Finite Group Databasebeta

← C29×#3308 #16817022

Subgroups — C29×#3308 #16817022

Order 3712.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#548C211yesmaximal, characteristic, complemented
2C29×#547C211yesmaximal, characteristic, complemented
3C29×#489C211yesmaximal, characteristic, complemented
4C29×#484C211yesmaximal, characteristic, complemented
5C29×#480C211yesmaximal, characteristic, complemented
6C29×#477C211yesmaximal, characteristic, complemented
7C29×#468C211yesmaximal, characteristic, complemented
8C29×#466C211yesmaximal, characteristic, complemented
9C29×#463C211yesmaximal, characteristic, complemented
10C29×#449C211yesmaximal, characteristic, complemented
11C29×#448C211yesmaximal, characteristic, complemented
12C29×#440C211yesmaximal, characteristic, complemented
13C29×#435C211yesmaximal, characteristic, complemented
14C29×#417C211yesmaximal, characteristic, complemented
15C2×C29×#103C211yesmaximal, characteristic, complemented
16C2×#41×C29—21no—
17C2×#41×C29C2211yescharacteristic
18C22×Q8×C29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C2×SD16×C29C2211yescharacteristic
21C2×D8×C29C2211yescharacteristic
22C2×M16×C29C2211yescharacteristic
23C22×C8×C29C2211yescharacteristic
24C29×C4⋊Q8C2211yescharacteristic
25C29×#124—21no—
26C29×#124C2211yescharacteristic
27C29×#123—21no—
28C29×#123—21no—
29C29×C22⋊Q8—21no—
30C29×C22⋊Q8—21no—
31C29×C22⋊Q8C2211yescharacteristic
32C29×#121—21no—
33C29×#121C2211yescharacteristic
34C29×#121C2211yescharacteristic
35C29×#121C2211yescharacteristic
36C4×Q8×C29C2211yescharacteristic
37C4×D4×C29—21no—
38C4×D4×C29C2211yescharacteristic
39C4×D4×C29C2211yescharacteristic
40C2×C4⋊C4×C29C2211yescharacteristic
41C2×C4⋊C4×C29C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#107C2211yescharacteristic
45C29×C4⋊C8C2211yescharacteristic
46C29×#103C2211yescharacteristic
47C29×#103C2211yescharacteristic
48C29×#103C2211yescharacteristic
49C29×#103C2211yescharacteristic
50C29×#103C2211yescharacteristic
51C29×#103C2211yescharacteristic
52C29×#102C2211yescharacteristic
53C29×#102C2211yescharacteristic
54C29×#102C2211yescharacteristic
55C29×#102C2211yescharacteristic
56C29×C22⋊C8C2211yescharacteristic
57C29×C22⋊C8C2211yescharacteristic
58C29×#97C2211yescharacteristic
59#41×C29—22no—
60#41×C29—41no—
61#41×C29—44no—
62C2×Q8×C29—21no—
63C2×Q8×C29—21no—
64C2×Q8×C29—22no—
65C2×Q8×C29—41no—
66C2×Q8×C29C2311yescharacteristic
67C2×Q8×C29C2311yescharacteristic
68C2×D4×C29—21no—
69C2×D4×C29—21no—
70C2×D4×C29—21no—
71C2×D4×C29—21no—
72C2×D4×C29D411yescharacteristic
73C2×D4×C29C2311yescharacteristic
74C2×D4×C29C2311yescharacteristic
75C22×C4×C29—21no—
76C22×C4×C29—21no—
77C22×C4×C29—21no—
78C22×C4×C29—21no—
79C22×C4×C29—21no—
80C22×C4×C29C2311yescharacteristic
81C22×C4×C29C2311yescharacteristic
82SD16×C29—22no—
83SD16×C29—41no—
84D8×C29—41no—
85M16×C29—41no—
86C2×C8×C29—41no—
87C2×C8×C29C2311yescharacteristic
88C2×C8×C29C2311yescharacteristic
89C2×C8×C29C2311yescharacteristic
90C2×C8×C29C2311yescharacteristic
91C4⋊C4×C29—21no—
92C4⋊C4×C29—21no—
93C4⋊C4×C29—21no—
94C4⋊C4×C29—21no—
95C4⋊C4×C29—21no—
96C4⋊C4×C29D411yescharacteristic
97C4⋊C4×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C4⋊C4×C29C2311yescharacteristic
100C4⋊C4×C29C2311yescharacteristic
101C22⋊C4×C29—21no—
102C22⋊C4×C29—21no—
103C22⋊C4×C29—21no—
104C22⋊C4×C29—21no—
105C22⋊C4×C29—21no—
106C22⋊C4×C29—21no—
107C22⋊C4×C29—21no—
108C22⋊C4×C29D411yescharacteristic
