Finite Group Databasebeta

← C29×#11037 #20305937

Subgroups — C29×#11037 #20305937

Order 7424.

1252 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#575C211yesmaximal, characteristic
2C2×C29×#421C211yesmaximal, characteristic, complemented
3C29×#2896C211yesmaximal, characteristic, complemented
4C2×C29×#413C211yesmaximal, characteristic, complemented
5C29×#2879C211yesmaximal, characteristic, complemented
6C2×C29×#344C211yesmaximal, characteristic, complemented
7C29×#1738C211yesmaximal, characteristic, complemented
8C22×#41×C29C2211yescharacteristic
9C22×#41×C29C2211yescharacteristic
10C29×#575—22no—
11C29×#575—22no—
12C29×#575—22no—
13C29×#575C414yescomplemented
14C2×C29×#137—21no—
15C2×C29×#137—21no—
16C2×C29×AGL(1,ℤ/8)—21no—
17C2×C29×AGL(1,ℤ/8)—21no—
18C2×C29×#135—22no—
19C22×M16×C29C2211yescharacteristic
20C22×M16×C29C2211yescharacteristic
21C22×M16×C29C2211yescharacteristic
22C22×M16×C29C2211yescharacteristic
23C2×C29×#117C2211yescharacteristic
24C29×#421—22no—
25C29×#421—22no—
26C2×C29×#104—22no—
27C29×#419—21no—
28C29×#418—21no—
29C29×#417—22no—
30C29×#416—22no—
31C29×#413—22no—
32C29×#413—22no—
33C2×C29×#101—21no—
34C2×C29×#100—21no—
35C29×#408—22no—
36C29×#408—22no—
37C29×#407—22no—
38C29×#344—22no—
39C29×#341—22no—
40C2×#41×C29—21no—
41C2×#41×C29—21no—
42C2×#41×C29—21no—
43C2×#41×C29—21no—
44C2×#41×C29—21no—
45C2×#41×C29—21no—
46C2×#41×C29—21no—
47C2×#41×C29—21no—
48C2×#41×C29—21no—
49C2×#41×C29—21no—
50C2×#41×C29—21no—
51C2×#41×C29—21no—
52C2×#41×C29—21no—
53C2×#41×C29—21no—
54C2×#41×C29—21no—
55C2×#41×C29—21no—
56C2×#41×C29—21no—
57C2×#41×C29—21no—
58C2×#41×C29—21no—
59C2×#41×C29—21no—
60C2×#41×C29C2×C412yes—
61C2×#41×C29C2×C412yes—
62C2×#41×C29D412yes—
63C2×#41×C29D412yes—
64C22×Q8×C29D411yescharacteristic
65C22×Q8×C29D411yescharacteristic
66C22×D4×C29—21no—
67C22×D4×C29—21no—
68C22×D4×C29D411yescharacteristic
69C22×D4×C29D411yescharacteristic
70C23×C4×C29—21no—
71C23×C4×C29—21no—
72C23×C4×C29C2311yescharacteristic
73C29×#137—24no—
74C29×#137—24no—
75C29×#137—24no—
76C29×#137—24no—
77C29×AGL(1,ℤ/8)—24no—
78C29×AGL(1,ℤ/8)—24no—
79C29×AGL(1,ℤ/8)—24no—
80C29×AGL(1,ℤ/8)—24no—
81C29×#135—28no—
82C29×#135—28no—
83C2×Q16×C29—22no—
84C2×SD16×C29—22no—
85C2×SD16×C29—22no—
86C2×D8×C29—22no—
87C2×M16×C29—21no—
88C2×M16×C29—21no—
89C2×M16×C29—21no—
90C2×M16×C29—21no—
91C2×M16×C29—21no—
92C2×M16×C29—21no—
93C2×M16×C29—21no—
94C2×M16×C29—21no—
95C2×M16×C29—21no—
96C2×M16×C29—21no—
97C2×M16×C29—21no—
98C2×M16×C29—21no—
99C2×M16×C29—21no—
100C2×M16×C29—21no—
101C2×M16×C29—21no—
102C2×M16×C29—21no—
103C2×M16×C29—21no—
104C2×M16×C29—21no—
105C2×M16×C29—21no—
106C2×M16×C29C2×C412yes—
107C2×M16×C29D412yes—
108C2×M16×C29D412yes—
109C2×M16×C29D412yes—
110C2×M16×C29D412yes—
111C22×C8×C29—21no—
