Finite Group Databasebeta

← C29×#28999 #20323899

Subgroups — C29×#28999 #20323899

Order 7424.

870 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2491C211yesmaximal, characteristic, complemented
2C29×#2422C211yesmaximal, characteristic, complemented
3C29×#2076C211yesmaximal, characteristic, complemented
4C29×#2071C211yesmaximal, characteristic, complemented
5C29×#2023C211yesmaximal, characteristic, complemented
6C29×#1999C211yesmaximal, characteristic
7C29×#1990C211yesmaximal, characteristic, complemented
8C29×#1970C211yesmaximal, characteristic, complemented
9C29×#1936C211yesmaximal, characteristic, complemented
10C29×#1921C211yesmaximal, characteristic, complemented
11C29×#1895C211yesmaximal, characteristic, complemented
12C29×#1895C211yesmaximal, characteristic, complemented
13C29×#1879C211yesmaximal, characteristic, complemented
14C29×#1762C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C22×D8×C29C2211yescharacteristic
17C22×M16×C29C2211yescharacteristic
18C2×C29×C4⋊Q8C2211yescharacteristic
19C2×C29×#124—21no—
20C2×C29×#123—21no—
21C2×C29×#121C2211yescharacteristic
22C2×C29×#121C2211yescharacteristic
23C2×C4×D4×C29C2211yescharacteristic
24C2×C29×#107C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×C22⋊C8C2211yescharacteristic
32C2×C29×#97C2211yescharacteristic
33C2×C4×C8×C29C2211yescharacteristic
34C29×#397—21no—
35C29×#394—21no—
36C29×#394—21no—
37C29×#393—21no—
38C29×#390C2211yescharacteristic
39C29×#390C2211yescharacteristic
40C29×#390C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#388—21no—
43C29×#385—21no—
44C29×#384C2211yescharacteristic
45C29×#380C2211yescharacteristic
46C29×#380C2211yescharacteristic
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C22⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29—21no—
60C22×D4×C29—21no—
61C22×D4×C29—21no—
62C22×D4×C29C2311yescharacteristic
63C22×D4×C29C2311yescharacteristic
64C23×C4×C29—21no—
65C23×C4×C29C2311yescharacteristic
66C2×D8×C29—22no—
67C2×D8×C29—22no—
68C2×D8×C29—41no—
69C2×M16×C29—22no—
70C2×M16×C29—41no—
71C2×M16×C29—41no—
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C22×C8×C29C2311yescharacteristic
76C29×C4⋊Q8—22no—
77C29×C4⋊Q8—41no—
78C29×#124—44no—
79C29×#123—44no—
80C29×#121—22no—
81C29×#121—22no—
82C29×#121—41no—
83C29×#121—41no—
84C4×D4×C29—22no—
85C4×D4×C29—41no—
86C2×C4⋊C4×C29—21no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
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×C29—21no—
102C2×C22⋊C4×C29—21no—
103C2×C22⋊C4×C29—21no—
104C2×C22⋊C4×C29—21no—
105C2×C22⋊C4×C29—21no—
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29D411yescharacteristic
108C2×C22⋊C4×C29D411yescharacteristic
109C2×C42×C29—21no—
110C2×C42×C29C2311yescharacteristic
111C2×C42×C29C2311yescharacteristic
112C29×#107—22no—
113C29×#102—22no—
114C29×#102—22no—
115C29×#102—22no—
116C29×#102—41no—
117C29×#102—41no—
118C29×#102—41no—
119C29×C22⋊C8—22no—
120C29×#97—41no—
121C4×C8×C29—41no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95—21no—
126C29×#95D411yescharacteristic
127C29×#95D411yescharacteristic
128C24×C29—21no—
129C24×C29—21no—
130C24×C29C2×D411yescharacteristic
131C2×Q8×C29—42no—
132C2×Q8×C29—42no—
133C2×Q8×C29—81no—
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—21no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29—21no—
