Finite Group Databasebeta

← C29×#18262 #20313162

Subgroups — C29×#18262 #20313162

Order 7424.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3534C211yesmaximal, characteristic
2C29×#3094C211yesmaximal, characteristic, complemented
3C29×#3091C211yesmaximal, characteristic, complemented
4C29×#2498C211yesmaximal, characteristic, complemented
5C29×#1618C211yesmaximal, characteristic, complemented
6C29×#1616C211yesmaximal, characteristic, complemented
7C29×#1615C211yesmaximal, characteristic, complemented
8C29×#1613C211yesmaximal, characteristic, complemented
9C29×#1612C211yesmaximal, characteristic, complemented
10C29×#1610C211yesmaximal, characteristic, complemented
11C29×#1609C211yesmaximal, characteristic, complemented
12C29×#1607C211yesmaximal, characteristic, complemented
13C29×#1504C211yesmaximal, characteristic, complemented
14C2×C29×#327C211yesmaximal, characteristic, complemented
15C29×#1468C211yesmaximal, characteristic, complemented
16C29×#562—21no—
17C29×#560—21no—
18C29×#553—21no—
19C29×#551—21no—
20C29×#546—21no—
21C29×#546—21no—
22C29×#546—21no—
23D42×C29—21no—
24C29×#540—21no—
25C29×#539—21no—
26C29×#539C2211yescharacteristic
27C29×#538—21no—
28C29×#538C2211yescharacteristic
29C29×#537C2211yescharacteristic
30C29×#534—21no—
31C29×#534C2211yescharacteristic
32C29×#525C2211yescharacteristic
33C2×C29×#123C2211yescharacteristic
34C2×C29×#121C2211yescharacteristic
35C2×C29×#117C2211yescharacteristic, complemented
36C29×#485—21no—
37C29×#484C2211yescharacteristic, complemented
38C29×#483C2211yescharacteristic, complemented
39C29×#482—21no—
40C29×#482—21no—
41C29×#482—21no—
42C29×#481C2211yescharacteristic
43C29×#481C2211yescharacteristic, complemented
44C29×#481C2211yescharacteristic, complemented
45C29×#480C2211yescharacteristic
46C29×#480C2211yescharacteristic, complemented
47C29×#480C2211yescharacteristic, complemented
48C29×#428—21no—
49C29×#427—21no—
50C29×#418—21no—
51C29×#416—21no—
52C29×#407C2211yescharacteristic, complemented
53C2×C29×C22⋊C8C2211yescharacteristic, complemented
54C29×#400C2211yescharacteristic, complemented
55C29×#399C2211yescharacteristic, complemented
56C29×#398C2211yescharacteristic, complemented
57C29×#397C2211yescharacteristic, complemented
58C29×#388—21no—
59C29×#387—21no—
60C29×#386—21no—
61C29×#380—21no—
62C2×C29×#95C2211yescharacteristic, complemented
63C29×#328C2211yescharacteristic, complemented
64C29×#328C2211yescharacteristic, complemented
65C29×#327C2211yescharacteristic
66C29×#327C2211yescharacteristic
67C29×#327C2211yescharacteristic, complemented
68C29×#327C2211yescharacteristic, complemented
69C29×#327C2211yescharacteristic, complemented
70C29×#327C2211yescharacteristic, complemented
71C29×#324C2211yescharacteristic, complemented
72C29×#324C2211yescharacteristic, complemented
73C29×#323C2211yescharacteristic, complemented
74C29×#323C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29D411yescharacteristic
77C22×D4×C29—21no—
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29D411yescharacteristic
81C22×D4×C29D411yescharacteristic
82C23×C4×C29—21no—
