Finite Group Databasebeta

← C29×#18414 #20313314

Subgroups — C29×#18414 #20313314

Order 7424.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3534C211yesmaximal, characteristic, complemented
2C29×#3194C211yesmaximal, characteristic, complemented
3C29×#3186C211yesmaximal, characteristic, complemented
4C29×#2661C211yesmaximal, characteristic, complemented
5C29×#1612C211yesmaximal, characteristic, complemented
6C29×#1610C211yesmaximal, characteristic, complemented
7C29×#1609C211yesmaximal, characteristic, complemented
8C29×#1607C211yesmaximal, characteristic, complemented
9C29×#1600C211yesmaximal, characteristic, complemented
10C29×#1598C211yesmaximal, characteristic, complemented
11C29×#1597C211yesmaximal, characteristic, complemented
12C29×#1595C211yesmaximal, characteristic, complemented
13C29×#1507C211yesmaximal, characteristic, complemented
14C29×#1501C211yesmaximal, characteristic, complemented
15C29×#1468C211yesmaximal, characteristic, complemented
16C29×#562—21no—
17C29×#560—21no—
18C29×#553—21no—
19C29×#551—21no—
20C29×#546—21no—
21C29×#546—21no—
22C29×#546—21no—
23D42×C29—21no—
24C29×#540—21no—
25C29×#539—21no—
26C29×#539C2211yescharacteristic
27C29×#538—21no—
28C29×#538C2211yescharacteristic
29C29×#537C2211yescharacteristic
30C29×#534—21no—
31C29×#534C2211yescharacteristic
32C29×#525C2211yescharacteristic
33C2×C29×#123C2211yescharacteristic
34C2×C29×#121C2211yescharacteristic
35C2×C29×#121C2211yescharacteristic, complemented
36C29×#483C2211yescharacteristic, complemented
37C29×#482—21no—
38C29×#480—21no—
39C29×#480C2211yescharacteristic
40C29×#480C2211yescharacteristic, complemented
41C29×#480C2211yescharacteristic, complemented
42C29×#469—21no—
43C29×#468—21no—
44C29×#466—21no—
45C29×#466—21no—
46C29×#450C2211yescharacteristic, complemented
47C29×#449—21no—
48C29×#447—21no—
49C29×#447C2211yescharacteristic
50C29×#447C2211yescharacteristic, complemented
51C29×#447C2211yescharacteristic, complemented
52C29×#407C2211yescharacteristic, complemented
53C2×C29×C22⋊C8C2211yescharacteristic, complemented
54C29×#398C2211yescharacteristic, complemented
55C29×#397C2211yescharacteristic, complemented
56C29×#394—21no—
57C29×#394C2211yescharacteristic, complemented
58C29×#392—21no—
59C29×#392C2211yescharacteristic, complemented
60C29×#390—21no—
61C29×#388—21no—
62C4×C22⋊C4×C29C2211yescharacteristic, complemented
63C29×#328C2211yescharacteristic, complemented
64C29×#328C2211yescharacteristic, complemented
65C29×#327C2211yescharacteristic
66C29×#327C2211yescharacteristic
67C29×#327C2211yescharacteristic, complemented
68C29×#327C2211yescharacteristic, complemented
69C29×#327C2211yescharacteristic, complemented
70C29×#327C2211yescharacteristic, complemented
71C29×#324C2211yescharacteristic, complemented
72C29×#324C2211yescharacteristic, complemented
73C29×#323C2211yescharacteristic, complemented
74C29×#323C2211yescharacteristic, complemented
