Finite Group Databasebeta

← C29×#32734 #20327634

Subgroups — C29×#32734 #20327634

Order 7424.

766 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2624C211yesmaximal, characteristic, complemented
2C29×#2620C211yesmaximal, characteristic, complemented
3C29×#2099C211yesmaximal, characteristic, complemented
4C29×#2094C211yesmaximal, characteristic, complemented
5C29×#2066C211yesmaximal, characteristic, complemented
6C29×#2065C211yesmaximal, characteristic, complemented
7C29×#2055C211yesmaximal, characteristic, complemented
8C29×#2054C211yesmaximal, characteristic, complemented
9C29×#2042C211yesmaximal, characteristic, complemented
10C29×#2035C211yesmaximal, characteristic, complemented
11C29×#2034C211yesmaximal, characteristic, complemented
12C29×#2012C211yesmaximal, characteristic, complemented
13C29×#2000C211yesmaximal, characteristic, complemented
14C29×#1999C211yesmaximal, characteristic
15C29×#1798C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C22×D8×C29C2211yescharacteristic
18C2×C29×#124C2211yescharacteristic
19C2×C29×C22⋊Q8C2211yescharacteristic
20C2×C29×#121C2211yescharacteristic
21C2×C29×#121C2211yescharacteristic
22C2×C29×#117C2211yescharacteristic
23C2×C29×#106C2211yescharacteristic
24C2×C29×#106C2211yescharacteristic
25C2×C29×C4⋊C8C2211yescharacteristic
26C2×C29×C4⋊C8C2211yescharacteristic
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
37C29×#399—21no—
38C29×#397—21no—
39C29×#396—21no—
40C29×#396—21no—
41C29×#394—21no—
42C29×#394—21no—
43C29×#394—21no—
44C29×#394—21no—
45C29×#391C2211yescharacteristic
46C29×#390C2211yescharacteristic
47C29×#390C2211yescharacteristic
48C29×#390C2211yescharacteristic
49C29×#389C2211yescharacteristic
50C29×#389C2211yescharacteristic
51C29×#384C2211yescharacteristic
52C29×#380C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×D4×C29—21no—
61C22×D4×C29—21no—
62C22×D4×C29C2311yescharacteristic
63C22×D4×C29C2311yescharacteristic
64C23×C4×C29C2311yescharacteristic
65C2×SD16×C29—41no—
66C2×SD16×C29—41no—
67C2×SD16×C29—41no—
68C2×D8×C29—41no—
69C2×D8×C29—41no—
70C2×D8×C29—41no—
71C22×C8×C29C2311yescharacteristic
72C22×C8×C29C2311yescharacteristic
73C22×C8×C29C2311yescharacteristic
74C22×C8×C29C2311yescharacteristic
75C29×#124—41no—
76C29×#124—41no—
77C29×C22⋊Q8—41no—
78C29×C22⋊Q8—41no—
79C29×#121—41no—
80C29×#121—41no—
81C29×#121—41no—
82C29×#121—41no—
83C29×#117—41no—
84C29×#117—41no—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—21no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29—21no—
89C2×C4⋊C4×C29—21no—
90C2×C4⋊C4×C29D411yescharacteristic
91C2×C4⋊C4×C29D411yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C4⋊C4×C29C2311yescharacteristic
94C2×C4⋊C4×C29C2311yescharacteristic
95C2×C4⋊C4×C29C2311yescharacteristic
96C2×C4⋊C4×C29C2311yescharacteristic
97C2×C22⋊C4×C29—21no—
98C2×C22⋊C4×C29—21no—
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×C22⋊C4×C29D411yescharacteristic
110C2×C22⋊C4×C29D411yescharacteristic
111C2×C42×C29C2311yescharacteristic
112C2×C42×C29C2311yescharacteristic
113C29×#106—41no—
114C29×#106—41no—
115C29×C4⋊C8—41no—
116C29×C4⋊C8—41no—
117C29×#103—41no—
118C29×#103—41no—
119C29×#103—41no—
120C29×#102—41no—
121C29×#102—41no—
122C29×#102—41no—
123C29×#102—41no—
124C29×#102—41no—
125C29×C22⋊C8—41no—
126C29×C22⋊C8—41no—
127C29×#95—21no—
128C29×#95—21no—
129C29×#95—21no—
130C29×#95—21no—
131C29×#95—21no—
132C24×C29—21no—
133C24×C29—21no—
134C24×C29C2×D411yescharacteristic
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29—21no—
138C2×Q8×C29—21no—
139C2×Q8×C29—21no—
140C2×Q8×C29—21no—
