Finite Group Databasebeta

← C29×#18811 #20313711

Subgroups — C29×#18811 #20313711

Order 7424.

988 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3519C211yesmaximal, characteristic
2C29×#3252C211yesmaximal, characteristic, complemented
3C29×#3210C211yesmaximal, characteristic, complemented
4C29×#3077C211yesmaximal, characteristic, complemented
5C29×#1646C211yesmaximal, characteristic, complemented
6C29×#1644C211yesmaximal, characteristic, complemented
7C29×#1641C211yesmaximal, characteristic, complemented
8C29×#1639C211yesmaximal, characteristic, complemented
9C29×#1634C211yesmaximal, characteristic, complemented
10C29×#1632C211yesmaximal, characteristic, complemented
11C29×#1631C211yesmaximal, characteristic, complemented
12C29×#1629C211yesmaximal, characteristic, complemented
13C29×#1560C211yesmaximal, characteristic, complemented
14C29×#1495C211yesmaximal, characteristic, complemented
15C29×#1486C211yesmaximal, characteristic, complemented
16C29×#555C2211yescharacteristic
17C29×#554C2211yescharacteristic
18C29×#553—21no—
19C29×#553—21no—
20C29×#550C2211yescharacteristic
21C29×#546—22no—
22C29×#546—21no—
23D42×C29—21no—
24D42×C29C2211yescharacteristic
25C29×#540—21no—
26C29×#538—22no—
27C29×#533C2211yescharacteristic, complemented
28C29×#532C2211yescharacteristic
29C29×#529C2211yescharacteristic
30C29×#525—21no—
31C2×C29×#121—21no—
32C29×#518—21no—
33C2×C4×D4×C29C2211yescharacteristic
34C29×#494C2211yescharacteristic, complemented
35C29×#492C2211yescharacteristic, complemented
36C29×#487C2211yescharacteristic, complemented
37C29×#486C2211yescharacteristic, complemented
38C29×#479—21no—
39C29×#478—21no—
40C29×#478—21no—
41C29×#477C2211yescharacteristic, complemented
42C29×#476C2211yescharacteristic
43C29×#476C2211yescharacteristic, complemented
44C29×#476C2211yescharacteristic, complemented
45C29×#474C2211yescharacteristic
46C29×#474C2211yescharacteristic, complemented
47C29×#470—21no—
48C29×#468—21no—
49C29×#464—22no—
50C29×#464—21no—
51C29×#462C2211yescharacteristic, complemented
52C29×#461C2211yescharacteristic, complemented
53C29×#452—22no—
54C29×#431C2211yescharacteristic, complemented
55C29×#428—21no—
56C29×#423C2211yescharacteristic, complemented
57C29×#423C2211yescharacteristic, complemented
58C29×#418—21no—
59C29×#333C2211yescharacteristic, complemented
60C29×#333C2211yescharacteristic, complemented
61C29×#331C2211yescharacteristic, complemented
62C29×#331C2211yescharacteristic, complemented
63C29×Q8⋊C8C2211yescharacteristic, complemented
64C29×Q8⋊C8C2211yescharacteristic, complemented
65C29×D4⋊C8C2211yescharacteristic
66C29×D4⋊C8C2211yescharacteristic
67C29×D4⋊C8C2211yescharacteristic, complemented
68C29×D4⋊C8C2211yescharacteristic, complemented
69C29×D4⋊C8C2211yescharacteristic, complemented
70C29×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C29—21no—
72C2×#41×C29D412yes—
73C22×D4×C29—22no—
74C22×D4×C29—21no—
75C22×D4×C29—21no—
76C22×D4×C29D411yescharacteristic
77C23×C4×C29—21no—
78C2×Q16×C29—22no—
79C2×Q16×C29—21no—
80C2×SD16×C29—22no—
81C2×SD16×C29—21no—
82C2×M16×C29—21no—
83C2×M16×C29—21no—
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×C4⋊Q8C2311yescharacteristic
87C29×#127—21no—
