Finite Group Databasebeta

← C29×#33679 #20328579

Subgroups — C29×#33679 #20328579

Order 7424.

558 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3176C211yesmaximal, characteristic, complemented
2C29×#2951C211yesmaximal, characteristic, complemented
3C29×#2233C211yesmaximal, characteristic, complemented
4C29×#2232C211yesmaximal, characteristic, complemented
5C29×#2229C211yesmaximal, characteristic, complemented
6C29×#2228C211yesmaximal, characteristic, complemented
7C29×#2207C211yesmaximal, characteristic, complemented
8C29×#2206C211yesmaximal, characteristic, complemented
9C29×#2186C211yesmaximal, characteristic, complemented
10C29×#2186C211yesmaximal, characteristic, complemented
11C29×#2177C211yesmaximal, characteristic, complemented
12C29×#2175C211yesmaximal, characteristic, complemented
13C4×C29×SD32C211yesmaximal, characteristic, complemented
14C4×C29×D16C211yesmaximal, characteristic, complemented
15C29×#2164C211yesmaximal, characteristic, complemented
16C2×C29×#135C2211yescharacteristic
17C29×#540—21no—
18C29×#520—21no—
19C2×C29×SD32C2211yescharacteristic
20C2×C29×SD32C2211yescharacteristic
21C2×C29×D16C2211yescharacteristic
22C2×C29×D16C2211yescharacteristic
23C29×#499C2211yescharacteristic
24C29×#493C2211yescharacteristic
25C29×#490—21no—
26C29×#469—21no—
27C29×#466C2211yescharacteristic
28C29×#466C2211yescharacteristic
29C29×#442—21no—
30C29×#440—21no—
31C29×#440—21no—
32C4×Q16×C29C2211yescharacteristic
33C4×Q16×C29C2211yescharacteristic
34C4×D8×C29C2211yescharacteristic
35C4×D8×C29C2211yescharacteristic
36C4×D8×C29C2211yescharacteristic
37C4×D8×C29C2211yescharacteristic
38C2×C29×#107C2211yescharacteristic
39C29×#417—21no—
40C29×#405C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#366C2211yescharacteristic
44C29×#366C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×C4⋊C16C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#357C2211yescharacteristic
50C29×#357C2211yescharacteristic
51C29×#357C2211yescharacteristic
52C29×#357C2211yescharacteristic
53C29×#357C2211yescharacteristic
54C29×#357C2211yescharacteristic
55C29×C22⋊C16C2211yescharacteristic
56C29×C22⋊C16C2211yescharacteristic
57C29×#346C2211yescharacteristic
58C4×C16×C29C2211yescharacteristic
59C2×#41×C29—21no—
60C29×#135—22no—
61C29×#135—22no—
62C2×Q16×C29C2311yescharacteristic
63C2×SD16×C29—21no—
64C2×D8×C29—21no—
65C2×D8×C29C2311yescharacteristic
66C2×D8×C29C2311yescharacteristic
67C2×D8×C29C2311yescharacteristic
68C2×M16×C29D411yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C29×#127—21no—
71C29×#125—21no—
72C29×#123—41no—
73C29×#123—41no—
74C29×#121—21no—
75C29×#121—21no—
76C29×#121—41no—
77C29×#121—41no—
78C4×Q8×C29—21no—
79C4×Q8×C29—21no—
80C4×D4×C29—21no—
81C4×D4×C29—21no—
82C4×D4×C29—21no—
83C4×D4×C29—21no—
84C4×D4×C29—41no—
85C4×D4×C29—41no—
86C29×#117—41no—
87C29×#117D411yescharacteristic
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—41no—
90C29×SD32—22no—
91C29×SD32—22no—
92C29×D16—22no—
93C29×D16—22no—
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×#102—21no—
107C29×#102—21no—
108C29×#102—21no—
109C29×#102—21no—
110C29×#102—21no—
111C29×#102—21no—
112C29×#97D411yescharacteristic
