Finite Group Databasebeta

← C29×#19071 #20313971

Subgroups — C29×#19071 #20313971

Order 7424.

810 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3553C211yesmaximal, characteristic
2C29×#3240C211yesmaximal, characteristic, complemented
3C29×#3236C211yesmaximal, characteristic, complemented
4C29×#3172C211yesmaximal, characteristic, complemented
5C29×#1664C211yesmaximal, characteristic, complemented
6C29×#1664C211yesmaximal, characteristic, complemented
7C29×#1664C211yesmaximal, characteristic, complemented
8C29×#1663C211yesmaximal, characteristic, complemented
9C29×#1663C211yesmaximal, characteristic, complemented
10C29×#1662C211yesmaximal, characteristic, complemented
11C29×#1661C211yesmaximal, characteristic, complemented
12C29×#1660C211yesmaximal, characteristic, complemented
13C29×#1535C211yesmaximal, characteristic, complemented
14C29×#1529C211yesmaximal, characteristic, complemented
15C29×#1528C211yesmaximal, characteristic, complemented
16C29×#564C2211yescharacteristic
17C29×#563C2211yescharacteristic
18C29×#563C2211yescharacteristic
19C29×#562C2211yescharacteristic
20C29×#554—21no—
21C29×#554—21no—
22C29×#553—21no—
23C29×#553—21no—
24C29×#552—21no—
25C29×#552—21no—
26C29×#541—21no—
27C29×#541—21no—
28C29×#539—21no—
29C29×#539—21no—
30C29×#539—21no—
31C29×#539—21no—
32C29×#533C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C29×#529C2211yescharacteristic
35C2×C29×#125C2211yescharacteristic
36C29×#501C2211yescharacteristic
37C29×#501C2211yescharacteristic
38C29×#501C2211yescharacteristic
39C29×#501C2211yescharacteristic
40C29×#501C2211yescharacteristic
41C29×#497C2211yescharacteristic
42C29×#491C2211yescharacteristic
43C29×#491C2211yescharacteristic
44C29×#491C2211yescharacteristic
45C29×#489C2211yescharacteristic
46C29×#489C2211yescharacteristic
47C29×#489C2211yescharacteristic
48C29×#485—21no—
49C29×#484—21no—
50C29×#483—21no—
51C29×#482—21no—
52C29×#479—21no—
53C29×#479—21no—
54C29×#479—21no—
55C29×#478—21no—
56C29×#470—21no—
57C29×#468—21no—
58C4×Q16×C29—21no—
59C4×SD16×C29—21no—
60C29×#432C2211yescharacteristic
61C29×#432C2211yescharacteristic
62C4×M16×C29C2211yescharacteristic
63C29×#330C2211yescharacteristic
64C29×#330C2211yescharacteristic
65C29×#330C2211yescharacteristic
66C29×#330C2211yescharacteristic
67C29×#330C2211yescharacteristic
68C29×#330C2211yescharacteristic
69C29×#330C2211yescharacteristic
70C29×#330C2211yescharacteristic
71C29×#329C2211yescharacteristic
72C29×#329C2211yescharacteristic
73C29×#329C2211yescharacteristic
74C29×#329C2211yescharacteristic
75C2×Q16×C29—21no—
76C2×SD16×C29—21no—
77C2×M16×C29—21no—
78C29×C4⋊Q8—21no—
79C29×C4⋊Q8—21no—
80C29×C4⋊Q8C2311yescharacteristic
81C29×C4⋊Q8C2311yescharacteristic
82C29×#126—21no—
83C29×#126—21no—
84C29×#126—21no—
85C29×#126—21no—
86C29×#126—21no—
87C29×#126—21no—
88C29×#126—21no—
89C29×#126—21no—
90C29×#126—21no—
91C29×#126—21no—
92C29×#125—21no—
