Finite Group Databasebeta

← C29×#28927 #20323827

Subgroups — C29×#28927 #20323827

Order 7424.

898 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#487C211yesmaximal, characteristic, complemented
2C2×C29×#468C211yesmaximal, characteristic
3C29×#2491C211yesmaximal, characteristic
4C29×#2429C211yesmaximal, characteristic, complemented
5C29×#2057C211yesmaximal, characteristic, complemented
6C29×#2036C211yesmaximal, characteristic, complemented
7C29×#2013C211yesmaximal, characteristic, complemented
8C29×#2000C211yesmaximal, characteristic
9C29×#1973C211yesmaximal, characteristic, complemented
10C29×#1934C211yesmaximal, characteristic, complemented
11C29×#1928C211yesmaximal, characteristic, complemented
12C29×#1894C211yesmaximal, characteristic, complemented
13C29×#1880C211yesmaximal, characteristic, complemented
14C29×#1763C211yesmaximal, characteristic, complemented
15C29×#1753C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic
19C2×C29×C4⋊Q8C2211yescharacteristic
20C2×C29×C4⋊Q8C2211yescharacteristic
21C2×C29×#124—21no—
22C2×C29×C22⋊Q8C2211yescharacteristic
23C2×C29×C22⋊Q8C2211yescharacteristic
24C2×C29×#121C2211yescharacteristic
25C2×C4×Q8×C29C2211yescharacteristic
26C29×#487—24no—
27C29×#468—24no—
28C2×C29×#107C2211yescharacteristic
29C2×C29×#107C2211yescharacteristic
30C2×C29×#103C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#103C2211yescharacteristic
35C2×C29×#103C2211yescharacteristic
36C2×C29×#102C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×C22⋊C8C2211yescharacteristic
39C2×C29×#97C2211yescharacteristic
40C2×C4×C8×C29C2211yescharacteristic
41C29×#398—21no—
42C29×#396—21no—
43C29×#394—21no—
44C29×#393—21no—
45C29×#391C2211yescharacteristic
46C29×#390C2211yescharacteristic
47C29×#390C2211yescharacteristic
48C29×#389—21no—
49C29×#389C2211yescharacteristic
50C29×#388—21no—
51C29×#388—21no—
52C29×#380C2211yescharacteristic
53C4×C4⋊C4×C29C2211yescharacteristic
54C4×C22⋊C4×C29C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×Q8×C29—21no—
62C22×Q8×C29C2311yescharacteristic
63C22×Q8×C29C2311yescharacteristic
64C22×D4×C29—21no—
65C22×D4×C29C2311yescharacteristic
66C23×C4×C29C2311yescharacteristic
67C2×SD16×C29—22no—
68C2×SD16×C29—22no—
69C2×SD16×C29—22no—
70C2×SD16×C29—41no—
71C2×SD16×C29—41no—
72C2×SD16×C29—41no—
73C2×M16×C29—22no—
74C2×M16×C29—22no—
75C2×M16×C29—41no—
76C22×C8×C29C2311yescharacteristic
77C22×C8×C29C2311yescharacteristic
78C22×C8×C29C2311yescharacteristic
79C22×C8×C29C2311yescharacteristic
80C29×C4⋊Q8—22no—
81C29×C4⋊Q8—22no—
82C29×C4⋊Q8—41no—
83C29×C4⋊Q8—41no—
84C29×#124—44no—
85C29×C22⋊Q8—22no—
86C29×C22⋊Q8—22no—
87C29×C22⋊Q8—41no—
88C29×C22⋊Q8—41no—
89C29×#121—22no—
90C29×#121—41no—
91C4×Q8×C29—22no—
92C4×Q8×C29—41no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29—21no—
95C2×C4⋊C4×C29—21no—
96C2×C4⋊C4×C29—21no—
97C2×C4⋊C4×C29—21no—
98C2×C4⋊C4×C29—21no—
99C2×C4⋊C4×C29—21no—
100C2×C4⋊C4×C29C2311yescharacteristic
101C2×C4⋊C4×C29C2311yescharacteristic
102C2×C4⋊C4×C29C2311yescharacteristic
103C2×C4⋊C4×C29C2311yescharacteristic
