Finite Group Databasebeta

← C29×#13882 #20308782

Subgroups — C29×#13882 #20308782

Order 7424.

2222 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4⋊C4×C29C211yesmaximal, characteristic
2C2×C29×#387C212yesmaximal, complemented
3C2×C29×#380C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C29C211yesmaximal, characteristic
5C29×#1445C212yesmaximal, complemented
6C29×#1441C212yesmaximal, complemented
7C29×#1436C212yesmaximal, complemented
8C29×C22⋊#95C211yesmaximal, characteristic
9C29×C22⋊#95C211yesmaximal, characteristic
10C29×C22⋊#95C211yesmaximal, characteristic
11C29×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C29C2211yescharacteristic
13C24×C4×C29C2211yescharacteristic
14C24×C4×C29C2211yescharacteristic
15C22×C4⋊C4×C29—28no—
16C22×C4⋊C4×C29C418yescomplemented
17C22×C4⋊C4×C29C2212yes—
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C4⋊C4×C29C2211yescharacteristic
22C22×C22⋊C4×C29C2211yescharacteristic
23C22×C22⋊C4×C29C2211yescharacteristic
24C22×C22⋊C4×C29C2211yescharacteristic
25C22×C22⋊C4×C29C2211yescharacteristic
26C22×C42×C29C2212yes—
27C29×#387—28no—
28C29×#380—24no—
29C4×C22⋊C4×C29—24no—
30C2×C29×#95C2212yes—
31C2×C29×#95C2212yes—
32C2×C29×#95C2212yes—
33C2×C29×#95C2212yes—
34C2×C29×#95C2212yes—
35C2×C29×#95C2212yes—
36C2×C29×#95C2212yes—
37C2×C29×#95C2212yes—
38C2×C29×#95C2212yes—
39C2×C29×#95C2212yes—
40C25×C29C2311yescharacteristic
41C23×C4×C29—22no—
42C23×C4×C29—22no—
43C23×C4×C29—24no—
44C23×C4×C29—24no—
45C23×C4×C29—22no—
46C23×C4×C29—22no—
47C23×C4×C29—22no—
48C23×C4×C29—22no—
49C23×C4×C29—24no—
50C23×C4×C29—24no—
51C23×C4×C29—42no—
52C23×C4×C29—42no—
53C23×C4×C29C2×C414yes—
54C23×C4×C29C2×C414yes—
55C23×C4×C29C2×C414yes—
56C23×C4×C29C2312yes—
57C23×C4×C29C2312yes—
58C23×C4×C29C2311yescharacteristic
59C23×C4×C29C2311yescharacteristic
60C23×C4×C29C2312yes—
61C23×C4×C29C2312yes—
62C23×C4×C29C2311yescharacteristic
63C23×C4×C29C2311yescharacteristic
64C23×C4×C29C2311yescharacteristic
65C23×C4×C29C2311yescharacteristic
66C2×C4⋊C4×C29—24no—
67C2×C4⋊C4×C29—24no—
68C2×C4⋊C4×C29—24no—
69C2×C4⋊C4×C29—232no—
70C2×C4⋊C4×C29—24no—
71C2×C4⋊C4×C29—24no—
72C2×C4⋊C4×C29—42no—
73C2×C4⋊C4×C29C2×C414yes—
74C2×C4⋊C4×C29C2×C414yes—
75C2×C4⋊C4×C29C2×C414yes—
76C2×C4⋊C4×C29C2×C414yes—
77C2×C4⋊C4×C29D418yes—
78C2×C22⋊C4×C29—22no—
79C2×C22⋊C4×C29—22no—
80C2×C22⋊C4×C29—22no—
81C2×C22⋊C4×C29—22no—
82C2×C22⋊C4×C29—22no—
83C2×C22⋊C4×C29—22no—
84C2×C22⋊C4×C29—22no—
85C2×C22⋊C4×C29—22no—
86C2×C22⋊C4×C29—22no—
87C2×C22⋊C4×C29—22no—
88C2×C22⋊C4×C29D414yes—
89C2×C22⋊C4×C29Q814yes—
90C2×C42×C29—24no—
91C2×C42×C29—24no—
92C2×C42×C29—42no—
93C29×#95—24no—
94C29×#95—24no—
95C29×#95—24no—
96C29×#95—24no—
97C29×#95—24no—
98C29×#95—24no—
99C29×#95—24no—
100C29×#95—24no—
101C29×#95—42no—
102C29×#95—42no—
103C24×C29—22no—
104C24×C29—22no—
105C24×C29—22no—
106C24×C29—22no—
107C24×C29C22×C412yes—
