Finite Group Databasebeta

← C29×#18448 #20313348

Subgroups — C29×#18448 #20313348

Order 7424.

968 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3535C211yesmaximal, characteristic, complemented
2C29×#3193C211yesmaximal, characteristic, complemented
3C29×#3188C211yesmaximal, characteristic, complemented
4C29×#2813C211yesmaximal, characteristic, complemented
5C29×#1618C211yesmaximal, characteristic, complemented
6C29×#1617C211yesmaximal, characteristic, complemented
7C29×#1615C211yesmaximal, characteristic, complemented
8C29×#1614C211yesmaximal, characteristic, complemented
9C29×#1600C211yesmaximal, characteristic, complemented
10C29×#1599C211yesmaximal, characteristic, complemented
11C29×#1597C211yesmaximal, characteristic, complemented
12C29×#1596C211yesmaximal, characteristic, complemented
13C29×#1520C211yesmaximal, characteristic, complemented
14C29×#1513C211yesmaximal, characteristic, complemented
15C29×#1468C211yesmaximal, characteristic, complemented
16C29×#563—21no—
17C29×#562—21no—
18C29×#554—21no—
19C29×#552—21no—
20C29×#551—21no—
21C29×#551—21no—
22C29×#547—21no—
23C29×#546—21no—
24C29×#544C2211yescharacteristic
25C29×#543C2211yescharacteristic
26C29×#542—21no—
27C29×#539—21no—
28C29×#539—21no—
29C29×#539C2211yescharacteristic
30C29×#538C2211yescharacteristic
31C29×#536—21no—
32C29×#525C2211yescharacteristic
33C2×C29×#123C2211yescharacteristic
34C2×C29×C22⋊Q8C2211yescharacteristic
35C2×C29×#121C2211yescharacteristic
36C29×#484C2211yescharacteristic
37C29×#484C2211yescharacteristic
38C29×#484C2211yescharacteristic
39C29×#482—21no—
40C29×#481C2211yescharacteristic
41C29×#480—21no—
42C29×#468—21no—
43C29×#468—21no—
44C29×#466—21no—
45C29×#465—21no—
46C29×#450C2211yescharacteristic
47C29×#450C2211yescharacteristic
48C29×#450C2211yescharacteristic
49C29×#449—21no—
50C29×#448—21no—
51C29×#447C2211yescharacteristic
52C29×#407C2211yescharacteristic
53C2×C29×C22⋊C8C2211yescharacteristic
54C29×#400C2211yescharacteristic
55C29×#399C2211yescharacteristic
56C29×#396—21no—
57C29×#394—21no—
58C29×#394—21no—
59C29×#394C2211yescharacteristic
60C29×#392—21no—
61C29×#392C2211yescharacteristic
62C29×#380C2211yescharacteristic
63C29×#328C2211yescharacteristic
64C29×#328C2211yescharacteristic
65C29×#328C2211yescharacteristic
66C29×#328C2211yescharacteristic
67C29×#328C2211yescharacteristic
68C29×#328C2211yescharacteristic
69C29×#327C2211yescharacteristic
70C29×#327C2211yescharacteristic
71C29×#324C2211yescharacteristic
72C29×#324C2211yescharacteristic
73C29×#323C2211yescharacteristic
74C29×#323C2211yescharacteristic
75C2×#41×C29—21no—
76C2×#41×C29D411yescharacteristic, complemented
77C22×Q8×C29D411yescharacteristic, complemented
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29D411yescharacteristic
81C22×D4×C29C2311yescharacteristic
82C23×C4×C29C2311yescharacteristic
83C2×SD16×C29—21no—
84C2×SD16×C29—21no—
85C2×SD16×C29—21no—
86C2×D8×C29—21no—
87C2×M16×C29—21no—
88C22×C8×C29—21no—
89C29×C4⋊Q8—21no—
90C29×C4⋊Q8—21no—
91C29×C4⋊Q8—21no—
92C29×#126—21no—
93C29×#126—21no—
94C29×#126—21no—
95C29×#126—21no—
96C29×#126—21no—
97C29×#126—21no—
98C29×#125—21no—
99C29×#125—21no—
100C29×#125—21no—
101C29×#125—21no—
102C29×#125—21no—
103C29×#124—21no—
