Finite Group Databasebeta

← C29×#24087 #20318987

Subgroups — C29×#24087 #20318987

Order 7424.

984 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3495C211yesmaximal, characteristic
2C29×#3093C211yesmaximal, characteristic
3C29×#2911C211yesmaximal, characteristic, complemented
4C29×#2499C211yesmaximal, characteristic, complemented
5C29×#2061C211yesmaximal, characteristic, complemented
6C29×#2060C211yesmaximal, characteristic, complemented
7C29×#2038C211yesmaximal, characteristic, complemented
8C29×#2038C211yesmaximal, characteristic, complemented
9C29×#1901C211yesmaximal, characteristic, complemented
10C29×#1871C211yesmaximal, characteristic
11C29×#1860C211yesmaximal, characteristic, complemented
12C29×#1859C211yesmaximal, characteristic, complemented
13C29×#1857C211yesmaximal, characteristic, complemented
14C29×#1857C211yesmaximal, characteristic, complemented
15C29×#1826C211yesmaximal, characteristic, complemented
16C22×M16×C29C2211yescharacteristic
17C29×#556—21no—
18C29×#554—21no—
19C29×#552—21no—
20C29×#552—22no—
21C29×#552—21no—
22C29×#551—22no—
23C29×#544C2211yescharacteristic
24C29×#542—21no—
25C29×#541—21no—
26C29×#536C2211yescharacteristic
27C29×#533—21no—
28C29×#529—21no—
29C29×#525C2211yescharacteristic
30C2×C29×C22⋊Q8C2211yescharacteristic
31C29×#520C2211yescharacteristic
32C29×#519C2211yescharacteristic
33C2×C29×#117C2211yescharacteristic
34C2×C29×#117C2211yescharacteristic
35C29×#485—21no—
36C29×#485—21no—
37C29×#482—21no—
38C29×#482—21no—
39C29×#428—21no—
40C29×#428—21no—
41C29×#428C2211yescharacteristic
42C29×#428C2211yescharacteristic
43C29×#428C2211yescharacteristic
44C29×#428C2211yescharacteristic
45C29×#428C2211yescharacteristic
46C29×#428C2211yescharacteristic
47C29×#427—21no—
48C29×#427—21no—
49C2×C29×#104C2211yescharacteristic
50C2×C29×#104C2211yescharacteristic
51C29×#417C2211yescharacteristic
52C29×#417C2211yescharacteristic
53C2×C29×#101C2211yescharacteristic
54C2×C29×#101C2211yescharacteristic
55C29×#407C2211yescharacteristic
56C29×#397—22no—
57C29×#391C2211yescharacteristic
58C29×#391C2211yescharacteristic
59C29×#387—22no—
60C29×#384C2211yescharacteristic
61C29×#382C2211yescharacteristic
62C4×C22⋊C4×C29C2211yescharacteristic
63C29×#343C2211yescharacteristic
64C29×#343C2211yescharacteristic
65C29×#339C2211yescharacteristic
66C29×#339C2211yescharacteristic
67C29×#339C2211yescharacteristic
68C29×#339C2211yescharacteristic
69C29×#339C2211yescharacteristic
70C29×#339C2211yescharacteristic
71C2×#41×C29C2311yescharacteristic
72C22×Q8×C29C2311yescharacteristic
73C23×C4×C29C2311yescharacteristic
74C2×M16×C29—21no—
75C2×M16×C29—22no—
76C2×M16×C29—22no—
77C2×M16×C29C2311yescharacteristic
78C2×M16×C29C2311yescharacteristic
79C2×M16×C29C2311yescharacteristic
80C2×M16×C29C2311yescharacteristic
81C22×C8×C29—21no—
82C29×C4⋊Q8—21no—
83C29×C4⋊Q8—21no—
84C29×C4⋊Q8—21no—
85C29×#126—22no—
86C29×#126—22no—
87C29×#126—22no—
88C29×#126—22no—
89C29×#125—22no—
90C29×#125—22no—
