Finite Group Databasebeta

← C29×#29064 #20323964

Subgroups — C29×#29064 #20323964

Order 7424.

850 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2497C211yesmaximal, characteristic, complemented
2C29×#2428C211yesmaximal, characteristic
3C29×#2100C211yesmaximal, characteristic, complemented
4C29×#2041C211yesmaximal, characteristic, complemented
5C29×#2033C211yesmaximal, characteristic, complemented
6C29×#2033C211yesmaximal, characteristic, complemented
7C29×#1957C211yesmaximal, characteristic, complemented
8C29×#1942C211yesmaximal, characteristic, complemented
9C29×#1936C211yesmaximal, characteristic, complemented
10C29×#1925C211yesmaximal, characteristic, complemented
11C29×#1895C211yesmaximal, characteristic, complemented
12C29×#1895C211yesmaximal, characteristic, complemented
13C29×#1862C211yesmaximal, characteristic, complemented
14C29×#1762C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C22×M16×C29C2211yescharacteristic
17C2×C29×#127C2211yescharacteristic
18C2×C29×#121—21no—
19C2×C29×#121C2211yescharacteristic
20C2×C29×#121C2211yescharacteristic
21C2×C4×D4×C29C2211yescharacteristic
22C2×C29×#107C2211yescharacteristic
23C2×C29×#107C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×C22⋊C8C2211yescharacteristic
33C2×C29×#97C2211yescharacteristic
34C2×C4×C8×C29C2211yescharacteristic
35C29×#400—21no—
36C29×#396—21no—
37C29×#394—21no—
38C29×#392—21no—
39C29×#390C2211yescharacteristic
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#388—21no—
44C29×#387—21no—
45C29×#386—21no—
46C29×#384C2211yescharacteristic
47C29×#380C2211yescharacteristic
48C29×#380C2211yescharacteristic
49C4×C4⋊C4×C29C2211yescharacteristic
50C4×C22⋊C4×C29C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×D4×C29—21no—
60C22×D4×C29—21no—
61C22×D4×C29—21no—
62C22×D4×C29—21no—
63C22×D4×C29C2311yescharacteristic
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29—21no—
66C23×C4×C29C2311yescharacteristic
67C2×M16×C29—22no—
68C2×M16×C29—41no—
69C2×M16×C29—41no—
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C29×#127—22no—
75C29×#127—41no—
76C29×#121—22no—
77C29×#121—22no—
78C29×#121—44no—
79C29×#121—41no—
80C29×#121—41no—
81C4×D4×C29—22no—
82C4×D4×C29—41no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—21no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
99C2×C22⋊C4×C29—21no—
100C2×C22⋊C4×C29—21no—
101C2×C22⋊C4×C29D411yescharacteristic
102C2×C22⋊C4×C29D411yescharacteristic
103C2×C42×C29—21no—
104C2×C42×C29C2311yescharacteristic
105C2×C42×C29C2311yescharacteristic
106C29×#107—22no—
107C29×#107—41no—
108C29×#102—22no—
109C29×#102—22no—
110C29×#102—22no—
111C29×#102—22no—
112C29×#102—22no—
113C29×#102—41no—
114C29×#102—41no—
115C29×#102—41no—
116C29×C22⋊C8—22no—
117C29×#97—41no—
118C4×C8×C29—41no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95D411yescharacteristic
126C29×#95D411yescharacteristic
127C24×C29—21no—
128C24×C29—21no—
129C24×C29C2×D411yescharacteristic
130C2×D4×C29—21no—
131C2×D4×C29—21no—
132C2×D4×C29—21no—
133C2×D4×C29—21no—
134C2×D4×C29—21no—
135C2×D4×C29—21no—
136C2×D4×C29—21no—
137C2×D4×C29—21no—
138C2×D4×C29—21no—
139C2×D4×C29—21no—
140C2×D4×C29—21no—
141C2×D4×C29—42no—
142C2×D4×C29—42no—
143C2×D4×C29—42no—
144C2×D4×C29—42no—
145C2×D4×C29—42no—
146C2×D4×C29—42no—
147C2×D4×C29—42no—
148C2×D4×C29—42no—
149C2×D4×C29—81no—
150C2×D4×C29—81no—
151C2×D4×C29—81no—
152C2×D4×C29—81no—
153C2×D4×C29#4112yes—
154C22×C4×C29—21no—
155C22×C4×C29—21no—
156C22×C4×C29—21no—
157C22×C4×C29—21no—
