Finite Group Databasebeta

← C29×#18434 #20313334

Subgroups — C29×#18434 #20313334

Order 7424.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3560C211yesmaximal, characteristic, complemented
2C29×#3213C211yesmaximal, characteristic, complemented
3C29×#3211C211yesmaximal, characteristic, complemented
4C29×#2662C211yesmaximal, characteristic, complemented
5C29×#1606C211yesmaximal, characteristic, complemented
6C29×#1604C211yesmaximal, characteristic, complemented
7C29×#1603C211yesmaximal, characteristic, complemented
8C29×#1601C211yesmaximal, characteristic, complemented
9C29×#1600C211yesmaximal, characteristic, complemented
10C29×#1598C211yesmaximal, characteristic, complemented
11C29×#1597C211yesmaximal, characteristic, complemented
12C29×#1595C211yesmaximal, characteristic, complemented
13C29×#1509C211yesmaximal, characteristic, complemented
14C29×#1502C211yesmaximal, characteristic, complemented
15C29×#1473C211yesmaximal, characteristic, complemented
16C29×#563—21no—
17C29×#560—21no—
18C29×#553—21no—
19C29×#553—21no—
20C29×#551—21no—
21C29×#547—21no—
22C29×#546—21no—
23C29×#546—21no—
24C29×#542—21no—
25C29×#539—21no—
26C29×#539C2211yescharacteristic
27C29×#538—21no—
28C29×#538—21no—
29C29×#538C2211yescharacteristic
30C29×#537C2211yescharacteristic
31C29×#534C2211yescharacteristic
32C29×#532C2211yescharacteristic
33C29×#529C2211yescharacteristic
34C2×C29×#126C2211yescharacteristic
35C2×C29×#124C2211yescharacteristic, complemented
36C29×#496—21no—
37C29×#495—21no—
38C29×#489—21no—
39C29×#488—21no—
40C29×#464—21no—
41C29×#463—21no—
42C29×#463—21no—
43C29×#463—21no—
44C29×#451C2211yescharacteristic, complemented
45C29×#450C2211yescharacteristic, complemented
46C29×#448C2211yescharacteristic
47C29×#448C2211yescharacteristic
48C29×#448C2211yescharacteristic, complemented
49C29×#447C2211yescharacteristic
50C29×#447C2211yescharacteristic
51C29×#447C2211yescharacteristic, complemented
52C29×#432C2211yescharacteristic, complemented
53C29×#431C2211yescharacteristic, complemented
54C29×#396—21no—
55C29×#395C2211yescharacteristic, complemented
56C29×#394—21no—
57C29×#394C2211yescharacteristic, complemented
58C29×#393C2211yescharacteristic
59C29×#392C2211yescharacteristic
60C29×#390—21no—
61C29×#388—21no—
62C4×C4⋊C4×C29C2211yescharacteristic, complemented
63C29×#328C2211yescharacteristic, complemented
64C29×#328C2211yescharacteristic, complemented
65C29×#327C2211yescharacteristic
66C29×#327C2211yescharacteristic
67C29×#327C2211yescharacteristic
68C29×#327C2211yescharacteristic
69C29×#327C2211yescharacteristic, complemented
70C29×#327C2211yescharacteristic, complemented
71C29×#324C2211yescharacteristic, complemented
72C29×#324C2211yescharacteristic, complemented
73C29×#323C2211yescharacteristic
74C29×#323C2211yescharacteristic
75C2×#41×C29—21no—
76C2×#41×C29—21no—
77C22×Q8×C29C2311yescharacteristic
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29C2311yescharacteristic
81C2×Q16×C29—21no—
82C2×SD16×C29—21no—
83C2×SD16×C29—21no—
84C2×SD16×C29—21no—
85C2×SD16×C29—21no—
86C2×D8×C29—21no—
87C2×D8×C29—21no—
88C2×D8×C29—21no—
89C29×C4⋊Q8—21no—
90C29×C4⋊Q8D411yescharacteristic, complemented
91C29×#127D411yescharacteristic, complemented
92C29×#126—21no—
93C29×#126—21no—
94C29×#126—21no—
95C29×#126—21no—
96C29×#126—21no—
97C29×#126—21no—
98C29×#126—21no—
99C29×#126—21no—
100C29×#126—21no—
101C29×#125—21no—
102C29×#125—21no—
103C29×#125D411yescharacteristic, complemented
104C29×#124—21no—
105C29×#124—21no—
106C29×#124—21no—
107C29×#124—21no—
108C29×#124—21no—
109C29×#124—21no—
110C29×#124—21no—
