Finite Group Databasebeta

← C29×#33912 #20328812

Subgroups — C29×#33912 #20328812

Order 7424.

516 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3339C211yesmaximal, characteristic, complemented
2C29×#3334C211yesmaximal, characteristic, complemented
3C29×#2255C211yesmaximal, characteristic, complemented
4C29×#2234C211yesmaximal, characteristic, complemented
5C29×#2233C211yesmaximal, characteristic, complemented
6C29×#2233C211yesmaximal, characteristic, complemented
7C29×#2232C211yesmaximal, characteristic, complemented
8C29×#2228C211yesmaximal, characteristic, complemented
9C29×#2226C211yesmaximal, characteristic, complemented
10C29×#2218C211yesmaximal, characteristic, complemented
11C29×#2215C211yesmaximal, characteristic, complemented
12C29×#2177C211yesmaximal, characteristic, complemented
13C29×#2168C211yesmaximal, characteristic, complemented
14C29×#2159C211yesmaximal, characteristic, complemented
15C2×C29×#367C211yesmaximal, characteristic, complemented
16C29×#553—21no—
17C29×#547—21no—
18C2×C29×D16C2211yescharacteristic
19C2×C29×M32C2211yescharacteristic
20C22×C16×C29C2211yescharacteristic
21C29×#500C2211yescharacteristic
22C29×#499C2211yescharacteristic
23C29×#482—21no—
24C29×#481—21no—
25C29×#480—21no—
26C29×#480—21no—
27C29×#478—21no—
28C29×#474—21no—
29C29×#466C2211yescharacteristic
30C29×#466C2211yescharacteristic
31C29×#466C2211yescharacteristic
32C29×#466C2211yescharacteristic
33C4×D8×C29C2211yescharacteristic
34C4×D8×C29C2211yescharacteristic
35C8×D4×C29C2211yescharacteristic
36C29×#427C2211yescharacteristic
37C2×C29×#107C2211yescharacteristic
38C2×C29×#107C2211yescharacteristic
39C2×C29×#107C2211yescharacteristic
40C29×#367C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#367C2211yescharacteristic
44C29×#367C2211yescharacteristic
45C29×#367C2211yescharacteristic
46C29×#366C2211yescharacteristic
47C29×#366C2211yescharacteristic
48C29×#366C2211yescharacteristic
49C29×C4⋊C16C2211yescharacteristic
50C29×#357C2211yescharacteristic
51C29×#357C2211yescharacteristic
52C29×#357C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×#357C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×C22⋊C16C2211yescharacteristic
58C29×#346C2211yescharacteristic
59C2×#41×C29—41no—
60C2×D8×C29C2311yescharacteristic
61C2×D8×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C29×C4⋊Q8—21no—
65C29×#126—41no—
66C29×#125—21no—
67C29×#123—41no—
68C29×#123—41no—
69C29×#123—41no—
70C29×C22⋊Q8—41no—
71C29×#121—21no—
72C29×#121—21no—
73C29×#121—21no—
74C29×#121—21no—
75C29×#121—41no—
76C4×D4×C29—21no—
77C4×D4×C29—21no—
78C4×D4×C29—41no—
79C4×D4×C29D411yescharacteristic
80C29×#117—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C29×D16—22no—
85C29×M32—22no—
86C2×C16×C29—22no—
87C2×C16×C29C2311yescharacteristic
88C2×C16×C29C2311yescharacteristic
89C2×C16×C29C2311yescharacteristic
90C2×C16×C29C2311yescharacteristic
91C29×#107—21no—
92C29×#107—21no—
93C29×#107—21no—
94C29×#107—21no—
95C29×#107C2311yescharacteristic
96C29×#107C2311yescharacteristic
97C29×#107C2311yescharacteristic
98C29×#107C2311yescharacteristic
99C29×#107C2311yescharacteristic
100C29×#107C2311yescharacteristic
101C29×#106—21no—
102C29×#106—21no—
103C29×C4⋊C8D411yescharacteristic
104C29×#102—21no—
105C29×#102—21no—
106C29×#102—21no—
107C29×#102—21no—
108C29×#102—21no—
109C29×#102—21no—
110C29×C22⋊C8D411yescharacteristic
111C29×C22⋊C8D411yescharacteristic
112C4×C8×C29C2311yescharacteristic
113#41×C29—84no—
114C2×Q8×C29—41no—
115C2×D4×C29—21no—
116C2×D4×C29—21no—
117C2×D4×C29—41no—
118C2×D4×C29—41no—
119C2×D4×C29—41no—
120C2×D4×C29—41no—
121C2×D4×C29D811yescharacteristic
122C22×C4×C29—41no—
123C22×C4×C29—41no—
124C22×C4×C29—41no—
125C22×C4×C29—41no—
126C22×C4×C29—41no—
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129D8×C29—21no—
130D8×C29—21no—
131D8×C29—21no—
132D8×C29—21no—
133C2×C8×C29—21no—
134C2×C8×C29—21no—
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—21no—
146C4⋊C4×C29—21no—
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×C29D811yescharacteristic
154C22⋊C4×C29—41no—
155C22⋊C4×C29—41no—
