Finite Group Databasebeta

← C29×#11292 #20306192

Subgroups — C29×#11292 #20306192

Order 7424.

842 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#389C211yesmaximal, characteristic
2C2×C29×#340C211yesmaximal, characteristic
3C2×C29×#340C211yesmaximal, characteristic
4C2×C29×#340C211yesmaximal, characteristic
5C2×C29×#340C211yesmaximal, characteristic
6C2×C29×#336C211yesmaximal, characteristic
7C29×C4⋊#95C211yesmaximal, characteristic
8C23×C8×C29C2211yescharacteristic
9C23×C8×C29C2211yescharacteristic
10C22×C4⋊C4×C29—21no—
11C22×C4⋊C4×C29C2211yescharacteristic
12C22×C4⋊C4×C29C2211yescharacteristic
13C22×C4⋊C4×C29C2211yescharacteristic
14C22×C4⋊C4×C29C2211yescharacteristic
15C22×C42×C29C2211yescharacteristic
16C29×#389—22no—
17C29×#389—22no—
18C2×C29×#95—21no—
19C2×C29×#95—21no—
20C2×C29×#95—21no—
21C29×#340—22no—
22C29×#340—22no—
23C29×#340—22no—
24C29×#340C414yescomplemented
25C29×#336—22no—
26C23×C4×C29—21no—
27C23×C4×C29—21no—
28C23×C4×C29—21no—
29C23×C4×C29—21no—
30C23×C4×C29D411yescharacteristic
31C23×C4×C29D411yescharacteristic
32C23×C4×C29C2311yescharacteristic
33C22×C8×C29—21no—
34C22×C8×C29—21no—
35C22×C8×C29—21no—
36C22×C8×C29—21no—
37C22×C8×C29—21no—
38C22×C8×C29—21no—
39C22×C8×C29—21no—
40C22×C8×C29—21no—
41C22×C8×C29—21no—
42C22×C8×C29—21no—
43C22×C8×C29—21no—
44C22×C8×C29—21no—
45C22×C8×C29C2×C412yes—
46C22×C8×C29D412yes—
47C2×C4⋊C4×C29—21no—
48C2×C4⋊C4×C29—21no—
49C2×C4⋊C4×C29—21no—
50C2×C4⋊C4×C29—21no—
51C2×C4⋊C4×C29—21no—
52C2×C4⋊C4×C29—21no—
53C2×C4⋊C4×C29—21no—
54C2×C4⋊C4×C29—21no—
55C2×C4⋊C4×C29—21no—
56C2×C4⋊C4×C29—21no—
57C2×C4⋊C4×C29—21no—
58C2×C4⋊C4×C29—21no—
59C2×C4⋊C4×C29—21no—
60C2×C4⋊C4×C29—21no—
61C2×C4⋊C4×C29—21no—
62C2×C4⋊C4×C29—24no—
63C2×C4⋊C4×C29—21no—
64C2×C4⋊C4×C29—21no—
65C2×C4⋊C4×C29—21no—
66C2×C4⋊C4×C29—42no—
67C2×C4⋊C4×C29—42no—
68C2×C4⋊C4×C29C2×C412yes—
69C2×C4⋊C4×C29C2×C412yes—
70C2×C4⋊C4×C29D412yes—
71C2×C4⋊C4×C29D412yes—
72C2×C4⋊C4×C29Q812yes—
73C2×C4⋊C4×C29Q812yes—
74C2×C42×C29—21no—
75C2×C42×C29—21no—
76C2×C42×C29—21no—
77C2×C42×C29—21no—
78C2×C42×C29—21no—
79C2×C42×C29—21no—
80C29×#95—24no—
81C29×#95—42no—
82C29×#95—42no—
83C24×C29C2×D411yescharacteristic
84C22×C4×C29—22no—
85C22×C4×C29—21no—
86C22×C4×C29—21no—
87C22×C4×C29—22no—
88C22×C4×C29—21no—
89C22×C4×C29—21no—
90C22×C4×C29—22no—
91C22×C4×C29—21no—
92C22×C4×C29—21no—
93C22×C4×C29—21no—
94C22×C4×C29—21no—
95C22×C4×C29—21no—
96C22×C4×C29—21no—
97C22×C4×C29—21no—
98C22×C4×C29—21no—
99C22×C4×C29—22no—
100C22×C4×C29—22no—
101C22×C4×C29—22no—
102C22×C4×C29—41no—
103C22×C4×C29—41no—
104C22×C4×C29—41no—
105C22×C4×C29—41no—
106C22×C4×C29—41no—
107C22×C4×C29—41no—
108C22×C4×C29—41no—
109C22×C4×C29—41no—
110C22×C4×C29—41no—
111C22×C4×C29—41no—
112C22×C4×C29—41no—
113C22×C4×C29—41no—
114C22×C4×C29—41no—
115C22×C4×C29—41no—
116C22×C4×C29—41no—
117C22×C4×C29—41no—
118C22×C4×C29—41no—
119C22×C4×C29—41no—
120C22×C4×C29—41no—
121C22×C4×C29—41no—
122C22×C4×C29—41no—
123C22×C4×C29—41no—
124C22×C4×C29D812yes—
125C22×C4×C29SD1612yes—
126C22×C4×C29C22×C411yescharacteristic