83C23×C4×C29C2311yescharacteristic
84C2×M16×C29—21no—
85C22×C8×C29—21no—
86C29×#127—21no—
87C29×#126—21no—
88C29×#126—21no—
89C29×#126—21no—
90C29×#126—21no—
91C29×#125—21no—
92C29×#125—21no—
93C29×#124—21no—
94C29×#124—21no—
95C29×#124—21no—
96C29×#123—21no—
97C29×#123—21no—
98C29×#123—21no—
99C29×#123—21no—
100C29×#123—21no—
101C29×#123—21no—
102C29×#123—21no—
103C29×#123—21no—
104C29×#123—21no—
105C29×#123—21no—
106C29×#123—21no—
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×C22⋊Q8—21no—
111C29×C22⋊Q8—21no—
112C29×C22⋊Q8—21no—
113C29×C22⋊Q8—21no—
114C29×C22⋊Q8—21no—
115C29×C22⋊Q8D411yescharacteristic
116C29×C22⋊Q8C2311yescharacteristic
117C29×#121—21no—
118C29×#121—21no—
119C29×#121—21no—
120C29×#121—21no—
121C29×#121—21no—
122C29×#121—21no—
123C29×#121—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—21no—
127C29×#121—21no—
128C29×#121—21no—
129C29×#121—21no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121D411yescharacteristic
133C29×#121D411yescharacteristic
134C29×#121D411yescharacteristic
135C29×#121C2311yescharacteristic
136C29×#121C2311yescharacteristic
137C29×#121C2311yescharacteristic
138C29×#120—21no—
139C29×#120—21no—
140C29×#120—21no—
141C29×#120—21no—
142C29×#120—21no—
143C29×#120—21no—
144C29×#120—21no—
145C29×#120—21no—
146C4×D4×C29—21no—
147C4×D4×C29—21no—
148C4×D4×C29—21no—
149C4×D4×C29—21no—
150C4×D4×C29—21no—
151C4×D4×C29—21no—
152C4×D4×C29—21no—
153C4×D4×C29—21no—
154C29×#117—21no—
155C29×#117—21no—
156C29×#117—21no—
157C29×#117—21no—
158C29×#117—21no—
159C29×#117D411yescharacteristic
160C2×C4⋊C4×C29—21no—
161C2×C4⋊C4×C29—21no—
162C2×C4⋊C4×C29D411yescharacteristic
163C2×C4⋊C4×C29D411yescharacteristic
164C2×C4⋊C4×C29C2311yescharacteristic
165C2×C4⋊C4×C29C2311yescharacteristic
166C2×C4⋊C4×C29C2311yescharacteristic
167C2×C22⋊C4×C29—21no—
168C2×C22⋊C4×C29—21no—
169C2×C22⋊C4×C29—21no—
170C2×C22⋊C4×C29—21no—
171C2×C22⋊C4×C29—21no—
172C2×C22⋊C4×C29—21no—
173C2×C22⋊C4×C29D411yescharacteristic
174C2×C22⋊C4×C29D411yescharacteristic
175C2×C22⋊C4×C29C2311yescharacteristic
176C2×C42×C29—21no—
177C29×#107—21no—
178C29×#107—21no—
179C29×#107—21no—
180C29×#107—21no—
181C29×#106—21no—
182C29×#106—21no—
183C29×#106—21no—
184C29×#106—21no—
185C29×#103—21no—
186C29×#103—21no—
187C29×#102—21no—
188C29×#102—21no—
189C29×#102—21no—
190C29×#102—21no—
191C29×#102—21no—
192C29×#102—21no—
193C29×C22⋊C8—21no—
194C29×C22⋊C8—21no—
195C29×C22⋊C8C2311yescharacteristic
196C29×C22⋊C8C2311yescharacteristic
197C29×C22⋊C8C2311yescharacteristic
198C29×C22⋊C8C2311yescharacteristic
199C29×#95—21no—
200C29×#95—21no—
201C29×#95—21no—
202C29×#95—21no—
203C29×#95—21no—
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29—21no—
208C24×C29C2×D411yescharacteristic
209C24×C29C2×D411yescharacteristic
210#41×C29—42no—
211#41×C29—81no—
212#41×C29—81no—
213C2×Q8×C29—21no—
214C2×Q8×C29C2×D411yescharacteristic
215C2×D4×C29—21no—
216C2×D4×C29—21no—
217C2×D4×C29—21no—
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—21no—
228C2×D4×C29—21no—
229C2×D4×C29—21no—
230C2×D4×C29—21no—
231C2×D4×C29—21no—
232C2×D4×C29—42no—
233C2×D4×C29—42no—
234C2×D4×C29—81no—
