Finite Group Databasebeta

← C29×#22051 #20316951

Subgroups — C29×#22051 #20316951

Order 7424.

1084 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#449C211yesmaximal, characteristic
2C4×C29×#121C211yesmaximal, characteristic, complemented
3C29×#2297C211yesmaximal, characteristic, complemented
4C29×#1973C211yesmaximal, characteristic, complemented
5C29×#1972C211yesmaximal, characteristic, complemented
6C29×#1936C211yesmaximal, characteristic, complemented
7C29×#1935C211yesmaximal, characteristic, complemented
8C29×#1927C211yesmaximal, characteristic, complemented
9C29×#1925C211yesmaximal, characteristic, complemented
10C29×#1879C211yesmaximal, characteristic, complemented
11C29×#1877C211yesmaximal, characteristic, complemented
12C29×#1875C211yesmaximal, characteristic, complemented
13C29×#1854C211yesmaximal, characteristic, complemented
14C29×#1788C211yesmaximal, characteristic, complemented
15C29×#1749C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C22×SD16×C29C2211yescharacteristic
18C22×D8×C29C2211yescharacteristic
19C2×C29×#121C2211yescharacteristic
20C2×C4×D4×C29—21no—
21C2×C4×D4×C29C2211yescharacteristic
22C2×C29×#117C2211yescharacteristic
23C22×C42×C29C2211yescharacteristic
24C29×#449C418yescomplemented
25C2×C29×#107C2211yescharacteristic
26C2×C29×#106C2211yescharacteristic
27C2×C29×#103C2211yescharacteristic
28C2×C29×#103C2211yescharacteristic
29C2×C29×#103C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#102C2211yescharacteristic
32C2×C29×#102C2211yescharacteristic
33C2×C29×#102C2211yescharacteristic
34C2×C29×#102C2211yescharacteristic
35C2×C29×C22⋊C8C2211yescharacteristic
36C2×C29×C22⋊C8C2211yescharacteristic
37C2×C29×#97C2211yescharacteristic
38C2×C29×#97C2211yescharacteristic
39C29×#391C2211yescharacteristic
40C29×#391C2211yescharacteristic
41C29×#390C2211yescharacteristic
42C29×#390C2211yescharacteristic
43C29×#390C2211yescharacteristic
44C29×#389C2211yescharacteristic
45C29×#388—21no—
46C29×#386—21no—
47C29×#386—21no—
48C29×#386—21no—
49C29×#380C2211yescharacteristic
50C4×C4⋊C4×C29C2211yescharacteristic
51C4×C22⋊C4×C29—21no—
52C4×C22⋊C4×C29—21no—
53C4×C22⋊C4×C29—21no—
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#340C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C29×#336C2211yescharacteristic
60C2×#41×C29—22no—
61C2×#41×C29—41no—
62C2×#41×C29—41no—
63C2×#41×C29—41no—
64C2×#41×C29—41no—
65C2×#41×C29C2×C414yescomplemented
66C22×Q8×C29C2311yescharacteristic
67C22×D4×C29—21no—
68C22×D4×C29—21no—
69C22×D4×C29C2311yescharacteristic
70C22×D4×C29C2311yescharacteristic
71C23×C4×C29—21no—
72C23×C4×C29—21no—
73C23×C4×C29D411yescharacteristic
74C23×C4×C29D411yescharacteristic
75C23×C4×C29C2311yescharacteristic
76C2×SD16×C29—41no—
77C2×SD16×C29—41no—
78C2×SD16×C29C2×C414yescomplemented
79C2×D8×C29—41no—
80C2×D8×C29—41no—
81C2×D8×C29C2×C414yescomplemented