104C29×#124—21no—
105C29×#124—21no—
106C29×#124—21no—
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×#123—21no—
111C29×#123—21no—
112C29×#123—21no—
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×C22⋊Q8—21no—
122C29×C22⋊Q8—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⋊Q8D411yescharacteristic, complemented
136C29×C22⋊Q8D411yescharacteristic, complemented
137C29×C22⋊Q8D411yescharacteristic, complemented
138C29×C22⋊Q8C2311yescharacteristic
139C29×C22⋊Q8C2311yescharacteristic
140C29×C22⋊Q8C2311yescharacteristic
141C29×#121—21no—
142C29×#121—21no—
143C29×#121—21no—
144C29×#121—21no—
145C29×#121—21no—
146C29×#121—21no—
147C29×#121—21no—
148C29×#121—21no—
149C29×#121D411yescharacteristic, complemented
150C29×#121C2311yescharacteristic
151C29×#120—21no—
152C29×#120—21no—
153C4×Q8×C29—21no—
154C4×D4×C29—21no—
155C4×D4×C29—21no—
156C4×D4×C29—21no—
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29—21no—
160C4×D4×C29—21no—
161C29×#117—21no—
162C29×#117—21no—
163C29×#117—21no—
164C29×#117D411yescharacteristic, complemented
165C2×C4⋊C4×C29—21no—
166C2×C4⋊C4×C29—21no—
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29D411yescharacteristic
170C2×C4⋊C4×C29D411yescharacteristic, complemented
171C2×C4⋊C4×C29C2311yescharacteristic
172C2×C4⋊C4×C29C2311yescharacteristic
173C2×C22⋊C4×C29—21no—
174C2×C22⋊C4×C29—21no—
175C2×C22⋊C4×C29—21no—
176C2×C22⋊C4×C29—21no—
177C2×C22⋊C4×C29—21no—
178C2×C22⋊C4×C29—21no—
179C2×C22⋊C4×C29—21no—
180C2×C22⋊C4×C29—21no—
181C2×C22⋊C4×C29D411yescharacteristic
182C2×C22⋊C4×C29D411yescharacteristic
183C2×C22⋊C4×C29C2311yescharacteristic
184C29×#107—21no—
185C29×#107—21no—
186C29×#107—21no—
187C29×#106—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#102—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×C22⋊C8—21no—
197C29×C22⋊C8—21no—
198C29×C22⋊C8C2311yescharacteristic
199C29×C22⋊C8C2311yescharacteristic
200C29×C22⋊C8C2311yescharacteristic
201C29×C22⋊C8C2311yescharacteristic
202C29×#95—21no—
203C29×#95—21no—
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29C2×D411yescharacteristic
208C24×C29C2×D411yescharacteristic
209#41×C29—82no—
210#41×C29—81no—
211C2×Q8×C29—21no—
212C2×Q8×C29—21no—
213C2×Q8×C29—21no—
214C2×Q8×C29—81no—
215C2×Q8×C29C2×D411yescharacteristic
216C2×Q8×C29C2×D411yescharacteristic
217C2×Q8×C29C2×D411yescharacteristic
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—21no—
222C2×D4×C29—21no—
223C2×D4×C29—21no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—21no—
227C2×D4×C29—41no—
228C2×D4×C29—41no—
229C2×D4×C29—81no—
230C2×D4×C29—81no—
231C2×D4×C29—81no—
232C2×D4×C29—81no—
233C2×D4×C29—81no—
234C2×D4×C29—81no—
235C2×D4×C29—81no—
236C2×D4×C29C2×D411yescharacteristic
237C22×C4×C29—21no—
238C22×C4×C29—21no—
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—81no—
248C22×C4×C29C2×D411yescharacteristic
249C22×C4×C29C2×D411yescharacteristic
250C22×C4×C29C2×D411yescharacteristic
251C22×C4×C29C2×D411yescharacteristic
252C22×C4×C29C2×D411yescharacteristic
253C22×C4×C29C2×D411yescharacteristic
254C22×C4×C29C2×D411yescharacteristic
255C22×C4×C29C2×D411yescharacteristic
256C22×C4×C29C2411yescharacteristic
257SD16×C29—81no—
258SD16×C29—81no—
259SD16×C29—81no—
260D8×C29—81no—
