Finite Group Databasebeta

← C29×#24469 #20319369

Subgroups — C29×#24469 #20319369

Order 7424.

1402 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3489C211yesmaximal, characteristic, complemented
2C29×#3055C211yesmaximal, characteristic, complemented
3C2×C29×#454C211yesmaximal, characteristic, complemented
4C29×#3006C211yesmaximal, characteristic, complemented
5C2×C29×#421C211yesmaximal, characteristic, complemented
6C29×#2620C211yesmaximal, characteristic, complemented
7C29×#2039C211yesmaximal, characteristic, complemented
8C29×#2038C211yesmaximal, characteristic, complemented
9C29×#2006C211yesmaximal, characteristic, complemented
10C29×#2003C211yesmaximal, characteristic, complemented
11C29×#1901C211yesmaximal, characteristic, complemented
12C29×#1897C211yesmaximal, characteristic, complemented
13C29×#1883C211yesmaximal, characteristic, complemented
14C29×#1859C211yesmaximal, characteristic, complemented
15C29×#1793C211yesmaximal, characteristic, complemented
16C2×C29×2−1+4C2211yescharacteristic
17C22×#41×C29C2211yescharacteristic
18C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
19C2×C29×AGL(1,ℤ/8)C2211yescharacteristic
20C2×C29×AGL(1,ℤ/8)C2211yescharacteristic, complemented
21C22×M16×C29C2211yescharacteristic
22D4×Q8×C29—21no—
23C29×#548—21no—
24C29×#547—21no—
25C29×#547—22no—
26C29×#546—21no—
27C29×#546—22no—
28C29×#537—21no—
29C29×#537C2211yescharacteristic
30C29×#536—21no—
31C29×#536C2211yescharacteristic
32C2×C29×#124C2211yescharacteristic, complemented
33C29×#525—21no—
34C29×#525C2211yescharacteristic
35C2×C29×C22⋊Q8—21no—
36C2×C29×C22⋊Q8C2211yescharacteristic
37C2×C29×#121C2211yescharacteristic
38C29×#520C2211yescharacteristic
39C2×C29×#117C2211yescharacteristic
40C29×#469—21no—
41C29×#468—21no—
42C29×#466—21no—
43C29×#465—21no—
44C29×#454—24no—
45C29×#449—21no—
46C29×#449—21no—
47C29×#448—21no—
48C29×#447—21no—
49C29×#428C2211yescharacteristic, complemented
50C29×#421—24no—
51C2×C29×#104C2211yescharacteristic
52C2×C29×#104C2211yescharacteristic
53C2×C29×#104C2211yescharacteristic
54C2×C29×#104C2211yescharacteristic
55C2×C29×#104C2211yescharacteristic, complemented
56C2×C29×#104C2211yescharacteristic, complemented
57C29×#418C2211yescharacteristic, complemented
58C29×#417C2211yescharacteristic
59C29×#417C2211yescharacteristic
60C29×#417C2211yescharacteristic, complemented
61C2×C29×#101C2211yescharacteristic, complemented
62C2×C29×#101C2211yescharacteristic, complemented
63C29×#407C2211yescharacteristic
64C29×#396—22no—
65C29×#394—22no—
66C29×#391C2211yescharacteristic, complemented
67C29×#390C2211yescharacteristic, complemented
68C29×#384C2211yescharacteristic, complemented
69C29×#343C2211yescharacteristic, complemented
70C29×#343C2211yescharacteristic, complemented
71C29×#339C2211yescharacteristic, complemented
72C29×#339C2211yescharacteristic, complemented
73C29×2−1+4—22no—
74C29×2−1+4—22no—
75C29×2−1+4—41no—
76C29×2−1+4—41no—
77C2×#41×C29—21no—
