Finite Group Databasebeta

← C29×#62863 #20357763

Subgroups — C29×#62863 #20357763

Order 7424.

7466 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3560C218yesmaximal, complemented
2C29×#3558C218yesmaximal, complemented
3C29×#3537C218yesmaximal, complemented
4C29×#3534C218yesmaximal, complemented
5C29×#3533C218yesmaximal, complemented
6C29×#3532C218yesmaximal, complemented
7C29×#3505C214yesmaximal, complemented
8C29×#3496C214yesmaximal, complemented
9C29×#3484C214yesmaximal, complemented
10C2×C29×#538C212yesmaximal, complemented
11C2×C29×#534C211yesmaximal, characteristic, complemented
12C2×C29×H(5,𝔽2)C2214yescomplemented
13C23×D4×C29C2212yescomplemented
14C29×#563C2218yescomplemented
15C29×#562C22116yescomplemented
16C29×H(3,𝔽4)C2218yescomplemented
17C29×#560C22116yescomplemented
18C29×#560C2218yescomplemented
19C29×#560C2218yescomplemented
20C29×#559C2218yescomplemented
21C29×#553C22116yescomplemented
22C29×#553C2218yescomplemented
23C29×#553C22116yescomplemented
24C29×#552C2218yescomplemented
25C29×#551C22116yescomplemented
26C29×#551C2218yescomplemented
27C29×#551C2218yescomplemented
28C29×#548C2218yescomplemented
29C29×#547C2218yescomplemented
30C29×#547C2218yescomplemented
31C29×#546C2218yescomplemented
32C29×#546C22116yescomplemented
33C29×#546C22116yescomplemented
34C29×#546C22116yescomplemented
35C29×#546C22116yescomplemented
36C29×#546C22116yescomplemented
37D42×C29C2218yescomplemented
38D42×C29C22116yescomplemented
39D42×C29C22116yescomplemented
40D42×C29C2218yescomplemented
41D42×C29C2218yescomplemented
42C29×#542C22116yescomplemented
43C29×#540C22116yescomplemented
44C29×#539C22116yescomplemented
45C29×#539C2218yescomplemented
46C29×#538C22116yescomplemented
47C29×#538C2218yescomplemented
48C29×#538C2218yescomplemented
49C29×#538C22116yescomplemented
50C29×#538C22116yescomplemented
51C29×#538C22116yescomplemented
52C29×#538C2218yescomplemented
53C29×#537C2218yescomplemented
54C29×#535C2218yescomplemented
55C29×#535C22116yescomplemented
56C29×#534C2218yescomplemented
57C29×#534C2218yescomplemented
58C29×#534C2218yescomplemented
59C29×#534C2218yescomplemented
60C29×#534C22116yescomplemented
61C29×#534C2218yescomplemented
62C29×#532C2218yescomplemented
63C29×#529C2218yescomplemented
64C2×C29×#126C2214yescomplemented
65C2×C29×#124C2214yescomplemented
66C29×#525C2218yescomplemented
67C29×#525C2218yescomplemented
68C2×C29×#123C2214yescomplemented
69C2×C29×#123C2214yescomplemented
70C2×C29×C22⋊Q8C2212yescomplemented
71C2×C29×#121C2214yescomplemented
72C2×C29×#121C2214yescomplemented
73C2×C29×#121C2212yescomplemented
74C2×C29×#121C2218yescomplemented
75C2×C29×#120C2214yescomplemented
76C2×C29×#120C2214yescomplemented
77C2×C29×#120C2218yescomplemented
78C29×#518C2214yescomplemented
79C2×C4×D4×C29C2214yescomplemented
80C22×C22⋊C4×C29C2211yescharacteristic, complemented
81C25×C29C2311yescharacteristic
82C25×C29C2312yes—
83C29×H(5,𝔽2)—416no—
84C2×#41×C29C2318yes—
85C2×#41×C29C23116yescomplemented
86C2×#41×C29C2318yescomplemented
87C22×Q8×C29C2312yescomplemented
88C22×D4×C29—48no—
89C22×D4×C29C2314yes—
90C22×D4×C29C2314yes—
91C22×D4×C29C2314yes—
92C22×D4×C29C2318yes—
93C22×D4×C29C23116yes—
94C22×D4×C29C2314yes—
95C22×D4×C29C2314yes—
96C22×D4×C29C2314yes—
97C22×D4×C29C23116yescomplemented
98C22×D4×C29C23116yescomplemented
99C22×D4×C29C2312yescomplemented
100C22×D4×C29C2318yescomplemented
101C23×C4×C29C2312yes—
102C23×C4×C29C2312yes—
103C23×C4×C29C2314yescomplemented
104C29×C4⋊Q8C2318yescomplemented
105C29×#127C2318yes—
106C29×#127C2318yes—
107C29×#127C2318yescomplemented
108C29×#126C23116yescomplemented
109C29×#126C23116yescomplemented
110C29×#126C23116yescomplemented
111C29×#126C23116yescomplemented
