Finite Group Databasebeta

← C29×#25563 #20320463

Subgroups — C29×#25563 #20320463

Order 7424.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3490C211yesmaximal, characteristic, complemented
2C29×#2410C212yesmaximal, complemented
3C29×#2405C211yesmaximal, characteristic, complemented
4C29×#2062C211yesmaximal, characteristic, complemented
5C29×#2044C211yesmaximal, characteristic, complemented
6C29×#2029C211yesmaximal, characteristic, complemented
7C29×#2021C211yesmaximal, characteristic, complemented
8C29×#1898C212yesmaximal, complemented
9C29×#1889C212yesmaximal, complemented
10C29×#1867C212yesmaximal, complemented
11C2×C29×#342C211yesmaximal, characteristic, complemented
12C23×D4×C29C2211yescharacteristic
13C29×#551—22no—
14C29×#551—22no—
15C29×#546—22no—
16C29×#546—22no—
17C29×#543C2211yescharacteristic
18C29×#538—21no—
19C29×#538—21no—
20C29×#534C2211yescharacteristic
21C29×#525—21no—
22C29×#525—21no—
23C2×C29×#123—21no—
24C2×C29×#121—22no—
25C2×C29×#120C2212yes—
26C2×C29×#120C2212yes—
27C29×#518C2212yes—
28C22×C22⋊C4×C29C2211yescharacteristic
29C22×C22⋊C4×C29C2212yes—
30C2×C29×#99C2212yes—
31C2×C29×#99C2212yes—
32C29×#394—21no—
33C29×#394—21no—
34C29×#394—22no—
35C29×#392—22no—
36C29×#386—21no—
37C29×#386—22no—
38C29×#386C2212yes—
39C29×#385C2211yescharacteristic
40C29×#385C2212yes—
41C29×#385C2211yescharacteristic
42C29×#379C2211yescharacteristic
43C29×#379C2212yes—
44C29×#379C2211yescharacteristic
45C29×#379C2211yescharacteristic
46C29×#342C2211yescharacteristic
47C29×#342C2211yescharacteristic
48C29×#342C2212yes—
49C29×#342C2212yes—
50C29×#342C2212yes—
51C25×C29C2311yescharacteristic
52C25×C29C2311yescharacteristic
53C2×#41×C29—21no—
54C2×#41×C29—21no—
55C22×D4×C29—22no—
56C22×D4×C29—21no—
57C22×D4×C29—22no—
58C22×D4×C29—21no—
59C22×D4×C29—22no—
60C22×D4×C29—44no—
61C22×D4×C29D412yescomplemented
62C22×D4×C29D412yescomplemented
63C22×D4×C29C2312yes—
64C23×C4×C29—22no—
65C23×C4×C29D411yescharacteristic, complemented
66C23×C4×C29D411yescharacteristic, complemented
67C23×C4×C29C2311yescharacteristic
68C29×#126—22no—
69C29×#126—22no—
70C29×#124—22no—
71C29×#124—22no—
72C29×#123—22no—
73C29×#123—22no—
74C29×#123—22no—
75C29×#123—22no—
76C29×#123—22no—
77C29×#123—44no—
78C29×C22⋊Q8—21no—
79C29×C22⋊Q8—21no—
80C29×C22⋊Q8—21no—
81C29×C22⋊Q8—21no—
82C29×C22⋊Q8—22no—
83C29×C22⋊Q8—22no—
84C29×#121—21no—
85C29×#121—21no—
86C29×#121—22no—
87C29×#121—22no—
88C29×#121—21no—
89C29×#121—21no—
90C29×#121—48no—
91C29×#120—22no—
92C29×#120—22no—
93C29×#120—22no—
94C29×#120—22no—
95C29×#120—22no—
96C29×#120—24no—
97C29×#120—42no—
98C4×D4×C29—22no—
99C4×D4×C29—22no—
100C4×D4×C29—22no—
101C4×D4×C29—22no—
102C4×D4×C29—22no—
103C4×D4×C29—22no—
104C29×#117—21no—
105C29×#117—21no—
106C29×#117—22no—
107C2×C4⋊C4×C29—22no—
108C2×C4⋊C4×C29—21no—
109C2×C4⋊C4×C29—21no—
110C2×C22⋊C4×C29—22no—
111C2×C22⋊C4×C29—22no—
112C2×C22⋊C4×C29—22no—
113C2×C22⋊C4×C29—24no—
114C2×C22⋊C4×C29—22no—
115C2×C22⋊C4×C29—22no—
116C2×C22⋊C4×C29—21no—
117C2×C22⋊C4×C29—22no—
118C2×C22⋊C4×C29—22no—