75C2×#41×C29—21no—
76C2×#41×C29D411yescharacteristic, complemented
77C22×D4×C29—21no—
78C22×D4×C29—21no—
79C22×D4×C29—21no—
80C22×D4×C29—21no—
81C22×D4×C29—21no—
82C22×D4×C29D411yescharacteristic
83C22×D4×C29D411yescharacteristic, complemented
84C22×D4×C29C2311yescharacteristic
85C23×C4×C29C2311yescharacteristic
86C2×SD16×C29—21no—
87C2×D8×C29—21no—
88C2×D8×C29—21no—
89C2×D8×C29—21no—
90C2×M16×C29—21no—
91C22×C8×C29—21no—
92C29×#127—21no—
93C29×#126—21no—
94C29×#126—21no—
95C29×#126—21no—
96C29×#126—21no—
97C29×#125—21no—
98C29×#125—21no—
99C29×#124—21no—
100C29×#124—21no—
101C29×#124—21no—
102C29×#123—21no—
103C29×#123—21no—
104C29×#123—21no—
105C29×#123—21no—
106C29×#123—21no—
107C29×#123—21no—
108C29×#123—21no—
109C29×#123—21no—
110C29×#123—21no—
111C29×#123—21no—
112C29×#123—21no—
113C29×#123—21no—
114C29×#123—21no—
115C29×#123—21no—
116C29×C22⋊Q8—21no—
117C29×C22⋊Q8—21no—
118C29×C22⋊Q8—21no—
119C29×C22⋊Q8—21no—
120C29×C22⋊Q8—21no—
121C29×C22⋊Q8D411yescharacteristic, complemented
122C29×C22⋊Q8C2311yescharacteristic
123C29×#121—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—21no—
127C29×#121—21no—
128C29×#121—21no—
129C29×#121—21no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121—21no—
133C29×#121—21no—
134C29×#121—21no—
135C29×#121—21no—
136C29×#121—21no—
137C29×#121—21no—
138C29×#121—21no—
139C29×#121—21no—
140C29×#121—21no—
141C29×#121—21no—
142C29×#121D411yescharacteristic, complemented
143C29×#121D411yescharacteristic, complemented
144C29×#121D411yescharacteristic, complemented
145C29×#121C2311yescharacteristic
146C29×#121C2311yescharacteristic
147C29×#121C2311yescharacteristic
148C29×#120—21no—
149C29×#120—21no—
150C29×#120—21no—
151C29×#120—21no—
152C29×#120—21no—
153C29×#120—21no—
154C29×#120—21no—
155C29×#120—21no—
156C4×D4×C29—21no—
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×C29—21no—
164C29×#117—21no—
165C29×#117D411yescharacteristic, complemented
166C2×C4⋊C4×C29—21no—
167C2×C4⋊C4×C29D411yescharacteristic
168C2×C4⋊C4×C29D411yescharacteristic, complemented
169C2×C4⋊C4×C29C2311yescharacteristic
170C2×C4⋊C4×C29C2311yescharacteristic
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×C22⋊C4×C29—21no—
177C2×C22⋊C4×C29—21no—
178C2×C22⋊C4×C29—21no—
179C2×C22⋊C4×C29—21no—
180C2×C22⋊C4×C29D411yescharacteristic
181C2×C22⋊C4×C29D411yescharacteristic
182C2×C22⋊C4×C29C2311yescharacteristic
183C2×C42×C29—21no—
184C29×#107—21no—
185C29×#107—21no—
186C29×#107—21no—
187C29×#106—21no—
188C29×#103—21no—
189C29×#102—21no—
190C29×#102—21no—
191C29×#102—21no—
192C29×#102—21no—
193C29×#102—21no—
194C29×#102—21no—
195C29×#102—21no—
196C29×C22⋊C8—21no—
197C29×C22⋊C8—21no—
198C29×C22⋊C8C2311yescharacteristic
199C29×C22⋊C8C2311yescharacteristic
200C29×C22⋊C8C2311yescharacteristic
201C29×C22⋊C8C2311yescharacteristic
202C29×#95—21no—
203C29×#95—21no—
204C29×#95C2311yescharacteristic
205C29×#95C2311yescharacteristic