109C22⋊C4×C29D411yescharacteristic
110C42×C29—21no—
111C42×C29C2311yescharacteristic
112C23×C29—21no—
113C23×C29—21no—
114C23×C29C2×D411yescharacteristic
115C23×C29C2×D411yescharacteristic
116Q8×C29—21no—
117Q8×C29—21no—
118Q8×C29—21no—
119Q8×C29—42no—
120Q8×C29—42no—
121Q8×C29#4112yescomplemented
122D4×C29—22no—
123D4×C29—21no—
124D4×C29—21no—
125D4×C29—21no—
126D4×C29—21no—
127D4×C29—42no—
128D4×C29—42no—
129D4×C29—42no—
130D4×C29—42no—
131C2×C4×C29—21no—
132C2×C4×C29—21no—
133C2×C4×C29—21no—
134C2×C4×C29—21no—
135C2×C4×C29—21no—
136C2×C4×C29—21no—
137C2×C4×C29—21no—
138C2×C4×C29—21no—
139C2×C4×C29—21no—
140C2×C4×C29—21no—
141C2×C4×C29—42no—
142C2×C4×C29—42no—
143C2×C4×C29—42no—
144C2×C4×C29—42no—
145C2×C4×C29—42no—
146C2×C4×C29C2×D411yescharacteristic
147C2×C4×C29C2×D411yescharacteristic
148C2×C4×C29C2×D411yescharacteristic
149C2×C4×C29C2×D411yescharacteristic
150C2×C4×C29C2411yescharacteristic
151C8×C29—21no—
152C8×C29—21no—
153C8×C29—21no—
154C8×C29—21no—
155#3308C2911yesmaximal, characteristic, direct product factor, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—41no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29AGL(1,ℤ/8)12yes—
168C22×C29C22×D411yescharacteristic
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—22no—
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—41no—
175C4×C29—41no—
176C4×C29—41no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29C2×#4111yescharacteristic
180C4×C29H(5,𝔽2)11yescharacteristic
181#548C2×C2911yescharacteristic, complemented
182#547C2×C2911yescharacteristic, complemented
183#489C2×C2911yescharacteristic, complemented
184#484C2×C2911yescharacteristic, complemented
185#480C2×C2911yescharacteristic, complemented
186#477C2×C2911yescharacteristic, complemented
187#468C2×C2911yescharacteristic, complemented
188#466C2×C2911yescharacteristic, complemented
189#463C2×C2911yescharacteristic, complemented
190#449C2×C2911yescharacteristic, complemented
191#448C2×C2911yescharacteristic, complemented
192#440C2×C2911yescharacteristic, complemented
193#435C2×C2911yescharacteristic, complemented
194#417C2×C2911yescharacteristic, complemented
195C2×#103C2×C2911yescharacteristic, complemented
196C2×C29—22no—
197C2×C29—41no—
198C2×C29—81no—
199C2×C29—81no—
200C2×C29#54611yescharacteristic
201C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
202C2×C29#57811yescharacteristic
203C2×#41—21no—
204C2×#41C22×C2911yescharacteristic
205C22×Q8C22×C2911yescharacteristic
206C2×SD16C22×C2911yescharacteristic
207C2×SD16C22×C2911yescharacteristic
208C2×D8C22×C2911yescharacteristic
209C2×M16C22×C2911yescharacteristic
210C22×C8C22×C2911yescharacteristic
211C4⋊Q8C22×C2911yescharacteristic
212#124—21no—
213#124C22×C2911yescharacteristic
214#123—21no—
215#123—21no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8C22×C2911yescharacteristic
219#121—21no—
220#121C22×C2911yescharacteristic
221#121C22×C2911yescharacteristic
222#121C22×C2911yescharacteristic
223C4×Q8C22×C2911yescharacteristic
224C4×D4—21no—
225C4×D4C22×C2911yescharacteristic
226C4×D4C22×C2911yescharacteristic
227C2×C4⋊C4C22×C2911yescharacteristic
228C2×C4⋊C4C22×C2911yescharacteristic
229#107C22×C2911yescharacteristic
230#107C22×C2911yescharacteristic
231#107C22×C2911yescharacteristic
232C4⋊C8C22×C2911yescharacteristic
233#103C22×C2911yescharacteristic
234#103C22×C2911yescharacteristic
235#103C22×C2911yescharacteristic
236#103C22×C2911yescharacteristic
237#103C22×C2911yescharacteristic
