Finite Group Databasebeta

← C29×#18810 #20313710

Subgroups — C29×#18810 #20313710

Order 7424.

1042 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3519C211yesmaximal, characteristic, complemented
2C29×#3251C211yesmaximal, characteristic, complemented
3C29×#3207C211yesmaximal, characteristic, complemented
4C29×#3036C211yesmaximal, characteristic, complemented
5C29×#1646C211yesmaximal, characteristic, complemented
6C29×#1643C211yesmaximal, characteristic, complemented
7C29×#1642C211yesmaximal, characteristic, complemented
8C29×#1639C211yesmaximal, characteristic, complemented
9C29×#1624C211yesmaximal, characteristic, complemented
10C29×#1622C211yesmaximal, characteristic, complemented
11C29×#1621C211yesmaximal, characteristic, complemented
12C29×#1619C211yesmaximal, characteristic, complemented
13C29×#1560C211yesmaximal, characteristic, complemented
14C29×#1495C211yesmaximal, characteristic, complemented
15C29×#1486C211yesmaximal, characteristic, complemented
16C2×C29×AGL(1,ℤ/8)—21no—
17C29×#555C2211yescharacteristic
18C29×#554C2211yescharacteristic
19C29×#553—21no—
20C29×#553—21no—
21C29×#550C2211yescharacteristic
22C29×#546—22no—
23C29×#546—21no—
24D42×C29—21no—
25D42×C29C2211yescharacteristic
26C29×#540—21no—
27C29×#538—22no—
28C29×#532C2211yescharacteristic
29C29×#532C2211yescharacteristic, complemented
30C29×#529C2211yescharacteristic
31C29×#525—21no—
32C2×C29×#121—21no—
33C29×#518—21no—
34C2×C4×D4×C29C2211yescharacteristic
35C29×#493C2211yescharacteristic, complemented
36C29×#492C2211yescharacteristic, complemented
37C29×#487C2211yescharacteristic, complemented
38C29×#486C2211yescharacteristic, complemented
39C29×#478—21no—
40C29×#475C2211yescharacteristic, complemented
41C29×#474C2211yescharacteristic, complemented
42C29×#469—21no—
43C29×#468—21no—
44C29×#463—22no—
45C29×#463—21no—
46C29×#463—21no—
47C29×#463—21no—
48C29×#461C2211yescharacteristic
49C29×#461C2211yescharacteristic, complemented
50C29×#460C2211yescharacteristic, complemented
51C29×#459C2211yescharacteristic
52C29×#459C2211yescharacteristic, complemented
53C29×#459C2211yescharacteristic, complemented
54C29×#449—22no—
55C29×#431C2211yescharacteristic, complemented
56C29×#423C2211yescharacteristic, complemented
57C29×#423C2211yescharacteristic, complemented
58C29×#417—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×C29—21no—
73C2×#41×C29D412yes—
74C22×D4×C29—22no—
75C22×D4×C29—21no—
76C22×D4×C29—21no—
77C22×D4×C29D411yescharacteristic
78C23×C4×C29—21no—
79C29×AGL(1,ℤ/8)—44no—
80C2×SD16×C29—21no—
81C2×SD16×C29—21no—
82C2×SD16×C29—22no—
83C2×SD16×C29—21no—
84C2×D8×C29—21no—
85C2×D8×C29—21no—
86C2×D8×C29—22no—
87C2×D8×C29—21no—
88C2×M16×C29—21no—
89C2×M16×C29—21no—
90C29×C4⋊Q8C2311yescharacteristic
91C29×C4⋊Q8C2311yescharacteristic
92C29×#127—21no—
93C29×#127C2311yescharacteristic
94C29×#127C2311yescharacteristic
95C29×#126—22no—
96C29×#126—21no—
97C29×#125—21no—
98C29×#125D411yescharacteristic
99C29×#124—22no—
100C29×#124—21no—
101C29×#124D411yescharacteristic
102C29×#124D412yes—
103C29×#123—22no—
104C29×#123—22no—
105C29×#123—22no—
106C29×#123—21no—
107C29×C22⋊Q8—21no—
108C29×C22⋊Q8—22no—
109C29×C22⋊Q8D411yescharacteristic