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#4112yes—
152C22×C4×C29—21no—
153C22×C4×C29—21no—
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—42no—
165C22×C4×C29—42no—
166C22×C4×C29—81no—
167C22×C4×C29C2×D411yescharacteristic
168C22×C4×C29C2×D411yescharacteristic
169C22×C4×C29C2×D411yescharacteristic
170C22×C4×C29C2×D411yescharacteristic
171C22×C4×C29C2×D411yescharacteristic
172C22×C4×C29C2411yescharacteristic
173D8×C29—44no—
174M16×C29—44no—
175C2×C8×C29—21no—
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#4112yes—
186C2×C8×C29#4112yes—
187C4⋊C4×C29—21no—
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—42no—
199C4⋊C4×C29—42no—
200C4⋊C4×C29—42no—
201C4⋊C4×C29—81no—
202C4⋊C4×C29#4112yes—
203C22⋊C4×C29—22no—
204C22⋊C4×C29—22no—
205C22⋊C4×C29—42no—
206C22⋊C4×C29—42no—
207C22⋊C4×C29—42no—
208C22⋊C4×C29—42no—
209C22⋊C4×C29—42no—
210C22⋊C4×C29—42no—
211C22⋊C4×C29—42no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—42no—
214C22⋊C4×C29—42no—
215C22⋊C4×C29—81no—
216C42×C29—21no—
217C42×C29—21no—
218C42×C29—21no—
219C42×C29—21no—
220C42×C29—42no—
221#28999C2911yesmaximal, characteristic, direct product factor, Sylow
222C23×C29—21no—
223C23×C29—22no—
224C23×C29—21no—
225C23×C29—21no—
226C23×C29—21no—
227C23×C29—21no—
228C23×C29—21no—
229C23×C29—21no—
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×C29—41no—
242C23×C29—41no—
243C23×C29C22×D411yescharacteristic
244Q8×C29—84no—
245D4×C29—22no—
246D4×C29—22no—
247D4×C29—41no—
248D4×C29—41no—
249D4×C29—41no—
250D4×C29—41no—
251D4×C29—41no—
252D4×C29—41no—
253D4×C29—84no—
254D4×C29—84no—
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—21no—
262C2×C4×C29—21no—
263C2×C4×C29—21no—
264C2×C4×C29—22no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
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—41no—
290C2×C4×C29—84no—
291C2×C4×C29AGL(1,ℤ/8)12yes—
292C2×C4×C29AGL(1,ℤ/8)12yes—
293C2×C4×C29C2×#4111yescharacteristic
294C2×C4×C29C2×#4111yescharacteristic
295C2×C4×C29C2×#4111yescharacteristic
296C2×C4×C29C2×#4111yescharacteristic
297C2×C4×C29H(5,𝔽2)11yescharacteristic
298C2×C4×C29H(5,𝔽2)11yescharacteristic
299C8×C29—22no—
300C8×C29—22no—
301C8×C29—41no—
302C8×C29—41no—
303#2491C2×C2911yescharacteristic, complemented
304#2422C2×C2911yescharacteristic, complemented
305#2076C2×C2911yescharacteristic, complemented
306#2071C2×C2911yescharacteristic, complemented
307#2023C2×C2911yescharacteristic, complemented
308#1999C2×C2911yescharacteristic
309#1990C2×C2911yescharacteristic, complemented
310#1970C2×C2911yescharacteristic, complemented
311#1936C2×C2911yescharacteristic, complemented
312#1921C2×C2911yescharacteristic, complemented
313#1895C2×C2911yescharacteristic, complemented
314#1895C2×C2911yescharacteristic, complemented
315#1879C2×C2911yescharacteristic, complemented
316#1762C2×C2911yescharacteristic, complemented
317#1753C2×C2911yescharacteristic, complemented
318C22×C29—41no—
319C22×C29—42no—
320C22×C29—41no—
321C22×C29—41no—
322C22×C29—41no—
323C22×C29—41no—
324C22×C29—41no—
325C22×C29—42no—
326C22×C29—42no—
327C22×C29—41no—
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—81no—
339C22×C29#53211yescharacteristic
340C22×C29#54611yescharacteristic
341C22×C29#54611yescharacteristic
342C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C29#57611yescharacteristic