112C29×#126C23116yescomplemented
113C29×#125C2318yescomplemented
114C29×#125C23116yescomplemented
115C29×#124C2318yes—
116C29×#124C2318yes—
117C29×#124C23116yescomplemented
118C29×#124C23116yescomplemented
119C29×#124C2318yescomplemented
120C29×#124C23116yescomplemented
121C29×#124C23116yescomplemented
122C29×#123C23116yes—
123C29×#123C2318yes—
124C29×#123C2318yes—
125C29×#123C23116yes—
126C29×#123C2318yes—
127C29×#123C2318yes—
128C29×#123C23116yescomplemented
129C29×#123C23116yescomplemented
130C29×#123C23116yescomplemented
131C29×#123C23116yescomplemented
132C29×#123C23116yescomplemented
133C29×#123C23116yescomplemented
134C29×#123C23116yescomplemented
135C29×#123C23116yescomplemented
136C29×C22⋊Q8C2318yes—
137C29×C22⋊Q8C2318yescomplemented
138C29×C22⋊Q8C2318yescomplemented
139C29×C22⋊Q8C23116yescomplemented
140C29×C22⋊Q8C23116yescomplemented
141C29×C22⋊Q8C23116yescomplemented
142C29×C22⋊Q8C23116yescomplemented
143C29×#121C2318yes—
144C29×#121C2318yes—
145C29×#121C2318yes—
146C29×#121C2318yes—
147C29×#121C2318yes—
148C29×#121C23116yes—
149C29×#121C23116yes—
150C29×#121C23116yes—
151C29×#121C23116yes—
152C29×#121C2318yescomplemented
153C29×#121C23116yescomplemented
154C29×#121C23116yescomplemented
155C29×#121C23116yescomplemented
156C29×#121C2318yescomplemented
157C29×#121C23116yescomplemented
158C29×#121C2318yescomplemented
159C29×#121C2318yescomplemented
160C29×#121C23116yescomplemented
161C29×#121C23116yescomplemented
162C29×#121C23116yescomplemented
163C29×#121C23116yescomplemented
164C29×#121C23116yescomplemented
165C29×#120C23116yes—
166C29×#120C23116yes—
167C29×#120C2318yes—
168C29×#120C2318yes—
169C29×#120C23116yes—
170C29×#120C23116yes—
171C29×#120C2318yes—
172C29×#120C2318yes—
173C29×#120C23116yescomplemented
174C29×#120C23116yescomplemented
175C29×#120C23116yescomplemented
176C29×#120C23116yescomplemented
177C29×#120C23116yescomplemented
178C4×Q8×C29C2318yescomplemented
179C4×D4×C29C2318yes—
180C4×D4×C29C2318yes—
181C4×D4×C29C2318yescomplemented
182C4×D4×C29C2318yescomplemented
183C4×D4×C29C23116yescomplemented
184C4×D4×C29C23116yescomplemented
185C4×D4×C29C23116yescomplemented
186C4×D4×C29C23116yescomplemented
187C4×D4×C29C23116yescomplemented
188C4×D4×C29C2318yescomplemented
189C4×D4×C29C2318yescomplemented
190C4×D4×C29C2318yescomplemented
191C4×D4×C29C23116yescomplemented
192C29×#117C2318yes—
193C29×#117C2318yescomplemented
194C29×#117C23116yescomplemented
195C2×C4⋊C4×C29C2314yes—
196C2×C4⋊C4×C29C2314yescomplemented
197C2×C4⋊C4×C29C2314yescomplemented
198C2×C4⋊C4×C29C2312yescomplemented
199C2×C4⋊C4×C29C2318yescomplemented
200C2×C4⋊C4×C29C2312yescomplemented
201C2×C22⋊C4×C29C2314yes—
202C2×C22⋊C4×C29C2314yes—
203C2×C22⋊C4×C29C2314yes—
204C2×C22⋊C4×C29C2314yes—
205C2×C22⋊C4×C29C2318yes—
206C2×C22⋊C4×C29C2318yes—
207C2×C22⋊C4×C29C2314yes—
208C2×C22⋊C4×C29C2314yes—
209C2×C22⋊C4×C29C2314yescomplemented
210C2×C22⋊C4×C29C23116yescomplemented
211C2×C22⋊C4×C29C2314yescomplemented
212C2×C22⋊C4×C29C23116yescomplemented
213C2×C42×C29C2314yescomplemented
214C24×C29—24no—
215C24×C29—44no—
216C24×C29—82no—
217C24×C29—84no—
218C24×C29C2414yes—
219C24×C29C2414yes—
220C24×C29C2412yes—
221C24×C29C2414yes—
222C24×C29C2418yes—
223C24×C29C2418yes—
224C24×C29C2411yescharacteristic
225#41×C29—416no—
226#41×C29—432no—
227#41×C29—88no—
228C2×Q8×C29—82no—
229C2×Q8×C29C2418yes—
230C2×Q8×C29C2418yes—
231C2×D4×C29—216no—
232C2×D4×C29—216no—
233C2×D4×C29—48no—
234C2×D4×C29—432no—
235C2×D4×C29—416no—
236C2×D4×C29—432no—
237C2×D4×C29—84no—
238C2×D4×C29—84no—
239C2×D4×C29—84no—
240C2×D4×C29—82no—
241C2×D4×C29—88no—
242C2×D4×C29—816no—
243C2×D4×C29C2418yes—
244C2×D4×C29C2418yes—
245C2×D4×C29C24116yes—
246C2×D4×C29C2418yes—