127C22×C4×C29C2×D411yescharacteristic
128C22×C4×C29C2×D411yescharacteristic
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29C2×Q811yescharacteristic
131C22×C4×C29C2×Q811yescharacteristic
132C22×C4×C29#4111yescharacteristic
133C22×C4×C29#4111yescharacteristic
134C22×C4×C29#4111yescharacteristic
135C22×C4×C29#4111yescharacteristic
136C22×C4×C29#4111yescharacteristic
137C22×C4×C29#4111yescharacteristic
138C22×C4×C29#4111yescharacteristic
139C22×C4×C29#4111yescharacteristic
140C2×C8×C29—22no—
141C2×C8×C29—22no—
142C2×C8×C29—22no—
143C2×C8×C29—22no—
144C2×C8×C29—22no—
145C2×C8×C29—22no—
146C2×C8×C29—41no—
147C2×C8×C29—41no—
148C2×C8×C29—41no—
149C2×C8×C29—41no—
150C2×C8×C29—41no—
151C2×C8×C29—41no—
152C2×C8×C29—41no—
153C2×C8×C29—41no—
154C4⋊C4×C29—22no—
155C4⋊C4×C29—22no—
156C4⋊C4×C29—22no—
157C4⋊C4×C29—22no—
158C4⋊C4×C29—22no—
159C4⋊C4×C29—22no—
160C4⋊C4×C29—22no—
161C4⋊C4×C29—22no—
162C4⋊C4×C29—22no—
163C4⋊C4×C29—48no—
164C4⋊C4×C29—41no—
165C4⋊C4×C29—41no—
166C4⋊C4×C29—41no—
167C4⋊C4×C29—41no—
168C4⋊C4×C29—41no—
169C4⋊C4×C29—41no—
170C4⋊C4×C29C4⋊C414yes—
171C42×C29—41no—
172C42×C29—41no—
173C42×C29—41no—
174C42×C29—41no—
175#11292C2911yesmaximal, characteristic, direct product factor, Sylow
176C23×C29C4×D411yescharacteristic
177C23×C29#12011yescharacteristic
178C23×C29#12111yescharacteristic
179C23×C29C22⋊Q811yescharacteristic
180C23×C29C22⋊Q811yescharacteristic
181C23×C29#12311yescharacteristic
182C23×C29#12411yescharacteristic
183C23×C29C2×D811yescharacteristic
184C23×C29C2×SD1611yescharacteristic
185C23×C29#13511yescharacteristic
186C23×C29#13511yescharacteristic
187C23×C29AGL(1,ℤ/8)11yescharacteristic
188C23×C29#13711yescharacteristic
189C23×C29#13711yescharacteristic
190C23×C29#13711yescharacteristic
191C2×C4×C29—24no—
192C2×C4×C29—22no—
193C2×C4×C29—22no—
194C2×C4×C29—22no—
195C2×C4×C29—22no—
196C2×C4×C29—22no—
197C2×C4×C29—22no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—42no—
201C2×C4×C29—42no—
202C2×C4×C29—42no—
203C2×C4×C29—41no—
204C2×C4×C29—41no—
205C2×C4×C29—42no—
206C2×C4×C29—41no—
207C2×C4×C29—41no—
208C2×C4×C29—42no—
209C2×C4×C29—42no—
210C2×C4×C29—41no—
211C2×C4×C29—41no—
212C2×C4×C29—42no—
213C2×C4×C29—42no—
214C2×C4×C29—42no—
215C2×C4×C29—42no—
216C2×C4×C29—42no—
217C2×C4×C29—42no—
218C2×C4×C29—42no—
219C2×C4×C29—42no—
220C2×C4×C29—42no—
221C2×C4×C29—81no—
222C2×C4×C29—81no—
223C2×C4×C29—81no—
224C2×C4×C29—81no—
225C2×C4×C29—81no—
226C2×C4×C29—81no—
227C2×C4×C29—81no—
228C2×C4×C29—81no—
229C2×C4×C29—81no—
230C2×C4×C29—81no—
231C2×C4×C29—81no—
232C2×C4×C29—81no—
233C2×C4×C29C2×C4⋊C411yescharacteristic
234C2×C4×C29#11711yescharacteristic
235C2×C4×C29#11711yescharacteristic
236C2×C4×C29C4×D411yescharacteristic
237C2×C4×C29C4×D411yescharacteristic
238C2×C4×C29C4×Q811yescharacteristic
239C2×C4×C29#12111yescharacteristic
240C2×C4×C29#12111yescharacteristic
241C2×C4×C29C22⋊Q811yescharacteristic
242C2×C4×C29C22⋊Q811yescharacteristic
243C2×C4×C29C22⋊Q811yescharacteristic
244C2×C4×C29#12311yescharacteristic