238#103C22×C2911yescharacteristic
239#102C22×C2911yescharacteristic
240#102C22×C2911yescharacteristic
241#102C22×C2911yescharacteristic
242#102C22×C2911yescharacteristic
243C22⋊C8C22×C2911yescharacteristic
244C22⋊C8C22×C2911yescharacteristic
245#97C22×C2911yescharacteristic
246C29#330811yescharacteristic, direct product factor, Sylow
247#41—22no—
248#41—41no—
249#41—44no—
250C2×Q8—21no—
251C2×Q8—21no—
252C2×Q8—22no—
253C2×Q8—41no—
254C2×Q8C23×C2911yescharacteristic
255C2×Q8C23×C2911yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4D4×C2911yescharacteristic
261C2×D4C23×C2911yescharacteristic
262C2×D4C23×C2911yescharacteristic
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4C23×C2911yescharacteristic
269C22×C4C23×C2911yescharacteristic
270SD16—22no—
271SD16—41no—
272D8—41no—
273M16—41no—
274C2×C8—41no—
275C2×C8C23×C2911yescharacteristic
276C2×C8C23×C2911yescharacteristic
277C2×C8C23×C2911yescharacteristic
278C2×C8C23×C2911yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4D4×C2911yescharacteristic
285C4⋊C4C23×C2911yescharacteristic
286C4⋊C4C23×C2911yescharacteristic
287C4⋊C4C23×C2911yescharacteristic
288C4⋊C4C23×C2911yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—21no—
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4D4×C2911yescharacteristic
297C22⋊C4D4×C2911yescharacteristic
298C42—21no—
299C42C23×C2911yescharacteristic
300C23—21no—
301C23—21no—
302C23C2×D4×C2911yescharacteristic
303C23C2×D4×C2911yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—42no—
309Q8#41×C2912yescomplemented
310D4—22no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—42no—
316D4—42no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4C2×D4×C2911yescharacteristic
335C2×C4C2×D4×C2911yescharacteristic
336C2×C4C2×D4×C2911yescharacteristic
337C2×C4C2×D4×C2911yescharacteristic
338C2×C4C24×C2911yescharacteristic
339C8—21no—
340C8—21no—
341C8—21no—
342C8—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22C29×AGL(1,ℤ/8)12yes—
355C22C22×D4×C2911yescharacteristic
356C4—21no—
357C4—21no—
358C4—22no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—41no—
366C4C2×#41×C2911yescharacteristic
367C4C29×H(5,𝔽2)11yescharacteristic
368C2—22no—
369C2—41no—
370C2—81no—
371C2—81no—
372C2C29×#54611yescharacteristic
373C2C2×C29×AGL(1,ℤ/8)11yescharacteristic
374C2C29×#57811yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#548C2semidirect
2. C29×#547C2semidirect
3. C29×#489C2semidirect
4. C29×#484C2semidirect
5. C29×#480C2semidirect
6. C29×#477C2semidirect
7. C29×#468C2semidirect
8. C29×#466C2semidirect
9. C29×#463C2semidirect
10. C29×#449C2semidirect
11. C29×#448C2semidirect
12. C29×#440C2semidirect
13. C29×#435C2semidirect
14. C29×#417C2semidirect
15. C2×C29×#103C2semidirect
121. Q8×C29#41semidirect
155. #3308C29direct (N × H)
181. #548C2×C29semidirect
182. #547C2×C29semidirect
183. #489C2×C29semidirect
184. #484C2×C29semidirect
185. #480C2×C29semidirect
186. #477C2×C29semidirect
187. #468C2×C29semidirect
188. #466C2×C29semidirect
189. #463C2×C29semidirect
190. #449C2×C29semidirect
191. #448C2×C29semidirect
192. #440C2×C29semidirect
193. #435C2×C29semidirect
194. #417C2×C29semidirect
195. C2×#103C2×C29semidirect
246. C29#3308direct (N × H)
309. Q8#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#5482
C29×#5472
C29×#4892
C29×#4842
C29×#4802
C29×#4772
C29×#4682
C29×#4662
C29×#4632
C29×#4492
C29×#4482
C29×#4402
C29×#4352
C29×#4172
C2×C29×#1032
#330829