345C22×C29#57811yescharacteristic
346C4×C29—22no—
347C4×C29—22no—
348C4×C29—41no—
349C4×C29—42no—
350C4×C29—41no—
351C4×C29—41no—
352C4×C29—81no—
353C4×C29—81no—
354C4×C29—81no—
355C4×C29—81no—
356C4×C29—81no—
357C4×C29#52911yescharacteristic
358C4×C29#53811yescharacteristic
359C4×C29#55111yescharacteristic
360C4×C29#55911yescharacteristic
361C22×D8C22×C2911yescharacteristic
362C22×M16C22×C2911yescharacteristic
363C2×C4⋊Q8C22×C2911yescharacteristic
364C2×#124—21no—
365C2×#123—21no—
366C2×#121C22×C2911yescharacteristic
367C2×#121C22×C2911yescharacteristic
368C2×C4×D4C22×C2911yescharacteristic
369C2×#107C22×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#397—21no—
380#394—21no—
381#394—21no—
382#393—21no—
383#390C22×C2911yescharacteristic
384#390C22×C2911yescharacteristic
385#390C22×C2911yescharacteristic
386#389C22×C2911yescharacteristic
387#388—21no—
388#385—21no—
389#384C22×C2911yescharacteristic
390#380C22×C2911yescharacteristic
391#380C22×C2911yescharacteristic
392C4×C4⋊C4C22×C2911yescharacteristic
393C4×C22⋊C4C22×C2911yescharacteristic
394#340C22×C2911yescharacteristic
395#340C22×C2911yescharacteristic
396#340C22×C2911yescharacteristic
397#340C22×C2911yescharacteristic
398#340C22×C2911yescharacteristic
399#340C22×C2911yescharacteristic
400#340C22×C2911yescharacteristic
401#340C22×C2911yescharacteristic
402#336C22×C2911yescharacteristic
403#336C22×C2911yescharacteristic
404C2×C29—81no—
405C2×C29—82no—
406C2×C29—161no—
407C2×C29#255711yescharacteristic
408C2×C29#317511yescharacteristic
409C2×C29#318411yescharacteristic
410C2×C29#330811yescharacteristic
411C2×C29#331811yescharacteristic
412C2×C29#332511yescharacteristic
413C2×C29#333011yescharacteristic
414C22×Q8—21no—
415C22×D4—21no—
416C22×D4—21no—
417C22×D4C23×C2911yescharacteristic
418C22×D4C23×C2911yescharacteristic
419C23×C4—21no—
420C23×C4C23×C2911yescharacteristic
421C2×D8—22no—
422C2×D8—22no—
423C2×D8—41no—
424C2×M16—22no—
425C2×M16—41no—
426C2×M16—41no—
427C22×C8C23×C2911yescharacteristic
428C22×C8C23×C2911yescharacteristic
429C22×C8C23×C2911yescharacteristic
430C22×C8C23×C2911yescharacteristic
431C4⋊Q8—22no—
432C4⋊Q8—41no—
433#124—44no—
434#123—44no—
435#121—22no—
436#121—22no—
437#121—41no—
438#121—41no—
439C4×D4—22no—
440C4×D4—41no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C2911yescharacteristic
446C2×C4⋊C4C23×C2911yescharacteristic
447C2×C4⋊C4C23×C2911yescharacteristic
448C2×C4⋊C4C23×C2911yescharacteristic
449C2×C4⋊C4C23×C2911yescharacteristic
450C2×C4⋊C4C23×C2911yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C2911yescharacteristic
463C2×C22⋊C4D4×C2911yescharacteristic
464C2×C42—21no—
465C2×C42C23×C2911yescharacteristic
466C2×C42C23×C2911yescharacteristic
467#107—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471#102—41no—
472#102—41no—
473#102—41no—
474C22⋊C8—22no—
475#97—41no—
476C4×C8—41no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95D4×C2911yescharacteristic
482#95D4×C2911yescharacteristic
483C29#2899911yescharacteristic, direct product factor, Sylow
484C24—21no—
485C24—21no—
486C24C2×D4×C2911yescharacteristic
487C2×Q8—42no—
488C2×Q8—42no—
489C2×Q8—81no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4#41×C2912yes—
508C22×C4—21no—
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—42no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4C2×D4×C2911yescharacteristic
