Finite Group Databasebeta

← C29×#24467 #20319367

Subgroups — C29×#24467 #20319367

Order 7424.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3488C211yesmaximal, characteristic
2C29×#3056C211yesmaximal, characteristic, complemented
3C2×C29×#455C211yesmaximal, characteristic, complemented
4C29×#3007C211yesmaximal, characteristic, complemented
5C22×C29×#104C211yesmaximal, characteristic, complemented
6C29×#2850C211yesmaximal, characteristic, complemented
7C29×#2040C211yesmaximal, characteristic, complemented
8C29×#2037C211yesmaximal, characteristic, complemented
9C29×#2007C211yesmaximal, characteristic, complemented
10C29×#2004C211yesmaximal, characteristic, complemented
11C29×#1900C211yesmaximal, characteristic, complemented
12C29×#1896C211yesmaximal, characteristic, complemented
13C29×#1882C211yesmaximal, characteristic, complemented
14C29×#1860C211yesmaximal, characteristic, complemented
15C29×#1792C211yesmaximal, characteristic, complemented
16C2×C29×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C29C2211yescharacteristic
18C2×C29×#137C2211yescharacteristic
19C2×C29×#137C2211yescharacteristic, complemented
20C2×C29×#137C2211yescharacteristic, complemented
21C22×M16×C29C2211yescharacteristic, complemented
22C29×#550—21no—
23C29×#548—21no—
24C29×#546—21no—
25C29×#546—22no—
26D42×C29—22no—
27D42×C29—21no—
28C29×#537—21no—
29C29×#537C2211yescharacteristic
30C29×#535—21no—
31C29×#535C2211yescharacteristic
32C2×C29×#124C2211yescharacteristic, complemented
33C29×#525—21no—
34C29×#525C2211yescharacteristic
35C2×C29×C22⋊Q8C2211yescharacteristic, complemented
36C2×C29×#121—21no—
37C2×C29×#121C2211yescharacteristic
38C29×#520C2211yescharacteristic
39C22×C42×C29C2211yescharacteristic, complemented
40C29×#470—21no—
41C29×#468—21no—
42C29×#467—21no—
43C29×#465—21no—
44C29×#455—24no—
45C29×#452—21no—
46C29×#452—21no—
47C29×#451—21no—
48C29×#450—21no—
49C29×#428C2211yescharacteristic, complemented
50C2×C29×#104—24no—
51C2×C29×#104C2211yescharacteristic
52C2×C29×#104C2211yescharacteristic
53C2×C29×#104C2211yescharacteristic, complemented
54C2×C29×#104C2211yescharacteristic, complemented
55C2×C29×#104C2211yescharacteristic, complemented
56C2×C29×#104C2211yescharacteristic, complemented
57C29×#419C2211yescharacteristic, complemented
58C29×#417C2211yescharacteristic
59C29×#417C2211yescharacteristic, complemented
60C29×#417C2211yescharacteristic, complemented
61C2×C29×#100C2211yescharacteristic, complemented
62C2×C29×#100C2211yescharacteristic, complemented
63C29×#407C2211yescharacteristic, complemented
64C29×#391C2211yescharacteristic, complemented
65C29×#390C2211yescharacteristic, complemented
66C29×#388—22no—
67C29×#386—22no—
68C29×#382C2211yescharacteristic, complemented
69C29×#343C2211yescharacteristic, complemented
70C29×#343C2211yescharacteristic, complemented
