Finite Group Databasebeta

← C29×#18252 #20313152

Subgroups — C29×#18252 #20313152

Order 7424.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3534C211yesmaximal, characteristic, complemented
2C29×#3006C211yesmaximal, characteristic, complemented
3C29×#3002C211yesmaximal, characteristic, complemented
4C29×#2430C211yesmaximal, 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×#1504C211yesmaximal, characteristic, complemented
14C2×C29×#327C211yesmaximal, characteristic, complemented
15C29×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic, complemented
17C2×C29×AGL(1,ℤ/8)—21no—
18C2×C29×#135—21no—
19C29×#562—21no—
20C29×#560—21no—
21C29×#553—21no—
22C29×#551—21no—
23C29×#546—21no—
24C29×#546—21no—
25C29×#546—21no—
26D42×C29—21no—
27C29×#540—21no—
28C29×#539—21no—
29C29×#539C2211yescharacteristic
30C29×#538—21no—
31C29×#538C2211yescharacteristic
32C29×#537C2211yescharacteristic
33C29×#534—21no—
34C29×#534C2211yescharacteristic
35C29×#525C2211yescharacteristic
36C2×C29×#123C2211yescharacteristic
37C2×C29×#121—21no—
38C2×C29×#121C2211yescharacteristic
39C29×#452—21no—
40C29×#451C2211yescharacteristic, complemented
41C29×#450C2211yescharacteristic, complemented
42C29×#449—21no—
43C29×#449—21no—
44C29×#449—21no—
45C29×#448C2211yescharacteristic
46C29×#448C2211yescharacteristic, complemented
47C29×#448C2211yescharacteristic, complemented
48C29×#447C2211yescharacteristic
49C29×#447C2211yescharacteristic, complemented
50C29×#447C2211yescharacteristic, complemented
51C29×#417—21no—
52C29×#416—21no—
53C29×#407C2211yescharacteristic, complemented
54C2×C29×C22⋊C8C2211yescharacteristic, complemented
55C29×#395C2211yescharacteristic, complemented
56C29×#394C2211yescharacteristic, complemented
57C29×#393C2211yescharacteristic, complemented
58C29×#392C2211yescharacteristic, complemented
59C29×#386—21no—
60C29×#386—21no—
61C29×#385—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×C29—21no—
77C2×#41×C29—21no—
78C2×#41×C29—21no—
79C2×#41×C29—21no—
80C2×#41×C29—44no—
81C2×#41×C29D411yescharacteristic, complemented
82C22×Q8×C29C2311yescharacteristic
83C22×D4×C29—21no—
84C22×D4×C29—21no—
85C22×D4×C29—21no—
86C22×D4×C29—21no—
87C22×D4×C29—21no—
88C22×D4×C29D411yescharacteristic
89C22×D4×C29D411yescharacteristic, complemented
90C22×D4×C29C2311yescharacteristic
91C23×C4×C29—21no—
92C23×C4×C29—21no—
93C23×C4×C29C2311yescharacteristic
94C29×AGL(1,ℤ/8)—44no—
95C29×#135—44no—
96C2×Q16×C29—21no—
97C2×SD16×C29—21no—
98C2×SD16×C29—21no—
99C2×SD16×C29—21no—
100C2×SD16×C29—21no—
101C2×D8×C29—21no—
102C2×D8×C29—21no—
103C2×D8×C29—21no—
104C2×M16×C29—21no—
105C22×C8×C29—21no—
106C29×#127—21no—
107C29×#126—21no—
108C29×#126—21no—
109C29×#126—21no—
110C29×#126—21no—
111C29×#125—21no—
112C29×#125—21no—
113C29×#124—21no—
114C29×#124—21no—
115C29×#124—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×#123—21no—
