Finite Group Databasebeta

← C29×#24640 #20319540

Subgroups — C29×#24640 #20319540

Order 7424.

918 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
1C2×C29×#463C211yesmaximal, characteristic
2C2×C29×#440C211yesmaximal, characteristic, complemented
3C29×#2545C211yesmaximal, characteristic, complemented
4C29×#2354C211yesmaximal, characteristic, complemented
5C29×#2055C211yesmaximal, characteristic, complemented
6C29×#2054C211yesmaximal, characteristic
7C29×#2013C211yesmaximal, characteristic, complemented
8C29×#2012C211yesmaximal, characteristic
9C29×#1983C211yesmaximal, characteristic, complemented
10C29×#1981C211yesmaximal, characteristic, complemented
11C29×#1959C211yesmaximal, characteristic, complemented
12C29×#1940C211yesmaximal, characteristic, complemented
13C29×#1928C211yesmaximal, characteristic, complemented
14C29×#1925C211yesmaximal, characteristic, complemented
15C29×#1803C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×D8×C29C2211yescharacteristic
19C2×C29×C4⋊Q8C2211yescharacteristic
20C2×C29×#124C2211yescharacteristic
21C2×C29×#124C2211yescharacteristic
22C2×C4×Q8×C29C2211yescharacteristic
23C2×C4×D4×C29C2211yescharacteristic
24C2×C29×#117—21no—
25C29×#463—24no—
26C29×#440—24no—
27C2×C29×#107C2211yescharacteristic
28C2×C29×C4⋊C8C2211yescharacteristic
29C2×C29×C4⋊C8C2211yescharacteristic
30C2×C29×C4⋊C8C2211yescharacteristic
31C2×C29×#103C2211yescharacteristic
32C2×C29×#103C2211yescharacteristic
33C2×C29×#103C2211yescharacteristic
34C2×C29×#103C2211yescharacteristic
35C2×C29×#103C2211yescharacteristic
36C2×C29×#103C2211yescharacteristic
37C2×C29×#102C2211yescharacteristic
38C2×C29×#102C2211yescharacteristic
39C2×C29×#102C2211yescharacteristic
40C2×C29×#102C2211yescharacteristic
41C2×C29×#97C2211yescharacteristic
42C29×#396—21no—
43C29×#396—21no—
44C29×#391C2211yescharacteristic
45C29×#390C2211yescharacteristic
46C29×#390C2211yescharacteristic
47C29×#390C2211yescharacteristic
48C29×#388—21no—
49C29×#388—21no—
50C29×#388—21no—
51C29×#388—21no—
52C29×#384C2211yescharacteristic
53C29×#380—21no—
54C4×C4⋊C4×C29C2211yescharacteristic
55C4×C4⋊C4×C29C2211yescharacteristic
56C4×C4⋊C4×C29C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#340C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C29×#336C2211yescharacteristic
61C22×Q8×C29C2311yescharacteristic
62C22×Q8×C29C2311yescharacteristic
63C22×D4×C29C2311yescharacteristic
64C22×D4×C29C2311yescharacteristic
65C23×C4×C29—21no—
66C2×SD16×C29—22no—
67C2×SD16×C29—22no—
68C2×SD16×C29—22no—
69C2×SD16×C29—22no—
70C2×SD16×C29—41no—
71C2×SD16×C29—41no—
72C2×D8×C29—22no—
73C2×D8×C29—41no—
74C2×D8×C29—41no—
75C22×C8×C29C2311yescharacteristic
76C22×C8×C29C2311yescharacteristic
77C22×C8×C29C2311yescharacteristic
78C22×C8×C29C2311yescharacteristic
79C29×C4⋊Q8—22no—
80C29×C4⋊Q8—41no—
81C29×#124—22no—
82C29×#124—22no—
83C29×#124—22no—
84C29×#124—41no—
85C4×Q8×C29—22no—
86C4×Q8×C29—22no—
87C4×D4×C29—22no—
88C4×D4×C29D414yes—
89C29×#117—44no—
90C2×C4⋊C4×C29—21no—
91C2×C4⋊C4×C29—21no—
92C2×C4⋊C4×C29—21no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29—21no—
95C2×C4⋊C4×C29D411yescharacteristic
96C2×C4⋊C4×C29D411yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
99C2×C4⋊C4×C29C2311yescharacteristic
100C2×C4⋊C4×C29C2311yescharacteristic
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×C29—21no—
108C2×C22⋊C4×C29—21no—
109C2×C22⋊C4×C29—21no—
110C2×C22⋊C4×C29—21no—
111C2×C22⋊C4×C29—21no—
112C2×C42×C29—21no—
113C2×C42×C29—21no—
114C2×C42×C29—21no—
115C2×C42×C29C2311yescharacteristic
116C2×C42×C29C2311yescharacteristic
117C2×C42×C29C2311yescharacteristic
118C29×#107—22no—
119C29×C4⋊C8—22no—
120C29×C4⋊C8—41no—
121C29×C4⋊C8—41no—
122C29×#103—22no—
123C29×#103—22no—