93C29×#125—21no—
94C29×#125—21no—
95C29×#125—21no—
96C29×#125—21no—
97C29×#125—21no—
98C29×#125—21no—
99C29×#125—21no—
100C29×#125—21no—
101C29×#125—21no—
102C29×#125—21no—
103C29×#125—21no—
104C29×#125—21no—
105C29×#125D411yescharacteristic
106C29×#125D411yescharacteristic
107C29×#125C2311yescharacteristic
108C29×#125C2311yescharacteristic
109C29×#125C2311yescharacteristic
110C29×#125C2311yescharacteristic
111C29×#124C2311yescharacteristic
112C29×#124C2311yescharacteristic
113C29×#123—21no—
114C29×#123—21no—
115C29×#123—21no—
116C29×#123—21no—
117C29×#123—21no—
118C29×#123—21no—
119C29×#123—21no—
120C29×#123—21no—
121C29×#123—21no—
122C29×#123—21no—
123C29×C22⋊Q8—21no—
124C29×C22⋊Q8—21no—
125C29×C22⋊Q8—21no—
126C29×C22⋊Q8—21no—
127C29×C22⋊Q8—21no—
128C29×C22⋊Q8—21no—
129C29×C22⋊Q8—21no—
130C29×C22⋊Q8—21no—
131C29×C22⋊Q8—21no—
132C29×C22⋊Q8—21no—
133C29×C22⋊Q8—21no—
134C29×C22⋊Q8—21no—
135C29×C22⋊Q8—21no—
136C29×C22⋊Q8—21no—
137C29×C22⋊Q8D411yescharacteristic
138C29×C22⋊Q8D411yescharacteristic
139C29×#121—21no—
140C29×#121—21no—
141C29×#121—21no—
142C29×#121—21no—
143C29×#121D411yescharacteristic
144C29×#121D411yescharacteristic
145C4×Q8×C29—21no—
146C4×Q8×C29—21no—
147C4×Q8×C29—21no—
148C4×Q8×C29—21no—
149C4×Q8×C29D411yescharacteristic
150C4×Q8×C29D411yescharacteristic
151C4×D4×C29—21no—
152C4×D4×C29—21no—
153C4×D4×C29—21no—
154C4×D4×C29—21no—
155C4×D4×C29—21no—
156C4×D4×C29—21no—
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29D411yescharacteristic
160C4×D4×C29D411yescharacteristic
161C29×#117—21no—
162C29×#117—21no—
163C29×#117—21no—
164C29×#117—21no—
165C29×#117—21no—
166C2×C4⋊C4×C29—21no—
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29—21no—
170C2×C4⋊C4×C29D411yescharacteristic
171C2×C4⋊C4×C29D411yescharacteristic
172C2×C42×C29C2311yescharacteristic
173C29×#107—21no—
174C29×#107—21no—
175C29×#107—21no—
176C29×#107—21no—
177C29×#107—21no—
178C29×#106—21no—
179C29×#106—21no—
180C29×#106—21no—
181C29×#106—21no—
182C29×#106—21no—
183C29×C4⋊C8—21no—
184C29×C4⋊C8—21no—
185C29×#103—21no—
186C29×#103—21no—
187C29×#103—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#103—21no—
193C29×#103—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×#102—21no—
197C29×C22⋊C8—21no—
198C29×C22⋊C8—21no—
199C29×#97C2311yescharacteristic
200C29×#97C2311yescharacteristic
201C29×#97C2311yescharacteristic
202C29×#97C2311yescharacteristic
203C29×#97C2311yescharacteristic
204C29×#97C2311yescharacteristic
205C4×C8×C29—21no—
206C2×Q8×C29—21no—
207C2×Q8×C29—21no—
208C2×Q8×C29—21no—
209C2×Q8×C29—21no—
210C2×Q8×C29C2×D411yescharacteristic
211C2×Q8×C29C2×D411yescharacteristic
212C2×D4×C29—21no—
213C2×D4×C29—21no—
214C2×D4×C29—21no—
215C2×D4×C29—21no—
216C2×D4×C29C2×D411yescharacteristic
217C2×D4×C29C2×D411yescharacteristic
218C22×C4×C29—21no—
219C22×C4×C29—21no—
220C22×C4×C29—21no—
221C22×C4×C29—21no—
222C22×C4×C29—21no—
223C22×C4×C29—21no—
