Finite Group Databasebeta

← C29×#33904 #20328804

Subgroups — C29×#33904 #20328804

Order 7424.

482 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3339C211yesmaximal, characteristic
2C29×#3336C211yesmaximal, characteristic, complemented
3C29×#2253C211yesmaximal, characteristic, complemented
4C29×#2237C211yesmaximal, characteristic, complemented
5C29×#2236C211yesmaximal, characteristic, complemented
6C29×#2234C211yesmaximal, characteristic, complemented
7C29×#2232C211yesmaximal, characteristic, complemented
8C29×#2229C211yesmaximal, characteristic, complemented
9C29×#2228C211yesmaximal, characteristic, complemented
10C29×#2217C211yesmaximal, characteristic, complemented
11C29×#2217C211yesmaximal, characteristic, complemented
12C4×C29×SD32C211yesmaximal, characteristic, complemented
13D4×C16×C29C211yesmaximal, characteristic, complemented
14C29×#2158C211yesmaximal, characteristic, complemented
15C2×C29×#367C211yesmaximal, characteristic, complemented
16C29×#553—21no—
17C29×#552—21no—
18C2×C29×SD32C2211yescharacteristic
19C22×C16×C29C2211yescharacteristic
20C22×C16×C29C2211yescharacteristic
21C29×#499C2211yescharacteristic
22C29×#499C2211yescharacteristic
23C29×#485—21no—
24C29×#483—21no—
25C29×#482—21no—
26C29×#481—21no—
27C29×#479—21no—
28C29×#478—21no—
29C29×#467C2211yescharacteristic
30C29×#467C2211yescharacteristic
31C29×#466C2211yescharacteristic
32C29×#466C2211yescharacteristic
33C4×Q16×C29C2211yescharacteristic
34C4×D8×C29C2211yescharacteristic
35C8×D4×C29C2211yescharacteristic
36C29×#427C2211yescharacteristic
37C29×#427C2211yescharacteristic
38C2×C29×#107C2211yescharacteristic
39C2×C29×#107C2211yescharacteristic
40C29×#367C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#367C2211yescharacteristic
44C29×#367C2211yescharacteristic
45C29×#366C2211yescharacteristic
46C29×#366C2211yescharacteristic
47C29×#366C2211yescharacteristic
48C29×#366C2211yescharacteristic
49C29×C4⋊C16C2211yescharacteristic
50C29×#358C2211yescharacteristic
51C29×#358C2211yescharacteristic
52C29×#358C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×#357C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C4×C16×C29C2211yescharacteristic
59C2×Q16×C29C2311yescharacteristic
60C2×D8×C29C2311yescharacteristic
61C22×C8×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C29×#126—41no—
64C29×#126—41no—
65C29×#125—21no—
66C29×#125—21no—
67C29×#125—41no—
68C29×#123—41no—
69C29×#123—41no—
70C29×C22⋊Q8—21no—
71C29×C22⋊Q8—21no—
72C29×#121—21no—
73C29×#121—21no—
74C29×#121—41no—
75C4×Q8×C29—21no—
76C4×D4×C29—21no—
77C4×D4×C29—41no—
78C4×D4×C29D411yescharacteristic
79C29×#117—21no—
80C29×#117—21no—
81C29×#117—41no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C29×SD32—22no—
85C2×C16×C29—22no—
86C2×C16×C29—22no—
87C2×C16×C29C2311yescharacteristic
88C2×C16×C29C2311yescharacteristic
89C2×C16×C29C2311yescharacteristic
90C2×C16×C29C2311yescharacteristic
91C29×#107—21no—
92C29×#107—21no—
93C29×#107C2311yescharacteristic
94C29×#107C2311yescharacteristic
95C29×#107C2311yescharacteristic
96C29×#107C2311yescharacteristic