108C24×C29C2×D412yes—
109C24×C29C2×Q812yes—
110C24×C29#4112yes—
111C24×C29#4112yes—
112C24×C29#4112yes—
113C24×C29#4112yes—
114C24×C29C2411yescharacteristic
115C22×C4×C29—216no—
116C22×C4×C29—216no—
117C22×C4×C29—28no—
118C22×C4×C29—21no—
119C22×C4×C29—22no—
120C22×C4×C29—21no—
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—22no—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—22no—
129C22×C4×C29—22no—
130C22×C4×C29—28no—
131C22×C4×C29—28no—
132C22×C4×C29—28no—
133C22×C4×C29—28no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—22no—
142C22×C4×C29—22no—
143C22×C4×C29—22no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—22no—
147C22×C4×C29—22no—
148C22×C4×C29—22no—
149C22×C4×C29—22no—
150C22×C4×C29—22no—
151C22×C4×C29—22no—
152C22×C4×C29—22no—
153C22×C4×C29—22no—
154C22×C4×C29—28no—
155C22×C4×C29—28no—
156C22×C4×C29—22no—
157C22×C4×C29—22no—
158C22×C4×C29—22no—
159C22×C4×C29—22no—
160C22×C4×C29—22no—
161C22×C4×C29—22no—
162C22×C4×C29—22no—
163C22×C4×C29—22no—
164C22×C4×C29—22no—
165C22×C4×C29—22no—
166C22×C4×C29—22no—
167C22×C4×C29—22no—
168C22×C4×C29—22no—
169C22×C4×C29—22no—
170C22×C4×C29—44no—
171C22×C4×C29—44no—
172C22×C4×C29—48no—
173C22×C4×C29—48no—
174C22×C4×C29—48no—
175C22×C4×C29—48no—
176C22×C4×C29C22×C412yes—
177C22×C4×C29C22×C412yes—
178C22×C4×C29C22×C412yes—
179C22×C4×C29C22×C412yes—
180C22×C4×C29C22×C412yes—
181C22×C4×C29C22×C412yes—
182C22×C4×C29C2×D414yes—
183C22×C4×C29C2×D414yes—
184C22×C4×C29C2×D414yes—
185C22×C4×C29C2×D414yes—
186C22×C4×C29C2×Q814yes—
187C22×C4×C29#4114yes—
188C4⋊C4×C29—28no—
189C4⋊C4×C29—28no—
190C4⋊C4×C29—28no—
191C4⋊C4×C29—48no—
192C4⋊C4×C29C22⋊C4116yescomplemented
193C22⋊C4×C29—28no—
194C22⋊C4×C29—28no—
195C22⋊C4×C29—44no—
196C22⋊C4×C29—44no—
197C42×C29—48no—
198#13882C2911yesmaximal, characteristic, direct product factor, Sylow
199C23×C29—22no—
200C23×C29—22no—
201C23×C29—22no—
202C23×C29—22no—
203C23×C29—24no—
204C23×C29—24no—
205C23×C29—24no—
206C23×C29—24no—
207C23×C29—24no—
208C23×C29—24no—
209C23×C29—24no—
210C23×C29—24no—
211C23×C29—24no—
212C23×C29—24no—
213C23×C29—24no—
214C23×C29—24no—
215C23×C29#11714yes—
216C23×C29C4×D414yes—
217C23×C29C4×Q814yes—
218C23×C29C22⋊Q814yes—
219C23×C29#12314yes—
220C23×C29#12514yes—
221C23×C29#12614yes—
222C23×C29C23×C411yescharacteristic
223C23×C29C22×D412yes—
224C23×C29C22×D411yescharacteristic
225C23×C29C22×Q811yescharacteristic
226C23×C29C2×#4111yescharacteristic
227C23×C29C2×#4111yescharacteristic
228C23×C29C2×#4112yes—
229C23×C29C2×#4111yescharacteristic
230C23×C29C2×#4111yescharacteristic
231C23×C29H(5,𝔽2)12yes—
232C23×C292−1+412yes—
233C2×C4×C29—232no—
234C2×C4×C29—22no—
235C2×C4×C29—22no—
236C2×C4×C29—22no—
237C2×C4×C29—22no—
238C2×C4×C29—22no—
239C2×C4×C29—22no—
240C2×C4×C29—22no—
241C2×C4×C29—22no—
242C2×C4×C29—24no—
243C2×C4×C29—24no—
244C2×C4×C29—24no—
245C2×C4×C29—24no—
246C2×C4×C29—24no—