82C22×C8×C29C2311yescharacteristic
83C22×C8×C29C2311yescharacteristic
84C22×C8×C29C2311yescharacteristic
85C22×C8×C29C2311yescharacteristic
86C29×#121—22no—
87C29×#121C2×C414yes—
88C4×D4×C29—41no—
89C4×D4×C29—41no—
90C4×D4×C29—44no—
91C29×#117—41no—
92C29×#117—41no—
93C2×C4⋊C4×C29—21no—
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C4⋊C4×C29C2311yescharacteristic
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×C29—21no—
108C2×C22⋊C4×C29—21no—
109C2×C42×C29—21no—
110C2×C42×C29—21no—
111C2×C42×C29—41no—
112C2×C42×C29—41no—
113C2×C42×C29D411yescharacteristic
114C2×C42×C29D411yescharacteristic
115C2×C42×C29C2311yescharacteristic
116C2×C42×C29C2311yescharacteristic
117C29×#107—41no—
118C29×#106—41no—
119C29×#103—41no—
120C29×#103—41no—
121C29×#103C2×C414yescomplemented
122C29×#102—41no—
123C29×#102—41no—
124C29×#102—41no—
125C29×#102—41no—
126C29×#102C2×C414yescomplemented
127C29×C22⋊C8—22no—
128C29×C22⋊C8C2×C414yescomplemented
129C29×#97—41no—
130C29×#97—41no—
131C29×#95—21no—
132C29×#95—21no—
133C29×#95—21no—
134C29×#95—21no—
135C29×#95—21no—
136C29×#95—21no—
137C29×#95—21no—
138C24×C29—21no—
139C24×C29—21no—
140C24×C29C2×D411yescharacteristic
141#41×C29—44no—
142#41×C29—44no—
143#41×C29—44no—
144#41×C29—44no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—21no—
149C2×Q8×C29—21no—
150C2×Q8×C29C22×C412yes—
151C2×D4×C29—24no—
152C2×D4×C29—24no—
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—42no—
164C2×D4×C29—42no—
165C2×D4×C29—42no—
166C2×D4×C29—42no—
167C2×D4×C29C22×C412yes—
168C2×D4×C29C22×C412yes—
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—24no—
176C22×C4×C29—22no—
177C22×C4×C29—21no—
178C22×C4×C29—21no—
179C22×C4×C29—21no—
180C22×C4×C29—21no—
181C22×C4×C29—41no—
182C22×C4×C29—41no—
183C22×C4×C29—41no—
184C22×C4×C29—41no—
185C22×C4×C29—41no—
186C22×C4×C29—42no—
187C22×C4×C29—42no—
188C22×C4×C29—42no—
189C22×C4×C29—42no—
190C22×C4×C29—42no—
191C22×C4×C29C22×C412yes—
192C22×C4×C29C2×D411yescharacteristic
193C22×C4×C29C2×D411yescharacteristic
194C22×C4×C29C2×D411yescharacteristic
195C22×C4×C29C2×D411yescharacteristic
196C22×C4×C29C2×D411yescharacteristic
197C22×C4×C29#4112yes—
198C22×C4×C29C2411yescharacteristic
199SD16×C29—44no—
200D8×C29—44no—
201C2×C8×C29—21no—
202C2×C8×C29—21no—
203C2×C8×C29—21no—
204C2×C8×C29—21no—
205C2×C8×C29—21no—
206C2×C8×C29—21no—
207C2×C8×C29—21no—
208C2×C8×C29—21no—
209C2×C8×C29—21no—
210C2×C8×C29—21no—
211C2×C8×C29C22×C412yes—
212C2×C8×C29C22×C412yes—
213C4⋊C4×C29—21no—
214C4⋊C4×C29—21no—
215C4⋊C4×C29—21no—
216C4⋊C4×C29—21no—
217C4⋊C4×C29—21no—
218C4⋊C4×C29—21no—
219C4⋊C4×C29—21no—
220C4⋊C4×C29—21no—
221C4⋊C4×C29—21no—
222C4⋊C4×C29—42no—
223C4⋊C4×C29C22×C412yes—
224C22⋊C4×C29—24no—
225C22⋊C4×C29—42no—
226C22⋊C4×C29—42no—
227C22⋊C4×C29—42no—
228C22⋊C4×C29—42no—
229C22⋊C4×C29—42no—
230C22⋊C4×C29—42no—
231C22⋊C4×C29—42no—
232C22⋊C4×C29—42no—
