Finite Group Databasebeta

← C29×#19069 #20313969

Subgroups — C29×#19069 #20313969

Order 7424.

886 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3545C211yesmaximal, characteristic
2C29×#3240C211yesmaximal, characteristic, complemented
3C29×#3215C211yesmaximal, characteristic, complemented
4C29×#3172C211yesmaximal, characteristic, complemented
5C29×#1664C211yesmaximal, characteristic, complemented
6C29×#1662C211yesmaximal, characteristic, complemented
7C29×#1661C211yesmaximal, characteristic, complemented
8C29×#1661C211yesmaximal, characteristic, complemented
9C29×#1661C211yesmaximal, characteristic, complemented
10C29×#1660C211yesmaximal, characteristic, complemented
11C29×#1659C211yesmaximal, characteristic, complemented
12C29×#1659C211yesmaximal, characteristic, complemented
13C29×#1535C211yesmaximal, characteristic, complemented
14C29×#1529C211yesmaximal, characteristic, complemented
15C29×#1527C211yesmaximal, characteristic, complemented
16C29×#563C2211yescharacteristic
17C29×#562C2211yescharacteristic
18C29×#562C2211yescharacteristic
19C29×H(3,𝔽4)C2211yescharacteristic
20C29×#555—21no—
21C29×#551—21no—
22C29×#551—21no—
23C29×#551—21no—
24C29×#546—21no—
25C29×#546—21no—
26C29×#542—21no—
27C29×#542—21no—
28C29×#538—21no—
29C29×#538—21no—
30C29×#536—21no—
31C29×#534—21no—
32C29×#533C2211yescharacteristic, complemented
33C29×#529C2211yescharacteristic
34C29×#529C2211yescharacteristic
35C2×C29×#124C2211yescharacteristic
36C29×#501C2211yescharacteristic, complemented
37C29×#501C2211yescharacteristic, complemented
38C29×#501C2211yescharacteristic, complemented
39C29×#497C2211yescharacteristic
40C29×#497C2211yescharacteristic, complemented
41C29×#497C2211yescharacteristic, complemented
42C29×#491C2211yescharacteristic, complemented
43C29×#489C2211yescharacteristic
44C29×#489C2211yescharacteristic, complemented
45C29×#489C2211yescharacteristic, complemented
46C29×#489C2211yescharacteristic, complemented
47C29×#489C2211yescharacteristic, complemented
48C29×#485—21no—
49C29×#482—21no—
50C29×#479—21no—
51C29×#478—21no—
52C29×#470—21no—
53C29×#468—21no—
54C29×#464—21no—
55C29×#464—21no—
56C29×#451—21no—
57C29×#450—21no—
58C4×Q16×C29—21no—
59C4×SD16×C29—21no—
60C29×#432C2211yescharacteristic, complemented
61C29×#432C2211yescharacteristic, complemented
62C4×M16×C29C2211yescharacteristic, complemented
63C29×#330C2211yescharacteristic, complemented
64C29×#330C2211yescharacteristic, complemented
65C29×#330C2211yescharacteristic, complemented
66C29×#330C2211yescharacteristic, complemented
67C29×#329C2211yescharacteristic
68C29×#329C2211yescharacteristic
69C29×#329C2211yescharacteristic, complemented
70C29×#329C2211yescharacteristic, complemented
71C29×#329C2211yescharacteristic, complemented
72C29×#329C2211yescharacteristic, complemented
73C29×#329C2211yescharacteristic, complemented