71C29×#339C2211yescharacteristic, complemented
72C29×#339C2211yescharacteristic, complemented
73C29×H(5,𝔽2)—22no—
74C29×H(5,𝔽2)—22no—
75C29×H(5,𝔽2)—41no—
76C29×H(5,𝔽2)—41no—
77C2×#41×C29—21no—
78C2×#41×C29—21no—
79C2×#41×C29—21no—
80C2×#41×C29—21no—
81C2×#41×C29—22no—
82C2×#41×C29—22no—
83C2×#41×C29—41no—
84C2×#41×C29—41no—
85C2×#41×C29D411yescharacteristic
86C2×#41×C29D411yescharacteristic
87C2×#41×C29C2311yescharacteristic
88C2×#41×C29C2311yescharacteristic
89C2×#41×C29C2311yescharacteristic
90C22×Q8×C29D411yescharacteristic
91C22×Q8×C29C2311yescharacteristic
92C22×D4×C29—21no—
93C22×D4×C29—22no—
94C22×D4×C29—22no—
95C22×D4×C29—21no—
96C22×D4×C29—21no—
97C22×D4×C29D411yescharacteristic
98C22×D4×C29D412yes—
99C22×D4×C29C2311yescharacteristic
100C23×C4×C29—21no—
101C23×C4×C29—21no—
102C23×C4×C29C2311yescharacteristic
103C29×#137—22no—
104C29×#137—22no—
105C29×#137—22no—
106C29×#137—41no—
107C29×#137—41no—
108C29×#137—41no—
109C2×Q16×C29—21no—
110C2×Q16×C29—21no—
111C2×Q16×C29—21no—
112C2×SD16×C29—21no—
113C2×SD16×C29—21no—
114C2×SD16×C29—21no—
115C2×M16×C29—21no—
116C2×M16×C29—22no—
117C2×M16×C29—41no—
118C2×M16×C29C2311yescharacteristic
119C2×M16×C29C2311yescharacteristic
120C2×M16×C29C2311yescharacteristic
121C2×M16×C29C2311yescharacteristic
122C22×C8×C29—21no—
123C29×#127—22no—
124C29×#127—21no—
125C29×#124—22no—
126C29×#124—21no—
127C29×#124—22no—
128C29×#124—41no—
129C29×#123—22no—
130C29×#123—21no—
131C29×C22⋊Q8—22no—
132C29×C22⋊Q8—21no—
133C29×C22⋊Q8—21no—
134C29×C22⋊Q8—21no—
135C29×C22⋊Q8—21no—
136C29×C22⋊Q8—21no—
137C29×C22⋊Q8—21no—
138C29×C22⋊Q8D411yescharacteristic
139C29×C22⋊Q8D411yescharacteristic
140C29×#121—22no—
141C29×#121—22no—
142C29×#121—22no—
143C29×#121—22no—
144C29×#121—22no—
145C29×#121—21no—
146C29×#121—21no—
147C29×#121—21no—
148C29×#121—21no—
149C29×#121—21no—
150C29×#121—21no—
151C29×#121—22no—
152C29×#121—21no—
153C29×#121—21no—
154C29×#121D411yescharacteristic
155C29×#121D411yescharacteristic
156C29×#120—22no—
157C29×#120—22no—
158C29×#120—22no—
159C29×#120—21no—
160C29×#120—22no—
161C4×Q8×C29—21no—
162C4×D4×C29—22no—
163C4×D4×C29—22no—
164C4×D4×C29—21no—
165C4×D4×C29—22no—
166C4×D4×C29—21no—
167C4×D4×C29—21no—
168C29×#117—21no—
169C29×#117C2311yescharacteristic
170C2×C4⋊C4×C29—21no—
171C2×C4⋊C4×C29—21no—
172C2×C4⋊C4×C29C2311yescharacteristic
173C2×C4⋊C4×C29C2311yescharacteristic
174C2×C22⋊C4×C29—22no—
175C2×C22⋊C4×C29—21no—
176C2×C22⋊C4×C29—22no—
177C2×C22⋊C4×C29—22no—
178C2×C22⋊C4×C29D412yes—
179C2×C42×C29—22no—
180C2×C42×C29—21no—
181C2×C42×C29—41no—
182C2×C42×C29C2311yescharacteristic
183C2×C42×C29C2311yescharacteristic
184C29×#107—21no—
185C29×#106—21no—
186C29×#104—22no—
187C29×#104—22no—
188C29×#104—22no—
189C29×#104—22no—
190C29×#104—41no—
191C29×#104D414yescomplemented
192C29×#103—21no—
193C29×#103—21no—
194C29×#103—21no—