113C29×#97D411yescharacteristic
114C4×C8×C29C2311yescharacteristic
115C4×C8×C29C2311yescharacteristic
116#41×C29—24no—
117#41×C29—42no—
118C2×Q8×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—41no—
123C2×D4×C29—41no—
124C2×D4×C29—41no—
125C2×D4×C29—41no—
126C2×D4×C29—41no—
127C22×C4×C29—41no—
128C22×C4×C29—41no—
129C22×C4×C29—41no—
130C22×C4×C29—41no—
131C22×C4×C29—41no—
132C22×C4×C29—41no—
133C22×C4×C29C2×D411yescharacteristic
134Q16×C29—21no—
135Q16×C29#4112yes—
136SD16×C29—24no—
137D8×C29—21no—
138D8×C29—21no—
139D8×C29—21no—
140D8×C29—21no—
141D8×C29—21no—
142D8×C29—42no—
143D8×C29#4112yes—
144M16×C29—41no—
145C2×C8×C29—21no—
146C2×C8×C29—21no—
147C2×C8×C29C2×D411yescharacteristic
148C2×C8×C29C2×D411yescharacteristic
149C2×C8×C29C2×D411yescharacteristic
150C2×C8×C29C2411yescharacteristic
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29—41no—
158C4⋊C4×C29—41no—
159C4⋊C4×C29—41no—
160C4⋊C4×C29D811yescharacteristic
161C4⋊C4×C29D811yescharacteristic
162C22⋊C4×C29—41no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C22⋊C4×C29—41no—
166C22⋊C4×C29—41no—
167C22⋊C4×C29—41no—
168C22⋊C4×C29D811yescharacteristic
169C22⋊C4×C29D811yescharacteristic
170C42×C29—41no—
171C42×C29—41no—
172C42×C29C2×D411yescharacteristic
173C42×C29C2×D411yescharacteristic
174C16×C29—21no—
175C16×C29—21no—
176C16×C29—21no—
177C16×C29—21no—
178#33679C2911yesmaximal, characteristic, direct product factor, Sylow
179C23×C29—41no—
180C23×C29—41no—
181C23×C29—41no—
182C23×C29C2×D811yescharacteristic
183Q8×C29—22no—
184Q8×C29—41no—
185D4×C29—22no—
186D4×C29—44no—
187D4×C29—41no—
188D4×C29—41no—
189D4×C29—41no—
190D4×C29—41no—
191D4×C29—41no—
192D4×C29—161no—
193D4×C29—161no—
194D4×C29—161no—
195D4×C29—161no—
196C2×C4×C29—21no—
197C2×C4×C29—21no—
198C2×C4×C29—44no—
199C2×C4×C29—41no—
200C2×C4×C29—41no—
201C2×C4×C29—41no—
202C2×C4×C29—41no—
203C2×C4×C29—41no—
204C2×C4×C29—161no—
205C2×C4×C29—161no—
206C2×C4×C29—161no—
207C2×C4×C29—161no—
208C2×C4×C29—161no—
209C2×C4×C29C2×D811yescharacteristic
210C2×C4×C29C2×D811yescharacteristic
211C2×C4×C29C2×D811yescharacteristic
212C2×C4×C29C2×D811yescharacteristic
213C2×C4×C29C2×D811yescharacteristic
214C2×C4×C29C22×D411yescharacteristic
215C8×C29—21no—
216C8×C29—21no—
217C8×C29—21no—
218C8×C29C2×#4111yescharacteristic
219C8×C29C2×#4111yescharacteristic
220#3176C2×C2911yescharacteristic, complemented
221#2951C2×C2911yescharacteristic, complemented
222#2233C2×C2911yescharacteristic, complemented
223#2232C2×C2911yescharacteristic, complemented
224#2229C2×C2911yescharacteristic, complemented
225#2228C2×C2911yescharacteristic, complemented
226#2207C2×C2911yescharacteristic, complemented
227#2206C2×C2911yescharacteristic, complemented
228#2186C2×C2911yescharacteristic, complemented
229#2186C2×C2911yescharacteristic, complemented
230#2177C2×C2911yescharacteristic, complemented
231#2175C2×C2911yescharacteristic, complemented
232C4×SD32C2×C2911yescharacteristic, complemented
233C4×D16C2×C2911yescharacteristic, complemented
234#2164C2×C2911yescharacteristic, complemented
235C22×C29—21no—
236C22×C29—21no—
237C22×C29—21no—
238C22×C29—42no—
239C22×C29—81no—
240C22×C29—81no—
241C22×C29—81no—
242C22×C29—81no—