74C29×#329C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C22×Q8×C29D411yescharacteristic
77C22×D4×C29—21no—
78C22×D4×C29D411yescharacteristic
79C2×Q16×C29—21no—
80C2×Q16×C29—21no—
81C2×Q16×C29—21no—
82C2×SD16×C29—21no—
83C2×SD16×C29—21no—
84C2×SD16×C29—21no—
85C2×M16×C29—21no—
86C29×C4⋊Q8—21no—
87C29×C4⋊Q8—21no—
88C29×C4⋊Q8C2311yescharacteristic
89C29×C4⋊Q8C2311yescharacteristic
90C29×#126—21no—
91C29×#126—21no—
92C29×#126—21no—
93C29×#126—21no—
94C29×#126—21no—
95C29×#126—21no—
96C29×#125—21no—
97C29×#125C2311yescharacteristic
98C29×#125C2311yescharacteristic
99C29×#124—21no—
100C29×#124—21no—
101C29×#124—21no—
102C29×#124—21no—
103C29×#124—21no—
104C29×#124—21no—
105C29×#124—21no—
106C29×#124—21no—
107C29×#124D411yescharacteristic
108C29×#124D411yescharacteristic
109C29×#124C2311yescharacteristic
110C29×#124C2311yescharacteristic
111C29×#124C2311yescharacteristic
112C29×#124C2311yescharacteristic
113C29×#123—21no—
114C29×#123—21no—
115C29×#123—21no—
116C29×#123—21no—
117C29×#123—21no—
118C29×#123—21no—
119C29×#123—21no—
120C29×#123—21no—
121C29×#123—21no—
122C29×#123—21no—
123C29×#123—21no—
124C29×#123—21no—
125C29×C22⋊Q8—21no—
126C29×C22⋊Q8—21no—
127C29×C22⋊Q8—21no—
128C29×C22⋊Q8—21no—
129C29×C22⋊Q8—21no—
130C29×C22⋊Q8—21no—
131C29×C22⋊Q8—21no—
132C29×C22⋊Q8—21no—
133C29×C22⋊Q8—21no—
134C29×C22⋊Q8—21no—
135C29×C22⋊Q8D411yescharacteristic
136C29×C22⋊Q8D411yescharacteristic
137C29×#121—21no—
138C29×#121—21no—
139C29×#121—21no—
140C29×#121—21no—
141C29×#121—21no—
142C29×#121—21no—
143C29×#121—21no—
144C29×#121—21no—
145C29×#121D411yescharacteristic
146C29×#121D411yescharacteristic
147C29×#120—21no—
148C29×#120—21no—
149C29×#120—21no—
150C29×#120—21no—
151C29×#120—21no—
152C29×#120—21no—
153C4×Q8×C29—21no—
154C4×Q8×C29—21no—
155C4×Q8×C29D411yescharacteristic
156C4×Q8×C29D411yescharacteristic
157C4×D4×C29—21no—
158C4×D4×C29—21no—
159C4×D4×C29—21no—
160C4×D4×C29—21no—
161C4×D4×C29—21no—
162C4×D4×C29—21no—
163C4×D4×C29D411yescharacteristic
164C4×D4×C29D411yescharacteristic
165C29×#117—21no—
166C29×#117—21no—
167C29×#117—21no—
168C29×#117—21no—
169C29×#117—21no—
170C29×#117—21no—
171C2×C22⋊C4×C29—21no—
172C2×C22⋊C4×C29—21no—
173C2×C22⋊C4×C29—21no—
174C2×C22⋊C4×C29—21no—
175C2×C22⋊C4×C29—21no—
176C2×C42×C29C2311yescharacteristic
177C29×#107—21no—
178C29×#107—21no—
179C29×#107—21no—
180C29×#106—21no—
181C29×#106—21no—
182C29×#106—21no—
183C29×C4⋊C8—21no—
184C29×C4⋊C8—21no—
185C29×#103—21no—
186C29×#103—21no—
187C29×#103—21no—
188C29×#103—21no—
189C29×#103—21no—
190C29×#103—21no—
191C29×#103—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×#102—21no—
197C29×C22⋊C8—21no—
198C29×C22⋊C8—21no—
199C29×#97C2311yescharacteristic
200C29×#97C2311yescharacteristic
201C29×#97C2311yescharacteristic
202C29×#97C2311yescharacteristic
203C29×#97C2311yescharacteristic
204C29×#97C2311yescharacteristic
205C4×C8×C29—21no—
206C24×C29—21no—
207C24×C29—21no—