261M16×C29—81no—
262C2×C8×C29—21no—
263C2×C8×C29—21no—
264C2×C8×C29—21no—
265C2×C8×C29—21no—
266C2×C8×C29—81no—
267C4⋊C4×C29—21no—
268C4⋊C4×C29—21no—
269C4⋊C4×C29—21no—
270C4⋊C4×C29—21no—
271C4⋊C4×C29—21no—
272C4⋊C4×C29—21no—
273C4⋊C4×C29—21no—
274C4⋊C4×C29—21no—
275C4⋊C4×C29—21no—
276C4⋊C4×C29—21no—
277C4⋊C4×C29—21no—
278C4⋊C4×C29—21no—
279C4⋊C4×C29—21no—
280C4⋊C4×C29—21no—
281C4⋊C4×C29—21no—
282C4⋊C4×C29—21no—
283C4⋊C4×C29—21no—
284C4⋊C4×C29—21no—
285C4⋊C4×C29—21no—
286C4⋊C4×C29—21no—
287C4⋊C4×C29—21no—
288C4⋊C4×C29—21no—
289C4⋊C4×C29—21no—
290C4⋊C4×C29—21no—
291C4⋊C4×C29—21no—
292C4⋊C4×C29—81no—
293C4⋊C4×C29—81no—
294C4⋊C4×C29C2×D411yescharacteristic
295C4⋊C4×C29C2×D411yescharacteristic
296C4⋊C4×C29C2×D411yescharacteristic
297C4⋊C4×C29C2×D411yescharacteristic
298C22⋊C4×C29—21no—
299C22⋊C4×C29—21no—
300C22⋊C4×C29—21no—
301C22⋊C4×C29—21no—
302C22⋊C4×C29—21no—
303C22⋊C4×C29—21no—
304C22⋊C4×C29—21no—
305C22⋊C4×C29—21no—
306C22⋊C4×C29—21no—
307C22⋊C4×C29—21no—
308C22⋊C4×C29—21no—
309C22⋊C4×C29—21no—
310C22⋊C4×C29—21no—
311C22⋊C4×C29—21no—
312C22⋊C4×C29—21no—
313C22⋊C4×C29—21no—
314C22⋊C4×C29—21no—
315C22⋊C4×C29—21no—
316C22⋊C4×C29—21no—
317C22⋊C4×C29—21no—
318C22⋊C4×C29—21no—
319C22⋊C4×C29—21no—
320C22⋊C4×C29—21no—
321C22⋊C4×C29—41no—
322C22⋊C4×C29—41no—
323C22⋊C4×C29—81no—
324C22⋊C4×C29—81no—
325C22⋊C4×C29—81no—
326C22⋊C4×C29—81no—
327C22⋊C4×C29—81no—
328C42×C29—21no—
329C42×C29—21no—
330C42×C29—21no—
331C42×C29—21no—
332C42×C29—21no—
333#18448C2911yesmaximal, characteristic, direct product factor, Sylow
334C23×C29—21no—
335C23×C29—21no—
336C23×C29—21no—
337C23×C29—21no—
338C23×C29—21no—
339C23×C29—21no—
340C23×C29—41no—
341C23×C29—41no—
342C23×C29—41no—
343C23×C29—41no—
344C23×C29—41no—
345C23×C29—41no—
346C23×C29—41no—
347C23×C29—41no—
348C23×C29—41no—
349C23×C29—41no—
350C23×C29—41no—
351C23×C29#12011yescharacteristic
352C23×C29#12011yescharacteristic
353C23×C29C22×D411yescharacteristic
354Q8×C29—41no—
355Q8×C29—41no—
356Q8×C29—41no—
357Q8×C29—81no—
358Q8×C29—81no—
359Q8×C29—81no—
360D4×C29—41no—
361D4×C29—41no—
362D4×C29—41no—
363D4×C29—41no—
364D4×C29—41no—
365D4×C29—42no—
366D4×C29—42no—
367D4×C29—41no—
368D4×C29—41no—
369D4×C29—81no—
370D4×C29—81no—
371D4×C29—81no—
372D4×C29—81no—
373D4×C29—82no—
374D4×C29—82no—
375D4×C29—84no—
376C2×C4×C29—21no—
377C2×C4×C29—21no—
378C2×C4×C29—21no—
379C2×C4×C29—21no—
380C2×C4×C29—21no—
381C2×C4×C29—21no—
382C2×C4×C29—21no—
383C2×C4×C29—21no—
384C2×C4×C29—21no—
385C2×C4×C29—21no—
386C2×C4×C29—21no—
387C2×C4×C29—21no—
388C2×C4×C29—41no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—42no—
395C2×C4×C29—41no—
396C2×C4×C29—41no—
397C2×C4×C29—41no—
398C2×C4×C29—41no—
399C2×C4×C29—41no—
400C2×C4×C29—41no—
401C2×C4×C29—41no—
402C2×C4×C29—41no—
403C2×C4×C29—41no—
404C2×C4×C29—41no—
405C2×C4×C29—41no—
406C2×C4×C29—81no—
407C2×C4×C29—81no—
408C2×C4×C29—81no—
409C2×C4×C29—81no—
410C2×C4×C29—81no—
411C2×C4×C29—81no—
412C2×C4×C29#12011yescharacteristic
413C2×C4×C29#12011yescharacteristic
414C2×C4×C29C22×D411yescharacteristic
415C2×C4×C29C22×D411yescharacteristic
416C8×C29—41no—
417C8×C29—41no—
418C8×C29—41no—
419C8×C29—41no—
420#3535C2×C2911yescharacteristic, complemented
421#3193C2×C2911yescharacteristic, complemented