243C22×C29—81no—
244C22×C29—81no—
245C22×C29—81no—
246C22×C29—81no—
247C22×C29C22×D811yescharacteristic
248C4×C29—21no—
249C4×C29—21no—
250C4×C29—21no—
251C4×C29—21no—
252C4×C29—21no—
253C4×C29—42no—
254C4×C29—81no—
255C4×C29—81no—
256C4×C29—81no—
257C4×C29—81no—
258C4×C29#52511yescharacteristic
259C4×C29#57511yescharacteristic
260C2×#135C22×C2911yescharacteristic
261#540—21no—
262#520—21no—
263C2×SD32C22×C2911yescharacteristic
264C2×SD32C22×C2911yescharacteristic
265C2×D16C22×C2911yescharacteristic
266C2×D16C22×C2911yescharacteristic
267#499C22×C2911yescharacteristic
268#493C22×C2911yescharacteristic
269#490—21no—
270#469—21no—
271#466C22×C2911yescharacteristic
272#466C22×C2911yescharacteristic
273#442—21no—
274#440—21no—
275#440—21no—
276C4×Q16C22×C2911yescharacteristic
277C4×Q16C22×C2911yescharacteristic
278C4×D8C22×C2911yescharacteristic
279C4×D8C22×C2911yescharacteristic
280C4×D8C22×C2911yescharacteristic
281C4×D8C22×C2911yescharacteristic
282C2×#107C22×C2911yescharacteristic
283#417—21no—
284#405C22×C2911yescharacteristic
285#367C22×C2911yescharacteristic
286#367C22×C2911yescharacteristic
287#366C22×C2911yescharacteristic
288#366C22×C2911yescharacteristic
289C4⋊C16C22×C2911yescharacteristic
290C4⋊C16C22×C2911yescharacteristic
291#358C22×C2911yescharacteristic
292#358C22×C2911yescharacteristic
293#357C22×C2911yescharacteristic
294#357C22×C2911yescharacteristic
295#357C22×C2911yescharacteristic
296#357C22×C2911yescharacteristic
297#357C22×C2911yescharacteristic
298#357C22×C2911yescharacteristic
299C22⋊C16C22×C2911yescharacteristic
300C22⋊C16C22×C2911yescharacteristic
301#346C22×C2911yescharacteristic
302C4×C16C22×C2911yescharacteristic
303C2×C29—41no—
304C2×C29—82no—
305C2×C29—161no—
306C2×C29—161no—
307C2×C29#310011yescharacteristic
308C2×C29#341511yescharacteristic
309C2×C29#341611yescharacteristic
310C2×#41—21no—
311#135—22no—
312#135—22no—
313C2×Q16C23×C2911yescharacteristic
314C2×SD16—21no—
315C2×D8—21no—
316C2×D8C23×C2911yescharacteristic
317C2×D8C23×C2911yescharacteristic
318C2×D8C23×C2911yescharacteristic
319C2×M16D4×C2911yescharacteristic
320C22×C8C23×C2911yescharacteristic
321#127—21no—
322#125—21no—
323#123—41no—
324#123—41no—
325#121—21no—
326#121—21no—
327#121—41no—
328#121—41no—
329C4×Q8—21no—
330C4×Q8—21no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—41no—
336C4×D4—41no—
337#117—41no—
338#117D4×C2911yescharacteristic
339C2×C4⋊C4—21no—
340C2×C4⋊C4—41no—
341SD32—22no—
342SD32—22no—
343D16—22no—
344D16—22no—
345C2×C16C23×C2911yescharacteristic
346C2×C16C23×C2911yescharacteristic
347C2×C16C23×C2911yescharacteristic
348C2×C16C23×C2911yescharacteristic
349#107—21no—
350#107C23×C2911yescharacteristic
351#107C23×C2911yescharacteristic
352#107C23×C2911yescharacteristic
353#107C23×C2911yescharacteristic
354#106—21no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359#102—21no—
360#102—21no—
361#102—21no—
362#102—21no—
363#97D4×C2911yescharacteristic
364#97D4×C2911yescharacteristic
365C4×C8C23×C2911yescharacteristic
366C4×C8C23×C2911yescharacteristic
367C29#3367911yescharacteristic, direct product factor, Sylow
368#41—24no—
369#41—42no—