233C22⋊C4×C29—42no—
234C42×C29—21no—
235C42×C29—21no—
236C42×C29—21no—
237C42×C29—21no—
238C42×C29—41no—
239C42×C29—41no—
240C42×C29—42no—
241C42×C29—42no—
242#22051C2911yesmaximal, characteristic, direct product factor, Sylow
243C23×C29—21no—
244C23×C29—21no—
245C23×C29—21no—
246C23×C29—21no—
247C23×C29—21no—
248C23×C29—21no—
249C23×C29—22no—
250C23×C29—22no—
251C23×C29—41no—
252C23×C29—41no—
253C23×C29—41no—
254C23×C29—41no—
255C23×C29—41no—
256C23×C29—41no—
257C23×C29—41no—
258C23×C29—41no—
259C23×C29—41no—
260C23×C29—41no—
261C23×C29—41no—
262C23×C29—41no—
263C23×C29C4×D412yes—
264C23×C29C22×D411yescharacteristic
265Q8×C29—22no—
266Q8×C29—22no—
267Q8×C29—41no—
268Q8×C29—41no—
269D4×C29—22no—
270D4×C29—22no—
271D4×C29—22no—
272D4×C29—22no—
273D4×C29—48no—
274D4×C29—48no—
275D4×C29—41no—
276D4×C29—41no—
277D4×C29—41no—
278D4×C29—41no—
279C2×C4×C29—21no—
280C2×C4×C29—21no—
281C2×C4×C29—21no—
282C2×C4×C29—21no—
283C2×C4×C29—22no—
284C2×C4×C29—22no—
285C2×C4×C29—22no—
286C2×C4×C29—22no—
287C2×C4×C29—22no—
288C2×C4×C29—22no—
289C2×C4×C29—21no—
290C2×C4×C29—21no—
291C2×C4×C29—21no—
292C2×C4×C29—21no—
293C2×C4×C29—21no—
294C2×C4×C29—21no—
295C2×C4×C29—21no—
296C2×C4×C29—21no—
297C2×C4×C29—21no—
298C2×C4×C29—44no—
299C2×C4×C29—48no—
300C2×C4×C29—44no—
301C2×C4×C29—41no—
302C2×C4×C29—41no—
303C2×C4×C29—41no—
304C2×C4×C29—41no—
305C2×C4×C29—41no—
306C2×C4×C29—41no—
307C2×C4×C29—41no—
308C2×C4×C29—41no—
309C2×C4×C29—41no—
310C2×C4×C29—41no—
311C2×C4×C29—41no—
312C2×C4×C29—41no—
313C2×C4×C29—41no—
314C2×C4×C29—41no—
315C2×C4×C29—41no—
316C2×C4×C29—41no—
317C2×C4×C29—84no—
318C2×C4×C29C4×D412yes—
319C2×C4×C29AGL(1,ℤ/8)12yes—
320C2×C4×C29C23×C411yescharacteristic
321C2×C4×C29C2×#4111yescharacteristic
322C2×C4×C29H(5,𝔽2)11yescharacteristic
323C2×C4×C29H(5,𝔽2)11yescharacteristic
324C2×C4×C29H(5,𝔽2)11yescharacteristic
325C2×C4×C29H(5,𝔽2)11yescharacteristic
326C8×C29—22no—
327C8×C29—22no—
328C8×C29—41no—
329C8×C29—41no—
330C2×#449C2×C2911yescharacteristic
331C4×#121C2×C2911yescharacteristic, complemented
332#2297C2×C2911yescharacteristic, complemented
333#1973C2×C2911yescharacteristic, complemented
334#1972C2×C2911yescharacteristic, complemented
335#1936C2×C2911yescharacteristic, complemented
336#1935C2×C2911yescharacteristic, complemented
337#1927C2×C2911yescharacteristic, complemented
338#1925C2×C2911yescharacteristic, complemented
339#1879C2×C2911yescharacteristic, complemented
340#1877C2×C2911yescharacteristic, complemented
341#1875C2×C2911yescharacteristic, complemented
342#1854C2×C2911yescharacteristic, complemented
343#1788C2×C2911yescharacteristic, complemented
344#1749C2×C2911yescharacteristic, complemented
345C22×C29—22no—
346C22×C29—22no—
347C22×C29—22no—
348C22×C29—41no—
349C22×C29—41no—
350C22×C29—41no—
351C22×C29—41no—
352C22×C29—42no—
353C22×C29—42no—
354C22×C29—42no—
355C22×C29—42no—