195C29×#103—21no—
196C29×#103—21no—
197C29×#102—21no—
198C29×#102—21no—
199C29×#102—21no—
200C29×#100—22no—
201C29×#100—41no—
202C29×C22⋊C8—21no—
203C29×C22⋊C8—21no—
204C29×#95—22no—
205C29×#95—22no—
206C24×C29—22no—
207C24×C29—21no—
208C24×C29C2×D411yescharacteristic
209C24×C29C2×D412yes—
210#41×C29—21no—
211#41×C29—21no—
212#41×C29—22no—
213#41×C29—22no—
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—21no—
222#41×C29—42no—
223#41×C29—42no—
224#41×C29—41no—
225#41×C29—41no—
226#41×C29—42no—
227#41×C29—42no—
228#41×C29—42no—
229#41×C29—42no—
230#41×C29—42no—
231#41×C29—42no—
232#41×C29C2×D412yes—
233#41×C29#4112yes—
234C2×Q8×C29—21no—
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—41no—
243C2×Q8×C29C2×D411yescharacteristic
244C2×Q8×C29C2×D411yescharacteristic
245C2×Q8×C29C2×D411yescharacteristic
246C2×D4×C29—21no—
247C2×D4×C29—22no—
248C2×D4×C29—22no—
249C2×D4×C29—22no—
250C2×D4×C29—22no—
251C2×D4×C29—21no—
252C2×D4×C29—21no—
253C2×D4×C29—21no—
254C2×D4×C29—21no—
255C2×D4×C29—21no—
256C2×D4×C29—22no—
257C2×D4×C29—22no—
258C2×D4×C29—22no—
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—41no—
269C2×D4×C29—42no—
270C2×D4×C29—42no—
271C2×D4×C29—42no—
272C2×D4×C29—42no—
273C2×D4×C29—44no—
274C2×D4×C29—44no—
275C2×D4×C29—42no—
276C2×D4×C29—42no—
277C2×D4×C29—44no—
278C2×D4×C29—84no—
279C2×D4×C29C2×D411yescharacteristic
280C2×D4×C29C2×D411yescharacteristic
281C2×D4×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—22no—
288C22×C4×C29—21no—
289C22×C4×C29—21no—
290C22×C4×C29—21no—
291C22×C4×C29—22no—
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—42no—
299C22×C4×C29—42no—
300C22×C4×C29—42no—
301C22×C4×C29—42no—
302C22×C4×C29—42no—
303C22×C4×C29C2×D411yescharacteristic
304C22×C4×C29C2×D411yescharacteristic
305C22×C4×C29C2×D411yescharacteristic
306C22×C4×C29C2×D411yescharacteristic
307C22×C4×C29C2×D411yescharacteristic
308C22×C4×C29C2×D412yes—
309C22×C4×C29C2411yescharacteristic
310Q16×C29—42no—
311Q16×C29—42no—
312Q16×C29—42no—
313SD16×C29—42no—
314SD16×C29—42no—
315SD16×C29—42no—
316M16×C29—21no—
317M16×C29—21no—
318M16×C29—21no—
319M16×C29—21no—
320M16×C29—21no—
321M16×C29—21no—
322M16×C29—21no—
323M16×C29—42no—
324M16×C29C2×D412yescomplemented
325C2×C8×C29—21no—
326C2×C8×C29—21no—
327C2×C8×C29—21no—
328C2×C8×C29—21no—
329C2×C8×C29—42no—
330C4⋊C4×C29—22no—
331C4⋊C4×C29—22no—
332C4⋊C4×C29—21no—
333C4⋊C4×C29—21no—
334C4⋊C4×C29—21no—
335C4⋊C4×C29—21no—
336C4⋊C4×C29—21no—
337C4⋊C4×C29—21no—
338C4⋊C4×C29—41no—
339C4⋊C4×C29—41no—
340C4⋊C4×C29C2×D411yescharacteristic
341C4⋊C4×C29C2×D411yescharacteristic
342C22⋊C4×C29—22no—
343C22⋊C4×C29—22no—
344C22⋊C4×C29—22no—
345C22⋊C4×C29—22no—
346C22⋊C4×C29—22no—
347C22⋊C4×C29—21no—
348C22⋊C4×C29—21no—
349C22⋊C4×C29—21no—
350C22⋊C4×C29—21no—
351C22⋊C4×C29—22no—
352C22⋊C4×C29—22no—
353C22⋊C4×C29—21no—
354C22⋊C4×C29—44no—