126C29×#123—21no—
127C29×#123—21no—
128C29×#123—21no—
129C29×#123—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⋊Q8C2311yescharacteristic
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×#121—21no—
146C29×#121—21no—
147C29×#121—21no—
148C29×#121—21no—
149C29×#121—21no—
150C29×#121—21no—
151C29×#121—21no—
152C29×#121—44no—
153C29×#121D411yescharacteristic, complemented
154C29×#121D411yescharacteristic, complemented
155C29×#121D411yescharacteristic, complemented
156C29×#121C2311yescharacteristic
157C29×#121C2311yescharacteristic
158C29×#121C2311yescharacteristic
159C29×#120—21no—
160C29×#120—21no—
161C29×#120—21no—
162C29×#120—21no—
163C29×#120—21no—
164C29×#120—21no—
165C29×#120—21no—
166C29×#120—21no—
167C4×D4×C29—21no—
168C4×D4×C29—21no—
169C4×D4×C29—21no—
170C4×D4×C29—21no—
171C4×D4×C29—21no—
172C4×D4×C29—21no—
173C4×D4×C29—21no—
174C4×D4×C29—21no—
175C29×#117—21no—
176C29×#117D411yescharacteristic, complemented
177C2×C4⋊C4×C29—21no—
178C2×C4⋊C4×C29D411yescharacteristic
179C2×C4⋊C4×C29D411yescharacteristic, complemented
180C2×C4⋊C4×C29C2311yescharacteristic
181C2×C22⋊C4×C29—21no—
182C2×C22⋊C4×C29—21no—
183C2×C22⋊C4×C29—21no—
184C2×C22⋊C4×C29—21no—
185C2×C22⋊C4×C29—21no—
186C2×C22⋊C4×C29—21no—
187C2×C22⋊C4×C29—21no—
188C2×C22⋊C4×C29D411yescharacteristic
189C2×C22⋊C4×C29D411yescharacteristic
190C2×C22⋊C4×C29C2311yescharacteristic
191C29×#103—21no—
192C29×#103—21no—
193C29×#103—21no—
194C29×#103—21no—
195C29×#102—21no—
196C29×#102—21no—
197C29×#102—21no—
198C29×#102—21no—
199C29×C22⋊C8—21no—
200C29×C22⋊C8—21no—
201C29×C22⋊C8C2311yescharacteristic
202C29×C22⋊C8C2311yescharacteristic
203C29×C22⋊C8C2311yescharacteristic
204C29×C22⋊C8C2311yescharacteristic
205C29×#95—21no—
206C29×#95—21no—
207C29×#95—21no—
208C29×#95C2311yescharacteristic
209C29×#95C2311yescharacteristic
210C24×C29—21no—
211C24×C29—21no—
212C24×C29—21no—
213C24×C29C2×D411yescharacteristic
214C24×C29C2×D411yescharacteristic
215#41×C29—24no—
216#41×C29—24no—
217#41×C29—42no—
218#41×C29—42no—
219#41×C29—42no—
220#41×C29—42no—
221#41×C29—42no—
222#41×C29—42no—
223#41×C29—42no—
224#41×C29—81no—
225#41×C29—81no—
226C2×Q8×C29—21no—
227C2×Q8×C29—21no—
228C2×Q8×C29—21no—
229C2×Q8×C29—42no—
230C2×Q8×C29C2×D411yescharacteristic
231C2×D4×C29—24no—
232C2×D4×C29—21no—
233C2×D4×C29—21no—
234C2×D4×C29—21no—
235C2×D4×C29—21no—
236C2×D4×C29—21no—
237C2×D4×C29—21no—
238C2×D4×C29—21no—
239C2×D4×C29—21no—
240C2×D4×C29—21no—
241C2×D4×C29—21no—
242C2×D4×C29—21no—
243C2×D4×C29—21no—
244C2×D4×C29—21no—
245C2×D4×C29—21no—
246C2×D4×C29—21no—
247C2×D4×C29—21no—
248C2×D4×C29—21no—
249C2×D4×C29—21no—
250C2×D4×C29—21no—
251C2×D4×C29—42no—
252C2×D4×C29—42no—
253C2×D4×C29—42no—
254C2×D4×C29—42no—
255C2×D4×C29—41no—
256C2×D4×C29—41no—
257C2×D4×C29—42no—
258C2×D4×C29—42no—
259C2×D4×C29—81no—
