Finite Group Databasebeta

← C29×#3258 #16816972

Subgroups — C29×#3258 #16816972

Order 3712.

334 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#542C211yesmaximal, characteristic
2C29×#541C211yesmaximal, characteristic, complemented
3C29×#479C211yesmaximal, characteristic, complemented
4C29×#478C211yesmaximal, characteristic, complemented
5C29×#477C211yesmaximal, characteristic, complemented
6C29×#475C211yesmaximal, characteristic, complemented
7C29×#470C211yesmaximal, characteristic, complemented
8C29×#468C211yesmaximal, characteristic
9C29×#467C211yesmaximal, characteristic, complemented
10C29×#465C211yesmaximal, characteristic
11C29×#464C211yesmaximal, characteristic, complemented
12C29×#464C211yesmaximal, characteristic, complemented
13C29×#462C211yesmaximal, characteristic, complemented
14C29×#461C211yesmaximal, characteristic, complemented
15C29×#424C211yesmaximal, characteristic, complemented
16C2×Q16×C29C2211yescharacteristic
17C2×Q16×C29C2211yescharacteristic
18C2×SD16×C29C2211yescharacteristic
19C2×SD16×C29C2211yescharacteristic
20C2×M16×C29C2211yescharacteristic
21C22×C8×C29C2211yescharacteristic
22C29×C4⋊Q8C2211yescharacteristic
23C29×C4⋊Q8C2211yescharacteristic
24C29×#126—21no—
25C29×#126—21no—
26C29×#126—21no—
27C29×#125—21no—
28C29×#125—21no—
29C29×#125C2211yescharacteristic
30C29×#124—21no—
31C29×#124C2211yescharacteristic
32C29×#123—21no—
33C29×C22⋊Q8—21no—
34C29×C22⋊Q8C2211yescharacteristic
35C29×C22⋊Q8C2211yescharacteristic
36C29×C22⋊Q8C2211yescharacteristic
37C29×#121C2211yescharacteristic
38C4×Q8×C29C2211yescharacteristic
39C4×Q8×C29C2211yescharacteristic
40C4×Q8×C29C2211yescharacteristic
41C4×D4×C29C2211yescharacteristic
42C29×#117C2211yescharacteristic
43C29×#107C2211yescharacteristic
44C29×#107C2211yescharacteristic
45C29×#106C2211yescharacteristic
46C29×#106C2211yescharacteristic
47C29×C4⋊C8C2211yescharacteristic
48C29×C4⋊C8C2211yescharacteristic
49C29×C4⋊C8C2211yescharacteristic
50C29×C4⋊C8C2211yescharacteristic
51C29×#103C2211yescharacteristic
52C29×#103C2211yescharacteristic
53C29×#103C2211yescharacteristic
54C29×#103C2211yescharacteristic
55C29×#103C2211yescharacteristic
56C29×#103C2211yescharacteristic
57C29×#102C2211yescharacteristic
58C29×#102C2211yescharacteristic
59C2×Q8×C29—21no—
60C2×Q8×C29C2311yescharacteristic
61C2×Q8×C29C2311yescharacteristic
62C2×Q8×C29C2311yescharacteristic
63C2×D4×C29—21no—
64C2×D4×C29C2311yescharacteristic
65C22×C4×C29—21no—
66C22×C4×C29C2311yescharacteristic
67Q16×C29—41no—
68Q16×C29—41no—
69SD16×C29—41no—
70SD16×C29—41no—
71M16×C29—41no—
72C2×C8×C29—41no—
73C2×C8×C29C2311yescharacteristic
74C2×C8×C29C2311yescharacteristic
75C2×C8×C29C2311yescharacteristic
76C2×C8×C29C2311yescharacteristic
77C4⋊C4×C29—21no—
78C4⋊C4×C29—21no—
79C4⋊C4×C29—21no—
80C4⋊C4×C29—21no—
81C4⋊C4×C29—21no—
82C4⋊C4×C29—21no—
83C4⋊C4×C29—21no—
84C4⋊C4×C29—21no—
85C4⋊C4×C29—21no—
86C4⋊C4×C29—21no—
87C4⋊C4×C29—21no—
88C4⋊C4×C29D411yescharacteristic
89C4⋊C4×C29D411yescharacteristic
90C4⋊C4×C29C2311yescharacteristic
91C4⋊C4×C29C2311yescharacteristic
92C4⋊C4×C29C2311yescharacteristic
93C4⋊C4×C29C2311yescharacteristic
