Finite Group Databasebeta

← C29×#60621 #20355521

Subgroups — C29×#60621 #20355521

Order 7424.

2078 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
1C2×C29×#544C211yesmaximal, characteristic, complemented
2C29×#3449C211yesmaximal, characteristic
3C29×#3142C214yesmaximal, complemented
4C29×#3141C214yesmaximal, complemented
5C29×#3137C218yesmaximal, complemented
6C29×#3136C218yesmaximal, complemented
7C29×#2896C212yesmaximal, complemented
8C2×C29×#417C212yesmaximal, complemented
9C29×#2873C211yesmaximal, characteristic, complemented
10C22×#41×C29C2212yes—
11C22×M16×C29C2212yes—
12C29×#544—24no—
13C29×#544C2218yescomplemented
14C29×#537—21no—
15C29×#537—21no—
16C29×#536C2214yes—
17C29×#535C2214yes—
18C29×#534—22no—
19C29×#532C2214yes—
20C2×C29×C4⋊Q8—21no—
21C2×C29×C4⋊Q8C2212yescomplemented
22C2×C29×#125—21no—
23C2×C29×#125C2212yescomplemented
24C29×#525—24no—
25C2×C29×C22⋊Q8—22no—
26C2×C29×#117C2211yescharacteristic
27C2×C29×#117C2211yescharacteristic
28C22×C4⋊C4×C29C2211yescharacteristic
29C29×#491C2218yescomplemented
30C29×#490C2218yescomplemented
31C29×#489C22116yescomplemented
32C29×#488C22116yescomplemented
33C29×#487C2218yescomplemented
34C29×#486C2218yescomplemented
35C29×#419C2214yescomplemented
36C29×#418C2214yescomplemented
37C29×#417C2218yes—
38C29×#417C2214yescomplemented
39C29×#417C2218yescomplemented
40C29×#417C2214yescomplemented
41C29×#416C2218yes—
42C2×C29×#103C2214yescomplemented
43C2×C29×#102C2214yescomplemented
44C29×#405C2218yescomplemented
45C4×M16×C29C2214yescomplemented
46C2×#41×C29—22no—
47C2×#41×C29—22no—
48C2×#41×C29—28no—
49C2×#41×C29—28no—
50C2×#41×C29C2314yes—
51C2×#41×C29C2314yes—
52C22×Q8×C29—22no—
53C22×Q8×C29C2312yes—
54C22×D4×C29—22no—
55C22×D4×C29C2312yes—
56C23×C4×C29—21no—
57C23×C4×C29—22no—
58C23×C4×C29C2311yescharacteristic
59C2×M16×C29—28no—
60C2×M16×C29C2314yes—
61C2×M16×C29C2314yes—
62C22×C8×C29C2314yes—
63C29×C4⋊Q8—28no—
64C29×C4⋊Q8—24no—
65C29×C4⋊Q8C2314yes—
66C29×C4⋊Q8C2318yes—
67C29×#127C2314yes—
68C29×#125—28no—
69C29×#125—24no—
70C29×#125C2318yes—
71C29×#124C2318yes—
72C29×#123—28no—
73C29×C22⋊Q8—24no—
74C29×C22⋊Q8—24no—
75C29×C22⋊Q8—216no—
76C29×#121—24no—
77C29×#121—24no—
78C29×#121—24no—
79C29×#121—24no—
80C29×#120—28no—
81C4×D4×C29—24no—
82C4×D4×C29—24no—
83C29×#117—22no—
84C29×#117D414yes—
85C29×#117C2314yes—
86C29×#117C2314yes—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—22no—
89C2×C4⋊C4×C29—22no—
90C2×C4⋊C4×C29—22no—
91C2×C4⋊C4×C29—22no—
92C2×C4⋊C4×C29D411yescharacteristic
93C2×C4⋊C4×C29D411yescharacteristic
94C2×C4⋊C4×C29C2312yes—
95C2×C4⋊C4×C29C2314yes—
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29D412yes—
100C2×C42×C29—21no—
101C2×C42×C29C2312yes—
102C29×#103C2318yes—
103C29×#103C23116yes—
104C29×#103C2318yes—
105C29×#102C2318yes—
106C29×#102C23116yes—
107C29×#102C2318yes—
108C29×#97C2318yes—
109C4×C8×C29C2318yes—
110C24×C29—22no—
111C24×C29C2×D411yescharacteristic
112#41×C29—28no—
113#41×C29—28no—
114#41×C29—28no—
115#41×C29—28no—
116#41×C29—48no—
117#41×C29—48no—
118C2×Q8×C29—22no—
119C2×Q8×C29—28no—
