Finite Group Databasebeta

← C29×#19469 #20314369

Subgroups — C29×#19469 #20314369

Order 7424.

610 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×#3206C211yesmaximal, characteristic
2C29×#3112C211yesmaximal, characteristic
3C2×C29×#475C211yesmaximal, characteristic, complemented
4C29×#2984C211yesmaximal, characteristic, complemented
5C29×#1704C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1684C212yesmaximal, complemented
8C29×#1666C212yesmaximal, complemented
9C29×#1573C211yesmaximal, characteristic, complemented
10C29×#1556C211yesmaximal, characteristic, complemented
11C29×#1551C211yesmaximal, characteristic
12C29×#532C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C29C2211yescharacteristic
15C29×#492C2212yes—
16C29×#487C2212yes—
17C29×#480—21no—
18C29×#477C2211yescharacteristic
19C29×#477C2211yescharacteristic
20C29×#475—21no—
21C29×#475—21no—
22C29×#475C2212yes—
23C29×#475C2212yes—
24C29×#461—22no—
25C29×#460C2211yescharacteristic
26C29×#460C2211yescharacteristic
27C29×#448—21no—
28C29×#448—21no—
29C29×#448—21no—
30C29×#446—22no—
31C29×#446C2212yes—
32C8×Q8×C29C2212yes—
33C29×#440—21no—
34C29×#440—21no—
35C29×#432—21no—
36C29×#432C2211yescharacteristic
37C29×#432C2211yescharacteristic
38C29×#431—21no—
39C29×#431C2211yescharacteristic
40C2×C29×#106—21no—
41C2×C29×C4⋊C8C2211yescharacteristic
42C2×C29×#103—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C22×Q8×C29—21no—
51C22×Q8×C29D411yescharacteristic
52C2×SD16×C29—21no—
53C2×SD16×C29—21no—
54C2×SD16×C29—22no—
55C2×SD16×C29—22no—
56C22×C8×C29—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8C2312yes—
61C29×C4⋊Q8C2311yescharacteristic
62C29×#127C2311yescharacteristic
63C29×#124—21no—
64C29×#121—21no—
65C29×#121—21no—
66C4×Q8×C29—21no—
67C4×Q8×C29—21no—
68C4×Q8×C29D411yescharacteristic
69C4×Q8×C29D411yescharacteristic
70C4×Q8×C29C2311yescharacteristic
71C4×Q8×C29C2311yescharacteristic
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C42×C29—21no—
79C2×C42×C29C2311yescharacteristic
80C29×#107—21no—
81C29×#107—21no—
82C29×#106—22no—
83C29×#106—22no—
84C29×C4⋊C8—22no—
85C29×C4⋊C8—22no—
86C29×C4⋊C8—21no—
87C29×C4⋊C8D412yes—
88C29×C4⋊C8C2312yes—
89C29×C4⋊C8C2311yescharacteristic
90C29×C4⋊C8C2311yescharacteristic
91C29×C4⋊C8C2312yes—
92C29×#103—21no—
93C29×#103—21no—
94C29×#103—22no—
95C29×#103—22no—
96C29×#103—22no—
97C29×#103—22no—
98C29×#102—21no—
99C29×#102—21no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8D411yescharacteristic
103C29×C22⋊C8D411yescharacteristic
104C29×#97—22no—
105C29×#97—21no—
106C29×#97—21no—
107C4×C8×C29—22no—
108C4×C8×C29C2312yes—
109#41×C29—82no—
110C2×Q8×C29—21no—
111C2×Q8×C29—22no—
112C2×Q8×C29—22no—
113C2×Q8×C29—21no—
114C2×Q8×C29—41no—
115C2×Q8×C29—41no—
116C2×Q8×C29—82no—
117C2×Q8×C29C2×D411yescharacteristic
118C2×Q8×C29C2×D411yescharacteristic
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×C29—41no—
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29#4111yescharacteristic
130SD16×C29—42no—
131SD16×C29—42no—
132SD16×C29—82no—
133SD16×C29—82no—
134C2×C8×C29—22no—
135C2×C8×C29—21no—
136C2×C8×C29—21no—
137C2×C8×C29—22no—
138C2×C8×C29—42no—
139C2×C8×C29C2×D412yes—
140C2×C8×C29C2×D412yes—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—22no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29C2×D411yescharacteristic