97C29×#107C2311yescharacteristic
98C29×#107C2311yescharacteristic
99C29×#106—21no—
100C29×#106—21no—
101C29×#106—21no—
102C29×#106—21no—
103C29×C4⋊C8D411yescharacteristic
104C29×#103—21no—
105C29×#103—21no—
106C29×#103—21no—
107C29×#102—21no—
108C29×#102—21no—
109C29×#102—21no—
110C29×C22⋊C8D411yescharacteristic
111C29×C22⋊C8D411yescharacteristic
112C4×C8×C29C2311yescharacteristic
113C2×Q8×C29—21no—
114C2×D4×C29—21no—
115C2×D4×C29—41no—
116C2×D4×C29—41no—
117C2×D4×C29D811yescharacteristic
118C22×C4×C29—41no—
119C22×C4×C29—41no—
120C22×C4×C29—41no—
121C22×C4×C29C2×D411yescharacteristic
122C22×C4×C29C2×D411yescharacteristic
123Q16×C29—21no—
124Q16×C29—21no—
125D8×C29—21no—
126D8×C29—21no—
127C2×C8×C29—21no—
128C2×C8×C29—21no—
129C2×C8×C29—21no—
130C2×C8×C29—21no—
131C2×C8×C29C2×D411yescharacteristic
132C2×C8×C29C2×D411yescharacteristic
133C2×C8×C29C2×D411yescharacteristic
134C2×C8×C29C2411yescharacteristic
135C4⋊C4×C29—21no—
136C4⋊C4×C29—21no—
137C4⋊C4×C29—21no—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—21no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—41no—
142C4⋊C4×C29—41no—
143C4⋊C4×C29—41no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29D811yescharacteristic
151C22⋊C4×C29—41no—
152C22⋊C4×C29—41no—
153C22⋊C4×C29—41no—
154C22⋊C4×C29—41no—
155C22⋊C4×C29—41no—
156C22⋊C4×C29—41no—
157C22⋊C4×C29—41no—
158C22⋊C4×C29D811yescharacteristic
159C22⋊C4×C29D811yescharacteristic
160C42×C29—41no—
161C42×C29—41no—
162C42×C29—41no—
163C42×C29C2×D411yescharacteristic
164C16×C29—21no—
165C16×C29—21no—
166C16×C29—21no—
167C16×C29#4112yes—
168#33904C2911yesmaximal, characteristic, direct product factor, Sylow
169C23×C29—41no—
170C23×C29C2×D811yescharacteristic
171C23×C29C2×D811yescharacteristic
172Q8×C29—41no—
173Q8×C29—41no—
174D4×C29—22no—
175D4×C29—41no—
176D4×C29—41no—
177D4×C29—82no—
178D4×C29—161no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—21no—
182C2×C4×C29—21no—
183C2×C4×C29—41no—
184C2×C4×C29—41no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—82no—
191C2×C4×C29—161no—
192C2×C4×C29—161no—
193C2×C4×C29C2×D811yescharacteristic
194C2×C4×C29C2×D811yescharacteristic
195C2×C4×C29C2×D811yescharacteristic
196C2×C4×C29C2×D811yescharacteristic
197C2×C4×C29C22×D411yescharacteristic
198C8×C29—21no—
199C8×C29—21no—
200C8×C29—21no—
201C8×C29C2×#4111yescharacteristic
202C8×C292−1+411yescharacteristic
203#3339C2×C2911yescharacteristic
204#3336C2×C2911yescharacteristic, complemented
205#2253C2×C2911yescharacteristic, complemented
206#2237C2×C2911yescharacteristic, complemented
207#2236C2×C2911yescharacteristic, complemented
208#2234C2×C2911yescharacteristic, complemented
209#2232C2×C2911yescharacteristic, complemented
210#2229C2×C2911yescharacteristic, complemented
211#2228C2×C2911yescharacteristic, complemented
212#2217C2×C2911yescharacteristic, complemented
213#2217C2×C2911yescharacteristic, complemented
214C4×SD32C2×C2911yescharacteristic, complemented
215D4×C16C2×C2911yescharacteristic, complemented
216#2158C2×C2911yescharacteristic, complemented
217C2×#367C2×C2911yescharacteristic, complemented
