Finite Group Databasebeta

← C29×#61798 #20356698

Subgroups — C29×#61798 #20356698

Order 7424.

1674 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3550C211yesmaximal, characteristic, complemented
2C29×#3512C211yesmaximal, characteristic
3C29×#3350C214yesmaximal, complemented
4C29×#3349C214yesmaximal, complemented
5C29×#3320C214yesmaximal, complemented
6C29×#3312C214yesmaximal, complemented
7C29×#3236C212yesmaximal, complemented
8C29×#3201C214yesmaximal, complemented
9C29×#3116C212yesmaximal, complemented
10C29×#3097C214yesmaximal, complemented
11C29×#2980C211yesmaximal, characteristic, complemented
12C29×#563—22no—
13C29×#559—21no—
14Q82×C29—21no—
15C29×#556C2214yes—
16C29×#553—24no—
17C29×#553C2214yes—
18C29×#552C2214yes—
19D4×Q8×C29C2214yes—
20C29×#542—24no—
21C29×#541—21no—
22C29×#540—21no—
23C29×#537C2212yes—
24C29×#536C2214yes—
25C29×#533C2212yes—
26C29×#532C2211yescharacteristic
27C29×#529—22no—
28C2×C29×#125C2211yescharacteristic
29C29×#520C2212yes—
30C4×#41×C29C2211yescharacteristic
31C29×#501C2214yes—
32C29×#491C2214yes—
33C29×#485C2214yes—
34C29×#485C2214yes—
35C29×#485C2214yes—
36C29×#485C2214yes—
37C29×#484C2214yes—
38C29×#484C2214yes—
39C29×#483C2214yes—
40C29×#483C2214yes—
41C29×#482C2214yes—
42C29×#479C2214yes—
43C29×#479C2214yes—
44C29×#477C2212yes—
45C29×#476C2212yes—
46C29×#470C2214yes—
47C29×#468C2214yes—
48C29×#467C2214yes—
49C29×#465C2214yes—
50C29×#462C2212yes—
51C29×#461C2212yes—
52C29×#452C2214yes—
53C29×#451C2214yes—
54C29×#448C2214yes—
55C29×#441C2214yes—
56C29×#440C2214yes—
57C29×#435C2214yes—
58C29×#435C2214yes—
59C29×#432C2212yes—
60C29×#428C2214yes—
61C29×#427C2214yes—
62C29×#419C2214yes—
63C2×C29×#103C2214yes—
64C29×#408C2214yes—
65C2×#41×C29C2311yescharacteristic
66C2×#41×C29C2312yes—
67C22×Q8×C29C2314yes—
68C2×Q16×C29C2314yes—
69C2×SD16×C29C2314yes—
70C2×M16×C29C2314yes—
71C22×C8×C29C2314yes—
72C29×C4⋊Q8—24no—
73C29×C4⋊Q8—24no—
74C29×C4⋊Q8D411yescharacteristic
75C29×C4⋊Q8C2312yes—
76C29×C4⋊Q8C2312yes—
77C29×#127D411yescharacteristic
78C29×#126—24no—
79C29×#126—24no—
80C29×#126—24no—
81C29×#126—24no—
82C29×#125—24no—
83C29×#125—21no—
84C29×#125—21no—
85C29×#125—22no—
86C29×#125C2314yes—
87C29×#124—24no—
88C29×#124—24no—
89C29×#124D412yes—
90C29×#123—24no—
91C29×#123—24no—
92C29×#123—24no—
93C29×#123—24no—
94C29×C22⋊Q8—22no—
95C29×C22⋊Q8—22no—
96C29×C22⋊Q8—24no—
97C29×C22⋊Q8—24no—
98C29×C22⋊Q8C2314yes—
99C29×C22⋊Q8C2314yes—
100C29×C22⋊Q8C2314yes—
101C29×C22⋊Q8C2314yes—
102C29×#121—22no—
103C29×#121—24no—
104C29×#121—24no—
105C29×#121D414yes—
106C29×#121C2314yes—
107C4×Q8×C29—22no—
108C4×Q8×C29—24no—
109C4×Q8×C29—22no—
110C4×Q8×C29C2314yes—
111C4×Q8×C29C2312yes—
112C4×D4×C29—22no—
113C4×D4×C29—24no—
114C4×D4×C29—24no—
115C4×D4×C29—22no—
116C4×D4×C29—24no—
117C4×D4×C29C2312yes—
118C4×D4×C29C2314yes—
119C29×#117—22no—
120C29×#117—24no—
121C29×#117—21no—
122C29×#117C2314yes—
123C29×#117C2314yes—
124C29×#117C2311yescharacteristic
125C2×C4⋊C4×C29—22no—
126C2×C4⋊C4×C29C2314yes—
127C2×C4⋊C4×C29C2312yes—
128C2×C42×C29—21no—