104C2×C4⋊C4×C29C2311yescharacteristic
105C2×C22⋊C4×C29—21no—
106C2×C22⋊C4×C29—21no—
107C2×C22⋊C4×C29—21no—
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—21no—
110C2×C22⋊C4×C29—21no—
111C2×C22⋊C4×C29—21no—
112C2×C22⋊C4×C29—21no—
113C2×C22⋊C4×C29D411yescharacteristic
114C2×C22⋊C4×C29D411yescharacteristic
115C2×C42×C29—21no—
116C2×C42×C29—21no—
117C2×C42×C29C2311yescharacteristic
118C2×C42×C29C2311yescharacteristic
119C29×#107—22no—
120C29×#107—41no—
121C29×#103—22no—
122C29×#103—22no—
123C29×#103—22no—
124C29×#103—22no—
125C29×#103—22no—
126C29×#103D414yes—
127C29×#102—22no—
128C29×#102—22no—
129C29×C22⋊C8—22no—
130C29×#97—41no—
131C4×C8×C29—22no—
132C29×#95—21no—
133C29×#95—21no—
134C29×#95—21no—
135C29×#95—21no—
136C29×#95—21no—
137C29×#95D411yescharacteristic
138C29×#95D411yescharacteristic
139C24×C29—21no—
140C24×C29C2×D411yescharacteristic
141C2×Q8×C29—21no—
142C2×Q8×C29—21no—
143C2×Q8×C29—21no—
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29—21no—
151C2×Q8×C29—21no—
152C2×Q8×C29—42no—
153C2×Q8×C29—42no—
154C2×Q8×C29—81no—
155C2×Q8×C29C2×D412yes—
156C2×D4×C29—21no—
157C2×D4×C29—21no—
158C2×D4×C29—21no—
159C2×D4×C29—21no—
160C2×D4×C29—21no—
161C2×D4×C29—21no—
162C2×D4×C29—42no—
163C2×D4×C29—42no—
164C2×D4×C29—81no—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—21no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—21no—
173C22×C4×C29—21no—
174C22×C4×C29—21no—
175C22×C4×C29—21no—
176C22×C4×C29—21no—
177C22×C4×C29—21no—
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2×D411yescharacteristic
180C22×C4×C29C2×D411yescharacteristic
181C22×C4×C29C2×D411yescharacteristic
182C22×C4×C29C2×D411yescharacteristic
183C22×C4×C29C2411yescharacteristic
184SD16×C29—44no—
185SD16×C29—44no—
186M16×C29—44no—
187C2×C8×C29—21no—
188C2×C8×C29—21no—
189C2×C8×C29—21no—
190C2×C8×C29—21no—
191C2×C8×C29—21no—
192C2×C8×C29—21no—
193C2×C8×C29—21no—
194C2×C8×C29—21no—
195C2×C8×C29—21no—
196C2×C8×C29C2×D412yes—
197C2×C8×C29#4112yes—
198C2×C8×C29#4112yes—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—21no—
205C4⋊C4×C29—21no—
206C4⋊C4×C29—21no—
207C4⋊C4×C29—42no—
208C4⋊C4×C29—42no—
209C4⋊C4×C29—42no—
210C4⋊C4×C29—42no—
211C4⋊C4×C29—42no—
212C4⋊C4×C29—42no—
213C4⋊C4×C29—42no—
214C4⋊C4×C29C2×D412yes—
215C4⋊C4×C29#4112yes—
216C22⋊C4×C29—22no—
217C22⋊C4×C29—22no—
218C22⋊C4×C29—42no—
219C22⋊C4×C29—42no—
220C22⋊C4×C29—42no—
221C22⋊C4×C29—42no—
222C22⋊C4×C29—42no—
223C22⋊C4×C29—42no—
224C22⋊C4×C29—42no—
225C22⋊C4×C29—81no—
226C42×C29—21no—
227C42×C29—21no—
228C42×C29—21no—
229C42×C29—21no—
230C42×C29—42no—
231C42×C29—42no—
232#28927C2911yesmaximal, characteristic, direct product factor, Sylow
233C23×C29—21no—
234C23×C29—21no—
235C23×C29—21no—
236C23×C29—21no—
237C23×C29—21no—
238C23×C29—21no—
239C23×C29—21no—
240C23×C29—41no—
241C23×C29—41no—
242C23×C29—41no—
243C23×C29—41no—
244C23×C29—41no—
245C23×C29—41no—
246C23×C29—41no—
247C23×C29C22×D411yescharacteristic
248Q8×C29—22no—
249Q8×C29—22no—
250Q8×C29—41no—
251Q8×C29—41no—
252Q8×C29—41no—
253Q8×C29—41no—
254Q8×C29—41no—
