Finite Group Databasebeta

← C29×#3309 #16817023

Subgroups — C29×#3309 #16817023

Order 3712.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#553C211yesmaximal, characteristic, complemented
2C29×#550C211yesmaximal, characteristic, complemented
3C29×#490C211yesmaximal, characteristic, complemented
4C29×#482C211yesmaximal, characteristic, complemented
5C29×#480C211yesmaximal, characteristic, complemented
6C29×#479C211yesmaximal, characteristic, complemented
7C29×#469C211yesmaximal, characteristic, complemented
8C29×#466C211yesmaximal, characteristic, complemented
9C29×#459C211yesmaximal, characteristic, complemented
10C29×#449C211yesmaximal, characteristic, complemented
11C29×#449C211yesmaximal, characteristic, complemented
12C29×#440C211yesmaximal, characteristic, complemented
13C29×#435C211yesmaximal, characteristic, complemented
14C29×#417C211yesmaximal, characteristic, complemented
15C29×#416C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#41×C29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C2×D8×C29C2211yescharacteristic
20C2×D8×C29C2211yescharacteristic
21C2×M16×C29C2211yescharacteristic
22C22×C8×C29C2211yescharacteristic
23C29×#127—21no—
24C29×#127C2211yescharacteristic
25C29×#126—21no—
26C29×#125C2211yescharacteristic
27C29×#123—21no—
28C29×#121—21no—
29C29×#121—21no—
30C29×#121—21no—
31C29×#121C2211yescharacteristic
32C29×#121C2211yescharacteristic
33C29×#121C2211yescharacteristic
34C29×#121C2211yescharacteristic
35C4×Q8×C29C2211yescharacteristic
36C4×D4×C29—21no—
37C4×D4×C29—21no—
38C4×D4×C29C2211yescharacteristic
39C4×D4×C29C2211yescharacteristic
40C29×#117C2211yescharacteristic
41C2×C4⋊C4×C29C2211yescharacteristic
42C29×#107C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#106C2211yescharacteristic
45C29×C4⋊C8C2211yescharacteristic
46C29×#103C2211yescharacteristic
47C29×#103C2211yescharacteristic
48C29×#103C2211yescharacteristic
49C29×#102C2211yescharacteristic
50C29×#102C2211yescharacteristic
51C29×#102C2211yescharacteristic
52C29×#102C2211yescharacteristic
53C29×#102C2211yescharacteristic
54C29×#102C2211yescharacteristic
55C29×#102C2211yescharacteristic
56C29×C22⋊C8C2211yescharacteristic
57C29×C22⋊C8C2211yescharacteristic
58C29×#97C2211yescharacteristic
59#41×C29—22no—
60#41×C29—22no—
61#41×C29—41no—
62#41×C29—41no—
63C2×Q8×C29C2311yescharacteristic
64C2×D4×C29—21no—
65C2×D4×C29—21no—
66C2×D4×C29—21no—
67C2×D4×C29—21no—
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
75C2×D4×C29C2311yescharacteristic
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—
83D8×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×C29D411yescharacteristic
96C4⋊C4×C29C2311yescharacteristic
97C4⋊C4×C29C2311yescharacteristic
98C4⋊C4×C29C2311yescharacteristic
99C4⋊C4×C29C2311yescharacteristic
100C22⋊C4×C29—21no—
101C22⋊C4×C29—21no—
102C22⋊C4×C29—21no—
103C22⋊C4×C29—21no—
104C22⋊C4×C29—21no—
105C22⋊C4×C29—21no—
106C22⋊C4×C29D411yescharacteristic
107C22⋊C4×C29D411yescharacteristic
108C42×C29—21no—
109C42×C29—21no—
110C42×C29C2311yescharacteristic
111C23×C29—21no—
112C23×C29—21no—
113C23×C29—21no—
114C23×C29C2×D411yescharacteristic
115C23×C29C2×D411yescharacteristic
116Q8×C29—21no—