218C22×C29—21no—
219C22×C29—21no—
220C22×C29—21no—
221C22×C29—21no—
222C22×C29—21no—
223C22×C29—81no—
224C22×C29—81no—
225C22×C29—81no—
226C22×C29#50812yes—
227C22×C29C22×D811yescharacteristic
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—21no—
231C4×C29—21no—
232C4×C29—81no—
233C4×C29—81no—
234C4×C29—81no—
235C4×C29—81no—
236C4×C29—81no—
237C4×C29—81no—
238C4×C29—81no—
239C4×C29#54711yescharacteristic
240C4×C29#57811yescharacteristic
241#553—21no—
242#552—21no—
243C2×SD32C22×C2911yescharacteristic
244C22×C16C22×C2911yescharacteristic
245C22×C16C22×C2911yescharacteristic
246#499C22×C2911yescharacteristic
247#499C22×C2911yescharacteristic
248#485—21no—
249#483—21no—
250#482—21no—
251#481—21no—
252#479—21no—
253#478—21no—
254#467C22×C2911yescharacteristic
255#467C22×C2911yescharacteristic
256#466C22×C2911yescharacteristic
257#466C22×C2911yescharacteristic
258C4×Q16C22×C2911yescharacteristic
259C4×D8C22×C2911yescharacteristic
260C8×D4C22×C2911yescharacteristic
261#427C22×C2911yescharacteristic
262#427C22×C2911yescharacteristic
263C2×#107C22×C2911yescharacteristic
264C2×#107C22×C2911yescharacteristic
265#367C22×C2911yescharacteristic
266#367C22×C2911yescharacteristic
267#367C22×C2911yescharacteristic
268#367C22×C2911yescharacteristic
269#367C22×C2911yescharacteristic
270#366C22×C2911yescharacteristic
271#366C22×C2911yescharacteristic
272#366C22×C2911yescharacteristic
273#366C22×C2911yescharacteristic
274C4⋊C16C22×C2911yescharacteristic
275#358C22×C2911yescharacteristic
276#358C22×C2911yescharacteristic
277#358C22×C2911yescharacteristic
278#357C22×C2911yescharacteristic
279#357C22×C2911yescharacteristic
280#357C22×C2911yescharacteristic
281C22⋊C16C22×C2911yescharacteristic
282C22⋊C16C22×C2911yescharacteristic
283C4×C16C22×C2911yescharacteristic
284C2×C29—22no—
285C2×C29—41no—
286C2×C29—161no—
287C2×C29#333411yescharacteristic
288C2×C29C2×#50811yescharacteristic
289C2×C29#341611yescharacteristic
290C2×Q16C23×C2911yescharacteristic
291C2×D8C23×C2911yescharacteristic
292C22×C8C23×C2911yescharacteristic
293C22×C8C23×C2911yescharacteristic
294#126—41no—
295#126—41no—
296#125—21no—
297#125—21no—
298#125—41no—
299#123—41no—
300#123—41no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—21no—
304#121—21no—
305#121—41no—
306C4×Q8—21no—
307C4×D4—21no—
308C4×D4—41no—
309C4×D4D4×C2911yescharacteristic
310#117—21no—
311#117—21no—
312#117—41no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315SD32—22no—
316C2×C16—22no—
317C2×C16—22no—
318C2×C16C23×C2911yescharacteristic
319C2×C16C23×C2911yescharacteristic
320C2×C16C23×C2911yescharacteristic
321C2×C16C23×C2911yescharacteristic
322#107—21no—
323#107—21no—
324#107C23×C2911yescharacteristic
325#107C23×C2911yescharacteristic
326#107C23×C2911yescharacteristic
327#107C23×C2911yescharacteristic
328#107C23×C2911yescharacteristic
329#107C23×C2911yescharacteristic
330#106—21no—
331#106—21no—
332#106—21no—
333#106—21no—
334C4⋊C8D4×C2911yescharacteristic
335#103—21no—
336#103—21no—
337#103—21no—
338#102—21no—
339#102—21no—
340#102—21no—