153C4⋊C4×C29C2×D411yescharacteristic
154C22⋊C4×C29—41no—
155C22⋊C4×C29—41no—
156C42×C29—21no—
157C42×C29—21no—
158C42×C29—21no—
159C42×C29—21no—
160C42×C29C2×D411yescharacteristic
161C42×C29C2×D411yescharacteristic
162C42×C29#4111yescharacteristic
163C42×C29C2411yescharacteristic
164#19469C2911yesmaximal, characteristic, direct product factor, Sylow
165C23×C29—41no—
166C23×C29#12111yescharacteristic
167Q8×C29—21no—
168Q8×C29—21no—
169Q8×C29—21no—
170Q8×C29—42no—
171Q8×C29—42no—
172Q8×C29—42no—
173Q8×C29—81no—
174Q8×C29—82no—
175Q8×C29#13712yes—
176D4×C29—41no—
177D4×C29—41no—
178D4×C29—42no—
179D4×C29—81no—
180D4×C29—82no—
181C2×C4×C29—21no—
182C2×C4×C29—22no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—22no—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—42no—
190C2×C4×C29—42no—
191C2×C4×C29—41no—
192C2×C4×C29—42no—
193C2×C4×C29—82no—
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—22no—
203C8×C29—41no—
204C8×C29—42no—
205C8×C29—41no—
206C8×C29—42no—
207#3206C2×C2911yescharacteristic
208#3112C2×C2911yescharacteristic
209C2×#475C2×C2911yescharacteristic, complemented
210#2984C2×C2911yescharacteristic, complemented
211#1704C2×C2912yescomplemented
212#1686C2×C2912yescomplemented
213#1684C2×C2912yescomplemented
214#1666C2×C2912yescomplemented
215#1573C2×C2911yescharacteristic, complemented
216#1556C2×C2911yescharacteristic, complemented
217#1551C2×C2911yescharacteristic
218C22×C29—21no—
219C22×C29—21no—
220C22×C29—81no—
221C22×C29—81no—
222C22×C29—81no—
223C22×C29#47112yes—
224C22×C29C2×#12111yescharacteristic
225C4×C29—21no—
226C4×C29—21no—
227C4×C29—22no—
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—41no—
231C4×C29—41no—
232C4×C29—41no—
233C4×C29—82no—
234C4×C29—81no—
235C4×C29C2×#13711yescharacteristic
236C4×C29#57511yescharacteristic
237C4×C29#57712yes—
238#532C22×C2911yescharacteristic
239C2×C4⋊Q8C22×C2911yescharacteristic
240C2×C4×Q8C22×C2911yescharacteristic
241#492C22×C2912yes—
242#487C22×C2912yes—
243#480—21no—
244#477C22×C2911yescharacteristic
245#477C22×C2911yescharacteristic
246#475—21no—
247#475—21no—
248#475C22×C2912yes—
249#475C22×C2912yes—
250#461—22no—
251#460C22×C2911yescharacteristic
252#460C22×C2911yescharacteristic
253#448—21no—
254#448—21no—
255#448—21no—
256#446—22no—
257#446C22×C2912yes—
258C8×Q8C22×C2912yes—
259#440—21no—
260#440—21no—
261#432—21no—
262#432C22×C2911yescharacteristic
263#432C22×C2911yescharacteristic
264#431—21no—
265#431C22×C2911yescharacteristic
266C2×#106—21no—
267C2×C4⋊C8C22×C2911yescharacteristic
268C2×#103—21no—
269#335C22×C2912yes—
270#334C22×C2912yes—
271#333C22×C2912yes—
272#332C22×C2912yes—
273#332C22×C2912yes—
274#331C22×C2912yes—
275C2×C29—22no—
276C2×C29—161no—
277C2×C29#304311yescharacteristic
278C2×C29#305611yescharacteristic
279C2×C29C2×#47111yescharacteristic
280C2×#41—21no—
281C22×Q8—21no—
282C22×Q8D4×C2911yescharacteristic
283C2×SD16—21no—
284C2×SD16—21no—
285C2×SD16—22no—
286C2×SD16—22no—
287C22×C8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8C23×C2912yes—
292C4⋊Q8C23×C2911yescharacteristic
293#127C23×C2911yescharacteristic
294#124—21no—
295#121—21no—
296#121—21no—
297C4×Q8—21no—
298C4×Q8—21no—
299C4×Q8D4×C2911yescharacteristic
300C4×Q8D4×C2911yescharacteristic
301C4×Q8C23×C2911yescharacteristic