255Q8×C29—41no—
256Q8×C29—84no—
257D4×C29—41no—
258D4×C29—41no—
259D4×C29—41no—
260D4×C29—41no—
261D4×C29—84no—
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—22no—
269C2×C4×C29—22no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—22no—
273C2×C4×C29—21no—
274C2×C4×C29—21no—
275C2×C4×C29—21no—
276C2×C4×C29—21no—
277C2×C4×C29—21no—
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—41no—
291C2×C4×C29—41no—
292C2×C4×C29—41no—
293C2×C4×C29—41no—
294C2×C4×C29—41no—
295C2×C4×C29—41no—
296C2×C4×C29—41no—
297C2×C4×C29—41no—
298C2×C4×C29—41no—
299C2×C4×C29—41no—
300C2×C4×C29AGL(1,ℤ/8)12yes—
301C2×C4×C29#13712yes—
302C2×C4×C29C22×D411yescharacteristic
303C2×C4×C29C2×#4111yescharacteristic
304C2×C4×C29C2×#4111yescharacteristic
305C2×C4×C29C2×#4111yescharacteristic
306C2×C4×C29H(5,𝔽2)11yescharacteristic
307C2×C4×C29H(5,𝔽2)11yescharacteristic
308C8×C29—22no—
309C8×C29—22no—
310C8×C29—22no—
311C8×C29—41no—
312C2×#487C2×C2911yescharacteristic, complemented
313C2×#468C2×C2911yescharacteristic
314#2491C2×C2911yescharacteristic
315#2429C2×C2911yescharacteristic, complemented
316#2057C2×C2911yescharacteristic, complemented
317#2036C2×C2911yescharacteristic, complemented
318#2013C2×C2911yescharacteristic, complemented
319#2000C2×C2911yescharacteristic
320#1973C2×C2911yescharacteristic, complemented
321#1934C2×C2911yescharacteristic, complemented
322#1928C2×C2911yescharacteristic, complemented
323#1894C2×C2911yescharacteristic, complemented
324#1880C2×C2911yescharacteristic, complemented
325#1763C2×C2911yescharacteristic, complemented
326#1753C2×C2911yescharacteristic, complemented
327C22×C29—41no—
328C22×C29—41no—
329C22×C29—41no—
330C22×C29—41no—
331C22×C29—41no—
332C22×C29—41no—
333C22×C29—41no—
334C22×C29—81no—
335C22×C29—81no—
336C22×C29—81no—
337C22×C29—81no—
338C22×C29—81no—
339C22×C29—81no—
340C22×C29—81no—
341C22×C29#53211yescharacteristic
342C22×C29D4211yescharacteristic
343C22×C29#54611yescharacteristic
344C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C29C2×#13711yescharacteristic
346C22×C29#57711yescharacteristic
347C22×C29#57811yescharacteristic
348C4×C29—22no—
349C4×C29—22no—
350C4×C29—41no—
351C4×C29—41no—
352C4×C29—42no—
353C4×C29—42no—
354C4×C29—41no—
355C4×C29—42no—
356C4×C29—81no—
357C4×C29—81no—
358C4×C29—81no—
359C4×C29—81no—
360C4×C29#53211yescharacteristic
361C4×C29#53811yescharacteristic
362C4×C29#54611yescharacteristic
363C4×C29#55511yescharacteristic
364C22×SD16C22×C2911yescharacteristic
365C22×SD16C22×C2911yescharacteristic
366C22×M16C22×C2911yescharacteristic
367C2×C4⋊Q8C22×C2911yescharacteristic
368C2×C4⋊Q8C22×C2911yescharacteristic
369C2×#124—21no—
370C2×C22⋊Q8C22×C2911yescharacteristic
371C2×C22⋊Q8C22×C2911yescharacteristic
372C2×#121C22×C2911yescharacteristic
373C2×C4×Q8C22×C2911yescharacteristic
374#487—24no—
375#468—24no—
376C2×#107C22×C2911yescharacteristic
377C2×#107C22×C2911yescharacteristic
378C2×#103C22×C2911yescharacteristic
379C2×#103C22×C2911yescharacteristic
380C2×#103C22×C2911yescharacteristic
381C2×#103C22×C2911yescharacteristic