224C22×C4×C29—21no—
225C22×C4×C29—21no—
226C22×C4×C29C2×D411yescharacteristic
227C22×C4×C29C2×D411yescharacteristic
228C22×C4×C29C2×D411yescharacteristic
229Q16×C29—42no—
230SD16×C29—42no—
231M16×C29—42no—
232C2×C8×C29—21no—
233C2×C8×C29—21no—
234C2×C8×C29—21no—
235C2×C8×C29—21no—
236C2×C8×C29—21no—
237C2×C8×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—21no—
246C4⋊C4×C29—21no—
247C4⋊C4×C29—21no—
248C4⋊C4×C29—21no—
249C4⋊C4×C29—21no—
250C4⋊C4×C29—21no—
251C4⋊C4×C29—21no—
252C4⋊C4×C29—21no—
253C4⋊C4×C29—21no—
254C4⋊C4×C29—21no—
255C4⋊C4×C29—21no—
256C4⋊C4×C29—21no—
257C4⋊C4×C29—21no—
258C4⋊C4×C29—21no—
259C4⋊C4×C29—21no—
260C4⋊C4×C29—21no—
261C4⋊C4×C29—21no—
262C4⋊C4×C29—21no—
263C4⋊C4×C29—21no—
264C4⋊C4×C29—21no—
265C4⋊C4×C29—21no—
266C4⋊C4×C29—21no—
267C4⋊C4×C29—21no—
268C4⋊C4×C29—21no—
269C4⋊C4×C29—21no—
270C4⋊C4×C29—21no—
271C4⋊C4×C29—21no—
272C4⋊C4×C29—41no—
273C4⋊C4×C29—41no—
274C4⋊C4×C29C2×D411yescharacteristic
275C4⋊C4×C29C2×D411yescharacteristic
276C4⋊C4×C29C2×D411yescharacteristic
277C4⋊C4×C29C2×D411yescharacteristic
278C4⋊C4×C29C2×D411yescharacteristic
279C4⋊C4×C29C2×D411yescharacteristic
280C4⋊C4×C29C2×D411yescharacteristic
281C4⋊C4×C29C2×D411yescharacteristic
282C22⋊C4×C29—21no—
283C22⋊C4×C29—21no—
284C22⋊C4×C29—21no—
285C22⋊C4×C29—21no—
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
288C22⋊C4×C29—21no—
289C22⋊C4×C29—21no—
290C22⋊C4×C29—21no—
291C22⋊C4×C29—21no—
292C22⋊C4×C29—21no—
293C22⋊C4×C29—21no—
294C22⋊C4×C29—21no—
295C22⋊C4×C29—21no—
296C22⋊C4×C29—21no—
297C22⋊C4×C29—21no—
298C22⋊C4×C29—21no—
299C22⋊C4×C29—21no—
300C22⋊C4×C29—41no—
301C42×C29—21no—
302C42×C29—21no—
303C42×C29—21no—
304C42×C29—21no—
305C42×C29—21no—
306C42×C29—21no—
307C42×C29—41no—
308C42×C29C2×D411yescharacteristic
309C42×C29C2×D411yescharacteristic
310C42×C29C2×D411yescharacteristic
311C42×C29C2411yescharacteristic
312#19071C2911yesmaximal, characteristic, direct product factor, Sylow
313C23×C29—21no—
314C23×C29—21no—
315C23×C29#12011yescharacteristic
316Q8×C29—41no—
317Q8×C29—41no—
318Q8×C29—41no—
319Q8×C29—41no—
320Q8×C29—42no—
321Q8×C29—81no—
322Q8×C29—81no—
323D4×C29—41no—
324D4×C29—41no—
325D4×C29—42no—
326D4×C29—42no—
327D4×C29—81no—
328D4×C29—81no—
329C2×C4×C29—21no—
330C2×C4×C29—21no—
331C2×C4×C29—21no—
332C2×C4×C29—21no—
333C2×C4×C29—21no—
334C2×C4×C29—21no—
335C2×C4×C29—21no—
336C2×C4×C29—21no—
337C2×C4×C29—21no—
338C2×C4×C29—21no—
339C2×C4×C29—41no—
340C2×C4×C29—41no—
341C2×C4×C29—41no—
342C2×C4×C29—41no—
343C2×C4×C29—41no—
344C2×C4×C29—81no—
345C2×C4×C29—81no—
346C2×C4×C29—81no—
347C2×C4×C29—81no—
348C2×C4×C29—81no—
349C2×C4×C29—81no—
350C2×C4×C29—81no—
351C2×C4×C29—81no—
352C2×C4×C29#12011yescharacteristic
353C2×C4×C29#12011yescharacteristic
354C2×C4×C29#12011yescharacteristic
355C2×C4×C29C22×D411yescharacteristic
356C2×C4×C29C22×D411yescharacteristic
357C2×C4×C29C22×D411yescharacteristic
358C8×C29—22no—