206C24×C29—21no—
207C24×C29—21no—
208C24×C29—21no—
209C24×C29C2×D411yescharacteristic
210C24×C29C2×D411yescharacteristic
211#41×C29—81no—
212#41×C29—81no—
213#41×C29—81no—
214C2×Q8×C29—21no—
215C2×Q8×C29C2×D411yescharacteristic
216C2×D4×C29—21no—
217C2×D4×C29—21no—
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—21no—
229C2×D4×C29—21no—
230C2×D4×C29—21no—
231C2×D4×C29—21no—
232C2×D4×C29—21no—
233C2×D4×C29—21no—
234C2×D4×C29—21no—
235C2×D4×C29—42no—
236C2×D4×C29—41no—
237C2×D4×C29—41no—
238C2×D4×C29—81no—
239C2×D4×C29—81no—
240C2×D4×C29—81no—
241C2×D4×C29—81no—
242C2×D4×C29—81no—
243C2×D4×C29—81no—
244C2×D4×C29—81no—
245C2×D4×C29—81no—
246C2×D4×C29—81no—
247C2×D4×C29—81no—
248C2×D4×C29—81no—
249C2×D4×C29—82no—
250C2×D4×C29C2×D411yescharacteristic
251C2×D4×C29C2×D411yescharacteristic
252C2×D4×C29C2×D411yescharacteristic
253C22×C4×C29—21no—
254C22×C4×C29—21no—
255C22×C4×C29—21no—
256C22×C4×C29—21no—
257C22×C4×C29—21no—
258C22×C4×C29—21no—
259C22×C4×C29—21no—
260C22×C4×C29—21no—
261C22×C4×C29—21no—
262C22×C4×C29—21no—
263C22×C4×C29—81no—
264C22×C4×C29C2×D411yescharacteristic
265C22×C4×C29C2×D411yescharacteristic
266C22×C4×C29C2×D411yescharacteristic
267C22×C4×C29C2×D411yescharacteristic
268C22×C4×C29C2×D411yescharacteristic
269C22×C4×C29C2×D411yescharacteristic
270C22×C4×C29C2×D411yescharacteristic
271C22×C4×C29C2×D411yescharacteristic
272C22×C4×C29C2411yescharacteristic
273SD16×C29—81no—
274D8×C29—81no—
275D8×C29—81no—
276D8×C29—81no—
277M16×C29—81no—
278C2×C8×C29—21no—
279C2×C8×C29—21no—
280C2×C8×C29—21no—
281C2×C8×C29—21no—
282C2×C8×C29—81no—
283C4⋊C4×C29—21no—
284C4⋊C4×C29—21no—
285C4⋊C4×C29—21no—
286C4⋊C4×C29—21no—
287C4⋊C4×C29—21no—
288C4⋊C4×C29—21no—
289C4⋊C4×C29—21no—
290C4⋊C4×C29—21no—
291C4⋊C4×C29—21no—
292C4⋊C4×C29—21no—
293C4⋊C4×C29—21no—
294C4⋊C4×C29—21no—
295C4⋊C4×C29—21no—
296C4⋊C4×C29—21no—
297C4⋊C4×C29—21no—
298C4⋊C4×C29—81no—
299C4⋊C4×C29C2×D411yescharacteristic
300C4⋊C4×C29C2×D411yescharacteristic
301C4⋊C4×C29C2×D411yescharacteristic
302C4⋊C4×C29C2×D411yescharacteristic
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—21no—
311C22⋊C4×C29—21no—
312C22⋊C4×C29—21no—
313C22⋊C4×C29—21no—
314C22⋊C4×C29—21no—
315C22⋊C4×C29—21no—
316C22⋊C4×C29—21no—
317C22⋊C4×C29—21no—
318C22⋊C4×C29—21no—
319C22⋊C4×C29—21no—
320C22⋊C4×C29—21no—
321C22⋊C4×C29—21no—
322C22⋊C4×C29—21no—
323C22⋊C4×C29—21no—
324C22⋊C4×C29—21no—
325C22⋊C4×C29—21no—
326C22⋊C4×C29—21no—
327C22⋊C4×C29—21no—
328C22⋊C4×C29—42no—
329C22⋊C4×C29—42no—
330C22⋊C4×C29—41no—
331C22⋊C4×C29—41no—
332C22⋊C4×C29—81no—
333C22⋊C4×C29—81no—
334C22⋊C4×C29—81no—
335C42×C29—21no—
336C42×C29—21no—
337C42×C29—21no—
338C42×C29—81no—
339#18414C2911yesmaximal, characteristic, direct product factor, Sylow
340C23×C29—21no—
341C23×C29—21no—
342C23×C29—21no—
343C23×C29—21no—
344C23×C29—21no—
345C23×C29—21no—
346C23×C29—21no—
347C23×C29—21no—
348C23×C29—41no—
349C23×C29—41no—