78C2×#41×C29—21no—
79C2×#41×C29—21no—
80C2×#41×C29—22no—
81C2×#41×C29—21no—
82C2×#41×C29—22no—
83C2×#41×C29—22no—
84C2×#41×C29—41no—
85C2×#41×C29—41no—
86C2×#41×C29D411yescharacteristic
87C2×#41×C29D411yescharacteristic
88C2×#41×C29C2311yescharacteristic
89C2×#41×C29C2311yescharacteristic
90C2×#41×C29C2311yescharacteristic
91C22×Q8×C29—21no—
92C22×Q8×C29—21no—
93C22×Q8×C29D411yescharacteristic
94C22×Q8×C29C2311yescharacteristic
95C22×D4×C29—21no—
96C22×D4×C29—21no—
97C22×D4×C29D411yescharacteristic
98C22×D4×C29C2311yescharacteristic
99C23×C4×C29—21no—
100C23×C4×C29C2311yescharacteristic
101C29×AGL(1,ℤ/8)—22no—
102C29×AGL(1,ℤ/8)—22no—
103C29×AGL(1,ℤ/8)—22no—
104C29×AGL(1,ℤ/8)—41no—
105C29×AGL(1,ℤ/8)—41no—
106C29×AGL(1,ℤ/8)—41no—
107C2×SD16×C29—21no—
108C2×SD16×C29—21no—
109C2×SD16×C29—21no—
110C2×D8×C29—21no—
111C2×D8×C29—21no—
112C2×D8×C29—21no—
113C2×M16×C29—21no—
114C2×M16×C29—22no—
115C2×M16×C29—41no—
116C2×M16×C29C2311yescharacteristic
117C2×M16×C29C2311yescharacteristic
118C2×M16×C29C2311yescharacteristic
119C2×M16×C29C2311yescharacteristic
120C22×C8×C29—21no—
121C29×C4⋊Q8—22no—
122C29×C4⋊Q8—21no—
123C29×#124—22no—
124C29×#124—21no—
125C29×#124—22no—
126C29×#124—41no—
127C29×#123—22no—
128C29×#123—22no—
129C29×#123—22no—
130C29×#123—21no—
131C29×#123—22no—
132C29×C22⋊Q8—22no—
133C29×C22⋊Q8—22no—
134C29×C22⋊Q8—22no—
135C29×C22⋊Q8—21no—
136C29×C22⋊Q8—21no—
137C29×C22⋊Q8—21no—
138C29×C22⋊Q8—21no—
139C29×C22⋊Q8—21no—
140C29×C22⋊Q8—21no—
141C29×C22⋊Q8—21no—
142C29×C22⋊Q8—21no—
143C29×C22⋊Q8D411yescharacteristic
144C29×C22⋊Q8D411yescharacteristic
145C29×#121—22no—
146C29×#121—22no—
147C29×#121—22no—
148C29×#121—21no—
149C29×#121—21no—
150C29×#121—22no—
151C29×#121—21no—
152C29×#121—21no—
153C29×#121—21no—
154C29×#121—21no—
155C29×#121D411yescharacteristic
156C29×#121D411yescharacteristic
157C29×#120—22no—
158C29×#120—21no—
159C4×Q8×C29—21no—
160C4×D4×C29—22no—
161C4×D4×C29—22no—
162C4×D4×C29—21no—
163C4×D4×C29—22no—
164C4×D4×C29—21no—
165C4×D4×C29—21no—
166C29×#117—21no—
167C29×#117—22no—
168C29×#117—41no—
169C29×#117C2311yescharacteristic
170C2×C4⋊C4×C29—22no—
171C2×C4⋊C4×C29—21no—
172C2×C4⋊C4×C29—21no—
173C2×C4⋊C4×C29—22no—
174C2×C4⋊C4×C29D412yes—
175C2×C4⋊C4×C29C2311yescharacteristic
176C2×C4⋊C4×C29C2311yescharacteristic
177C2×C22⋊C4×C29—22no—
178C2×C22⋊C4×C29—21no—
179C2×C22⋊C4×C29—21no—
180C2×C22⋊C4×C29—22no—
181C2×C22⋊C4×C29—22no—
182C2×C22⋊C4×C29D412yes—
183C2×C42×C29C2311yescharacteristic
184C2×C42×C29C2311yescharacteristic
185C29×#107—21no—
186C29×#106—21no—
187C29×#104—22no—
188C29×#104—22no—
189C29×#104—22no—
190C29×#104—22no—
191C29×#104—41no—
192C29×#104D414yescomplemented
193C29×#103—21no—
194C29×#103—21no—
195C29×#103—21no—
196C29×#102—21no—
197C29×#102—21no—
198C29×#102—21no—
199C29×#102—21no—
200C29×#102—21no—
201C29×#101—22no—
202C29×#101—41no—
203C29×C22⋊C8—21no—
204C29×C22⋊C8—21no—
205C29×#95—22no—
206C24×C29—21no—
207C24×C29—21no—
208C24×C29C2×D411yescharacteristic