112C22×C8×C29—21no—
113C22×C8×C29—21no—
114C22×C8×C29D412yes—
115C29×#117—21no—
116C29×#117—21no—
117C29×#117—21no—
118C29×#117D412yes—
119C2×C4⋊C4×C29—21no—
120C2×C22⋊C4×C29—21no—
121C2×C42×C29—21no—
122C29×#104—28no—
123C29×#103—24no—
124C29×#102—24no—
125C29×#101—24no—
126C29×#100—24no—
127C29×C22⋊C8—28no—
128C24×C29—21no—
129C24×C29—21no—
130C24×C29#4111yescharacteristic
131#41×C29—22no—
132#41×C29—22no—
133#41×C29—22no—
134#41×C29—22no—
135#41×C29—22no—
136#41×C29—22no—
137#41×C29—22no—
138#41×C29—22no—
139#41×C29—22no—
140#41×C29—22no—
141#41×C29—22no—
142#41×C29—22no—
143#41×C29—22no—
144#41×C29—22no—
145#41×C29—22no—
146#41×C29—22no—
147#41×C29—41no—
148#41×C29—41no—
149#41×C29—41no—
150#41×C29—41no—
151#41×C29—41no—
152#41×C29—41no—
153#41×C29—41no—
154#41×C29—41no—
155#41×C29—41no—
156#41×C29—41no—
157#41×C29—41no—
158#41×C29—41no—
159#41×C29—41no—
160#41×C29—41no—
161#41×C29—41no—
162#41×C29—41no—
163C2×Q8×C29—21no—
164C2×Q8×C29—21no—
165C2×Q8×C29—21no—
166C2×Q8×C29—21no—
167C2×Q8×C29—21no—
168C2×Q8×C29—21no—
169C2×Q8×C29—21no—
170C2×Q8×C29—21no—
171C2×Q8×C29—21no—
172C2×Q8×C29—21no—
173C2×Q8×C29C22⋊C412yes—
174C2×Q8×C29C22⋊C412yes—
175C2×D4×C29—22no—
176C2×D4×C29—22no—
177C2×D4×C29—22no—
178C2×D4×C29—22no—
179C2×D4×C29—21no—
180C2×D4×C29—21no—
181C2×D4×C29—21no—
182C2×D4×C29—21no—
183C2×D4×C29—21no—
184C2×D4×C29—21no—
185C2×D4×C29—21no—
186C2×D4×C29—21no—
187C2×D4×C29—21no—
188C2×D4×C29—21no—
189C2×D4×C29—41no—
190C2×D4×C29—41no—
191C2×D4×C29—41no—
192C2×D4×C29—41no—
193C2×D4×C29—41no—
194C2×D4×C29—41no—
195C2×D4×C29—41no—
196C2×D4×C29—41no—
197C2×D4×C29C22⋊C412yes—
198C2×D4×C29C22⋊C412yes—
199C22×C4×C29—21no—
200C22×C4×C29—21no—
201C22×C4×C29—22no—
202C22×C4×C29—22no—
203C22×C4×C29—22no—
204C22×C4×C29—22no—
205C22×C4×C29—41no—
206C22×C4×C29—41no—
207C22×C4×C29—41no—
208C22×C4×C29—41no—
209C22×C4×C29—41no—
210C22×C4×C29—41no—
211C22×C4×C29—41no—
212C22×C4×C29—41no—
213C22×C4×C29—41no—
214C22×C4×C29C22×C411yescharacteristic
215C22×C4×C29C2×D411yescharacteristic
216C22×C4×C29C2×D411yescharacteristic
217C22×C4×C29C2×D411yescharacteristic
218C22×C4×C29C2×D411yescharacteristic
219C22×C4×C29C2×D411yescharacteristic
220C22×C4×C29C2×D411yescharacteristic
221C22×C4×C29C2×D411yescharacteristic
222C22×C4×C29C2×D411yescharacteristic
223C22×C4×C29C2×D411yescharacteristic
224C22×C4×C29C2×D411yescharacteristic
225C22×C4×C29#4111yescharacteristic
226C22×C4×C29#4111yescharacteristic
227C22×C4×C29#4111yescharacteristic
228Q16×C29—28no—
229SD16×C29—28no—
230SD16×C29—28no—
231D8×C29—28no—
232M16×C29—22no—
233M16×C29—22no—
234M16×C29—22no—
235M16×C29—22no—
236M16×C29—22no—
237M16×C29—22no—
238M16×C29—22no—
239M16×C29—22no—
240M16×C29—22no—
241M16×C29—22no—
242M16×C29—41no—
243M16×C29—41no—