350C23×C29—42no—
351C23×C29—41no—
352C23×C29—41no—
353C23×C29—41no—
354C23×C29—41no—
355C23×C29—41no—
356C23×C29—41no—
357C23×C29—41no—
358C23×C29—41no—
359C23×C29—41no—
360C23×C29—81no—
361C23×C29—81no—
362C23×C29—81no—
363C23×C29—81no—
364C23×C29—81no—
365C23×C29#12011yescharacteristic
366C23×C29#12011yescharacteristic
367C23×C29C22×D411yescharacteristic
368Q8×C29—41no—
369Q8×C29—81no—
370D4×C29—41no—
371D4×C29—41no—
372D4×C29—41no—
373D4×C29—41no—
374D4×C29—41no—
375D4×C29—41no—
376D4×C29—41no—
377D4×C29—42no—
378D4×C29—42no—
379D4×C29—41no—
380D4×C29—41no—
381D4×C29—41no—
382D4×C29—41no—
383D4×C29—41no—
384D4×C29—41no—
385D4×C29—81no—
386D4×C29—81no—
387D4×C29—81no—
388D4×C29—81no—
389D4×C29—81no—
390D4×C29—81no—
391D4×C29—81no—
392D4×C29—81no—
393D4×C29—81no—
394D4×C29—81no—
395D4×C29—81no—
396D4×C29—81no—
397D4×C29—84no—
398D4×C29—82no—
399D4×C29—82no—
400C2×C4×C29—22no—
401C2×C4×C29—21no—
402C2×C4×C29—21no—
403C2×C4×C29—21no—
404C2×C4×C29—21no—
405C2×C4×C29—21no—
406C2×C4×C29—21no—
407C2×C4×C29—21no—
408C2×C4×C29—21no—
409C2×C4×C29—21no—
410C2×C4×C29—21no—
411C2×C4×C29—41no—
412C2×C4×C29—41no—
413C2×C4×C29—41no—
414C2×C4×C29—41no—
415C2×C4×C29—41no—
416C2×C4×C29—41no—
417C2×C4×C29—41no—
418C2×C4×C29—41no—
419C2×C4×C29—41no—
420C2×C4×C29—41no—
421C2×C4×C29—41no—
422C2×C4×C29—41no—
423C2×C4×C29—41no—
424C2×C4×C29—41no—
425C2×C4×C29—41no—
426C2×C4×C29—41no—
427C2×C4×C29—81no—
428C2×C4×C29—81no—
429C2×C4×C29—81no—
430C2×C4×C29—81no—
431C2×C4×C29—81no—
432C2×C4×C29—81no—
433C2×C4×C29—81no—
434C2×C4×C29#12011yescharacteristic
435C2×C4×C29#12011yescharacteristic
436C2×C4×C29C22×D411yescharacteristic
437C2×C4×C29C22×D411yescharacteristic
438C8×C29—41no—
439C8×C29—41no—
440C8×C29—41no—
441C8×C29—41no—
442#3534C2×C2911yescharacteristic, complemented
443#3194C2×C2911yescharacteristic, complemented
444#3186C2×C2911yescharacteristic, complemented
445#2661C2×C2911yescharacteristic, complemented
446#1612C2×C2911yescharacteristic, complemented
447#1610C2×C2911yescharacteristic, complemented
448#1609C2×C2911yescharacteristic, complemented
449#1607C2×C2911yescharacteristic, complemented
450#1600C2×C2911yescharacteristic, complemented
451#1598C2×C2911yescharacteristic, complemented
452#1597C2×C2911yescharacteristic, complemented
453#1595C2×C2911yescharacteristic, complemented
454#1507C2×C2911yescharacteristic, complemented
455#1501C2×C2911yescharacteristic, complemented
456#1468C2×C2911yescharacteristic, complemented
457C22×C29—21no—
458C22×C29—21no—
459C22×C29—21no—
460C22×C29—21no—
461C22×C29—21no—
462C22×C29—21no—
463C22×C29—21no—
464C22×C29—21no—
465C22×C29—41no—
466C22×C29—41no—
467C22×C29—41no—
468C22×C29—41no—
469C22×C29—41no—
470C22×C29—41no—
471C22×C29—41no—
472C22×C29—41no—
473C22×C29—41no—
474C22×C29—41no—
475C22×C29—41no—
476C22×C29—41no—
477C22×C29—81no—
478C22×C29—81no—
479C22×C29—81no—
480C22×C29—81no—
481C22×C29—81no—
482C22×C29—81no—