355C22⋊C4×C29—44no—
356C22⋊C4×C29—41no—
357C22⋊C4×C29—41no—
358C42×C29—22no—
359C42×C29—21no—
360C42×C29—21no—
361C42×C29—21no—
362C42×C29—21no—
363C42×C29—42no—
364C42×C29C2×D412yescomplemented
365#24467C2911yesmaximal, characteristic, direct product factor, Sylow
366C23×C29—21no—
367C23×C29—21no—
368C23×C29—21no—
369C23×C29—22no—
370C23×C29—22no—
371C23×C29—21no—
372C23×C29—21no—
373C23×C29—22no—
374C23×C29—22no—
375C23×C29—41no—
376C23×C29—42no—
377C23×C29—44no—
378C23×C29—42no—
379C23×C29—42no—
380C23×C29—42no—
381C23×C29—81no—
382C23×C29—82no—
383C23×C29—82no—
384C23×C29#12011yescharacteristic
385C23×C29#12011yescharacteristic
386C23×C29C22×D411yescharacteristic
387Q8×C29—21no—
388Q8×C29—21no—
389Q8×C29—21no—
390Q8×C29—21no—
391Q8×C29—21no—
392Q8×C29—42no—
393Q8×C29—41no—
394Q8×C29—41no—
395Q8×C29—41no—
396Q8×C29—41no—
397Q8×C29#12112yes—
398D4×C29—22no—
399D4×C29—22no—
400D4×C29—21no—
401D4×C29—21no—
402D4×C29—21no—
403D4×C29—21no—
404D4×C29—21no—
405D4×C29—42no—
406D4×C29—42no—
407D4×C29—44no—
408D4×C29—42no—
409D4×C29—44no—
410D4×C29—41no—
411D4×C29—41no—
412D4×C29—41no—
413D4×C29—41no—
414D4×C29—44no—
415D4×C29—42no—
416D4×C29—41no—
417D4×C29—41no—
418D4×C29—41no—
419D4×C29—41no—
420D4×C29—81no—
421D4×C29—82no—
422D4×C29—82no—
423D4×C29—82no—
424D4×C29—82no—
425D4×C29#12112yes—
426C2×C4×C29—21no—
427C2×C4×C29—21no—
428C2×C4×C29—21no—
429C2×C4×C29—21no—
430C2×C4×C29—21no—
431C2×C4×C29—21no—
432C2×C4×C29—21no—
433C2×C4×C29—21no—
434C2×C4×C29—21no—
435C2×C4×C29—22no—
436C2×C4×C29—21no—
437C2×C4×C29—21no—
438C2×C4×C29—22no—
439C2×C4×C29—22no—
440C2×C4×C29—21no—
441C2×C4×C29—22no—
442C2×C4×C29—21no—
443C2×C4×C29—21no—
444C2×C4×C29—21no—
445C2×C4×C29—22no—
446C2×C4×C29—42no—
447C2×C4×C29—42no—
448C2×C4×C29—42no—
449C2×C4×C29—44no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—41no—
453C2×C4×C29—48no—
454C2×C4×C29—41no—
455C2×C4×C29—41no—
456C2×C4×C29—41no—
457C2×C4×C29—41no—
458C2×C4×C29—41no—
459C2×C4×C29—42no—
460C2×C4×C29—42no—
461C2×C4×C29—41no—
462C2×C4×C29—41no—
463C2×C4×C29—41no—
464C2×C4×C29—41no—
465C2×C4×C29—82no—
466C2×C4×C29#12011yescharacteristic
467C2×C4×C29#12011yescharacteristic
468C2×C4×C29C22×D411yescharacteristic
469C2×C4×C29C22×D411yescharacteristic
470C2×C4×C29C22×D411yescharacteristic
471C2×C4×C29C2×#4111yescharacteristic
472C2×C4×C29H(5,𝔽2)11yescharacteristic
473C2×C4×C29H(5,𝔽2)11yescharacteristic
474C8×C29—22no—
475C8×C29—41no—
476C8×C29—41no—
477C8×C29—41no—
478#3488C2×C2911yescharacteristic
479#3056C2×C2911yescharacteristic, complemented
480C2×#455C2×C2911yescharacteristic, complemented
481#3007C2×C2911yescharacteristic, complemented
482C22×#104C2×C2911yescharacteristic, complemented
483#2850C2×C2911yescharacteristic, complemented
484#2040C2×C2911yescharacteristic, complemented
485#2037C2×C2911yescharacteristic, complemented