124C29×#103—22no—
125C29×#103—41no—
126C29×#103—41no—
127C29×#103—41no—
128C29×#102—22no—
129C29×#102—22no—
130C29×#102—22no—
131C29×#102—41no—
132C29×#97—22no—
133C29×#95—21no—
134C29×#95—21no—
135C29×#95—21no—
136C29×#95—21no—
137C29×#95D411yescharacteristic
138C29×#95D411yescharacteristic
139C24×C29—21no—
140C24×C29—21no—
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#4112yes—
153C2×D4×C29—21no—
154C2×D4×C29—21no—
155C2×D4×C29—21no—
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—21no—
163C2×D4×C29—21no—
164C2×D4×C29C2×D412yes—
165C22×C4×C29—21no—
166C22×C4×C29—21no—
167C22×C4×C29—24no—
168C22×C4×C29—21no—
169C22×C4×C29—21no—
170C22×C4×C29—21no—
171C22×C4×C29—21no—
172C22×C4×C29—42no—
173C22×C4×C29—42no—
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2×D411yescharacteristic
177C22×C4×C29C2×D411yescharacteristic
178C22×C4×C29C2×D411yescharacteristic
179C22×C4×C29C2×D411yescharacteristic
180C22×C4×C29C2411yescharacteristic
181SD16×C29—28no—
182SD16×C29—44no—
183D8×C29—44no—
184C2×C8×C29—21no—
185C2×C8×C29—21no—
186C2×C8×C29—21no—
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#4112yes—
196C4⋊C4×C29—22no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—21no—
203C4⋊C4×C29—21no—
204C4⋊C4×C29—41no—
205C4⋊C4×C29—42no—
206C4⋊C4×C29—42no—
207C4⋊C4×C29—42no—
208C4⋊C4×C29—42no—
209C4⋊C4×C29—81no—
210C4⋊C4×C29C2×D412yes—
211C22⋊C4×C29—24no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—42no—
214C22⋊C4×C29—42no—
215C22⋊C4×C29—42no—
216C22⋊C4×C29—42no—
217C22⋊C4×C29—42no—
218C22⋊C4×C29—42no—
219C22⋊C4×C29—42no—
220C22⋊C4×C29—81no—
221C22⋊C4×C29—81no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—21no—
226C42×C29—42no—
227C42×C29—42no—
228C42×C29—42no—
229C42×C29C2×D412yes—
230C42×C29#4112yes—
231#24640C2911yesmaximal, characteristic, direct product factor, Sylow
232C23×C29—22no—
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×C29—41no—
244C23×C29—41no—
245C23×C29—41no—
246C23×C29C22×D411yescharacteristic
247Q8×C29—22no—
248Q8×C29—22no—
249Q8×C29—41no—
250Q8×C29—41no—
251Q8×C29—41no—
252Q8×C29—41no—
253Q8×C29—41no—
254Q8×C29—41no—
255D4×C29—22no—
256D4×C29—22no—
257D4×C29—41no—
258D4×C29—41no—
259D4×C29—41no—
260D4×C29—41no—
261D4×C29—41no—
262D4×C29—41no—
263C2×C4×C29—21no—
264C2×C4×C29—21no—
265C2×C4×C29—21no—
266C2×C4×C29—21no—
267C2×C4×C29—21no—
268C2×C4×C29—21no—
269C2×C4×C29—22no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—21no—
273C2×C4×C29—22no—
274C2×C4×C29—21no—
275C2×C4×C29—21no—
276C2×C4×C29—21no—
277C2×C4×C29—21no—
278C2×C4×C29—21no—
279C2×C4×C29—21no—
280C2×C4×C29—48no—
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#12112yes—
298C2×C4×C29#12112yes—
299C2×C4×C29AGL(1,ℤ/8)12yes—
300C2×C4×C29C22×D411yescharacteristic
301C2×C4×C29C2×#4111yescharacteristic
302C2×C4×C29C2×#4111yescharacteristic
303C2×C4×C29C2×#4111yescharacteristic
304C2×C4×C29H(5,𝔽2)11yescharacteristic
305C2×C4×C29H(5,𝔽2)11yescharacteristic
306C8×C29—22no—
307C8×C29—41no—
308C8×C29—41no—
309C8×C29—41no—
310C2×#463C2×C2911yescharacteristic
311C2×#440C2×C2911yescharacteristic, complemented
312#2545C2×C2911yescharacteristic, complemented
313#2354C2×C2911yescharacteristic, complemented
314#2055C2×C2911yescharacteristic, complemented
315#2054C2×C2911yescharacteristic
316#2013C2×C2911yescharacteristic, complemented
317#2012C2×C2911yescharacteristic
318#1983C2×C2911yescharacteristic, complemented
319#1981C2×C2911yescharacteristic, complemented
320#1959C2×C2911yescharacteristic, complemented
321#1940C2×C2911yescharacteristic, complemented
322#1928C2×C2911yescharacteristic, complemented
323#1925C2×C2911yescharacteristic, complemented
324#1803C2×C2911yescharacteristic, complemented
325C22×C29—42no—
326C22×C29—42no—
