Finite Group Databasebeta

← C29×#33824 #20328724

Subgroups — C29×#33824 #20328724

Order 7424.

476 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3177C211yesmaximal, characteristic, complemented
2C29×#3175C211yesmaximal, characteristic
3C29×#2229C211yesmaximal, characteristic, complemented
4C29×#2228C211yesmaximal, characteristic, complemented
5C29×#2227C211yesmaximal, characteristic, complemented
6C29×#2225C211yesmaximal, characteristic, complemented
7C29×#2220C211yesmaximal, characteristic
8C29×#2219C211yesmaximal, characteristic, complemented
9C29×#2217C211yesmaximal, characteristic
10C29×#2216C211yesmaximal, characteristic, complemented
11C29×#2211C211yesmaximal, characteristic, complemented
12C29×#2211C211yesmaximal, characteristic, complemented
13C29×#2209C211yesmaximal, characteristic, complemented
14C29×#2208C211yesmaximal, characteristic, complemented
15C29×#2151C211yesmaximal, characteristic, complemented
16C29×#542—21no—
17C29×#541—21no—
18C2×C29×Q32C2211yescharacteristic
19C2×C29×Q32C2211yescharacteristic
20C2×C29×SD32C2211yescharacteristic
21C2×C29×SD32C2211yescharacteristic
22C2×C29×M32C2211yescharacteristic
23C22×C16×C29C2211yescharacteristic
24C29×#500C2211yescharacteristic
25C29×#499C2211yescharacteristic
26C29×#495C2211yescharacteristic
27C29×#494C2211yescharacteristic
28C29×#491—21no—
29C29×#489—21no—
30C29×#470—21no—
31C29×#468—21no—
32C29×#467C2211yescharacteristic
33C29×#467C2211yescharacteristic
34C29×#467C2211yescharacteristic
35C29×#466C2211yescharacteristic
36C29×#441—21no—
37C29×#440—21no—
38C4×Q16×C29C2211yescharacteristic
39C4×Q16×C29C2211yescharacteristic
40C4×Q16×C29C2211yescharacteristic
41C4×D8×C29C2211yescharacteristic
42C29×#405C2211yescharacteristic
43C29×#367C2211yescharacteristic
44C29×#367C2211yescharacteristic
45C29×#366C2211yescharacteristic
46C29×#366C2211yescharacteristic
47C29×C4⋊C16C2211yescharacteristic
48C29×C4⋊C16C2211yescharacteristic
49C29×C4⋊C16C2211yescharacteristic
50C29×C4⋊C16C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#358C2211yescharacteristic
54C29×#358C2211yescharacteristic
55C29×#358C2211yescharacteristic
56C29×#358C2211yescharacteristic
57C29×#357C2211yescharacteristic
58C29×#357C2211yescharacteristic
59C2×Q16×C29—21no—
60C2×Q16×C29C2311yescharacteristic
61C2×Q16×C29C2311yescharacteristic
62C2×Q16×C29C2311yescharacteristic
63C2×SD16×C29—21no—
64C2×D8×C29C2311yescharacteristic
65C2×M16×C29D411yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C29×C4⋊Q8—21no—
68C29×C4⋊Q8—21no—
69C29×#126—41no—
70C29×#126—41no—
71C29×#126—41no—
72C29×#125—21no—
73C29×#125—41no—
74C29×#125—41no—
75C29×#124—21no—
76C29×#124—41no—
77C29×#123—41no—
78C29×C22⋊Q8—21no—
79C29×C22⋊Q8—21no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—41no—
82C29×#121—21no—
83C4×Q8×C29—21no—
84C4×Q8×C29—21no—
85C4×Q8×C29—21no—
86C4×D4×C29—21no—
87C29×#117D411yescharacteristic
88C29×Q32—41no—
89C29×Q32—41no—
90C29×SD32—41no—
91C29×SD32—41no—
92C29×M32—41no—
93C2×C16×C29—41no—
94C2×C16×C29C2311yescharacteristic
95C2×C16×C29C2311yescharacteristic