111C29×#124—21no—
112C29×#124D411yescharacteristic, complemented
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×#123—21no—
122C29×#123—21no—
123C29×#123—21no—
124C29×#123—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⋊Q8C2311yescharacteristic
133C29×#121—21no—
134C29×#121—21no—
135C29×#121—21no—
136C29×#121—21no—
137C29×#121—21no—
138C29×#121—21no—
139C29×#121—21no—
140C29×#121—21no—
141C29×#121—21no—
142C29×#121—21no—
143C29×#121—21no—
144C29×#121—21no—
145C29×#121C2311yescharacteristic
146C29×#121C2311yescharacteristic
147C29×#121C2311yescharacteristic
148C29×#120—21no—
149C29×#120—21no—
150C29×#120—21no—
151C29×#120—21no—
152C29×#120—21no—
153C4×Q8×C29D411yescharacteristic, complemented
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—
161C4×D4×C29—21no—
162C4×D4×C29D411yescharacteristic, complemented
163C4×D4×C29D411yescharacteristic, complemented
164C4×D4×C29D411yescharacteristic, complemented
165C29×#117—21no—
166C29×#117—21no—
167C2×C4⋊C4×C29—21no—
168C2×C4⋊C4×C29—21no—
169C2×C4⋊C4×C29—21no—
170C2×C4⋊C4×C29D411yescharacteristic
171C2×C4⋊C4×C29D411yescharacteristic
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
184C2×C42×C29—21no—
185C2×C42×C29C2311yescharacteristic
186C29×C4⋊C8—21no—
187C29×C4⋊C8—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×C22⋊C8C2311yescharacteristic
197C29×C22⋊C8C2311yescharacteristic
198C29×C22⋊C8C2311yescharacteristic
199C29×C22⋊C8C2311yescharacteristic
200C29×#97—21no—
201C4×C8×C29—21no—
202C29×#95—21no—
203C29×#95—21no—
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29—21no—
208C24×C29C2×D411yescharacteristic
209#41×C29—81no—
210#41×C29—81no—
211#41×C29—81no—
212#41×C29—81no—
213C2×Q8×C29—21no—
214C2×Q8×C29—21no—
215C2×Q8×C29—21no—
216C2×Q8×C29—21no—
217C2×Q8×C29—81no—
218C2×Q8×C29C2×D411yescharacteristic
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—21no—
233C2×D4×C29—42no—
234C2×D4×C29—81no—
235C2×D4×C29—81no—
236C2×D4×C29—81no—
237C2×D4×C29—81no—
238C2×D4×C29—81no—
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×C29C2×D411yescharacteristic
254C22×C4×C29C2×D411yescharacteristic
255C22×C4×C29C2×D411yescharacteristic
256C22×C4×C29C2×D411yescharacteristic
257C22×C4×C29C2×D411yescharacteristic
258C22×C4×C29C2411yescharacteristic
259Q16×C29—81no—
260SD16×C29—81no—
261SD16×C29—81no—
262SD16×C29—81no—
263SD16×C29—81no—
264D8×C29—81no—
265D8×C29—81no—
266D8×C29—81no—
267C2×C8×C29—21no—
268C2×C8×C29—21no—
269C2×C8×C29—21no—
270C2×C8×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—42no—
289C4⋊C4×C29—81no—
290C4⋊C4×C29C2×D411yescharacteristic
291C4⋊C4×C29C2×D411yescharacteristic
292C4⋊C4×C29C2×D411yescharacteristic
293C4⋊C4×C29C2×D411yescharacteristic
294C22⋊C4×C29—21no—
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—42no—
320C22⋊C4×C29—41no—
321C22⋊C4×C29—41no—
322C22⋊C4×C29—41no—
323C22⋊C4×C29—41no—
324C22⋊C4×C29—81no—
325C22⋊C4×C29—81no—
326C22⋊C4×C29—81no—
327C42×C29—21no—
328C42×C29—21no—
329C42×C29—21no—
330C42×C29—81no—
331C42×C29C2×D411yescharacteristic
332C42×C29C2×D411yescharacteristic
333C42×C29C2×D411yescharacteristic
334C42×C29C2×D411yescharacteristic
335#18434C2911yesmaximal, characteristic, direct product factor, Sylow
336C23×C29—21no—
337C23×C29—21no—
338C23×C29—21no—
339C23×C29—21no—
340C23×C29—21no—
341C23×C29—21no—
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—81no—
352C23×C29—81no—
353C23×C29—81no—
354C23×C29C22×D411yescharacteristic
355Q8×C29—41no—
356Q8×C29—41no—
357Q8×C29—41no—
358Q8×C29—41no—
359Q8×C29—41no—
360Q8×C29—81no—
361Q8×C29—81no—
362D4×C29—41no—