422#3188C2×C2911yescharacteristic, complemented
423#2813C2×C2911yescharacteristic, complemented
424#1618C2×C2911yescharacteristic, complemented
425#1617C2×C2911yescharacteristic, complemented
426#1615C2×C2911yescharacteristic, complemented
427#1614C2×C2911yescharacteristic, complemented
428#1600C2×C2911yescharacteristic, complemented
429#1599C2×C2911yescharacteristic, complemented
430#1597C2×C2911yescharacteristic, complemented
431#1596C2×C2911yescharacteristic, complemented
432#1520C2×C2911yescharacteristic, complemented
433#1513C2×C2911yescharacteristic, complemented
434#1468C2×C2911yescharacteristic, complemented
435C22×C29—21no—
436C22×C29—21no—
437C22×C29—21no—
438C22×C29—21no—
439C22×C29—21no—
440C22×C29—21no—
441C22×C29—21no—
442C22×C29—21no—
443C22×C29—41no—
444C22×C29—41no—
445C22×C29—41no—
446C22×C29—41no—
447C22×C29—41no—
448C22×C29—41no—
449C22×C29—81no—
450C22×C29—81no—
451C22×C29—81no—
452C22×C29—81no—
453C22×C29—81no—
454C22×C29—81no—
455C22×C29—81no—
456C22×C29—81no—
457C22×C29—81no—
458C22×C29—81no—
459C22×C29—81no—
460C22×C29C2×#12011yescharacteristic
461C22×C29#57711yescharacteristic
462C22×C29#57811yescharacteristic
463C4×C29—21no—
464C4×C29—21no—
465C4×C29—21no—
466C4×C29—21no—
467C4×C29—41no—
468C4×C29—41no—
469C4×C29—41no—
470C4×C29—41no—
471C4×C29—41no—
472C4×C29—41no—
473C4×C29—41no—
474C4×C29—41no—
475C4×C29—41no—
476C4×C29—41no—
477C4×C29—81no—
478C4×C29—81no—
479C4×C29—81no—
480#563—21no—
481#562—21no—
482#554—21no—
483#552—21no—
484#551—21no—
485#551—21no—
486#547—21no—
487#546—21no—
488#544C22×C2911yescharacteristic
489#543C22×C2911yescharacteristic
490#542—21no—
491#539—21no—
492#539—21no—
493#539C22×C2911yescharacteristic
494#538C22×C2911yescharacteristic
495#536—21no—
496#525C22×C2911yescharacteristic
497C2×#123C22×C2911yescharacteristic
498C2×C22⋊Q8C22×C2911yescharacteristic
499C2×#121C22×C2911yescharacteristic
500#484C22×C2911yescharacteristic
501#484C22×C2911yescharacteristic
502#484C22×C2911yescharacteristic
503#482—21no—
504#481C22×C2911yescharacteristic
505#480—21no—
506#468—21no—
507#468—21no—
508#466—21no—
509#465—21no—
510#450C22×C2911yescharacteristic
511#450C22×C2911yescharacteristic
512#450C22×C2911yescharacteristic
513#449—21no—
514#448—21no—
515#447C22×C2911yescharacteristic
516#407C22×C2911yescharacteristic
517C2×C22⋊C8C22×C2911yescharacteristic
518#400C22×C2911yescharacteristic
519#399C22×C2911yescharacteristic
520#396—21no—
521#394—21no—
522#394—21no—
523#394C22×C2911yescharacteristic
524#392—21no—
525#392C22×C2911yescharacteristic
526#380C22×C2911yescharacteristic
527#328C22×C2911yescharacteristic
528#328C22×C2911yescharacteristic
529#328C22×C2911yescharacteristic
530#328C22×C2911yescharacteristic
531#328C22×C2911yescharacteristic
532#328C22×C2911yescharacteristic
533#327C22×C2911yescharacteristic
534#327C22×C2911yescharacteristic
535#324C22×C2911yescharacteristic
536#324C22×C2911yescharacteristic
537#323C22×C2911yescharacteristic
538#323C22×C2911yescharacteristic
539C2×C29—21no—
540C2×C29—21no—
541C2×C29—41no—
542C2×C29—41no—
543C2×C29—81no—
544C2×C29—81no—
545C2×C29—161no—
546C2×C29#301311yescharacteristic
547C2×C29#302111yescharacteristic
548C2×C29#302611yescharacteristic
549C2×#41—21no—