88C29×#127C2311yescharacteristic
89C29×#126—22no—
90C29×#126—21no—
91C29×#125—21no—
92C29×#125—21no—
93C29×#125D411yescharacteristic
94C29×#124—22no—
95C29×#124D411yescharacteristic
96C29×#124D412yes—
97C29×#123—22no—
98C29×#123—22no—
99C29×#123—22no—
100C29×#123—21no—
101C29×C22⋊Q8—21no—
102C29×C22⋊Q8—22no—
103C29×C22⋊Q8—21no—
104C29×C22⋊Q8—21no—
105C29×C22⋊Q8D411yescharacteristic
106C29×#121—22no—
107C29×#121—22no—
108C29×#121—22no—
109C29×#121—22no—
110C29×#121—21no—
111C29×#121—22no—
112C29×#121—21no—
113C29×#121—21no—
114C29×#121—21no—
115C29×#121—21no—
116C29×#121—21no—
117C29×#121—21no—
118C29×#121D411yescharacteristic
119C29×#120—22no—
120C29×#120—22no—
121C29×#120—22no—
122C4×Q8×C29—21no—
123C4×Q8×C29—21no—
124C4×Q8×C29C2311yescharacteristic
125C4×D4×C29—22no—
126C4×D4×C29—22no—
127C4×D4×C29—22no—
128C4×D4×C29—21no—
129C4×D4×C29—21no—
130C4×D4×C29—21no—
131C4×D4×C29—21no—
132C4×D4×C29—21no—
133C4×D4×C29—21no—
134C4×D4×C29—21no—
135C4×D4×C29D411yescharacteristic
136C4×D4×C29D411yescharacteristic
137C4×D4×C29C2311yescharacteristic
138C4×D4×C29C2311yescharacteristic
139C4×D4×C29C2311yescharacteristic
140C29×#117—21no—
141C29×#117—21no—
142C29×#117—21no—
143C29×#117—21no—
144C2×C4⋊C4×C29—21no—
145C2×C4⋊C4×C29D411yescharacteristic
146C2×C22⋊C4×C29—22no—
147C2×C22⋊C4×C29—22no—
148C2×C22⋊C4×C29—21no—
149C2×C42×C29C2311yescharacteristic
150C29×#107—21no—
151C29×#107—21no—
152C29×#107—21no—
153C29×#106—21no—
154C29×#106—21no—
155C29×#106—21no—
156C29×C4⋊C8—21no—
157C29×C4⋊C8—21no—
158C29×C4⋊C8—21no—
159C29×C4⋊C8C2311yescharacteristic
160C29×C4⋊C8C2311yescharacteristic
161C29×C4⋊C8C2311yescharacteristic
162C29×C4⋊C8C2311yescharacteristic
163C29×#103—22no—
164C29×#103—21no—
165C29×#103—21no—
166C29×#103—21no—
167C29×#102—22no—
168C29×#102—21no—
169C29×#102—21no—
170C29×#102—21no—
171C29×#102—21no—
172C29×#102—21no—
173C29×C22⋊C8—21no—
174C4×C8×C29C2311yescharacteristic
175C4×C8×C29C2311yescharacteristic
176C24×C29—22no—
177C24×C29—21no—
178#41×C29—81no—
179#41×C29—81no—
180#41×C29—82no—
181C2×Q8×C29—21no—
182C2×Q8×C29—21no—
183C2×Q8×C29C2×D411yescharacteristic
184C2×Q8×C29C2×D412yes—
185C2×D4×C29—22no—
186C2×D4×C29—22no—
187C2×D4×C29—22no—
188C2×D4×C29—21no—
189C2×D4×C29—22no—
190C2×D4×C29—22no—
191C2×D4×C29—22no—
192C2×D4×C29—22no—
193C2×D4×C29—21no—
194C2×D4×C29—21no—
195C2×D4×C29—21no—
196C2×D4×C29—41no—
197C2×D4×C29—42no—
198C2×D4×C29—42no—
199C2×D4×C29—81no—
200C2×D4×C29—81no—
201C2×D4×C29—84no—
202C2×D4×C29C2×D411yescharacteristic
203C2×D4×C29C2×D411yescharacteristic
204C2×D4×C29C2×D411yescharacteristic
205C2×D4×C29C2×D412yes—
206C22×C4×C29—22no—
207C22×C4×C29—22no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29—21no—
212C22×C4×C29—21no—
213C22×C4×C29—22no—
214C22×C4×C29—21no—
215C22×C4×C29—81no—
216C22×C4×C29—81no—
217C22×C4×C29C2×D411yescharacteristic
218C22×C4×C29C2×D411yescharacteristic
219C22×C4×C29C2×D411yescharacteristic
220Q16×C29—81no—
221Q16×C29—82no—
222SD16×C29—81no—
223SD16×C29—82no—
224M16×C29—42no—
225M16×C29—81no—
226C2×C8×C29—21no—
227C2×C8×C29—21no—
228C2×C8×C29—21no—
229C2×C8×C29—21no—
230C2×C8×C29—21no—
231C2×C8×C29—21no—
232C4⋊C4×C29—22no—
233C4⋊C4×C29—22no—
234C4⋊C4×C29—21no—