96C2×C16×C29C2311yescharacteristic
97C2×C16×C29C2311yescharacteristic
98C29×#107—21no—
99C29×#107C2311yescharacteristic
100C29×#107C2311yescharacteristic
101C29×#107C2311yescharacteristic
102C29×#107C2311yescharacteristic
103C29×#106—21no—
104C29×#103—21no—
105C29×#103—21no—
106C29×#103—21no—
107C29×#103—21no—
108C29×#103—21no—
109C29×#103—21no—
110C29×#102—21no—
111C29×#102—21no—
112C29×#97D411yescharacteristic
113C29×#97D411yescharacteristic
114C4×C8×C29C2311yescharacteristic
115C4×C8×C29C2311yescharacteristic
116C2×Q8×C29—21no—
117C2×Q8×C29—21no—
118C2×Q8×C29—21no—
119C2×Q8×C29—41no—
120C2×D4×C29—21no—
121C2×D4×C29—41no—
122C22×C4×C29—41no—
123C22×C4×C29C2×D411yescharacteristic
124Q16×C29—21no—
125Q16×C29—21no—
126Q16×C29—21no—
127Q16×C29—21no—
128Q16×C29—21no—
129Q16×C29—21no—
130Q16×C29—42no—
131SD16×C29—42no—
132D8×C29—21no—
133D8×C29—21no—
134M16×C29—41no—
135C2×C8×C29—21no—
136C2×C8×C29—21no—
137C2×C8×C29C2×D411yescharacteristic
138C2×C8×C29C2×D411yescharacteristic
139C2×C8×C29C2×D411yescharacteristic
140C2×C8×C29C2411yescharacteristic
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29D811yescharacteristic
157C4⋊C4×C29D811yescharacteristic
158C22⋊C4×C29—41no—
159C22⋊C4×C29—41no—
160C22⋊C4×C29—41no—
161C22⋊C4×C29—41no—
162C22⋊C4×C29—41no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C22⋊C4×C29D811yescharacteristic
166C22⋊C4×C29D811yescharacteristic
167C42×C29—41no—
168C42×C29—41no—
169C42×C29—41no—
170C42×C29C2×D411yescharacteristic
171C42×C29C2×D411yescharacteristic
172C16×C29—21no—
173C16×C29—21no—
174C16×C29—21no—
175C16×C29—21no—
176#33824C2911yesmaximal, characteristic, direct product factor, Sylow
177C23×C29—41no—
178C23×C29C2×D811yescharacteristic
179Q8×C29—41no—
180Q8×C29—41no—
181Q8×C29—41no—
182Q8×C29—41no—
183Q8×C29—41no—
184Q8×C29—41no—
185Q8×C29—161no—
186D4×C29—41no—
187D4×C29—41no—
188D4×C29—161no—
189C2×C4×C29—21no—
190C2×C4×C29—21no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—41no—
194C2×C4×C29—41no—
195C2×C4×C29—41no—
196C2×C4×C29—41no—
197C2×C4×C29—41no—
198C2×C4×C29—161no—
199C2×C4×C29C2×D811yescharacteristic
200C2×C4×C29C2×D811yescharacteristic
201C2×C4×C29C2×D811yescharacteristic
202C2×C4×C29C2×D811yescharacteristic
203C2×C4×C29C2×D811yescharacteristic
204C2×C4×C29C22×D411yescharacteristic
205C8×C29—21no—
206C8×C29—21no—
207C8×C29—21no—
208C8×C29H(5,𝔽2)11yescharacteristic
209C8×C292−1+411yescharacteristic
210#3177C2×C2911yescharacteristic, complemented
211#3175C2×C2911yescharacteristic
212#2229C2×C2911yescharacteristic, complemented
213#2228C2×C2911yescharacteristic, complemented
214#2227C2×C2911yescharacteristic, complemented
215#2225C2×C2911yescharacteristic, complemented
216#2220C2×C2911yescharacteristic
217#2219C2×C2911yescharacteristic, complemented
218#2217C2×C2911yescharacteristic
219#2216C2×C2911yescharacteristic, complemented
220#2211C2×C2911yescharacteristic, complemented
221#2211C2×C2911yescharacteristic, complemented
222#2209C2×C2911yescharacteristic, complemented
223#2208C2×C2911yescharacteristic, complemented