129C2×C42×C29C2311yescharacteristic
130C29×#107C2314yes—
131C29×#107C2314yes—
132C29×#107C2314yes—
133C29×#106C2314yes—
134C29×#106C2314yes—
135C29×#106C2314yes—
136C29×C4⋊C8C2312yes—
137C29×C4⋊C8C2312yes—
138C29×#103C2314yes—
139C29×#103C2314yes—
140C29×#103C2314yes—
141C29×#103C2314yes—
142C29×#103C2314yes—
143C29×#103C2314yes—
144C29×#103C2314yes—
145C29×#102C2314yes—
146C29×C22⋊C8C2314yes—
147C29×C22⋊C8C2314yes—
148C29×C22⋊C8C2314yes—
149C29×#97C2314yes—
150#41×C29—42no—
151#41×C29—42no—
152#41×C29—42no—
153C2×Q8×C29—22no—
154C2×Q8×C29—24no—
155C2×Q8×C29—44no—
156C2×Q8×C29—44no—
157C2×Q8×C29C2×D412yes—
158C2×Q8×C29C2411yescharacteristic
159C2×Q8×C29C2414yes—
160C2×D4×C29—21no—
161C2×D4×C29—24no—
162C2×D4×C29C2×D414yes—
163C2×D4×C29C2×D414yes—
164C2×D4×C29C2×D412yes—
165C2×D4×C29C2411yescharacteristic
166C22×C4×C29—22no—
167C22×C4×C29—24no—
168C22×C4×C29—24no—
169C22×C4×C29—21no—
170C22×C4×C29—22no—
171C22×C4×C29C2×D412yes—
172C22×C4×C29C2411yescharacteristic
173C22×C4×C29C2414yes—
174Q16×C29—44no—
175SD16×C29—44no—
176M16×C29—44no—
177C2×C8×C29—44no—
178C2×C8×C29C2414yes—
179C2×C8×C29C2414yes—
180C4⋊C4×C29—24no—
181C4⋊C4×C29—24no—
182C4⋊C4×C29—22no—
183C4⋊C4×C29—24no—
184C4⋊C4×C29—22no—
185C4⋊C4×C29—24no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—24no—
190C4⋊C4×C29—24no—
191C4⋊C4×C29—24no—
192C4⋊C4×C29—24no—
193C4⋊C4×C29C2×D414yes—
194C4⋊C4×C29C2412yes—
195C4⋊C4×C29C2414yes—
196C4⋊C4×C29C2414yes—
197C22⋊C4×C29—24no—
198C22⋊C4×C29—24no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—24no—
201C22⋊C4×C29—24no—
202C22⋊C4×C29—24no—
203C22⋊C4×C29—24no—
204C22⋊C4×C29—22no—
205C22⋊C4×C29—24no—
206C22⋊C4×C29C2×D414yes—
207C22⋊C4×C29C2×D414yes—
208C42×C29—22no—
209C42×C29—21no—
210C42×C29—24no—
211C42×C29—24no—
212C42×C29—24no—
213C42×C29C2×D411yescharacteristic
214C42×C29C2×D411yescharacteristic
215C42×C29C2412yes—
216#61798C2911yesmaximal, characteristic, direct product factor, Sylow
217C23×C29—21no—
218C23×C29C22×D414yes—
219C23×C29C22×D411yescharacteristic
220Q8×C29—24no—
221Q8×C29—22no—
222Q8×C29—24no—
223Q8×C29—42no—
224Q8×C29—44no—
225Q8×C29—84no—
226D4×C29—22no—
227D4×C29—44no—
228D4×C29—42no—
229D4×C29—44no—
230D4×C29—42no—
231D4×C29—84no—
232C2×C4×C29—24no—
233C2×C4×C29—24no—
234C2×C4×C29—22no—
235C2×C4×C29—22no—
236C2×C4×C29—24no—
237C2×C4×C29—21no—
238C2×C4×C29—24no—
239C2×C4×C29—24no—
240C2×C4×C29—42no—
241C2×C4×C29—42no—
242C2×C4×C29—82no—
243C2×C4×C29—84no—
244C2×C4×C29—82no—
245C2×C4×C29—84no—
246C2×C4×C29C22×D412yes—
247C2×C4×C29C22×D414yes—
248C2×C4×C29C22×D411yescharacteristic
249C2×C4×C29C22×D412yes—
250C2×C4×C29C2511yescharacteristic
251C8×C29—24no—
252C8×C29—24no—
253#3550C2×C2911yescharacteristic, complemented
254#3512C2×C2911yescharacteristic
255#3350C2×C2914yescomplemented
256#3349C2×C2914yescomplemented
257#3320C2×C2914yescomplemented
258#3312C2×C2914yescomplemented
259#3236C2×C2912yescomplemented
260#3201C2×C2914yescomplemented
261#3116C2×C2912yescomplemented
262#3097C2×C2914yescomplemented
263#2980C2×C2911yescharacteristic, complemented