235C2×D4×C29—81no—
236C2×D4×C29—81no—
237C2×D4×C29—81no—
238C2×D4×C29—82no—
239C2×D4×C29C2×D411yescharacteristic
240C2×D4×C29C2×D411yescharacteristic
241C2×D4×C29C2×D411yescharacteristic
242C22×C4×C29—21no—
243C22×C4×C29—21no—
244C22×C4×C29—21no—
245C22×C4×C29—21no—
246C22×C4×C29—21no—
247C22×C4×C29—21no—
248C22×C4×C29—21no—
249C22×C4×C29—21no—
250C22×C4×C29—21no—
251C22×C4×C29—21no—
252C22×C4×C29—21no—
253C22×C4×C29—42no—
254C22×C4×C29—42no—
255C22×C4×C29—42no—
256C22×C4×C29—81no—
257C22×C4×C29C2×D411yescharacteristic
258C22×C4×C29C2×D411yescharacteristic
259C22×C4×C29C2×D411yescharacteristic
260C22×C4×C29C2×D411yescharacteristic
261C22×C4×C29C2×D411yescharacteristic
262C22×C4×C29C2×D411yescharacteristic
263C22×C4×C29C2×D411yescharacteristic
264C22×C4×C29C2×D411yescharacteristic
265C22×C4×C29C2411yescharacteristic
266M16×C29—42no—
267C2×C8×C29—21no—
268C2×C8×C29—21no—
269C2×C8×C29—21no—
270C2×C8×C29—21no—
271C2×C8×C29—42no—
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—42no—
290C4⋊C4×C29—81no—
291C4⋊C4×C29C2×D411yescharacteristic
292C4⋊C4×C29C2×D411yescharacteristic
293C4⋊C4×C29C2×D411yescharacteristic
294C4⋊C4×C29C2×D411yescharacteristic
295C22⋊C4×C29—21no—
296C22⋊C4×C29—21no—
297C22⋊C4×C29—21no—
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—42no—
321C22⋊C4×C29—41no—
322C22⋊C4×C29—41no—
323C22⋊C4×C29—81no—
324C42×C29—21no—
325C42×C29—21no—
326C42×C29—21no—
327C42×C29—41no—
328C42×C29—41no—
329#18262C2911yesmaximal, characteristic, direct product factor, Sylow
330C23×C29—21no—
331C23×C29—21no—
332C23×C29—22no—
333C23×C29—21no—
334C23×C29—21no—
335C23×C29—21no—
336C23×C29—21no—
337C23×C29—21no—
338C23×C29—21no—
339C23×C29—41no—
340C23×C29—41no—
341C23×C29—41no—
342C23×C29—42no—
343C23×C29—81no—
344C23×C29—81no—
345C23×C29—81no—
346C23×C29—81no—
347C23×C29—81no—
348C23×C29#12011yescharacteristic
349C23×C29#12011yescharacteristic
350C23×C29C22×D411yescharacteristic
351Q8×C29—41no—
352Q8×C29—81no—
353D4×C29—41no—
354D4×C29—41no—
355D4×C29—41no—
356D4×C29—41no—
357D4×C29—41no—
358D4×C29—41no—
359D4×C29—41no—
360D4×C29—41no—
361D4×C29—41no—
362D4×C29—42no—
363D4×C29—42no—
364D4×C29—81no—
365D4×C29—81no—
366D4×C29—81no—
367D4×C29—81no—
368D4×C29—81no—
369D4×C29—81no—
370D4×C29—81no—
371D4×C29—81no—
372D4×C29—81no—
373D4×C29—81no—
374D4×C29—81no—
375D4×C29—81no—
376C2×C4×C29—22no—
377C2×C4×C29—22no—
378C2×C4×C29—22no—
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—21no—
389C2×C4×C29—41no—
390C2×C4×C29—41no—
391C2×C4×C29—41no—
392C2×C4×C29—41no—
393C2×C4×C29—41no—
394C2×C4×C29—41no—
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—81no—
413C2×C4×C29—84no—
414C2×C4×C29#12011yescharacteristic
415C2×C4×C29#12011yescharacteristic
416C2×C4×C29C22×D411yescharacteristic
417C2×C4×C29C22×D411yescharacteristic
418C8×C29—41no—
419C8×C29—41no—
420C8×C29—41no—
421C8×C29—41no—
422#3534C2×C2911yescharacteristic
423#3094C2×C2911yescharacteristic, complemented
424#3091C2×C2911yescharacteristic, complemented
425#2498C2×C2911yescharacteristic, complemented
426#1618C2×C2911yescharacteristic, complemented
