Finite Group Databasebeta

← C29×#3516 #16817230

Subgroups — C29×#3516 #16817230

Order 3712.

1012 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#557C211yesmaximal, characteristic, complemented
2C29×#556C213yesmaximal, complemented
3C29×#554C213yesmaximal, complemented
4C29×#553C213yesmaximal, complemented
5C29×#552C213yesmaximal, complemented
6D4×Q8×C29C211yesmaximal, characteristic, complemented
7C29×#548C211yesmaximal, characteristic, complemented
8C29×#548C211yesmaximal, characteristic, complemented
9C29×#542C213yesmaximal, complemented
10C29×#541C213yesmaximal, complemented
11C29×#529C213yesmaximal, complemented
12C29×#529C213yesmaximal, complemented
13C29×#520C211yesmaximal, characteristic, complemented
14C29×#519C211yesmaximal, characteristic, complemented
15C2×C4×Q8×C29C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C22×Q8×C29C2211yescharacteristic
18C22×Q8×C29C2211yescharacteristic
19C29×C4⋊Q8C2213yes—
20C29×C4⋊Q8C2213yes—
21C29×#126C2216yes—
22C29×#126C2213yes—
23C29×#126C2213yes—
24C29×#126C2216yes—
25C29×#125C2213yes—
26C29×#125C2213yes—
27C29×#125C2216yes—
28C29×#125C2213yes—
29C29×#124C2213yes—
30C29×#124C2213yes—
31C29×#124C2213yes—
32C29×#123C2211yescharacteristic
33C29×#123C2213yes—
34C29×#123C2216yes—
35C29×C22⋊Q8C2213yes—
36C29×C22⋊Q8C2213yes—
37C29×C22⋊Q8C2213yes—
38C29×C22⋊Q8C2213yes—
39C29×C22⋊Q8C2213yes—
40C29×C22⋊Q8C2216yes—
41C29×#121C2213yes—
42C29×#121C2213yes—
43C29×#121C2213yes—
44C4×Q8×C29C2211yescharacteristic
45C4×Q8×C29C2213yes—
46C4×Q8×C29C2211yescharacteristic
47C4×Q8×C29C2213yes—
48C4×Q8×C29C2213yes—
49C4×Q8×C29C2211yescharacteristic
50C4×Q8×C29C2213yes—
51C4×Q8×C29C2211yescharacteristic
52C4×Q8×C29C2213yes—
53C4×D4×C29C2213yes—
54C4×D4×C29C2213yes—
55C4×D4×C29C2213yes—
56C4×D4×C29C2213yes—
57C4×D4×C29C2213yes—
58C4×D4×C29C2216yes—
59C29×#117C2213yes—
60C29×#117C2213yes—
61C29×#117C2213yes—
62C29×#117C2216yes—
63C2×C4⋊C4×C29C2213yes—
64C2×C4⋊C4×C29C2213yes—
65C2×C42×C29C2213yes—
66#41×C29—24no—
67C2×Q8×C29—24no—
68C2×Q8×C29—24no—
69C2×Q8×C29C2313yes—
70C2×Q8×C29C2313yes—
71C2×Q8×C29C2313yes—
72C2×Q8×C29C2311yescharacteristic
73C2×D4×C29C2313yes—
74C2×D4×C29C2311yescharacteristic
75C2×D4×C29C2313yes—
76C2×D4×C29C2313yes—
77C22×C4×C29C2311yescharacteristic
78C22×C4×C29C2313yes—
79C22×C4×C29C2313yes—
80C22×C4×C29C2313yes—
81C22×C4×C29C2313yes—
82C22×C4×C29C2316yes—
83C4⋊C4×C29C2313yes—
84C4⋊C4×C29C2313yes—
85C4⋊C4×C29C2313yes—
86C4⋊C4×C29C2313yes—
87C4⋊C4×C29C2316yes—
88C4⋊C4×C29C2311yescharacteristic
89C4⋊C4×C29C2313yes—
90C4⋊C4×C29C2313yes—
91C4⋊C4×C29C2313yes—
92C4⋊C4×C29C2313yes—
93C4⋊C4×C29C2316yes—
94C4⋊C4×C29C2313yes—
95C4⋊C4×C29C2313yes—
96C4⋊C4×C29C2316yes—
97C4⋊C4×C29C2313yes—
98C4⋊C4×C29C2311yescharacteristic
99C4⋊C4×C29C2313yes—
100C22⋊C4×C29C2313yes—
101C22⋊C4×C29C2311yescharacteristic
102C22⋊C4×C29C2313yes—
103C22⋊C4×C29C2313yes—
104C22⋊C4×C29C2313yes—
105C22⋊C4×C29C2316yes—
106C22⋊C4×C29C2311yescharacteristic
107C22⋊C4×C29C2313yes—
108C22⋊C4×C29C2311yescharacteristic
109C22⋊C4×C29C2316yes—
110C22⋊C4×C29C2313yes—
111C22⋊C4×C29C2313yes—
112C42×C29C2313yes—
113C42×C29C2313yes—
114C42×C29C2313yes—
115C42×C29C2313yes—
116C42×C29C2316yes—
117C42×C29C2313yes—
118C42×C29C2313yes—
119C23×C29C2411yescharacteristic
120C23×C29C2413yes—