247C2×C4×C29—24no—
248C2×C4×C29—24no—
249C2×C4×C29—24no—
250C2×C4×C29—22no—
251C2×C4×C29—22no—
252C2×C4×C29—22no—
253C2×C4×C29—22no—
254C2×C4×C29—22no—
255C2×C4×C29—22no—
256C2×C4×C29—24no—
257C2×C4×C29—24no—
258C2×C4×C29—24no—
259C2×C4×C29—24no—
260C2×C4×C29—24no—
261C2×C4×C29—24no—
262C2×C4×C29—416no—
263C2×C4×C29—416no—
264C2×C4×C29—42no—
265C2×C4×C29—42no—
266C2×C4×C29—42no—
267C2×C4×C29—42no—
268C2×C4×C29—42no—
269C2×C4×C29—42no—
270C2×C4×C29—42no—
271C2×C4×C29—42no—
272C2×C4×C29—42no—
273C2×C4×C29—42no—
274C2×C4×C29—42no—
275C2×C4×C29—42no—
276C2×C4×C29—42no—
277C2×C4×C29—42no—
278C2×C4×C29—42no—
279C2×C4×C29—42no—
280C2×C4×C29—42no—
281C2×C4×C29—42no—
282C2×C4×C29—42no—
283C2×C4×C29—42no—
284C2×C4×C29—42no—
285C2×C4×C29—42no—
286C2×C4×C29—42no—
287C2×C4×C29—42no—
288C2×C4×C29—42no—
289C2×C4×C29—42no—
290C2×C4×C29C2×C22⋊C414yes—
291C2×C4×C29C2×C22⋊C414yes—
292C2×C4×C29C2×C22⋊C414yes—
293C2×C4×C29#11714yes—
294C23×C4⋊C4C2×C2911yescharacteristic
295C2×#387C2×C2912yescomplemented
296C2×#380C2×C2911yescharacteristic
297C2×C4×C22⋊C4C2×C2911yescharacteristic
298#1445C2×C2912yescomplemented
299#1441C2×C2912yescomplemented
300#1436C2×C2912yescomplemented
301C22⋊#95C2×C2911yescharacteristic
302C22⋊#95C2×C2911yescharacteristic
303C22⋊#95C2×C2911yescharacteristic
304C22⋊#95C2×C2911yescharacteristic
305C22×C29—24no—
306C22×C29—24no—
307C22×C29—24no—
308C22×C29—24no—
309C22×C29—24no—
310C22×C29—28no—
311C22×C29—28no—
312C22×C29—28no—
313C22×C29—28no—
314C22×C29—24no—
315C22×C29#38718yescomplemented
316C22×C29C22×C22⋊C411yescharacteristic
317C22×C29C2×#11711yescharacteristic
318C22×C29C2×#11711yescharacteristic
319C22×C29C2×C4×D411yescharacteristic
320C22×C29C2×C4×Q811yescharacteristic
321C22×C29#51811yescharacteristic
322C22×C29#51911yescharacteristic
323C22×C29C2×C22⋊Q811yescharacteristic
324C22×C29C2×#12311yescharacteristic
325C22×C29#52512yes—
326C22×C29#52512yes—
327C22×C29C2×#12511yescharacteristic
328C22×C29C2×#12611yescharacteristic
329C22×C29#53912yes—
330C22×C29#53912yes—
331C22×C29D4212yes—
332C22×C29#54612yes—
333C22×C29#54712yes—
334C22×C29#54812yes—
335C22×C29D4×Q812yes—
336C22×C29#55212yes—
337C22×C29#55312yes—
338C22×C29#55412yes—
339C4×C29—24no—
340C4×C29—24no—
341C4×C29—24no—
342C4×C29—24no—
343C4×C29—42no—
344C4×C29—42no—
345C4×C29—44no—
346C4×C29—44no—
347C4×C29—82no—
348C4×C29—82no—
349C24×C4C22×C2911yescharacteristic
350C24×C4C22×C2911yescharacteristic
351C24×C4C22×C2911yescharacteristic
352C22×C4⋊C4—28no—
353C22×C4⋊C4C4×C2918yescomplemented
354C22×C4⋊C4C22×C2912yes—
355C22×C4⋊C4C22×C2911yescharacteristic
356C22×C4⋊C4C22×C2911yescharacteristic
357C22×C4⋊C4C22×C2911yescharacteristic
358C22×C4⋊C4C22×C2911yescharacteristic
359C22×C22⋊C4C22×C2911yescharacteristic
360C22×C22⋊C4C22×C2911yescharacteristic
361C22×C22⋊C4C22×C2911yescharacteristic
362C22×C22⋊C4C22×C2911yescharacteristic