356C22×C29—42no—
357C22×C29—42no—
358C22×C29—81no—
359C22×C29—81no—
360C22×C29—81no—
361C22×C29—81no—
362C22×C29—81no—
363C22×C29—81no—
364C22×C29—81no—
365C22×C29—81no—
366C22×C29C2×C4×D411yescharacteristic
367C22×C29#53411yescharacteristic
368C22×C29#53511yescharacteristic
369C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C29#57511yescharacteristic
371C22×C29#57511yescharacteristic
372C22×C29#57511yescharacteristic
373C4×C29—22no—
374C4×C29—22no—
375C4×C29—42no—
376C4×C29—41no—
377C4×C29—41no—
378C4×C29—41no—
379C4×C29—42no—
380C4×C29—81no—
381C4×C29—81no—
382C4×C29—81no—
383C4×C29—81no—
384C4×C29#51811yescharacteristic
385C4×C29#51811yescharacteristic
386C4×C29#53811yescharacteristic
387C4×C29#53811yescharacteristic
388C22×#41C22×C2911yescharacteristic
389C22×SD16C22×C2911yescharacteristic
390C22×D8C22×C2911yescharacteristic
391C2×#121C22×C2911yescharacteristic
392C2×C4×D4—21no—
393C2×C4×D4C22×C2911yescharacteristic
394C2×#117C22×C2911yescharacteristic
395C22×C42C22×C2911yescharacteristic
396#449C4×C2918yescomplemented
397C2×#107C22×C2911yescharacteristic
398C2×#106C22×C2911yescharacteristic
399C2×#103C22×C2911yescharacteristic
400C2×#103C22×C2911yescharacteristic
401C2×#103C22×C2911yescharacteristic
402C2×#102C22×C2911yescharacteristic
403C2×#102C22×C2911yescharacteristic
404C2×#102C22×C2911yescharacteristic
405C2×#102C22×C2911yescharacteristic
406C2×#102C22×C2911yescharacteristic
407C2×C22⋊C8C22×C2911yescharacteristic
408C2×C22⋊C8C22×C2911yescharacteristic
409C2×#97C22×C2911yescharacteristic
410C2×#97C22×C2911yescharacteristic
411#391C22×C2911yescharacteristic
412#391C22×C2911yescharacteristic
413#390C22×C2911yescharacteristic
414#390C22×C2911yescharacteristic
415#390C22×C2911yescharacteristic
416#389C22×C2911yescharacteristic
417#388—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#380C22×C2911yescharacteristic
422C4×C4⋊C4C22×C2911yescharacteristic
423C4×C22⋊C4—21no—
424C4×C22⋊C4—21no—
425C4×C22⋊C4—21no—
426#340C22×C2911yescharacteristic
427#340C22×C2911yescharacteristic
428#340C22×C2911yescharacteristic
429#340C22×C2911yescharacteristic
430#336C22×C2911yescharacteristic
431#336C22×C2911yescharacteristic
432C2×C29—42no—
433C2×C29—82no—
434C2×C29—82no—
435C2×C29#232111yescharacteristic
436C2×C29#294311yescharacteristic
437C2×C29C4×AGL(1,ℤ/8)11yescharacteristic
438C2×C29#319411yescharacteristic
439C2×C29#319711yescharacteristic
440C2×C29#321411yescharacteristic
441C2×C29#321911yescharacteristic
442C2×#41—22no—
443C2×#41—41no—
444C2×#41—41no—
445C2×#41—41no—
446C2×#41—41no—
447C2×#41C2×C4×C2914yescomplemented
448C22×Q8C23×C2911yescharacteristic
449C22×D4—21no—
450C22×D4—21no—
451C22×D4C23×C2911yescharacteristic
452C22×D4C23×C2911yescharacteristic
453C23×C4—21no—
454C23×C4—21no—
455C23×C4D4×C2911yescharacteristic
456C23×C4D4×C2911yescharacteristic
457C23×C4C23×C2911yescharacteristic