245C2×C4×C29#12311yescharacteristic
246C2×C4×C29#12311yescharacteristic
247C2×C4×C29#12311yescharacteristic
248C2×C4×C29#12411yescharacteristic
249C2×C4×C29#12411yescharacteristic
250C2×C4×C29#12411yescharacteristic
251C2×C4×C29#12511yescharacteristic
252C2×C4×C29#12511yescharacteristic
253C2×C4×C29#12511yescharacteristic
254C2×C4×C29#12511yescharacteristic
255C2×C4×C29#12511yescharacteristic
256C2×C4×C29#12611yescharacteristic
257C2×C4×C29#12611yescharacteristic
258C2×C4×C29#12611yescharacteristic
259C2×C4×C29#12611yescharacteristic
260C2×C4×C29C4⋊Q811yescharacteristic
261C8×C29—42no—
262C8×C29—42no—
263C2×#389C2×C2911yescharacteristic
264C2×#340C2×C2911yescharacteristic
265C2×#340C2×C2911yescharacteristic
266C2×#340C2×C2911yescharacteristic
267C2×#340C2×C2911yescharacteristic
268C2×#336C2×C2911yescharacteristic
269C4⋊#95C2×C2911yescharacteristic
270C22×C29#38511yescharacteristic
271C22×C29#38711yescharacteristic
272C22×C29#38811yescharacteristic
273C22×C29#39311yescharacteristic
274C22×C29#39411yescharacteristic
275C22×C29#39811yescharacteristic
276C22×C29#40011yescharacteristic
277C22×C29C4×D811yescharacteristic
278C22×C29C4×SD1611yescharacteristic
279C22×C29#44011yescharacteristic
280C22×C29#44111yescharacteristic
281C22×C29#44711yescharacteristic
282C22×C29#44811yescharacteristic
283C22×C29#45211yescharacteristic
284C22×C29#45211yescharacteristic
285C22×C29#46511yescharacteristic
286C22×C29#46611yescharacteristic
287C22×C29#46811yescharacteristic
288C22×C29#47011yescharacteristic
289C22×C29#47411yescharacteristic
290C22×C29#47411yescharacteristic
291C22×C29#47511yescharacteristic
292C22×C29#47611yescharacteristic
293C22×C29#47811yescharacteristic
294C22×C29#47911yescharacteristic
295C22×C29#47911yescharacteristic
296C22×C29#47911yescharacteristic
297C22×C29#48011yescharacteristic
298C22×C29#48211yescharacteristic
299C22×C29#48311yescharacteristic
300C22×C29#48511yescharacteristic
301C22×C29#48611yescharacteristic
302C22×C29#48811yescharacteristic
303C22×C29#48911yescharacteristic
304C22×C29#49111yescharacteristic
305C4×C29—44no—
306C4×C29—42no—
307C4×C29—42no—
308C4×C29—82no—
309C4×C29—82no—
310C4×C29—82no—
311C4×C29#38211yescharacteristic
312C4×C29#38711yescharacteristic
313C4×C29#38811yescharacteristic
314C4×C29#38911yescharacteristic
315C4×C29#39711yescharacteristic
316C4×C29#39811yescharacteristic
317C4×C29#40011yescharacteristic
318C4×C29#40011yescharacteristic
319C23×C8C22×C2911yescharacteristic
320C23×C8C22×C2911yescharacteristic
321C22×C4⋊C4—21no—
322C22×C4⋊C4C22×C2911yescharacteristic
323C22×C4⋊C4C22×C2911yescharacteristic
324C22×C4⋊C4C22×C2911yescharacteristic
325C22×C4⋊C4C22×C2911yescharacteristic
326C22×C42C22×C2911yescharacteristic
327#389—22no—
328#389—22no—
329C2×#95—21no—
330C2×#95—21no—
331C2×#95—21no—
332#340—22no—
333#340—22no—
334#340—22no—
335#340C4×C2914yescomplemented
336#336—22no—
337C2×C29#144211yescharacteristic
338C2×C29#186211yescharacteristic
339C2×C29#186511yescharacteristic
340C2×C29#191811yescharacteristic