119C2×C22⋊C4×C29—21no—
120C2×C22⋊C4×C29—21no—
121C2×C22⋊C4×C29—21no—
122C2×C22⋊C4×C29—22no—
123C2×C22⋊C4×C29—21no—
124C2×C22⋊C4×C29—21no—
125C2×C22⋊C4×C29—42no—
126C2×C22⋊C4×C29D411yescharacteristic, complemented
127C2×C22⋊C4×C29D411yescharacteristic, complemented
128C2×C22⋊C4×C29D412yescomplemented
129C2×C22⋊C4×C29D412yescomplemented
130C2×C22⋊C4×C29C2312yes—
131C2×C22⋊C4×C29C2311yescharacteristic
132C2×C22⋊C4×C29C2311yescharacteristic
133C2×C22⋊C4×C29C2311yescharacteristic
134C2×C22⋊C4×C29C2311yescharacteristic
135C2×C22⋊C4×C29C2312yes—
136C2×C22⋊C4×C29C2312yes—
137C29×#99—24no—
138C29×#99—42no—
139C29×#95—22no—
140C29×#95—21no—
141C29×#95—21no—
142C29×#95—22no—
143C24×C29—22no—
144C24×C29—21no—
145C24×C29—21no—
146C24×C29—21no—
147C24×C29—22no—
148C24×C29—22no—
149C24×C29—21no—
150C24×C29—21no—
151C24×C29—42no—
152C24×C29—42no—
153C24×C29—81no—
154C24×C29—81no—
155C24×C29C2×D412yes—
156C24×C29C2×D411yescharacteristic
157C24×C29C2×D412yes—
158C24×C29C2×D412yes—
159C24×C29C2×D411yescharacteristic
160C24×C29C2411yescharacteristic
161#41×C29—82no—
162#41×C29—82no—
163C2×Q8×C29—21no—
164C2×Q8×C29—21no—
165C2×D4×C29—28no—
166C2×D4×C29—24no—
167C2×D4×C29—22no—
168C2×D4×C29—22no—
169C2×D4×C29—22no—
170C2×D4×C29—22no—
171C2×D4×C29—22no—
172C2×D4×C29—22no—
173C2×D4×C29—22no—
174C2×D4×C29—22no—
175C2×D4×C29—21no—
176C2×D4×C29—21no—
177C2×D4×C29—22no—
178C2×D4×C29—22no—
179C2×D4×C29—44no—
180C2×D4×C29—42no—
181C2×D4×C29—44no—
182C2×D4×C29—42no—
183C2×D4×C29—44no—
184C2×D4×C29—42no—
185C2×D4×C29—44no—
186C2×D4×C29—42no—
187C2×D4×C29—41no—
188C2×D4×C29—41no—
189C2×D4×C29—44no—
190C2×D4×C29—44no—
191C2×D4×C29—82no—
192C2×D4×C29—82no—
193C22×C4×C29—21no—
194C22×C4×C29—21no—
195C22×C4×C29—22no—
196C22×C4×C29—22no—
197C22×C4×C29—21no—
198C22×C4×C29—22no—
199C22×C4×C29—22no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—22no—
205C22×C4×C29—42no—
206C22×C4×C29—44no—
207C22×C4×C29—42no—
208C22×C4×C29—44no—
209C22×C4×C29—81no—
210C22×C4×C29—82no—
211C22×C4×C29C2×D412yes—
212C22×C4×C29C2×D411yescharacteristic
213C22×C4×C29C2×D412yes—
214C22×C4×C29C2×D411yescharacteristic
215C22×C4×C29C2×D411yescharacteristic
216C22×C4×C29C2×D412yes—
217C22×C4×C29C2×D411yescharacteristic
218C4⋊C4×C29—22no—
219C4⋊C4×C29—22no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29—21no—
222C4⋊C4×C29—21no—
223C4⋊C4×C29—21no—
224C4⋊C4×C29—22no—
225C4⋊C4×C29—22no—
226C4⋊C4×C29—44no—
227C4⋊C4×C29—42no—
228C4⋊C4×C29—42no—
229C22⋊C4×C29—22no—
230C22⋊C4×C29—22no—
231C22⋊C4×C29—22no—
232C22⋊C4×C29—22no—
233C22⋊C4×C29—22no—
234C22⋊C4×C29—22no—
235C22⋊C4×C29—22no—
236C22⋊C4×C29—22no—
237C22⋊C4×C29—22no—
238C22⋊C4×C29—22no—
239C22⋊C4×C29—22no—
240C22⋊C4×C29—22no—
241C22⋊C4×C29—22no—
242C22⋊C4×C29—22no—
243C22⋊C4×C29—22no—
244C22⋊C4×C29—22no—
245C22⋊C4×C29—22no—
246C22⋊C4×C29—22no—
247C22⋊C4×C29—21no—
248C22⋊C4×C29—21no—
249C22⋊C4×C29—44no—
250C22⋊C4×C29—44no—
251C22⋊C4×C29—44no—
252C22⋊C4×C29—44no—
253C22⋊C4×C29—42no—
254C22⋊C4×C29—42no—
255C22⋊C4×C29—42no—
256C22⋊C4×C29—81no—
257C22⋊C4×C29—81no—
258C22⋊C4×C29—82no—