156C22⋊C4×C29—41no—
157C22⋊C4×C29—41no—
158C22⋊C4×C29—41no—
159C22⋊C4×C29—41no—
160C22⋊C4×C29—41no—
161C22⋊C4×C29D811yescharacteristic
162C22⋊C4×C29D811yescharacteristic
163C42×C29—41no—
164C42×C29C2×D411yescharacteristic
165C16×C29—21no—
166C16×C29—21no—
167C16×C29—21no—
168C16×C29#4112yescomplemented
169#33912C2911yesmaximal, characteristic, direct product factor, Sylow
170C23×C29—41no—
171C23×C29—41no—
172C23×C29C2×D811yescharacteristic
173C23×C29C2×D811yescharacteristic
174Q8×C29—82no—
175D4×C29—22no—
176D4×C29—41no—
177D4×C29—41no—
178D4×C29—41no—
179D4×C29—41no—
180D4×C29—82no—
181D4×C29—82no—
182D4×C29—82no—
183D4×C29—161no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—41no—
189C2×C4×C29—41no—
190C2×C4×C29—41no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—41no—
194C2×C4×C29—82no—
195C2×C4×C29—82no—
196C2×C4×C29—82no—
197C2×C4×C29—161no—
198C2×C4×C29—161no—
199C2×C4×C29C2×D811yescharacteristic
200C2×C4×C29C2×D811yescharacteristic
201C2×C4×C29C2×D811yescharacteristic
202C2×C4×C29C2×D811yescharacteristic
203C2×C4×C29C22×D411yescharacteristic
204C8×C29—21no—
205C8×C29—21no—
206C8×C29—21no—
207C8×C29C2×#4111yescharacteristic
208C8×C292−1+411yescharacteristic
209#3339C2×C2911yescharacteristic, complemented
210#3334C2×C2911yescharacteristic, complemented
211#2255C2×C2911yescharacteristic, complemented
212#2234C2×C2911yescharacteristic, complemented
213#2233C2×C2911yescharacteristic, complemented
214#2233C2×C2911yescharacteristic, complemented
215#2232C2×C2911yescharacteristic, complemented
216#2228C2×C2911yescharacteristic, complemented
217#2226C2×C2911yescharacteristic, complemented
218#2218C2×C2911yescharacteristic, complemented
219#2215C2×C2911yescharacteristic, complemented
220#2177C2×C2911yescharacteristic, complemented
221#2168C2×C2911yescharacteristic, complemented
222#2159C2×C2911yescharacteristic, complemented
223C2×#367C2×C2911yescharacteristic, complemented
224C22×C29—21no—
225C22×C29—21no—
226C22×C29—21no—
227C22×C29—21no—
228C22×C29—21no—
229C22×C29—81no—
230C22×C29—81no—
231C22×C29—81no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29—81no—
235C22×C29#50912yes—
236C22×C29C22×D811yescharacteristic
237C4×C29—21no—
238C4×C29—21no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—81no—
242C4×C29—81no—
243C4×C29—81no—
244C4×C29—81no—
245C4×C29—81no—
246C4×C29—81no—
247C4×C29#54711yescharacteristic
248C4×C29#57811yescharacteristic
249#553—21no—
250#547—21no—
251C2×D16C22×C2911yescharacteristic
252C2×M32C22×C2911yescharacteristic
253C22×C16C22×C2911yescharacteristic
254#500C22×C2911yescharacteristic
255#499C22×C2911yescharacteristic
256#482—21no—
257#481—21no—
258#480—21no—
259#480—21no—
260#478—21no—
261#474—21no—
262#466C22×C2911yescharacteristic
263#466C22×C2911yescharacteristic
264#466C22×C2911yescharacteristic
265#466C22×C2911yescharacteristic
266C4×D8C22×C2911yescharacteristic
267C4×D8C22×C2911yescharacteristic
268C8×D4C22×C2911yescharacteristic
269#427C22×C2911yescharacteristic
270C2×#107C22×C2911yescharacteristic
271C2×#107C22×C2911yescharacteristic
272C2×#107C22×C2911yescharacteristic
273#367C22×C2911yescharacteristic
274#367C22×C2911yescharacteristic
275#367C22×C2911yescharacteristic
276#367C22×C2911yescharacteristic
277#367C22×C2911yescharacteristic
278#367C22×C2911yescharacteristic
279#366C22×C2911yescharacteristic
280#366C22×C2911yescharacteristic
281#366C22×C2911yescharacteristic
282C4⋊C16C22×C2911yescharacteristic
283#357C22×C2911yescharacteristic
284#357C22×C2911yescharacteristic
285#357C22×C2911yescharacteristic
286#357C22×C2911yescharacteristic
287#357C22×C2911yescharacteristic
288#357C22×C2911yescharacteristic
289C22⋊C16C22×C2911yescharacteristic
290C22⋊C16C22×C2911yescharacteristic
291#346C22×C2911yescharacteristic
292C2×C29—22no—
293C2×C29—41no—
294C2×C29—161no—
295C2×C29—161no—
296C2×C29#333411yescharacteristic
297C2×C29C2×#50911yescharacteristic
298C2×C29#341611yescharacteristic
299C2×#41—41no—
300C2×D8C23×C2911yescharacteristic
301C2×D8C23×C2911yescharacteristic
302C22×C8C23×C2911yescharacteristic
303C22×C8C23×C2911yescharacteristic