117Q8×C29#4112yes—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—21no—
121D4×C29—21no—
122D4×C29—21no—
123D4×C29—21no—
124D4×C29—41no—
125D4×C29—42no—
126D4×C29—42no—
127D4×C29—42no—
128D4×C29—42no—
129D4×C29—81no—
130D4×C29—81no—
131D4×C29—81no—
132D4×C29—81no—
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—21no—
142C2×C4×C29—42no—
143C2×C4×C29—42no—
144C2×C4×C29—81no—
145C2×C4×C29—81no—
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#3309C2911yesmaximal, characteristic, direct product factor, Sylow
156C22×C29—21no—
157C22×C29—21no—
158C22×C29—21no—
159C22×C29—21no—
160C22×C29—21no—
161C22×C29—21no—
162C22×C29—41no—
163C22×C29—41no—
164C22×C29—41no—
165C22×C29—41no—
166C22×C29—41no—
167C22×C29—41no—
168C22×C29—41no—
169C22×C29—41no—
170C22×C29—41no—
171C22×C29C22×D411yescharacteristic
172C4×C29—21no—
173C4×C29—21no—
174C4×C29—22no—
175C4×C29—21no—
176C4×C29—21no—
177C4×C29—41no—
178C4×C29—41no—
179C4×C29—41no—
180C4×C29—41no—
181C4×C29C2×#4111yescharacteristic
182C4×C29H(5,𝔽2)11yescharacteristic
183#553C2×C2911yescharacteristic, complemented
184#550C2×C2911yescharacteristic, complemented
185#490C2×C2911yescharacteristic, complemented
186#482C2×C2911yescharacteristic, complemented
187#480C2×C2911yescharacteristic, complemented
188#479C2×C2911yescharacteristic, complemented
189#469C2×C2911yescharacteristic, complemented
190#466C2×C2911yescharacteristic, complemented
191#459C2×C2911yescharacteristic, complemented
192#449C2×C2911yescharacteristic, complemented
193#449C2×C2911yescharacteristic, complemented
194#440C2×C2911yescharacteristic, complemented
195#435C2×C2911yescharacteristic, complemented
196#417C2×C2911yescharacteristic, complemented
197#416C2×C2911yescharacteristic, complemented
198C2×C29—41no—
199C2×C29—41no—
200C2×C29—81no—
201C2×C29—81no—
202C2×C29—81no—
203C2×C29#54611yescharacteristic
204C2×C29#57511yescharacteristic
205C2×C29#57611yescharacteristic
206C2×#41C22×C2911yescharacteristic
207C2×#41C22×C2911yescharacteristic
208C2×SD16C22×C2911yescharacteristic
209C2×D8C22×C2911yescharacteristic
210C2×D8C22×C2911yescharacteristic
211C2×M16C22×C2911yescharacteristic
212C22×C8C22×C2911yescharacteristic
213#127—21no—
214#127C22×C2911yescharacteristic
215#126—21no—
216#125C22×C2911yescharacteristic
217#123—21no—
218#121—21no—
219#121—21no—
220#121—21no—
221#121C22×C2911yescharacteristic
222#121C22×C2911yescharacteristic
223#121C22×C2911yescharacteristic
224#121C22×C2911yescharacteristic
225C4×Q8C22×C2911yescharacteristic
226C4×D4—21no—
227C4×D4—21no—
228C4×D4C22×C2911yescharacteristic
229C4×D4C22×C2911yescharacteristic
230#117C22×C2911yescharacteristic
231C2×C4⋊C4C22×C2911yescharacteristic
232#107C22×C2911yescharacteristic
233#107C22×C2911yescharacteristic
234#106C22×C2911yescharacteristic
235C4⋊C8C22×C2911yescharacteristic
236#103C22×C2911yescharacteristic
237#103C22×C2911yescharacteristic
238#103C22×C2911yescharacteristic
239#102C22×C2911yescharacteristic
240#102C22×C2911yescharacteristic
241#102C22×C2911yescharacteristic
242#102C22×C2911yescharacteristic
243#102C22×C2911yescharacteristic
244#102C22×C2911yescharacteristic
245#102C22×C2911yescharacteristic