208#41×C29—82no—
209C2×Q8×C29—21no—
210C2×Q8×C29—21no—
211C2×Q8×C29—21no—
212C2×Q8×C29—21no—
213C2×Q8×C29—81no—
214C2×Q8×C29C2×D411yescharacteristic
215C2×Q8×C29C2×D411yescharacteristic
216C2×Q8×C29C2×D411yescharacteristic
217C2×Q8×C29C2×D411yescharacteristic
218C2×D4×C29—21no—
219C2×D4×C29—21no—
220C2×D4×C29—21no—
221C2×D4×C29—21no—
222C2×D4×C29—21no—
223C2×D4×C29—21no—
224C2×D4×C29—21no—
225C2×D4×C29—21no—
226C2×D4×C29—21no—
227C2×D4×C29—21no—
228C2×D4×C29—81no—
229C2×D4×C29—82no—
230C2×D4×C29C2×D411yescharacteristic
231C2×D4×C29C2×D411yescharacteristic
232C2×D4×C29C2×D411yescharacteristic
233C2×D4×C29C2×D411yescharacteristic
234C22×C4×C29—21no—
235C22×C4×C29—21no—
236C22×C4×C29—21no—
237C22×C4×C29—21no—
238C22×C4×C29—21no—
239C22×C4×C29—21no—
240C22×C4×C29—21no—
241C22×C4×C29—21no—
242C22×C4×C29C2×D411yescharacteristic
243C22×C4×C29C2×D411yescharacteristic
244C22×C4×C29C2×D411yescharacteristic
245Q16×C29—42no—
246Q16×C29—81no—
247Q16×C29—81no—
248SD16×C29—42no—
249SD16×C29—81no—
250SD16×C29—81no—
251M16×C29—42no—
252C2×C8×C29—21no—
253C2×C8×C29—21no—
254C2×C8×C29—21no—
255C2×C8×C29—21no—
256C2×C8×C29—21no—
257C2×C8×C29—21no—
258C4⋊C4×C29—21no—
259C4⋊C4×C29—21no—
260C4⋊C4×C29—21no—
261C4⋊C4×C29—21no—
262C4⋊C4×C29—21no—
263C4⋊C4×C29—21no—
264C4⋊C4×C29—21no—
265C4⋊C4×C29—21no—
266C4⋊C4×C29—21no—
267C4⋊C4×C29—21no—
268C4⋊C4×C29—21no—
269C4⋊C4×C29—21no—
270C4⋊C4×C29—21no—
271C4⋊C4×C29—21no—
272C4⋊C4×C29—21no—
273C4⋊C4×C29—21no—
274C4⋊C4×C29—21no—
275C4⋊C4×C29—21no—
276C4⋊C4×C29—41no—
277C4⋊C4×C29—41no—
278C4⋊C4×C29C2×D411yescharacteristic
279C4⋊C4×C29C2×D411yescharacteristic
280C4⋊C4×C29C2×D411yescharacteristic
281C4⋊C4×C29C2×D411yescharacteristic
282C22⋊C4×C29—21no—
283C22⋊C4×C29—21no—
284C22⋊C4×C29—21no—
285C22⋊C4×C29—21no—
286C22⋊C4×C29—21no—
287C22⋊C4×C29—21no—
288C22⋊C4×C29—21no—
289C22⋊C4×C29—21no—
290C22⋊C4×C29—21no—
291C22⋊C4×C29—21no—
292C22⋊C4×C29—21no—
293C22⋊C4×C29—21no—
294C22⋊C4×C29—21no—
295C22⋊C4×C29—21no—
296C22⋊C4×C29—21no—
297C22⋊C4×C29—21no—
298C22⋊C4×C29—21no—
299C22⋊C4×C29—21no—
300C22⋊C4×C29—21no—
301C22⋊C4×C29—21no—
302C22⋊C4×C29—21no—
303C22⋊C4×C29—21no—
304C22⋊C4×C29—21no—
305C22⋊C4×C29—21no—
306C22⋊C4×C29—21no—
307C22⋊C4×C29—21no—
308C22⋊C4×C29—21no—
309C22⋊C4×C29—21no—
310C22⋊C4×C29—41no—
311C42×C29—21no—
312C42×C29—21no—
313C42×C29—21no—
314C42×C29—21no—
315C42×C29—41no—
316C42×C29C2×D411yescharacteristic
317C42×C29C2×D411yescharacteristic
318C42×C29C2×D411yescharacteristic
319C42×C29C2411yescharacteristic
320#19069C2911yesmaximal, characteristic, direct product factor, Sylow
321C23×C29—21no—
322C23×C29—21no—
323C23×C29—21no—
324C23×C29—21no—
325C23×C29—42no—
326C23×C29—81no—
327C23×C29—81no—
328C23×C29—81no—
329C23×C29—81no—
330C23×C29—81no—
331C23×C29#12011yescharacteristic
332Q8×C29—41no—
333Q8×C29—41no—
334Q8×C29—41no—
335Q8×C29—41no—
336Q8×C29—41no—
337Q8×C29—41no—
338Q8×C29—41no—