483C22×C29—81no—
484C22×C29—81no—
485C22×C29—81no—
486C22×C29—81no—
487C22×C29—81no—
488C22×C29—162no—
489C22×C29—162no—
490C22×C29C2×#12011yescharacteristic
491C22×C29#57611yescharacteristic
492C22×C29#57611yescharacteristic
493C4×C29—21no—
494C4×C29—21no—
495C4×C29—21no—
496C4×C29—21no—
497C4×C29—42no—
498C4×C29—41no—
499C4×C29—41no—
500C4×C29—41no—
501C4×C29—41no—
502C4×C29—41no—
503C4×C29—41no—
504C4×C29—41no—
505C4×C29—41no—
506C4×C29—81no—
507C4×C29—81no—
508#562—21no—
509#560—21no—
510#553—21no—
511#551—21no—
512#546—21no—
513#546—21no—
514#546—21no—
515D42—21no—
516#540—21no—
517#539—21no—
518#539C22×C2911yescharacteristic
519#538—21no—
520#538C22×C2911yescharacteristic
521#537C22×C2911yescharacteristic
522#534—21no—
523#534C22×C2911yescharacteristic
524#525C22×C2911yescharacteristic
525C2×#123C22×C2911yescharacteristic
526C2×#121C22×C2911yescharacteristic
527C2×#121C22×C2911yescharacteristic, complemented
528#483C22×C2911yescharacteristic, complemented
529#482—21no—
530#480—21no—
531#480C22×C2911yescharacteristic
532#480C22×C2911yescharacteristic, complemented
533#480C22×C2911yescharacteristic, complemented
534#469—21no—
535#468—21no—
536#466—21no—
537#466—21no—
538#450C22×C2911yescharacteristic, complemented
539#449—21no—
540#447—21no—
541#447C22×C2911yescharacteristic
542#447C22×C2911yescharacteristic, complemented
543#447C22×C2911yescharacteristic, complemented
544#407C22×C2911yescharacteristic, complemented
545C2×C22⋊C8C22×C2911yescharacteristic, complemented
546#398C22×C2911yescharacteristic, complemented
547#397C22×C2911yescharacteristic, complemented
548#394—21no—
549#394C22×C2911yescharacteristic, complemented
550#392—21no—
551#392C22×C2911yescharacteristic, complemented
552#390—21no—
553#388—21no—
554C4×C22⋊C4C22×C2911yescharacteristic, complemented
555#328C22×C2911yescharacteristic, complemented
556#328C22×C2911yescharacteristic, complemented
557#327C22×C2911yescharacteristic
558#327C22×C2911yescharacteristic
559#327C22×C2911yescharacteristic, complemented
560#327C22×C2911yescharacteristic, complemented
561#327C22×C2911yescharacteristic, complemented
562#327C22×C2911yescharacteristic, complemented
563#324C22×C2911yescharacteristic, complemented
564#324C22×C2911yescharacteristic, complemented
565#323C22×C2911yescharacteristic, complemented
566#323C22×C2911yescharacteristic, complemented
567C2×C29—21no—
568C2×C29—21no—
569C2×C29—41no—
570C2×C29—41no—
571C2×C29—81no—
572C2×C29—81no—
573C2×C29—81no—
574C2×C29—81no—
575C2×C29—161no—
576C2×C29#300811yescharacteristic
577C2×C29#301811yescharacteristic
578C2×C29#302611yescharacteristic
579C2×#41—21no—
580C2×#41D4×C2911yescharacteristic, complemented
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4D4×C2911yescharacteristic
587C22×D4D4×C2911yescharacteristic, complemented
588C22×D4C23×C2911yescharacteristic
589C23×C4C23×C2911yescharacteristic
590C2×SD16—21no—