363D4×C29—41no—
364D4×C29—41no—
365D4×C29—41no—
366D4×C29—41no—
367D4×C29—41no—
368D4×C29—41no—
369D4×C29—41no—
370D4×C29—41no—
371D4×C29—41no—
372D4×C29—41no—
373D4×C29—41no—
374D4×C29—41no—
375D4×C29—81no—
376D4×C29—81no—
377D4×C29—81no—
378D4×C29—81no—
379D4×C29—81no—
380D4×C29—81no—
381D4×C29—81no—
382D4×C29—81no—
383D4×C29—81no—
384D4×C29—84no—
385C2×C4×C29—21no—
386C2×C4×C29—21no—
387C2×C4×C29—22no—
388C2×C4×C29—21no—
389C2×C4×C29—21no—
390C2×C4×C29—21no—
391C2×C4×C29—21no—
392C2×C4×C29—21no—
393C2×C4×C29—21no—
394C2×C4×C29—21no—
395C2×C4×C29—21no—
396C2×C4×C29—21no—
397C2×C4×C29—21no—
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—41no—
407C2×C4×C29—41no—
408C2×C4×C29—41no—
409C2×C4×C29—41no—
410C2×C4×C29—81no—
411C2×C4×C29—81no—
412C2×C4×C29—81no—
413C2×C4×C29—81no—
414C2×C4×C29—81no—
415C2×C4×C29—81no—
416C2×C4×C29—81no—
417C2×C4×C29—81no—
418C2×C4×C29#12011yescharacteristic
419C2×C4×C29#12011yescharacteristic
420C2×C4×C29#12011yescharacteristic
421C2×C4×C29#12011yescharacteristic
422C2×C4×C29C22×D411yescharacteristic
423C2×C4×C29C22×D411yescharacteristic
424C8×C29—41no—
425C8×C29—41no—
426C8×C29—41no—
427C8×C29—41no—
428#3560C2×C2911yescharacteristic, complemented
429#3213C2×C2911yescharacteristic, complemented
430#3211C2×C2911yescharacteristic, complemented
431#2662C2×C2911yescharacteristic, complemented
432#1606C2×C2911yescharacteristic, complemented
433#1604C2×C2911yescharacteristic, complemented
434#1603C2×C2911yescharacteristic, complemented
435#1601C2×C2911yescharacteristic, complemented
436#1600C2×C2911yescharacteristic, complemented
437#1598C2×C2911yescharacteristic, complemented
438#1597C2×C2911yescharacteristic, complemented
439#1595C2×C2911yescharacteristic, complemented
440#1509C2×C2911yescharacteristic, complemented
441#1502C2×C2911yescharacteristic, complemented
442#1473C2×C2911yescharacteristic, complemented
443C22×C29—21no—
444C22×C29—21no—
445C22×C29—41no—
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—81no—
458C22×C29—81no—
459C22×C29—81no—
460C22×C29—81no—
461C22×C29—81no—
462C22×C29—81no—
463C22×C29—81no—
464C22×C29—81no—
465C22×C29—81no—
466C22×C29—162no—
467C22×C29C2×#12011yescharacteristic
468C22×C29#57611yescharacteristic
469C22×C29#57711yescharacteristic
470C4×C29—21no—
471C4×C29—21no—
472C4×C29—21no—
473C4×C29—21no—
474C4×C29—21no—
475C4×C29—21no—
476C4×C29—42no—
477C4×C29—41no—
478C4×C29—41no—
479C4×C29—41no—
480C4×C29—41no—
481C4×C29—41no—
482C4×C29—41no—
483C4×C29—41no—
484C4×C29—41no—
485C4×C29—81no—
486C4×C29—81no—
487#563—21no—
488#560—21no—
489#553—21no—
490#553—21no—
491#551—21no—
492#547—21no—
493#546—21no—
494#546—21no—
495#542—21no—
496#539—21no—
497#539C22×C2911yescharacteristic
498#538—21no—
499#538—21no—
500#538C22×C2911yescharacteristic
501#537C22×C2911yescharacteristic
502#534C22×C2911yescharacteristic
503#532C22×C2911yescharacteristic
504#529C22×C2911yescharacteristic
505C2×#126C22×C2911yescharacteristic
506C2×#124C22×C2911yescharacteristic, complemented
507#496—21no—
508#495—21no—
509#489—21no—
510#488—21no—
511#464—21no—
512#463—21no—
513#463—21no—
514#463—21no—
515#451C22×C2911yescharacteristic, complemented
516#450C22×C2911yescharacteristic, complemented
517#448C22×C2911yescharacteristic
518#448C22×C2911yescharacteristic
519#448C22×C2911yescharacteristic, complemented
520#447C22×C2911yescharacteristic
521#447C22×C2911yescharacteristic
522#447C22×C2911yescharacteristic, complemented
523#432C22×C2911yescharacteristic, complemented
524#431C22×C2911yescharacteristic, complemented
525#396—21no—
526#395C22×C2911yescharacteristic, complemented