339Q8×C29—41no—
340Q8×C29—81no—
341Q8×C29—81no—
342D4×C29—41no—
343D4×C29—41no—
344D4×C29—41no—
345D4×C29—41no—
346D4×C29—42no—
347D4×C29—42no—
348D4×C29—81no—
349D4×C29—81no—
350D4×C29—81no—
351D4×C29—81no—
352D4×C29—81no—
353D4×C29—81no—
354D4×C29—81no—
355D4×C29—81no—
356C2×C4×C29—21no—
357C2×C4×C29—21no—
358C2×C4×C29—21no—
359C2×C4×C29—21no—
360C2×C4×C29—21no—
361C2×C4×C29—21no—
362C2×C4×C29—21no—
363C2×C4×C29—21no—
364C2×C4×C29—41no—
365C2×C4×C29—41no—
366C2×C4×C29—41no—
367C2×C4×C29—42no—
368C2×C4×C29—41no—
369C2×C4×C29—41no—
370C2×C4×C29—81no—
371C2×C4×C29—81no—
372C2×C4×C29—81no—
373C2×C4×C29—81no—
374C2×C4×C29—81no—
375C2×C4×C29—81no—
376C2×C4×C29—81no—
377C2×C4×C29#12011yescharacteristic
378C2×C4×C29#12011yescharacteristic
379C2×C4×C29#12011yescharacteristic
380C2×C4×C29C22×D411yescharacteristic
381C2×C4×C29C22×D411yescharacteristic
382C2×C4×C29C22×D411yescharacteristic
383C8×C29—22no—
384C8×C29—41no—
385C8×C29—41no—
386C8×C29—41no—
387C8×C29—41no—
388C8×C29—41no—
389#3545C2×C2911yescharacteristic
390#3240C2×C2911yescharacteristic, complemented
391#3215C2×C2911yescharacteristic, complemented
392#3172C2×C2911yescharacteristic, complemented
393#1664C2×C2911yescharacteristic, complemented
394#1662C2×C2911yescharacteristic, complemented
395#1661C2×C2911yescharacteristic, complemented
396#1661C2×C2911yescharacteristic, complemented
397#1661C2×C2911yescharacteristic, complemented
398#1660C2×C2911yescharacteristic, complemented
399#1659C2×C2911yescharacteristic, complemented
400#1659C2×C2911yescharacteristic, complemented
401#1535C2×C2911yescharacteristic, complemented
402#1529C2×C2911yescharacteristic, complemented
403#1527C2×C2911yescharacteristic, complemented
404C22×C29—21no—
405C22×C29—21no—
406C22×C29—21no—
407C22×C29—41no—
408C22×C29—41no—
409C22×C29—41no—
410C22×C29—41no—
411C22×C29—41no—
412C22×C29—41no—
413C22×C29—41no—
414C22×C29—41no—
415C22×C29—41no—
416C22×C29—41no—
417C22×C29—41no—
418C22×C29—41no—
419C22×C29—162no—
420C22×C29—162no—
421C22×C29C2×#12011yescharacteristic
422C4×C29—21no—
423C4×C29—21no—
424C4×C29—21no—
425C4×C29—21no—
426C4×C29—21no—
427C4×C29—21no—
428C4×C29—41no—
429C4×C29—41no—
430C4×C29—41no—
431C4×C29—41no—
432C4×C29—41no—
433C4×C29—41no—
434C4×C29—41no—
435C4×C29—41no—
436C4×C29—81no—
437C4×C29—81no—
438#563C22×C2911yescharacteristic
439#562C22×C2911yescharacteristic
440#562C22×C2911yescharacteristic
441H(3,𝔽4)C22×C2911yescharacteristic
442#555—21no—
443#551—21no—
444#551—21no—
445#551—21no—
446#546—21no—
447#546—21no—
448#542—21no—
449#542—21no—
450#538—21no—
451#538—21no—
452#536—21no—
453#534—21no—
454#533C22×C2911yescharacteristic, complemented
455#529C22×C2911yescharacteristic
456#529C22×C2911yescharacteristic
457C2×#124C22×C2911yescharacteristic
458#501C22×C2911yescharacteristic, complemented
459#501C22×C2911yescharacteristic, complemented
460#501C22×C2911yescharacteristic, complemented