224#2151C2×C2911yescharacteristic, complemented
225C22×C29—21no—
226C22×C29—21no—
227C22×C29—21no—
228C22×C29—81no—
229C22×C29—81no—
230C22×C29—81no—
231C22×C29C22×D811yescharacteristic
232C4×C29—21no—
233C4×C29—21no—
234C4×C29—21no—
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—81no—
238C4×C29—81no—
239C4×C29—81no—
240C4×C29—81no—
241C4×C29—81no—
242C4×C29—81no—
243C4×C29—81no—
244C4×C29#53711yescharacteristic
245C4×C29#57511yescharacteristic
246#542—21no—
247#541—21no—
248C2×Q32C22×C2911yescharacteristic
249C2×Q32C22×C2911yescharacteristic
250C2×SD32C22×C2911yescharacteristic
251C2×SD32C22×C2911yescharacteristic
252C2×M32C22×C2911yescharacteristic
253C22×C16C22×C2911yescharacteristic
254#500C22×C2911yescharacteristic
255#499C22×C2911yescharacteristic
256#495C22×C2911yescharacteristic
257#494C22×C2911yescharacteristic
258#491—21no—
259#489—21no—
260#470—21no—
261#468—21no—
262#467C22×C2911yescharacteristic
263#467C22×C2911yescharacteristic
264#467C22×C2911yescharacteristic
265#466C22×C2911yescharacteristic
266#441—21no—
267#440—21no—
268C4×Q16C22×C2911yescharacteristic
269C4×Q16C22×C2911yescharacteristic
270C4×Q16C22×C2911yescharacteristic
271C4×D8C22×C2911yescharacteristic
272#405C22×C2911yescharacteristic
273#367C22×C2911yescharacteristic
274#367C22×C2911yescharacteristic
275#366C22×C2911yescharacteristic
276#366C22×C2911yescharacteristic
277C4⋊C16C22×C2911yescharacteristic
278C4⋊C16C22×C2911yescharacteristic
279C4⋊C16C22×C2911yescharacteristic
280C4⋊C16C22×C2911yescharacteristic
281#358C22×C2911yescharacteristic
282#358C22×C2911yescharacteristic
283#358C22×C2911yescharacteristic
284#358C22×C2911yescharacteristic
285#358C22×C2911yescharacteristic
286#358C22×C2911yescharacteristic
287#357C22×C2911yescharacteristic
288#357C22×C2911yescharacteristic
289C2×C29—41no—
290C2×C29—161no—
291C2×C29#324511yescharacteristic
292C2×C29#341611yescharacteristic
293C2×C29#341711yescharacteristic
294C2×Q16—21no—
295C2×Q16C23×C2911yescharacteristic
296C2×Q16C23×C2911yescharacteristic
297C2×Q16C23×C2911yescharacteristic
298C2×SD16—21no—
299C2×D8C23×C2911yescharacteristic
300C2×M16D4×C2911yescharacteristic
301C22×C8C23×C2911yescharacteristic
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304#126—41no—
305#126—41no—
306#126—41no—
307#125—21no—
308#125—41no—
309#125—41no—
310#124—21no—
311#124—41no—
312#123—41no—
313C22⋊Q8—21no—
314C22⋊Q8—21no—
315C22⋊Q8—21no—
316C22⋊Q8—41no—
317#121—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×D4—21no—
322#117D4×C2911yescharacteristic
323Q32—41no—
324Q32—41no—
325SD32—41no—
326SD32—41no—
327M32—41no—
328C2×C16—41no—
329C2×C16C23×C2911yescharacteristic
330C2×C16C23×C2911yescharacteristic
331C2×C16C23×C2911yescharacteristic
332C2×C16C23×C2911yescharacteristic
333#107—21no—
334#107C23×C2911yescharacteristic
335#107C23×C2911yescharacteristic
336#107C23×C2911yescharacteristic
337#107C23×C2911yescharacteristic
338#106—21no—
339#103—21no—
340#103—21no—
341#103—21no—
342#103—21no—
343#103—21no—
344#103—21no—
345#102—21no—
346#102—21no—
347#97D4×C2911yescharacteristic