327C22×C29—42no—
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×C29C2×#12111yescharacteristic
340C22×C29#54611yescharacteristic
341C22×C29#55011yescharacteristic
342C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
343C22×C29#57511yescharacteristic
344C22×C29#57711yescharacteristic
345C22×C29#57811yescharacteristic
346C4×C29—22no—
347C4×C29—22no—
348C4×C29—22no—
349C4×C29—42no—
350C4×C29—42no—
351C4×C29—41no—
352C4×C29—41no—
353C4×C29—41no—
354C4×C29—81no—
355C4×C29—81no—
356C4×C29—81no—
357C4×C29—81no—
358C4×C29#52511yescharacteristic
359C4×C29#53511yescharacteristic
360C4×C29#55311yescharacteristic
361C4×C29#55511yescharacteristic
362C22×SD16C22×C2911yescharacteristic
363C22×SD16C22×C2911yescharacteristic
364C22×D8C22×C2911yescharacteristic
365C2×C4⋊Q8C22×C2911yescharacteristic
366C2×#124C22×C2911yescharacteristic
367C2×#124C22×C2911yescharacteristic
368C2×C4×Q8C22×C2911yescharacteristic
369C2×C4×D4C22×C2911yescharacteristic
370C2×#117—21no—
371#463—24no—
372#440—24no—
373C2×#107C22×C2911yescharacteristic
374C2×C4⋊C8C22×C2911yescharacteristic
375C2×C4⋊C8C22×C2911yescharacteristic
376C2×C4⋊C8C22×C2911yescharacteristic
377C2×#103C22×C2911yescharacteristic
378C2×#103C22×C2911yescharacteristic
379C2×#103C22×C2911yescharacteristic
380C2×#103C22×C2911yescharacteristic
381C2×#103C22×C2911yescharacteristic
382C2×#103C22×C2911yescharacteristic
383C2×#102C22×C2911yescharacteristic
384C2×#102C22×C2911yescharacteristic
385C2×#102C22×C2911yescharacteristic
386C2×#102C22×C2911yescharacteristic
387C2×#97C22×C2911yescharacteristic
388#396—21no—
389#396—21no—
390#391C22×C2911yescharacteristic
391#390C22×C2911yescharacteristic
392#390C22×C2911yescharacteristic
393#390C22×C2911yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#384C22×C2911yescharacteristic
399#380—21no—
400C4×C4⋊C4C22×C2911yescharacteristic
401C4×C4⋊C4C22×C2911yescharacteristic
402C4×C4⋊C4C22×C2911yescharacteristic
403#340C22×C2911yescharacteristic
404#340C22×C2911yescharacteristic
405#336C22×C2911yescharacteristic
406#336C22×C2911yescharacteristic
407C2×C29—82no—
408C2×C29—161no—
409C2×C29#241411yescharacteristic
410C2×C29#303611yescharacteristic
411C2×C29#304611yescharacteristic
412C2×C29#330811yescharacteristic
413C2×C29#332111yescharacteristic
414C2×C29#339711yescharacteristic
415C2×C29#340211yescharacteristic
416C22×Q8C23×C2911yescharacteristic
417C22×Q8C23×C2911yescharacteristic
418C22×D4C23×C2911yescharacteristic
419C22×D4C23×C2911yescharacteristic
420C23×C4—21no—
421C2×SD16—22no—
422C2×SD16—22no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—41no—
426C2×SD16—41no—
427C2×D8—22no—
428C2×D8—41no—
429C2×D8—41no—
430C22×C8C23×C2911yescharacteristic
431C22×C8C23×C2911yescharacteristic
432C22×C8C23×C2911yescharacteristic
433C22×C8C23×C2911yescharacteristic
434C4⋊Q8—22no—
435C4⋊Q8—41no—
436#124—22no—
437#124—22no—
438#124—22no—
439#124—41no—
440C4×Q8—22no—
441C4×Q8—22no—
442C4×D4—22no—
443C4×D4D4×C2914yes—
444#117—44no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4D4×C2911yescharacteristic
451C2×C4⋊C4D4×C2911yescharacteristic
452C2×C4⋊C4C23×C2911yescharacteristic
453C2×C4⋊C4C23×C2911yescharacteristic
454C2×C4⋊C4C23×C2911yescharacteristic
455C2×C4⋊C4C23×C2911yescharacteristic
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⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42C23×C2911yescharacteristic
471C2×C42C23×C2911yescharacteristic
472C2×C42C23×C2911yescharacteristic
473#107—22no—
474C4⋊C8—22no—
475C4⋊C8—41no—
476C4⋊C8—41no—
477#103—22no—
478#103—22no—
479#103—22no—
480#103—41no—
481#103—41no—
482#103—41no—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—41no—
487#97—22no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95D4×C2911yescharacteristic