244M16×C29—41no—
245M16×C29—41no—
246M16×C29—41no—
247M16×C29—41no—
248C2×C8×C29—22no—
249C2×C8×C29—22no—
250C2×C8×C29—22no—
251C2×C8×C29—22no—
252C2×C8×C29—22no—
253C2×C8×C29—41no—
254C2×C8×C29—41no—
255C2×C8×C29—41no—
256C2×C8×C29—41no—
257C2×C8×C29—41no—
258C2×C8×C29—41no—
259C2×C8×C29C22⋊C414yes—
260C4⋊C4×C29—22no—
261C4⋊C4×C29—41no—
262C22⋊C4×C29—22no—
263C22⋊C4×C29—41no—
264C42×C29—22no—
265C42×C29—41no—
266#11037C2911yesmaximal, characteristic, direct product factor, Sylow
267C23×C29—22no—
268C23×C29—22no—
269C23×C29—41no—
270C23×C29—41no—
271C23×C29—41no—
272C23×C29—41no—
273C23×C29—81no—
274C23×C29—82no—
275C23×C29—82no—
276C23×C29C4×D411yescharacteristic
277C23×C29#12111yescharacteristic
278C23×C29#12111yescharacteristic
279C23×C29#12111yescharacteristic
280C23×C29#12311yescharacteristic
281C23×C29#12311yescharacteristic
282C23×C29#12411yescharacteristic
283Q8×C29—22no—
284Q8×C29—22no—
285Q8×C29—22no—
286Q8×C29—22no—
287Q8×C29—41no—
288Q8×C29—41no—
289Q8×C29—41no—
290Q8×C29—41no—
291D4×C29—22no—
292D4×C29—22no—
293D4×C29—22no—
294D4×C29—22no—
295D4×C29—42no—
296D4×C29—42no—
297D4×C29—42no—
298D4×C29—42no—
299D4×C29—42no—
300D4×C29—42no—
301D4×C29—42no—
302D4×C29—42no—
303D4×C29—41no—
304D4×C29—41no—
305D4×C29—41no—
306D4×C29—41no—
307C2×C4×C29—22no—
308C2×C4×C29—22no—
309C2×C4×C29—41no—
310C2×C4×C29—41no—
311C2×C4×C29—41no—
312C2×C4×C29—41no—
313C2×C4×C29—42no—
314C2×C4×C29—42no—
315C2×C4×C29—42no—
316C2×C4×C29—42no—
317C2×C4×C29—42no—
318C2×C4×C29—42no—
319C2×C4×C29—42no—
320C2×C4×C29—42no—
321C2×C4×C29—42no—
322C2×C4×C29—82no—
323C2×C4×C29C2×C22⋊C411yescharacteristic
324C2×C4×C29C2×C22⋊C411yescharacteristic
325C2×C4×C29C2×C22⋊C411yescharacteristic
326C2×C4×C29C4×D411yescharacteristic
327C2×C4×C29C4×D411yescharacteristic
328C2×C4×C29C4×D411yescharacteristic
329C2×C4×C29#12011yescharacteristic
330C2×C4×C29#12011yescharacteristic
331C2×C4×C29#12011yescharacteristic
332C2×C4×C29#12011yescharacteristic
333C2×C4×C29#12011yescharacteristic
334C2×C4×C29#12011yescharacteristic
335C2×C4×C29#12011yescharacteristic
336C2×C4×C29#12011yescharacteristic
337C2×C4×C29#12111yescharacteristic
338C2×C4×C29#12111yescharacteristic
339C2×C4×C29#12111yescharacteristic
340C2×C4×C29#12111yescharacteristic
341C2×C4×C29#12111yescharacteristic
342C2×C4×C29#12111yescharacteristic
343C2×C4×C29#12111yescharacteristic
344C2×C4×C29#12111yescharacteristic
345C2×C4×C29#12111yescharacteristic
346C2×C4×C29#12311yescharacteristic
347C2×C4×C29#12311yescharacteristic
348C2×C4×C29#12411yescharacteristic
349C2×C4×C29#12711yescharacteristic
350C2×C4×C29#12711yescharacteristic
351C8×C29—24no—
352C8×C29—42no—
353C8×C29—42no—
354C8×C29—42no—
355C2×#575C2×C2911yescharacteristic
356C2×#421C2×C2911yescharacteristic, complemented