91C29×#125—22no—
92C29×#125—21no—
93C29×#125—21no—
94C29×#124—22no—
95C29×#124—21no—
96C29×#123—22no—
97C29×#123—22no—
98C29×#123—21no—
99C29×#123—22no—
100C29×C22⋊Q8—22no—
101C29×C22⋊Q8—22no—
102C29×C22⋊Q8—21no—
103C29×C22⋊Q8—21no—
104C29×C22⋊Q8—21no—
105C29×C22⋊Q8—21no—
106C29×C22⋊Q8—22no—
107C29×C22⋊Q8—21no—
108C29×C22⋊Q8—21no—
109C29×C22⋊Q8D411yescharacteristic
110C29×C22⋊Q8D411yescharacteristic
111C29×#121D411yescharacteristic
112C29×#121D411yescharacteristic
113C29×#120—21no—
114C4×Q8×C29—22no—
115C4×Q8×C29—21no—
116C4×Q8×C29—21no—
117C4×Q8×C29—21no—
118C4×Q8×C29—21no—
119C4×Q8×C29—21no—
120C4×D4×C29—22no—
121C4×D4×C29—21no—
122C4×D4×C29—22no—
123C4×D4×C29—21no—
124C4×D4×C29—21no—
125C29×#117—22no—
126C29×#117—22no—
127C29×#117—21no—
128C29×#117—21no—
129C29×#117—22no—
130C29×#117—21no—
131C29×#117—21no—
132C29×#117—21no—
133C29×#117—21no—
134C29×#117—21no—
135C29×#117D411yescharacteristic
136C29×#117D411yescharacteristic
137C29×#117C2311yescharacteristic
138C29×#117C2311yescharacteristic
139C29×#117C2311yescharacteristic
140C2×C4⋊C4×C29—21no—
141C2×C4⋊C4×C29—22no—
142C2×C4⋊C4×C29D412yes—
143C2×C4⋊C4×C29D411yescharacteristic
144C2×C4⋊C4×C29D411yescharacteristic
145C2×C4⋊C4×C29C2311yescharacteristic
146C2×C4⋊C4×C29C2311yescharacteristic
147C2×C4⋊C4×C29C2311yescharacteristic
148C2×C22⋊C4×C29—21no—
149C2×C22⋊C4×C29—21no—
150C2×C22⋊C4×C29—21no—
151C2×C22⋊C4×C29D412yes—
152C2×C42×C29—21no—
153C2×C42×C29—21no—
154C2×C42×C29C2311yescharacteristic
155C2×C42×C29C2311yescharacteristic
156C29×#107—21no—
157C29×#107—21no—
158C29×#107—21no—
159C29×#107—21no—
160C29×#107—21no—
161C29×#107—21no—
162C29×#106—21no—
163C29×#106—21no—
164C29×#106—21no—
165C29×#106—21no—
166C29×#106—21no—
167C29×#106—21no—
168C29×#104—22no—
169C29×#104—22no—
170C29×#103—21no—
171C29×#103—21no—
172C29×#102—21no—
173C29×#102—21no—
174C29×#101—22no—
175C29×#101—22no—
176C29×C22⋊C8—21no—
177C29×C22⋊C8—21no—
178C29×#95—21no—
179C29×#95—22no—
180C29×#95—22no—
181C29×#95—22no—
182C24×C29C2×D411yescharacteristic
183#41×C29—21no—
184#41×C29—21no—
185#41×C29—21no—
186#41×C29—21no—
187C2×Q8×C29—22no—
188C2×Q8×C29—21no—
189C2×Q8×C29—21no—
190C2×Q8×C29—21no—
191C2×Q8×C29—21no—
192C2×Q8×C29—21no—
193C2×Q8×C29—21no—
194C2×Q8×C29C2×D411yescharacteristic
195C2×D4×C29—21no—
196C2×D4×C29—21no—
197C2×D4×C29—21no—
198C2×D4×C29C2×D411yescharacteristic
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—21no—
202C22×C4×C29—21no—
203C22×C4×C29—21no—
204C22×C4×C29—21no—
205C22×C4×C29—22no—
206C22×C4×C29—21no—
207C22×C4×C29—21no—
208C22×C4×C29—21no—
209C22×C4×C29—21no—
210C22×C4×C29—21no—
211C22×C4×C29C2×D412yes—
212C22×C4×C29C2×D411yescharacteristic
213C22×C4×C29C2×D411yescharacteristic
214C22×C4×C29C2×D411yescharacteristic
215C22×C4×C29C2×D411yescharacteristic
216C22×C4×C29C2×D411yescharacteristic
217C22×C4×C29C2×D412yes—
218C22×C4×C29C2411yescharacteristic
219M16×C29—24no—
220M16×C29—21no—
221M16×C29—21no—
222M16×C29—21no—