264C22×C29—22no—
265C22×C29—24no—
266C22×C29—24no—
267C22×C29—24no—
268C22×C29—21no—
269C22×C29—42no—
270C22×C29—41no—
271C22×C29C23×D411yescharacteristic
272C4×C29—22no—
273C4×C29—22no—
274C4×C29—21no—
275C4×C29—24no—
276C4×C29—42no—
277C4×C29—44no—
278C4×C29—44no—
279C4×C29—41no—
280C4×C29—44no—
281C4×C29#58512yes—
282#563—22no—
283#559—21no—
284Q82—21no—
285#556C22×C2914yes—
286#553—24no—
287#553C22×C2914yes—
288#552C22×C2914yes—
289D4×Q8C22×C2914yes—
290#542—24no—
291#541—21no—
292#540—21no—
293#537C22×C2912yes—
294#536C22×C2914yes—
295#533C22×C2912yes—
296#532C22×C2911yescharacteristic
297#529—22no—
298C2×#125C22×C2911yescharacteristic
299#520C22×C2912yes—
300C4×#41C22×C2911yescharacteristic
301#501C22×C2914yes—
302#491C22×C2914yes—
303#485C22×C2914yes—
304#485C22×C2914yes—
305#485C22×C2914yes—
306#485C22×C2914yes—
307#484C22×C2914yes—
308#484C22×C2914yes—
309#483C22×C2914yes—
310#483C22×C2914yes—
311#482C22×C2914yes—
312#479C22×C2914yes—
313#479C22×C2914yes—
314#477C22×C2912yes—
315#476C22×C2912yes—
316#470C22×C2914yes—
317#468C22×C2914yes—
318#467C22×C2914yes—
319#465C22×C2914yes—
320#462C22×C2912yes—
321#461C22×C2912yes—
322#452C22×C2914yes—
323#451C22×C2914yes—
324#448C22×C2914yes—
325#441C22×C2914yes—
326#440C22×C2914yes—
327#435C22×C2914yes—
328#435C22×C2914yes—
329#432C22×C2912yes—
330#428C22×C2914yes—
331#427C22×C2914yes—
332#419C22×C2914yes—
333C2×#103C22×C2914yes—
334#408C22×C2914yes—
335C2×C29—41no—
336C2×C29—44no—
337C2×C29—81no—
338C2×C29#348511yescharacteristic
339C2×C29#358612yes—
340C2×#41C23×C2911yescharacteristic
341C2×#41C23×C2912yes—
342C22×Q8C23×C2914yes—
343C2×Q16C23×C2914yes—
344C2×SD16C23×C2914yes—
345C2×M16C23×C2914yes—
346C22×C8C23×C2914yes—
347C4⋊Q8—24no—
348C4⋊Q8—24no—
349C4⋊Q8D4×C2911yescharacteristic
350C4⋊Q8C23×C2912yes—
351C4⋊Q8C23×C2912yes—
352#127D4×C2911yescharacteristic
353#126—24no—
354#126—24no—
355#126—24no—
356#126—24no—
357#125—24no—
358#125—21no—
359#125—21no—
360#125—22no—
361#125C23×C2914yes—
362#124—24no—
363#124—24no—
364#124D4×C2912yes—
365#123—24no—
366#123—24no—
367#123—24no—
368#123—24no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C22⋊Q8—24no—
372C22⋊Q8—24no—
373C22⋊Q8C23×C2914yes—
374C22⋊Q8C23×C2914yes—
375C22⋊Q8C23×C2914yes—
376C22⋊Q8C23×C2914yes—
377#121—22no—
378#121—24no—
379#121—24no—
380#121D4×C2914yes—
381#121C23×C2914yes—
382C4×Q8—22no—
383C4×Q8—24no—
384C4×Q8—22no—
385C4×Q8C23×C2912yes—
386C4×Q8C23×C2914yes—
387C4×D4—22no—
388C4×D4—24no—
389C4×D4—24no—
390C4×D4—22no—
391C4×D4—24no—
392C4×D4C23×C2912yes—
393C4×D4C23×C2914yes—
394#117—22no—
395#117—24no—
396#117—21no—
397#117C23×C2911yescharacteristic
398#117C23×C2914yes—
399#117C23×C2914yes—
400C2×C4⋊C4—22no—
401C2×C4⋊C4C23×C2912yes—
402C2×C4⋊C4C23×C2914yes—
403C2×C42—21no—
404C2×C42C23×C2911yescharacteristic
405#107C23×C2914yes—
406#107C23×C2914yes—
407#107C23×C2914yes—
408#106C23×C2914yes—
409#106C23×C2914yes—
410#106C23×C2914yes—
411C4⋊C8C23×C2912yes—
412C4⋊C8C23×C2912yes—
413#103C23×C2914yes—
414#103C23×C2914yes—