94C22⋊C4×C29—21no—
95C22⋊C4×C29—21no—
96C22⋊C4×C29—21no—
97C22⋊C4×C29—21no—
98C22⋊C4×C29—21no—
99C22⋊C4×C29—21no—
100C22⋊C4×C29—21no—
101C22⋊C4×C29D411yescharacteristic
102C22⋊C4×C29D411yescharacteristic
103C42×C29—21no—
104C42×C29—21no—
105C42×C29—21no—
106C42×C29C2311yescharacteristic
107C42×C29C2311yescharacteristic
108C23×C29—21no—
109C23×C29C2×D411yescharacteristic
110Q8×C29—21no—
111Q8×C29—21no—
112Q8×C29—21no—
113Q8×C29—21no—
114Q8×C29—21no—
115Q8×C29—21no—
116Q8×C29—81no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—81no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—21no—
125C2×C4×C29—21no—
126C2×C4×C29—21no—
127C2×C4×C29—21no—
128C2×C4×C29—21no—
129C2×C4×C29—81no—
130C2×C4×C29C2×D411yescharacteristic
131C2×C4×C29C2×D411yescharacteristic
132C2×C4×C29C2×D411yescharacteristic
133C2×C4×C29C2×D411yescharacteristic
134C2×C4×C29C2×D411yescharacteristic
135C2×C4×C29C2411yescharacteristic
136C8×C29—21no—
137C8×C29—21no—
138C8×C29—21no—
139C8×C29—21no—
140#3258C2911yesmaximal, characteristic, direct product factor, Sylow
141C22×C29—21no—
142C22×C29—21no—
143C22×C29—21no—
144C22×C29—41no—
145C22×C29—41no—
146C22×C29—41no—
147C22×C29C22×D411yescharacteristic
148C4×C29—21no—
149C4×C29—21no—
150C4×C29—21no—
151C4×C29—21no—
152C4×C29—21no—
153C4×C29—41no—
154C4×C29—41no—
155C4×C29—41no—
156C4×C29—41no—
157C4×C29—41no—
158C4×C29—41no—
159C4×C29—41no—
160C4×C29H(5,𝔽2)11yescharacteristic
161C4×C292−1+411yescharacteristic
162#542C2×C2911yescharacteristic
163#541C2×C2911yescharacteristic, complemented
164#479C2×C2911yescharacteristic, complemented
165#478C2×C2911yescharacteristic, complemented
166#477C2×C2911yescharacteristic, complemented
167#475C2×C2911yescharacteristic, complemented
168#470C2×C2911yescharacteristic, complemented
169#468C2×C2911yescharacteristic
170#467C2×C2911yescharacteristic, complemented
171#465C2×C2911yescharacteristic
172#464C2×C2911yescharacteristic, complemented
173#464C2×C2911yescharacteristic, complemented
174#462C2×C2911yescharacteristic, complemented
175#461C2×C2911yescharacteristic, complemented
176#424C2×C2911yescharacteristic, complemented
177C2×C29—41no—
178C2×C29—81no—
179C2×C29#53711yescharacteristic
180C2×C29#57711yescharacteristic
181C2×C29#57811yescharacteristic
182C2×Q16C22×C2911yescharacteristic
183C2×Q16C22×C2911yescharacteristic
184C2×SD16C22×C2911yescharacteristic
185C2×SD16C22×C2911yescharacteristic
186C2×M16C22×C2911yescharacteristic
187C22×C8C22×C2911yescharacteristic
188C4⋊Q8C22×C2911yescharacteristic
189C4⋊Q8C22×C2911yescharacteristic
190#126—21no—
191#126—21no—
192#126—21no—
193#125—21no—
194#125—21no—
195#125C22×C2911yescharacteristic
196#124—21no—
197#124C22×C2911yescharacteristic
198#123—21no—
199C22⋊Q8—21no—
200C22⋊Q8C22×C2911yescharacteristic
201C22⋊Q8C22×C2911yescharacteristic
202C22⋊Q8C22×C2911yescharacteristic
203#121C22×C2911yescharacteristic
204C4×Q8C22×C2911yescharacteristic
205C4×Q8C22×C2911yescharacteristic
206C4×Q8C22×C2911yescharacteristic
207C4×D4C22×C2911yescharacteristic
208#117C22×C2911yescharacteristic
209#107C22×C2911yescharacteristic
210#107C22×C2911yescharacteristic