591C2×D8—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×M16—21no—
595C22×C8—21no—
596#127—21no—
597#126—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#125—21no—
602#125—21no—
603#124—21no—
604#124—21no—
605#124—21no—
606#123—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8D4×C2911yescharacteristic, complemented
626C22⋊Q8C23×C2911yescharacteristic
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121D4×C2911yescharacteristic, complemented
647#121D4×C2911yescharacteristic, complemented
648#121D4×C2911yescharacteristic, complemented
649#121C23×C2911yescharacteristic
650#121C23×C2911yescharacteristic
651#121C23×C2911yescharacteristic
652#120—21no—
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668#117—21no—
669#117D4×C2911yescharacteristic, complemented
670C2×C4⋊C4—21no—
671C2×C4⋊C4D4×C2911yescharacteristic
672C2×C4⋊C4D4×C2911yescharacteristic, complemented
673C2×C4⋊C4C23×C2911yescharacteristic
674C2×C4⋊C4C23×C2911yescharacteristic
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4D4×C2911yescharacteristic
685C2×C22⋊C4D4×C2911yescharacteristic
686C2×C22⋊C4C23×C2911yescharacteristic
687C2×C42—21no—
688#107—21no—
689#107—21no—
690#107—21no—
691#106—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8C23×C2911yescharacteristic
703C22⋊C8C23×C2911yescharacteristic
704C22⋊C8C23×C2911yescharacteristic
705C22⋊C8C23×C2911yescharacteristic
706#95—21no—
707#95—21no—
708#95C23×C2911yescharacteristic
709#95C23×C2911yescharacteristic
710C29#1841411yescharacteristic, direct product factor, Sylow
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C2911yescharacteristic
715C24C2×D4×C2911yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C2911yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C2911yescharacteristic
756C2×D4C2×D4×C2911yescharacteristic
757C2×D4C2×D4×C2911yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C2911yescharacteristic
770C22×C4C2×D4×C2911yescharacteristic
771C22×C4C2×D4×C2911yescharacteristic
772C22×C4C2×D4×C2911yescharacteristic
773C22×C4C2×D4×C2911yescharacteristic
774C22×C4C2×D4×C2911yescharacteristic
775C22×C4C2×D4×C2911yescharacteristic
776C22×C4C2×D4×C2911yescharacteristic
777C22×C4C24×C2911yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C2911yescharacteristic
805C4⋊C4C2×D4×C2911yescharacteristic
806C4⋊C4C2×D4×C2911yescharacteristic
807C4⋊C4C2×D4×C2911yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23C29×#12011yescharacteristic
870C23C29×#12011yescharacteristic
871C23C22×D4×C2911yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4C29×#12011yescharacteristic
939C2×C4C29×#12011yescharacteristic
940C2×C4C22×D4×C2911yescharacteristic
941C2×C4C22×D4×C2911yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×C29×#12011yescharacteristic
980C22C29×#57611yescharacteristic
981C22C29×#57611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C29×#300811yescharacteristic
