×C29—21no—
141C22⋊C4×C29—21no—
142C22⋊C4×C29—21no—
143C22⋊C4×C29—41no—
144C22⋊C4×C29—41no—
145C42×C29—21no—
146#9264C2911yesmaximal, characteristic, direct product factor, Sylow
147C23×C29—21no—
148C23×C29—21no—
149C23×C29—21no—
150C23×C29—21no—
151C23×C29—21no—
152C23×C29—41no—
153C23×C29—41no—
154C23×C29—41no—
155C23×C29—41no—
156C23×C29—81no—
157C23×C29—81no—
158C23×C29C4×D411yescharacteristic
159C23×C29#12111yescharacteristic
160C23×C29#12311yescharacteristic
161Q8×C29—41no—
162D4×C29—41no—
163D4×C29—41no—
164D4×C29—41no—
165D4×C29—41no—
166D4×C29—41no—
167D4×C29—41no—
168D4×C29—41no—
169D4×C29—81no—
170D4×C29—81no—
171D4×C29—82no—
172D4×C29—81no—
173D4×C29—81no—
174C2×C4×C29—21no—
175C2×C4×C29—21no—
176C2×C4×C29—21no—
177C2×C4×C29—41no—
178C2×C4×C29—41no—
179C2×C4×C29—41no—
180C2×C4×C29—41no—
181C2×C4×C29—41no—
182C2×C4×C29—41no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—42no—
186C2×C4×C29—41no—
187C2×C4×C29—81no—
188C2×C4×C29—82no—
189C2×C4×C29—81no—
190C2×C4×C29—81no—
191C2×C4×C29—82no—
192C2×C4×C29C2×C22⋊C411yescharacteristic
193C2×C4×C29C4×D411yescharacteristic
194C2×C4×C29#12011yescharacteristic
195C2×C4×C29#12111yescharacteristic
196C8×C29—41no—
197C8×C29—41no—
198C8×C29—41no—
199C8×C29—41no—
200C8×C29—41no—
201C8×C29—41no—
202C8×C29—81no—
203#3188C2×C2911yescharacteristic
204#2977C2×C2911yescharacteristic, complemented
205#1504C2×C2911yescharacteristic, complemented
206C2×#327C2×C2911yescharacteristic, complemented
207#1471C2×C2911yescharacteristic, complemented
208#1298C2×C2911yescharacteristic, complemented
209#1280C2×C2911yescharacteristic, complemented
210C22×C29—21no—
211C22×C29—21no—
212C22×C29—21no—
213C22×C29—21no—
214C22×C29—21no—
215C22×C29—21no—
216C22×C29—21no—
217C22×C29—41no—
218C22×C29—41no—
219C22×C29—41no—
220C22×C29—41no—
221C22×C29—41no—
222C22×C29—41no—
223C22×C29—41no—
224C22×C29—81no—
225C22×C29—81no—
226C22×C29—81no—
227C22×C29—161no—
228C22×C29—161no—
229C22×C29#38611yescharacteristic
230C22×C29#44311yescharacteristic
231C22×C29#44411yescharacteristic
232C22×C29#47111yescharacteristic
233C22×C29#47211yescharacteristic
234C4×C29—21no—
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—41no—
239C4×C29—41no—
240C4×C29—41no—
241C4×C29—82no—
242C4×C29—81no—
243#525C22×C2911yescharacteristic
244C2×#121C22×C2911yescharacteristic
245#484C4×C2911yescharacteristic, complemented
246#482—21no—
247#481C4×C2911yescharacteristic, complemented
248#466—21no—
249#465—21no—
250#450C4×C2911yescharacteristic, complemented
251#449—21no—
252#447C4×C2911yescharacteristic, complemented
253#435—21no—
254#435—21no—
255C8×D4—21no—
256C8×D4—21no—
257#433—21no—
258#408—21no—
259#407C22×C2911yescharacteristic
260C2×C22⋊C8C22×C2911yescharacteristic
261C2×C22⋊C8C22×C2911yescharacteristic
262C2×C22⋊C8C22×C2911yescharacteristic
263C2×#95C22×C2911yescharacteristic
264#328—21no—
265#327—21no—
266#327—21no—
267#327—21no—
268#323—21no—
269#323—21no—
270C2×C29—21no—
271C2×C29—21no—
272C2×C29—21no—
273C2×C29—21no—
274C2×C29—41no—
275C2×C29—81no—
276C2×C29—161no—
277C2×C29#187611yescharacteristic
278C2×C29#190711yescharacteristic
279C2×C29#191311yescharacteristic
280C2×#41D4×C2911yescharacteristic
281C22×D4—21no—
282C22×D4C2×C4×C2911yescharacteristic
283C23×C4—21no—
284C23×C4C23×C2911yescharacteristic
285C2×SD16—21no—
286C2×D8—21no—
287C2×M16—21no—
288C2×M16—21no—
289C22×C8—21no—
290C22×C8—21no—
291C22×C8—21no—
292C22×C8—21no—
293#123—21no—
294C22⋊Q8C2×C4×C2911yescharacteristic
295C22⋊Q8D4×C2911yescharacteristic
296#121—21no—
297#121—21no—
298#121—21no—
299#121—21no—
300#121C2×C4×C2911yescharacteristic
301#121D4×C2911yescharacteristic
302#120—21no—
303C4×D4—21no—
304C4×D4—21no—
305#117D4×C2911yescharacteristic