246C22⋊C8C22×C2911yescharacteristic
247C22⋊C8C22×C2911yescharacteristic
248#97C22×C2911yescharacteristic
249C29#330911yescharacteristic, direct product factor, Sylow
250#41—22no—
251#41—22no—
252#41—41no—
253#41—41no—
254C2×Q8C23×C2911yescharacteristic
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4D4×C2911yescharacteristic
264C2×D4C23×C2911yescharacteristic
265C2×D4C23×C2911yescharacteristic
266C2×D4C23×C2911yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4C23×C2911yescharacteristic
272C22×C4C23×C2911yescharacteristic
273SD16—22no—
274D8—41no—
275D8—41no—
276M16—41no—
277C2×C8—41no—
278C2×C8C23×C2911yescharacteristic
279C2×C8C23×C2911yescharacteristic
280C2×C8C23×C2911yescharacteristic
281C2×C8C23×C2911yescharacteristic
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4D4×C2911yescharacteristic
287C4⋊C4C23×C2911yescharacteristic
288C4⋊C4C23×C2911yescharacteristic
289C4⋊C4C23×C2911yescharacteristic
290C4⋊C4C23×C2911yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—21no—
297C22⋊C4D4×C2911yescharacteristic
298C22⋊C4D4×C2911yescharacteristic
299C42—21no—
300C42—21no—
301C42C23×C2911yescharacteristic
302C23—21no—
303C23—21no—
304C23—21no—
305C23C2×D4×C2911yescharacteristic
306C23C2×D4×C2911yescharacteristic
307Q8—21no—
308Q8#41×C2912yes—
309D4—21no—
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—21no—
315D4—41no—
316D4—42no—
317D4—42no—
318D4—42no—
319D4—42no—
320D4—81no—
321D4—81no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4C2×D4×C2911yescharacteristic
338C2×C4C2×D4×C2911yescharacteristic
339C2×C4C2×D4×C2911yescharacteristic
340C2×C4C2×D4×C2911yescharacteristic
341C2×C4C24×C2911yescharacteristic
342C8—21no—
343C8—21no—
344C8—21no—
345C8—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22C22×D4×C2911yescharacteristic
362C4—21no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—21no—
367C4—41no—
368C4—41no—
369C4—41no—
370C4—41no—
371C4C2×#41×C2911yescharacteristic
372C4C29×H(5,𝔽2)11yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—81no—
377C2—81no—
378C2C29×#54611yescharacteristic
379C2C29×#57511yescharacteristic
380C2C29×#57611yescharacteristic
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×#553C2semidirect
2. C29×#550C2semidirect
3. C29×#490C2semidirect
4. C29×#482C2semidirect
5. C29×#480C2semidirect
6. C29×#479C2semidirect
7. C29×#469C2semidirect
8. C29×#466C2semidirect
9. C29×#459C2semidirect
10. C29×#449C2semidirect
11. C29×#449C2semidirect
12. C29×#440C2semidirect
13. C29×#435C2semidirect
14. C29×#417C2semidirect
15. C29×#416C2semidirect
155. #3309C29direct (N × H)
183. #553C2×C29semidirect
184. #550C2×C29semidirect
185. #490C2×C29semidirect
186. #482C2×C29semidirect
187. #480C2×C29semidirect
188. #479C2×C29semidirect
189. #469C2×C29semidirect
190. #466C2×C29semidirect
191. #459C2×C29semidirect
192. #449C2×C29semidirect
193. #449C2×C29semidirect
194. #440C2×C29semidirect
195. #435C2×C29semidirect
196. #417C2×C29semidirect
197. #416C2×C29semidirect
249. C29#3309direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5532
C29×#5502
C29×#4902
C29×#4822
C29×#4802
C29×#4792
C29×#4692
C29×#4662
C29×#4592
C29×#4492
C29×#4402
C29×#4352
C29×#4172
C29×#4162
#330929