486#2007C2×C2911yescharacteristic, complemented
487#2004C2×C2911yescharacteristic, complemented
488#1900C2×C2911yescharacteristic, complemented
489#1896C2×C2911yescharacteristic, complemented
490#1882C2×C2911yescharacteristic, complemented
491#1860C2×C2911yescharacteristic, complemented
492#1792C2×C2911yescharacteristic, complemented
493C22×C29—21no—
494C22×C29—21no—
495C22×C29—21no—
496C22×C29—21no—
497C22×C29—21no—
498C22×C29—22no—
499C22×C29—21no—
500C22×C29—21no—
501C22×C29—42no—
502C22×C29—42no—
503C22×C29—41no—
504C22×C29—41no—
505C22×C29—41no—
506C22×C29—41no—
507C22×C29—42no—
508C22×C29—42no—
509C22×C29—41no—
510C22×C29—41no—
511C22×C29—41no—
512C22×C29—42no—
513C22×C29—41no—
514C22×C29—84no—
515C22×C29—82no—
516C22×C29—82no—
517C22×C29—164no—
518C22×C29#45512yescomplemented
519C22×C29C2×#12011yescharacteristic
520C22×C29D4211yescharacteristic
521C22×C29#54611yescharacteristic
522C4×C29—21no—
523C4×C29—21no—
524C4×C29—22no—
525C4×C29—42no—
526C4×C29—42no—
527C4×C29—41no—
528C4×C29—41no—
529C4×C29—42no—
530C4×C29—41no—
531C4×C29—41no—
532C4×C29—81no—
533C4×C29—81no—
534C4×C29C2×#12111yescharacteristic
535C4×C29#53411yescharacteristic
536C4×C29D4211yescharacteristic
537C4×C29#54611yescharacteristic
538C2×H(5,𝔽2)C22×C2911yescharacteristic
539C22×#41C22×C2911yescharacteristic
540C2×#137C22×C2911yescharacteristic
541C2×#137C22×C2911yescharacteristic, complemented
542C2×#137C22×C2911yescharacteristic, complemented
543C22×M16C22×C2911yescharacteristic, complemented
544#550—21no—
545#548—21no—
546#546—21no—
547#546—22no—
548D42—22no—
549D42—21no—
550#537—21no—
551#537C22×C2911yescharacteristic
552#535—21no—
553#535C22×C2911yescharacteristic
554C2×#124C22×C2911yescharacteristic, complemented
555#525—21no—
556#525C22×C2911yescharacteristic
557C2×C22⋊Q8C22×C2911yescharacteristic, complemented
558C2×#121—21no—
559C2×#121C22×C2911yescharacteristic
560#520C22×C2911yescharacteristic
561C22×C42C22×C2911yescharacteristic, complemented
562#470—21no—
563#468—21no—
564#467—21no—
565#465—21no—
566#455—24no—
567#452—21no—
568#452—21no—
569#451—21no—
570#450—21no—
571#428C22×C2911yescharacteristic, complemented
572C2×#104—24no—
573C2×#104C22×C2911yescharacteristic
574C2×#104C22×C2911yescharacteristic
575C2×#104C22×C2911yescharacteristic, complemented
576C2×#104C22×C2911yescharacteristic, complemented
577C2×#104C22×C2911yescharacteristic, complemented
578C2×#104C22×C2911yescharacteristic, complemented
579#419C22×C2911yescharacteristic, complemented
580#417C22×C2911yescharacteristic
581#417C22×C2911yescharacteristic, complemented
582#417C22×C2911yescharacteristic, complemented
583C2×#100C22×C2911yescharacteristic, complemented
584C2×#100C22×C2911yescharacteristic, complemented
585#407C22×C2911yescharacteristic, complemented
586#391C22×C2911yescharacteristic, complemented