550C2×#41D4×C2911yescharacteristic, complemented
551C22×Q8D4×C2911yescharacteristic, complemented
552C22×D4—21no—
553C22×D4—21no—
554C22×D4D4×C2911yescharacteristic
555C22×D4C23×C2911yescharacteristic
556C23×C4C23×C2911yescharacteristic
557C2×SD16—21no—
558C2×SD16—21no—
559C2×SD16—21no—
560C2×D8—21no—
561C2×M16—21no—
562C22×C8—21no—
563C4⋊Q8—21no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#126—21no—
570#126—21no—
571#126—21no—
572#125—21no—
573#125—21no—
574#125—21no—
575#125—21no—
576#125—21no—
577#124—21no—
578#124—21no—
579#124—21no—
580#124—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595C22⋊Q8—21no—
596C22⋊Q8—21no—
597C22⋊Q8—21no—
598C22⋊Q8—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8D4×C2911yescharacteristic, complemented
610C22⋊Q8D4×C2911yescharacteristic, complemented
611C22⋊Q8D4×C2911yescharacteristic, complemented
612C22⋊Q8C23×C2911yescharacteristic
613C22⋊Q8C23×C2911yescharacteristic
614C22⋊Q8C23×C2911yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121D4×C2911yescharacteristic, complemented
624#121C23×C2911yescharacteristic
625#120—21no—
626#120—21no—
627C4×Q8—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632C4×D4—21no—
633C4×D4—21no—
634C4×D4—21no—
635#117—21no—
636#117—21no—
637#117—21no—
638#117D4×C2911yescharacteristic, complemented
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4D4×C2911yescharacteristic
644C2×C4⋊C4D4×C2911yescharacteristic, complemented
645C2×C4⋊C4C23×C2911yescharacteristic
646C2×C4⋊C4C23×C2911yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4D4×C2911yescharacteristic
656C2×C22⋊C4D4×C2911yescharacteristic
657C2×C22⋊C4C23×C2911yescharacteristic
658#107—21no—
659#107—21no—
660#107—21no—
661#106—21no—
662#103—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670C22⋊C8—21no—
671C22⋊C8—21no—
672C22⋊C8C23×C2911yescharacteristic
673C22⋊C8C23×C2911yescharacteristic
674C22⋊C8C23×C2911yescharacteristic
675C22⋊C8C23×C2911yescharacteristic
676#95—21no—
677#95—21no—
678#95C23×C2911yescharacteristic
679#95C23×C2911yescharacteristic
680C29#1844811yescharacteristic, direct product factor, Sylow
681C24—21no—
682C24C2×D4×C2911yescharacteristic
683C24C2×D4×C2911yescharacteristic
684#41—82no—
685#41—81no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—81no—
690C2×Q8C2×D4×C2911yescharacteristic
691C2×Q8C2×D4×C2911yescharacteristic
692C2×Q8C2×D4×C2911yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—41no—
703C2×D4—41no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4C2×D4×C2911yescharacteristic
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—81no—
723C22×C4C2×D4×C2911yescharacteristic
724C22×C4C2×D4×C2911yescharacteristic
725C22×C4C2×D4×C2911yescharacteristic
726C22×C4C2×D4×C2911yescharacteristic
727C22×C4C2×D4×C2911yescharacteristic
728C22×C4C2×D4×C2911yescharacteristic
729C22×C4C2×D4×C2911yescharacteristic
730C22×C4C2×D4×C2911yescharacteristic
731C22×C4C24×C2911yescharacteristic
732SD16—81no—
733SD16—81no—
734SD16—81no—
735D8—81no—
736M16—81no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—81no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—21no—
748C4⋊C4—21no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—81no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C2911yescharacteristic