110C29×#121—22no—
111C29×#121—22no—
112C29×#121—22no—
113C29×#121—22no—
114C29×#121—21no—
115C29×#121—22no—
116C29×#121—21no—
117C29×#121—21no—
118C29×#121—21no—
119C29×#121—21no—
120C29×#121—21no—
121C29×#121—21no—
122C29×#121—21no—
123C29×#121—21no—
124C29×#121D411yescharacteristic
125C29×#120—22no—
126C29×#120—22no—
127C29×#120—22no—
128C4×Q8×C29C2311yescharacteristic
129C4×D4×C29—22no—
130C4×D4×C29—22no—
131C4×D4×C29—22no—
132C4×D4×C29—21no—
133C4×D4×C29—21no—
134C4×D4×C29—21no—
135C4×D4×C29—21no—
136C4×D4×C29—21no—
137C4×D4×C29—21no—
138C4×D4×C29—21no—
139C4×D4×C29—21no—
140C4×D4×C29—21no—
141C4×D4×C29D411yescharacteristic
142C4×D4×C29D411yescharacteristic
143C4×D4×C29C2311yescharacteristic
144C4×D4×C29C2311yescharacteristic
145C4×D4×C29C2311yescharacteristic
146C29×#117—21no—
147C29×#117—21no—
148C29×#117—21no—
149C2×C4⋊C4×C29—21no—
150C2×C4⋊C4×C29D411yescharacteristic
151C2×C22⋊C4×C29—22no—
152C2×C22⋊C4×C29—22no—
153C2×C22⋊C4×C29—21no—
154C2×C42×C29C2311yescharacteristic
155C29×#107—21no—
156C29×#106—21no—
157C29×C4⋊C8—21no—
158C29×C4⋊C8—21no—
159C29×C4⋊C8—21no—
160C29×C4⋊C8C2311yescharacteristic
161C29×C4⋊C8C2311yescharacteristic
162C29×C4⋊C8C2311yescharacteristic
163C29×C4⋊C8C2311yescharacteristic
164C29×#103—22no—
165C29×#103—21no—
166C29×#103—21no—
167C29×#103—21no—
168C29×#102—22no—
169C29×#102—21no—
170C29×#102—21no—
171C29×#102—21no—
172C29×#102—21no—
173C29×#102—21no—
174C29×C22⋊C8—21no—
175C4×C8×C29C2311yescharacteristic
176C4×C8×C29C2311yescharacteristic
177C24×C29—22no—
178C24×C29—21no—
179#41×C29—42no—
180#41×C29—42no—
181#41×C29—81no—
182#41×C29—81no—
183#41×C29—82no—
184C2×Q8×C29—21no—
185C2×Q8×C29C2×D411yescharacteristic
186C2×Q8×C29C2×D412yes—
187C2×D4×C29—22no—
188C2×D4×C29—22no—
189C2×D4×C29—22no—
190C2×D4×C29—21no—
191C2×D4×C29—22no—
192C2×D4×C29—22no—
193C2×D4×C29—22no—
194C2×D4×C29—22no—
195C2×D4×C29—21no—
196C2×D4×C29—21no—
197C2×D4×C29—21no—
198C2×D4×C29—21no—
199C2×D4×C29—21no—
200C2×D4×C29—21no—
201C2×D4×C29—41no—
202C2×D4×C29—42no—
203C2×D4×C29—42no—
204C2×D4×C29—41no—
205C2×D4×C29—81no—
206C2×D4×C29—81no—
207C2×D4×C29—84no—
208C2×D4×C29C2×D411yescharacteristic
209C2×D4×C29C2×D411yescharacteristic
210C2×D4×C29C2×D411yescharacteristic
211C2×D4×C29C2×D412yes—
212C22×C4×C29—22no—
213C22×C4×C29—22no—
214C22×C4×C29—21no—
215C22×C4×C29—21no—
216C22×C4×C29—21no—
217C22×C4×C29—21no—
218C22×C4×C29—21no—
219C22×C4×C29—22no—
220C22×C4×C29—21no—
221C22×C4×C29—41no—
222C22×C4×C29—81no—
223C22×C4×C29—81no—
224C22×C4×C29C2×D411yescharacteristic
225C22×C4×C29C2×D411yescharacteristic
226C22×C4×C29C2×D411yescharacteristic
227SD16×C29—42no—
228SD16×C29—42no—
229SD16×C29—81no—
230SD16×C29—82no—
231D8×C29—42no—
232D8×C29—42no—
233D8×C29—81no—
234D8×C29—82no—
235M16×C29—42no—
236M16×C29—81no—
237C2×C8×C29—21no—
238C2×C8×C29—21no—
239C2×C8×C29—21no—
240C2×C8×C29—21no—
241C2×C8×C29—21no—
242C2×C8×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—21no—
254C4⋊C4×C29C2×D411yescharacteristic
255C4⋊C4×C29C2×D411yescharacteristic
256C4⋊C4×C29C2×D411yescharacteristic
257C4⋊C4×C29C2×D411yescharacteristic
258C22⋊C4×C29—22no—
259C22⋊C4×C29—22no—
260C22⋊C4×C29—22no—
261C22⋊C4×C29—22no—
262C22⋊C4×C29—22no—