359C8×C29—41no—
360C8×C29—41no—
361C8×C29—41no—
362C8×C29—41no—
363C8×C29—41no—
364#3553C2×C2911yescharacteristic
365#3240C2×C2911yescharacteristic, complemented
366#3236C2×C2911yescharacteristic, complemented
367#3172C2×C2911yescharacteristic, complemented
368#1664C2×C2911yescharacteristic, complemented
369#1664C2×C2911yescharacteristic, complemented
370#1664C2×C2911yescharacteristic, complemented
371#1663C2×C2911yescharacteristic, complemented
372#1663C2×C2911yescharacteristic, complemented
373#1662C2×C2911yescharacteristic, complemented
374#1661C2×C2911yescharacteristic, complemented
375#1660C2×C2911yescharacteristic, complemented
376#1535C2×C2911yescharacteristic, complemented
377#1529C2×C2911yescharacteristic, complemented
378#1528C2×C2911yescharacteristic, complemented
379C22×C29—21no—
380C22×C29—21no—
381C22×C29—21no—
382C22×C29—41no—
383C22×C29—41no—
384C22×C29—41no—
385C22×C29—41no—
386C22×C29—41no—
387C22×C29—41no—
388C22×C29C2×#12011yescharacteristic
389C4×C29—21no—
390C4×C29—21no—
391C4×C29—21no—
392C4×C29—21no—
393C4×C29—21no—
394C4×C29—21no—
395C4×C29—41no—
396C4×C29—41no—
397C4×C29—41no—
398C4×C29—41no—
399C4×C29—41no—
400C4×C29—41no—
401C4×C29—41no—
402C4×C29—41no—
403C4×C29—41no—
404C4×C29—41no—
405C4×C29—81no—
406C4×C29—81no—
407#564C22×C2911yescharacteristic
408#563C22×C2911yescharacteristic
409#563C22×C2911yescharacteristic
410#562C22×C2911yescharacteristic
411#554—21no—
412#554—21no—
413#553—21no—
414#553—21no—
415#552—21no—
416#552—21no—
417#541—21no—
418#541—21no—
419#539—21no—
420#539—21no—
421#539—21no—
422#539—21no—
423#533C22×C2911yescharacteristic
424#529C22×C2911yescharacteristic
425#529C22×C2911yescharacteristic
426C2×#125C22×C2911yescharacteristic
427#501C22×C2911yescharacteristic
428#501C22×C2911yescharacteristic
429#501C22×C2911yescharacteristic
430#501C22×C2911yescharacteristic
431#501C22×C2911yescharacteristic
432#497C22×C2911yescharacteristic
433#491C22×C2911yescharacteristic
434#491C22×C2911yescharacteristic
435#491C22×C2911yescharacteristic
436#489C22×C2911yescharacteristic
437#489C22×C2911yescharacteristic
438#489C22×C2911yescharacteristic
439#485—21no—
440#484—21no—
441#483—21no—
442#482—21no—
443#479—21no—
444#479—21no—
445#479—21no—
446#478—21no—
447#470—21no—
448#468—21no—
449C4×Q16—21no—
450C4×SD16—21no—
451#432C22×C2911yescharacteristic
452#432C22×C2911yescharacteristic
453C4×M16C22×C2911yescharacteristic
454#330C22×C2911yescharacteristic
455#330C22×C2911yescharacteristic
456#330C22×C2911yescharacteristic
457#330C22×C2911yescharacteristic
458#330C22×C2911yescharacteristic
459#330C22×C2911yescharacteristic
460#330C22×C2911yescharacteristic
461#330C22×C2911yescharacteristic
462#329C22×C2911yescharacteristic
463#329C22×C2911yescharacteristic
464#329C22×C2911yescharacteristic
465#329C22×C2911yescharacteristic
466C2×C29—41no—
467C2×C29—81no—
468C2×C29—81no—
469C2×C29#301811yescharacteristic