247C2×D4×C29C2418yes—
248C2×D4×C29C24116yes—
249C2×D4×C29C24116yes—
250C2×D4×C29C24116yes—
251C2×D4×C29C24116yes—
252C2×D4×C29C2418yes—
253C2×D4×C29C2418yes—
254C2×D4×C29C2418yes—
255C2×D4×C29C24116yes—
256C2×D4×C29C2418yes—
257C22×C4×C29—44no—
258C22×C4×C29—82no—
259C22×C4×C29—84no—
260C22×C4×C29C2414yes—
261C22×C4×C29C2414yes—
262C22×C4×C29C2414yes—
263C22×C4×C29C2414yes—
264C22×C4×C29C2414yes—
265C22×C4×C29C2412yes—
266C22×C4×C29C2412yes—
267C22×C4×C29C2414yes—
268C22×C4×C29C24116yes—
269C22×C4×C29C2418yes—
270C22×C4×C29C2418yes—
271C22×C4×C29C24116yes—
272C22×C4×C29C2418yes—
273C22×C4×C29C2418yes—
274C4⋊C4×C29C2418yes—
275C4⋊C4×C29C2418yes—
276C4⋊C4×C29C2418yes—
277C4⋊C4×C29C24116yes—
278C4⋊C4×C29C24116yes—
279C4⋊C4×C29C2418yes—
280C4⋊C4×C29C2418yes—
281C4⋊C4×C29C2418yes—
282C4⋊C4×C29C24116yes—
283C4⋊C4×C29C24116yes—
284C22⋊C4×C29C2418yes—
285C22⋊C4×C29C2414yes—
286C22⋊C4×C29C2418yes—
287C22⋊C4×C29C2414yes—
288C22⋊C4×C29C24116yes—
289C22⋊C4×C29C24116yes—
290C22⋊C4×C29C24116yes—
291C22⋊C4×C29C24116yes—
292C22⋊C4×C29C2418yes—
293C22⋊C4×C29C2418yes—
294C22⋊C4×C29C2418yes—
295C22⋊C4×C29C24116yes—
296C22⋊C4×C29C24116yes—
297C22⋊C4×C29C24116yes—
298C22⋊C4×C29C24116yes—
299C22⋊C4×C29C2418yes—
300C22⋊C4×C29C2418yes—
301C22⋊C4×C29C24116yes—
302C42×C29C2418yes—
303C42×C29C2418yes—
304C42×C29C2418yes—
305C42×C29C2418yes—
306#62863C2911yesmaximal, characteristic, direct product factor, Sylow
307C23×C29—24no—
308C23×C29—28no—
309C23×C29—28no—
310C23×C29—28no—
311C23×C29—42no—
312C23×C29—44no—
313C23×C29—44no—
314C23×C29—48no—
315C23×C29—44no—
316C23×C29—44no—
317C23×C29—44no—
318C23×C29—48no—
319C23×C29—416no—
320C23×C29—48no—
321C23×C29—416no—
322C23×C29—88no—
323C23×C29—816no—
324C23×C29H(5,𝔽2)14yes—
325C23×C29C2514yes—
326C23×C29C2518yes—
327C23×C29C2518yes—
328C23×C29C2511yescharacteristic
329C23×C29C2512yes—
330Q8×C29—48no—
331Q8×C29—48no—
332D4×C29—232no—
333D4×C29—216no—
334D4×C29—216no—
335D4×C29—48no—
336D4×C29—48no—
337D4×C29—48no—
338D4×C29—416no—
339D4×C29—416no—
340D4×C29—48no—
341D4×C29—416no—
342D4×C29—48no—
343D4×C29—416no—
344D4×C29—48no—
345D4×C29—416no—
346C2×C4×C29—28no—
347C2×C4×C29—28no—
348C2×C4×C29—48no—
349C2×C4×C29—44no—
350C2×C4×C29—42no—
351C2×C4×C29—44no—
352C2×C4×C29—48no—
353C2×C4×C29—44no—
354C2×C4×C29—42no—
355C2×C4×C29—48no—
356C2×C4×C29—416no—
357C2×C4×C29—48no—
358C2×C4×C29—44no—
359C2×C4×C29—416no—
360C2×C4×C29C2518yes—
361C2×C4×C29C2514yes—
362C2×C4×C29C2514yes—
363C2×C4×C29C2518yes—
364C2×C4×C29C2518yes—
365C2×C4×C29C2518yes—
366#3560C2×C2918yescomplemented
367#3558C2×C2918yescomplemented
368#3537C2×C2918yescomplemented
369#3534C2×C2918yescomplemented
370#3533C2×C2918yescomplemented
371#3532C2×C2918yescomplemented
372#3505C2×C2914yescomplemented
373#3496C2×C2914yescomplemented
374#3484C2×C2914yescomplemented
375C2×#538C2×C2912yescomplemented
376C2×#534C2×C2911yescharacteristic, complemented
377C22×C29—22no—
378C22×C29—22no—
379C22×C29—22no—
380C22×C29—28no—
381C22×C29—24no—
382C22×C29—28no—
383C22×C29—28no—
384C22×C29—216no—
385C22×C29—28no—
386C22×C29—28no—
387C22×C29—44no—
388C22×C29—48no—
389C22×C29—88no—
390C22×C29—88no—
391C22×C29—88no—
392C22×C29—816no—
393C22×C29—168no—
394C22×C29C2×H(5,𝔽2)12yes—
395C22×C29C2×H(5,𝔽2)14yes—
396C22×C29C2611yescharacteristic
397C4×C29—28no—
398C4×C29—28no—
399C4×C29—24no—
400C4×C29—28no—
401C4×C29—24no—
402C4×C29—28no—
403C2×H(5,𝔽2)C22×C2914yescomplemented
404C23×D4C22×C2912yescomplemented
405#563C22×C2918yescomplemented
406#562C22×C29116yescomplemented
407H(3,𝔽4)C22×C2918yescomplemented
408#560C22×C29116yescomplemented
409#560C22×C2918yescomplemented
410#560C22×C2918yescomplemented
411#559C22×C2918yescomplemented
412#553C22×C29116yescomplemented