341C22⋊C8D4×C2911yescharacteristic
342C22⋊C8D4×C2911yescharacteristic
343C4×C8C23×C2911yescharacteristic
344C29#3390411yescharacteristic, direct product factor, Sylow
345C2×Q8—21no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4D8×C2911yescharacteristic
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4C2×D4×C2911yescharacteristic
354C22×C4C2×D4×C2911yescharacteristic
355Q16—21no—
356Q16—21no—
357D8—21no—
358D8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8C2×D4×C2911yescharacteristic
364C2×C8C2×D4×C2911yescharacteristic
365C2×C8C2×D4×C2911yescharacteristic
366C2×C8C24×C2911yescharacteristic
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4D8×C2911yescharacteristic
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4D8×C2911yescharacteristic
391C22⋊C4D8×C2911yescharacteristic
392C42—41no—
393C42—41no—
394C42—41no—
395C42C2×D4×C2911yescharacteristic
396C16—21no—
397C16—21no—
398C16—21no—
399C16#41×C2912yes—
400C23—41no—
401C23C2×D8×C2911yescharacteristic
402C23C2×D8×C2911yescharacteristic
403Q8—41no—
404Q8—41no—
405D4—22no—
406D4—41no—
407D4—41no—
408D4—82no—
409D4—161no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—82no—
422C2×C4—161no—
423C2×C4—161no—
424C2×C4C2×D8×C2911yescharacteristic
425C2×C4C2×D8×C2911yescharacteristic
426C2×C4C2×D8×C2911yescharacteristic
427C2×C4C2×D8×C2911yescharacteristic
428C2×C4C22×D4×C2911yescharacteristic
429C8—21no—
430C8—21no—
431C8—21no—
432C8C2×#41×C2911yescharacteristic
433C8C29×2−1+411yescharacteristic
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22C29×#50812yes—
443C22C22×D8×C2911yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—81no—
451C4—81no—
452C4—81no—
453C4—81no—
454C4—81no—
455C4C29×#54711yescharacteristic
456C4C29×#57811yescharacteristic
457C2—22no—
458C2—41no—
459C2—161no—
460C2C29×#333411yescharacteristic
461C2C2×C29×#50811yescharacteristic
462C2C29×#341611yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#3339C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×D4×C29 ◁ C8×D4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3336C2semidirect
3. C29×#2253C2semidirect
4. C29×#2237C2semidirect
5. C29×#2236C2semidirect
6. C29×#2234C2semidirect
7. C29×#2232C2semidirect
8. C29×#2229C2semidirect
9. C29×#2228C2semidirect
10. C29×#2217C2semidirect
11. C29×#2217C2semidirect
12. C4×C29×SD32C2semidirect
13. D4×C16×C29C2semidirect
14. C29×#2158C2semidirect
15. C2×C29×#367C2semidirect
168. #33904C29direct (N × H)
204. #3336C2×C29semidirect
205. #2253C2×C29semidirect
206. #2237C2×C29semidirect
207. #2236C2×C29semidirect
208. #2234C2×C29semidirect
209. #2232C2×C29semidirect
210. #2229C2×C29semidirect
211. #2228C2×C29semidirect
212. #2217C2×C29semidirect
213. #2217C2×C29semidirect
214. C4×SD32C2×C29semidirect
215. D4×C16C2×C29semidirect
216. #2158C2×C29semidirect
217. C2×#367C2×C29semidirect
344. C29#33904direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#33392
C29×#33362
C29×#22532
C29×#22372
C29×#22362
C29×#22342
C29×#22322
C29×#22292
C29×#22282
C29×#22172
C4×C29×SD322
D4×C16×C292
C29×#21582
C2×C29×#3672
#3390429