304C4⋊Q8—21no—
305#126—41no—
306#125—21no—
307#123—41no—
308#123—41no—
309#123—41no—
310C22⋊Q8—41no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—41no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—41no—
319C4×D4D4×C2911yescharacteristic
320#117—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324D16—22no—
325M32—22no—
326C2×C16—22no—
327C2×C16C23×C2911yescharacteristic
328C2×C16C23×C2911yescharacteristic
329C2×C16C23×C2911yescharacteristic
330C2×C16C23×C2911yescharacteristic
331#107—21no—
332#107—21no—
333#107—21no—
334#107—21no—
335#107C23×C2911yescharacteristic
336#107C23×C2911yescharacteristic
337#107C23×C2911yescharacteristic
338#107C23×C2911yescharacteristic
339#107C23×C2911yescharacteristic
340#107C23×C2911yescharacteristic
341#106—21no—
342#106—21no—
343C4⋊C8D4×C2911yescharacteristic
344#102—21no—
345#102—21no—
346#102—21no—
347#102—21no—
348#102—21no—
349#102—21no—
350C22⋊C8D4×C2911yescharacteristic
351C22⋊C8D4×C2911yescharacteristic
352C4×C8C23×C2911yescharacteristic
353C29#3391211yescharacteristic, direct product factor, Sylow
354#41—84no—
355C2×Q8—41no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4D8×C2911yescharacteristic
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4C2×D4×C2911yescharacteristic
369C22×C4C2×D4×C2911yescharacteristic
370D8—21no—
371D8—21no—
372D8—21no—
373D8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8C2×D4×C2911yescharacteristic
379C2×C8C2×D4×C2911yescharacteristic
380C2×C8C2×D4×C2911yescharacteristic
381C2×C8C24×C2911yescharacteristic
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4D8×C2911yescharacteristic
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4D8×C2911yescharacteristic
403C22⋊C4D8×C2911yescharacteristic
404C42—41no—
405C42C2×D4×C2911yescharacteristic
406C16—21no—
407C16—21no—
408C16—21no—
409C16#41×C2912yescomplemented
410C23—41no—
411C23—41no—
412C23C2×D8×C2911yescharacteristic
413C23C2×D8×C2911yescharacteristic
414Q8—82no—
415D4—22no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—82no—
421D4—82no—
422D4—82no—
423D4—161no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—82no—
436C2×C4—82no—
437C2×C4—161no—
438C2×C4—161no—
439C2×C4C2×D8×C2911yescharacteristic
440C2×C4C2×D8×C2911yescharacteristic
441C2×C4C2×D8×C2911yescharacteristic
442C2×C4C2×D8×C2911yescharacteristic
443C2×C4C22×D4×C2911yescharacteristic
444C8—21no—
445C8—21no—
446C8—21no—
447C8C2×#41×C2911yescharacteristic
448C8C29×2−1+411yescharacteristic
449C22—21no—
450C22—21no—
451C22—21no—
452C22—21no—
453C22—21no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22C29×#50912yes—
461C22C22×D8×C2911yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4C29×#54711yescharacteristic
473C4C29×#57811yescharacteristic
474C2—22no—
475C2—41no—
476C2—161no—
477C2—161no—
478C2C29×#333411yescharacteristic
479C2C2×C29×#50911yescharacteristic
480C2C29×#341611yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
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
1. C29×#3339C2semidirect
2. C29×#3334C2semidirect
3. C29×#2255C2semidirect
4. C29×#2234C2semidirect
5. C29×#2233C2semidirect
6. C29×#2233C2semidirect
7. C29×#2232C2semidirect
8. C29×#2228C2semidirect
9. C29×#2226C2semidirect
10. C29×#2218C2semidirect
11. C29×#2215C2semidirect
12. C29×#2177C2semidirect
13. C29×#2168C2semidirect
14. C29×#2159C2semidirect
15. C2×C29×#367C2semidirect
168. C16×C29#41semidirect
169. #33912C29direct (N × H)
209. #3339C2×C29semidirect
210. #3334C2×C29semidirect
211. #2255C2×C29semidirect
212. #2234C2×C29semidirect
213. #2233C2×C29semidirect
214. #2233C2×C29semidirect
215. #2232C2×C29semidirect
216. #2228C2×C29semidirect
217. #2226C2×C29semidirect
218. #2218C2×C29semidirect
219. #2215C2×C29semidirect
220. #2177C2×C29semidirect
221. #2168C2×C29semidirect
222. #2159C2×C29semidirect
223. C2×#367C2×C29semidirect
353. C29#33912direct (N × H)
409. C16#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#33392
C29×#33342
C29×#22552
C29×#22342
C29×#22332
C29×#22322
C29×#22282
C29×#22262
C29×#22182
C29×#22152
C29×#21772
C29×#21682
C29×#21592
C2×C29×#3672
#3391229