413#553C22×C2918yescomplemented
414#553C22×C29116yescomplemented
415#552C22×C2918yescomplemented
416#551C22×C29116yescomplemented
417#551C22×C2918yescomplemented
418#551C22×C2918yescomplemented
419#548C22×C2918yescomplemented
420#547C22×C2918yescomplemented
421#547C22×C2918yescomplemented
422#546C22×C2918yescomplemented
423#546C22×C29116yescomplemented
424#546C22×C29116yescomplemented
425#546C22×C29116yescomplemented
426#546C22×C29116yescomplemented
427#546C22×C29116yescomplemented
428D42C22×C2918yescomplemented
429D42C22×C29116yescomplemented
430D42C22×C29116yescomplemented
431D42C22×C2918yescomplemented
432D42C22×C2918yescomplemented
433#542C22×C29116yescomplemented
434#540C22×C29116yescomplemented
435#539C22×C29116yescomplemented
436#539C22×C2918yescomplemented
437#538C22×C29116yescomplemented
438#538C22×C2918yescomplemented
439#538C22×C2918yescomplemented
440#538C22×C29116yescomplemented
441#538C22×C29116yescomplemented
442#538C22×C29116yescomplemented
443#538C22×C2918yescomplemented
444#537C22×C2918yescomplemented
445#535C22×C2918yescomplemented
446#535C22×C29116yescomplemented
447#534C22×C2918yescomplemented
448#534C22×C2918yescomplemented
449#534C22×C2918yescomplemented
450#534C22×C2918yescomplemented
451#534C22×C29116yescomplemented
452#534C22×C2918yescomplemented
453#532C22×C2918yescomplemented
454#529C22×C2918yescomplemented
455C2×#126C22×C2914yescomplemented
456C2×#124C22×C2914yescomplemented
457#525C22×C2918yescomplemented
458#525C22×C2918yescomplemented
459C2×#123C22×C2914yescomplemented
460C2×#123C22×C2914yescomplemented
461C2×C22⋊Q8C22×C2912yescomplemented
462C2×#121C22×C2914yescomplemented
463C2×#121C22×C2914yescomplemented
464C2×#121C22×C2912yescomplemented
465C2×#121C22×C2918yescomplemented
466C2×#120C22×C2914yescomplemented
467C2×#120C22×C2914yescomplemented
468C2×#120C22×C2918yescomplemented
469#518C22×C2914yescomplemented
470C2×C4×D4C22×C2914yescomplemented
471C22×C22⋊C4C22×C2911yescharacteristic, complemented
472C2×C29—22no—
473C2×C29—24no—
474C2×C29—44no—
475C2×C29—48no—
476C2×C29—48no—
477C2×C29C22×H(5,𝔽2)11yescharacteristic
478C2×C29H(7,𝔽2)12yes—
479C25C23×C2911yescharacteristic
480C25C23×C2912yes—
481H(5,𝔽2)—416no—
482C2×#41C23×C2918yes—
483C2×#41C23×C29116yescomplemented
484C2×#41C23×C2918yescomplemented
485C22×Q8C23×C2912yescomplemented
486C22×D4—48no—
487C22×D4C23×C2914yes—
488C22×D4C23×C2914yes—
489C22×D4C23×C2914yes—
490C22×D4C23×C2918yes—
491C22×D4C23×C29116yes—
492C22×D4C23×C2914yes—
493C22×D4C23×C2914yes—
494C22×D4C23×C2914yes—
495C22×D4C23×C29116yescomplemented
496C22×D4C23×C29116yescomplemented
497C22×D4C23×C2912yescomplemented
498C22×D4C23×C2918yescomplemented
499C23×C4C23×C2912yes—
500C23×C4C23×C2912yes—
501C23×C4C23×C2914yescomplemented
502C4⋊Q8C23×C2918yescomplemented
503#127C23×C2918yes—
504#127C23×C2918yes—
505#127C23×C2918yescomplemented
506#126C23×C29116yescomplemented
507#126C23×C29116yescomplemented
508#126C23×C29116yescomplemented
509#126C23×C29116yescomplemented
510#126C23×C29116yescomplemented
511#125C23×C2918yescomplemented
512#125C23×C29116yescomplemented
513#124C23×C2918yes—
514#124C23×C2918yes—
515#124C23×C29116yescomplemented
516#124C23×C29116yescomplemented
517#124C23×C2918yescomplemented
518#124C23×C29116yescomplemented
519#124C23×C29116yescomplemented
520#123C23×C29116yes—
521#123C23×C2918yes—
522#123C23×C2918yes—
523#123C23×C29116yes—
524#123C23×C2918yes—
525#123C23×C2918yes—
526#123C23×C29116yescomplemented
527#123C23×C29116yescomplemented
528#123C23×C29116yescomplemented
529#123C23×C29116yescomplemented
530#123C23×C29116yescomplemented
531#123C23×C29116yescomplemented
532#123C23×C29116yescomplemented
533#123C23×C29116yescomplemented
534C22⋊Q8C23×C2918yes—