587#390C22×C2911yescharacteristic, complemented
588#388—22no—
589#386—22no—
590#382C22×C2911yescharacteristic, complemented
591#343C22×C2911yescharacteristic, complemented
592#343C22×C2911yescharacteristic, complemented
593#339C22×C2911yescharacteristic, complemented
594#339C22×C2911yescharacteristic, complemented
595C2×C29—21no—
596C2×C29—21no—
597C2×C29—22no—
598C2×C29—41no—
599C2×C29—42no—
600C2×C29—81no—
601C2×C29—82no—
602C2×C29—81no—
603C2×C29#241011yescharacteristic
604C2×C29C2×#45511yescharacteristic
605C2×C29#301811yescharacteristic
606H(5,𝔽2)—22no—
607H(5,𝔽2)—22no—
608H(5,𝔽2)—41no—
609H(5,𝔽2)—41no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—22no—
615C2×#41—22no—
616C2×#41—41no—
617C2×#41—41no—
618C2×#41D4×C2911yescharacteristic
619C2×#41D4×C2911yescharacteristic
620C2×#41C23×C2911yescharacteristic
621C2×#41C23×C2911yescharacteristic
622C2×#41C23×C2911yescharacteristic
623C22×Q8D4×C2911yescharacteristic
624C22×Q8C23×C2911yescharacteristic
625C22×D4—21no—
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—21no—
629C22×D4—21no—
630C22×D4D4×C2911yescharacteristic
631C22×D4D4×C2912yes—
632C22×D4C23×C2911yescharacteristic
633C23×C4—21no—
634C23×C4—21no—
635C23×C4C23×C2911yescharacteristic
636#137—22no—
637#137—22no—
638#137—22no—
639#137—41no—
640#137—41no—
641#137—41no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16—21no—
645C2×SD16—21no—
646C2×SD16—21no—
647C2×SD16—21no—
648C2×M16—21no—
649C2×M16—22no—
650C2×M16—41no—
651C2×M16C23×C2911yescharacteristic
652C2×M16C23×C2911yescharacteristic
653C2×M16C23×C2911yescharacteristic
654C2×M16C23×C2911yescharacteristic
655C22×C8—21no—
656#127—22no—
657#127—21no—
658#124—22no—
659#124—21no—
660#124—22no—
661#124—41no—
662#123—22no—
663#123—21no—
664C22⋊Q8—22no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8D4×C2911yescharacteristic
672C22⋊Q8D4×C2911yescharacteristic
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—22no—
685#121—21no—
686#121—21no—
687#121D4×C2911yescharacteristic
688#121D4×C2911yescharacteristic
689#120—22no—
690#120—22no—
691#120—22no—
692#120—21no—
693#120—22no—
694C4×Q8—21no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—22no—
699C4×D4—21no—
700C4×D4—21no—
701#117—21no—
702#117C23×C2911yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4C23×C2911yescharacteristic
706C2×C4⋊C4C23×C2911yescharacteristic
707C2×C22⋊C4—22no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4D4×C2912yes—
712C2×C42—22no—
713C2×C42—21no—
714C2×C42—41no—
715C2×C42C23×C2911yescharacteristic
716C2×C42C23×C2911yescharacteristic
717#107—21no—
718#106—21no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—22no—
723#104—41no—
724#104D4×C2914yescomplemented
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#103—21no—
730#102—21no—
731#102—21no—
732#102—21no—
733#100—22no—
734#100—41no—