259C22⋊C4×C29—81no—
260C22⋊C4×C29#4114yescomplemented
261C42×C29—22no—
262C42×C29—22no—
263#25563C2911yesmaximal, characteristic, direct product factor, Sylow
264C23×C29—21no—
265C23×C29—21no—
266C23×C29—22no—
267C23×C29—22no—
268C23×C29—22no—
269C23×C29—24no—
270C23×C29—21no—
271C23×C29—21no—
272C23×C29—22no—
273C23×C29—22no—
274C23×C29—22no—
275C23×C29—24no—
276C23×C29—22no—
277C23×C29—22no—
278C23×C29—22no—
279C23×C29—41no—
280C23×C29—41no—
281C23×C29—42no—
282C23×C29—41no—
283C23×C29—41no—
284C23×C29—41no—
285C23×C29—42no—
286C23×C29—42no—
287C23×C29—41no—
288C23×C29—41no—
289C23×C29—42no—
290C23×C29—41no—
291C23×C29—42no—
292C23×C29—42no—
293C23×C29—42no—
294C23×C29—42no—
295C23×C29—41no—
296C23×C29—41no—
297C23×C29—41no—
298C23×C29—42no—
299C23×C29—42no—
300C23×C29—84no—
301C23×C29—84no—
302C23×C29—82no—
303C23×C29—82no—
304C23×C29—82no—
305C23×C29—82no—
306C23×C29#12012yes—
307C23×C29#12011yescharacteristic
308C23×C29#12011yescharacteristic
309C23×C29C22×D411yescharacteristic
310C23×C29C22×D412yes—
311C23×C29C2×#4112yes—
312C23×C29H(5,𝔽2)11yescharacteristic
313C23×C292−1+411yescharacteristic
314Q8×C29—81no—
315Q8×C29—81no—
316D4×C29—44no—
317D4×C29—48no—
318D4×C29—44no—
319D4×C29—42no—
320D4×C29—42no—
321D4×C29—42no—
322D4×C29—42no—
323D4×C29—44no—
324D4×C29—44no—
325D4×C29—82no—
326D4×C29—82no—
327D4×C29—81no—
328D4×C29—81no—
329D4×C29—88no—
330C2×C4×C29—24no—
331C2×C4×C29—22no—
332C2×C4×C29—22no—
333C2×C4×C29—21no—
334C2×C4×C29—21no—
335C2×C4×C29—22no—
336C2×C4×C29—22no—
337C2×C4×C29—21no—
338C2×C4×C29—21no—
339C2×C4×C29—24no—
340C2×C4×C29—22no—
341C2×C4×C29—22no—
342C2×C4×C29—42no—
343C2×C4×C29—41no—
344C2×C4×C29—42no—
345C2×C4×C29—42no—
346C2×C4×C29—42no—
347C2×C4×C29—41no—
348C2×C4×C29—42no—
349C2×C4×C29—41no—
350C2×C4×C29—41no—
351C2×C4×C29—42no—
352C2×C4×C29—41no—
353C2×C4×C29—41no—
354C2×C4×C29—42no—
355C2×C4×C29—41no—
356C2×C4×C29—41no—
357C2×C4×C29—42no—
358C2×C4×C29—41no—
359C2×C4×C29—41no—
360C2×C4×C29—42no—
361C2×C4×C29—41no—
362C2×C4×C29—41no—
363C2×C4×C29—42no—
364C2×C4×C29—81no—
365C2×C4×C29—81no—
366C2×C4×C29—82no—
367C2×C4×C29—82no—
368C2×C4×C29—88no—
369#3490C2×C2911yescharacteristic, complemented
370#2410C2×C2912yescomplemented
371#2405C2×C2911yescharacteristic, complemented
372#2062C2×C2911yescharacteristic, complemented
373#2044C2×C2911yescharacteristic, complemented
374#2029C2×C2911yescharacteristic, complemented
375#2021C2×C2911yescharacteristic, complemented
376#1898C2×C2912yescomplemented
377#1889C2×C2912yescomplemented
378#1867C2×C2912yescomplemented
379C2×#342C2×C2911yescharacteristic, complemented
380C22×C29—21no—
381C22×C29—21no—
382C22×C29—22no—
383C22×C29—21no—
384C22×C29—22no—
385C22×C29—21no—
386C22×C29—21no—
387C22×C29—22no—
388C22×C29—21no—
389C22×C29—22no—
390C22×C29—21no—
391C22×C29—22no—
392C22×C29—42no—
393C22×C29—41no—
394C22×C29—41no—
395C22×C29—44no—
396C22×C29—42no—
397C22×C29—42no—
398C22×C29—44no—
399C22×C29—44no—
400C22×C29—42no—
401C22×C29—42no—
402C22×C29—44no—
403C22×C29—42no—
404C22×C29—42no—
405C22×C29—42no—