141C2×D4×C29—21no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29—21no—
145C2×D4×C29—21no—
146C2×D4×C29—21no—
147C2×D4×C29—21no—
148C2×D4×C29—21no—
149C2×D4×C29—21no—
150C2×D4×C29—21no—
151C2×D4×C29—21no—
152C2×D4×C29—21no—
153C2×D4×C29—42no—
154C2×D4×C29—42no—
155C2×D4×C29—81no—
156C2×D4×C29—81no—
157C2×D4×C29—81no—
158C2×D4×C29—81no—
159C22×C4×C29—21no—
160C22×C4×C29—21no—
161C22×C4×C29—21no—
162C22×C4×C29—21no—
163C22×C4×C29—21no—
164C22×C4×C29—21no—
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×C29C2×D411yescharacteristic
172C22×C4×C29C2×D411yescharacteristic
173C22×C4×C29C2×D411yescharacteristic
174C22×C4×C29C2×D411yescharacteristic
175C22×C4×C29C2×D411yescharacteristic
176C22×C4×C29C2411yescharacteristic
177SD16×C29—44no—
178D8×C29—44no—
179C2×C8×C29—21no—
180C2×C8×C29—21no—
181C2×C8×C29—21no—
182C2×C8×C29—21no—
183C2×C8×C29—21no—
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—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—21no—
193C4⋊C4×C29—21no—
194C4⋊C4×C29—21no—
195C4⋊C4×C29—21no—
196C4⋊C4×C29—21no—
197C4⋊C4×C29—21no—
198C4⋊C4×C29—21no—
199C4⋊C4×C29—21no—
200C4⋊C4×C29—21no—
201C4⋊C4×C29—41no—
202C4⋊C4×C29—41no—
203C4⋊C4×C29—42no—
204C4⋊C4×C29—81no—
205C4⋊C4×C29—81no—
206C4⋊C4×C29—81no—
207C4⋊C4×C29—81no—
208C22⋊C4×C29—41no—
209C22⋊C4×C29—41no—
210C22⋊C4×C29—42no—
211C22⋊C4×C29—42no—
212C22⋊C4×C29—42no—
213C22⋊C4×C29—42no—
214C22⋊C4×C29—42no—
215C22⋊C4×C29—81no—
216C22⋊C4×C29—81no—
217C22⋊C4×C29—81no—
218C22⋊C4×C29—81no—
219C22⋊C4×C29—81no—
220C22⋊C4×C29—81no—
221C22⋊C4×C29—81no—
222C42×C29—21no—
223C42×C29—21no—
224C42×C29—21no—
225C42×C29—21no—
226#32734C2911yesmaximal, characteristic, direct product factor, Sylow
227C23×C29—21no—
228C23×C29—21no—
229C23×C29—21no—
230C23×C29—21no—
231C23×C29—21no—
232C23×C29—21no—
233C23×C29—21no—
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×C29—41no—
247C23×C29—41no—
248C23×C29C22×D411yescharacteristic
249Q8×C29—41no—
250Q8×C29—41no—
251Q8×C29—41no—
252Q8×C29—41no—
253D4×C29—41no—
254D4×C29—41no—
255D4×C29—41no—
256D4×C29—41no—
257D4×C29—41no—
258D4×C29—41no—
259D4×C29—41no—
260D4×C29—41no—
261D4×C29—84no—
262D4×C29—84no—
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—21no—
270C2×C4×C29—21no—
271C2×C4×C29—21no—
272C2×C4×C29—21no—
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×C29H(5,𝔽2)11yescharacteristic
301C2×C4×C29H(5,𝔽2)11yescharacteristic
302C2×C4×C29H(5,𝔽2)11yescharacteristic
303C2×C4×C29H(5,𝔽2)11yescharacteristic
304C2×C4×C29H(5,𝔽2)11yescharacteristic
305C2×C4×C292−1+411yescharacteristic
306C8×C29—41no—
307C8×C29—41no—
308C8×C29—41no—
309C8×C29—41no—
310#2624C2×C2911yescharacteristic, complemented
311#2620C2×C2911yescharacteristic, complemented
312#2099C2×C2911yescharacteristic, complemented
313#2094C2×C2911yescharacteristic, complemented
314#2066C2×C2911yescharacteristic, complemented
315#2065C2×C2911yescharacteristic, complemented
316#2055C2×C2911yescharacteristic, complemented
317#2054C2×C2911yescharacteristic, complemented
318#2042C2×C2911yescharacteristic, complemented
319#2035C2×C2911yescharacteristic, complemented
320#2034C2×C2911yescharacteristic, complemented
321#2012C2×C2911yescharacteristic, complemented
322#2000C2×C2911yescharacteristic, complemented
323#1999C2×C2911yescharacteristic
324#1798C2×C2911yescharacteristic, complemented
325C22×C29—41no—
326C22×C29—41no—
327C22×C29—41no—
328C22×C29—41no—
329C22×C29—41no—
330C22×C29—41no—
331C22×C29—41no—
332C22×C29—81no—
333C22×C29—81no—
334C22×C29—81no—
335C22×C29—81no—
336C22×C29—81no—
337C22×C29—81no—
338C22×C29—81no—
339C22×C29—81no—
340C22×C29—81no—
341C22×C29—81no—
342C22×C29—81no—