223M16×C29—21no—
224M16×C29—21no—
225M16×C29—21no—
226M16×C29#4112yes—
227M16×C29#4112yes—
228C2×C8×C29—24no—
229C2×C8×C29—21no—
230C2×C8×C29—21no—
231C2×C8×C29—21no—
232C2×C8×C29—21no—
233C4⋊C4×C29—22no—
234C4⋊C4×C29—22no—
235C4⋊C4×C29—22no—
236C4⋊C4×C29—22no—
237C4⋊C4×C29—22no—
238C4⋊C4×C29—22no—
239C4⋊C4×C29—22no—
240C4⋊C4×C29—22no—
241C4⋊C4×C29—21no—
242C4⋊C4×C29—21no—
243C4⋊C4×C29—22no—
244C4⋊C4×C29—22no—
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—44no—
254C4⋊C4×C29C2×D411yescharacteristic
255C4⋊C4×C29C2×D411yescharacteristic
256C4⋊C4×C29C2×D411yescharacteristic
257C4⋊C4×C29C2×D411yescharacteristic
258C4⋊C4×C29C2×D411yescharacteristic
259C4⋊C4×C29C2×D411yescharacteristic
260C22⋊C4×C29—22no—
261C22⋊C4×C29—22no—
262C22⋊C4×C29—22no—
263C22⋊C4×C29—21no—
264C22⋊C4×C29—21no—
265C22⋊C4×C29—22no—
266C22⋊C4×C29—22no—
267C22⋊C4×C29—21no—
268C22⋊C4×C29—21no—
269C22⋊C4×C29—21no—
270C22⋊C4×C29—21no—
271C22⋊C4×C29—21no—
272C22⋊C4×C29—21no—
273C22⋊C4×C29—21no—
274C22⋊C4×C29—42no—
275C22⋊C4×C29—41no—
276C22⋊C4×C29—41no—
277C42×C29—22no—
278C42×C29—22no—
279C42×C29—22no—
280C42×C29—21no—
281C42×C29—21no—
282C42×C29—21no—
283C42×C29—21no—
284C42×C29—21no—
285C42×C29—21no—
286C42×C29—21no—
287C42×C29—21no—
288C42×C29—21no—
289C42×C29—41no—
290C42×C29—41no—
291#24087C2911yesmaximal, characteristic, direct product factor, Sylow
292C23×C29—21no—
293C23×C29—21no—
294C23×C29—21no—
295C23×C29—41no—
296C23×C29—41no—
297C23×C29#12011yescharacteristic
298C23×C29#12011yescharacteristic
299C23×C29C22×D411yescharacteristic
300Q8×C29—21no—
301Q8×C29—21no—
302Q8×C29—41no—
303Q8×C29—41no—
304Q8×C29—41no—
305Q8×C29—41no—
306Q8×C29—82no—
307D4×C29—21no—
308D4×C29—21no—
309D4×C29—42no—
310D4×C29—41no—
311D4×C29—41no—
312D4×C29—81no—
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—21no—
320C2×C4×C29—21no—
321C2×C4×C29—21no—
322C2×C4×C29—21no—
323C2×C4×C29—22no—
324C2×C4×C29—21no—
325C2×C4×C29—21no—
326C2×C4×C29—21no—
327C2×C4×C29—21no—
328C2×C4×C29—21no—
329C2×C4×C29—22no—
330C2×C4×C29—21no—
331C2×C4×C29—21no—
332C2×C4×C29—22no—
333C2×C4×C29—22no—
334C2×C4×C29—22no—
335C2×C4×C29—41no—
336C2×C4×C29—42no—
337C2×C4×C29—41no—
338C2×C4×C29—41no—
339C2×C4×C29—41no—
340C2×C4×C29—42no—
341C2×C4×C29—41no—
342C2×C4×C29—42no—
343C2×C4×C29—41no—
344C2×C4×C29—42no—
345C2×C4×C29—41no—
346C2×C4×C29—41no—
347C2×C4×C29—41no—
348C2×C4×C29—81no—
349C2×C4×C29—82no—
350C2×C4×C29#12011yescharacteristic
351C2×C4×C29#12011yescharacteristic
352C2×C4×C29C22×D411yescharacteristic
353C2×C4×C29C22×D411yescharacteristic
354C2×C4×C29C2×#4111yescharacteristic
355C2×C4×C29C2×#4111yescharacteristic
356C2×C4×C292−1+411yescharacteristic
357C2×C4×C292−1+411yescharacteristic
358C8×C29—22no—
359C8×C29—22no—
360C8×C29—41no—
361C8×C29—41no—
362#3495C2×C2911yescharacteristic
363#3093C2×C2911yescharacteristic
364#2911C2×C2911yescharacteristic, complemented
365#2499C2×C2911yescharacteristic, complemented
366#2061C2×C2911yescharacteristic, complemented