341C2×C29#192011yescharacteristic
342C2×C29#193411yescharacteristic
343C2×C29#193511yescharacteristic
344C2×C29#202311yescharacteristic
345C2×C29#202611yescharacteristic
346C2×C29#203311yescharacteristic
347C2×C29#203511yescharacteristic
348C2×C29#208611yescharacteristic
349C2×C29#208811yescharacteristic
350C2×C29#209911yescharacteristic
351C2×C29#210111yescharacteristic
352C23×C4—21no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4D4×C2911yescharacteristic
357C23×C4D4×C2911yescharacteristic
358C23×C4C23×C2911yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8C2×C4×C2912yes—
372C22×C8D4×C2912yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—42no—
393C2×C4⋊C4—42no—
394C2×C4⋊C4C2×C4×C2912yes—
395C2×C4⋊C4C2×C4×C2912yes—
396C2×C4⋊C4D4×C2912yes—
397C2×C4⋊C4D4×C2912yes—
398C2×C4⋊C4Q8×C2912yes—
399C2×C4⋊C4Q8×C2912yes—
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—21no—
406#95—24no—
407#95—42no—
408#95—42no—
409C29#1129211yescharacteristic, direct product factor, Sylow
410C24C2×D4×C2911yescharacteristic
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4D8×C2912yes—
452C22×C4SD16×C2912yes—
453C22×C4C22×C4×C2911yescharacteristic
454C22×C4C2×D4×C2911yescharacteristic
455C22×C4C2×D4×C2911yescharacteristic
456C22×C4C2×D4×C2911yescharacteristic
457C22×C4C2×Q8×C2911yescharacteristic
458C22×C4C2×Q8×C2911yescharacteristic
459C22×C4#41×C2911yescharacteristic
460C22×C4#41×C2911yescharacteristic
461C22×C4#41×C2911yescharacteristic
462C22×C4#41×C2911yescharacteristic
463C22×C4#41×C2911yescharacteristic
464C22×C4#41×C2911yescharacteristic
465C22×C4#41×C2911yescharacteristic
466C22×C4#41×C2911yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—48no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4—41no—
496C4⋊C4—41no—
497C4⋊C4C4⋊C4×C2914yes—
498C42—41no—
499C42—41no—
500C42—41no—
501C42—41no—
502C23C4×D4×C2911yescharacteristic
503C23C29×#12011yescharacteristic
504C23C29×#12111yescharacteristic
505C23C29×C22⋊Q811yescharacteristic
506C23C29×C22⋊Q811yescharacteristic
507C23C29×#12311yescharacteristic
508C23C29×#12411yescharacteristic
509C23C2×D8×C2911yescharacteristic
510C23C2×SD16×C2911yescharacteristic
511C23C29×#13511yescharacteristic
512C23C29×#13511yescharacteristic
513C23C29×AGL(1,ℤ/8)11yescharacteristic
514C23C29×#13711yescharacteristic
515C23C29×#13711yescharacteristic
516C23C29×#13711yescharacteristic
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—81no—
551C2×C4—81no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—81no—
555C2×C4—81no—
556C2×C4—81no—
557C2×C4—81no—
558C2×C4—81no—
559C2×C4C2×C4⋊C4×C2911yescharacteristic
560C2×C4C29×#11711yescharacteristic
561C2×C4C29×#11711yescharacteristic
562C2×C4C4×D4×C2911yescharacteristic
563C2×C4C4×D4×C2911yescharacteristic
564C2×C4C4×Q8×C2911yescharacteristic
565C2×C4C29×#12111yescharacteristic
566C2×C4C29×#12111yescharacteristic
567C2×C4C29×C22⋊Q811yescharacteristic
568C2×C4C29×C22⋊Q811yescharacteristic
569C2×C4C29×C22⋊Q811yescharacteristic
570C2×C4C29×#12311yescharacteristic
