Finite Group Databasebeta

← C29×#3271 #16816985

Subgroups — C29×#3271 #16816985

Order 3712.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#137C211yesmaximal, characteristic, complemented
2C2×C29×#135C211yesmaximal, characteristic, complemented
3C29×#550C211yesmaximal, characteristic, complemented
4C29×#548C211yesmaximal, characteristic, complemented
5C29×#496C211yesmaximal, characteristic, complemented
6C29×#469C211yesmaximal, characteristic, complemented
7C29×#465C211yesmaximal, characteristic, complemented
8C29×#464C211yesmaximal, characteristic, complemented
9C29×#460C211yesmaximal, characteristic, complemented
10C29×#452C211yesmaximal, characteristic, complemented
11C29×#449C211yesmaximal, characteristic, complemented
12C29×#449C211yesmaximal, characteristic, complemented
13C29×#448C211yesmaximal, characteristic, complemented
14C29×#441C211yesmaximal, characteristic, complemented
15C29×#435C211yesmaximal, characteristic, complemented
16C2×#41×C29C2211yescharacteristic
17C2×#41×C29C2211yescharacteristic
18C2×#41×C29C2211yescharacteristic
19C22×Q8×C29C2211yescharacteristic
20C29×#137—24no—
21C29×#135—24no—
22C2×Q16×C29C2211yescharacteristic
23C2×Q16×C29C2211yescharacteristic
24C2×SD16×C29C2211yescharacteristic
25C2×SD16×C29C2211yescharacteristic
26C2×SD16×C29C2211yescharacteristic
27C2×SD16×C29C2211yescharacteristic
28C2×SD16×C29C2211yescharacteristic
29C2×D8×C29C2211yescharacteristic
30C2×D8×C29C2211yescharacteristic
31C2×M16×C29C2211yescharacteristic
32C22×C8×C29C2211yescharacteristic
33C29×#127—21no—
34C29×#127C2211yescharacteristic
35C29×#124—21no—
36C29×#124C2211yescharacteristic
37C29×C22⋊Q8—21no—
38C29×C22⋊Q8C2211yescharacteristic
39C29×#121—21no—
40C29×#121—21no—
41C29×#121—21no—
42C29×#121C2211yescharacteristic
43C29×#121C2211yescharacteristic
44C29×#121C2211yescharacteristic
45C4×Q8×C29C2211yescharacteristic
46C4×Q8×C29C2211yescharacteristic
47C4×D4×C29—21no—
48C4×D4×C29—21no—
49C4×D4×C29C2211yescharacteristic
50C29×#106C2211yescharacteristic
51C29×C4⋊C8C2211yescharacteristic
52C29×#103C2211yescharacteristic
53C29×#103C2211yescharacteristic
54C29×#103C2211yescharacteristic
55C29×#102C2211yescharacteristic
56C29×#102C2211yescharacteristic
57C29×#102C2211yescharacteristic
58C29×C22⋊C8C2211yescharacteristic
59C29×C22⋊C8C2211yescharacteristic
60C29×#97C2211yescharacteristic
61#41×C29—22no—
62#41×C29—22no—
63#41×C29—22no—
64#41×C29—41no—
65#41×C29—41no—
66#41×C29—41no—
67C2×Q8×C29—21no—
68C2×Q8×C29—22no—
69C2×Q8×C29—41no—
70C2×Q8×C29C2311yescharacteristic
71C2×Q8×C29C2311yescharacteristic
72C2×Q8×C29C2311yescharacteristic
73C2×D4×C29—21no—
74C2×D4×C29—21no—
75C2×D4×C29—21no—
76C2×D4×C29—21no—
77C2×D4×C29—21no—
78C2×D4×C29—21no—
79C2×D4×C29—21no—
80C2×D4×C29—21no—
81C2×D4×C29D411yescharacteristic
82C2×D4×C29C2311yescharacteristic
83C2×D4×C29C2311yescharacteristic
84C2×D4×C29C2311yescharacteristic
85C22×C4×C29—21no—
86C22×C4×C29—21no—
87C22×C4×C29—21no—
88C22×C4×C29—21no—
89C22×C4×C29C2311yescharacteristic
90C22×C4×C29C2311yescharacteristic
91Q16×C29—22no—
92Q16×C29D414yescomplemented
93SD16×C29—22no—
94SD16×C29—22no—
95SD16×C29—22no—
96SD16×C29—22no—
97SD16×C29—41no—
98D8×C29—22no—
99D8×C29—41no—
100M16×C29—22no—
101C2×C8×C29—22no—
102C2×C8×C29C2311yescharacteristic
103C2×C8×C29C2311yescharacteristic
104C2×C8×C29C2311yescharacteristic
105C2×C8×C29C2311yescharacteristic
106C4⋊C4×C29—21no—
107C4⋊C4×C29—21no—
108C4⋊C4×C29—21no—
109C4⋊C4×C29D411yescharacteristic
110C4⋊C4×C29C2311yescharacteristic
111C4⋊C4×C29C2311yescharacteristic
112C22⋊C4×C29—21no—
113C22⋊C4×C29—21no—
114C22⋊C4×C29—21no—
115C22⋊C4×C29—21no—
116C22⋊C4×C29—21no—
117C22⋊C4×C29—21no—
118C22⋊C4×C29D411yescharacteristic