415#103C23×C2914yes—
416#103C23×C2914yes—
417#103C23×C2914yes—
418#103C23×C2914yes—
419#103C23×C2914yes—
420#102C23×C2914yes—
421C22⋊C8C23×C2914yes—
422C22⋊C8C23×C2914yes—
423C22⋊C8C23×C2914yes—
424#97C23×C2914yes—
425C29#6179811yescharacteristic, direct product factor, Sylow
426#41—42no—
427#41—42no—
428#41—42no—
429C2×Q8—22no—
430C2×Q8—24no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8C2×D4×C2912yes—
434C2×Q8C24×C2914yes—
435C2×Q8C24×C2911yescharacteristic
436C2×D4—21no—
437C2×D4—24no—
438C2×D4C2×D4×C2914yes—
439C2×D4C2×D4×C2914yes—
440C2×D4C2×D4×C2912yes—
441C2×D4C24×C2911yescharacteristic
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4C2×D4×C2912yes—
448C22×C4C24×C2911yescharacteristic
449C22×C4C24×C2914yes—
450Q16—44no—
451SD16—44no—
452M16—44no—
453C2×C8—44no—
454C2×C8C24×C2914yes—
455C2×C8C24×C2914yes—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4C2×D4×C2914yes—
470C4⋊C4C24×C2914yes—
471C4⋊C4C24×C2912yes—
472C4⋊C4C24×C2914yes—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—21no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—24no—
482C22⋊C4C2×D4×C2914yes—
483C22⋊C4C2×D4×C2914yes—
484C42—22no—
485C42—21no—
486C42—24no—
487C42—24no—
488C42—24no—
489C42C2×D4×C2911yescharacteristic
490C42C2×D4×C2911yescharacteristic
491C42C24×C2912yes—
492C23—21no—
493C23C22×D4×C2914yes—
494C23C22×D4×C2911yescharacteristic
495Q8—24no—
496Q8—22no—
497Q8—24no—
498Q8—42no—
499Q8—44no—
500Q8—84no—
501D4—22no—
502D4—42no—
503D4—44no—
504D4—44no—
505D4—42no—
506D4—84no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4—84no—
520C2×C4—82no—
521C2×C4C22×D4×C2912yes—
522C2×C4C22×D4×C2914yes—
523C2×C4C22×D4×C2911yescharacteristic
524C2×C4C22×D4×C2912yes—
525C2×C4C25×C2911yescharacteristic
526C8—24no—
527C8—24no—
528C22—24no—
529C22—21no—
530C22—22no—
531C22—24no—
532C22—24no—
533C22—41no—
534C22—42no—
535C22C23×D4×C2911yescharacteristic
536C4—21no—
537C4—24no—
538C4—22no—
539C4—22no—
540C4—41no—
541C4—44no—
542C4—42no—
543C4—44no—
544C4—44no—
545C4C29×#58512yes—
546C2—44no—
547C2—41no—
548C2—81no—
549C2C29×#348511yescharacteristic
550C2C29×#358612yes—
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC29×#3512C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C29×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3550C2semidirect
3. C29×#3350C2semidirect
4. C29×#3349C2semidirect
5. C29×#3320C2semidirect
6. C29×#3312C2semidirect
7. C29×#3236C2semidirect
8. C29×#3201C2semidirect
9. C29×#3116C2semidirect
10. C29×#3097C2semidirect
11. C29×#2980C2semidirect
216. #61798C29direct (N × H)
253. #3550C2×C29semidirect
255. #3350C2×C29semidirect
256. #3349C2×C29semidirect
257. #3320C2×C29semidirect
258. #3312C2×C29semidirect
259. #3236C2×C29semidirect
260. #3201C2×C29semidirect
261. #3116C2×C29semidirect
262. #3097C2×C29semidirect
263. #2980C2×C29semidirect
425. C29#61798direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35502
C29×#35122
C29×#33502
C29×#33492
C29×#33202
C29×#33122
C29×#32362
C29×#32012
C29×#31162
C29×#30972
C29×#29802
#6179829