535C22⋊Q8C23×C2918yescomplemented
536C22⋊Q8C23×C2918yescomplemented
537C22⋊Q8C23×C29116yescomplemented
538C22⋊Q8C23×C29116yescomplemented
539C22⋊Q8C23×C29116yescomplemented
540C22⋊Q8C23×C29116yescomplemented
541#121C23×C2918yes—
542#121C23×C2918yes—
543#121C23×C2918yes—
544#121C23×C2918yes—
545#121C23×C2918yes—
546#121C23×C29116yes—
547#121C23×C29116yes—
548#121C23×C29116yes—
549#121C23×C29116yes—
550#121C23×C2918yescomplemented
551#121C23×C29116yescomplemented
552#121C23×C29116yescomplemented
553#121C23×C29116yescomplemented
554#121C23×C2918yescomplemented
555#121C23×C29116yescomplemented
556#121C23×C2918yescomplemented
557#121C23×C2918yescomplemented
558#121C23×C29116yescomplemented
559#121C23×C29116yescomplemented
560#121C23×C29116yescomplemented
561#121C23×C29116yescomplemented
562#121C23×C29116yescomplemented
563#120C23×C29116yes—
564#120C23×C29116yes—
565#120C23×C2918yes—
566#120C23×C2918yes—
567#120C23×C29116yes—
568#120C23×C29116yes—
569#120C23×C2918yes—
570#120C23×C2918yes—
571#120C23×C29116yescomplemented
572#120C23×C29116yescomplemented
573#120C23×C29116yescomplemented
574#120C23×C29116yescomplemented
575#120C23×C29116yescomplemented
576C4×Q8C23×C2918yescomplemented
577C4×D4C23×C2918yes—
578C4×D4C23×C2918yes—
579C4×D4C23×C2918yescomplemented
580C4×D4C23×C2918yescomplemented
581C4×D4C23×C29116yescomplemented
582C4×D4C23×C29116yescomplemented
583C4×D4C23×C29116yescomplemented
584C4×D4C23×C29116yescomplemented
585C4×D4C23×C29116yescomplemented
586C4×D4C23×C2918yescomplemented
587C4×D4C23×C2918yescomplemented
588C4×D4C23×C2918yescomplemented
589C4×D4C23×C29116yescomplemented
590#117C23×C2918yes—
591#117C23×C2918yescomplemented
592#117C23×C29116yescomplemented
593C2×C4⋊C4C23×C2914yes—
594C2×C4⋊C4C23×C2914yescomplemented
595C2×C4⋊C4C23×C2914yescomplemented
596C2×C4⋊C4C23×C2912yescomplemented
597C2×C4⋊C4C23×C2918yescomplemented
598C2×C4⋊C4C23×C2912yescomplemented
599C2×C22⋊C4C23×C2914yes—
600C2×C22⋊C4C23×C2914yes—
601C2×C22⋊C4C23×C2914yes—
602C2×C22⋊C4C23×C2914yes—
603C2×C22⋊C4C23×C2918yes—
604C2×C22⋊C4C23×C2918yes—
605C2×C22⋊C4C23×C2914yes—
606C2×C22⋊C4C23×C2914yes—
607C2×C22⋊C4C23×C2914yescomplemented
608C2×C22⋊C4C23×C29116yescomplemented
609C2×C22⋊C4C23×C2914yescomplemented
610C2×C22⋊C4C23×C29116yescomplemented
611C2×C42C23×C2914yescomplemented
612C29#6286311yescharacteristic, direct product factor, Sylow
613C24—24no—
614C24—44no—
615C24—82no—
616C24—84no—
617C24C24×C2914yes—
618C24C24×C2914yes—
619C24C24×C2912yes—
620C24C24×C2914yes—
621C24C24×C2918yes—
622C24C24×C2918yes—
623C24C24×C2911yescharacteristic
624#41—416no—
625#41—432no—
626#41—88no—
627C2×Q8—82no—
628C2×Q8C24×C2918yes—
629C2×Q8C24×C2918yes—
630C2×D4—216no—
631C2×D4—216no—
632C2×D4—48no—
633C2×D4—432no—
634C2×D4—416no—
635C2×D4—432no—
636C2×D4—84no—
637C2×D4—84no—
638C2×D4—84no—
639C2×D4—82no—
640C2×D4—88no—
641C2×D4—816no—
642C2×D4C24×C2918yes—
643C2×D4C24×C2918yes—
644C2×D4C24×C29116yes—
645C2×D4C24×C2918yes—
646C2×D4C24×C2918yes—
647C2×D4C24×C29116yes—
648C2×D4C24×C29116yes—
649C2×D4C24×C29116yes—
650C2×D4C24×C29116yes—
651C2×D4C24×C2918yes—
652C2×D4C24×C2918yes—
653C2×D4C24×C2918yes—
654C2×D4C24×C29116yes—
655C2×D4C24×C2918yes—
656C22×C4—44no—
657C22×C4—82no—
658C22×C4—84no—
659C22×C4C24×C2914yes—
660C22×C4C24×C2914yes—
661C22×C4C24×C2914yes—
662C22×C4C24×C2914yes—
663C22×C4C24×C2914yes—
664C22×C4C24×C2912yes—
665C22×C4C24×C2912yes—
666C22×C4C24×C2914yes—
667C22×C4C24×C29116yes—
668C22×C4C24×C2918yes—
669C22×C4C24×C2918yes—
670C22×C4C24×C29116yes—
671C22×C4C24×C2918yes—
672C22×C4C24×C2918yes—
673C4⋊C4C24×C2918yes—
674C4⋊C4C24×C2918yes—
675C4⋊C4C24×C2918yes—
676C4⋊C4C24×C29116yes—
677C4⋊C4C24×C29116yes—
678C4⋊C4C24×C2918yes—
679C4⋊C4C24×C2918yes—