458C2×SD16—41no—
459C2×SD16—41no—
460C2×SD16C2×C4×C2914yescomplemented
461C2×D8—41no—
462C2×D8—41no—
463C2×D8C2×C4×C2914yescomplemented
464C22×C8C23×C2911yescharacteristic
465C22×C8C23×C2911yescharacteristic
466C22×C8C23×C2911yescharacteristic
467C22×C8C23×C2911yescharacteristic
468#121—22no—
469#121C2×C4×C2914yes—
470C4×D4—41no—
471C4×D4—41no—
472C4×D4—44no—
473#117—41no—
474#117—41no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4C23×C2911yescharacteristic
477C2×C4⋊C4C23×C2911yescharacteristic
478C2×C4⋊C4C23×C2911yescharacteristic
479C2×C4⋊C4C23×C2911yescharacteristic
480C2×C4⋊C4C23×C2911yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—41no—
494C2×C42—41no—
495C2×C42D4×C2911yescharacteristic
496C2×C42D4×C2911yescharacteristic
497C2×C42C23×C2911yescharacteristic
498C2×C42C23×C2911yescharacteristic
499#107—41no—
500#106—41no—
501#103—41no—
502#103—41no—
503#103C2×C4×C2914yescomplemented
504#102—41no—
505#102—41no—
506#102—41no—
507#102—41no—
508#102C2×C4×C2914yescomplemented
509C22⋊C8—22no—
510C22⋊C8C2×C4×C2914yescomplemented
511#97—41no—
512#97—41no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520C29#2205111yescharacteristic, direct product factor, Sylow
521C24—21no—
522C24—21no—
523C24C2×D4×C2911yescharacteristic
524#41—44no—
525#41—44no—
526#41—44no—
527#41—44no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C22×C4×C2912yes—
534C2×D4—24no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4—42no—
549C2×D4—42no—
550C2×D4C22×C4×C2912yes—
551C2×D4C22×C4×C2912yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—41no—
565C22×C4—41no—
566C22×C4—41no—
567C22×C4—41no—
568C22×C4—41no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4C22×C4×C2912yes—
575C22×C4C2×D4×C2911yescharacteristic
576C22×C4C2×D4×C2911yescharacteristic
577C22×C4C2×D4×C2911yescharacteristic
578C22×C4C2×D4×C2911yescharacteristic
579C22×C4C2×D4×C2911yescharacteristic
580C22×C4#41×C2912yes—
581C22×C4C24×C2911yescharacteristic
582SD16—44no—
583D8—44no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8C22×C4×C2912yes—
595C2×C8C22×C4×C2912yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4C22×C4×C2912yes—
607C22⋊C4—24no—
608C22⋊C4—42no—
609C22⋊C4—42no—
610C22⋊C4—42no—
611C22⋊C4—42no—
612C22⋊C4—42no—
613C22⋊C4—42no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C42—21no—
618C42—21no—
619C42—21no—
620C42—21no—
621C42—41no—
622C42—41no—
623C42—42no—
624C42—42no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—22no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23C4×D4×C2912yes—
646C23C22×D4×C2911yescharacteristic
647Q8—22no—
648Q8—22no—
649Q8—41no—
650Q8—41no—
651D4—22no—
652D4—22no—
653D4—22no—
654D4—22no—
655D4—48no—
656D4—48no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—48no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—84no—
700C2×C4C4×D4×C2912yes—
701C2×C4C29×AGL(1,ℤ/8)12yes—