235C4⋊C4×C29—21no—
236C4⋊C4×C29—21no—
237C4⋊C4×C29—21no—
238C4⋊C4×C29—21no—
239C4⋊C4×C29—21no—
240C4⋊C4×C29—21no—
241C4⋊C4×C29—21no—
242C4⋊C4×C29—21no—
243C4⋊C4×C29—21no—
244C4⋊C4×C29—21no—
245C4⋊C4×C29—41no—
246C4⋊C4×C29—41no—
247C4⋊C4×C29C2×D411yescharacteristic
248C4⋊C4×C29C2×D411yescharacteristic
249C4⋊C4×C29C2×D411yescharacteristic
250C4⋊C4×C29C2×D411yescharacteristic
251C22⋊C4×C29—22no—
252C22⋊C4×C29—22no—
253C22⋊C4×C29—22no—
254C22⋊C4×C29—22no—
255C22⋊C4×C29—22no—
256C22⋊C4×C29—21no—
257C22⋊C4×C29—21no—
258C22⋊C4×C29—21no—
259C22⋊C4×C29—21no—
260C22⋊C4×C29—22no—
261C22⋊C4×C29—21no—
262C22⋊C4×C29—21no—
263C22⋊C4×C29—22no—
264C22⋊C4×C29—21no—
265C22⋊C4×C29—21no—
266C22⋊C4×C29—21no—
267C22⋊C4×C29—41no—
268C42×C29—22no—
269C42×C29—21no—
270C42×C29—41no—
271C42×C29C2×D411yescharacteristic
272C42×C29C2×D411yescharacteristic
273C42×C29C2×D411yescharacteristic
274C42×C29C2411yescharacteristic
275#18811C2911yesmaximal, characteristic, direct product factor, Sylow
276C23×C29—21no—
277C23×C29—21no—
278C23×C29—21no—
279C23×C29—22no—
280C23×C29—42no—
281C23×C29—42no—
282C23×C29—44no—
283C23×C29—81no—
284C23×C29—82no—
285C23×C29—82no—
286C23×C29#12011yescharacteristic
287Q8×C29—21no—
288Q8×C29—21no—
289Q8×C29—42no—
290Q8×C29—42no—
291Q8×C29—41no—
292Q8×C29—41no—
293D4×C29—21no—
294D4×C29—21no—
295D4×C29—21no—
296D4×C29—21no—
297D4×C29—21no—
298D4×C29—42no—
299D4×C29—42no—
300D4×C29—44no—
301D4×C29—42no—
302D4×C29—44no—
303D4×C29—41no—
304D4×C29—41no—
305D4×C29—41no—
306D4×C29—41no—
307D4×C29—82no—
308D4×C29—82no—
309D4×C29—82no—
310D4×C29—82no—
311D4×C29#13712yes—
312C2×C4×C29—21no—
313C2×C4×C29—21no—
314C2×C4×C29—21no—
315C2×C4×C29—21no—
316C2×C4×C29—21no—
317C2×C4×C29—21no—
318C2×C4×C29—21no—
319C2×C4×C29—22no—
320C2×C4×C29—21no—
321C2×C4×C29—21no—
322C2×C4×C29—41no—
323C2×C4×C29—41no—
324C2×C4×C29—41no—
325C2×C4×C29—41no—
326C2×C4×C29—41no—
327C2×C4×C29—41no—
328C2×C4×C29—41no—
329C2×C4×C29—41no—
330C2×C4×C29—41no—
331C2×C4×C29—81no—
332C2×C4×C29—81no—
333C2×C4×C29—82no—
334C2×C4×C29—81no—
335C2×C4×C29—82no—
336C2×C4×C29—82no—
337C2×C4×C29#12011yescharacteristic
338C2×C4×C29#12011yescharacteristic
339C2×C4×C29#12011yescharacteristic
340C2×C4×C29C22×D411yescharacteristic
341C2×C4×C29C22×D411yescharacteristic
342C2×C4×C29C22×D411yescharacteristic
343C8×C29—41no—
344C8×C29—41no—
345C8×C29—41no—
346C8×C29—41no—
347C8×C29—41no—
348C8×C29—41no—
349#3519C2×C2911yescharacteristic
350#3252C2×C2911yescharacteristic, complemented
351#3210C2×C2911yescharacteristic, complemented
352#3077C2×C2911yescharacteristic, complemented
353#1646C2×C2911yescharacteristic, complemented
354#1644C2×C2911yescharacteristic, complemented
355#1641C2×C2911yescharacteristic, complemented
356#1639C2×C2911yescharacteristic, complemented
357#1634C2×C2911yescharacteristic, complemented
358#1632C2×C2911yescharacteristic, complemented
359#1631C2×C2911yescharacteristic, complemented
360#1629C2×C2911yescharacteristic, complemented
361#1560C2×C2911yescharacteristic, complemented
362#1495C2×C2911yescharacteristic, complemented
363#1486C2×C2911yescharacteristic, complemented
364C22×C29—21no—
365C22×C29—22no—
366C22×C29—21no—
367C22×C29—21no—
368C22×C29—41no—
369C22×C29—41no—