406C22×C29—42no—
407C22×C29—82no—
408C22×C29—81no—
409C22×C29—81no—
410C22×C29—82no—
411C22×C29—82no—
412C22×C29—82no—
413C22×C29—82no—
414C22×C29—81no—
415C22×C29—81no—
416C22×C29—82no—
417C22×C29—81no—
418C22×C29—81no—
419C22×C29B(4,𝔽2)12yes—
420C22×C29C2×#12011yescharacteristic
421C22×C29#53211yescharacteristic
422C22×C29#53711yescharacteristic
423C22×C29#54612yes—
424C22×C29#54712yes—
425C4×C29—44no—
426C4×C29—42no—
427C4×C29—42no—
428C4×C29—41no—
429C4×C29—41no—
430C4×C29—42no—
431C4×C29—41no—
432C4×C29—41no—
433C4×C29—42no—
434C4×C29—81no—
435C4×C29—81no—
436C4×C29—82no—
437C23×D4C22×C2911yescharacteristic
438#551—22no—
439#551—22no—
440#546—22no—
441#546—22no—
442#543C22×C2911yescharacteristic
443#538—21no—
444#538—21no—
445#534C22×C2911yescharacteristic
446#525—21no—
447#525—21no—
448C2×#123—21no—
449C2×#121—22no—
450C2×#120C22×C2912yes—
451C2×#120C22×C2912yes—
452#518C22×C2912yes—
453C22×C22⋊C4C22×C2911yescharacteristic
454C22×C22⋊C4C22×C2912yes—
455C2×#99C22×C2912yes—
456C2×#99C22×C2912yes—
457#394—21no—
458#394—21no—
459#394—22no—
460#392—22no—
461#386—21no—
462#386—22no—
463#386C22×C2912yes—
464#385C22×C2912yes—
465#385C22×C2911yescharacteristic
466#385C22×C2911yescharacteristic
467#379C22×C2911yescharacteristic
468#379C22×C2912yes—
469#379C22×C2911yescharacteristic
470#379C22×C2911yescharacteristic
471#342C22×C2912yes—
472#342C22×C2911yescharacteristic
473#342C22×C2912yes—
474#342C22×C2912yes—
475#342C22×C2911yescharacteristic
476C2×C29—22no—
477C2×C29—21no—
478C2×C29—21no—
479C2×C29—22no—
480C2×C29—22no—
481C2×C29—41no—
482C2×C29—42no—
483C2×C29—82no—
484C2×C29—82no—
485C2×C29#243011yescharacteristic
486C2×C29C2×B(4,𝔽2)11yescharacteristic
487C2×C29#302611yescharacteristic
488C25C23×C2911yescharacteristic
489C25C23×C2911yescharacteristic
490C2×#41—21no—
491C2×#41—21no—
492C22×D4—22no—
493C22×D4—21no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—44no—
498C22×D4D4×C2912yescomplemented
499C22×D4D4×C2912yescomplemented
500C22×D4C23×C2912yes—
501C23×C4—22no—
502C23×C4D4×C2911yescharacteristic, complemented
503C23×C4D4×C2911yescharacteristic, complemented
504C23×C4C23×C2911yescharacteristic
505#126—22no—
506#126—22no—
507#124—22no—
508#124—22no—
509#123—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—44no—
515C22⋊Q8—21no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—22no—
520C22⋊Q8—22no—
521#121—21no—
522#121—21no—
523#121—22no—
524#121—22no—
525#121—21no—
526#121—21no—
527#121—48no—
528#120—22no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—24no—
534#120—42no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541#117—21no—
542#117—21no—
543#117—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4D4×C2911yescharacteristic, complemented
564C2×C22⋊C4D4×C2911yescharacteristic, complemented
565C2×C22⋊C4D4×C2912yescomplemented
566C2×C22⋊C4D4×C2912yescomplemented
567C2×C22⋊C4C23×C2912yes—
568C2×C22⋊C4C23×C2911yescharacteristic
569C2×C22⋊C4C23×C2911yescharacteristic
570C2×C22⋊C4C23×C2911yescharacteristic
571C2×C22⋊C4C23×C2911yescharacteristic