524C22×C4C2×D4×C2911yescharacteristic
525C22×C4C2×D4×C2911yescharacteristic
526C22×C4C2×D4×C2911yescharacteristic
527C22×C4C2×D4×C2911yescharacteristic
528C22×C4C24×C2911yescharacteristic
529D8—44no—
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—42no—
557C4⋊C4—81no—
558C4⋊C4#41×C2912yes—
559C22⋊C4—22no—
560C22⋊C4—22no—
561C22⋊C4—42no—
562C22⋊C4—42no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—81no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—42no—
577C23—21no—
578C23—22no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C22×D4×C2911yescharacteristic
599Q8—84no—
600D4—22no—
601D4—22no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—84no—
609D4—84no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—22no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
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—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4C29×AGL(1,ℤ/8)12yes—
647C2×C4C29×AGL(1,ℤ/8)12yes—
648C2×C4C2×#41×C2911yescharacteristic
649C2×C4C2×#41×C2911yescharacteristic
650C2×C4C2×#41×C2911yescharacteristic
651C2×C4C2×#41×C2911yescharacteristic
652C2×C4C29×H(5,𝔽2)11yescharacteristic
653C2×C4C29×H(5,𝔽2)11yescharacteristic
654C8—22no—
655C8—22no—
656C8—41no—
657C8—41no—
658C22—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—42no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—41no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C29×#53211yescharacteristic
680C22C29×#54611yescharacteristic
681C22C29×#54611yescharacteristic
682C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
683C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
684C22C29×#57611yescharacteristic
685C22C29×#57811yescharacteristic
686C4—22no—
687C4—22no—
688C4—42no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C29×#52911yescharacteristic
698C4C29×#53811yescharacteristic
699C4C29×#55111yescharacteristic
700C4C29×#55911yescharacteristic
701C2—81no—
702C2—82no—
703C2—161no—
704C2C29×#255711yescharacteristic
705C2C29×#317511yescharacteristic
706C2C29×#318411yescharacteristic
707C2C29×#330811yescharacteristic
708C2C29×#331811yescharacteristic
709C2C29×#332511yescharacteristic
710C2C29×#333011yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#1999C2
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×#2491C2semidirect
2. C29×#2422C2semidirect
3. C29×#2076C2semidirect
4. C29×#2071C2semidirect
5. C29×#2023C2semidirect
7. C29×#1990C2semidirect
8. C29×#1970C2semidirect
9. C29×#1936C2semidirect
10. C29×#1921C2semidirect
11. C29×#1895C2semidirect
12. C29×#1895C2semidirect
13. C29×#1879C2semidirect
14. C29×#1762C2semidirect
15. C29×#1753C2semidirect
221. #28999C29direct (N × H)
303. #2491C2×C29semidirect
304. #2422C2×C29semidirect
305. #2076C2×C29semidirect
306. #2071C2×C29semidirect
307. #2023C2×C29semidirect
309. #1990C2×C29semidirect
310. #1970C2×C29semidirect
311. #1936C2×C29semidirect
312. #1921C2×C29semidirect
313. #1895C2×C29semidirect
314. #1895C2×C29semidirect
315. #1879C2×C29semidirect
316. #1762C2×C29semidirect
317. #1753C2×C29semidirect
483. C29#28999direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#24912
C29×#24222
C29×#20762
C29×#20712
C29×#20232
C29×#19992
C29×#19902
C29×#19702
C29×#19362
C29×#19212
C29×#18952
C29×#18792
C29×#17622
C29×#17532
#2899929