120C2×Q8×C29—24no—
121C2×Q8×C29—24no—
122C2×Q8×C29—84no—
123C2×Q8×C29C2414yes—
124C2×D4×C29—24no—
125C2×D4×C29—24no—
126C2×D4×C29—22no—
127C2×D4×C29—24no—
128C2×D4×C29—24no—
129C2×D4×C29—24no—
130C2×D4×C29—24no—
131C2×D4×C29—48no—
132C2×D4×C29C2414yes—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—24no—
138C22×C4×C29—24no—
139C22×C4×C29—24no—
140C22×C4×C29—48no—
141C22×C4×C29—82no—
142C22×C4×C29C2×D412yes—
143C22×C4×C29C2×D412yes—
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2×D412yes—
146C22×C4×C29#4118yes—
147C22×C4×C29C2411yescharacteristic
148C22×C4×C29C2412yes—
149M16×C29—28no—
150M16×C29—28no—
151C2×C8×C29—28no—
152C2×C8×C29C2418yes—
153C4⋊C4×C29—24no—
154C4⋊C4×C29—22no—
155C4⋊C4×C29—28no—
156C4⋊C4×C29—28no—
157C4⋊C4×C29—28no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—24no—
161C4⋊C4×C29—24no—
162C4⋊C4×C29C2×D414yes—
163C4⋊C4×C29C2×D414yes—
164C4⋊C4×C29C2414yes—
165C4⋊C4×C29C2412yes—
166C4⋊C4×C29C2412yes—
167C22⋊C4×C29—24no—
168C22⋊C4×C29—28no—
169C22⋊C4×C29—28no—
170C22⋊C4×C29C2×D418yes—
171C42×C29—24no—
172C42×C29C2×D414yes—
173C42×C29C2414yes—
174#60621C2911yesmaximal, characteristic, direct product factor, Sylow
175C23×C29—24no—
176C23×C29—41no—
177C23×C29—41no—
178C23×C29—44no—
179C23×C29—82no—
180C23×C29—82no—
181C23×C29#12414yes—
182C23×C29C22×D412yes—
183C23×C29C22×D411yescharacteristic
184Q8×C29—24no—
185Q8×C29—24no—
186Q8×C29—44no—
187Q8×C29—88no—
188D4×C29—24no—
189D4×C29—24no—
190D4×C29—48no—
191D4×C29—48no—
192D4×C29—44no—
193D4×C29—84no—
194D4×C29—84no—
195C2×C4×C29—22no—
196C2×C4×C29—22no—
197C2×C4×C29—24no—
198C2×C4×C29—24no—
199C2×C4×C29—42no—
200C2×C4×C29—42no—
201C2×C4×C29—42no—
202C2×C4×C29—44no—
203C2×C4×C29—42no—
204C2×C4×C29—44no—
205C2×C4×C29—48no—
206C2×C4×C29—48no—
207C2×C4×C29—84no—
208C2×C4×C29#12418yes—
209C2×C4×C29#12414yes—
210C2×C4×C29C22×D414yes—
211C2×C4×C29C22×D414yes—
212C2×C4×C29C22×D412yes—
213C2×C4×C29C22×D411yescharacteristic
214C2×C4×C29C2×#4114yes—
215C2×C4×C29C2×#4114yes—
216C2×C4×C29C2×#4114yes—
217C2×C4×C29C2511yescharacteristic
218C8×C29—28no—
219C2×#544C2×C2911yescharacteristic, complemented
220#3449C2×C2911yescharacteristic
221#3142C2×C2914yescomplemented
222#3141C2×C2914yescomplemented
223#3137C2×C2918yescomplemented
224#3136C2×C2918yescomplemented
225#2896C2×C2912yescomplemented
226C2×#417C2×C2912yescomplemented
227#2873C2×C2911yescharacteristic, complemented
228C22×C29—21no—
229C22×C29—22no—
230C22×C29—21no—
231C22×C29—22no—
232C22×C29—44no—
233C22×C29—44no—
234C22×C29—44no—
235C22×C29—44no—
236C22×C29—88no—
237C22×C29C2×#12414yes—
238C22×C29C2×#12412yes—
239C22×C29C23×D411yescharacteristic
240C4×C29—24no—
241C4×C29—24no—
242C4×C29—44no—
243C4×C29—42no—
244C4×C29—42no—
245C4×C29—44no—
246C4×C29C2×#12412yes—
247C4×C29C2×#12414yes—
248C4×C29C22×#4112yes—
249C22×#41C22×C2912yes—
250C22×M16C22×C2912yes—
251#544—24no—
252#544C22×C2918yescomplemented
253#537—21no—
254#537—21no—
255#536C22×C2914yes—
256#535C22×C2914yes—
257#534—22no—
258#532C22×C2914yes—
259C2×C4⋊Q8—21no—
260C2×C4⋊Q8C22×C2912yescomplemented
261C2×#125—21no—