427#1616C2×C2911yescharacteristic, complemented
428#1615C2×C2911yescharacteristic, complemented
429#1613C2×C2911yescharacteristic, complemented
430#1612C2×C2911yescharacteristic, complemented
431#1610C2×C2911yescharacteristic, complemented
432#1609C2×C2911yescharacteristic, complemented
433#1607C2×C2911yescharacteristic, complemented
434#1504C2×C2911yescharacteristic, complemented
435C2×#327C2×C2911yescharacteristic, complemented
436#1468C2×C2911yescharacteristic, complemented
437C22×C29—21no—
438C22×C29—21no—
439C22×C29—21no—
440C22×C29—21no—
441C22×C29—21no—
442C22×C29—21no—
443C22×C29—21no—
444C22×C29—42no—
445C22×C29—42no—
446C22×C29—41no—
447C22×C29—41no—
448C22×C29—41no—
449C22×C29—41no—
450C22×C29—41no—
451C22×C29—41no—
452C22×C29—41no—
453C22×C29—41no—
454C22×C29—41no—
455C22×C29—41no—
456C22×C29—41no—
457C22×C29—41no—
458C22×C29—81no—
459C22×C29—81no—
460C22×C29—162no—
461C22×C29—162no—
462C22×C29#45812yes—
463C22×C29C2×#12011yescharacteristic
464C22×C29#57611yescharacteristic
465C22×C29#57711yescharacteristic
466C4×C29—21no—
467C4×C29—21no—
468C4×C29—21no—
469C4×C29—21no—
470C4×C29—42no—
471C4×C29—41no—
472C4×C29—41no—
473C4×C29—41no—
474C4×C29—41no—
475C4×C29—41no—
476C4×C29—41no—
477C4×C29—41no—
478C4×C29—41no—
479C4×C29—81no—
480C4×C29—81no—
481C4×C29—81no—
482#562—21no—
483#560—21no—
484#553—21no—
485#551—21no—
486#546—21no—
487#546—21no—
488#546—21no—
489D42—21no—
490#540—21no—
491#539—21no—
492#539C22×C2911yescharacteristic
493#538—21no—
494#538C22×C2911yescharacteristic
495#537C22×C2911yescharacteristic
496#534—21no—
497#534C22×C2911yescharacteristic
498#525C22×C2911yescharacteristic
499C2×#123C22×C2911yescharacteristic
500C2×#121C22×C2911yescharacteristic
501C2×#117C22×C2911yescharacteristic, complemented
502#485—21no—
503#484C22×C2911yescharacteristic, complemented
504#483C22×C2911yescharacteristic, complemented
505#482—21no—
506#482—21no—
507#482—21no—
508#481C22×C2911yescharacteristic
509#481C22×C2911yescharacteristic, complemented
510#481C22×C2911yescharacteristic, complemented
511#480C22×C2911yescharacteristic
512#480C22×C2911yescharacteristic, complemented
513#480C22×C2911yescharacteristic, complemented
514#428—21no—
515#427—21no—
516#418—21no—
517#416—21no—
518#407C22×C2911yescharacteristic, complemented
519C2×C22⋊C8C22×C2911yescharacteristic, complemented
520#400C22×C2911yescharacteristic, complemented
521#399C22×C2911yescharacteristic, complemented
522#398C22×C2911yescharacteristic, complemented
523#397C22×C2911yescharacteristic, complemented
524#388—21no—
525#387—21no—
526#386—21no—
527#380—21no—
528C2×#95C22×C2911yescharacteristic, complemented
529#328C22×C2911yescharacteristic, complemented
530#328C22×C2911yescharacteristic, complemented
531#327C22×C2911yescharacteristic
532#327C22×C2911yescharacteristic
533#327C22×C2911yescharacteristic, complemented
534#327C22×C2911yescharacteristic, complemented
535#327C22×C2911yescharacteristic, complemented
536#327C22×C2911yescharacteristic, complemented
537#324C22×C2911yescharacteristic, complemented
538#324C22×C2911yescharacteristic, complemented
539#323C22×C2911yescharacteristic, complemented