209#41×C29—21no—
210#41×C29—21no—
211#41×C29—22no—
212#41×C29—22no—
213#41×C29—21no—
214#41×C29—21no—
215#41×C29—21no—
216#41×C29—21no—
217#41×C29—21no—
218#41×C29—21no—
219#41×C29—21no—
220#41×C29—21no—
221#41×C29—42no—
222#41×C29—42no—
223#41×C29—41no—
224#41×C29—41no—
225#41×C29—42no—
226#41×C29—42no—
227#41×C29—42no—
228#41×C29—42no—
229#41×C29—44no—
230#41×C29—44no—
231#41×C29—42no—
232#41×C29—42no—
233#41×C29C2×D412yes—
234#41×C29#4112yes—
235C2×Q8×C29—22no—
236C2×Q8×C29—21no—
237C2×Q8×C29—21no—
238C2×Q8×C29—21no—
239C2×Q8×C29—21no—
240C2×Q8×C29—21no—
241C2×Q8×C29—21no—
242C2×Q8×C29—21no—
243C2×Q8×C29—22no—
244C2×Q8×C29—41no—
245C2×Q8×C29—42no—
246C2×Q8×C29—42no—
247C2×Q8×C29—42no—
248C2×Q8×C29—42no—
249C2×Q8×C29C2×D411yescharacteristic
250C2×Q8×C29C2×D411yescharacteristic
251C2×Q8×C29C2×D411yescharacteristic
252C2×D4×C29—21no—
253C2×D4×C29—22no—
254C2×D4×C29—22no—
255C2×D4×C29—21no—
256C2×D4×C29—21no—
257C2×D4×C29—21no—
258C2×D4×C29—21no—
259C2×D4×C29—21no—
260C2×D4×C29—22no—
261C2×D4×C29—21no—
262C2×D4×C29—21no—
263C2×D4×C29—21no—
264C2×D4×C29—21no—
265C2×D4×C29—21no—
266C2×D4×C29—21no—
267C2×D4×C29—21no—
268C2×D4×C29—21no—
269C2×D4×C29—41no—
270C2×D4×C29—42no—
271C2×D4×C29—42no—
272C2×D4×C29—41no—
273C2×D4×C29—41no—
274C2×D4×C29—82no—
275C2×D4×C29C2×D411yescharacteristic
276C2×D4×C29C2×D411yescharacteristic
277C2×D4×C29C2×D411yescharacteristic
278C22×C4×C29—21no—
279C22×C4×C29—21no—
280C22×C4×C29—21no—
281C22×C4×C29—21no—
282C22×C4×C29—21no—
283C22×C4×C29—22no—
284C22×C4×C29—22no—
285C22×C4×C29—21no—
286C22×C4×C29—21no—
287C22×C4×C29—22no—
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—42no—
295C22×C4×C29—42no—
296C22×C4×C29C2×D412yes—
297C22×C4×C29C2×D411yescharacteristic
298C22×C4×C29C2×D411yescharacteristic
299C22×C4×C29C2×D411yescharacteristic
300C22×C4×C29C2×D411yescharacteristic
301C22×C4×C29C2×D411yescharacteristic
302C22×C4×C29C2×D412yes—
303C22×C4×C29C2411yescharacteristic
304SD16×C29—42no—
305SD16×C29—42no—
306SD16×C29—42no—
307D8×C29—42no—
308D8×C29—42no—
309D8×C29—42no—
310M16×C29—21no—
311M16×C29—21no—
312M16×C29—21no—
313M16×C29—21no—
314M16×C29—21no—
315M16×C29—21no—
316M16×C29—21no—
317M16×C29—42no—
318M16×C29C2×D412yes—
319C2×C8×C29—21no—
320C2×C8×C29—21no—
321C2×C8×C29—21no—
322C2×C8×C29—21no—
323C2×C8×C29—42no—
324C4⋊C4×C29—22no—
325C4⋊C4×C29—22no—
326C4⋊C4×C29—22no—
327C4⋊C4×C29—22no—
328C4⋊C4×C29—21no—
329C4⋊C4×C29—22no—
330C4⋊C4×C29—22no—
331C4⋊C4×C29—21no—
332C4⋊C4×C29—21no—
333C4⋊C4×C29—21no—
334C4⋊C4×C29—21no—
335C4⋊C4×C29—21no—
336C4⋊C4×C29—42no—
337C4⋊C4×C29—82no—
338C4⋊C4×C29C2×D411yescharacteristic
339C4⋊C4×C29C2×D411yescharacteristic
340C22⋊C4×C29—22no—
341C22⋊C4×C29—22no—
342C22⋊C4×C29—22no—
343C22⋊C4×C29—22no—
344C22⋊C4×C29—22no—
345C22⋊C4×C29—21no—
346C22⋊C4×C29—22no—
347C22⋊C4×C29—22no—
348C22⋊C4×C29—21no—
349C22⋊C4×C29—21no—
350C22⋊C4×C29—21no—
351C22⋊C4×C29—21no—
352C22⋊C4×C29—44no—
353C22⋊C4×C29—42no—
354C22⋊C4×C29—41no—
