Finite Group Databasebeta

← C29×#33685 #20328585

Subgroups — C29×#33685 #20328585

Order 7424.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3175C211yesmaximal, characteristic, complemented
2C29×#2951C211yesmaximal, characteristic, complemented
3C29×#2235C211yesmaximal, characteristic, complemented
4C29×#2233C211yesmaximal, characteristic, complemented
5C29×#2226C211yesmaximal, characteristic, complemented
6C29×#2225C211yesmaximal, characteristic, complemented
7C29×#2211C211yesmaximal, characteristic, complemented
8C29×#2210C211yesmaximal, characteristic, complemented
9C29×#2189C211yesmaximal, characteristic, complemented
10C29×#2186C211yesmaximal, characteristic
11C29×#2177C211yesmaximal, characteristic, complemented
12C29×#2176C211yesmaximal, characteristic, complemented
13C4×C29×SD32C211yesmaximal, characteristic, complemented
14C4×C29×SD32C211yesmaximal, characteristic, complemented
15C29×#2164C211yesmaximal, characteristic, complemented
16C2×C29×#135C2211yescharacteristic
17C29×#542—21no—
18C29×#520—21no—
19C2×C29×Q32C2211yescharacteristic
20C2×C29×SD32C2211yescharacteristic
21C2×C29×SD32C2211yescharacteristic
22C2×C29×D16C2211yescharacteristic
23C29×#500C2211yescharacteristic
24C29×#495C2211yescharacteristic
25C29×#489—21no—
26C29×#468—21no—
27C29×#467C2211yescharacteristic
28C29×#466C2211yescharacteristic
29C29×#440—21no—
30C29×#440—21no—
31C29×#440—21no—
32C4×Q16×C29C2211yescharacteristic
33C4×Q16×C29C2211yescharacteristic
34C4×Q16×C29C2211yescharacteristic
35C4×D8×C29C2211yescharacteristic
36C4×D8×C29C2211yescharacteristic
37C4×D8×C29C2211yescharacteristic
38C2×C29×#107C2211yescharacteristic
39C29×#417—21no—
40C29×#405C2211yescharacteristic
41C29×#367C2211yescharacteristic
42C29×#367C2211yescharacteristic
43C29×#367C2211yescharacteristic
44C29×#367C2211yescharacteristic
45C29×C4⋊C16C2211yescharacteristic
46C29×C4⋊C16C2211yescharacteristic
47C29×#358C2211yescharacteristic
48C29×#358C2211yescharacteristic
49C29×#358C2211yescharacteristic
50C29×#358C2211yescharacteristic
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×Q16×C29C2311yescharacteristic
64C2×SD16×C29—21no—
65C2×SD16×C29—21no—
66C2×D8×C29C2311yescharacteristic
67C2×D8×C29C2311yescharacteristic
68C2×M16×C29D411yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C29×C4⋊Q8—21no—
71C29×#126—41no—
72C29×#124—21no—
73C29×#124—41no—
74C29×#123—41no—
75C29×C22⋊Q8—21no—
76C29×C22⋊Q8—41no—
77C29×#121—21no—
78C4×Q8×C29—21no—
79C4×Q8×C29—21no—
80C4×Q8×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×Q32—22no—
91C29×SD32—22no—
92C29×SD32—22no—
93C29×D16—22no—
94C2×C16×C29C2311yescharacteristic
95C2×C16×C29C2311yescharacteristic
96C2×C16×C29C2311yescharacteristic
97C2×C16×C29C2311yescharacteristic
98C29×#107—21no—
99C29×#107—21no—
100C29×#107C2311yescharacteristic
101C29×#107C2311yescharacteristic
102C29×#107C2311yescharacteristic
103C29×#107C2311yescharacteristic
104C29×#103—21no—
105C29×#103—21no—
106C29×#103—21no—
107C29×#103—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×Q8×C29—21no—
120C2×Q8×C29—41no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—41no—
124C2×D4×C29—41no—
125C22×C4×C29—41no—
126C22×C4×C29—41no—
127C22×C4×C29—41no—
128C22×C4×C29—41no—
129C22×C4×C29—41no—
130C22×C4×C29C2×D411yescharacteristic
131Q16×C29—21no—
132Q16×C29—21no—
133Q16×C29—21no—
134Q16×C29#4112yes—
135SD16×C29—24no—
136SD16×C29—42no—
137D8×C29—21no—
138D8×C29—21no—
139D8×C29—21no—
140D8×C29#4112yes—
141M16×C29—41no—
142C2×C8×C29—21no—
143C2×C8×C29—21no—
144C2×C8×C29C2×D411yescharacteristic
145C2×C8×C29C2×D411yescharacteristic
146C2×C8×C29C2×D411yescharacteristic
147C2×C8×C29C2411yescharacteristic
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29—41no—
154C4⋊C4×C29—41no—
155C4⋊C4×C29—41no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29—41no—
158C4⋊C4×C29D811yescharacteristic
159C4⋊C4×C29D811yescharacteristic
160C22⋊C4×C29—41no—
161C22⋊C4×C29—41no—
162C22⋊C4×C29—41no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C22⋊C4×C29—41no—
166C22⋊C4×C29—41no—