262C2×#125C22×C2912yescomplemented
263#525—24no—
264C2×C22⋊Q8—22no—
265C2×#117C22×C2911yescharacteristic
266C2×#117C22×C2911yescharacteristic
267C22×C4⋊C4C22×C2911yescharacteristic
268#491C22×C2918yescomplemented
269#490C22×C2918yescomplemented
270#489C22×C29116yescomplemented
271#488C22×C29116yescomplemented
272#487C22×C2918yescomplemented
273#486C22×C2918yescomplemented
274#419C22×C2914yescomplemented
275#418C22×C2914yescomplemented
276#417C22×C2918yes—
277#417C22×C2914yescomplemented
278#417C22×C2918yescomplemented
279#417C22×C2914yescomplemented
280#416C22×C2918yes—
281C2×#103C22×C2914yescomplemented
282C2×#102C22×C2914yescomplemented
283#405C22×C2918yescomplemented
284C4×M16C22×C2914yescomplemented
285C2×C29—24no—
286C2×C29—22no—
287C2×C29—84no—
288C2×C29C22×#12411yescharacteristic
289C2×C29#358511yescharacteristic
290C2×C29#358611yescharacteristic
291C2×#41—22no—
292C2×#41—22no—
293C2×#41—28no—
294C2×#41—28no—
295C2×#41C23×C2914yes—
296C2×#41C23×C2914yes—
297C22×Q8—22no—
298C22×Q8C23×C2912yes—
299C22×D4—22no—
300C22×D4C23×C2912yes—
301C23×C4—21no—
302C23×C4—22no—
303C23×C4C23×C2911yescharacteristic
304C2×M16—28no—
305C2×M16C23×C2914yes—
306C2×M16C23×C2914yes—
307C22×C8C23×C2914yes—
308C4⋊Q8—28no—
309C4⋊Q8—24no—
310C4⋊Q8C23×C2914yes—
311C4⋊Q8C23×C2918yes—
312#127C23×C2914yes—
313#125—28no—
314#125—24no—
315#125C23×C2918yes—
316#124C23×C2918yes—
317#123—28no—
318C22⋊Q8—24no—
319C22⋊Q8—24no—
320C22⋊Q8—216no—
321#121—24no—
322#121—24no—
323#121—24no—
324#121—24no—
325#120—28no—
326C4×D4—24no—
327C4×D4—24no—
328#117—22no—
329#117D4×C2914yes—
330#117C23×C2914yes—
331#117C23×C2914yes—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4D4×C2911yescharacteristic
338C2×C4⋊C4D4×C2911yescharacteristic
339C2×C4⋊C4C23×C2912yes—
340C2×C4⋊C4C23×C2914yes—
341C2×C4⋊C4C23×C2911yescharacteristic
342C2×C4⋊C4C23×C2911yescharacteristic
343C2×C22⋊C4—21no—
344C2×C22⋊C4D4×C2912yes—
345C2×C42—21no—
346C2×C42C23×C2912yes—
347#103C23×C29116yes—
348#103C23×C2918yes—
349#103C23×C2918yes—
350#102C23×C29116yes—
351#102C23×C2918yes—
352#102C23×C2918yes—
353#97C23×C2918yes—
354C4×C8C23×C2918yes—
355C29#6062111yescharacteristic, direct product factor, Sylow
356C24—22no—
357C24C2×D4×C2911yescharacteristic
358#41—28no—
359#41—28no—
360#41—28no—
361#41—28no—
362#41—48no—
363#41—48no—
364C2×Q8—22no—
365C2×Q8—28no—
366C2×Q8—24no—
367C2×Q8—24no—
368C2×Q8—84no—
369C2×Q8C24×C2914yes—
370C2×D4—24no—
371C2×D4—24no—
372C2×D4—22no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—24no—
376C2×D4—24no—
377C2×D4—48no—
378C2×D4C24×C2914yes—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—48no—
387C22×C4—82no—
388C22×C4C2×D4×C2912yes—
389C22×C4C2×D4×C2912yes—
390C22×C4C2×D4×C2911yescharacteristic
391C22×C4C2×D4×C2912yes—
392C22×C4#41×C2918yes—
393C22×C4C24×C2911yescharacteristic
394C22×C4C24×C2912yes—
395M16—28no—
396M16—28no—
397C2×C8—28no—
398C2×C8C24×C2918yes—
399C4⋊C4—24no—
400C4⋊C4—22no—
401C4⋊C4—28no—
402C4⋊C4—28no—
403C4⋊C4—28no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4C2×D4×C2914yes—
409C4⋊C4C2×D4×C2914yes—