702C2×C4C23×C4×C2911yescharacteristic
703C2×C4C2×#41×C2911yescharacteristic
704C2×C4C29×H(5,𝔽2)11yescharacteristic
705C2×C4C29×H(5,𝔽2)11yescharacteristic
706C2×C4C29×H(5,𝔽2)11yescharacteristic
707C2×C4C29×H(5,𝔽2)11yescharacteristic
708C8—22no—
709C8—22no—
710C8—41no—
711C8—41no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—41no—
716C22—41no—
717C22—41no—
718C22—41no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—81no—
732C22—81no—
733C22C2×C4×D4×C2911yescharacteristic
734C22C29×#53411yescharacteristic
735C22C29×#53511yescharacteristic
736C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
737C22C29×#57511yescharacteristic
738C22C29×#57511yescharacteristic
739C22C29×#57511yescharacteristic
740C4—22no—
741C4—22no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4—81no—
748C4—81no—
749C4—81no—
750C4—81no—
751C4C29×#51811yescharacteristic
752C4C29×#51811yescharacteristic
753C4C29×#53811yescharacteristic
754C4C29×#53811yescharacteristic
755C2—42no—
756C2—82no—
757C2—82no—
758C2C29×#232111yescharacteristic
759C2C29×#294311yescharacteristic
760C2C4×C29×AGL(1,ℤ/8)11yescharacteristic
761C2C29×#319411yescharacteristic
762C2C29×#319711yescharacteristic
763C2C29×#321411yescharacteristic
764C2C29×#321911yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutatorC2×C4C23×C4×C29
Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C22×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×C29×#121C2semidirect
3. C29×#2297C2semidirect
4. C29×#1973C2semidirect
5. C29×#1972C2semidirect
6. C29×#1936C2semidirect
7. C29×#1935C2semidirect
8. C29×#1927C2semidirect
9. C29×#1925C2semidirect
10. C29×#1879C2semidirect
11. C29×#1877C2semidirect
12. C29×#1875C2semidirect
13. C29×#1854C2semidirect
14. C29×#1788C2semidirect
15. C29×#1749C2semidirect
24. C29×#449C4semidirect
65. C2×#41×C29C2×C4semidirect
78. C2×SD16×C29C2×C4semidirect
81. C2×D8×C29C2×C4semidirect
121. C29×#103C2×C4semidirect
126. C29×#102C2×C4semidirect
128. C29×C22⋊C8C2×C4semidirect
242. #22051C29direct (N × H)
331. C4×#121C2×C29semidirect
332. #2297C2×C29semidirect
333. #1973C2×C29semidirect
334. #1972C2×C29semidirect
335. #1936C2×C29semidirect
336. #1935C2×C29semidirect
337. #1927C2×C29semidirect
338. #1925C2×C29semidirect
339. #1879C2×C29semidirect
340. #1877C2×C29semidirect
341. #1875C2×C29semidirect
342. #1854C2×C29semidirect
343. #1788C2×C29semidirect
344. #1749C2×C29semidirect
396. #449C4×C29semidirect
447. C2×#41C2×C4×C29semidirect
460. C2×SD16C2×C4×C29semidirect
463. C2×D8C2×C4×C29semidirect
503. #103C2×C4×C29semidirect
508. #102C2×C4×C29semidirect
510. C22⋊C8C2×C4×C29semidirect
520. C29#22051direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4492
C4×C29×#1212
C29×#22972
C29×#19732
C29×#19722
C29×#19362
C29×#19352
C29×#19272
C29×#19252
C29×#18792
C29×#18772
C29×#18752
C29×#18542
C29×#17882
C29×#17492
#2205129