571C2×C4C29×#12311yescharacteristic
572C2×C4C29×#12311yescharacteristic
573C2×C4C29×#12311yescharacteristic
574C2×C4C29×#12411yescharacteristic
575C2×C4C29×#12411yescharacteristic
576C2×C4C29×#12411yescharacteristic
577C2×C4C29×#12511yescharacteristic
578C2×C4C29×#12511yescharacteristic
579C2×C4C29×#12511yescharacteristic
580C2×C4C29×#12511yescharacteristic
581C2×C4C29×#12511yescharacteristic
582C2×C4C29×#12611yescharacteristic
583C2×C4C29×#12611yescharacteristic
584C2×C4C29×#12611yescharacteristic
585C2×C4C29×#12611yescharacteristic
586C2×C4C29×C4⋊Q811yescharacteristic
587C8—42no—
588C8—42no—
589C22C29×#38511yescharacteristic
590C22C29×#38711yescharacteristic
591C22C29×#38811yescharacteristic
592C22C29×#39311yescharacteristic
593C22C29×#39411yescharacteristic
594C22C29×#39811yescharacteristic
595C22C29×#40011yescharacteristic
596C22C4×D8×C2911yescharacteristic
597C22C4×SD16×C2911yescharacteristic
598C22C29×#44011yescharacteristic
599C22C29×#44111yescharacteristic
600C22C29×#44711yescharacteristic
601C22C29×#44811yescharacteristic
602C22C29×#45211yescharacteristic
603C22C29×#45211yescharacteristic
604C22C29×#46511yescharacteristic
605C22C29×#46611yescharacteristic
606C22C29×#46811yescharacteristic
607C22C29×#47011yescharacteristic
608C22C29×#47411yescharacteristic
609C22C29×#47411yescharacteristic
610C22C29×#47511yescharacteristic
611C22C29×#47611yescharacteristic
612C22C29×#47811yescharacteristic
613C22C29×#47911yescharacteristic
614C22C29×#47911yescharacteristic
615C22C29×#47911yescharacteristic
616C22C29×#48011yescharacteristic
617C22C29×#48211yescharacteristic
618C22C29×#48311yescharacteristic
619C22C29×#48511yescharacteristic
620C22C29×#48611yescharacteristic
621C22C29×#48811yescharacteristic
622C22C29×#48911yescharacteristic
623C22C29×#49111yescharacteristic
624C4—42no—
625C4—42no—
626C4—44no—
627C4—82no—
628C4—82no—
629C4—82no—
630C4C29×#38211yescharacteristic
631C4C29×#38711yescharacteristic
632C4C29×#38811yescharacteristic
633C4C29×#38911yescharacteristic
634C4C29×#39711yescharacteristic
635C4C29×#39811yescharacteristic
636C4C29×#40011yescharacteristic
637C4C29×#40011yescharacteristic
638C2C29×#144211yescharacteristic
639C2C29×#186211yescharacteristic
640C2C29×#186511yescharacteristic
641C2C29×#191811yescharacteristic
642C2C29×#192011yescharacteristic
643C2C29×#193411yescharacteristic
644C2C29×#193511yescharacteristic
645C2C29×#202311yescharacteristic
646C2C29×#202611yescharacteristic
647C2C29×#203311yescharacteristic
648C2C29×#203511yescharacteristic
649C2C29×#208611yescharacteristic
650C2C29×#208811yescharacteristic
651C2C29×#209911yescharacteristic
652C2C29×#210111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C29C2×D4
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C29 ◁ C22×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
24. C29×#340C4semidirect
175. #11292C29direct (N × H)
335. #340C4×C29semidirect
409. C29#11292direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#3892
C2×C29×#3402
C2×C29×#3362
C29×C4⋊#952
#1129229