370C22×C29—41no—
371C22×C29—41no—
372C22×C29—42no—
373C22×C29—41no—
374C22×C29—42no—
375C22×C29—41no—
376C22×C29—42no—
377C22×C29—41no—
378C22×C29—41no—
379C22×C29—84no—
380C22×C29—164no—
381C22×C29C2×#12011yescharacteristic
382C4×C29—21no—
383C4×C29—21no—
384C4×C29—21no—
385C4×C29—21no—
386C4×C29—41no—
387C4×C29—41no—
388C4×C29—41no—
389C4×C29—41no—
390C4×C29—41no—
391C4×C29—42no—
392C4×C29—81no—
393C4×C29—81no—
394C4×C29C2×#13711yescharacteristic
395C4×C29#57511yescharacteristic
396C4×C29#57611yescharacteristic
397C4×C29#57711yescharacteristic
398#555C22×C2911yescharacteristic
399#554C22×C2911yescharacteristic
400#553—21no—
401#553—21no—
402#550C22×C2911yescharacteristic
403#546—22no—
404#546—21no—
405D42—21no—
406D42C22×C2911yescharacteristic
407#540—21no—
408#538—22no—
409#533C22×C2911yescharacteristic, complemented
410#532C22×C2911yescharacteristic
411#529C22×C2911yescharacteristic
412#525—21no—
413C2×#121—21no—
414#518—21no—
415C2×C4×D4C22×C2911yescharacteristic
416#494C22×C2911yescharacteristic, complemented
417#492C22×C2911yescharacteristic, complemented
418#487C22×C2911yescharacteristic, complemented
419#486C22×C2911yescharacteristic, complemented
420#479—21no—
421#478—21no—
422#478—21no—
423#477C22×C2911yescharacteristic, complemented
424#476C22×C2911yescharacteristic
425#476C22×C2911yescharacteristic, complemented
426#476C22×C2911yescharacteristic, complemented
427#474C22×C2911yescharacteristic
428#474C22×C2911yescharacteristic, complemented
429#470—21no—
430#468—21no—
431#464—22no—
432#464—21no—
433#462C22×C2911yescharacteristic, complemented
434#461C22×C2911yescharacteristic, complemented
435#452—22no—
436#431C22×C2911yescharacteristic, complemented
437#428—21no—
438#423C22×C2911yescharacteristic, complemented
439#423C22×C2911yescharacteristic, complemented
440#418—21no—
441#333C22×C2911yescharacteristic, complemented
442#333C22×C2911yescharacteristic, complemented
443#331C22×C2911yescharacteristic, complemented
444#331C22×C2911yescharacteristic, complemented
445Q8⋊C8C22×C2911yescharacteristic, complemented
446Q8⋊C8C22×C2911yescharacteristic, complemented
447D4⋊C8C22×C2911yescharacteristic
448D4⋊C8C22×C2911yescharacteristic
449D4⋊C8C22×C2911yescharacteristic, complemented
450D4⋊C8C22×C2911yescharacteristic, complemented
451D4⋊C8C22×C2911yescharacteristic, complemented
452D4⋊C8C22×C2911yescharacteristic, complemented
453C2×C29—41no—
454C2×C29—42no—
455C2×C29—81no—
456C2×C29—82no—
457C2×C29—81no—
458C2×C29#300711yescharacteristic
459C2×C29#301211yescharacteristic
460C2×C29#301911yescharacteristic
461C2×#41—21no—
462C2×#41D4×C2912yes—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—21no—
466C22×D4D4×C2911yescharacteristic
467C23×C4—21no—
468C2×Q16—22no—
469C2×Q16—21no—
470C2×SD16—22no—
471C2×SD16—21no—
472C2×M16—21no—
473C2×M16—21no—
474C4⋊Q8C23×C2911yescharacteristic
475C4⋊Q8C23×C2911yescharacteristic
476C4⋊Q8C23×C2911yescharacteristic
477#127—21no—
478#127C23×C2911yescharacteristic
479#126—22no—
480#126—21no—
481#125—21no—
482#125—21no—
483#125D4×C2911yescharacteristic
484#124—22no—
485#124D4×C2911yescharacteristic
486#124D4×C2912yes—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—21no—
491C22⋊Q8—21no—
