Finite Group Databasebeta

← C29×#19520 #20314420

Subgroups — C29×#19520 #20314420

Order 7424.

612 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3237C211yesmaximal, characteristic, complemented
2C29×#3208C211yesmaximal, characteristic
3C29×#3208C211yesmaximal, characteristic
4C29×#2985C211yesmaximal, characteristic, complemented
5C29×#1698C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1678C212yesmaximal, complemented
8C29×#1666C212yesmaximal, complemented
9C29×#1572C211yesmaximal, characteristic, complemented
10C29×#1555C211yesmaximal, characteristic
11C29×#1554C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C29×#533C2211yescharacteristic
14C2×C29×#127C2211yescharacteristic
15C29×#501—21no—
16C29×#492—21no—
17C29×#492C2211yescharacteristic
18C29×#492C2211yescharacteristic
19C29×#491—21no—
20C29×#486—21no—
21C29×#486C2211yescharacteristic
22C29×#486C2211yescharacteristic
23C29×#485—22no—
24C29×#477C2212yescomplemented
25C29×#475C2212yescomplemented
26C29×#460—22no—
27C29×#460C2212yes—
28C29×#460C2212yes—
29C29×#450—22no—
30C29×#450—22no—
31C29×#446—22no—
32C29×#446C2212yescomplemented
33C8×Q8×C29C2212yescomplemented
34C29×#433—22no—
35C29×#432C2211yescharacteristic
36C29×#432C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#431C2211yescharacteristic
39C29×#335C2212yescomplemented
40C29×#334C2212yescomplemented
41C29×#333C2212yescomplemented
42C29×#332C2212yescomplemented
43C29×#331C2212yes—
44C29×#331C2212yes—
45C22×D4×C29—21no—
46C22×D4×C29—21no—
47C22×D4×C29—21no—
48C2×SD16×C29—22no—
49C2×SD16×C29—22no—
50C2×SD16×C29—22no—
51C2×SD16×C29—22no—
52C29×C4⋊Q8D411yescharacteristic
53C29×C4⋊Q8D411yescharacteristic
54C29×C4⋊Q8C2311yescharacteristic
55C29×C4⋊Q8C2311yescharacteristic
56C29×#127—21no—
57C29×#127—21no—
58C29×#127—21no—
59C29×#127C2311yescharacteristic
60C29×#127C2311yescharacteristic
61C29×#125—21no—
62C29×#125—21no—
63C29×C22⋊Q8—21no—
64C29×C22⋊Q8—21no—
65C29×C22⋊Q8—21no—
66C29×C22⋊Q8D412yes—
67C4×Q8×C29—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29—21no—
70C4×Q8×C29C2312yes—
71C29×#117—21no—
72C29×#117—21no—
73C2×C42×C29C2311yescharacteristic
74C29×#107—22no—
75C29×#106—22no—
76C29×C4⋊C8—22no—
77C29×C4⋊C8—22no—
78C29×C4⋊C8D412yes—
79C29×C4⋊C8C2312yes—
80C29×C4⋊C8C2312yes—
81C29×C4⋊C8C2312yes—
82C29×#103—22no—
83C29×#103—22no—
84C29×#102—22no—
85C29×#102—22no—
86C29×#102—22no—
87C29×#102—22no—
88C29×C22⋊C8—21no—
89C29×C22⋊C8—21no—
90C29×C22⋊C8—21no—
91C29×C22⋊C8D412yes—
92C29×#97—22no—
93C29×#97—21no—
94C29×#97—21no—
95C4×C8×C29—22no—
96C4×C8×C29—21no—
97C4×C8×C29C2311yescharacteristic
98C4×C8×C29C2311yescharacteristic
99C24×C29—41no—
100C2×Q8×C29—21no—
101C2×Q8×C29—21no—
102C2×Q8×C29—21no—
103C2×Q8×C29C2×D412yes—
104C2×D4×C29—21no—
105C2×D4×C29—21no—
106C2×D4×C29—21no—
107C2×D4×C29—21no—
108C2×D4×C29—21no—
109C2×D4×C29—21no—
110C2×D4×C29—41no—
111C2×D4×C29—41no—
112C2×D4×C29—41no—
113C2×D4×C29—82no—
114C2×D4×C29—82no—
115C2×D4×C29—82no—
116C22×C4×C29C2×D411yescharacteristic
117C22×C4×C29C2×D411yescharacteristic
118C22×C4×C29#4111yescharacteristic
119SD16×C29—82no—
120SD16×C29—82no—
121SD16×C29—82no—
122SD16×C29—82no—
123C2×C8×C29—22no—
124C2×C8×C29—22no—
125C2×C8×C29—22no—
126C2×C8×C29C2×D412yes—
127C2×C8×C29C2×D412yes—
128C4⋊C4×C29—21no—
129C4⋊C4×C29—21no—
130C4⋊C4×C29—21no—
131C4⋊C4×C29—22no—
132C4⋊C4×C29—22no—
133C4⋊C4×C29—21no—
134C4⋊C4×C29—21no—
135C4⋊C4×C29—21no—
136C4⋊C4×C29—21no—
137C4⋊C4×C29—41no—
138C4⋊C4×C29—41no—