770C4⋊C4C2×D4×C2911yescharacteristic
771C4⋊C4C2×D4×C2911yescharacteristic
772C4⋊C4C2×D4×C2911yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—41no—
797C22⋊C4—41no—
798C22⋊C4—81no—
799C22⋊C4—81no—
800C22⋊C4—81no—
801C22⋊C4—81no—
802C22⋊C4—81no—
803C42—21no—
804C42—21no—
805C42—21no—
806C42—21no—
807C42—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23C29×#12011yescharacteristic
826C23C29×#12011yescharacteristic
827C23C22×D4×C2911yescharacteristic
828Q8—41no—
829Q8—41no—
830Q8—41no—
831Q8—81no—
832Q8—81no—
833Q8—81no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—41no—
842D4—41no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—82no—
848D4—82no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—42no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—81no—
881C2×C4—81no—
882C2×C4—81no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4C29×#12011yescharacteristic
887C2×C4C29×#12011yescharacteristic
888C2×C4C22×D4×C2911yescharacteristic
889C2×C4C22×D4×C2911yescharacteristic
890C8—41no—
891C8—41no—
892C8—41no—
893C8—41no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22C2×C29×#12011yescharacteristic
920C22C29×#57711yescharacteristic
921C22C29×#57811yescharacteristic
922C4—21no—
923C4—21no—
924C4—21no—
925C4—21no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—41no—
930C4—41no—
931C4—41no—
932C4—41no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—81no—
937C4—81no—
938C4—81no—
939C2—21no—
940C2—21no—
941C2—41no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—161no—
946C2C29×#301311yescharacteristic
947C2C29×#302111yescharacteristic
948C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3535C2semidirect
2. C29×#3193C2semidirect
3. C29×#3188C2semidirect
4. C29×#2813C2semidirect
5. C29×#1618C2semidirect
6. C29×#1617C2semidirect
7. C29×#1615C2semidirect
8. C29×#1614C2semidirect
9. C29×#1600C2semidirect
10. C29×#1599C2semidirect
11. C29×#1597C2semidirect
12. C29×#1596C2semidirect
13. C29×#1520C2semidirect
14. C29×#1513C2semidirect
15. C29×#1468C2semidirect
76. C2×#41×C29D4semidirect
77. C22×Q8×C29D4semidirect
135. C29×C22⋊Q8D4semidirect
136. C29×C22⋊Q8D4semidirect
137. C29×C22⋊Q8D4semidirect
149. C29×#121D4semidirect
164. C29×#117D4semidirect
170. C2×C4⋊C4×C29D4semidirect
333. #18448C29direct (N × H)
420. #3535C2×C29semidirect
421. #3193C2×C29semidirect
422. #3188C2×C29semidirect
423. #2813C2×C29semidirect
424. #1618C2×C29semidirect
425. #1617C2×C29semidirect
426. #1615C2×C29semidirect
427. #1614C2×C29semidirect
428. #1600C2×C29semidirect
429. #1599C2×C29semidirect
430. #1597C2×C29semidirect
431. #1596C2×C29semidirect
432. #1520C2×C29semidirect
433. #1513C2×C29semidirect
434. #1468C2×C29semidirect
550. C2×#41D4×C29semidirect
551. C22×Q8D4×C29semidirect
609. C22⋊Q8D4×C29semidirect
610. C22⋊Q8D4×C29semidirect
611. C22⋊Q8D4×C29semidirect
623. #121D4×C29semidirect
638. #117D4×C29semidirect
644. C2×C4⋊C4D4×C29semidirect
680. C29#18448direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35352
C29×#31932
C29×#31882
C29×#28132
C29×#16182
C29×#16172
C29×#16152
C29×#16142
C29×#16002
C29×#15992
C29×#15972
C29×#15962
C29×#15202
C29×#15132
C29×#14682
#1844829