260C2×D4×C29—81no—
261C2×D4×C29—81no—
262C2×D4×C29—81no—
263C2×D4×C29—81no—
264C2×D4×C29—82no—
265C2×D4×C29C2×D411yescharacteristic
266C2×D4×C29C2×D411yescharacteristic
267C2×D4×C29C2×D411yescharacteristic
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—21no—
275C22×C4×C29—21no—
276C22×C4×C29—21no—
277C22×C4×C29—21no—
278C22×C4×C29—42no—
279C22×C4×C29—42no—
280C22×C4×C29—42no—
281C22×C4×C29—42no—
282C22×C4×C29—41no—
283C22×C4×C29—41no—
284C22×C4×C29—42no—
285C22×C4×C29—81no—
286C22×C4×C29C2×D411yescharacteristic
287C22×C4×C29C2×D411yescharacteristic
288C22×C4×C29C2×D411yescharacteristic
289C22×C4×C29C2×D411yescharacteristic
290C22×C4×C29C2×D411yescharacteristic
291C22×C4×C29C2×D411yescharacteristic
292C22×C4×C29C2×D411yescharacteristic
293C22×C4×C29C2×D411yescharacteristic
294C22×C4×C29C2411yescharacteristic
295Q16×C29—42no—
296SD16×C29—42no—
297SD16×C29—42no—
298SD16×C29—42no—
299SD16×C29—42no—
300D8×C29—42no—
301D8×C29—42no—
302D8×C29—42no—
303M16×C29—42no—
304C2×C8×C29—21no—
305C2×C8×C29—21no—
306C2×C8×C29—21no—
307C2×C8×C29—21no—
308C2×C8×C29—42no—
309C4⋊C4×C29—21no—
310C4⋊C4×C29—21no—
311C4⋊C4×C29—21no—
312C4⋊C4×C29—21no—
313C4⋊C4×C29—21no—
314C4⋊C4×C29—21no—
315C4⋊C4×C29—21no—
316C4⋊C4×C29—21no—
317C4⋊C4×C29—21no—
318C4⋊C4×C29—21no—
319C4⋊C4×C29—21no—
320C4⋊C4×C29—21no—
321C4⋊C4×C29—21no—
322C4⋊C4×C29—42no—
323C4⋊C4×C29C2×D411yescharacteristic
324C4⋊C4×C29C2×D411yescharacteristic
325C4⋊C4×C29C2×D411yescharacteristic
326C4⋊C4×C29C2×D411yescharacteristic
327C22⋊C4×C29—21no—
328C22⋊C4×C29—21no—
329C22⋊C4×C29—21no—
330C22⋊C4×C29—21no—
331C22⋊C4×C29—21no—
332C22⋊C4×C29—21no—
333C22⋊C4×C29—21no—
334C22⋊C4×C29—21no—
335C22⋊C4×C29—21no—
336C22⋊C4×C29—21no—
337C22⋊C4×C29—21no—
338C22⋊C4×C29—21no—
339C22⋊C4×C29—21no—
340C22⋊C4×C29—21no—
341C22⋊C4×C29—21no—
342C22⋊C4×C29—21no—
343C22⋊C4×C29—21no—
344C22⋊C4×C29—21no—
345C22⋊C4×C29—21no—
346C22⋊C4×C29—21no—
347C22⋊C4×C29—21no—
348C22⋊C4×C29—21no—
349C22⋊C4×C29—21no—
350C22⋊C4×C29—21no—
351C22⋊C4×C29—21no—
352C22⋊C4×C29—42no—
353C22⋊C4×C29—42no—
354C22⋊C4×C29—42no—
355C22⋊C4×C29—81no—
356C42×C29—21no—
357C42×C29—21no—
358C42×C29—21no—
359#18252C2911yesmaximal, characteristic, direct product factor, Sylow
360C23×C29—21no—
361C23×C29—21no—
362C23×C29—22no—
363C23×C29—22no—
364C23×C29—21no—
365C23×C29—21no—
366C23×C29—21no—
367C23×C29—21no—
368C23×C29—21no—
369C23×C29—21no—
370C23×C29—41no—
371C23×C29—41no—
372C23×C29—41no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—41no—
376C23×C29—41no—
377C23×C29—41no—
378C23×C29—41no—
379C23×C29—42no—
380C23×C29—81no—
381C23×C29—81no—
382C23×C29—81no—
383C23×C29—81no—
384C23×C29—81no—
385C23×C29#12011yescharacteristic
386C23×C29#12011yescharacteristic
387C23×C29C22×D411yescharacteristic
388Q8×C29—22no—
389Q8×C29—22no—
390Q8×C29—41no—
391Q8×C29—41no—
392Q8×C29—41no—