158C22×C4×C29—21no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
165C22×C4×C29—21no—
166C22×C4×C29—42no—
167C22×C4×C29—42no—
168C22×C4×C29—81no—
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2411yescharacteristic
175M16×C29—44no—
176C2×C8×C29—21no—
177C2×C8×C29—21no—
178C2×C8×C29—21no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29#4112yes—
187C2×C8×C29#4112yes—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—42no—
200C4⋊C4×C29—42no—
201C4⋊C4×C29—81no—
202C4⋊C4×C29—81no—
203C4⋊C4×C29—81no—
204C4⋊C4×C29#4112yes—
205C22⋊C4×C29—22no—
206C22⋊C4×C29—22no—
207C22⋊C4×C29—42no—
208C22⋊C4×C29—42no—
209C22⋊C4×C29—42no—
210C22⋊C4×C29—42no—
211C22⋊C4×C29—81no—
212C22⋊C4×C29—81no—
213C22⋊C4×C29—81no—
214C42×C29—21no—
215C42×C29—21no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—81no—
219#29064C2911yesmaximal, characteristic, direct product factor, Sylow
220C23×C29—21no—
221C23×C29—22no—
222C23×C29—21no—
223C23×C29—21no—
224C23×C29—21no—
225C23×C29—21no—
226C23×C29—21no—
227C23×C29—21no—
228C23×C29—41no—
229C23×C29—41no—
230C23×C29—41no—
231C23×C29—41no—
232C23×C29—41no—
233C23×C29—41no—
234C23×C29—41no—
235C23×C29—41no—
236C23×C29—41no—
237C23×C29—41no—
238C23×C29—41no—
239C23×C29—41no—
240C23×C29—41no—
241C23×C29C22×D411yescharacteristic
242D4×C29—22no—
243D4×C29—22no—
244D4×C29—41no—
245D4×C29—41no—
246D4×C29—41no—
247D4×C29—41no—
248D4×C29—41no—
249D4×C29—41no—
250D4×C29—84no—
251D4×C29—84no—
252D4×C29—84no—
253D4×C29—84no—
254C2×C4×C29—21no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—21no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—21no—
261C2×C4×C29—22no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—41no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29—41no—
273C2×C4×C29—41no—
274C2×C4×C29—41no—
275C2×C4×C29—41no—
276C2×C4×C29—41no—
277C2×C4×C29—41no—
278C2×C4×C29—41no—
279C2×C4×C29—41no—
280C2×C4×C29—41no—
281C2×C4×C29—41no—
282C2×C4×C29—41no—
283C2×C4×C29—41no—
284C2×C4×C29—41no—
285C2×C4×C29—41no—
286C2×C4×C29—41no—
287C2×C4×C29—41no—
288C2×C4×C29—41no—
289C2×C4×C29—84no—
290C2×C4×C29AGL(1,ℤ/8)12yes—
291C2×C4×C29#13712yes—
292C2×C4×C29C2×#4111yescharacteristic
293C2×C4×C29C2×#4111yescharacteristic
294C2×C4×C29C2×#4111yescharacteristic
295C2×C4×C29C2×#4111yescharacteristic
296C2×C4×C29H(5,𝔽2)11yescharacteristic
297C2×C4×C29H(5,𝔽2)11yescharacteristic
298C8×C29—22no—
299C8×C29—22no—
300C8×C29—41no—
301C8×C29—41no—
302#2497C2×C2911yescharacteristic, complemented
303#2428C2×C2911yescharacteristic
304#2100C2×C2911yescharacteristic, complemented
305#2041C2×C2911yescharacteristic, complemented
306#2033C2×C2911yescharacteristic, complemented
307#2033C2×C2911yescharacteristic, complemented
308#1957C2×C2911yescharacteristic, complemented
309#1942C2×C2911yescharacteristic, complemented
310#1936C2×C2911yescharacteristic, complemented
311#1925C2×C2911yescharacteristic, complemented
312#1895C2×C2911yescharacteristic, complemented
313#1895C2×C2911yescharacteristic, complemented
314#1862C2×C2911yescharacteristic, complemented
315#1762C2×C2911yescharacteristic, complemented
316#1753C2×C2911yescharacteristic, complemented
317C22×C29—41no—
318C22×C29—41no—
319C22×C29—41no—
320C22×C29—42no—
321C22×C29—41no—
322C22×C29—41no—
323C22×C29—42no—
324C22×C29—41no—
325C22×C29—41no—
326C22×C29—42no—
327C22×C29—81no—
328C22×C29—81no—
329C22×C29—81no—
330C22×C29—81no—
331C22×C29—81no—
332C22×C29—81no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29—81no—
336C22×C29—81no—
337C22×C29—81no—
338C22×C29#53211yescharacteristic