343C22×C29—81no—
344C22×C29—81no—
345C22×C29—81no—
346C22×C29#53411yescharacteristic
347C22×C29#53511yescharacteristic
348C22×C29#53711yescharacteristic
349C22×C29#57611yescharacteristic
350C22×C29#57711yescharacteristic
351C22×C29#57711yescharacteristic
352C22×C29#57711yescharacteristic
353C4×C29—41no—
354C4×C29—41no—
355C4×C29—41no—
356C4×C29—41no—
357C4×C29—41no—
358C4×C29—81no—
359C4×C29—81no—
360C4×C29—81no—
361C4×C29—81no—
362C4×C29—81no—
363C4×C29—81no—
364C4×C29#56011yescharacteristic
365C4×C29#56011yescharacteristic
366C4×C29#56211yescharacteristic
367C4×C29#56211yescharacteristic
368C22×SD16C22×C2911yescharacteristic
369C22×D8C22×C2911yescharacteristic
370C2×#124C22×C2911yescharacteristic
371C2×C22⋊Q8C22×C2911yescharacteristic
372C2×#121C22×C2911yescharacteristic
373C2×#121C22×C2911yescharacteristic
374C2×#117C22×C2911yescharacteristic
375C2×#106C22×C2911yescharacteristic
376C2×#106C22×C2911yescharacteristic
377C2×C4⋊C8C22×C2911yescharacteristic
378C2×C4⋊C8C22×C2911yescharacteristic
379C2×#103C22×C2911yescharacteristic
380C2×#103C22×C2911yescharacteristic
381C2×#103C22×C2911yescharacteristic
382C2×#102C22×C2911yescharacteristic
383C2×#102C22×C2911yescharacteristic
384C2×#102C22×C2911yescharacteristic
385C2×#102C22×C2911yescharacteristic
386C2×#102C22×C2911yescharacteristic
387C2×C22⋊C8C22×C2911yescharacteristic
388C2×C22⋊C8C22×C2911yescharacteristic
389#399—21no—
390#397—21no—
391#396—21no—
392#396—21no—
393#394—21no—
394#394—21no—
395#394—21no—
396#394—21no—
397#391C22×C2911yescharacteristic
398#390C22×C2911yescharacteristic
399#390C22×C2911yescharacteristic
400#390C22×C2911yescharacteristic
401#389C22×C2911yescharacteristic
402#389C22×C2911yescharacteristic
403#384C22×C2911yescharacteristic
404#380C22×C2911yescharacteristic
405#340C22×C2911yescharacteristic
406#340C22×C2911yescharacteristic
407#340C22×C2911yescharacteristic
408#340C22×C2911yescharacteristic
409#336C22×C2911yescharacteristic
410#336C22×C2911yescharacteristic
411C2×C29—81no—
412C2×C29—161no—
413C2×C29—161no—
414C2×C29#281311yescharacteristic
415C2×C29#319811yescharacteristic
416C2×C29#320411yescharacteristic
417C2×C29#322111yescharacteristic
418C2×C29#322411yescharacteristic
419C2×C29#325711yescharacteristic
420C2×C29#326311yescharacteristic
421C22×Q8C23×C2911yescharacteristic
422C22×D4—21no—
423C22×D4—21no—
424C22×D4C23×C2911yescharacteristic
425C22×D4C23×C2911yescharacteristic
426C23×C4C23×C2911yescharacteristic
427C2×SD16—41no—
428C2×SD16—41no—
429C2×SD16—41no—
430C2×D8—41no—
431C2×D8—41no—
432C2×D8—41no—
433C22×C8C23×C2911yescharacteristic
434C22×C8C23×C2911yescharacteristic
435C22×C8C23×C2911yescharacteristic
436C22×C8C23×C2911yescharacteristic
437#124—41no—
438#124—41no—
439C22⋊Q8—41no—
440C22⋊Q8—41no—
441#121—41no—
442#121—41no—
443#121—41no—
444#121—41no—
445#117—41no—
446#117—41no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4D4×C2911yescharacteristic
453C2×C4⋊C4D4×C2911yescharacteristic
454C2×C4⋊C4C23×C2911yescharacteristic
455C2×C4⋊C4C23×C2911yescharacteristic
456C2×C4⋊C4C23×C2911yescharacteristic
457C2×C4⋊C4C23×C2911yescharacteristic
458C2×C4⋊C4C23×C2911yescharacteristic
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×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4D4×C2911yescharacteristic
472C2×C22⋊C4D4×C2911yescharacteristic
473C2×C42C23×C2911yescharacteristic
474C2×C42C23×C2911yescharacteristic
475#106—41no—
476#106—41no—
477C4⋊C8—41no—
478C4⋊C8—41no—
479#103—41no—
480#103—41no—
481#103—41no—
482#102—41no—
483#102—41no—
484#102—41no—
485#102—41no—
486#102—41no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494C29#3273411yescharacteristic, direct product factor, Sylow