680C4⋊C4C24×C2918yes—
681C4⋊C4C24×C29116yes—
682C4⋊C4C24×C29116yes—
683C22⋊C4C24×C2918yes—
684C22⋊C4C24×C2914yes—
685C22⋊C4C24×C2918yes—
686C22⋊C4C24×C2914yes—
687C22⋊C4C24×C29116yes—
688C22⋊C4C24×C29116yes—
689C22⋊C4C24×C29116yes—
690C22⋊C4C24×C29116yes—
691C22⋊C4C24×C2918yes—
692C22⋊C4C24×C2918yes—
693C22⋊C4C24×C2918yes—
694C22⋊C4C24×C29116yes—
695C22⋊C4C24×C29116yes—
696C22⋊C4C24×C29116yes—
697C22⋊C4C24×C29116yes—
698C22⋊C4C24×C2918yes—
699C22⋊C4C24×C2918yes—
700C22⋊C4C24×C29116yes—
701C42C24×C2918yes—
702C42C24×C2918yes—
703C42C24×C2918yes—
704C42C24×C2918yes—
705C23—24no—
706C23—28no—
707C23—28no—
708C23—28no—
709C23—42no—
710C23—44no—
711C23—44no—
712C23—48no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—48no—
717C23—416no—
718C23—48no—
719C23—416no—
720C23—88no—
721C23—816no—
722C23C29×H(5,𝔽2)14yes—
723C23C25×C2914yes—
724C23C25×C2918yes—
725C23C25×C2918yes—
726C23C25×C2911yescharacteristic
727C23C25×C2912yes—
728Q8—48no—
729Q8—48no—
730D4—232no—
731D4—216no—
732D4—216no—
733D4—48no—
734D4—48no—
735D4—48no—
736D4—416no—
737D4—416no—
738D4—48no—
739D4—416no—
740D4—48no—
741D4—416no—
742D4—48no—
743D4—416no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—48no—
747C2×C4—44no—
748C2×C4—42no—
749C2×C4—44no—
750C2×C4—48no—
751C2×C4—44no—
752C2×C4—42no—
753C2×C4—48no—
754C2×C4—416no—
755C2×C4—48no—
756C2×C4—44no—
757C2×C4—416no—
758C2×C4C25×C2918yes—
759C2×C4C25×C2914yes—
760C2×C4C25×C2914yes—
761C2×C4C25×C2918yes—
762C2×C4C25×C2918yes—
763C2×C4C25×C2918yes—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—216no—
772C22—28no—
773C22—28no—
774C22—44no—
775C22—48no—
776C22—88no—
777C22—88no—
778C22—88no—
779C22—816no—
780C22—168no—
781C22C2×C29×H(5,𝔽2)12yes—
782C22C2×C29×H(5,𝔽2)14yes—
783C22C26×C2911yescharacteristic
784C4—28no—
785C4—28no—
786C4—24no—
787C4—28no—
788C4—24no—
789C4—28no—
790C2—22no—
791C2—24no—
792C2—44no—
793C2—48no—
794C2—48no—
795C2C22×C29×H(5,𝔽2)11yescharacteristic
796C2C29×H(7,𝔽2)12yes—
subgroupG/H
center, socleC22×C29C26
commutator, Frattini, cosocleC22C26×C29
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3560C2semidirect
2. C29×#3558C2semidirect
3. C29×#3537C2semidirect
4. C29×#3534C2semidirect
5. C29×#3533C2semidirect
6. C29×#3532C2semidirect
7. C29×#3505C2semidirect
8. C29×#3496C2semidirect
9. C29×#3484C2semidirect
10. C2×C29×#538C2semidirect
11. C2×C29×#534C2semidirect
12. C2×C29×H(5,𝔽2)C22semidirect
13. C23×D4×C29C22semidirect
14. C29×#563C22semidirect
15. C29×#562C22semidirect
16. C29×H(3,𝔽4)C22semidirect
17. C29×#560C22semidirect
18. C29×#560C22semidirect
19. C29×#560C22semidirect
20. C29×#559C22semidirect
21. C29×#553C22semidirect
22. C29×#553C22semidirect
23. C29×#553C22semidirect
24. C29×#552C22semidirect
25. C29×#551C22semidirect
26. C29×#551C22semidirect
27. C29×#551C22semidirect
28. C29×#548C22semidirect
29. C29×#547C22semidirect
30. C29×#547C22semidirect
31. C29×#546C22semidirect
32. C29×#546C22semidirect
33. C29×#546C22semidirect
34. C29×#546C22semidirect
35. C29×#546C22semidirect
36. C29×#546C22semidirect
37. D42×C29C22semidirect
38. D42×C29C22semidirect
39. D42×C29C22semidirect
40. D42×C29C22semidirect
41. D42×C29C22semidirect
42. C29×#542C22semidirect
43. C29×#540C22semidirect
44. C29×#539C22semidirect
45. C29×#539C22semidirect
46. C29×#538C22semidirect
47. C29×#538C22semidirect
48. C29×#538C22semidirect
49. C29×#538C22semidirect
50. C29×#538C22semidirect
51. C29×#538C22semidirect
52. C29×#538C22semidirect
53. C29×#537C22semidirect
54. C29×#535C22semidirect
55. C29×#535C22semidirect
56. C29×#534C22semidirect
57. C29×#534C22semidirect
58. C29×#534C22semidirect
59. C29×#534C22semidirect
60. C29×#534C22semidirect
61. C29×#534C22semidirect