540#323C22×C2911yescharacteristic, complemented
541C2×C29—21no—
542C2×C29—21no—
543C2×C29—22no—
544C2×C29—41no—
545C2×C29—81no—
546C2×C29—81no—
547C2×C29—81no—
548C2×C29—81no—
549C2×C29#301211yescharacteristic
550C2×C29#301811yescharacteristic
551C2×C29C2×#45811yescharacteristic
552C2×#41—21no—
553C2×#41D4×C2911yescharacteristic
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4D4×C2911yescharacteristic
558C22×D4D4×C2911yescharacteristic
559C23×C4—21no—
560C23×C4C23×C2911yescharacteristic
561C2×M16—21no—
562C22×C8—21no—
563#127—21no—
564#126—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#125—21no—
569#125—21no—
570#124—21no—
571#124—21no—
572#124—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587C22⋊Q8—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8D4×C2911yescharacteristic
593C22⋊Q8C23×C2911yescharacteristic
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121D4×C2911yescharacteristic
610#121D4×C2911yescharacteristic
611#121D4×C2911yescharacteristic
612#121C23×C2911yescharacteristic
613#121C23×C2911yescharacteristic
614#121C23×C2911yescharacteristic
615#120—21no—
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623C4×D4—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631#117—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117D4×C2911yescharacteristic
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4D4×C2911yescharacteristic
640C2×C4⋊C4D4×C2911yescharacteristic
641C2×C4⋊C4C23×C2911yescharacteristic
642C2×C4⋊C4C23×C2911yescharacteristic
643C2×C4⋊C4C23×C2911yescharacteristic
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4D4×C2911yescharacteristic
651C2×C22⋊C4D4×C2911yescharacteristic
652C2×C22⋊C4C23×C2911yescharacteristic
653C2×C42—21no—
654#107—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#106—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#103—21no—
663#103—21no—
664#102—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#95—21no—
679#95—21no—
680#95—21no—
681#95C23×C2911yescharacteristic
682#95C23×C2911yescharacteristic
683C29#1826211yescharacteristic, direct product factor, Sylow
684C24—21no—
685C24—21no—
686C24C2×D4×C2911yescharacteristic
687C24C2×D4×C2911yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
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—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C2911yescharacteristic
718C2×D4C2×D4×C2911yescharacteristic
719C2×D4C2×D4×C2911yescharacteristic
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C2911yescharacteristic
736C22×C4C2×D4×C2911yescharacteristic
737C22×C4C2×D4×C2911yescharacteristic
738C22×C4C2×D4×C2911yescharacteristic
739C22×C4C2×D4×C2911yescharacteristic
740C22×C4C2×D4×C2911yescharacteristic
741C22×C4C2×D4×C2911yescharacteristic
742C22×C4C2×D4×C2911yescharacteristic
743C22×C4C24×C2911yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
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—42no—
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—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23C29×#12011yescharacteristic
826C23C29×#12011yescharacteristic