339C22×C29#54611yescharacteristic
340C22×C29#54611yescharacteristic
341C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C29C2×#13711yescharacteristic
343C22×C29#57611yescharacteristic
344C22×C29#57611yescharacteristic
345C4×C29—22no—
346C4×C29—22no—
347C4×C29—41no—
348C4×C29—41no—
349C4×C29—42no—
350C4×C29—41no—
351C4×C29—81no—
352C4×C29—81no—
353C4×C29—81no—
354C4×C29—81no—
355C4×C29—81no—
356C4×C29#52911yescharacteristic
357C4×C29#53811yescharacteristic
358C4×C29#55311yescharacteristic
359C4×C29#55311yescharacteristic
360C22×M16C22×C2911yescharacteristic
361C2×#127C22×C2911yescharacteristic
362C2×#121—21no—
363C2×#121C22×C2911yescharacteristic
364C2×#121C22×C2911yescharacteristic
365C2×C4×D4C22×C2911yescharacteristic
366C2×#107C22×C2911yescharacteristic
367C2×#107C22×C2911yescharacteristic
368C2×#102C22×C2911yescharacteristic
369C2×#102C22×C2911yescharacteristic
370C2×#102C22×C2911yescharacteristic
371C2×#102C22×C2911yescharacteristic
372C2×#102C22×C2911yescharacteristic
373C2×#102C22×C2911yescharacteristic
374C2×#102C22×C2911yescharacteristic
375C2×#102C22×C2911yescharacteristic
376C2×C22⋊C8C22×C2911yescharacteristic
377C2×#97C22×C2911yescharacteristic
378C2×C4×C8C22×C2911yescharacteristic
379#400—21no—
380#396—21no—
381#394—21no—
382#392—21no—
383#390C22×C2911yescharacteristic
384#389C22×C2911yescharacteristic
385#389C22×C2911yescharacteristic
386#389C22×C2911yescharacteristic
387#388—21no—
388#387—21no—
389#386—21no—
390#384C22×C2911yescharacteristic
391#380C22×C2911yescharacteristic
392#380C22×C2911yescharacteristic
393C4×C4⋊C4C22×C2911yescharacteristic
394C4×C22⋊C4C22×C2911yescharacteristic
395#340C22×C2911yescharacteristic
396#340C22×C2911yescharacteristic
397#340C22×C2911yescharacteristic
398#340C22×C2911yescharacteristic
399#340C22×C2911yescharacteristic
400#340C22×C2911yescharacteristic
401#336C22×C2911yescharacteristic
402#336C22×C2911yescharacteristic
403C2×C29—81no—
404C2×C29—82no—
405C2×C29—161no—
406C2×C29#255911yescharacteristic
407C2×C29#317611yescharacteristic
408C2×C29#318211yescharacteristic
409C2×C29#331411yescharacteristic
410C2×C29#331811yescharacteristic
411C2×C29#332511yescharacteristic
412C2×C29#333311yescharacteristic
413C22×D4—21no—
414C22×D4—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4C23×C2911yescharacteristic
418C22×D4C23×C2911yescharacteristic
419C23×C4—21no—
420C23×C4C23×C2911yescharacteristic
421C2×M16—22no—
422C2×M16—41no—
423C2×M16—41no—
424C22×C8C23×C2911yescharacteristic
425C22×C8C23×C2911yescharacteristic
426C22×C8C23×C2911yescharacteristic
427C22×C8C23×C2911yescharacteristic
428#127—22no—
429#127—41no—
430#121—22no—
431#121—22no—
432#121—44no—
433#121—41no—
434#121—41no—
435C4×D4—22no—
436C4×D4—41no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4C23×C2911yescharacteristic
443C2×C4⋊C4C23×C2911yescharacteristic
444C2×C4⋊C4C23×C2911yescharacteristic
445C2×C4⋊C4C23×C2911yescharacteristic
446C2×C4⋊C4C23×C2911yescharacteristic
447C2×C4⋊C4C23×C2911yescharacteristic
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4D4×C2911yescharacteristic
456C2×C22⋊C4D4×C2911yescharacteristic
457C2×C42—21no—
458C2×C42C23×C2911yescharacteristic
459C2×C42C23×C2911yescharacteristic
460#107—22no—
461#107—41no—
462#102—22no—
463#102—22no—
464#102—22no—
465#102—22no—
466#102—22no—
467#102—41no—
468#102—41no—
469#102—41no—
470C22⋊C8—22no—
471#97—41no—
472C4×C8—41no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95D4×C2911yescharacteristic
480#95D4×C2911yescharacteristic