527#394—21no—
528#394C22×C2911yescharacteristic, complemented
529#393C22×C2911yescharacteristic
530#392C22×C2911yescharacteristic
531#390—21no—
532#388—21no—
533C4×C4⋊C4C22×C2911yescharacteristic, complemented
534#328C22×C2911yescharacteristic, complemented
535#328C22×C2911yescharacteristic, complemented
536#327C22×C2911yescharacteristic
537#327C22×C2911yescharacteristic
538#327C22×C2911yescharacteristic
539#327C22×C2911yescharacteristic
540#327C22×C2911yescharacteristic, complemented
541#327C22×C2911yescharacteristic, complemented
542#324C22×C2911yescharacteristic, complemented
543#324C22×C2911yescharacteristic, complemented
544#323C22×C2911yescharacteristic
545#323C22×C2911yescharacteristic
546C2×C29—21no—
547C2×C29—21no—
548C2×C29—81no—
549C2×C29—81no—
550C2×C29—81no—
551C2×C29—81no—
552C2×C29—161no—
553C2×C29#301211yescharacteristic
554C2×C29#301811yescharacteristic
555C2×C29#302711yescharacteristic
556C2×#41—21no—
557C2×#41—21no—
558C22×Q8C23×C2911yescharacteristic
559C22×D4—21no—
560C22×D4—21no—
561C22×D4C23×C2911yescharacteristic
562C2×Q16—21no—
563C2×SD16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×D8—21no—
568C2×D8—21no—
569C2×D8—21no—
570C4⋊Q8—21no—
571C4⋊Q8D4×C2911yescharacteristic, complemented
572#127D4×C2911yescharacteristic, complemented
573#126—21no—
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#125—21no—
583#125—21no—
584#125D4×C2911yescharacteristic, complemented
585#124—21no—
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124D4×C2911yescharacteristic, complemented
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8C23×C2911yescharacteristic
614#121—21no—
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#121—21no—
624#121—21no—
625#121—21no—
626#121C23×C2911yescharacteristic
627#121C23×C2911yescharacteristic
628#121C23×C2911yescharacteristic
629#120—21no—
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634C4×Q8D4×C2911yescharacteristic, complemented
635C4×D4—21no—
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4D4×C2911yescharacteristic, complemented
644C4×D4D4×C2911yescharacteristic, complemented
645C4×D4D4×C2911yescharacteristic, complemented
646#117—21no—
647#117—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4D4×C2911yescharacteristic
652C2×C4⋊C4D4×C2911yescharacteristic
653C2×C4⋊C4C23×C2911yescharacteristic
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C2911yescharacteristic
663C2×C22⋊C4D4×C2911yescharacteristic
664C2×C22⋊C4C23×C2911yescharacteristic
665C2×C42—21no—
666C2×C42C23×C2911yescharacteristic
667C4⋊C8—21no—
668C4⋊C8—21no—
669#103—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#102—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677C22⋊C8C23×C2911yescharacteristic
678C22⋊C8C23×C2911yescharacteristic
679C22⋊C8C23×C2911yescharacteristic
680C22⋊C8C23×C2911yescharacteristic
681#97—21no—
682C4×C8—21no—
683#95—21no—
684#95—21no—
685#95C23×C2911yescharacteristic
686#95C23×C2911yescharacteristic
687C29#1843411yescharacteristic, direct product factor, Sylow
688C24—21no—
689C24—21no—
690C24C2×D4×C2911yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C2911yescharacteristic
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—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C2911yescharacteristic
722C2×D4C2×D4×C2911yescharacteristic
723C2×D4C2×D4×C2911yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C2911yescharacteristic
736C22×C4C2×D4×C2911yescharacteristic
737C22×C4C2×D4×C2911yescharacteristic
738C22×C4C2×D4×C2911yescharacteristic
739C22×C4C2×D4×C2911yescharacteristic