167C22⋊C4×C29D811yescharacteristic
168C22⋊C4×C29D811yescharacteristic
169C42×C29—41no—
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#33685C2911yesmaximal, characteristic, direct product factor, Sylow
179C23×C29—41no—
180C23×C29—41no—
181C23×C29C2×D811yescharacteristic
182Q8×C29—22no—
183Q8×C29—41no—
184Q8×C29—41no—
185Q8×C29—41no—
186Q8×C29—161no—
187D4×C29—22no—
188D4×C29—44no—
189D4×C29—41no—
190D4×C29—41no—
191D4×C29—41no—
192D4×C29—161no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—44no—
196C2×C4×C29—41no—
197C2×C4×C29—41no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—41no—
201C2×C4×C29—41no—
202C2×C4×C29—161no—
203C2×C4×C29—161no—
204C2×C4×C29—161no—
205C2×C4×C29—161no—
206C2×C4×C29C2×D811yescharacteristic
207C2×C4×C29C2×D811yescharacteristic
208C2×C4×C29C2×D811yescharacteristic
209C2×C4×C29C2×D811yescharacteristic
210C2×C4×C29C2×D811yescharacteristic
211C2×C4×C29C22×D411yescharacteristic
212C8×C29—21no—
213C8×C29—21no—
214C8×C29—21no—
215C8×C29C2×#4111yescharacteristic
216C8×C29C2×#4111yescharacteristic
217#3175C2×C2911yescharacteristic, complemented
218#2951C2×C2911yescharacteristic, complemented
219#2235C2×C2911yescharacteristic, complemented
220#2233C2×C2911yescharacteristic, complemented
221#2226C2×C2911yescharacteristic, complemented
222#2225C2×C2911yescharacteristic, complemented
223#2211C2×C2911yescharacteristic, complemented
224#2210C2×C2911yescharacteristic, complemented
225#2189C2×C2911yescharacteristic, complemented
226#2186C2×C2911yescharacteristic
227#2177C2×C2911yescharacteristic, complemented
228#2176C2×C2911yescharacteristic, complemented
229C4×SD32C2×C2911yescharacteristic, complemented
230C4×SD32C2×C2911yescharacteristic, complemented
231#2164C2×C2911yescharacteristic, complemented
232C22×C29—21no—
233C22×C29—21no—
234C22×C29—21no—
235C22×C29—42no—
236C22×C29—81no—
237C22×C29—81no—
238C22×C29—81no—
239C22×C29—81no—
240C22×C29—81no—
241C22×C29C22×D811yescharacteristic
242C4×C29—21no—
243C4×C29—21no—
244C4×C29—21no—
245C4×C29—21no—
246C4×C29—21no—
247C4×C29—42no—
248C4×C29—81no—
249C4×C29—81no—
250C4×C29—81no—
251C4×C29—81no—
252C4×C29—81no—
253C4×C29#52511yescharacteristic
254C4×C29#57511yescharacteristic
255C2×#135C22×C2911yescharacteristic
256#542—21no—
257#520—21no—
258C2×Q32C22×C2911yescharacteristic
259C2×SD32C22×C2911yescharacteristic
260C2×SD32C22×C2911yescharacteristic
261C2×D16C22×C2911yescharacteristic
262#500C22×C2911yescharacteristic
263#495C22×C2911yescharacteristic
264#489—21no—
265#468—21no—
266#467C22×C2911yescharacteristic
267#466C22×C2911yescharacteristic
268#440—21no—
269#440—21no—
270#440—21no—
271C4×Q16C22×C2911yescharacteristic
272C4×Q16C22×C2911yescharacteristic
273C4×Q16C22×C2911yescharacteristic
274C4×D8C22×C2911yescharacteristic
275C4×D8C22×C2911yescharacteristic
276C4×D8C22×C2911yescharacteristic
277C2×#107C22×C2911yescharacteristic
278#417—21no—
279#405C22×C2911yescharacteristic
280#367C22×C2911yescharacteristic
281#367C22×C2911yescharacteristic
282#367C22×C2911yescharacteristic
283#367C22×C2911yescharacteristic
284C4⋊C16C22×C2911yescharacteristic
285C4⋊C16C22×C2911yescharacteristic
286#358C22×C2911yescharacteristic
287#358C22×C2911yescharacteristic
288#358C22×C2911yescharacteristic
289#358C22×C2911yescharacteristic
290#357C22×C2911yescharacteristic
291#357C22×C2911yescharacteristic
292#357C22×C2911yescharacteristic
293#357C22×C2911yescharacteristic
294C22⋊C16C22×C2911yescharacteristic
295C22⋊C16C22×C2911yescharacteristic
296#346C22×C2911yescharacteristic
297C4×C16C22×C2911yescharacteristic
298C2×C29—41no—
299C2×C29—82no—
300C2×C29—161no—
301C2×C29#310011yescharacteristic
302C2×C29#341611yescharacteristic
303C2×C29#341611yescharacteristic
304C2×#41—21no—
305#135—22no—
306#135—22no—
307C2×Q16C23×C2911yescharacteristic
308C2×Q16C23×C2911yescharacteristic
309C2×SD16—21no—
310C2×SD16—21no—
311C2×D8C23×C2911yescharacteristic
312C2×D8C23×C2911yescharacteristic
313C2×M16D4×C2911yescharacteristic
314C22×C8C23×C2911yescharacteristic
315C4⋊Q8—21no—
316#126—41no—
317#124—21no—