355C22⋊C4×C29—41no—
356C22⋊C4×C29—82no—
357C42×C29—22no—
358C42×C29—21no—
359C42×C29—21no—
360C42×C29—21no—
361C42×C29—21no—
362C42×C29C2×D412yes—
363#24469C2911yesmaximal, characteristic, direct product factor, Sylow
364C23×C29—21no—
365C23×C29—21no—
366C23×C29—21no—
367C23×C29—21no—
368C23×C29—21no—
369C23×C29—41no—
370C23×C29—41no—
371C23×C29—42no—
372C23×C29—42no—
373C23×C29—42no—
374C23×C29—42no—
375C23×C29—41no—
376C23×C29—41no—
377C23×C29—41no—
378C23×C29—81no—
379C23×C29#12011yescharacteristic
380C23×C29#12011yescharacteristic
381C23×C29C22×D411yescharacteristic
382Q8×C29—21no—
383Q8×C29—21no—
384Q8×C29—21no—
385Q8×C29—21no—
386Q8×C29—21no—
387Q8×C29—42no—
388Q8×C29—44no—
389Q8×C29—41no—
390Q8×C29—41no—
391Q8×C29—41no—
392Q8×C29—41no—
393Q8×C29#12112yes—
394D4×C29—22no—
395D4×C29—22no—
396D4×C29—21no—
397D4×C29—21no—
398D4×C29—21no—
399D4×C29—21no—
400D4×C29—21no—
401D4×C29—42no—
402D4×C29—42no—
403D4×C29—42no—
404D4×C29—42no—
405D4×C29—44no—
406D4×C29—41no—
407D4×C29—41no—
408D4×C29—41no—
409D4×C29—41no—
410D4×C29—41no—
411D4×C29—41no—
412D4×C29—41no—
413D4×C29—41no—
414D4×C29—81no—
415D4×C29—82no—
416D4×C29—82no—
417D4×C29—82no—
418D4×C29#12112yes—
419C2×C4×C29—21no—
420C2×C4×C29—21no—
421C2×C4×C29—21no—
422C2×C4×C29—21no—
423C2×C4×C29—21no—
424C2×C4×C29—21no—
425C2×C4×C29—21no—
426C2×C4×C29—21no—
427C2×C4×C29—21no—
428C2×C4×C29—22no—
429C2×C4×C29—21no—
430C2×C4×C29—21no—
431C2×C4×C29—22no—
432C2×C4×C29—21no—
433C2×C4×C29—22no—
434C2×C4×C29—21no—
435C2×C4×C29—21no—
436C2×C4×C29—22no—
437C2×C4×C29—21no—
438C2×C4×C29—22no—
439C2×C4×C29—22no—
440C2×C4×C29—22no—
441C2×C4×C29—42no—
442C2×C4×C29—42no—
443C2×C4×C29—42no—
444C2×C4×C29—44no—
445C2×C4×C29—41no—
446C2×C4×C29—41no—
447C2×C4×C29—44no—
448C2×C4×C29—41no—
449C2×C4×C29—41no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—42no—
453C2×C4×C29—41no—
454C2×C4×C29—42no—
455C2×C4×C29—41no—
456C2×C4×C29—41no—
457C2×C4×C29—41no—
458C2×C4×C29—82no—
459C2×C4×C29#12011yescharacteristic
460C2×C4×C29#12011yescharacteristic
461C2×C4×C29C22×D411yescharacteristic
462C2×C4×C29C22×D411yescharacteristic
463C2×C4×C29C22×D411yescharacteristic
464C2×C4×C29C2×#4111yescharacteristic
465C2×C4×C29H(5,𝔽2)11yescharacteristic
466C2×C4×C29H(5,𝔽2)11yescharacteristic
467C8×C29—22no—
468C8×C29—41no—
469C8×C29—41no—
470C8×C29—41no—
471#3489C2×C2911yescharacteristic, complemented
472#3055C2×C2911yescharacteristic, complemented
473C2×#454C2×C2911yescharacteristic, complemented
474#3006C2×C2911yescharacteristic, complemented
475C2×#421C2×C2911yescharacteristic, complemented
476#2620C2×C2911yescharacteristic, complemented
477#2039C2×C2911yescharacteristic, complemented
478#2038C2×C2911yescharacteristic, complemented
479#2006C2×C2911yescharacteristic, complemented
480#2003C2×C2911yescharacteristic, complemented
481#1901C2×C2911yescharacteristic, complemented
482#1897C2×C2911yescharacteristic, complemented
483#1883C2×C2911yescharacteristic, complemented