740C22×C4C24×C2911yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—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—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C2911yescharacteristic
773C4⋊C4C2×D4×C2911yescharacteristic
774C4⋊C4C2×D4×C2911yescharacteristic
775C4⋊C4C2×D4×C2911yescharacteristic
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—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C2911yescharacteristic
814C42C2×D4×C2911yescharacteristic
815C42C2×D4×C2911yescharacteristic
816C42C2×D4×C2911yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C2911yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4C29×#12011yescharacteristic
900C2×C4C29×#12011yescharacteristic
901C2×C4C29×#12011yescharacteristic
902C2×C4C29×#12011yescharacteristic
903C2×C4C22×D4×C2911yescharacteristic
904C2×C4C22×D4×C2911yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×C29×#12011yescharacteristic
934C22C29×#57611yescharacteristic
935C22C29×#57711yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C29×#301211yescharacteristic
961C2C29×#301811yescharacteristic
962C2C29×#302711yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ 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×#3560C2semidirect
2. C29×#3213C2semidirect
3. C29×#3211C2semidirect
4. C29×#2662C2semidirect
5. C29×#1606C2semidirect
6. C29×#1604C2semidirect
7. C29×#1603C2semidirect
8. C29×#1601C2semidirect
9. C29×#1600C2semidirect
10. C29×#1598C2semidirect
11. C29×#1597C2semidirect
12. C29×#1595C2semidirect
13. C29×#1509C2semidirect
14. C29×#1502C2semidirect
15. C29×#1473C2semidirect
35. C2×C29×#124C22semidirect
44. C29×#451C22semidirect
45. C29×#450C22semidirect
48. C29×#448C22semidirect
51. C29×#447C22semidirect
52. C29×#432C22semidirect
53. C29×#431C22semidirect
55. C29×#395C22semidirect
57. C29×#394C22semidirect
62. C4×C4⋊C4×C29C22semidirect
63. C29×#328C22semidirect
64. C29×#328C22semidirect
69. C29×#327C22semidirect
70. C29×#327C22semidirect
71. C29×#324C22semidirect
72. C29×#324C22semidirect
90. C29×C4⋊Q8D4semidirect
91. C29×#127D4semidirect
103. C29×#125D4semidirect
112. C29×#124D4semidirect
153. C4×Q8×C29D4semidirect
162. C4×D4×C29D4semidirect
163. C4×D4×C29D4semidirect
164. C4×D4×C29D4semidirect
335. #18434C29direct (N × H)
428. #3560C2×C29semidirect
429. #3213C2×C29semidirect
430. #3211C2×C29semidirect
431. #2662C2×C29semidirect
432. #1606C2×C29semidirect
433. #1604C2×C29semidirect
434. #1603C2×C29semidirect
435. #1601C2×C29semidirect
436. #1600C2×C29semidirect
437. #1598C2×C29semidirect
438. #1597C2×C29semidirect
439. #1595C2×C29semidirect
440. #1509C2×C29semidirect
441. #1502C2×C29semidirect
442. #1473C2×C29semidirect
506. C2×#124C22×C29semidirect
515. #451C22×C29semidirect
516. #450C22×C29semidirect
519. #448C22×C29semidirect
522. #447C22×C29semidirect
523. #432C22×C29semidirect
524. #431C22×C29semidirect
526. #395C22×C29semidirect
528. #394C22×C29semidirect
533. C4×C4⋊C4C22×C29semidirect
534. #328C22×C29semidirect
535. #328C22×C29semidirect
540. #327C22×C29semidirect
541. #327C22×C29semidirect
542. #324C22×C29semidirect
543. #324C22×C29semidirect
571. C4⋊Q8D4×C29semidirect
572. #127D4×C29semidirect
584. #125D4×C29semidirect
593. #124D4×C29semidirect
634. C4×Q8D4×C29semidirect
643. C4×D4D4×C29semidirect
644. C4×D4D4×C29semidirect
645. C4×D4D4×C29semidirect
687. C29#18434direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35602
C29×#32132
C29×#32112
C29×#26622
C29×#16062
C29×#16042
C29×#16032
C29×#16012
C29×#16002
C29×#15982
C29×#15972
C29×#15952
C29×#15092
C29×#15022
C29×#14732
#1843429