393Q8×C29—81no—
394D4×C29—22no—
395D4×C29—22no—
396D4×C29—41no—
397D4×C29—41no—
398D4×C29—41no—
399D4×C29—41no—
400D4×C29—41no—
401D4×C29—44no—
402D4×C29—41no—
403D4×C29—41no—
404D4×C29—41no—
405D4×C29—41no—
406D4×C29—41no—
407D4×C29—41no—
408D4×C29—44no—
409D4×C29—42no—
410D4×C29—42no—
411D4×C29—81no—
412D4×C29—81no—
413D4×C29—81no—
414D4×C29—81no—
415D4×C29—81no—
416D4×C29—81no—
417D4×C29—81no—
418D4×C29—81no—
419D4×C29—81no—
420D4×C29—81no—
421D4×C29—81no—
422D4×C29—81no—
423D4×C29—84no—
424C2×C4×C29—22no—
425C2×C4×C29—22no—
426C2×C4×C29—22no—
427C2×C4×C29—22no—
428C2×C4×C29—21no—
429C2×C4×C29—21no—
430C2×C4×C29—21no—
431C2×C4×C29—21no—
432C2×C4×C29—21no—
433C2×C4×C29—21no—
434C2×C4×C29—21no—
435C2×C4×C29—21no—
436C2×C4×C29—21no—
437C2×C4×C29—21no—
438C2×C4×C29—41no—
439C2×C4×C29—41no—
440C2×C4×C29—41no—
441C2×C4×C29—41no—
442C2×C4×C29—44no—
443C2×C4×C29—44no—
444C2×C4×C29—41no—
445C2×C4×C29—41no—
446C2×C4×C29—41no—
447C2×C4×C29—41no—
448C2×C4×C29—41no—
449C2×C4×C29—41no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—41no—
453C2×C4×C29—81no—
454C2×C4×C29—81no—
455C2×C4×C29—81no—
456C2×C4×C29—81no—
457C2×C4×C29—81no—
458C2×C4×C29—81no—
459C2×C4×C29—81no—
460C2×C4×C29—84no—
461C2×C4×C29#12011yescharacteristic
462C2×C4×C29#12011yescharacteristic
463C2×C4×C29C22×D411yescharacteristic
464C2×C4×C29C22×D411yescharacteristic
465C8×C29—41no—
466C8×C29—41no—
467C8×C29—41no—
468C8×C29—41no—
469#3534C2×C2911yescharacteristic, complemented
470#3006C2×C2911yescharacteristic, complemented
471#3002C2×C2911yescharacteristic, complemented
472#2430C2×C2911yescharacteristic, complemented
473#1606C2×C2911yescharacteristic, complemented
474#1604C2×C2911yescharacteristic, complemented
475#1603C2×C2911yescharacteristic, complemented
476#1601C2×C2911yescharacteristic, complemented
477#1600C2×C2911yescharacteristic, complemented
478#1598C2×C2911yescharacteristic, complemented
479#1597C2×C2911yescharacteristic, complemented
480#1595C2×C2911yescharacteristic, complemented
481#1504C2×C2911yescharacteristic, complemented
482C2×#327C2×C2911yescharacteristic, complemented
483#1468C2×C2911yescharacteristic, complemented
484C22×C29—21no—
485C22×C29—21no—
486C22×C29—21no—
487C22×C29—21no—
488C22×C29—21no—
489C22×C29—21no—
490C22×C29—21no—
491C22×C29—42no—
492C22×C29—42no—
493C22×C29—42no—
494C22×C29—42no—
495C22×C29—41no—
496C22×C29—41no—
497C22×C29—41no—
498C22×C29—41no—
499C22×C29—41no—
500C22×C29—41no—
501C22×C29—41no—
502C22×C29—41no—
503C22×C29—42no—
504C22×C29—41no—
505C22×C29—41no—
506C22×C29—41no—
507C22×C29—41no—
508C22×C29—81no—
509C22×C29—81no—
510C22×C29—81no—
511C22×C29—81no—
512C22×C29—81no—
513C22×C29—81no—
514C22×C29—162no—
515C22×C29—162no—
516C22×C29B(4,𝔽2)12yes—
517C22×C29C2×#12011yescharacteristic
518C22×C29#57611yescharacteristic
519C22×C29#57711yescharacteristic