493#95D4×C2911yescharacteristic
494C29#2464011yescharacteristic, direct product factor, Sylow
495C24—21no—
496C24—21no—
497C2×Q8—21no—
498C2×Q8—21no—
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#41×C2912yes—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4C2×D4×C2912yes—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—24no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4C2×D4×C2911yescharacteristic
531C22×C4C2×D4×C2911yescharacteristic
532C22×C4C2×D4×C2911yescharacteristic
533C22×C4C2×D4×C2911yescharacteristic
534C22×C4C2×D4×C2911yescharacteristic
535C22×C4C2×D4×C2911yescharacteristic
536C22×C4C24×C2911yescharacteristic
537SD16—28no—
538SD16—44no—
539D8—44no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8#41×C2912yes—
552C4⋊C4—22no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—41no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—42no—
565C4⋊C4—81no—
566C4⋊C4C2×D4×C2912yes—
567C22⋊C4—24no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C42—21no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—42no—
583C42—42no—
584C42—42no—
585C42C2×D4×C2912yes—
586C42#41×C2912yes—
587C23—22no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23C22×D4×C2911yescharacteristic
602Q8—22no—
603Q8—22no—
604Q8—41no—
605Q8—41no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610D4—22no—
611D4—22no—
612D4—41no—
613D4—41no—
614D4—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—48no—
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×C4C29×#12112yes—
653C2×C4C29×#12112yes—
654C2×C4C29×AGL(1,ℤ/8)12yes—
655C2×C4C22×D4×C2911yescharacteristic
656C2×C4C2×#41×C2911yescharacteristic
657C2×C4C2×#41×C2911yescharacteristic
658C2×C4C2×#41×C2911yescharacteristic
659C2×C4C29×H(5,𝔽2)11yescharacteristic
660C2×C4C29×H(5,𝔽2)11yescharacteristic
661C8—22no—
662C8—41no—
663C8—41no—
664C8—41no—
665C22—42no—
666C22—42no—
667C22—42no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×C29×#12111yescharacteristic
680C22C29×#54611yescharacteristic
681C22C29×#55011yescharacteristic
682C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
683C22C29×#57511yescharacteristic
684C22C29×#57711yescharacteristic
685C22C29×#57811yescharacteristic
686C4—22no—
687C4—22no—
688C4—22no—
689C4—42no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4—81no—
698C4C29×#52511yescharacteristic
699C4C29×#53511yescharacteristic
700C4C29×#55311yescharacteristic
701C4C29×#55511yescharacteristic
702C2—82no—
703C2—161no—
704C2C29×#241411yescharacteristic
705C2C29×#303611yescharacteristic
706C2C29×#304611yescharacteristic
707C2C29×#330811yescharacteristic
708C2C29×#332111yescharacteristic
709C2C29×#339711yescharacteristic
710C2C29×#340211yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D8×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#440C2semidirect
3. C29×#2545C2semidirect
4. C29×#2354C2semidirect
5. C29×#2055C2semidirect
7. C29×#2013C2semidirect
9. C29×#1983C2semidirect
10. C29×#1981C2semidirect
11. C29×#1959C2semidirect
12. C29×#1940C2semidirect
13. C29×#1928C2semidirect
14. C29×#1925C2semidirect
15. C29×#1803C2semidirect
231. #24640C29direct (N × H)
311. C2×#440C2×C29semidirect
312. #2545C2×C29semidirect
313. #2354C2×C29semidirect
314. #2055C2×C29semidirect
316. #2013C2×C29semidirect
318. #1983C2×C29semidirect
319. #1981C2×C29semidirect
320. #1959C2×C29semidirect
321. #1940C2×C29semidirect
322. #1928C2×C29semidirect
323. #1925C2×C29semidirect
324. #1803C2×C29semidirect
494. C29#24640direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4632
C2×C29×#4402
C29×#25452
C29×#23542
C29×#20552
C29×#20542
C29×#20132
C29×#20122
C29×#19832
C29×#19812
C29×#19592
C29×#19402
C29×#19282
C29×#19252
C29×#18032
#2464029