470C2×C29#302011yescharacteristic
471C2×C29#302211yescharacteristic
472C2×Q16—21no—
473C2×SD16—21no—
474C2×M16—21no—
475C4⋊Q8—21no—
476C4⋊Q8—21no—
477C4⋊Q8C23×C2911yescharacteristic
478C4⋊Q8C23×C2911yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#126—21no—
484#126—21no—
485#126—21no—
486#126—21no—
487#126—21no—
488#126—21no—
489#125—21no—
490#125—21no—
491#125—21no—
492#125—21no—
493#125—21no—
494#125—21no—
495#125—21no—
496#125—21no—
497#125—21no—
498#125—21no—
499#125—21no—
500#125—21no—
501#125—21no—
502#125D4×C2911yescharacteristic
503#125D4×C2911yescharacteristic
504#125C23×C2911yescharacteristic
505#125C23×C2911yescharacteristic
506#125C23×C2911yescharacteristic
507#125C23×C2911yescharacteristic
508#124C23×C2911yescharacteristic
509#124C23×C2911yescharacteristic
510#123—21no—
511#123—21no—
512#123—21no—
513#123—21no—
514#123—21no—
515#123—21no—
516#123—21no—
517#123—21no—
518#123—21no—
519#123—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—21no—
527C22⋊Q8—21no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—21no—
532C22⋊Q8—21no—
533C22⋊Q8—21no—
534C22⋊Q8D4×C2911yescharacteristic
535C22⋊Q8D4×C2911yescharacteristic
536#121—21no—
537#121—21no—
538#121—21no—
539#121—21no—
540#121D4×C2911yescharacteristic
541#121D4×C2911yescharacteristic
542C4×Q8—21no—
543C4×Q8—21no—
544C4×Q8—21no—
545C4×Q8—21no—
546C4×Q8D4×C2911yescharacteristic
547C4×Q8D4×C2911yescharacteristic
548C4×D4—21no—
549C4×D4—21no—
550C4×D4—21no—
551C4×D4—21no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4D4×C2911yescharacteristic
557C4×D4D4×C2911yescharacteristic
558#117—21no—
559#117—21no—
560#117—21no—
561#117—21no—
562#117—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4D4×C2911yescharacteristic
568C2×C4⋊C4D4×C2911yescharacteristic
569C2×C42C23×C2911yescharacteristic
570#107—21no—
571#107—21no—
572#107—21no—
573#107—21no—
574#107—21no—
575#106—21no—
576#106—21no—
577#106—21no—
578#106—21no—
579#106—21no—
580C4⋊C8—21no—
581C4⋊C8—21no—
582#103—21no—
583#103—21no—
584#103—21no—
585#103—21no—
586#103—21no—
587#103—21no—
588#103—21no—
589#103—21no—
590#103—21no—
591#102—21no—
592#102—21no—
593#102—21no—
594C22⋊C8—21no—
595C22⋊C8—21no—
596#97C23×C2911yescharacteristic
597#97C23×C2911yescharacteristic
598#97C23×C2911yescharacteristic
599#97C23×C2911yescharacteristic
600#97C23×C2911yescharacteristic
601#97C23×C2911yescharacteristic
602C4×C8—21no—
603C29#1907111yescharacteristic, direct product factor, Sylow
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8C2×D4×C2911yescharacteristic
609C2×Q8C2×D4×C2911yescharacteristic
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4C2×D4×C2911yescharacteristic
615C2×D4C2×D4×C2911yescharacteristic
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4C2×D4×C2911yescharacteristic
625C22×C4C2×D4×C2911yescharacteristic
626C22×C4C2×D4×C2911yescharacteristic
627Q16—42no—
628SD16—42no—