520C4×C29—21no—
521C4×C29—21no—
522C4×C29—21no—
523C4×C29—21no—
524C4×C29—42no—
525C4×C29—41no—
526C4×C29—41no—
527C4×C29—41no—
528C4×C29—41no—
529C4×C29—41no—
530C4×C29—41no—
531C4×C29—42no—
532C4×C29—41no—
533C4×C29—41no—
534C4×C29—81no—
535C22×#41C22×C2911yescharacteristic, complemented
536C2×AGL(1,ℤ/8)—21no—
537C2×#135—21no—
538#562—21no—
539#560—21no—
540#553—21no—
541#551—21no—
542#546—21no—
543#546—21no—
544#546—21no—
545D42—21no—
546#540—21no—
547#539—21no—
548#539C22×C2911yescharacteristic
549#538—21no—
550#538C22×C2911yescharacteristic
551#537C22×C2911yescharacteristic
552#534—21no—
553#534C22×C2911yescharacteristic
554#525C22×C2911yescharacteristic
555C2×#123C22×C2911yescharacteristic
556C2×#121—21no—
557C2×#121C22×C2911yescharacteristic
558#452—21no—
559#451C22×C2911yescharacteristic, complemented
560#450C22×C2911yescharacteristic, complemented
561#449—21no—
562#449—21no—
563#449—21no—
564#448C22×C2911yescharacteristic
565#448C22×C2911yescharacteristic, complemented
566#448C22×C2911yescharacteristic, complemented
567#447C22×C2911yescharacteristic
568#447C22×C2911yescharacteristic, complemented
569#447C22×C2911yescharacteristic, complemented
570#417—21no—
571#416—21no—
572#407C22×C2911yescharacteristic, complemented
573C2×C22⋊C8C22×C2911yescharacteristic, complemented
574#395C22×C2911yescharacteristic, complemented
575#394C22×C2911yescharacteristic, complemented
576#393C22×C2911yescharacteristic, complemented
577#392C22×C2911yescharacteristic, complemented
578#386—21no—
579#386—21no—
580#385—21no—
581C2×#95C22×C2911yescharacteristic, complemented
582#328C22×C2911yescharacteristic, complemented
583#328C22×C2911yescharacteristic, complemented
584#327C22×C2911yescharacteristic
585#327C22×C2911yescharacteristic
586#327C22×C2911yescharacteristic, complemented
587#327C22×C2911yescharacteristic, complemented
588#327C22×C2911yescharacteristic, complemented
589#327C22×C2911yescharacteristic, complemented
590#324C22×C2911yescharacteristic, complemented
591#324C22×C2911yescharacteristic, complemented
592#323C22×C2911yescharacteristic, complemented
593#323C22×C2911yescharacteristic, complemented
594C2×C29—21no—
595C2×C29—21no—
596C2×C29—22no—
597C2×C29—41no—
598C2×C29—82no—
599C2×C29—81no—
600C2×C29—81no—
601C2×C29—81no—
602C2×C29—81no—
603C2×C29#301211yescharacteristic
604C2×C29#301811yescharacteristic
605C2×C29C2×B(4,𝔽2)11yescharacteristic
606C2×#41—21no—
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—44no—
612C2×#41D4×C2911yescharacteristic, complemented
613C22×Q8C23×C2911yescharacteristic
614C22×D4—21no—
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4D4×C2911yescharacteristic
620C22×D4D4×C2911yescharacteristic, complemented
621C22×D4C23×C2911yescharacteristic
622C23×C4—21no—
623C23×C4—21no—
624C23×C4C23×C2911yescharacteristic
625AGL(1,ℤ/8)—44no—