363C22×C42C22×C2912yes—
364#387—28no—
365#380—24no—
366C4×C22⋊C4—24no—
367C2×#95C22×C2912yes—
368C2×#95C22×C2912yes—
369C2×#95C22×C2912yes—
370C2×#95C22×C2912yes—
371C2×#95C22×C2912yes—
372C2×#95C22×C2912yes—
373C2×#95C22×C2912yes—
374C2×#95C22×C2912yes—
375C2×#95C22×C2912yes—
376C2×#95C22×C2912yes—
377C2×C29—28no—
378C2×C29#228011yescharacteristic
379C2×C29C2×#38711yescharacteristic
380C2×C29#231311yescharacteristic
381C2×C29D4×C22⋊C411yescharacteristic
382C2×C29Q8×C22⋊C411yescharacteristic
383C2×C29#234411yescharacteristic
384C2×C29#234511yescharacteristic
385C2×C29#244312yes—
386C2×C29#244912yes—
387C2×C29#247312yes—
388C2×C29#248112yes—
389C25C23×C2911yescharacteristic
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4C2×C4×C2914yes—
403C23×C4C2×C4×C2914yes—
404C23×C4C2×C4×C2914yes—
405C23×C4C23×C2912yes—
406C23×C4C23×C2912yes—
407C23×C4C23×C2911yescharacteristic
408C23×C4C23×C2911yescharacteristic
409C23×C4C23×C2912yes—
410C23×C4C23×C2912yes—
411C23×C4C23×C2911yescharacteristic
412C23×C4C23×C2911yescharacteristic
413C23×C4C23×C2911yescharacteristic
414C23×C4C23×C2911yescharacteristic
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—232no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4C2×C4×C2914yes—
423C2×C4⋊C4C2×C4×C2914yes—
424C2×C4⋊C4C2×C4×C2914yes—
425C2×C4⋊C4C2×C4×C2914yes—
426C2×C4⋊C4D4×C2918yes—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4D4×C2914yes—
438C2×C22⋊C4Q8×C2914yes—
439C2×C42—24no—
440C2×C42—24no—
441C2×C42—42no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—24no—
446#95—24no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—42no—
451#95—42no—
452C29#1388211yescharacteristic, direct product factor, Sylow
453C24—22no—
454C24—22no—
455C24—22no—
456C24—22no—
457C24C22×C4×C2912yes—
458C24C2×D4×C2912yes—
459C24C2×Q8×C2912yes—
460C24#41×C2912yes—
461C24#41×C2912yes—
462C24#41×C2912yes—
463C24#41×C2912yes—
464C24C24×C2911yescharacteristic
465C22×C4—216no—
466C22×C4—216no—
467C22×C4—28no—
468C22×C4—21no—
469C22×C4—22no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—28no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—28no—
505C22×C4—28no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—48no—
523C22×C4—48no—
524C22×C4—48no—
525C22×C4—48no—
526C22×C4C22×C4×C2912yes—
527C22×C4C22×C4×C2912yes—
528C22×C4C22×C4×C2912yes—
529C22×C4C22×C4×C2912yes—
530C22×C4C22×C4×C2912yes—
531C22×C4C22×C4×C2912yes—
532C22×C4C2×D4×C2914yes—
533C22×C4C2×D4×C2914yes—
534C22×C4C2×D4×C2914yes—
535C22×C4C2×D4×C2914yes—
536C22×C4C2×Q8×C2914yes—
537C22×C4#41×C2914yes—
538C4⋊C4—28no—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—48no—
542C4⋊C4C22⋊C4×C29116yescomplemented
543C22⋊C4—28no—
544C22⋊C4—28no—
545C22⋊C4—44no—
546C22⋊C4—44no—
547C42—48no—
548C23—22no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—24no—