119C22⋊C4×C29D411yescharacteristic
120C42×C29—21no—
121C42×C29—21no—
122C42×C29C2311yescharacteristic
123C23×C29—21no—
124C23×C29—21no—
125C23×C29—21no—
126C23×C29C2×D411yescharacteristic
127C23×C29C2×D411yescharacteristic
128Q8×C29—21no—
129Q8×C29—21no—
130Q8×C29—21no—
131Q8×C29—21no—
132Q8×C29—42no—
133Q8×C29C2×D412yes—
134Q8×C29C2×D412yes—
135D4×C29—21no—
136D4×C29—21no—
137D4×C29—21no—
138D4×C29—21no—
139D4×C29—21no—
140D4×C29—21no—
141D4×C29—41no—
142D4×C29—42no—
143D4×C29—42no—
144D4×C29—42no—
145D4×C29—42no—
146D4×C29—42no—
147D4×C29—81no—
148D4×C29—81no—
149D4×C29—81no—
150C2×C4×C29—21no—
151C2×C4×C29—21no—
152C2×C4×C29—21no—
153C2×C4×C29—21no—
154C2×C4×C29—21no—
155C2×C4×C29—21no—
156C2×C4×C29—21no—
157C2×C4×C29—21no—
158C2×C4×C29—21no—
159C2×C4×C29—42no—
160C2×C4×C29—42no—
161C2×C4×C29—42no—
162C2×C4×C29—42no—
163C2×C4×C29C2×D411yescharacteristic
164C2×C4×C29C2×D411yescharacteristic
165C2×C4×C29C2×D411yescharacteristic
166C2×C4×C29C2×D411yescharacteristic
167C2×C4×C29C2411yescharacteristic
168C8×C29—21no—
169C8×C29—21no—
170C8×C29—21no—
171C8×C29C2×D412yes—
172#3271C2911yesmaximal, characteristic, direct product factor, Sylow
173C22×C29—21no—
174C22×C29—21no—
175C22×C29—21no—
176C22×C29—21no—
177C22×C29—21no—
178C22×C29—21no—
179C22×C29—41no—
180C22×C29—41no—
181C22×C29—41no—
182C22×C29—41no—
183C22×C29—41no—
184C22×C29—41no—
185C22×C29—41no—
186C22×C29—41no—
187C22×C29—41no—
188C22×C29C22×D411yescharacteristic
189C4×C29—21no—
190C4×C29—21no—
191C4×C29—22no—
192C4×C29—22no—
193C4×C29—21no—
194C4×C29—21no—
195C4×C29—41no—
196C4×C29—41no—
197C4×C29—41no—
198C4×C29C22×D411yescharacteristic
199C4×C29H(5,𝔽2)11yescharacteristic
200C2×#137C2×C2911yescharacteristic, complemented
201C2×#135C2×C2911yescharacteristic, complemented
202#550C2×C2911yescharacteristic, complemented
203#548C2×C2911yescharacteristic, complemented
204#496C2×C2911yescharacteristic, complemented
205#469C2×C2911yescharacteristic, complemented
206#465C2×C2911yescharacteristic, complemented
207#464C2×C2911yescharacteristic, complemented
208#460C2×C2911yescharacteristic, complemented
209#452C2×C2911yescharacteristic, complemented
210#449C2×C2911yescharacteristic, complemented
211#449C2×C2911yescharacteristic, complemented
212#448C2×C2911yescharacteristic, complemented
213#441C2×C2911yescharacteristic, complemented
214#435C2×C2911yescharacteristic, complemented
215C2×C29—41no—
216C2×C29—41no—
217C2×C29—81no—
218C2×C29—81no—
219C2×C29—81no—
220C2×C29D4211yescharacteristic
221C2×C29#57511yescharacteristic
222C2×C29#57711yescharacteristic
223C2×#41C22×C2911yescharacteristic
224C2×#41C22×C2911yescharacteristic
225C2×#41C22×C2911yescharacteristic
226C22×Q8C22×C2911yescharacteristic
227#137—24no—
228#135—24no—
229C2×Q16C22×C2911yescharacteristic
230C2×Q16C22×C2911yescharacteristic
231C2×SD16C22×C2911yescharacteristic
232C2×SD16C22×C2911yescharacteristic
233C2×SD16C22×C2911yescharacteristic
234C2×SD16C22×C2911yescharacteristic
235C2×SD16C22×C2911yescharacteristic
236C2×D8C22×C2911yescharacteristic
237C2×D8C22×C2911yescharacteristic
238C2×M16C22×C2911yescharacteristic
239C22×C8C22×C2911yescharacteristic
240#127—21no—
241#127C22×C2911yescharacteristic
242#124—21no—
243#124C22×C2911yescharacteristic
244C22⋊Q8—21no—
245C22⋊Q8C22×C2911yescharacteristic
246#121—21no—
247#121—21no—
248#121—21no—
249#121C22×C2911yescharacteristic
250#121C22×C2911yescharacteristic
251#121C22×C2911yescharacteristic
252C4×Q8C22×C2911yescharacteristic
253C4×Q8C22×C2911yescharacteristic
254C4×D4—21no—
255C4×D4—21no—
256C4×D4C22×C2911yescharacteristic
257#106C22×C2911yescharacteristic
258C4⋊C8C22×C2911yescharacteristic
259#103C22×C2911yescharacteristic
260#103C22×C2911yescharacteristic