139C4⋊C4×C29C2×D412yes—
140C22⋊C4×C29—22no—
141C22⋊C4×C29—41no—
142C42×C29—22no—
143C42×C29—41no—
144C42×C29C2×D411yescharacteristic
145C42×C29C2×D411yescharacteristic
146C42×C29#4111yescharacteristic
147C42×C29C2411yescharacteristic
148#19520C2911yesmaximal, characteristic, direct product factor, Sylow
149C23×C29—41no—
150C23×C29—41no—
151C23×C29—82no—
152C23×C29—82no—
153C23×C29—82no—
154C23×C29#12111yescharacteristic
155Q8×C29—22no—
156Q8×C29—22no—
157Q8×C29—42no—
158Q8×C29—81no—
159Q8×C29—81no—
160D4×C29—42no—
161D4×C29—42no—
162D4×C29—42no—
163D4×C29—42no—
164D4×C29—81no—
165D4×C29—81no—
166D4×C29—82no—
167D4×C29—82no—
168D4×C29—82no—
169C2×C4×C29—22no—
170C2×C4×C29—22no—
171C2×C4×C29—22no—
172C2×C4×C29—22no—
173C2×C4×C29—41no—
174C2×C4×C29—41no—
175C2×C4×C29—41no—
176C2×C4×C29#12111yescharacteristic
177C2×C4×C29#12111yescharacteristic
178C2×C4×C29#12111yescharacteristic
179C2×C4×C29C22×D411yescharacteristic
180C2×C4×C29C22×D411yescharacteristic
181C2×C4×C29C2×#4111yescharacteristic
182C8×C29—22no—
183C8×C29—22no—
184C8×C29—42no—
185C8×C29—42no—
186C8×C29—42no—
187#3237C2×C2911yescharacteristic, complemented
188#3208C2×C2911yescharacteristic
189#3208C2×C2911yescharacteristic
190#2985C2×C2911yescharacteristic, complemented
191#1698C2×C2912yescomplemented
192#1686C2×C2912yescomplemented
193#1678C2×C2912yescomplemented
194#1666C2×C2912yescomplemented
195#1572C2×C2911yescharacteristic, complemented
196#1555C2×C2911yescharacteristic
197#1554C2×C2911yescharacteristic, complemented
198C22×C29—21no—
199C22×C29—21no—
200C22×C29—21no—
201C22×C29—81no—
202C22×C29—81no—
203C22×C29—81no—
204C22×C29—81no—
205C22×C29—81no—
206C22×C29—81no—
207C22×C29—164no—
208C22×C29C2×#12111yescharacteristic
209C4×C29—21no—
210C4×C29—21no—
211C4×C29—21no—
212C4×C29—21no—
213C4×C29—42no—
214C4×C29—42no—
215C4×C29—81no—
216C4×C29—81no—
217C4×C29#57712yes—
218C4×C29#57712yes—
219#533C22×C2911yescharacteristic
220#533C22×C2911yescharacteristic
221C2×#127C22×C2911yescharacteristic
222#501—21no—
223#492—21no—
224#492C22×C2911yescharacteristic
225#492C22×C2911yescharacteristic
226#491—21no—
227#486—21no—
228#486C22×C2911yescharacteristic
229#486C22×C2911yescharacteristic
230#485—22no—
231#477C22×C2912yescomplemented
232#475C22×C2912yescomplemented
233#460—22no—
234#460C22×C2912yes—
235#460C22×C2912yes—
236#450—22no—
237#450—22no—
238#446—22no—
239#446C22×C2912yescomplemented
240C8×Q8C22×C2912yescomplemented
241#433—22no—
242#432C22×C2911yescharacteristic
243#432C22×C2911yescharacteristic
244#431C22×C2911yescharacteristic
245#431C22×C2911yescharacteristic
246#335C22×C2912yescomplemented
247#334C22×C2912yescomplemented
248#333C22×C2912yescomplemented
249#332C22×C2912yescomplemented
250#331C22×C2912yes—
251#331C22×C2912yes—
252C2×C29—41no—
253C2×C29—161no—
254C2×C29—161no—
255C2×C29#304311yescharacteristic
256C2×C29#305711yescharacteristic
257C2×C29#306811yescharacteristic
258C22×D4—21no—
259C22×D4—21no—
260C22×D4—21no—
261C2×SD16—22no—
262C2×SD16—22no—
263C2×SD16—22no—
264C2×SD16—22no—
265C4⋊Q8D4×C2911yescharacteristic
266C4⋊Q8D4×C2911yescharacteristic
267C4⋊Q8C23×C2911yescharacteristic
268C4⋊Q8C23×C2911yescharacteristic
269#127—21no—
270#127—21no—
271#127—21no—
272#127C23×C2911yescharacteristic
273#127C23×C2911yescharacteristic
274#125—21no—
275#125—21no—
276C22⋊Q8—21no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8D4×C2912yes—
280C4×Q8—21no—
281C4×Q8—21no—
282C4×Q8—21no—