492C22⋊Q8—22no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8D4×C2911yescharacteristic
496#121—22no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—21no—
501#121—22no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121D4×C2911yescharacteristic
509#120—22no—
510#120—22no—
511#120—22no—
512C4×Q8—21no—
513C4×Q8—21no—
514C4×Q8C23×C2911yescharacteristic
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C2911yescharacteristic
526C4×D4D4×C2911yescharacteristic
527C4×D4C23×C2911yescharacteristic
528C4×D4C23×C2911yescharacteristic
529C4×D4C23×C2911yescharacteristic
530#117—21no—
531#117—21no—
532#117—21no—
533#117—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4D4×C2911yescharacteristic
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—21no—
539C2×C42C23×C2911yescharacteristic
540#107—21no—
541#107—21no—
542#107—21no—
543#106—21no—
544#106—21no—
545#106—21no—
546C4⋊C8—21no—
547C4⋊C8—21no—
548C4⋊C8—21no—
549C4⋊C8C23×C2911yescharacteristic
550C4⋊C8C23×C2911yescharacteristic
551C4⋊C8C23×C2911yescharacteristic
552C4⋊C8C23×C2911yescharacteristic
553#103—22no—
554#103—21no—
555#103—21no—
556#103—21no—
557#102—21no—
558#102—21no—
559#102—21no—
560#102—21no—
561#102—22no—
562#102—21no—
563C22⋊C8—21no—
564C4×C8C23×C2911yescharacteristic
565C4×C8C23×C2911yescharacteristic
566C29#1881111yescharacteristic, direct product factor, Sylow
567C24—22no—
568C24—21no—
569#41—81no—
570#41—81no—
571#41—82no—
572C2×Q8—21no—
573C2×Q8—21no—
574C2×Q8C2×D4×C2911yescharacteristic
575C2×Q8C2×D4×C2912yes—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—84no—
593C2×D4C2×D4×C2911yescharacteristic
594C2×D4C2×D4×C2911yescharacteristic
595C2×D4C2×D4×C2911yescharacteristic
596C2×D4C2×D4×C2912yes—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C2911yescharacteristic
609C22×C4C2×D4×C2911yescharacteristic
610C22×C4C2×D4×C2911yescharacteristic
611Q16—81no—
612Q16—82no—
613SD16—81no—
614SD16—82no—
615M16—42no—
616M16—81no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C4⋊C4—22no—
624C4⋊C4—22no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—41no—
637C4⋊C4—41no—
638C4⋊C4C2×D4×C2911yescharacteristic
639C4⋊C4C2×D4×C2911yescharacteristic
640C4⋊C4C2×D4×C2911yescharacteristic
641C4⋊C4C2×D4×C2911yescharacteristic
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—22no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—41no—
659C42—22no—
660C42—21no—
661C42—41no—
662C42C2×D4×C2911yescharacteristic
663C42C2×D4×C2911yescharacteristic
664C42C2×D4×C2911yescharacteristic
665C42C24×C2911yescharacteristic
666C23—21no—
667C23—21no—
668C23—21no—
669C23—22no—
670C23—42no—
671C23—42no—
672C23—44no—
673C23—81no—
674C23—82no—
675C23—82no—
676C23C29×#12011yescharacteristic
677Q8—21no—
678Q8—21no—
679Q8—42no—
680Q8—42no—
681Q8—41no—
682Q8—41no—
683D4—21no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—21no—
688D4—42no—
689D4—42no—
690D4—44no—
691D4—42no—
692D4—44no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—82no—
698D4—82no—
699D4—82no—
700D4—82no—
701D4C29×#13712yes—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4—82no—
724C2×C4—81no—
725C2×C4—82no—
726C2×C4—82no—
727C2×C4C29×#12011yescharacteristic