348#97D4×C2911yescharacteristic
349C4×C8C23×C2911yescharacteristic
350C4×C8C23×C2911yescharacteristic
351C29#3382411yescharacteristic, direct product factor, Sylow
352C2×Q8—21no—
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—41no—
356C2×D4—21no—
357C2×D4—41no—
358C22×C4—41no—
359C22×C4C2×D4×C2911yescharacteristic
360Q16—21no—
361Q16—21no—
362Q16—21no—
363Q16—21no—
364Q16—21no—
365Q16—21no—
366Q16—42no—
367SD16—42no—
368D8—21no—
369D8—21no—
370M16—41no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8C2×D4×C2911yescharacteristic
374C2×C8C2×D4×C2911yescharacteristic
375C2×C8C2×D4×C2911yescharacteristic
376C2×C8C24×C2911yescharacteristic
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4D8×C2911yescharacteristic
393C4⋊C4D8×C2911yescharacteristic
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4D8×C2911yescharacteristic
402C22⋊C4D8×C2911yescharacteristic
403C42—41no—
404C42—41no—
405C42—41no—
406C42C2×D4×C2911yescharacteristic
407C42C2×D4×C2911yescharacteristic
408C16—21no—
409C16—21no—
410C16—21no—
411C16—21no—
412C23—41no—
413C23C2×D8×C2911yescharacteristic
414Q8—41no—
415Q8—41no—
416Q8—41no—
417Q8—41no—
418Q8—41no—
419Q8—41no—
420Q8—161no—
421D4—41no—
422D4—41no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—161no—
434C2×C4C2×D8×C2911yescharacteristic
435C2×C4C2×D8×C2911yescharacteristic
436C2×C4C2×D8×C2911yescharacteristic
437C2×C4C2×D8×C2911yescharacteristic
438C2×C4C2×D8×C2911yescharacteristic
439C2×C4C22×D4×C2911yescharacteristic
440C8—21no—
441C8—21no—
442C8—21no—
443C8C29×H(5,𝔽2)11yescharacteristic
444C8C29×2−1+411yescharacteristic
445C22—21no—
446C22—21no—
447C22—21no—
448C22—81no—
449C22—81no—
450C22—81no—
451C22C22×D8×C2911yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—81no—
458C4—81no—
459C4—81no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4C29×#53711yescharacteristic
465C4C29×#57511yescharacteristic
466C2—41no—
467C2—161no—
468C2C29×#324511yescharacteristic
469C2C29×#341611yescharacteristic
470C2C29×#341711yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#466C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C29×#117 ◁ C29×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3177C2semidirect
3. C29×#2229C2semidirect
4. C29×#2228C2semidirect
5. C29×#2227C2semidirect
6. C29×#2225C2semidirect
8. C29×#2219C2semidirect
10. C29×#2216C2semidirect
11. C29×#2211C2semidirect
12. C29×#2211C2semidirect
13. C29×#2209C2semidirect
14. C29×#2208C2semidirect
15. C29×#2151C2semidirect
176. #33824C29direct (N × H)
210. #3177C2×C29semidirect
212. #2229C2×C29semidirect
213. #2228C2×C29semidirect
214. #2227C2×C29semidirect
215. #2225C2×C29semidirect
217. #2219C2×C29semidirect
219. #2216C2×C29semidirect
220. #2211C2×C29semidirect
221. #2211C2×C29semidirect
222. #2209C2×C29semidirect
223. #2208C2×C29semidirect
224. #2151C2×C29semidirect
351. C29#33824direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31772
C29×#31752
C29×#22292
C29×#22282
C29×#22272
C29×#22252
C29×#22202
C29×#22192
C29×#22172
C29×#22162
C29×#22112
C29×#22092
C29×#22082
C29×#21512
#3382429