559C23—24no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23C29×#11714yes—
565C23C4×D4×C2914yes—
566C23C4×Q8×C2914yes—
567C23C29×C22⋊Q814yes—
568C23C29×#12314yes—
569C23C29×#12514yes—
570C23C29×#12614yes—
571C23C23×C4×C2911yescharacteristic
572C23C22×D4×C2912yes—
573C23C22×D4×C2911yescharacteristic
574C23C22×Q8×C2911yescharacteristic
575C23C2×#41×C2911yescharacteristic
576C23C2×#41×C2911yescharacteristic
577C23C2×#41×C2912yes—
578C23C2×#41×C2911yescharacteristic
579C23C2×#41×C2911yescharacteristic
580C23C29×H(5,𝔽2)12yes—
581C23C29×2−1+412yes—
582C2×C4—232no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—416no—
612C2×C4—416no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4C2×C22⋊C4×C2914yes—
640C2×C4C2×C22⋊C4×C2914yes—
641C2×C4C2×C22⋊C4×C2914yes—
642C2×C4C29×#11714yes—
643C22—28no—
644C22—28no—
645C22—28no—
646C22—28no—
647C22—24no—
648C22—24no—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22C29×#38718yescomplemented
654C22C22×C22⋊C4×C2911yescharacteristic
655C22C2×C29×#11711yescharacteristic
656C22C2×C29×#11711yescharacteristic
657C22C2×C4×D4×C2911yescharacteristic
658C22C2×C4×Q8×C2911yescharacteristic
659C22C29×#51811yescharacteristic
660C22C29×#51911yescharacteristic
661C22C2×C29×C22⋊Q811yescharacteristic
662C22C2×C29×#12311yescharacteristic
663C22C29×#52512yes—
664C22C29×#52512yes—
665C22C2×C29×#12511yescharacteristic
666C22C2×C29×#12611yescharacteristic
667C22C29×#53912yes—
668C22C29×#53912yes—
669C22D42×C2912yes—
670C22C29×#54612yes—
671C22C29×#54712yes—
672C22C29×#54812yes—
673C22D4×Q8×C2912yes—
674C22C29×#55212yes—
675C22C29×#55312yes—
676C22C29×#55412yes—
677C4—24no—
678C4—24no—
679C4—24no—
680C4—24no—
681C4—44no—
682C4—44no—
683C4—42no—
684C4—42no—
685C4—82no—
686C4—82no—
687C2—28no—
688C2C29×#228011yescharacteristic
689C2C2×C29×#38711yescharacteristic
690C2C29×#231311yescharacteristic
691C2D4×C22⋊C4×C2911yescharacteristic
692C2Q8×C22⋊C4×C2911yescharacteristic
693C2C29×#234411yescharacteristic
694C2C29×#234511yescharacteristic
695C2C29×#244312yes—
696C2C29×#244912yes—
697C2C29×#247312yes—
698C2C29×#248112yes—
subgroupG/H
center, socleC24×C29C24
commutatorC23C23×C4×C29
Frattini, cosocleC24C24×C29
prime radicalC25×C29C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#387C2semidirect
5. C29×#1445C2semidirect
6. C29×#1441C2semidirect
7. C29×#1436C2semidirect
16. C22×C4⋊C4×C29C4semidirect
192. C4⋊C4×C29C22⋊C4semidirect
198. #13882C29direct (N × H)
295. C2×#387C2×C29semidirect
298. #1445C2×C29semidirect
299. #1441C2×C29semidirect
300. #1436C2×C29semidirect
315. C22×C29#387semidirect
353. C22×C4⋊C4C4×C29semidirect
452. C29#13882direct (N × H)
542. C4⋊C4C22⋊C4×C29semidirect
653. C22C29×#387semidirect

Maximal subgroups

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

subgroupindex
C23×C4⋊C4×C292
C2×C29×#3872
C2×C29×#3802
C2×C4×C22⋊C4×C292
C29×#14452
C29×#14412
C29×#14362
C29×C22⋊#952
#1388229