461#497C22×C2911yescharacteristic
462#497C22×C2911yescharacteristic, complemented
463#497C22×C2911yescharacteristic, complemented
464#491C22×C2911yescharacteristic, complemented
465#489C22×C2911yescharacteristic
466#489C22×C2911yescharacteristic, complemented
467#489C22×C2911yescharacteristic, complemented
468#489C22×C2911yescharacteristic, complemented
469#489C22×C2911yescharacteristic, complemented
470#485—21no—
471#482—21no—
472#479—21no—
473#478—21no—
474#470—21no—
475#468—21no—
476#464—21no—
477#464—21no—
478#451—21no—
479#450—21no—
480C4×Q16—21no—
481C4×SD16—21no—
482#432C22×C2911yescharacteristic, complemented
483#432C22×C2911yescharacteristic, complemented
484C4×M16C22×C2911yescharacteristic, complemented
485#330C22×C2911yescharacteristic, complemented
486#330C22×C2911yescharacteristic, complemented
487#330C22×C2911yescharacteristic, complemented
488#330C22×C2911yescharacteristic, complemented
489#329C22×C2911yescharacteristic
490#329C22×C2911yescharacteristic
491#329C22×C2911yescharacteristic, complemented
492#329C22×C2911yescharacteristic, complemented
493#329C22×C2911yescharacteristic, complemented
494#329C22×C2911yescharacteristic, complemented
495#329C22×C2911yescharacteristic, complemented
496#329C22×C2911yescharacteristic, complemented
497C2×C29—41no—
498C2×C29—81no—
499C2×C29—81no—
500C2×C29—81no—
501C2×C29—81no—
502C2×C29#301811yescharacteristic
503C2×C29#301911yescharacteristic
504C2×C29#302211yescharacteristic
505C2×#41—21no—
506C22×Q8D4×C2911yescharacteristic
507C22×D4—21no—
508C22×D4D4×C2911yescharacteristic
509C2×Q16—21no—
510C2×Q16—21no—
511C2×Q16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16—21no—
515C2×M16—21no—
516C4⋊Q8—21no—
517C4⋊Q8—21no—
518C4⋊Q8C23×C2911yescharacteristic
519C4⋊Q8C23×C2911yescharacteristic
520#126—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#126—21no—
526#125—21no—
527#125C23×C2911yescharacteristic
528#125C23×C2911yescharacteristic
529#124—21no—
530#124—21no—
531#124—21no—
532#124—21no—
533#124—21no—
534#124—21no—
535#124—21no—
536#124—21no—
537#124D4×C2911yescharacteristic
538#124D4×C2911yescharacteristic
539#124C23×C2911yescharacteristic
540#124C23×C2911yescharacteristic
541#124C23×C2911yescharacteristic
542#124C23×C2911yescharacteristic
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552#123—21no—
553#123—21no—
554#123—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—21no—
562C22⋊Q8—21no—
563C22⋊Q8—21no—
564C22⋊Q8—21no—
565C22⋊Q8D4×C2911yescharacteristic
566C22⋊Q8D4×C2911yescharacteristic
567#121—21no—
568#121—21no—
569#121—21no—
570#121—21no—
571#121—21no—
572#121—21no—
573#121—21no—
574#121—21no—
575#121D4×C2911yescharacteristic
576#121D4×C2911yescharacteristic
577#120—21no—
578#120—21no—
579#120—21no—
580#120—21no—
581#120—21no—
582#120—21no—
583C4×Q8—21no—
584C4×Q8—21no—
585C4×Q8D4×C2911yescharacteristic