367#2060C2×C2911yescharacteristic, complemented
368#2038C2×C2911yescharacteristic, complemented
369#2038C2×C2911yescharacteristic, complemented
370#1901C2×C2911yescharacteristic, complemented
371#1871C2×C2911yescharacteristic
372#1860C2×C2911yescharacteristic, complemented
373#1859C2×C2911yescharacteristic, complemented
374#1857C2×C2911yescharacteristic, complemented
375#1857C2×C2911yescharacteristic, complemented
376#1826C2×C2911yescharacteristic, complemented
377C22×C29—21no—
378C22×C29—21no—
379C22×C29—21no—
380C22×C29—21no—
381C22×C29—21no—
382C22×C29—21no—
383C22×C29—21no—
384C22×C29—21no—
385C22×C29—41no—
386C22×C29—41no—
387C22×C29—41no—
388C22×C29—81no—
389C22×C29—81no—
390C22×C29C2×#12011yescharacteristic
391C22×C29#54711yescharacteristic
392C22×C29#54711yescharacteristic
393C4×C29—21no—
394C4×C29—21no—
395C4×C29—42no—
396C4×C29—42no—
397C4×C29—41no—
398C4×C29—42no—
399C4×C29—41no—
400C4×C29—41no—
401C4×C29—41no—
402C4×C29—41no—
403C4×C29—41no—
404C4×C29—41no—
405C4×C29—81no—
406C4×C29—81no—
407C4×C29—81no—
408C4×C29#52511yescharacteristic
409C4×C29#53611yescharacteristic
410C4×C29#54711yescharacteristic
411C4×C29#54711yescharacteristic
412C22×M16C22×C2911yescharacteristic
413#556—21no—
414#554—21no—
415#552—21no—
416#552—22no—
417#552—21no—
418#551—22no—
419#544C22×C2911yescharacteristic
420#542—21no—
421#541—21no—
422#536C22×C2911yescharacteristic
423#533—21no—
424#529—21no—
425#525C22×C2911yescharacteristic
426C2×C22⋊Q8C22×C2911yescharacteristic
427#520C22×C2911yescharacteristic
428#519C22×C2911yescharacteristic
429C2×#117C22×C2911yescharacteristic
430C2×#117C22×C2911yescharacteristic
431#485—21no—
432#485—21no—
433#482—21no—
434#482—21no—
435#428—21no—
436#428—21no—
437#428C22×C2911yescharacteristic
438#428C22×C2911yescharacteristic
439#428C22×C2911yescharacteristic
440#428C22×C2911yescharacteristic
441#428C22×C2911yescharacteristic
442#428C22×C2911yescharacteristic
443#427—21no—
444#427—21no—
445C2×#104C22×C2911yescharacteristic
446C2×#104C22×C2911yescharacteristic
447#417C22×C2911yescharacteristic
448#417C22×C2911yescharacteristic
449C2×#101C22×C2911yescharacteristic
450C2×#101C22×C2911yescharacteristic
451#407C22×C2911yescharacteristic
452#397—22no—
453#391C22×C2911yescharacteristic
454#391C22×C2911yescharacteristic
455#387—22no—
456#384C22×C2911yescharacteristic
457#382C22×C2911yescharacteristic
458C4×C22⋊C4C22×C2911yescharacteristic
459#343C22×C2911yescharacteristic
460#343C22×C2911yescharacteristic
461#339C22×C2911yescharacteristic
462#339C22×C2911yescharacteristic
463#339C22×C2911yescharacteristic
464#339C22×C2911yescharacteristic
465#339C22×C2911yescharacteristic
466#339C22×C2911yescharacteristic
467C2×C29—21no—
468C2×C29—21no—
469C2×C29—41no—
470C2×C29—41no—
471C2×C29—81no—
472C2×C29#240611yescharacteristic
473C2×C29#301811yescharacteristic
474C2×C29#302011yescharacteristic
475C2×#41C23×C2911yescharacteristic
476C22×Q8C23×C2911yescharacteristic