827C23C22×D4×C2911yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—42no—
834D4—42no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
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—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4C29×#12011yescharacteristic
892C2×C4C29×#12011yescharacteristic
893C2×C4C22×D4×C2911yescharacteristic
894C2×C4C22×D4×C2911yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22C29×#45812yes—
925C22C2×C29×#12011yescharacteristic
926C22C29×#57611yescharacteristic
927C22C29×#57711yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C29×#301211yescharacteristic
953C2C29×#301811yescharacteristic
954C2C2×C29×#45811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3534C2
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
2. C29×#3094C2semidirect
3. C29×#3091C2semidirect
4. C29×#2498C2semidirect
5. C29×#1618C2semidirect
6. C29×#1616C2semidirect
7. C29×#1615C2semidirect
8. C29×#1613C2semidirect
9. C29×#1612C2semidirect
10. C29×#1610C2semidirect
11. C29×#1609C2semidirect
12. C29×#1607C2semidirect
13. C29×#1504C2semidirect
14. C2×C29×#327C2semidirect
15. C29×#1468C2semidirect
35. C2×C29×#117C22semidirect
37. C29×#484C22semidirect
38. C29×#483C22semidirect
43. C29×#481C22semidirect
44. C29×#481C22semidirect
46. C29×#480C22semidirect
47. C29×#480C22semidirect
52. C29×#407C22semidirect
53. C2×C29×C22⋊C8C22semidirect
54. C29×#400C22semidirect
55. C29×#399C22semidirect
56. C29×#398C22semidirect
57. C29×#397C22semidirect
62. C2×C29×#95C22semidirect
63. C29×#328C22semidirect
64. C29×#328C22semidirect
67. C29×#327C22semidirect
68. C29×#327C22semidirect
69. C29×#327C22semidirect
70. C29×#327C22semidirect
71. C29×#324C22semidirect
72. C29×#324C22semidirect
73. C29×#323C22semidirect
74. C29×#323C22semidirect
329. #18262C29direct (N × H)
423. #3094C2×C29semidirect
424. #3091C2×C29semidirect
425. #2498C2×C29semidirect
426. #1618C2×C29semidirect
427. #1616C2×C29semidirect
428. #1615C2×C29semidirect
429. #1613C2×C29semidirect
430. #1612C2×C29semidirect
431. #1610C2×C29semidirect
432. #1609C2×C29semidirect
433. #1607C2×C29semidirect
434. #1504C2×C29semidirect
435. C2×#327C2×C29semidirect
436. #1468C2×C29semidirect
501. C2×#117C22×C29semidirect
503. #484C22×C29semidirect
504. #483C22×C29semidirect
509. #481C22×C29semidirect
510. #481C22×C29semidirect
512. #480C22×C29semidirect
513. #480C22×C29semidirect
518. #407C22×C29semidirect
519. C2×C22⋊C8C22×C29semidirect
520. #400C22×C29semidirect
521. #399C22×C29semidirect
522. #398C22×C29semidirect
523. #397C22×C29semidirect
528. C2×#95C22×C29semidirect
529. #328C22×C29semidirect
530. #328C22×C29semidirect
533. #327C22×C29semidirect
534. #327C22×C29semidirect
535. #327C22×C29semidirect
536. #327C22×C29semidirect
537. #324C22×C29semidirect
538. #324C22×C29semidirect
539. #323C22×C29semidirect
540. #323C22×C29semidirect
683. C29#18262direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35342
C29×#30942
C29×#30912
C29×#24982
C29×#16182
C29×#16162
C29×#16152
C29×#16132
C29×#16122
C29×#16102
C29×#16092
C29×#16072
C29×#15042
C2×C29×#3272
C29×#14682
#1826229