1007C2C29×#301811yescharacteristic
1008C2C29×#302611yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3534C2semidirect
2. C29×#3194C2semidirect
3. C29×#3186C2semidirect
4. C29×#2661C2semidirect
5. C29×#1612C2semidirect
6. C29×#1610C2semidirect
7. C29×#1609C2semidirect
8. C29×#1607C2semidirect
9. C29×#1600C2semidirect
10. C29×#1598C2semidirect
11. C29×#1597C2semidirect
12. C29×#1595C2semidirect
13. C29×#1507C2semidirect
14. C29×#1501C2semidirect
15. C29×#1468C2semidirect
35. C2×C29×#121C22semidirect
36. C29×#483C22semidirect
40. C29×#480C22semidirect
41. C29×#480C22semidirect
46. C29×#450C22semidirect
50. C29×#447C22semidirect
51. C29×#447C22semidirect
52. C29×#407C22semidirect
53. C2×C29×C22⋊C8C22semidirect
54. C29×#398C22semidirect
55. C29×#397C22semidirect
57. C29×#394C22semidirect
59. C29×#392C22semidirect
62. C4×C22⋊C4×C29C22semidirect
63. C29×#328C22semidirect
64. C29×#328C22semidirect
67. C29×#327C22semidirect
68. C29×#327C22semidirect
69. C29×#327C22semidirect
70. C29×#327C22semidirect
71. C29×#324C22semidirect
72. C29×#324C22semidirect
73. C29×#323C22semidirect
74. C29×#323C22semidirect
76. C2×#41×C29D4semidirect
83. C22×D4×C29D4semidirect
121. C29×C22⋊Q8D4semidirect
142. C29×#121D4semidirect
143. C29×#121D4semidirect
144. C29×#121D4semidirect
165. C29×#117D4semidirect
168. C2×C4⋊C4×C29D4semidirect
339. #18414C29direct (N × H)
442. #3534C2×C29semidirect
443. #3194C2×C29semidirect
444. #3186C2×C29semidirect
445. #2661C2×C29semidirect
446. #1612C2×C29semidirect
447. #1610C2×C29semidirect
448. #1609C2×C29semidirect
449. #1607C2×C29semidirect
450. #1600C2×C29semidirect
451. #1598C2×C29semidirect
452. #1597C2×C29semidirect
453. #1595C2×C29semidirect
454. #1507C2×C29semidirect
455. #1501C2×C29semidirect
456. #1468C2×C29semidirect
527. C2×#121C22×C29semidirect
528. #483C22×C29semidirect
532. #480C22×C29semidirect
533. #480C22×C29semidirect
538. #450C22×C29semidirect
542. #447C22×C29semidirect
543. #447C22×C29semidirect
544. #407C22×C29semidirect
545. C2×C22⋊C8C22×C29semidirect
546. #398C22×C29semidirect
547. #397C22×C29semidirect
549. #394C22×C29semidirect
551. #392C22×C29semidirect
554. C4×C22⋊C4C22×C29semidirect
555. #328C22×C29semidirect
556. #328C22×C29semidirect
559. #327C22×C29semidirect
560. #327C22×C29semidirect
561. #327C22×C29semidirect
562. #327C22×C29semidirect
563. #324C22×C29semidirect
564. #324C22×C29semidirect
565. #323C22×C29semidirect
566. #323C22×C29semidirect
580. C2×#41D4×C29semidirect
587. C22×D4D4×C29semidirect
625. C22⋊Q8D4×C29semidirect
646. #121D4×C29semidirect
647. #121D4×C29semidirect
648. #121D4×C29semidirect
669. #117D4×C29semidirect
672. C2×C4⋊C4D4×C29semidirect
710. C29#18414direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35342
C29×#31942
C29×#31862
C29×#26612
C29×#16122
C29×#16102
C29×#16092
C29×#16072
C29×#16002
C29×#15982
C29×#15972
C29×#15952
C29×#15072
C29×#15012
C29×#14682
#1841429