306C2×C4⋊C4C2×C4×C2911yescharacteristic
307C2×C22⋊C4—21no—
308#107—21no—
309#106—21no—
310C4⋊C8—21no—
311C4⋊C8—21no—
312#103—21no—
313#102—21no—
314#102—21no—
315#102—21no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323C22⋊C8C2×C4×C2911yescharacteristic
324C22⋊C8C2×C4×C2911yescharacteristic
325C22⋊C8D4×C2911yescharacteristic
326C22⋊C8D4×C2911yescharacteristic
327C22⋊C8D4×C2911yescharacteristic
328C22⋊C8D4×C2911yescharacteristic
329#97—21no—
330C4×C8—21no—
331#95—21no—
332#95—21no—
333C29#926411yescharacteristic, direct product factor, Sylow
334C24—21no—
335C24#41×C2911yescharacteristic
336#41—81no—
337C2×Q8C22⋊C4×C2911yescharacteristic
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—81no—
346C2×D4—81no—
347C2×D4—81no—
348C2×D4C22⋊C4×C2911yescharacteristic
349C22×C4—21no—
350C22×C4—22no—
351C22×C4—21no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—81no—
355C22×C4—81no—
356C22×C4—81no—
357C22×C4C22×C4×C2911yescharacteristic
358C22×C4C2×D4×C2911yescharacteristic
359C22×C4C2×D4×C2911yescharacteristic
360C22×C4C2×D4×C2911yescharacteristic
361C22×C4C2×D4×C2911yescharacteristic
362C22×C4#41×C2911yescharacteristic
363SD16—81no—
364D8—81no—
365M16—81no—
366M16—81no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—41no—
374C2×C8—81no—
375C2×C8—81no—
376C2×C8—81no—
377C2×C8—81no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4C22⋊C4×C2911yescharacteristic
383C4⋊C4C22⋊C4×C2911yescharacteristic
384C22⋊C4—21no—
385C22⋊C4—21no—
386C22⋊C4—21no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C42—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—41no—
401C23—81no—
402C23—81no—
403C23C4×D4×C2911yescharacteristic
404C23C29×#12111yescharacteristic
405C23C29×#12311yescharacteristic
406Q8—41no—
407D4—41no—
408D4—41no—
409D4—41no—
410D4—41no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—81no—
415D4—81no—
416D4—82no—
417D4—81no—
418D4—81no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—82no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—82no—
437C2×C4C2×C22⋊C4×C2911yescharacteristic
438C2×C4C4×D4×C2911yescharacteristic
439C2×C4C29×#12011yescharacteristic
440C2×C4C29×#12111yescharacteristic
441C8—41no—
442C8—41no—
443C8—41no—
444C8—41no—
445C8—41no—
446C8—41no—
447C8—81no—
448C22—21no—
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—21no—
455C22—41no—
456C22—41no—
457C22—41no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—161no—
466C22—161no—
467C22C29×#38611yescharacteristic
468C22C29×#44311yescharacteristic
469C22C29×#44411yescharacteristic
470C22C29×#47111yescharacteristic
471C22C29×#47211yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—41no—
477C4—41no—
478C4—41no—
479C4—82no—
480C4—81no—
481C2—21no—
482C2—21no—
483C2—21no—
484C2—21no—
485C2—41no—
486C2—81no—
487C2—161no—
488C2C29×#187611yescharacteristic
489C2C29×#190711yescharacteristic
490C2C29×#191311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC29×#3188C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C29×#2977C2semidirect
3. C29×#1504C2semidirect
4. C2×C29×#327C2semidirect
5. C29×#1471C2semidirect
6. C29×#1298C2semidirect
7. C29×#1280C2semidirect
10. C29×#484C4semidirect
12. C29×#481C4semidirect
15. C29×#450C4semidirect
17. C29×#447C4semidirect
146. #9264C29direct (N × H)
204. #2977C2×C29semidirect
205. #1504C2×C29semidirect
206. C2×#327C2×C29semidirect
207. #1471C2×C29semidirect
208. #1298C2×C29semidirect
209. #1280C2×C29semidirect
245. #484C4×C29semidirect
247. #481C4×C29semidirect
250. #450C4×C29semidirect
252. #447C4×C29semidirect
333. C29#9264direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31882
C29×#29772
C29×#15042
C2×C29×#3272
C29×#14712
C29×#12982
C29×#12802
#926429