382C2×#103C22×C2911yescharacteristic
383C2×#103C22×C2911yescharacteristic
384C2×#102C22×C2911yescharacteristic
385C2×#102C22×C2911yescharacteristic
386C2×C22⋊C8C22×C2911yescharacteristic
387C2×#97C22×C2911yescharacteristic
388C2×C4×C8C22×C2911yescharacteristic
389#398—21no—
390#396—21no—
391#394—21no—
392#393—21no—
393#391C22×C2911yescharacteristic
394#390C22×C2911yescharacteristic
395#390C22×C2911yescharacteristic
396#389—21no—
397#389C22×C2911yescharacteristic
398#388—21no—
399#388—21no—
400#380C22×C2911yescharacteristic
401C4×C4⋊C4C22×C2911yescharacteristic
402C4×C22⋊C4C22×C2911yescharacteristic
403#340C22×C2911yescharacteristic
404#340C22×C2911yescharacteristic
405#340C22×C2911yescharacteristic
406#340C22×C2911yescharacteristic
407#336C22×C2911yescharacteristic
408#336C22×C2911yescharacteristic
409C2×C29—81no—
410C2×C29—161no—
411C2×C29#255511yescharacteristic
412C2×C29#317811yescharacteristic
413C2×C29#318211yescharacteristic
414C2×C29#326511yescharacteristic
415C2×C29#327011yescharacteristic
416C2×C29#332911yescharacteristic
417C2×C29#333011yescharacteristic
418C22×Q8—21no—
419C22×Q8C23×C2911yescharacteristic
420C22×Q8C23×C2911yescharacteristic
421C22×D4—21no—
422C22×D4C23×C2911yescharacteristic
423C23×C4C23×C2911yescharacteristic
424C2×SD16—22no—
425C2×SD16—22no—
426C2×SD16—22no—
427C2×SD16—41no—
428C2×SD16—41no—
429C2×SD16—41no—
430C2×M16—22no—
431C2×M16—22no—
432C2×M16—41no—
433C22×C8C23×C2911yescharacteristic
434C22×C8C23×C2911yescharacteristic
435C22×C8C23×C2911yescharacteristic
436C22×C8C23×C2911yescharacteristic
437C4⋊Q8—22no—
438C4⋊Q8—22no—
439C4⋊Q8—41no—
440C4⋊Q8—41no—
441#124—44no—
442C22⋊Q8—22no—
443C22⋊Q8—22no—
444C22⋊Q8—41no—
445C22⋊Q8—41no—
446#121—22no—
447#121—41no—
448C4×Q8—22no—
449C4×Q8—41no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—21no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4C23×C2911yescharacteristic
458C2×C4⋊C4C23×C2911yescharacteristic
459C2×C4⋊C4C23×C2911yescharacteristic
460C2×C4⋊C4C23×C2911yescharacteristic
461C2×C4⋊C4C23×C2911yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4D4×C2911yescharacteristic
471C2×C22⋊C4D4×C2911yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42C23×C2911yescharacteristic
475C2×C42C23×C2911yescharacteristic
476#107—22no—
477#107—41no—
478#103—22no—
479#103—22no—
480#103—22no—
481#103—22no—
482#103—22no—
483#103D4×C2914yes—
484#102—22no—
485#102—22no—
486C22⋊C8—22no—
487#97—41no—
488C4×C8—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95D4×C2911yescharacteristic
495#95D4×C2911yescharacteristic
496C29#2892711yescharacteristic, direct product factor, Sylow
497C24—21no—
498C24C2×D4×C2911yescharacteristic
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—42no—
511C2×Q8—42no—
512C2×Q8—81no—
513C2×Q8C2×D4×C2912yes—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—42no—
521C2×D4—42no—
522C2×D4—81no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4C2×D4×C2911yescharacteristic
537C22×C4C2×D4×C2911yescharacteristic
538C22×C4C2×D4×C2911yescharacteristic
539C22×C4C2×D4×C2911yescharacteristic