626#135—44no—
627C2×Q16—21no—
628C2×SD16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×D8—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×M16—21no—
636C22×C8—21no—
637#127—21no—
638#126—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#125—21no—
643#125—21no—
644#124—21no—
645#124—21no—
646#124—21no—
647#123—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8D4×C2911yescharacteristic, complemented
667C22⋊Q8C23×C2911yescharacteristic
668#121—21no—
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—44no—
684#121D4×C2911yescharacteristic, complemented
685#121D4×C2911yescharacteristic, complemented
686#121D4×C2911yescharacteristic, complemented
687#121C23×C2911yescharacteristic
688#121C23×C2911yescharacteristic
689#121C23×C2911yescharacteristic
690#120—21no—
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698C4×D4—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706#117—21no—
707#117D4×C2911yescharacteristic, complemented
708C2×C4⋊C4—21no—
709C2×C4⋊C4D4×C2911yescharacteristic
710C2×C4⋊C4D4×C2911yescharacteristic, complemented
711C2×C4⋊C4C23×C2911yescharacteristic
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4D4×C2911yescharacteristic
720C2×C22⋊C4D4×C2911yescharacteristic
721C2×C22⋊C4C23×C2911yescharacteristic
722#103—21no—
723#103—21no—
724#103—21no—
725#103—21no—
726#102—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730C22⋊C8—21no—
731C22⋊C8—21no—
732C22⋊C8C23×C2911yescharacteristic
733C22⋊C8C23×C2911yescharacteristic
734C22⋊C8C23×C2911yescharacteristic
735C22⋊C8C23×C2911yescharacteristic
736#95—21no—
737#95—21no—
738#95—21no—
739#95C23×C2911yescharacteristic
740#95C23×C2911yescharacteristic
741C29#1825211yescharacteristic, direct product factor, Sylow
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C2911yescharacteristic
746C24C2×D4×C2911yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C2911yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C2911yescharacteristic
798C2×D4C2×D4×C2911yescharacteristic
799C2×D4C2×D4×C2911yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C2911yescharacteristic
819C22×C4C2×D4×C2911yescharacteristic
820C22×C4C2×D4×C2911yescharacteristic
821C22×C4C2×D4×C2911yescharacteristic
822C22×C4C2×D4×C2911yescharacteristic
823C22×C4C2×D4×C2911yescharacteristic
824C22×C4C2×D4×C2911yescharacteristic
825C22×C4C2×D4×C2911yescharacteristic
826C22×C4C24×C2911yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C2911yescharacteristic
856C4⋊C4C2×D4×C2911yescharacteristic
857C4⋊C4C2×D4×C2911yescharacteristic
858C4⋊C4C2×D4×C2911yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23C29×#12011yescharacteristic
917C23C29×#12011yescharacteristic
918C23C22×D4×C2911yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4C29×#12011yescharacteristic
993C2×C4C29×#12011yescharacteristic