211#106C22×C2911yescharacteristic
212#106C22×C2911yescharacteristic
213C4⋊C8C22×C2911yescharacteristic
214C4⋊C8C22×C2911yescharacteristic
215C4⋊C8C22×C2911yescharacteristic
216C4⋊C8C22×C2911yescharacteristic
217#103C22×C2911yescharacteristic
218#103C22×C2911yescharacteristic
219#103C22×C2911yescharacteristic
220#103C22×C2911yescharacteristic
221#103C22×C2911yescharacteristic
222#103C22×C2911yescharacteristic
223#102C22×C2911yescharacteristic
224#102C22×C2911yescharacteristic
225C29#325811yescharacteristic, direct product factor, Sylow
226C2×Q8—21no—
227C2×Q8C23×C2911yescharacteristic
228C2×Q8C23×C2911yescharacteristic
229C2×Q8C23×C2911yescharacteristic
230C2×D4—21no—
231C2×D4C23×C2911yescharacteristic
232C22×C4—21no—
233C22×C4C23×C2911yescharacteristic
234Q16—41no—
235Q16—41no—
236SD16—41no—
237SD16—41no—
238M16—41no—
239C2×C8—41no—
240C2×C8C23×C2911yescharacteristic
241C2×C8C23×C2911yescharacteristic
242C2×C8C23×C2911yescharacteristic
243C2×C8C23×C2911yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4D4×C2911yescharacteristic
256C4⋊C4D4×C2911yescharacteristic
257C4⋊C4C23×C2911yescharacteristic
258C4⋊C4C23×C2911yescharacteristic
259C4⋊C4C23×C2911yescharacteristic
260C4⋊C4C23×C2911yescharacteristic
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4D4×C2911yescharacteristic
269C22⋊C4D4×C2911yescharacteristic
270C42—21no—
271C42—21no—
272C42—21no—
273C42C23×C2911yescharacteristic
274C42C23×C2911yescharacteristic
275C23—21no—
276C23C2×D4×C2911yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—81no—
297C2×C4C2×D4×C2911yescharacteristic
298C2×C4C2×D4×C2911yescharacteristic
299C2×C4C2×D4×C2911yescharacteristic
300C2×C4C2×D4×C2911yescharacteristic
301C2×C4C2×D4×C2911yescharacteristic
302C2×C4C24×C2911yescharacteristic
303C8—21no—
304C8—21no—
305C8—21no—
306C8—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22C22×D4×C2911yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C29×H(5,𝔽2)11yescharacteristic
327C4C29×2−1+411yescharacteristic
328C2—41no—
329C2—81no—
330C2C29×#53711yescharacteristic
331C2C29×#57711yescharacteristic
332C2C29×#57811yescharacteristic
subgroupG/H
center, socleC22×C29C22×D4
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC29×#121C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#541C2semidirect
3. C29×#479C2semidirect
4. C29×#478C2semidirect
5. C29×#477C2semidirect
6. C29×#475C2semidirect
7. C29×#470C2semidirect
9. C29×#467C2semidirect
11. C29×#464C2semidirect
12. C29×#464C2semidirect
13. C29×#462C2semidirect
14. C29×#461C2semidirect
15. C29×#424C2semidirect
140. #3258C29direct (N × H)
163. #541C2×C29semidirect
164. #479C2×C29semidirect
165. #478C2×C29semidirect
166. #477C2×C29semidirect
167. #475C2×C29semidirect
168. #470C2×C29semidirect
170. #467C2×C29semidirect
172. #464C2×C29semidirect
173. #464C2×C29semidirect
174. #462C2×C29semidirect
175. #461C2×C29semidirect
176. #424C2×C29semidirect
225. C29#3258direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5422
C29×#5412
C29×#4792
C29×#4782
C29×#4772
C29×#4752
C29×#4702
C29×#4682
C29×#4672
C29×#4652
C29×#4642
C29×#4622
C29×#4612
C29×#4242
#325829