283C4×Q8C23×C2912yes—
284#117—21no—
285#117—21no—
286C2×C42C23×C2911yescharacteristic
287#107—22no—
288#106—22no—
289C4⋊C8—22no—
290C4⋊C8—22no—
291C4⋊C8D4×C2912yes—
292C4⋊C8C23×C2912yes—
293C4⋊C8C23×C2912yes—
294C4⋊C8C23×C2912yes—
295#103—22no—
296#103—22no—
297#102—22no—
298#102—22no—
299#102—22no—
300#102—22no—
301C22⋊C8—21no—
302C22⋊C8—21no—
303C22⋊C8—21no—
304C22⋊C8D4×C2912yes—
305#97—22no—
306#97—21no—
307#97—21no—
308C4×C8—22no—
309C4×C8—21no—
310C4×C8C23×C2911yescharacteristic
311C4×C8C23×C2911yescharacteristic
312C29#1952011yescharacteristic, direct product factor, Sylow
313C24—41no—
314C2×Q8—21no—
315C2×Q8—21no—
316C2×Q8—21no—
317C2×Q8C2×D4×C2912yes—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—82no—
328C2×D4—82no—
329C2×D4—82no—
330C22×C4C2×D4×C2911yescharacteristic
331C22×C4C2×D4×C2911yescharacteristic
332C22×C4#41×C2911yescharacteristic
333SD16—82no—
334SD16—82no—
335SD16—82no—
336SD16—82no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—22no—
340C2×C8C2×D4×C2912yes—
341C2×C8C2×D4×C2912yes—
342C4⋊C4—21no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4C2×D4×C2912yes—
354C22⋊C4—22no—
355C22⋊C4—41no—
356C42—22no—
357C42—41no—
358C42C2×D4×C2911yescharacteristic
359C42C2×D4×C2911yescharacteristic
360C42#41×C2911yescharacteristic
361C42C24×C2911yescharacteristic
362C23—41no—
363C23—41no—
364C23—82no—
365C23—82no—
366C23—82no—
367C23C29×#12111yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—42no—
371Q8—81no—
372Q8—81no—
373D4—42no—
374D4—42no—
375D4—42no—
376D4—42no—
377D4—81no—
378D4—81no—
379D4—82no—
380D4—82no—
381D4—82no—
382C2×C4—22no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4C29×#12111yescharacteristic
390C2×C4C29×#12111yescharacteristic
391C2×C4C29×#12111yescharacteristic
392C2×C4C22×D4×C2911yescharacteristic
393C2×C4C22×D4×C2911yescharacteristic
394C2×C4C2×#41×C2911yescharacteristic
395C8—22no—
396C8—22no—
397C8—42no—
398C8—42no—
399C8—42no—
400C22—21no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—164no—
410C22C2×C29×#12111yescharacteristic
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—42no—
416C4—42no—
417C4—81no—
418C4—81no—
419C4C29×#57712yes—
420C4C29×#57712yes—
421C2—41no—
422C2—161no—
423C2—161no—
424C2C29×#304311yescharacteristic
425C2C29×#305711yescharacteristic
426C2C29×#306811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×C29×#127C22
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×#2985C2semidirect
5. C29×#1698C2semidirect
6. C29×#1686C2semidirect
7. C29×#1678C2semidirect
8. C29×#1666C2semidirect
9. C29×#1572C2semidirect
11. C29×#1554C2semidirect
24. C29×#477C22semidirect
25. C29×#475C22semidirect
32. C29×#446C22semidirect
33. C8×Q8×C29C22semidirect
39. C29×#335C22semidirect
40. C29×#334C22semidirect
41. C29×#333C22semidirect
42. C29×#332C22semidirect
148. #19520C29direct (N × H)
187. #3237C2×C29semidirect
190. #2985C2×C29semidirect
191. #1698C2×C29semidirect
192. #1686C2×C29semidirect
193. #1678C2×C29semidirect
194. #1666C2×C29semidirect
195. #1572C2×C29semidirect
197. #1554C2×C29semidirect
231. #477C22×C29semidirect
232. #475C22×C29semidirect
239. #446C22×C29semidirect
240. C8×Q8C22×C29semidirect
246. #335C22×C29semidirect
247. #334C22×C29semidirect
248. #333C22×C29semidirect
249. #332C22×C29semidirect
312. C29#19520direct (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×#32082
C29×#29852
C29×#16982
C29×#16862
C29×#16782
C29×#16662
C29×#15722
C29×#15552
C29×#15542
#1952029