357#2896C2×C2911yescharacteristic, complemented
358C2×#413C2×C2911yescharacteristic, complemented
359#2879C2×C2911yescharacteristic, complemented
360C2×#344C2×C2911yescharacteristic, complemented
361#1738C2×C2911yescharacteristic, complemented
362C22×C29—41no—
363C22×C29—41no—
364C22×C29—41no—
365C22×C29—41no—
366C22×C29—41no—
367C22×C29—41no—
368C22×C29—41no—
369C22×C29—44no—
370C22×C29—42no—
371C22×C29—42no—
372C22×C29—82no—
373C22×C29—82no—
374C22×C29—82no—
375C22×C29—82no—
376C22×C29—82no—
377C22×C29#38611yescharacteristic
378C22×C29#38611yescharacteristic
379C22×C29#39011yescharacteristic
380C22×C29#39211yescharacteristic
381C22×C29#39411yescharacteristic
382C22×C29#39411yescharacteristic
383C22×C29#39411yescharacteristic
384C4×C29—42no—
385C4×C29—42no—
386C4×C29—82no—
387C4×C29#37911yescharacteristic
388C4×C29#38611yescharacteristic
389C4×C29#38611yescharacteristic
390C4×C29#39011yescharacteristic
391C4×C29#39211yescharacteristic
392C4×C29#39211yescharacteristic
393C4×C29#39211yescharacteristic
394C4×C29#39411yescharacteristic
395C22×#41C22×C2911yescharacteristic
396C22×#41C22×C2911yescharacteristic
397#575—22no—
398#575—22no—
399#575—22no—
400#575C4×C2914yescomplemented
401C2×#137—21no—
402C2×#137—21no—
403C2×AGL(1,ℤ/8)—21no—
404C2×AGL(1,ℤ/8)—21no—
405C2×#135—22no—
406C22×M16C22×C2911yescharacteristic
407C22×M16C22×C2911yescharacteristic
408C22×M16C22×C2911yescharacteristic
409C22×M16C22×C2911yescharacteristic
410C2×#117C22×C2911yescharacteristic
411#421—22no—
412#421—22no—
413C2×#104—22no—
414#419—21no—
415#418—21no—
416#417—22no—
417#416—22no—
418#413—22no—
419#413—22no—
420C2×#101—21no—
421C2×#100—21no—
422#408—22no—
423#408—22no—
424#407—22no—
425#344—22no—
426#341—22no—
427C2×C29—21no—
428C2×C29—21no—
429C2×C29—21no—
430C2×C29—21no—
431C2×C29—21no—
432C2×C29—21no—
433C2×C29—21no—
434C2×C29—82no—
435C2×C29—82no—
436C2×C29#143811yescharacteristic
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—21no—
452C2×#41—21no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41C2×C4×C2912yes—
458C2×#41C2×C4×C2912yes—
459C2×#41D4×C2912yes—
460C2×#41D4×C2912yes—
461C22×Q8D4×C2911yescharacteristic
462C22×Q8D4×C2911yescharacteristic
463C22×D4—21no—
464C22×D4—21no—
465C22×D4D4×C2911yescharacteristic
466C22×D4D4×C2911yescharacteristic
467C23×C4—21no—
468C23×C4—21no—
469C23×C4C23×C2911yescharacteristic
470#137—24no—
471#137—24no—
472#137—24no—
473#137—24no—
474AGL(1,ℤ/8)—24no—
475AGL(1,ℤ/8)—24no—
476AGL(1,ℤ/8)—24no—
477AGL(1,ℤ/8)—24no—
478#135—28no—
479#135—28no—
480C2×Q16—22no—
481C2×SD16—22no—
482C2×SD16—22no—
483C2×D8—22no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—21no—
487C2×M16—21no—
488C2×M16—21no—
489C2×M16—21no—
490C2×M16—21no—
491C2×M16—21no—
492C2×M16—21no—
493C2×M16—21no—