481C29#2906411yescharacteristic, direct product factor, Sylow
482C24—21no—
483C24—21no—
484C24C2×D4×C2911yescharacteristic
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4#41×C2912yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4C2×D4×C2911yescharacteristic
525C22×C4C2×D4×C2911yescharacteristic
526C22×C4C2×D4×C2911yescharacteristic
527C22×C4C2×D4×C2911yescharacteristic
528C22×C4C2×D4×C2911yescharacteristic
529C22×C4C24×C2911yescharacteristic
530M16—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8#41×C2912yes—
542C2×C8#41×C2912yes—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—42no—
555C4⋊C4—42no—
556C4⋊C4—81no—
557C4⋊C4—81no—
558C4⋊C4—81no—
559C4⋊C4#41×C2912yes—
560C22⋊C4—22no—
561C22⋊C4—22no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—81no—
567C22⋊C4—81no—
568C22⋊C4—81no—
569C42—21no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—81no—
574C23—21no—
575C23—22no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C22×D4×C2911yescharacteristic
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605D4—84no—
606D4—84no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—84no—
644C2×C4C29×AGL(1,ℤ/8)12yes—
645C2×C4C29×#13712yes—
646C2×C4C2×#41×C2911yescharacteristic
647C2×C4C2×#41×C2911yescharacteristic
648C2×C4C2×#41×C2911yescharacteristic
649C2×C4C2×#41×C2911yescharacteristic
650C2×C4C29×H(5,𝔽2)11yescharacteristic
651C2×C4C29×H(5,𝔽2)11yescharacteristic
652C8—22no—
653C8—22no—
654C8—41no—
655C8—41no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—41no—
663C22—42no—
664C22—41no—
665C22—41no—
666C22—81no—
667C22—81no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22C29×#53211yescharacteristic
678C22C29×#54611yescharacteristic
679C22C29×#54611yescharacteristic
680C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
681C22C2×C29×#13711yescharacteristic
682C22C29×#57611yescharacteristic
683C22C29×#57611yescharacteristic
684C4—22no—
685C4—22no—
686C4—41no—
687C4—42no—
688C4—41no—
689C4—41no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4C29×#52911yescharacteristic
696C4C29×#53811yescharacteristic
697C4C29×#55311yescharacteristic
698C4C29×#55311yescharacteristic
699C2—81no—
700C2—82no—
701C2—161no—
702C2C29×#255911yescharacteristic
703C2C29×#317611yescharacteristic
704C2C29×#318211yescharacteristic
705C2C29×#331411yescharacteristic
706C2C29×#331811yescharacteristic
707C2C29×#332511yescharacteristic
708C2C29×#333311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C22⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2497C2semidirect
3. C29×#2100C2semidirect
4. C29×#2041C2semidirect
5. C29×#2033C2semidirect
6. C29×#2033C2semidirect
7. C29×#1957C2semidirect
8. C29×#1942C2semidirect
9. C29×#1936C2semidirect
10. C29×#1925C2semidirect
11. C29×#1895C2semidirect
12. C29×#1895C2semidirect
13. C29×#1862C2semidirect
14. C29×#1762C2semidirect
15. C29×#1753C2semidirect
219. #29064C29direct (N × H)
302. #2497C2×C29semidirect
304. #2100C2×C29semidirect
305. #2041C2×C29semidirect
306. #2033C2×C29semidirect
307. #2033C2×C29semidirect
308. #1957C2×C29semidirect
309. #1942C2×C29semidirect
310. #1936C2×C29semidirect
311. #1925C2×C29semidirect
312. #1895C2×C29semidirect
313. #1895C2×C29semidirect
314. #1862C2×C29semidirect
315. #1762C2×C29semidirect
316. #1753C2×C29semidirect
481. C29#29064direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24972
C29×#24282
C29×#21002
C29×#20412
C29×#20332
C29×#19572
C29×#19422
C29×#19362
C29×#19252
C29×#18952
C29×#18622
C29×#17622
C29×#17532
#2906429