586C4×Q8D4×C2911yescharacteristic
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4—21no—
591C4×D4—21no—
592C4×D4—21no—
593C4×D4D4×C2911yescharacteristic
594C4×D4D4×C2911yescharacteristic
595#117—21no—
596#117—21no—
597#117—21no—
598#117—21no—
599#117—21no—
600#117—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C42C23×C2911yescharacteristic
607#107—21no—
608#107—21no—
609#107—21no—
610#106—21no—
611#106—21no—
612#106—21no—
613C4⋊C8—21no—
614C4⋊C8—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103—21no—
622#102—21no—
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627C22⋊C8—21no—
628C22⋊C8—21no—
629#97C23×C2911yescharacteristic
630#97C23×C2911yescharacteristic
631#97C23×C2911yescharacteristic
632#97C23×C2911yescharacteristic
633#97C23×C2911yescharacteristic
634#97C23×C2911yescharacteristic
635C4×C8—21no—
636C29#1906911yescharacteristic, direct product factor, Sylow
637C24—21no—
638C24—21no—
639#41—82no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—81no—
645C2×Q8C2×D4×C2911yescharacteristic
646C2×Q8C2×D4×C2911yescharacteristic
647C2×Q8C2×D4×C2911yescharacteristic
648C2×Q8C2×D4×C2911yescharacteristic
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—81no—
660C2×D4—82no—
661C2×D4C2×D4×C2911yescharacteristic
662C2×D4C2×D4×C2911yescharacteristic
663C2×D4C2×D4×C2911yescharacteristic
664C2×D4C2×D4×C2911yescharacteristic
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4C2×D4×C2911yescharacteristic
674C22×C4C2×D4×C2911yescharacteristic
675C22×C4C2×D4×C2911yescharacteristic
676Q16—42no—
677Q16—81no—
678Q16—81no—
679SD16—42no—
680SD16—81no—
681SD16—81no—
682M16—42no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—41no—
708C4⋊C4—41no—
709C4⋊C4C2×D4×C2911yescharacteristic
710C4⋊C4C2×D4×C2911yescharacteristic
711C4⋊C4C2×D4×C2911yescharacteristic
712C4⋊C4C2×D4×C2911yescharacteristic
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—41no—
742C42—21no—
743C42—21no—
744C42—21no—
745C42—21no—
746C42—41no—
747C42C2×D4×C2911yescharacteristic
748C42C2×D4×C2911yescharacteristic
749C42C2×D4×C2911yescharacteristic
750C42C24×C2911yescharacteristic
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—42no—
756C23—81no—
757C23—81no—
758C23—81no—
759C23—81no—
760C23—81no—
761C23C29×#12011yescharacteristic
762Q8—41no—
763Q8—41no—
764Q8—41no—
765Q8—41no—
766Q8—41no—
767Q8—41no—
768Q8—41no—
769Q8—41no—
770Q8—81no—
771Q8—81no—
772D4—41no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—42no—
777D4—42no—
778D4—81no—
779D4—81no—
780D4—81no—
781D4—81no—
782D4—81no—
783D4—81no—
784D4—81no—
785D4—81no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—81no—
804C2×C4—81no—
805C2×C4—81no—
806C2×C4—81no—
807C2×C4C29×#12011yescharacteristic
808C2×C4C29×#12011yescharacteristic
809C2×C4C29×#12011yescharacteristic
810C2×C4C22×D4×C2911yescharacteristic
811C2×C4C22×D4×C2911yescharacteristic
812C2×C4C22×D4×C2911yescharacteristic