494C2×M16—21no—
495C2×M16—21no—
496C2×M16—21no—
497C2×M16—21no—
498C2×M16—21no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16C2×C4×C2912yes—
504C2×M16D4×C2912yes—
505C2×M16D4×C2912yes—
506C2×M16D4×C2912yes—
507C2×M16D4×C2912yes—
508C22×C8—21no—
509C22×C8—21no—
510C22×C8—21no—
511C22×C8D4×C2912yes—
512#117—21no—
513#117—21no—
514#117—21no—
515#117D4×C2912yes—
516C2×C4⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#104—28no—
520#103—24no—
521#102—24no—
522#101—24no—
523#100—24no—
524C22⋊C8—28no—
525C29#1103711yescharacteristic, direct product factor, Sylow
526C24—21no—
527C24—21no—
528C24#41×C2911yescharacteristic
529#41—22no—
530#41—22no—
531#41—22no—
532#41—22no—
533#41—22no—
534#41—22no—
535#41—22no—
536#41—22no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—41no—
546#41—41no—
547#41—41no—
548#41—41no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557#41—41no—
558#41—41no—
559#41—41no—
560#41—41no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8C22⋊C4×C2912yes—
572C2×Q8C22⋊C4×C2912yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—41no—
590C2×D4—41no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C22⋊C4×C2912yes—
596C2×D4C22⋊C4×C2912yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—41no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4C22×C4×C2911yescharacteristic
613C22×C4C2×D4×C2911yescharacteristic
614C22×C4C2×D4×C2911yescharacteristic
615C22×C4C2×D4×C2911yescharacteristic
616C22×C4C2×D4×C2911yescharacteristic
617C22×C4C2×D4×C2911yescharacteristic
618C22×C4C2×D4×C2911yescharacteristic
619C22×C4C2×D4×C2911yescharacteristic
620C22×C4C2×D4×C2911yescharacteristic
621C22×C4C2×D4×C2911yescharacteristic
622C22×C4C2×D4×C2911yescharacteristic
623C22×C4#41×C2911yescharacteristic
624C22×C4#41×C2911yescharacteristic
625C22×C4#41×C2911yescharacteristic
626Q16—28no—
627SD16—28no—
628SD16—28no—
629D8—28no—
630M16—22no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—22no—
636M16—22no—
637M16—22no—
638M16—22no—
639M16—22no—
640M16—41no—
641M16—41no—
642M16—41no—
643M16—41no—
644M16—41no—
645M16—41no—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—22no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—41no—
652C2×C8—41no—
653C2×C8—41no—
654C2×C8—41no—
655C2×C8—41no—
656C2×C8—41no—
657C2×C8C22⋊C4×C2914yes—
658C4⋊C4—22no—
659C4⋊C4—41no—
660C22⋊C4—22no—
661C22⋊C4—41no—
662C42—22no—
663C42—41no—
664C23—22no—
665C23—22no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—81no—
671C23—82no—
672C23—82no—
673C23C4×D4×C2911yescharacteristic
674C23C29×#12111yescharacteristic
675C23C29×#12111yescharacteristic
676C23C29×#12111yescharacteristic
677C23C29×#12311yescharacteristic
678C23C29×#12311yescharacteristic
679C23C29×#12411yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—41no—