121C23×C29C2411yescharacteristic
122Q8×C29—26no—
123Q8×C29—26no—
124Q8×C29—43no—
125Q8×C29#4114yes—
126D4×C29—26no—
127D4×C29—22no—
128D4×C29—26no—
129D4×C29—43no—
130C2×C4×C29—22no—
131C2×C4×C29—26no—
132C2×C4×C29—26no—
133C2×C4×C29—26no—
134C2×C4×C29—46no—
135C2×C4×C29—43no—
136C2×C4×C29C2411yescharacteristic
137C2×C4×C29C2411yescharacteristic
138C2×C4×C29C2413yes—
139C2×C4×C29C2411yescharacteristic
140C2×C4×C29C2413yes—
141C2×C4×C29C2411yescharacteristic
142C2×C4×C29C2413yes—
143C2×C4×C29C2413yes—
144C2×C4×C29C2413yes—
145C2×C4×C29C2413yes—
146C2×C4×C29C2411yescharacteristic
147C2×C4×C29C2413yes—
148#3516C2911yesmaximal, characteristic, direct product factor, Sylow
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—23no—
153C22×C29—21no—
154C22×C29—23no—
155C22×C29—23no—
156C22×C29—21no—
157C22×C292−1+412yes—
158C22×C29C2511yescharacteristic
159C4×C29—21no—
160C4×C29—23no—
161C4×C29—23no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—23no—
165C4×C29—21no—
166C4×C29—23no—
167C4×C29—23no—
168C4×C29—23no—
169C4×C29—21no—
170C4×C29C2×#4116yes—
171#557C2×C2911yescharacteristic, complemented
172#556C2×C2913yescomplemented
173#554C2×C2913yescomplemented
174#553C2×C2913yescomplemented
175#552C2×C2913yescomplemented
176D4×Q8C2×C2911yescharacteristic, complemented
177#548C2×C2911yescharacteristic, complemented
178#548C2×C2911yescharacteristic, complemented
179#542C2×C2913yescomplemented
180#541C2×C2913yescomplemented
181#529C2×C2913yescomplemented
182#529C2×C2913yescomplemented
183#520C2×C2911yescharacteristic, complemented
184#519C2×C2911yescharacteristic, complemented
185C2×C4×Q8C2×C2911yescharacteristic, complemented
186C2×C29—22no—
187C2×C29—41no—
188C2×C29—43no—
189C2×C29C22×#4111yescharacteristic
190C2×C29C2×2−1+411yescharacteristic
191C2×C29#58511yescharacteristic
192C2×#41C22×C2911yescharacteristic
193C22×Q8C22×C2911yescharacteristic
194C22×Q8C22×C2911yescharacteristic
195C4⋊Q8C22×C2913yes—
196C4⋊Q8C22×C2913yes—
197#126C22×C2916yes—
198#126C22×C2913yes—
199#126C22×C2913yes—
200#126C22×C2916yes—
201#125C22×C2913yes—
202#125C22×C2913yes—
203#125C22×C2916yes—
204#125C22×C2913yes—
205#124C22×C2913yes—
206#124C22×C2913yes—
207#124C22×C2913yes—
208#123C22×C2911yescharacteristic
209#123C22×C2913yes—
210#123C22×C2916yes—
211C22⋊Q8C22×C2913yes—
212C22⋊Q8C22×C2913yes—
213C22⋊Q8C22×C2913yes—
214C22⋊Q8C22×C2913yes—
215C22⋊Q8C22×C2913yes—
216C22⋊Q8C22×C2916yes—
217#121C22×C2913yes—
218#121C22×C2913yes—
219#121C22×C2913yes—
220C4×Q8C22×C2911yescharacteristic
221C4×Q8C22×C2913yes—
222C4×Q8C22×C2911yescharacteristic
223C4×Q8C22×C2913yes—
224C4×Q8C22×C2913yes—
225C4×Q8C22×C2911yescharacteristic
226C4×Q8C22×C2913yes—
227C4×Q8C22×C2911yescharacteristic
228C4×Q8C22×C2913yes—
229C4×D4C22×C2913yes—
230C4×D4C22×C2913yes—
231C4×D4C22×C2913yes—
232C4×D4C22×C2913yes—
233C4×D4C22×C2913yes—
234C4×D4C22×C2916yes—
235#117C22×C2913yes—
236#117C22×C2913yes—
237#117C22×C2913yes—
238#117C22×C2916yes—
239C2×C4⋊C4C22×C2913yes—
240C2×C4⋊C4C22×C2913yes—
241C2×C42C22×C2913yes—
242C29#351611yescharacteristic, direct product factor, Sylow
243#41—24no—
244C2×Q8—24no—
245C2×Q8—24no—
246C2×Q8C23×C2913yes—
247C2×Q8C23×C2913yes—
248C2×Q8C23×C2913yes—
249C2×Q8C23×C2911yescharacteristic
250C2×D4C23×C2913yes—
251C2×D4C23×C2911yescharacteristic