540C22×C4C2×D4×C2911yescharacteristic
541C22×C4C24×C2911yescharacteristic
542SD16—44no—
543SD16—44no—
544M16—44no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8C2×D4×C2912yes—
555C2×C8#41×C2912yes—
556C2×C8#41×C2912yes—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4C2×D4×C2912yes—
573C4⋊C4#41×C2912yes—
574C22⋊C4—22no—
575C22⋊C4—22no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—81no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—42no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23C22×D4×C2911yescharacteristic
605Q8—22no—
606Q8—22no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8—41no—
613Q8—84no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—84no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
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—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4C29×AGL(1,ℤ/8)12yes—
658C2×C4C29×#13712yes—
659C2×C4C22×D4×C2911yescharacteristic
660C2×C4C2×#41×C2911yescharacteristic
661C2×C4C2×#41×C2911yescharacteristic
662C2×C4C2×#41×C2911yescharacteristic
663C2×C4C29×H(5,𝔽2)11yescharacteristic
664C2×C4C29×H(5,𝔽2)11yescharacteristic
665C8—22no—
666C8—22no—
667C8—22no—
668C8—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22C29×#53211yescharacteristic
684C22D42×C2911yescharacteristic
685C22C29×#54611yescharacteristic
686C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
687C22C2×C29×#13711yescharacteristic
688C22C29×#57711yescharacteristic
689C22C29×#57811yescharacteristic
690C4—22no—
691C4—22no—
692C4—42no—
693C4—41no—
694C4—42no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—81no—
699C4—81no—
700C4—81no—
701C4—81no—
702C4C29×#53211yescharacteristic
703C4C29×#53811yescharacteristic
704C4C29×#54611yescharacteristic
705C4C29×#55511yescharacteristic
706C2—81no—
707C2—161no—
708C2C29×#255511yescharacteristic
709C2C29×#317811yescharacteristic
710C2C29×#318211yescharacteristic
711C2C29×#326511yescharacteristic
712C2C29×#327011yescharacteristic
713C2C29×#332911yescharacteristic
714C2C29×#333011yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
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. C2×C29×#487C2semidirect
4. C29×#2429C2semidirect
5. C29×#2057C2semidirect
6. C29×#2036C2semidirect
7. C29×#2013C2semidirect
9. C29×#1973C2semidirect
10. C29×#1934C2semidirect
11. C29×#1928C2semidirect
12. C29×#1894C2semidirect
13. C29×#1880C2semidirect
14. C29×#1763C2semidirect
15. C29×#1753C2semidirect
232. #28927C29direct (N × H)
312. C2×#487C2×C29semidirect
315. #2429C2×C29semidirect
316. #2057C2×C29semidirect
317. #2036C2×C29semidirect
318. #2013C2×C29semidirect
320. #1973C2×C29semidirect
321. #1934C2×C29semidirect
322. #1928C2×C29semidirect
323. #1894C2×C29semidirect
324. #1880C2×C29semidirect
325. #1763C2×C29semidirect
326. #1753C2×C29semidirect
496. C29#28927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4872
C2×C29×#4682
C29×#24912
C29×#24292
C29×#20572
C29×#20362
C29×#20132
C29×#20002
C29×#19732
C29×#19342
C29×#19282
C29×#18942
C29×#18802
C29×#17632
C29×#17532
#2892729