994C2×C4C22×D4×C2911yescharacteristic
995C2×C4C22×D4×C2911yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22C29×B(4,𝔽2)12yes—
1033C22C2×C29×#12011yescharacteristic
1034C22C29×#57611yescharacteristic
1035C22C29×#57711yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C29×#301211yescharacteristic
1061C2C29×#301811yescharacteristic
1062C2C2×C29×B(4,𝔽2)11yescharacteristic
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×#3534C2semidirect
2. C29×#3006C2semidirect
3. C29×#3002C2semidirect
4. C29×#2430C2semidirect
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×#1504C2semidirect
14. C2×C29×#327C2semidirect
15. C29×#1468C2semidirect
16. C22×#41×C29C22semidirect
40. C29×#451C22semidirect
41. C29×#450C22semidirect
46. C29×#448C22semidirect
47. C29×#448C22semidirect
49. C29×#447C22semidirect
50. C29×#447C22semidirect
53. C29×#407C22semidirect
54. C2×C29×C22⋊C8C22semidirect
55. C29×#395C22semidirect
56. C29×#394C22semidirect
57. C29×#393C22semidirect
58. C29×#392C22semidirect
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
81. C2×#41×C29D4semidirect
89. C22×D4×C29D4semidirect
135. C29×C22⋊Q8D4semidirect
153. C29×#121D4semidirect
154. C29×#121D4semidirect
155. C29×#121D4semidirect
176. C29×#117D4semidirect
179. C2×C4⋊C4×C29D4semidirect
359. #18252C29direct (N × H)
469. #3534C2×C29semidirect
470. #3006C2×C29semidirect
471. #3002C2×C29semidirect
472. #2430C2×C29semidirect
473. #1606C2×C29semidirect
474. #1604C2×C29semidirect
475. #1603C2×C29semidirect
476. #1601C2×C29semidirect
477. #1600C2×C29semidirect
478. #1598C2×C29semidirect
479. #1597C2×C29semidirect
480. #1595C2×C29semidirect
481. #1504C2×C29semidirect
482. C2×#327C2×C29semidirect
483. #1468C2×C29semidirect
535. C22×#41C22×C29semidirect
559. #451C22×C29semidirect
560. #450C22×C29semidirect
565. #448C22×C29semidirect
566. #448C22×C29semidirect
568. #447C22×C29semidirect
569. #447C22×C29semidirect
572. #407C22×C29semidirect
573. C2×C22⋊C8C22×C29semidirect
574. #395C22×C29semidirect
575. #394C22×C29semidirect
576. #393C22×C29semidirect
577. #392C22×C29semidirect
581. C2×#95C22×C29semidirect
582. #328C22×C29semidirect
583. #328C22×C29semidirect
586. #327C22×C29semidirect
587. #327C22×C29semidirect
588. #327C22×C29semidirect
589. #327C22×C29semidirect
590. #324C22×C29semidirect
591. #324C22×C29semidirect
592. #323C22×C29semidirect
593. #323C22×C29semidirect
612. C2×#41D4×C29semidirect
620. C22×D4D4×C29semidirect
666. C22⋊Q8D4×C29semidirect
684. #121D4×C29semidirect
685. #121D4×C29semidirect
686. #121D4×C29semidirect
707. #117D4×C29semidirect
710. C2×C4⋊C4D4×C29semidirect
741. C29#18252direct (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×#30062
C29×#30022
C29×#24302
C29×#16062
C29×#16042
C29×#16032
C29×#16012
C29×#16002
C29×#15982
C29×#15972
C29×#15952
C29×#15042
C2×C29×#3272
C29×#14682
#1825229