263C22⋊C4×C29—21no—
264C22⋊C4×C29—21no—
265C22⋊C4×C29—21no—
266C22⋊C4×C29—21no—
267C22⋊C4×C29—22no—
268C22⋊C4×C29—21no—
269C22⋊C4×C29—21no—
270C22⋊C4×C29—22no—
271C22⋊C4×C29—21no—
272C22⋊C4×C29—21no—
273C22⋊C4×C29—21no—
274C22⋊C4×C29—41no—
275C22⋊C4×C29—41no—
276C42×C29—22no—
277C42×C29—21no—
278C42×C29C2×D411yescharacteristic
279C42×C29C2×D411yescharacteristic
280C42×C29C2×D411yescharacteristic
281C42×C29C2411yescharacteristic
282#18810C2911yesmaximal, characteristic, direct product factor, Sylow
283C23×C29—21no—
284C23×C29—21no—
285C23×C29—21no—
286C23×C29—22no—
287C23×C29—42no—
288C23×C29—42no—
289C23×C29—44no—
290C23×C29—41no—
291C23×C29—81no—
292C23×C29—82no—
293C23×C29—82no—
294C23×C29#12011yescharacteristic
295Q8×C29—21no—
296Q8×C29—21no—
297Q8×C29—42no—
298Q8×C29—41no—
299Q8×C29—41no—
300D4×C29—21no—
301D4×C29—21no—
302D4×C29—21no—
303D4×C29—21no—
304D4×C29—21no—
305D4×C29—42no—
306D4×C29—42no—
307D4×C29—42no—
308D4×C29—44no—
309D4×C29—42no—
310D4×C29—44no—
311D4×C29—41no—
312D4×C29—41no—
313D4×C29—41no—
314D4×C29—41no—
315D4×C29—41no—
316D4×C29—41no—
317D4×C29—41no—
318D4×C29—41no—
319D4×C29—82no—
320D4×C29—82no—
321D4×C29—82no—
322D4×C29—82no—
323D4×C29—82no—
324D4×C29AGL(1,ℤ/8)12yes—
325C2×C4×C29—21no—
326C2×C4×C29—21no—
327C2×C4×C29—21no—
328C2×C4×C29—21no—
329C2×C4×C29—21no—
330C2×C4×C29—21no—
331C2×C4×C29—21no—
332C2×C4×C29—22no—
333C2×C4×C29—21no—
334C2×C4×C29—21no—
335C2×C4×C29—41no—
336C2×C4×C29—41no—
337C2×C4×C29—41no—
338C2×C4×C29—41no—
339C2×C4×C29—41no—
340C2×C4×C29—41no—
341C2×C4×C29—41no—
342C2×C4×C29—41no—
343C2×C4×C29—81no—
344C2×C4×C29—81no—
345C2×C4×C29—82no—
346C2×C4×C29—82no—
347C2×C4×C29—81no—
348C2×C4×C29—82no—
349C2×C4×C29—82no—
350C2×C4×C29#12011yescharacteristic
351C2×C4×C29#12011yescharacteristic
352C2×C4×C29#12011yescharacteristic
353C2×C4×C29C22×D411yescharacteristic
354C2×C4×C29C22×D411yescharacteristic
355C2×C4×C29C22×D411yescharacteristic
356C8×C29—41no—
357C8×C29—41no—
358C8×C29—41no—
359C8×C29—41no—
360C8×C29—41no—
361C8×C29—41no—
362#3519C2×C2911yescharacteristic, complemented
363#3251C2×C2911yescharacteristic, complemented
364#3207C2×C2911yescharacteristic, complemented
365#3036C2×C2911yescharacteristic, complemented
366#1646C2×C2911yescharacteristic, complemented
367#1643C2×C2911yescharacteristic, complemented
368#1642C2×C2911yescharacteristic, complemented
369#1639C2×C2911yescharacteristic, complemented
370#1624C2×C2911yescharacteristic, complemented
371#1622C2×C2911yescharacteristic, complemented
372#1621C2×C2911yescharacteristic, complemented
373#1619C2×C2911yescharacteristic, complemented
374#1560C2×C2911yescharacteristic, complemented
375#1495C2×C2911yescharacteristic, complemented
376#1486C2×C2911yescharacteristic, complemented
377C22×C29—21no—
378C22×C29—22no—
379C22×C29—21no—
380C22×C29—21no—
381C22×C29—41no—
382C22×C29—41no—
383C22×C29—41no—
384C22×C29—41no—
385C22×C29—42no—
386C22×C29—41no—
387C22×C29—42no—
388C22×C29—41no—
389C22×C29—42no—
390C22×C29—41no—
391C22×C29—41no—
392C22×C29—84no—
393C22×C29—81no—
394C22×C29—81no—
395C22×C29—81no—
396C22×C29—164no—
397C22×C29C2×#12011yescharacteristic
398C4×C29—21no—
399C4×C29—21no—
400C4×C29—21no—
401C4×C29—21no—