477C23×C4C23×C2911yescharacteristic
478C2×M16—21no—
479C2×M16—22no—
480C2×M16—22no—
481C2×M16C23×C2911yescharacteristic
482C2×M16C23×C2911yescharacteristic
483C2×M16C23×C2911yescharacteristic
484C2×M16C23×C2911yescharacteristic
485C22×C8—21no—
486C4⋊Q8—21no—
487C4⋊Q8—21no—
488C4⋊Q8—21no—
489#126—22no—
490#126—22no—
491#126—22no—
492#126—22no—
493#125—22no—
494#125—22no—
495#125—22no—
496#125—21no—
497#125—21no—
498#124—22no—
499#124—21no—
500#123—22no—
501#123—22no—
502#123—21no—
503#123—22no—
504C22⋊Q8—22no—
505C22⋊Q8—22no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—22no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8D4×C2911yescharacteristic
514C22⋊Q8D4×C2911yescharacteristic
515#121D4×C2911yescharacteristic
516#121D4×C2911yescharacteristic
517#120—21no—
518C4×Q8—22no—
519C4×Q8—21no—
520C4×Q8—21no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×D4—22no—
525C4×D4—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529#117—22no—
530#117—22no—
531#117—21no—
532#117—21no—
533#117—22no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—21no—
539#117D4×C2911yescharacteristic
540#117D4×C2911yescharacteristic
541#117C23×C2911yescharacteristic
542#117C23×C2911yescharacteristic
543#117C23×C2911yescharacteristic
544C2×C4⋊C4—21no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4D4×C2912yes—
547C2×C4⋊C4D4×C2911yescharacteristic
548C2×C4⋊C4D4×C2911yescharacteristic
549C2×C4⋊C4C23×C2911yescharacteristic
550C2×C4⋊C4C23×C2911yescharacteristic
551C2×C4⋊C4C23×C2911yescharacteristic
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C2912yes—
556C2×C42—21no—
557C2×C42—21no—
558C2×C42C23×C2911yescharacteristic
559C2×C42C23×C2911yescharacteristic
560#107—21no—
561#107—21no—
562#107—21no—
563#107—21no—
564#107—21no—
565#107—21no—
566#106—21no—
567#106—21no—
568#106—21no—
569#106—21no—
570#106—21no—
571#106—21no—
572#104—22no—
573#104—22no—
574#103—21no—
575#103—21no—
576#102—21no—
577#102—21no—
578#101—22no—
579#101—22no—
580C22⋊C8—21no—
581C22⋊C8—21no—
582#95—21no—
583#95—22no—
584#95—22no—
585#95—22no—
586C29#2408711yescharacteristic, direct product factor, Sylow
587C24C2×D4×C2911yescharacteristic
588#41—21no—
589#41—21no—
590#41—21no—
591#41—21no—
592C2×Q8—22no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8C2×D4×C2911yescharacteristic
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4C2×D4×C2911yescharacteristic
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4C2×D4×C2912yes—
617C22×C4C2×D4×C2911yescharacteristic
618C22×C4C2×D4×C2911yescharacteristic
619C22×C4C2×D4×C2911yescharacteristic
620C22×C4C2×D4×C2911yescharacteristic
621C22×C4C2×D4×C2911yescharacteristic
622C22×C4C2×D4×C2912yes—
623C22×C4C24×C2911yescharacteristic
624M16—24no—
625M16—21no—
626M16—21no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16#41×C2912yes—
632M16#41×C2912yes—
633C2×C8—24no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—22no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