318#124—41no—
319#123—41no—
320C22⋊Q8—21no—
321C22⋊Q8—41no—
322#121—21no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×D4—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—41no—
330C4×D4—41no—
331#117—41no—
332#117D4×C2911yescharacteristic
333C2×C4⋊C4—21no—
334C2×C4⋊C4—41no—
335Q32—22no—
336SD32—22no—
337SD32—22no—
338D16—22no—
339C2×C16C23×C2911yescharacteristic
340C2×C16C23×C2911yescharacteristic
341C2×C16C23×C2911yescharacteristic
342C2×C16C23×C2911yescharacteristic
343#107—21no—
344#107—21no—
345#107C23×C2911yescharacteristic
346#107C23×C2911yescharacteristic
347#107C23×C2911yescharacteristic
348#107C23×C2911yescharacteristic
349#103—21no—
350#103—21no—
351#103—21no—
352#103—21no—
353#102—21no—
354#102—21no—
355#102—21no—
356#102—21no—
357#97D4×C2911yescharacteristic
358#97D4×C2911yescharacteristic
359C4×C8C23×C2911yescharacteristic
360C4×C8C23×C2911yescharacteristic
361C29#3368511yescharacteristic, direct product factor, Sylow
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—41no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—41no—
370C2×D4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4C2×D4×C2911yescharacteristic
377Q16—21no—
378Q16—21no—
379Q16—21no—
380Q16#41×C2912yes—
381SD16—24no—
382SD16—42no—
383D8—21no—
384D8—21no—
385D8—21no—
386D8#41×C2912yes—
387M16—41no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×D4×C2911yescharacteristic
391C2×C8C2×D4×C2911yescharacteristic
392C2×C8C2×D4×C2911yescharacteristic
393C2×C8C24×C2911yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4D8×C2911yescharacteristic
405C4⋊C4D8×C2911yescharacteristic
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4D8×C2911yescharacteristic
414C22⋊C4D8×C2911yescharacteristic
415C42—41no—
416C42—41no—
417C42—41no—
418C42C2×D4×C2911yescharacteristic
419C42C2×D4×C2911yescharacteristic
420C16—21no—
421C16—21no—
422C16—21no—
423C16—21no—
424C23—41no—
425C23—41no—
426C23C2×D8×C2911yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431Q8—161no—
432D4—22no—
433D4—44no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—161no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—44no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—161no—
448C2×C4—161no—
449C2×C4—161no—
450C2×C4—161no—
451C2×C4C2×D8×C2911yescharacteristic
452C2×C4C2×D8×C2911yescharacteristic
453C2×C4C2×D8×C2911yescharacteristic
454C2×C4C2×D8×C2911yescharacteristic
455C2×C4C2×D8×C2911yescharacteristic
456C2×C4C22×D4×C2911yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#41×C2911yescharacteristic
461C8C2×#41×C2911yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22C22×D8×C2911yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4C29×#52511yescharacteristic
484C4C29×#57511yescharacteristic
485C2—41no—
486C2—82no—
487C2—161no—
488C2C29×#310011yescharacteristic
489C2C29×#341611yescharacteristic
490C2C29×#341611yescharacteristic
subgroupG/H
center, socleC22×C29C22×D8
commutator, Frattini, cosocleC2×C8C24×C29
prime radicalC29×#2186C2
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×#3175C2semidirect
2. C29×#2951C2semidirect
3. C29×#2235C2semidirect
4. C29×#2233C2semidirect
5. C29×#2226C2semidirect
6. C29×#2225C2semidirect
7. C29×#2211C2semidirect
8. C29×#2210C2semidirect
9. C29×#2189C2semidirect
11. C29×#2177C2semidirect
12. C29×#2176C2semidirect
13. C4×C29×SD32C2semidirect
14. C4×C29×SD32C2semidirect
15. C29×#2164C2semidirect
178. #33685C29direct (N × H)
217. #3175C2×C29semidirect
218. #2951C2×C29semidirect
219. #2235C2×C29semidirect
220. #2233C2×C29semidirect
221. #2226C2×C29semidirect
222. #2225C2×C29semidirect
223. #2211C2×C29semidirect
224. #2210C2×C29semidirect
225. #2189C2×C29semidirect
227. #2177C2×C29semidirect
228. #2176C2×C29semidirect
229. C4×SD32C2×C29semidirect
230. C4×SD32C2×C29semidirect
231. #2164C2×C29semidirect
361. C29#33685direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31752
C29×#29512
C29×#22352
C29×#22332
C29×#22262
C29×#22252
C29×#22112
C29×#22102
C29×#21892
C29×#21862
C29×#21772
C29×#21762
C4×C29×SD322
C29×#21642
#3368529