402C4×C29—41no—
403C4×C29—41no—
404C4×C29—41no—
405C4×C29—41no—
406C4×C29—41no—
407C4×C29—42no—
408C4×C29—81no—
409C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
410C4×C29#57511yescharacteristic
411C4×C29#57611yescharacteristic
412C4×C29#57711yescharacteristic
413C2×AGL(1,ℤ/8)—21no—
414#555C22×C2911yescharacteristic
415#554C22×C2911yescharacteristic
416#553—21no—
417#553—21no—
418#550C22×C2911yescharacteristic
419#546—22no—
420#546—21no—
421D42—21no—
422D42C22×C2911yescharacteristic
423#540—21no—
424#538—22no—
425#532C22×C2911yescharacteristic
426#532C22×C2911yescharacteristic, complemented
427#529C22×C2911yescharacteristic
428#525—21no—
429C2×#121—21no—
430#518—21no—
431C2×C4×D4C22×C2911yescharacteristic
432#493C22×C2911yescharacteristic, complemented
433#492C22×C2911yescharacteristic, complemented
434#487C22×C2911yescharacteristic, complemented
435#486C22×C2911yescharacteristic, complemented
436#478—21no—
437#475C22×C2911yescharacteristic, complemented
438#474C22×C2911yescharacteristic, complemented
439#469—21no—
440#468—21no—
441#463—22no—
442#463—21no—
443#463—21no—
444#463—21no—
445#461C22×C2911yescharacteristic
446#461C22×C2911yescharacteristic, complemented
447#460C22×C2911yescharacteristic, complemented
448#459C22×C2911yescharacteristic
449#459C22×C2911yescharacteristic, complemented
450#459C22×C2911yescharacteristic, complemented
451#449—22no—
452#431C22×C2911yescharacteristic, complemented
453#423C22×C2911yescharacteristic, complemented
454#423C22×C2911yescharacteristic, complemented
455#417—21no—
456#333C22×C2911yescharacteristic, complemented
457#333C22×C2911yescharacteristic, complemented
458#331C22×C2911yescharacteristic, complemented
459#331C22×C2911yescharacteristic, complemented
460Q8⋊C8C22×C2911yescharacteristic, complemented
461Q8⋊C8C22×C2911yescharacteristic, complemented
462D4⋊C8C22×C2911yescharacteristic
463D4⋊C8C22×C2911yescharacteristic
464D4⋊C8C22×C2911yescharacteristic, complemented
465D4⋊C8C22×C2911yescharacteristic, complemented
466D4⋊C8C22×C2911yescharacteristic, complemented
467D4⋊C8C22×C2911yescharacteristic, complemented
468C2×C29—41no—
469C2×C29—42no—
470C2×C29—81no—
471C2×C29—82no—
472C2×C29—81no—
473C2×C29—161no—
474C2×C29#300611yescharacteristic
475C2×C29#301211yescharacteristic
476C2×C29#301911yescharacteristic
477C2×#41—21no—
478C2×#41—21no—
479C2×#41D4×C2912yes—
480C22×D4—22no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4D4×C2911yescharacteristic
484C23×C4—21no—
485AGL(1,ℤ/8)—44no—
486C2×SD16—21no—
487C2×SD16—21no—
488C2×SD16—22no—
489C2×SD16—21no—
490C2×D8—21no—
491C2×D8—21no—
492C2×D8—22no—
493C2×D8—21no—
494C2×M16—21no—
495C2×M16—21no—
496C4⋊Q8C23×C2911yescharacteristic
497C4⋊Q8C23×C2911yescharacteristic
498#127—21no—
499#127C23×C2911yescharacteristic
500#127C23×C2911yescharacteristic
501#126—22no—
502#126—21no—
503#125—21no—
504#125D4×C2911yescharacteristic
505#124—22no—
506#124—21no—
507#124D4×C2911yescharacteristic
508#124D4×C2912yes—
509#123—22no—
510#123—22no—
511#123—22no—
512#123—21no—
513C22⋊Q8—21no—
514C22⋊Q8—22no—
515C22⋊Q8D4×C2911yescharacteristic
516#121—22no—
517#121—22no—
518#121—22no—
519#121—22no—
520#121—21no—
521#121—22no—
522#121—21no—