728C2×C4C29×#12011yescharacteristic
729C2×C4C29×#12011yescharacteristic
730C2×C4C22×D4×C2911yescharacteristic
731C2×C4C22×D4×C2911yescharacteristic
732C2×C4C22×D4×C2911yescharacteristic
733C8—41no—
734C8—41no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—41no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—42no—
748C22—41no—
749C22—42no—
750C22—41no—
751C22—42no—
752C22—41no—
753C22—41no—
754C22—84no—
755C22—164no—
756C22C2×C29×#12011yescharacteristic
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4C2×C29×#13711yescharacteristic
770C4C29×#57511yescharacteristic
771C4C29×#57611yescharacteristic
772C4C29×#57711yescharacteristic
773C2—41no—
774C2—42no—
775C2—81no—
776C2—81no—
777C2—82no—
778C2C29×#300711yescharacteristic
779C2C29×#301211yescharacteristic
780C2C29×#301911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3519C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3252C2semidirect
3. C29×#3210C2semidirect
4. C29×#3077C2semidirect
5. C29×#1646C2semidirect
6. C29×#1644C2semidirect
7. C29×#1641C2semidirect
8. C29×#1639C2semidirect
9. C29×#1634C2semidirect
10. C29×#1632C2semidirect
11. C29×#1631C2semidirect
12. C29×#1629C2semidirect
13. C29×#1560C2semidirect
14. C29×#1495C2semidirect
15. C29×#1486C2semidirect
27. C29×#533C22semidirect
34. C29×#494C22semidirect
35. C29×#492C22semidirect
36. C29×#487C22semidirect
37. C29×#486C22semidirect
41. C29×#477C22semidirect
43. C29×#476C22semidirect
44. C29×#476C22semidirect
46. C29×#474C22semidirect
51. C29×#462C22semidirect
52. C29×#461C22semidirect
54. C29×#431C22semidirect
56. C29×#423C22semidirect
57. C29×#423C22semidirect
59. C29×#333C22semidirect
60. C29×#333C22semidirect
61. C29×#331C22semidirect
62. C29×#331C22semidirect
63. C29×Q8⋊C8C22semidirect
64. C29×Q8⋊C8C22semidirect
67. C29×D4⋊C8C22semidirect
68. C29×D4⋊C8C22semidirect
69. C29×D4⋊C8C22semidirect
70. C29×D4⋊C8C22semidirect
275. #18811C29direct (N × H)
350. #3252C2×C29semidirect
351. #3210C2×C29semidirect
352. #3077C2×C29semidirect
353. #1646C2×C29semidirect
354. #1644C2×C29semidirect
355. #1641C2×C29semidirect
356. #1639C2×C29semidirect
357. #1634C2×C29semidirect
358. #1632C2×C29semidirect
359. #1631C2×C29semidirect
360. #1629C2×C29semidirect
361. #1560C2×C29semidirect
362. #1495C2×C29semidirect
363. #1486C2×C29semidirect
409. #533C22×C29semidirect
416. #494C22×C29semidirect
417. #492C22×C29semidirect
418. #487C22×C29semidirect
419. #486C22×C29semidirect
423. #477C22×C29semidirect
425. #476C22×C29semidirect
426. #476C22×C29semidirect
428. #474C22×C29semidirect
433. #462C22×C29semidirect
434. #461C22×C29semidirect
436. #431C22×C29semidirect
438. #423C22×C29semidirect
439. #423C22×C29semidirect
441. #333C22×C29semidirect
442. #333C22×C29semidirect
443. #331C22×C29semidirect
444. #331C22×C29semidirect
445. Q8⋊C8C22×C29semidirect
446. Q8⋊C8C22×C29semidirect
449. D4⋊C8C22×C29semidirect
450. D4⋊C8C22×C29semidirect
451. D4⋊C8C22×C29semidirect
452. D4⋊C8C22×C29semidirect
566. C29#18811direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35192
C29×#32522
C29×#32102
C29×#30772
C29×#16462
C29×#16442
C29×#16412
C29×#16392
C29×#16342
C29×#16322
C29×#16312
C29×#16292
C29×#15602
C29×#14952
C29×#14862
#1881129