62. C29×#532C22semidirect
63. C29×#529C22semidirect
64. C2×C29×#126C22semidirect
65. C2×C29×#124C22semidirect
66. C29×#525C22semidirect
67. C29×#525C22semidirect
68. C2×C29×#123C22semidirect
69. C2×C29×#123C22semidirect
70. C2×C29×C22⋊Q8C22semidirect
71. C2×C29×#121C22semidirect
72. C2×C29×#121C22semidirect
73. C2×C29×#121C22semidirect
74. C2×C29×#121C22semidirect
75. C2×C29×#120C22semidirect
76. C2×C29×#120C22semidirect
77. C2×C29×#120C22semidirect
78. C29×#518C22semidirect
79. C2×C4×D4×C29C22semidirect
80. C22×C22⋊C4×C29C22semidirect
85. C2×#41×C29C23semidirect
86. C2×#41×C29C23semidirect
87. C22×Q8×C29C23semidirect
97. C22×D4×C29C23semidirect
98. C22×D4×C29C23semidirect
99. C22×D4×C29C23semidirect
100. C22×D4×C29C23semidirect
103. C23×C4×C29C23semidirect
104. C29×C4⋊Q8C23semidirect
107. C29×#127C23semidirect
108. C29×#126C23semidirect
109. C29×#126C23semidirect
110. C29×#126C23semidirect
111. C29×#126C23semidirect
112. C29×#126C23semidirect
113. C29×#125C23semidirect
114. C29×#125C23semidirect
117. C29×#124C23semidirect
118. C29×#124C23semidirect
119. C29×#124C23semidirect
120. C29×#124C23semidirect
121. C29×#124C23semidirect
128. C29×#123C23semidirect
129. C29×#123C23semidirect
130. C29×#123C23semidirect
131. C29×#123C23semidirect
132. C29×#123C23semidirect
133. C29×#123C23semidirect
134. C29×#123C23semidirect
135. C29×#123C23semidirect
137. C29×C22⋊Q8C23semidirect
138. C29×C22⋊Q8C23semidirect
139. C29×C22⋊Q8C23semidirect
140. C29×C22⋊Q8C23semidirect
141. C29×C22⋊Q8C23semidirect
142. C29×C22⋊Q8C23semidirect
152. C29×#121C23semidirect
153. C29×#121C23semidirect
154. C29×#121C23semidirect
155. C29×#121C23semidirect
156. C29×#121C23semidirect
157. C29×#121C23semidirect
158. C29×#121C23semidirect
159. C29×#121C23semidirect
160. C29×#121C23semidirect
161. C29×#121C23semidirect
162. C29×#121C23semidirect
163. C29×#121C23semidirect
164. C29×#121C23semidirect
173. C29×#120C23semidirect
174. C29×#120C23semidirect
175. C29×#120C23semidirect
176. C29×#120C23semidirect
177. C29×#120C23semidirect
178. C4×Q8×C29C23semidirect
181. C4×D4×C29C23semidirect
182. C4×D4×C29C23semidirect
183. C4×D4×C29C23semidirect
184. C4×D4×C29C23semidirect
185. C4×D4×C29C23semidirect
186. C4×D4×C29C23semidirect
187. C4×D4×C29C23semidirect
188. C4×D4×C29C23semidirect
189. C4×D4×C29C23semidirect
190. C4×D4×C29C23semidirect
191. C4×D4×C29C23semidirect
193. C29×#117C23semidirect
194. C29×#117C23semidirect
196. C2×C4⋊C4×C29C23semidirect
197. C2×C4⋊C4×C29C23semidirect
198. C2×C4⋊C4×C29C23semidirect
199. C2×C4⋊C4×C29C23semidirect
200. C2×C4⋊C4×C29C23semidirect
209. C2×C22⋊C4×C29C23semidirect
210. C2×C22⋊C4×C29C23semidirect
211. C2×C22⋊C4×C29C23semidirect
212. C2×C22⋊C4×C29C23semidirect
213. C2×C42×C29C23semidirect
306. #62863C29direct (N × H)
366. #3560C2×C29semidirect
367. #3558C2×C29semidirect
368. #3537C2×C29semidirect
369. #3534C2×C29semidirect
370. #3533C2×C29semidirect
371. #3532C2×C29semidirect
372. #3505C2×C29semidirect
373. #3496C2×C29semidirect
374. #3484C2×C29semidirect
375. C2×#538C2×C29semidirect
376. C2×#534C2×C29semidirect
403. C2×H(5,𝔽2)C22×C29semidirect
404. C23×D4C22×C29semidirect
405. #563C22×C29semidirect
406. #562C22×C29semidirect
407. H(3,𝔽4)C22×C29semidirect
408. #560C22×C29semidirect
409. #560C22×C29semidirect
410. #560C22×C29semidirect
411. #559C22×C29semidirect
412. #553C22×C29semidirect
413. #553C22×C29semidirect
414. #553C22×C29semidirect
415. #552C22×C29semidirect
416. #551C22×C29semidirect
417. #551C22×C29semidirect
418. #551C22×C29semidirect
419. #548C22×C29semidirect
420. #547C22×C29semidirect
421. #547C22×C29semidirect
422. #546C22×C29semidirect
423. #546C22×C29semidirect
424. #546C22×C29semidirect
425. #546C22×C29semidirect