701D4—41no—
702D4—41no—
703D4—41no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—82no—
720C2×C4C2×C22⋊C4×C2911yescharacteristic
721C2×C4C2×C22⋊C4×C2911yescharacteristic
722C2×C4C2×C22⋊C4×C2911yescharacteristic
723C2×C4C4×D4×C2911yescharacteristic
724C2×C4C4×D4×C2911yescharacteristic
725C2×C4C4×D4×C2911yescharacteristic
726C2×C4C29×#12011yescharacteristic
727C2×C4C29×#12011yescharacteristic
728C2×C4C29×#12011yescharacteristic
729C2×C4C29×#12011yescharacteristic
730C2×C4C29×#12011yescharacteristic
731C2×C4C29×#12011yescharacteristic
732C2×C4C29×#12011yescharacteristic
733C2×C4C29×#12011yescharacteristic
734C2×C4C29×#12111yescharacteristic
735C2×C4C29×#12111yescharacteristic
736C2×C4C29×#12111yescharacteristic
737C2×C4C29×#12111yescharacteristic
738C2×C4C29×#12111yescharacteristic
739C2×C4C29×#12111yescharacteristic
740C2×C4C29×#12111yescharacteristic
741C2×C4C29×#12111yescharacteristic
742C2×C4C29×#12111yescharacteristic
743C2×C4C29×#12311yescharacteristic
744C2×C4C29×#12311yescharacteristic
745C2×C4C29×#12411yescharacteristic
746C2×C4C29×#12711yescharacteristic
747C2×C4C29×#12711yescharacteristic
748C8—24no—
749C8—42no—
750C8—42no—
751C8—42no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—44no—
760C22—42no—
761C22—42no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22C29×#38611yescharacteristic
768C22C29×#38611yescharacteristic
769C22C29×#39011yescharacteristic
770C22C29×#39211yescharacteristic
771C22C29×#39411yescharacteristic
772C22C29×#39411yescharacteristic
773C22C29×#39411yescharacteristic
774C4—42no—
775C4—42no—
776C4—82no—
777C4C29×#37911yescharacteristic
778C4C29×#38611yescharacteristic
779C4C29×#38611yescharacteristic
780C4C29×#39011yescharacteristic
781C4C29×#39211yescharacteristic
782C4C29×#39211yescharacteristic
783C4C29×#39211yescharacteristic
784C4C29×#39411yescharacteristic
785C2—21no—
786C2—21no—
787C2—21no—
788C2—21no—
789C2—21no—
790C2—21no—
791C2—21no—
792C2—82no—
793C2—82no—
794C2C29×#143811yescharacteristic
subgroupG/H
centerC4×C29#392
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
socleC2×C29#1438
prime radicalC2×C29×#575C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#421C2semidirect
3. C29×#2896C2semidirect
4. C2×C29×#413C2semidirect
5. C29×#2879C2semidirect
6. C2×C29×#344C2semidirect
7. C29×#1738C2semidirect
13. C29×#575C4semidirect
266. #11037C29direct (N × H)
356. C2×#421C2×C29semidirect
357. #2896C2×C29semidirect
358. C2×#413C2×C29semidirect
359. #2879C2×C29semidirect
360. C2×#344C2×C29semidirect
361. #1738C2×C29semidirect
400. #575C4×C29semidirect
525. C29#11037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#5752
C2×C29×#4212
C29×#28962
C2×C29×#4132
C29×#28792
C2×C29×#3442
C29×#17382
#1103729