484#1859C2×C2911yescharacteristic, complemented
485#1793C2×C2911yescharacteristic, complemented
486C22×C29—21no—
487C22×C29—21no—
488C22×C29—21no—
489C22×C29—21no—
490C22×C29—22no—
491C22×C29—21no—
492C22×C29—21no—
493C22×C29—21no—
494C22×C29—21no—
495C22×C29—41no—
496C22×C29—41no—
497C22×C29—41no—
498C22×C29—41no—
499C22×C29—41no—
500C22×C29—41no—
501C22×C29—41no—
502C22×C29—41no—
503C22×C29—81no—
504C22×C29—81no—
505C22×C29—82no—
506C22×C29—82no—
507C22×C29—84no—
508C22×C29—81no—
509C22×C29—81no—
510C22×C29—81no—
511C22×C29C2×#12011yescharacteristic
512C22×C29D4211yescharacteristic
513C22×C29#54611yescharacteristic
514C4×C29—21no—
515C4×C29—21no—
516C4×C29—22no—
517C4×C29—42no—
518C4×C29—42no—
519C4×C29—41no—
520C4×C29—41no—
521C4×C29—41no—
522C4×C29—42no—
523C4×C29—41no—
524C4×C29—81no—
525C4×C29—81no—
526C4×C29C2×#12111yescharacteristic
527C4×C29#53411yescharacteristic
528C4×C29D4211yescharacteristic
529C4×C29#54611yescharacteristic
530C2×2−1+4C22×C2911yescharacteristic
531C22×#41C22×C2911yescharacteristic
532C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
533C2×AGL(1,ℤ/8)C22×C2911yescharacteristic
534C2×AGL(1,ℤ/8)C22×C2911yescharacteristic, complemented
535C22×M16C22×C2911yescharacteristic
536D4×Q8—21no—
537#548—21no—
538#547—21no—
539#547—22no—
540#546—21no—
541#546—22no—
542#537—21no—
543#537C22×C2911yescharacteristic
544#536—21no—
545#536C22×C2911yescharacteristic
546C2×#124C22×C2911yescharacteristic, complemented
547#525—21no—
548#525C22×C2911yescharacteristic
549C2×C22⋊Q8—21no—
550C2×C22⋊Q8C22×C2911yescharacteristic
551C2×#121C22×C2911yescharacteristic
552#520C22×C2911yescharacteristic
553C2×#117C22×C2911yescharacteristic
554#469—21no—
555#468—21no—
556#466—21no—
557#465—21no—
558#454—24no—
559#449—21no—
560#449—21no—
561#448—21no—
562#447—21no—
563#428C22×C2911yescharacteristic, complemented
564#421—24no—
565C2×#104C22×C2911yescharacteristic
566C2×#104C22×C2911yescharacteristic
567C2×#104C22×C2911yescharacteristic
568C2×#104C22×C2911yescharacteristic
569C2×#104C22×C2911yescharacteristic, complemented
570C2×#104C22×C2911yescharacteristic, complemented
571#418C22×C2911yescharacteristic, complemented
572#417C22×C2911yescharacteristic
573#417C22×C2911yescharacteristic
574#417C22×C2911yescharacteristic, complemented
575C2×#101C22×C2911yescharacteristic, complemented
576C2×#101C22×C2911yescharacteristic, complemented
577#407C22×C2911yescharacteristic
578#396—22no—
579#394—22no—
580#391C22×C2911yescharacteristic, complemented
581#390C22×C2911yescharacteristic, complemented
582#384C22×C2911yescharacteristic, complemented
583#343C22×C2911yescharacteristic, complemented
584#343C22×C2911yescharacteristic, complemented
585#339C22×C2911yescharacteristic, complemented
586#339C22×C2911yescharacteristic, complemented
587C2×C29—21no—
588C2×C29—21no—
589C2×C29—41no—
590C2×C29—41no—
591C2×C29—42no—
592C2×C29—81no—
593C2×C29—81no—
594C2×C29—161no—
595C2×C29#241011yescharacteristic