523#121—21no—
524#121—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121D4×C2911yescharacteristic
531#120—22no—
532#120—22no—
533#120—22no—
534C4×Q8C23×C2911yescharacteristic
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4D4×C2911yescharacteristic
548C4×D4D4×C2911yescharacteristic
549C4×D4C23×C2911yescharacteristic
550C4×D4C23×C2911yescharacteristic
551C4×D4C23×C2911yescharacteristic
552#117—21no—
553#117—21no—
554#117—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4D4×C2911yescharacteristic
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C42C23×C2911yescharacteristic
561#107—21no—
562#106—21no—
563C4⋊C8—21no—
564C4⋊C8—21no—
565C4⋊C8—21no—
566C4⋊C8C23×C2911yescharacteristic
567C4⋊C8C23×C2911yescharacteristic
568C4⋊C8C23×C2911yescharacteristic
569C4⋊C8C23×C2911yescharacteristic
570#103—22no—
571#103—21no—
572#103—21no—
573#103—21no—
574#102—22no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580C22⋊C8—21no—
581C4×C8C23×C2911yescharacteristic
582C4×C8C23×C2911yescharacteristic
583C29#1881011yescharacteristic, direct product factor, Sylow
584C24—22no—
585C24—21no—
586#41—42no—
587#41—42no—
588#41—81no—
589#41—81no—
590#41—82no—
591C2×Q8—21no—
592C2×Q8C2×D4×C2911yescharacteristic
593C2×Q8C2×D4×C2912yes—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—41no—
609C2×D4—42no—
610C2×D4—42no—
611C2×D4—41no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4—84no—
615C2×D4C2×D4×C2911yescharacteristic
616C2×D4C2×D4×C2911yescharacteristic
617C2×D4C2×D4×C2911yescharacteristic
618C2×D4C2×D4×C2912yes—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—22no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—81no—
630C22×C4—81no—
631C22×C4C2×D4×C2911yescharacteristic
632C22×C4C2×D4×C2911yescharacteristic
633C22×C4C2×D4×C2911yescharacteristic
634SD16—42no—
635SD16—42no—
636SD16—81no—
637SD16—82no—
638D8—42no—
639D8—42no—
640D8—81no—
641D8—82no—
642M16—42no—
643M16—81no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C4⋊C4—22no—
651C4⋊C4—22no—
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⋊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—22no—
669C22⋊C4—22no—
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—22no—
675C22⋊C4—21no—
676C22⋊C4—21no—
677C22⋊C4—22no—
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C42—22no—
684C42—21no—
685C42C2×D4×C2911yescharacteristic
686C42C2×D4×C2911yescharacteristic
687C42C2×D4×C2911yescharacteristic
688C42C24×C2911yescharacteristic
689C23—21no—
690C23—21no—
691C23—21no—
692C23—22no—
693C23—42no—
694C23—42no—
695C23—44no—
696C23—41no—
697C23—81no—
698C23—82no—
699C23—82no—
700C23C29×#12011yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—42no—
704Q8—41no—
705Q8—41no—
706D4—21no—
707D4—21no—
708D4—21no—
709D4—21no—
710D4—21no—
711D4—42no—
712D4—42no—
713D4—42no—
714D4—44no—
715D4—42no—
716D4—44no—
717D4—41no—
718D4—41no—
719D4—41no—
720D4—41no—
721D4—41no—
722D4—41no—
723D4—41no—
724D4—41no—
725D4—82no—
726D4—82no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4C29×AGL(1,ℤ/8)12yes—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—81no—
750C2×C4—81no—
751C2×C4—82no—
752C2×C4—82no—
753C2×C4—81no—
754C2×C4—82no—
755C2×C4—82no—