261#103C22×C2911yescharacteristic
262#102C22×C2911yescharacteristic
263#102C22×C2911yescharacteristic
264#102C22×C2911yescharacteristic
265C22⋊C8C22×C2911yescharacteristic
266C22⋊C8C22×C2911yescharacteristic
267#97C22×C2911yescharacteristic
268C29#327111yescharacteristic, direct product factor, Sylow
269#41—22no—
270#41—22no—
271#41—22no—
272#41—41no—
273#41—41no—
274#41—41no—
275C2×Q8—21no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8C23×C2911yescharacteristic
279C2×Q8C23×C2911yescharacteristic
280C2×Q8C23×C2911yescharacteristic
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—21no—
285C2×D4—21no—
286C2×D4—21no—
287C2×D4—21no—
288C2×D4—21no—
289C2×D4D4×C2911yescharacteristic
290C2×D4C23×C2911yescharacteristic
291C2×D4C23×C2911yescharacteristic
292C2×D4C23×C2911yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4C23×C2911yescharacteristic
298C22×C4C23×C2911yescharacteristic
299Q16—22no—
300Q16D4×C2914yescomplemented
301SD16—22no—
302SD16—22no—
303SD16—22no—
304SD16—22no—
305SD16—41no—
306D8—22no—
307D8—41no—
308M16—22no—
309C2×C8—22no—
310C2×C8C23×C2911yescharacteristic
311C2×C8C23×C2911yescharacteristic
312C2×C8C23×C2911yescharacteristic
313C2×C8C23×C2911yescharacteristic
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4D4×C2911yescharacteristic
318C4⋊C4C23×C2911yescharacteristic
319C4⋊C4C23×C2911yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4D4×C2911yescharacteristic
327C22⋊C4D4×C2911yescharacteristic
328C42—21no—
329C42—21no—
330C42C23×C2911yescharacteristic
331C23—21no—
332C23—21no—
333C23—21no—
334C23C2×D4×C2911yescharacteristic
335C23C2×D4×C2911yescharacteristic
336Q8—21no—
337Q8—21no—
338Q8—21no—
339Q8—21no—
340Q8—42no—
341Q8C2×D4×C2912yes—
342Q8C2×D4×C2912yes—
343D4—21no—
344D4—21no—
345D4—21no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—42no—
353D4—42no—
354D4—42no—
355D4—81no—
356D4—81no—
357D4—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4C2×D4×C2911yescharacteristic
372C2×C4C2×D4×C2911yescharacteristic
373C2×C4C2×D4×C2911yescharacteristic
374C2×C4C2×D4×C2911yescharacteristic
375C2×C4C24×C2911yescharacteristic
376C8—21no—
377C8—21no—
378C8—21no—
379C8C2×D4×C2912yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22C22×D4×C2911yescharacteristic
396C4—21no—
397C4—21no—
398C4—22no—
399C4—22no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4C22×D4×C2911yescharacteristic
406C4C29×H(5,𝔽2)11yescharacteristic
407C2—41no—
408C2—41no—
409C2—81no—
410C2—81no—
411C2—81no—
412C2D42×C2911yescharacteristic
413C2C29×#57511yescharacteristic
414C2C29×#57711yescharacteristic
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. C2×C29×#137C2semidirect
2. C2×C29×#135C2semidirect
3. C29×#550C2semidirect
4. C29×#548C2semidirect
5. C29×#496C2semidirect
6. C29×#469C2semidirect
7. C29×#465C2semidirect
8. C29×#464C2semidirect
9. C29×#460C2semidirect
10. C29×#452C2semidirect
11. C29×#449C2semidirect
12. C29×#449C2semidirect
13. C29×#448C2semidirect
14. C29×#441C2semidirect
15. C29×#435C2semidirect
92. Q16×C29D4semidirect
172. #3271C29direct (N × H)
200. C2×#137C2×C29semidirect
201. C2×#135C2×C29semidirect
202. #550C2×C29semidirect
203. #548C2×C29semidirect
204. #496C2×C29semidirect
205. #469C2×C29semidirect
206. #465C2×C29semidirect
207. #464C2×C29semidirect
208. #460C2×C29semidirect
209. #452C2×C29semidirect
210. #449C2×C29semidirect
211. #449C2×C29semidirect
212. #448C2×C29semidirect
213. #441C2×C29semidirect
214. #435C2×C29semidirect
268. C29#3271direct (N × H)
300. Q16D4×C29semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#1372
C2×C29×#1352
C29×#5502
C29×#5482
C29×#4962
C29×#4692
C29×#4652
C29×#4642
C29×#4602
C29×#4522
C29×#4492
C29×#4482
C29×#4412
C29×#4352
#327129