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—44no—
659C4⋊C4C2×D4×C2911yescharacteristic
660C4⋊C4C2×D4×C2911yescharacteristic
661C4⋊C4C2×D4×C2911yescharacteristic
662C4⋊C4C2×D4×C2911yescharacteristic
663C4⋊C4C2×D4×C2911yescharacteristic
664C4⋊C4C2×D4×C2911yescharacteristic
665C22⋊C4—22no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—21no—
678C22⋊C4—21no—
679C22⋊C4—42no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C42—22no—
683C42—22no—
684C42—22no—
685C42—21no—
686C42—21no—
687C42—21no—
688C42—21no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—41no—
695C42—41no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—41no—
700C23—41no—
701C23C29×#12011yescharacteristic
702C23C29×#12011yescharacteristic
703C23C22×D4×C2911yescharacteristic
704Q8—21no—
705Q8—21no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—82no—
711D4—21no—
712D4—21no—
713D4—42no—
714D4—41no—
715D4—41no—
716D4—81no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—41no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—81no—
753C2×C4—82no—
754C2×C4C29×#12011yescharacteristic
755C2×C4C29×#12011yescharacteristic
756C2×C4C22×D4×C2911yescharacteristic
757C2×C4C22×D4×C2911yescharacteristic
758C2×C4C2×#41×C2911yescharacteristic
759C2×C4C2×#41×C2911yescharacteristic
760C2×C4C29×2−1+411yescharacteristic
761C2×C4C29×2−1+411yescharacteristic
762C8—22no—
763C8—22no—
764C8—41no—
765C8—41no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—81no—
778C22—81no—
779C22C2×C29×#12011yescharacteristic
780C22C29×#54711yescharacteristic
781C22C29×#54711yescharacteristic
782C4—21no—
783C4—21no—
784C4—42no—
785C4—42no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—42no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—81no—
797C4C29×#52511yescharacteristic
798C4C29×#53611yescharacteristic
799C4C29×#54711yescharacteristic
800C4C29×#54711yescharacteristic
801C2—21no—
802C2—21no—
803C2—41no—
804C2—41no—
805C2—81no—
806C2C29×#240611yescharacteristic
807C2C29×#301811yescharacteristic
808C2C29×#302011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#2911C2semidirect
4. C29×#2499C2semidirect
5. C29×#2061C2semidirect
6. C29×#2060C2semidirect
7. C29×#2038C2semidirect
8. C29×#2038C2semidirect
9. C29×#1901C2semidirect
11. C29×#1860C2semidirect
12. C29×#1859C2semidirect
13. C29×#1857C2semidirect
14. C29×#1857C2semidirect
15. C29×#1826C2semidirect
291. #24087C29direct (N × H)
364. #2911C2×C29semidirect
365. #2499C2×C29semidirect
366. #2061C2×C29semidirect
367. #2060C2×C29semidirect
368. #2038C2×C29semidirect
369. #2038C2×C29semidirect
370. #1901C2×C29semidirect
372. #1860C2×C29semidirect
373. #1859C2×C29semidirect
374. #1857C2×C29semidirect
375. #1857C2×C29semidirect
376. #1826C2×C29semidirect
586. C29#24087direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34952
C29×#30932
C29×#29112
C29×#24992
C29×#20612
C29×#20602
C29×#20382
C29×#19012
C29×#18712
C29×#18602
C29×#18592
C29×#18572
C29×#18262
#2408729