410C4⋊C4C24×C2914yes—
411C4⋊C4C24×C2912yes—
412C4⋊C4C24×C2912yes—
413C22⋊C4—24no—
414C22⋊C4—28no—
415C22⋊C4—28no—
416C22⋊C4C2×D4×C2918yes—
417C42—24no—
418C42C2×D4×C2914yes—
419C42C24×C2914yes—
420C23—24no—
421C23—41no—
422C23—41no—
423C23—44no—
424C23—82no—
425C23—82no—
426C23C29×#12414yes—
427C23C22×D4×C2912yes—
428C23C22×D4×C2911yescharacteristic
429Q8—24no—
430Q8—24no—
431Q8—44no—
432Q8—88no—
433D4—24no—
434D4—24no—
435D4—48no—
436D4—48no—
437D4—44no—
438D4—84no—
439D4—84no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—44no—
450C2×C4—48no—
451C2×C4—48no—
452C2×C4—84no—
453C2×C4C29×#12418yes—
454C2×C4C29×#12414yes—
455C2×C4C22×D4×C2914yes—
456C2×C4C22×D4×C2914yes—
457C2×C4C22×D4×C2912yes—
458C2×C4C22×D4×C2911yescharacteristic
459C2×C4C2×#41×C2914yes—
460C2×C4C2×#41×C2914yes—
461C2×C4C2×#41×C2914yes—
462C2×C4C25×C2911yescharacteristic
463C8—28no—
464C22—21no—
465C22—22no—
466C22—21no—
467C22—22no—
468C22—44no—
469C22—44no—
470C22—44no—
471C22—44no—
472C22—88no—
473C22C2×C29×#12414yes—
474C22C2×C29×#12412yes—
475C22C23×D4×C2911yescharacteristic
476C4—24no—
477C4—24no—
478C4—44no—
479C4—42no—
480C4—42no—
481C4—44no—
482C4C2×C29×#12412yes—
483C4C2×C29×#12414yes—
484C4C22×#41×C2912yes—
485C2—24no—
486C2—22no—
487C2—84no—
488C2C22×C29×#12411yescharacteristic
489C2C29×#358511yescharacteristic
490C2C29×#358611yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC29×#3449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#544C2semidirect
3. C29×#3142C2semidirect
4. C29×#3141C2semidirect
5. C29×#3137C2semidirect
6. C29×#3136C2semidirect
7. C29×#2896C2semidirect
8. C2×C29×#417C2semidirect
9. C29×#2873C2semidirect
13. C29×#544C22semidirect
21. C2×C29×C4⋊Q8C22semidirect
23. C2×C29×#125C22semidirect
29. C29×#491C22semidirect
30. C29×#490C22semidirect
31. C29×#489C22semidirect
32. C29×#488C22semidirect
33. C29×#487C22semidirect
34. C29×#486C22semidirect
35. C29×#419C22semidirect
36. C29×#418C22semidirect
38. C29×#417C22semidirect
39. C29×#417C22semidirect
40. C29×#417C22semidirect
42. C2×C29×#103C22semidirect
43. C2×C29×#102C22semidirect
44. C29×#405C22semidirect
45. C4×M16×C29C22semidirect
174. #60621C29direct (N × H)
219. C2×#544C2×C29semidirect
221. #3142C2×C29semidirect
222. #3141C2×C29semidirect
223. #3137C2×C29semidirect
224. #3136C2×C29semidirect
225. #2896C2×C29semidirect
226. C2×#417C2×C29semidirect
227. #2873C2×C29semidirect
252. #544C22×C29semidirect
260. C2×C4⋊Q8C22×C29semidirect
262. C2×#125C22×C29semidirect
268. #491C22×C29semidirect
269. #490C22×C29semidirect
270. #489C22×C29semidirect
271. #488C22×C29semidirect
272. #487C22×C29semidirect
273. #486C22×C29semidirect
274. #419C22×C29semidirect
275. #418C22×C29semidirect
277. #417C22×C29semidirect
278. #417C22×C29semidirect
279. #417C22×C29semidirect
281. C2×#103C22×C29semidirect
282. C2×#102C22×C29semidirect
283. #405C22×C29semidirect
284. C4×M16C22×C29semidirect
355. C29#60621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5442
C29×#34492
C29×#31422
C29×#31412
C29×#31372
C29×#31362
C29×#28962
C2×C29×#4172
C29×#28732
#6062129