596C2×C29#302011yescharacteristic
597C2×C29#302111yescharacteristic
5982−1+4—22no—
5992−1+4—22no—
6002−1+4—41no—
6012−1+4—41no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—21no—
605C2×#41—22no—
606C2×#41—21no—
607C2×#41—22no—
608C2×#41—22no—
609C2×#41—41no—
610C2×#41—41no—
611C2×#41D4×C2911yescharacteristic
612C2×#41D4×C2911yescharacteristic
613C2×#41C23×C2911yescharacteristic
614C2×#41C23×C2911yescharacteristic
615C2×#41C23×C2911yescharacteristic
616C22×Q8—21no—
617C22×Q8—21no—
618C22×Q8D4×C2911yescharacteristic
619C22×Q8C23×C2911yescharacteristic
620C22×D4—21no—
621C22×D4—21no—
622C22×D4D4×C2911yescharacteristic
623C22×D4C23×C2911yescharacteristic
624C23×C4—21no—
625C23×C4C23×C2911yescharacteristic
626AGL(1,ℤ/8)—22no—
627AGL(1,ℤ/8)—22no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—41no—
630AGL(1,ℤ/8)—41no—
631AGL(1,ℤ/8)—41no—
632C2×SD16—21no—
633C2×SD16—21no—
634C2×SD16—21no—
635C2×D8—21no—
636C2×D8—21no—
637C2×D8—21no—
638C2×M16—21no—
639C2×M16—22no—
640C2×M16—41no—
641C2×M16C23×C2911yescharacteristic
642C2×M16C23×C2911yescharacteristic
643C2×M16C23×C2911yescharacteristic
644C2×M16C23×C2911yescharacteristic
645C22×C8—21no—
646C4⋊Q8—22no—
647C4⋊Q8—21no—
648#124—22no—
649#124—21no—
650#124—22no—
651#124—41no—
652#123—22no—
653#123—22no—
654#123—22no—
655#123—21no—
656#123—22no—
657C22⋊Q8—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—21no—
661C22⋊Q8—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8D4×C2911yescharacteristic
669C22⋊Q8D4×C2911yescharacteristic
670#121—22no—
671#121—22no—
672#121—22no—
673#121—21no—
674#121—21no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121D4×C2911yescharacteristic
681#121D4×C2911yescharacteristic
682#120—22no—
683#120—21no—
684C4×Q8—21no—
685C4×D4—22no—
686C4×D4—22no—
687C4×D4—21no—
688C4×D4—22no—
689C4×D4—21no—
690C4×D4—21no—
691#117—21no—
692#117—22no—
693#117—41no—
694#117C23×C2911yescharacteristic
695C2×C4⋊C4—22no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4D4×C2912yes—
700C2×C4⋊C4C23×C2911yescharacteristic
701C2×C4⋊C4C23×C2911yescharacteristic
702C2×C22⋊C4—22no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4D4×C2912yes—
708C2×C42C23×C2911yescharacteristic
709C2×C42C23×C2911yescharacteristic
710#107—21no—
711#106—21no—
712#104—22no—
713#104—22no—
714#104—22no—
715#104—22no—
716#104—41no—
717#104D4×C2914yescomplemented
718#103—21no—
719#103—21no—
720#103—21no—
721#102—21no—
722#102—21no—
723#102—21no—
724#102—21no—
725#102—21no—
726#101—22no—
727#101—41no—
728C22⋊C8—21no—
729C22⋊C8—21no—
730#95—22no—
731C29#2446911yescharacteristic, direct product factor, Sylow
732C24—21no—
733C24—21no—
734C24C2×D4×C2911yescharacteristic
735#41—21no—
736#41—21no—
737#41—22no—
738#41—22no—
739#41—21no—
740#41—21no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—42no—
748#41—42no—
749#41—41no—
750#41—41no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—44no—
756#41—44no—
757#41—42no—