495C24—21no—
496C24—21no—
497C24C2×D4×C2911yescharacteristic
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—42no—
517C2×D4—42no—
518C2×D4—81no—
519C2×D4—81no—
520C2×D4—81no—
521C2×D4—81no—
522C22×C4—21no—
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×C4C2×D4×C2911yescharacteristic
535C22×C4C2×D4×C2911yescharacteristic
536C22×C4C2×D4×C2911yescharacteristic
537C22×C4C2×D4×C2911yescharacteristic
538C22×C4C2×D4×C2911yescharacteristic
539C22×C4C24×C2911yescharacteristic
540SD16—44no—
541D8—44no—
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—21no—
552C2×C8—21no—
553C2×C8—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—41no—
565C4⋊C4—41no—
566C4⋊C4—42no—
567C4⋊C4—81no—
568C4⋊C4—81no—
569C4⋊C4—81no—
570C4⋊C4—81no—
571C22⋊C4—41no—
572C22⋊C4—41no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—42no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—81no—
579C22⋊C4—81no—
580C22⋊C4—81no—
581C22⋊C4—81no—
582C22⋊C4—81no—
583C22⋊C4—81no—
584C22⋊C4—81no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23C22×D4×C2911yescharacteristic
611Q8—41no—
612Q8—41no—
613Q8—41no—
614Q8—41no—
615D4—41no—
616D4—41no—
617D4—41no—
618D4—41no—
619D4—41no—
620D4—41no—
621D4—41no—
622D4—41no—
623D4—84no—
624D4—84no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
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×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4C29×H(5,𝔽2)11yescharacteristic
663C2×C4C29×H(5,𝔽2)11yescharacteristic
664C2×C4C29×H(5,𝔽2)11yescharacteristic
665C2×C4C29×H(5,𝔽2)11yescharacteristic
666C2×C4C29×H(5,𝔽2)11yescharacteristic
667C2×C4C29×2−1+411yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—81no—
680C22—81no—
681C22—81no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22C29×#53411yescharacteristic
694C22C29×#53511yescharacteristic
695C22C29×#53711yescharacteristic
696C22C29×#57611yescharacteristic
697C22C29×#57711yescharacteristic
698C22C29×#57711yescharacteristic
699C22C29×#57711yescharacteristic
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4C29×#56011yescharacteristic
712C4C29×#56011yescharacteristic
713C4C29×#56211yescharacteristic
714C4C29×#56211yescharacteristic
715C2—81no—
716C2—161no—
717C2—161no—
718C2C29×#281311yescharacteristic
719C2C29×#319811yescharacteristic
720C2C29×#320411yescharacteristic
721C2C29×#322111yescharacteristic
722C2C29×#322411yescharacteristic
723C2C29×#325711yescharacteristic
724C2C29×#326311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#1999C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2624C2semidirect
2. C29×#2620C2semidirect
3. C29×#2099C2semidirect
4. C29×#2094C2semidirect
5. C29×#2066C2semidirect
6. C29×#2065C2semidirect
7. C29×#2055C2semidirect
8. C29×#2054C2semidirect
9. C29×#2042C2semidirect
10. C29×#2035C2semidirect
11. C29×#2034C2semidirect
12. C29×#2012C2semidirect
13. C29×#2000C2semidirect
15. C29×#1798C2semidirect
226. #32734C29direct (N × H)
310. #2624C2×C29semidirect
311. #2620C2×C29semidirect
312. #2099C2×C29semidirect
313. #2094C2×C29semidirect
314. #2066C2×C29semidirect
315. #2065C2×C29semidirect
316. #2055C2×C29semidirect
317. #2054C2×C29semidirect
318. #2042C2×C29semidirect
319. #2035C2×C29semidirect
320. #2034C2×C29semidirect
321. #2012C2×C29semidirect
322. #2000C2×C29semidirect
324. #1798C2×C29semidirect
494. C29#32734direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26242
C29×#26202
C29×#20992
C29×#20942
C29×#20662
C29×#20652
C29×#20552
C29×#20542
C29×#20422
C29×#20352
C29×#20342
C29×#20122
C29×#20002
C29×#19992
C29×#17982
#3273429