426. #546C22×C29semidirect
427. #546C22×C29semidirect
428. D42C22×C29semidirect
429. D42C22×C29semidirect
430. D42C22×C29semidirect
431. D42C22×C29semidirect
432. D42C22×C29semidirect
433. #542C22×C29semidirect
434. #540C22×C29semidirect
435. #539C22×C29semidirect
436. #539C22×C29semidirect
437. #538C22×C29semidirect
438. #538C22×C29semidirect
439. #538C22×C29semidirect
440. #538C22×C29semidirect
441. #538C22×C29semidirect
442. #538C22×C29semidirect
443. #538C22×C29semidirect
444. #537C22×C29semidirect
445. #535C22×C29semidirect
446. #535C22×C29semidirect
447. #534C22×C29semidirect
448. #534C22×C29semidirect
449. #534C22×C29semidirect
450. #534C22×C29semidirect
451. #534C22×C29semidirect
452. #534C22×C29semidirect
453. #532C22×C29semidirect
454. #529C22×C29semidirect
455. C2×#126C22×C29semidirect
456. C2×#124C22×C29semidirect
457. #525C22×C29semidirect
458. #525C22×C29semidirect
459. C2×#123C22×C29semidirect
460. C2×#123C22×C29semidirect
461. C2×C22⋊Q8C22×C29semidirect
462. C2×#121C22×C29semidirect
463. C2×#121C22×C29semidirect
464. C2×#121C22×C29semidirect
465. C2×#121C22×C29semidirect
466. C2×#120C22×C29semidirect
467. C2×#120C22×C29semidirect
468. C2×#120C22×C29semidirect
469. #518C22×C29semidirect
470. C2×C4×D4C22×C29semidirect
471. C22×C22⋊C4C22×C29semidirect
483. C2×#41C23×C29semidirect
484. C2×#41C23×C29semidirect
485. C22×Q8C23×C29semidirect
495. C22×D4C23×C29semidirect
496. C22×D4C23×C29semidirect
497. C22×D4C23×C29semidirect
498. C22×D4C23×C29semidirect
501. C23×C4C23×C29semidirect
502. C4⋊Q8C23×C29semidirect
505. #127C23×C29semidirect
506. #126C23×C29semidirect
507. #126C23×C29semidirect
508. #126C23×C29semidirect
509. #126C23×C29semidirect
510. #126C23×C29semidirect
511. #125C23×C29semidirect
512. #125C23×C29semidirect
515. #124C23×C29semidirect
516. #124C23×C29semidirect
517. #124C23×C29semidirect
518. #124C23×C29semidirect
519. #124C23×C29semidirect
526. #123C23×C29semidirect
527. #123C23×C29semidirect
528. #123C23×C29semidirect
529. #123C23×C29semidirect
530. #123C23×C29semidirect
531. #123C23×C29semidirect
532. #123C23×C29semidirect
533. #123C23×C29semidirect
535. C22⋊Q8C23×C29semidirect
536. C22⋊Q8C23×C29semidirect
537. C22⋊Q8C23×C29semidirect
538. C22⋊Q8C23×C29semidirect
539. C22⋊Q8C23×C29semidirect
540. C22⋊Q8C23×C29semidirect
550. #121C23×C29semidirect
551. #121C23×C29semidirect
552. #121C23×C29semidirect
553. #121C23×C29semidirect
554. #121C23×C29semidirect
555. #121C23×C29semidirect
556. #121C23×C29semidirect
557. #121C23×C29semidirect
558. #121C23×C29semidirect
559. #121C23×C29semidirect
560. #121C23×C29semidirect
561. #121C23×C29semidirect
562. #121C23×C29semidirect
571. #120C23×C29semidirect
572. #120C23×C29semidirect
573. #120C23×C29semidirect
574. #120C23×C29semidirect
575. #120C23×C29semidirect
576. C4×Q8C23×C29semidirect
579. C4×D4C23×C29semidirect
580. C4×D4C23×C29semidirect
581. C4×D4C23×C29semidirect
582. C4×D4C23×C29semidirect
583. C4×D4C23×C29semidirect
584. C4×D4C23×C29semidirect
585. C4×D4C23×C29semidirect
586. C4×D4C23×C29semidirect
587. C4×D4C23×C29semidirect
588. C4×D4C23×C29semidirect
589. C4×D4C23×C29semidirect
591. #117C23×C29semidirect
592. #117C23×C29semidirect
594. C2×C4⋊C4C23×C29semidirect
595. C2×C4⋊C4C23×C29semidirect
596. C2×C4⋊C4C23×C29semidirect
597. C2×C4⋊C4C23×C29semidirect
598. C2×C4⋊C4C23×C29semidirect
607. C2×C22⋊C4C23×C29semidirect
608. C2×C22⋊C4C23×C29semidirect
609. C2×C22⋊C4C23×C29semidirect
610. C2×C22⋊C4C23×C29semidirect
611. C2×C42C23×C29semidirect
612. C29#62863direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35602
C29×#35582
C29×#35372
C29×#35342
C29×#35332
C29×#35322
C29×#35052
C29×#34962
C29×#34842
C2×C29×#5382
C2×C29×#5342
#6286329