756C2×C4C29×#12011yescharacteristic
757C2×C4C29×#12011yescharacteristic
758C2×C4C29×#12011yescharacteristic
759C2×C4C22×D4×C2911yescharacteristic
760C2×C4C22×D4×C2911yescharacteristic
761C2×C4C22×D4×C2911yescharacteristic
762C8—41no—
763C8—41no—
764C8—41no—
765C8—41no—
766C8—41no—
767C8—41no—
768C22—21no—
769C22—22no—
770C22—21no—
771C22—21no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—42no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—41no—
783C22—84no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—164no—
788C22C2×C29×#12011yescharacteristic
789C4—21no—
790C4—21no—
791C4—21no—
792C4—21no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—41no—
798C4—42no—
799C4—81no—
800C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
801C4C29×#57511yescharacteristic
802C4C29×#57611yescharacteristic
803C4C29×#57711yescharacteristic
804C2—41no—
805C2—42no—
806C2—81no—
807C2—81no—
808C2—82no—
809C2—161no—
810C2C29×#300611yescharacteristic
811C2C29×#301211yescharacteristic
812C2C29×#301911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
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
1. C29×#3519C2semidirect
2. C29×#3251C2semidirect
3. C29×#3207C2semidirect
4. C29×#3036C2semidirect
5. C29×#1646C2semidirect
6. C29×#1643C2semidirect
7. C29×#1642C2semidirect
8. C29×#1639C2semidirect
9. C29×#1624C2semidirect
10. C29×#1622C2semidirect
11. C29×#1621C2semidirect
12. C29×#1619C2semidirect
13. C29×#1560C2semidirect
14. C29×#1495C2semidirect
15. C29×#1486C2semidirect
29. C29×#532C22semidirect
35. C29×#493C22semidirect
36. C29×#492C22semidirect
37. C29×#487C22semidirect
38. C29×#486C22semidirect
40. C29×#475C22semidirect
41. C29×#474C22semidirect
49. C29×#461C22semidirect
50. C29×#460C22semidirect
52. C29×#459C22semidirect
53. C29×#459C22semidirect
55. 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
282. #18810C29direct (N × H)
362. #3519C2×C29semidirect
363. #3251C2×C29semidirect
364. #3207C2×C29semidirect
365. #3036C2×C29semidirect
366. #1646C2×C29semidirect
367. #1643C2×C29semidirect
368. #1642C2×C29semidirect
369. #1639C2×C29semidirect
370. #1624C2×C29semidirect
371. #1622C2×C29semidirect
372. #1621C2×C29semidirect
373. #1619C2×C29semidirect
374. #1560C2×C29semidirect
375. #1495C2×C29semidirect
376. #1486C2×C29semidirect
426. #532C22×C29semidirect
432. #493C22×C29semidirect
433. #492C22×C29semidirect
434. #487C22×C29semidirect
435. #486C22×C29semidirect
437. #475C22×C29semidirect
438. #474C22×C29semidirect
446. #461C22×C29semidirect
447. #460C22×C29semidirect
449. #459C22×C29semidirect
450. #459C22×C29semidirect
452. #431C22×C29semidirect
453. #423C22×C29semidirect
454. #423C22×C29semidirect
456. #333C22×C29semidirect
457. #333C22×C29semidirect
458. #331C22×C29semidirect
459. #331C22×C29semidirect
460. Q8⋊C8C22×C29semidirect
461. Q8⋊C8C22×C29semidirect
464. D4⋊C8C22×C29semidirect
465. D4⋊C8C22×C29semidirect
466. D4⋊C8C22×C29semidirect
467. D4⋊C8C22×C29semidirect
583. C29#18810direct (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×#32512
C29×#32072
C29×#30362
C29×#16462
C29×#16432
C29×#16422
C29×#16392
C29×#16242
C29×#16222
C29×#16212
C29×#16192
C29×#15602
C29×#14952
C29×#14862
#1881029