572C2×C22⋊C4C23×C2912yes—
573C2×C22⋊C4C23×C2912yes—
574#99—24no—
575#99—42no—
576#95—22no—
577#95—21no—
578#95—21no—
579#95—22no—
580C29#2556311yescharacteristic, direct product factor, Sylow
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C2912yes—
594C24C2×D4×C2911yescharacteristic
595C24C2×D4×C2912yes—
596C24C2×D4×C2912yes—
597C24C2×D4×C2911yescharacteristic
598C24C24×C2911yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C2912yes—
650C22×C4C2×D4×C2911yescharacteristic
651C22×C4C2×D4×C2912yes—
652C22×C4C2×D4×C2911yescharacteristic
653C22×C4C2×D4×C2911yescharacteristic
654C22×C4C2×D4×C2912yes—
655C22×C4C2×D4×C2911yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C2914yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23C29×#12012yes—
744C23C29×#12011yescharacteristic
745C23C29×#12011yescharacteristic
746C23C22×D4×C2911yescharacteristic
747C23C22×D4×C2912yes—
748C23C2×#41×C2912yes—
749C23C29×H(5,𝔽2)11yescharacteristic
750C23C29×2−1+411yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—21no—
808C22—22no—
809C22—21no—
810C22—22no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22C29×B(4,𝔽2)12yes—
846C22C2×C29×#12011yescharacteristic
847C22C29×#53211yescharacteristic
848C22C29×#53711yescharacteristic
849C22C29×#54612yes—
850C22C29×#54712yes—
851C4—44no—
852C4—42no—
853C4—42no—
854C4—41no—
855C4—41no—
856C4—42no—
857C4—41no—
858C4—41no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C29×#243011yescharacteristic
873C2C2×C29×B(4,𝔽2)11yescharacteristic
874C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC24C24×C29
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C25×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3490C2semidirect
2. C29×#2410C2semidirect
3. C29×#2405C2semidirect
4. C29×#2062C2semidirect
5. C29×#2044C2semidirect
6. C29×#2029C2semidirect
7. C29×#2021C2semidirect
8. C29×#1898C2semidirect
9. C29×#1889C2semidirect
10. C29×#1867C2semidirect
11. C2×C29×#342C2semidirect
61. C22×D4×C29D4semidirect
62. C22×D4×C29D4semidirect
65. C23×C4×C29D4semidirect
66. C23×C4×C29D4semidirect
126. C2×C22⋊C4×C29D4semidirect
127. C2×C22⋊C4×C29D4semidirect
128. C2×C22⋊C4×C29D4semidirect
129. C2×C22⋊C4×C29D4semidirect
260. C22⋊C4×C29#41semidirect
263. #25563C29direct (N × H)
369. #3490C2×C29semidirect
370. #2410C2×C29semidirect
371. #2405C2×C29semidirect
372. #2062C2×C29semidirect
373. #2044C2×C29semidirect
374. #2029C2×C29semidirect
375. #2021C2×C29semidirect
376. #1898C2×C29semidirect
377. #1889C2×C29semidirect
378. #1867C2×C29semidirect
379. C2×#342C2×C29semidirect
498. C22×D4D4×C29semidirect
499. C22×D4D4×C29semidirect
502. C23×C4D4×C29semidirect
503. C23×C4D4×C29semidirect
563. C2×C22⋊C4D4×C29semidirect
564. C2×C22⋊C4D4×C29semidirect
565. C2×C22⋊C4D4×C29semidirect
566. C2×C22⋊C4D4×C29semidirect
580. C29#25563direct (N × H)
698. C22⋊C4#41×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#34902
C29×#24102
C29×#24052
C29×#20622
C29×#20442
C29×#20292
C29×#20212
C29×#18982
C29×#18892
C29×#18672
C2×C29×#3422
#2556329