758#41—42no—
759#41C2×D4×C2912yes—
760#41#41×C2912yes—
761C2×Q8—22no—
762C2×Q8—21no—
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—42no—
772C2×Q8—42no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8C2×D4×C2911yescharacteristic
776C2×Q8C2×D4×C2911yescharacteristic
777C2×Q8C2×D4×C2911yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—41no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—41no—
799C2×D4—41no—
800C2×D4—82no—
801C2×D4C2×D4×C2911yescharacteristic
802C2×D4C2×D4×C2911yescharacteristic
803C2×D4C2×D4×C2911yescharacteristic
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4C2×D4×C2912yes—
823C22×C4C2×D4×C2911yescharacteristic
824C22×C4C2×D4×C2911yescharacteristic
825C22×C4C2×D4×C2911yescharacteristic
826C22×C4C2×D4×C2911yescharacteristic
827C22×C4C2×D4×C2911yescharacteristic
828C22×C4C2×D4×C2912yes—
829C22×C4C24×C2911yescharacteristic
830SD16—42no—
831SD16—42no—
832SD16—42no—
833D8—42no—
834D8—42no—
835D8—42no—
836M16—21no—
837M16—21no—
838M16—21no—
839M16—21no—
840M16—21no—
841M16—21no—
842M16—21no—
843M16—42no—
844M16C2×D4×C2912yes—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
849C2×C8—42no—
850C4⋊C4—22no—
851C4⋊C4—22no—
852C4⋊C4—22no—
853C4⋊C4—22no—
854C4⋊C4—21no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—42no—
863C4⋊C4—82no—
864C4⋊C4C2×D4×C2911yescharacteristic
865C4⋊C4C2×D4×C2911yescharacteristic
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—21no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—44no—
879C22⋊C4—42no—
880C22⋊C4—41no—
881C22⋊C4—41no—
882C22⋊C4—82no—
883C42—22no—
884C42—21no—
885C42—21no—
886C42—21no—
887C42—21no—
888C42C2×D4×C2912yes—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—21no—
894C23—41no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—81no—
904C23C29×#12011yescharacteristic
905C23C29×#12011yescharacteristic
906C23C22×D4×C2911yescharacteristic
907Q8—21no—
908Q8—21no—
909Q8—21no—
910Q8—21no—
911Q8—21no—
912Q8—42no—
913Q8—44no—
914Q8—41no—
915Q8—41no—
916Q8—41no—
917Q8—41no—
918Q8C29×#12112yes—
919D4—22no—
920D4—22no—
921D4—21no—
922D4—21no—
923D4—21no—
924D4—21no—
925D4—21no—
926D4—42no—
927D4—42no—
928D4—42no—
929D4—44no—
930D4—42no—
931D4—41no—
932D4—41no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—81no—
940D4—82no—
941D4—82no—
942D4—82no—
943D4C29×#12112yes—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—22no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—44no—
970C2×C4—41no—
971C2×C4—44no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—41no—
979C2×C4—42no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—82no—
984C2×C4C29×#12011yescharacteristic
985C2×C4C29×#12011yescharacteristic
986C2×C4C22×D4×C2911yescharacteristic
987C2×C4C22×D4×C2911yescharacteristic
988C2×C4C22×D4×C2911yescharacteristic
989C2×C4C2×#41×C2911yescharacteristic
990C2×C4C29×H(5,𝔽2)11yescharacteristic
991C2×C4C29×H(5,𝔽2)11yescharacteristic
992C8—22no—
993C8—41no—
994C8—41no—