370C2×Q8—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—21no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4C2×D4×C2911yescharacteristic
386Q16—21no—
387Q16#41×C2912yes—
388SD16—24no—
389D8—21no—
390D8—21no—
391D8—21no—
392D8—21no—
393D8—21no—
394D8—42no—
395D8#41×C2912yes—
396M16—41no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8C2×D4×C2911yescharacteristic
400C2×C8C2×D4×C2911yescharacteristic
401C2×C8C2×D4×C2911yescharacteristic
402C2×C8C24×C2911yescharacteristic
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4D8×C2911yescharacteristic
413C4⋊C4D8×C2911yescharacteristic
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4D8×C2911yescharacteristic
421C22⋊C4D8×C2911yescharacteristic
422C42—41no—
423C42—41no—
424C42C2×D4×C2911yescharacteristic
425C42C2×D4×C2911yescharacteristic
426C16—21no—
427C16—21no—
428C16—21no—
429C16—21no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23C2×D8×C2911yescharacteristic
434Q8—22no—
435Q8—41no—
436D4—22no—
437D4—44no—
438D4—41no—
439D4—41no—
440D4—41no—
441D4—41no—
442D4—41no—
443D4—161no—
444D4—161no—
445D4—161no—
446D4—161no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—44no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—161no—
456C2×C4—161no—
457C2×C4—161no—
458C2×C4—161no—
459C2×C4—161no—
460C2×C4C2×D8×C2911yescharacteristic
461C2×C4C2×D8×C2911yescharacteristic
462C2×C4C2×D8×C2911yescharacteristic
463C2×C4C2×D8×C2911yescharacteristic
464C2×C4C2×D8×C2911yescharacteristic
465C2×C4C22×D4×C2911yescharacteristic
466C8—21no—
467C8—21no—
468C8—21no—
469C8C2×#41×C2911yescharacteristic
470C8C2×#41×C2911yescharacteristic
471C22—21no—
472C22—21no—
473C22—21no—
474C22—42no—
475C22—81no—
476C22—81no—
477C22—81no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22C22×D8×C2911yescharacteristic
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—81no—
494C4C29×#52511yescharacteristic
495C4C29×#57511yescharacteristic
496C2—41no—
497C2—82no—
498C2—161no—
499C2—161no—
500C2C29×#310011yescharacteristic
501C2C29×#341511yescharacteristic
502C2C29×#341611yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
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×#3176C2semidirect
2. C29×#2951C2semidirect
3. C29×#2233C2semidirect
4. C29×#2232C2semidirect
5. C29×#2229C2semidirect
6. C29×#2228C2semidirect
7. C29×#2207C2semidirect
8. C29×#2206C2semidirect
9. C29×#2186C2semidirect
10. C29×#2186C2semidirect
11. C29×#2177C2semidirect
12. C29×#2175C2semidirect
13. C4×C29×SD32C2semidirect
14. C4×C29×D16C2semidirect
15. C29×#2164C2semidirect
178. #33679C29direct (N × H)
220. #3176C2×C29semidirect
221. #2951C2×C29semidirect
222. #2233C2×C29semidirect
223. #2232C2×C29semidirect
224. #2229C2×C29semidirect
225. #2228C2×C29semidirect
226. #2207C2×C29semidirect
227. #2206C2×C29semidirect
228. #2186C2×C29semidirect
229. #2186C2×C29semidirect
230. #2177C2×C29semidirect
231. #2175C2×C29semidirect
232. C4×SD32C2×C29semidirect
233. C4×D16C2×C29semidirect
234. #2164C2×C29semidirect
367. C29#33679direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31762
C29×#29512
C29×#22332
C29×#22322
C29×#22292
C29×#22282
C29×#22072
C29×#22062
C29×#21862
C29×#21772
C29×#21752
C4×C29×SD322
C4×C29×D162
C29×#21642
#3367929