252C2×D4C23×C2913yes—
253C2×D4C23×C2913yes—
254C22×C4C23×C2911yescharacteristic
255C22×C4C23×C2913yes—
256C22×C4C23×C2913yes—
257C22×C4C23×C2913yes—
258C22×C4C23×C2913yes—
259C22×C4C23×C2916yes—
260C4⋊C4C23×C2913yes—
261C4⋊C4C23×C2913yes—
262C4⋊C4C23×C2913yes—
263C4⋊C4C23×C2913yes—
264C4⋊C4C23×C2916yes—
265C4⋊C4C23×C2911yescharacteristic
266C4⋊C4C23×C2913yes—
267C4⋊C4C23×C2913yes—
268C4⋊C4C23×C2913yes—
269C4⋊C4C23×C2913yes—
270C4⋊C4C23×C2916yes—
271C4⋊C4C23×C2913yes—
272C4⋊C4C23×C2913yes—
273C4⋊C4C23×C2916yes—
274C4⋊C4C23×C2913yes—
275C4⋊C4C23×C2911yescharacteristic
276C4⋊C4C23×C2913yes—
277C22⋊C4C23×C2913yes—
278C22⋊C4C23×C2911yescharacteristic
279C22⋊C4C23×C2913yes—
280C22⋊C4C23×C2913yes—
281C22⋊C4C23×C2913yes—
282C22⋊C4C23×C2916yes—
283C22⋊C4C23×C2911yescharacteristic
284C22⋊C4C23×C2913yes—
285C22⋊C4C23×C2911yescharacteristic
286C22⋊C4C23×C2916yes—
287C22⋊C4C23×C2913yes—
288C22⋊C4C23×C2913yes—
289C42C23×C2913yes—
290C42C23×C2913yes—
291C42C23×C2913yes—
292C42C23×C2913yes—
293C42C23×C2916yes—
294C42C23×C2913yes—
295C42C23×C2913yes—
296C23C24×C2911yescharacteristic
297C23C24×C2913yes—
298C23C24×C2911yescharacteristic
299Q8—26no—
300Q8—26no—
301Q8—43no—
302Q8#41×C2914yes—
303D4—26no—
304D4—22no—
305D4—26no—
306D4—43no—
307C2×C4—22no—
308C2×C4—26no—
309C2×C4—26no—
310C2×C4—26no—
311C2×C4—46no—
312C2×C4—43no—
313C2×C4C24×C2911yescharacteristic
314C2×C4C24×C2911yescharacteristic
315C2×C4C24×C2913yes—
316C2×C4C24×C2911yescharacteristic
317C2×C4C24×C2913yes—
318C2×C4C24×C2911yescharacteristic
319C2×C4C24×C2913yes—
320C2×C4C24×C2913yes—
321C2×C4C24×C2913yes—
322C2×C4C24×C2913yes—
323C2×C4C24×C2911yescharacteristic
324C2×C4C24×C2913yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—23no—
329C22—21no—
330C22—23no—
331C22—23no—
332C22—21no—
333C22C29×2−1+412yes—
334C22C25×C2911yescharacteristic
335C4—21no—
336C4—23no—
337C4—23no—
338C4—21no—
339C4—21no—
340C4—23no—
341C4—21no—
342C4—23no—
343C4—23no—
344C4—23no—
345C4—21no—
346C4C2×#41×C2916yes—
347C2—22no—
348C2—41no—
349C2—43no—
350C2C22×#41×C2911yescharacteristic
351C2C2×C29×2−1+411yescharacteristic
352C2C29×#58511yescharacteristic
subgroupG/H
center, socleC22×C29C25
commutator, Frattini, cosocleC22C25×C29
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#557C2semidirect
2. C29×#556C2semidirect
3. C29×#554C2semidirect
4. C29×#553C2semidirect
5. C29×#552C2semidirect
6. D4×Q8×C29C2semidirect
7. C29×#548C2semidirect
8. C29×#548C2semidirect
9. C29×#542C2semidirect
10. C29×#541C2semidirect
11. C29×#529C2semidirect
12. C29×#529C2semidirect
13. C29×#520C2semidirect
14. C29×#519C2semidirect
15. C2×C4×Q8×C29C2semidirect
148. #3516C29direct (N × H)
171. #557C2×C29semidirect
172. #556C2×C29semidirect
173. #554C2×C29semidirect
174. #553C2×C29semidirect
175. #552C2×C29semidirect
176. D4×Q8C2×C29semidirect
177. #548C2×C29semidirect
178. #548C2×C29semidirect
179. #542C2×C29semidirect
180. #541C2×C29semidirect
181. #529C2×C29semidirect
182. #529C2×C29semidirect
183. #520C2×C29semidirect
184. #519C2×C29semidirect
185. C2×C4×Q8C2×C29semidirect
242. C29#3516direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#5572
C29×#5562
C29×#5542
C29×#5532
C29×#5522
D4×Q8×C292
C29×#5482
C29×#5422
C29×#5412
C29×#5292
C29×#5202
C29×#5192
C2×C4×Q8×C292
#351629