813C8—22no—
814C8—41no—
815C8—41no—
816C8—41no—
817C8—41no—
818C8—41no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—162no—
835C22—162no—
836C22C2×C29×#12011yescharacteristic
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—41no—
844C4—41no—
845C4—41no—
846C4—41no—
847C4—41no—
848C4—41no—
849C4—41no—
850C4—41no—
851C4—81no—
852C4—81no—
853C2—41no—
854C2—81no—
855C2—81no—
856C2—81no—
857C2—81no—
858C2C29×#301811yescharacteristic
859C2C29×#301911yescharacteristic
860C2C29×#302211yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3545C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#3240C2semidirect
3. C29×#3215C2semidirect
4. C29×#3172C2semidirect
5. C29×#1664C2semidirect
6. C29×#1662C2semidirect
7. C29×#1661C2semidirect
8. C29×#1661C2semidirect
9. C29×#1661C2semidirect
10. C29×#1660C2semidirect
11. C29×#1659C2semidirect
12. C29×#1659C2semidirect
13. C29×#1535C2semidirect
14. C29×#1529C2semidirect
15. C29×#1527C2semidirect
32. C29×#533C22semidirect
36. C29×#501C22semidirect
37. C29×#501C22semidirect
38. C29×#501C22semidirect
40. C29×#497C22semidirect
41. C29×#497C22semidirect
42. C29×#491C22semidirect
44. C29×#489C22semidirect
45. C29×#489C22semidirect
46. C29×#489C22semidirect
47. C29×#489C22semidirect
60. C29×#432C22semidirect
61. C29×#432C22semidirect
62. C4×M16×C29C22semidirect
63. C29×#330C22semidirect
64. C29×#330C22semidirect
65. C29×#330C22semidirect
66. C29×#330C22semidirect
69. C29×#329C22semidirect
70. C29×#329C22semidirect
71. C29×#329C22semidirect
72. C29×#329C22semidirect
73. C29×#329C22semidirect
74. C29×#329C22semidirect
320. #19069C29direct (N × H)
390. #3240C2×C29semidirect
391. #3215C2×C29semidirect
392. #3172C2×C29semidirect
393. #1664C2×C29semidirect
394. #1662C2×C29semidirect
395. #1661C2×C29semidirect
396. #1661C2×C29semidirect
397. #1661C2×C29semidirect
398. #1660C2×C29semidirect
399. #1659C2×C29semidirect
400. #1659C2×C29semidirect
401. #1535C2×C29semidirect
402. #1529C2×C29semidirect
403. #1527C2×C29semidirect
454. #533C22×C29semidirect
458. #501C22×C29semidirect
459. #501C22×C29semidirect
460. #501C22×C29semidirect
462. #497C22×C29semidirect
463. #497C22×C29semidirect
464. #491C22×C29semidirect
466. #489C22×C29semidirect
467. #489C22×C29semidirect
468. #489C22×C29semidirect
469. #489C22×C29semidirect
482. #432C22×C29semidirect
483. #432C22×C29semidirect
484. C4×M16C22×C29semidirect
485. #330C22×C29semidirect
486. #330C22×C29semidirect
487. #330C22×C29semidirect
488. #330C22×C29semidirect
491. #329C22×C29semidirect
492. #329C22×C29semidirect
493. #329C22×C29semidirect
494. #329C22×C29semidirect
495. #329C22×C29semidirect
496. #329C22×C29semidirect
636. C29#19069direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35452
C29×#32402
C29×#32152
C29×#31722
C29×#16642
C29×#16622
C29×#16612
C29×#16602
C29×#16592
C29×#15352
C29×#15292
C29×#15272
#1906929