995C8—41no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—22no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—41no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—81no—
1014C22—81no—
1015C22—82no—
1016C22—82no—
1017C22—84no—
1018C22—81no—
1019C22—81no—
1020C22—81no—
1021C22C2×C29×#12011yescharacteristic
1022C22D42×C2911yescharacteristic
1023C22C29×#54611yescharacteristic
1024C4—21no—
1025C4—21no—
1026C4—22no—
1027C4—42no—
1028C4—41no—
1029C4—42no—
1030C4—41no—
1031C4—42no—
1032C4—41no—
1033C4—41no—
1034C4—81no—
1035C4—81no—
1036C4C2×C29×#12111yescharacteristic
1037C4C29×#53411yescharacteristic
1038C4D42×C2911yescharacteristic
1039C4C29×#54611yescharacteristic
1040C2—21no—
1041C2—21no—
1042C2—41no—
1043C2—41no—
1044C2—42no—
1045C2—81no—
1046C2—81no—
1047C2—161no—
1048C2C29×#241011yescharacteristic
1049C2C29×#302011yescharacteristic
1050C2C29×#302111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3489C2semidirect
2. C29×#3055C2semidirect
3. C2×C29×#454C2semidirect
4. C29×#3006C2semidirect
5. C2×C29×#421C2semidirect
6. C29×#2620C2semidirect
7. C29×#2039C2semidirect
8. C29×#2038C2semidirect
9. C29×#2006C2semidirect
10. C29×#2003C2semidirect
11. C29×#1901C2semidirect
12. C29×#1897C2semidirect
13. C29×#1883C2semidirect
14. C29×#1859C2semidirect
15. C29×#1793C2semidirect
20. C2×C29×AGL(1,ℤ/8)C22semidirect
32. C2×C29×#124C22semidirect
49. C29×#428C22semidirect
55. C2×C29×#104C22semidirect
56. C2×C29×#104C22semidirect
57. C29×#418C22semidirect
60. C29×#417C22semidirect
61. C2×C29×#101C22semidirect
62. C2×C29×#101C22semidirect
66. C29×#391C22semidirect
67. C29×#390C22semidirect
68. C29×#384C22semidirect
69. C29×#343C22semidirect
70. C29×#343C22semidirect
71. C29×#339C22semidirect
72. C29×#339C22semidirect
192. C29×#104D4semidirect
363. #24469C29direct (N × H)
471. #3489C2×C29semidirect
472. #3055C2×C29semidirect
473. C2×#454C2×C29semidirect
474. #3006C2×C29semidirect
475. C2×#421C2×C29semidirect
476. #2620C2×C29semidirect
477. #2039C2×C29semidirect
478. #2038C2×C29semidirect
479. #2006C2×C29semidirect
480. #2003C2×C29semidirect
481. #1901C2×C29semidirect
482. #1897C2×C29semidirect
483. #1883C2×C29semidirect
484. #1859C2×C29semidirect
485. #1793C2×C29semidirect
534. C2×AGL(1,ℤ/8)C22×C29semidirect
546. C2×#124C22×C29semidirect
563. #428C22×C29semidirect
569. C2×#104C22×C29semidirect
570. C2×#104C22×C29semidirect
571. #418C22×C29semidirect
574. #417C22×C29semidirect
575. C2×#101C22×C29semidirect
576. C2×#101C22×C29semidirect
580. #391C22×C29semidirect
581. #390C22×C29semidirect
582. #384C22×C29semidirect
583. #343C22×C29semidirect
584. #343C22×C29semidirect
585. #339C22×C29semidirect
586. #339C22×C29semidirect
717. #104D4×C29semidirect
731. C29#24469direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34892
C29×#30552
C2×C29×#4542
C29×#30062
C2×C29×#4212
C29×#26202
C29×#20392
C29×#20382
C29×#20062
C29×#20032
C29×#19012
C29×#18972
C29×#18832
C29×#18592
C29×#17932
#2446929