629M16—42no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—41no—
671C4⋊C4—41no—
672C4⋊C4C2×D4×C2911yescharacteristic
673C4⋊C4C2×D4×C2911yescharacteristic
674C4⋊C4C2×D4×C2911yescharacteristic
675C4⋊C4C2×D4×C2911yescharacteristic
676C4⋊C4C2×D4×C2911yescharacteristic
677C4⋊C4C2×D4×C2911yescharacteristic
678C4⋊C4C2×D4×C2911yescharacteristic
679C4⋊C4C2×D4×C2911yescharacteristic
680C22⋊C4—21no—
681C22⋊C4—21no—
682C22⋊C4—21no—
683C22⋊C4—21no—
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—21no—
687C22⋊C4—21no—
688C22⋊C4—21no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—21no—
697C22⋊C4—21no—
698C22⋊C4—41no—
699C42—21no—
700C42—21no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—21no—
705C42—41no—
706C42C2×D4×C2911yescharacteristic
707C42C2×D4×C2911yescharacteristic
708C42C2×D4×C2911yescharacteristic
709C42C24×C2911yescharacteristic
710C23—21no—
711C23—21no—
712C23C29×#12011yescharacteristic
713Q8—41no—
714Q8—41no—
715Q8—41no—
716Q8—41no—
717Q8—42no—
718Q8—81no—
719Q8—81no—
720D4—41no—
721D4—41no—
722D4—42no—
723D4—42no—
724D4—81no—
725D4—81no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—81no—
742C2×C4—81no—
743C2×C4—81no—
744C2×C4—81no—
745C2×C4—81no—
746C2×C4—81no—
747C2×C4—81no—
748C2×C4—81no—
749C2×C4C29×#12011yescharacteristic
750C2×C4C29×#12011yescharacteristic
751C2×C4C29×#12011yescharacteristic
752C2×C4C22×D4×C2911yescharacteristic
753C2×C4C22×D4×C2911yescharacteristic
754C2×C4C22×D4×C2911yescharacteristic
755C8—22no—
756C8—41no—
757C8—41no—
758C8—41no—
759C8—41no—
760C8—41no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22C2×C29×#12011yescharacteristic
771C4—21no—
772C4—21no—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—81no—
788C4—81no—
789C2—41no—
790C2—81no—
791C2—81no—
792C2C29×#301811yescharacteristic
793C2C29×#302011yescharacteristic
794C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3553C2
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×#3240C2semidirect
3. C29×#3236C2semidirect
4. C29×#3172C2semidirect
5. C29×#1664C2semidirect
6. C29×#1664C2semidirect
7. C29×#1664C2semidirect
8. C29×#1663C2semidirect
9. C29×#1663C2semidirect
10. C29×#1662C2semidirect
11. C29×#1661C2semidirect
12. C29×#1660C2semidirect
13. C29×#1535C2semidirect
14. C29×#1529C2semidirect
15. C29×#1528C2semidirect
312. #19071C29direct (N × H)
365. #3240C2×C29semidirect
366. #3236C2×C29semidirect
367. #3172C2×C29semidirect
368. #1664C2×C29semidirect
369. #1664C2×C29semidirect
370. #1664C2×C29semidirect
371. #1663C2×C29semidirect
372. #1663C2×C29semidirect
373. #1662C2×C29semidirect
374. #1661C2×C29semidirect
375. #1660C2×C29semidirect
376. #1535C2×C29semidirect
377. #1529C2×C29semidirect
378. #1528C2×C29semidirect
603. C29#19071direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35532
C29×#32402
C29×#32362
C29×#31722
C29×#16642
C29×#16632
C29×#16622
C29×#16612
C29×#16602
C29×#15352
C29×#15292
C29×#15282
#1907129