302C4×Q8C23×C2911yescharacteristic
303C4×D4—21no—
304C4×D4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4D4×C2911yescharacteristic
309C2×C42—21no—
310C2×C42C23×C2911yescharacteristic
311#107—21no—
312#107—21no—
313#106—22no—
314#106—22no—
315C4⋊C8—22no—
316C4⋊C8—22no—
317C4⋊C8—21no—
318C4⋊C8D4×C2912yes—
319C4⋊C8C23×C2912yes—
320C4⋊C8C23×C2912yes—
321C4⋊C8C23×C2911yescharacteristic
322C4⋊C8C23×C2911yescharacteristic
323#103—22no—
324#103—22no—
325#103—21no—
326#103—21no—
327#103—22no—
328#103—22no—
329#102—21no—
330#102—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8D4×C2911yescharacteristic
334C22⋊C8D4×C2911yescharacteristic
335#97—22no—
336#97—21no—
337#97—21no—
338C4×C8—22no—
339C4×C8C23×C2912yes—
340C29#1946911yescharacteristic, direct product factor, Sylow
341#41—82no—
342C2×Q8—21no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—21no—
346C2×Q8—41no—
347C2×Q8—41no—
348C2×Q8—82no—
349C2×Q8C2×D4×C2911yescharacteristic
350C2×Q8C2×D4×C2911yescharacteristic
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C2911yescharacteristic
360C22×C4C2×D4×C2911yescharacteristic
361C22×C4#41×C2911yescharacteristic
362SD16—42no—
363SD16—42no—
364SD16—82no—
365SD16—82no—
366C2×C8—22no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—42no—
371C2×C8C2×D4×C2912yes—
372C2×C8C2×D4×C2912yes—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4C2×D4×C2911yescharacteristic
385C4⋊C4C2×D4×C2911yescharacteristic
386C22⋊C4—41no—
387C22⋊C4—41no—
388C42—21no—
389C42—21no—
390C42—21no—
391C42—21no—
392C42C2×D4×C2911yescharacteristic
393C42C2×D4×C2911yescharacteristic
394C42#41×C2911yescharacteristic
395C42C24×C2911yescharacteristic
396C23—41no—
397C23C29×#12111yescharacteristic
398Q8—21no—
399Q8—21no—
400Q8—21no—
401Q8—42no—
402Q8—42no—
403Q8—42no—
404Q8—81no—
405Q8—82no—
406Q8C29×#13712yes—
407D4—41no—
408D4—41no—
409D4—42no—
410D4—81no—
411D4—82no—
412C2×C4—22no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—22no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—82no—
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—22no—
434C8—41no—
435C8—42no—
436C8—41no—
437C8—42no—
438C22—21no—
439C22—21no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22C29×#47112yes—
444C22C2×C29×#12111yescharacteristic
445C4—21no—
446C4—21no—
447C4—22no—
448C4—21no—
449C4—21no—
450C4—41no—
451C4—41no—
452C4—41no—
453C4—82no—
454C4—81no—
455C4C2×C29×#13711yescharacteristic
456C4C29×#57511yescharacteristic
457C4C29×#57712yes—
458C2—22no—
459C2—161no—
460C2C29×#304311yescharacteristic
461C2C29×#305611yescharacteristic
462C2C2×C29×#47111yescharacteristic
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
3. C2×C29×#475C2semidirect
4. C29×#2984C2semidirect
5. C29×#1704C2semidirect
6. C29×#1686C2semidirect
7. C29×#1684C2semidirect
8. C29×#1666C2semidirect
9. C29×#1573C2semidirect
10. C29×#1556C2semidirect
164. #19469C29direct (N × H)
209. C2×#475C2×C29semidirect
210. #2984C2×C29semidirect
211. #1704C2×C29semidirect
212. #1686C2×C29semidirect
213. #1684C2×C29semidirect
214. #1666C2×C29semidirect
215. #1573C2×C29semidirect
216. #1556C2×C29semidirect
340. C29#19469direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32062
C29×#31122
C2×C29×#4752
C29×#29842
C29×#17042
C29×#16862
C29×#16842
C29×#16662
C29×#15732
C29×#15562
C29×#15512
#1946929