735C22⋊C8—21no—
736C22⋊C8—21no—
737#95—22no—
738#95—22no—
739C29#2446711yescharacteristic, direct product factor, Sylow
740C24—22no—
741C24—21no—
742C24C2×D4×C2911yescharacteristic
743C24C2×D4×C2912yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41C2×D4×C2912yes—
767#41#41×C2912yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—41no—
777C2×Q8C2×D4×C2911yescharacteristic
778C2×Q8C2×D4×C2911yescharacteristic
779C2×Q8C2×D4×C2911yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×D4×C2911yescharacteristic
814C2×D4C2×D4×C2911yescharacteristic
815C2×D4C2×D4×C2911yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4C2×D4×C2911yescharacteristic
838C22×C4C2×D4×C2911yescharacteristic
839C22×C4C2×D4×C2911yescharacteristic
840C22×C4C2×D4×C2911yescharacteristic
841C22×C4C2×D4×C2911yescharacteristic
842C22×C4C2×D4×C2912yes—
843C22×C4C24×C2911yescharacteristic
844Q16—42no—
845Q16—42no—
846Q16—42no—
847SD16—42no—
848SD16—42no—
849SD16—42no—
850M16—21no—
851M16—21no—
852M16—21no—
853M16—21no—
854M16—21no—
855M16—21no—
856M16—21no—
857M16—42no—
858M16C2×D4×C2912yescomplemented
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—42no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—41no—
873C4⋊C4—41no—
874C4⋊C4C2×D4×C2911yescharacteristic
875C4⋊C4C2×D4×C2911yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—41no—
891C22⋊C4—41no—
892C42—22no—
893C42—21no—
894C42—21no—
895C42—21no—
896C42—21no—
897C42—42no—
898C42C2×D4×C2912yescomplemented
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23C29×#12011yescharacteristic
918C23C29×#12011yescharacteristic
919C23C22×D4×C2911yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—41no—
927Q8—41no—
928Q8—41no—
929Q8—41no—
930Q8C29×#12112yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—82no—
954D4—81no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4C29×#12112yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—22no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—44no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—48no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—82no—
999C2×C4C29×#12011yescharacteristic
1000C2×C4C29×#12011yescharacteristic
1001C2×C4C22×D4×C2911yescharacteristic
1002C2×C4C22×D4×C2911yescharacteristic
1003C2×C4C22×D4×C2911yescharacteristic
1004C2×C4C2×#41×C2911yescharacteristic
1005C2×C4C29×H(5,𝔽2)11yescharacteristic
1006C2×C4C29×H(5,𝔽2)11yescharacteristic
1007C8—22no—
1008C8—41no—
1009C8—41no—
1010C8—41no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22C29×#45512yescomplemented
1037C22C2×C29×#12011yescharacteristic
1038C22D42×C2911yescharacteristic
1039C22C29×#54611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—41no—
1047C4—41no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C4—81no—
1052C4C2×C29×#12111yescharacteristic
1053C4C29×#53411yescharacteristic
1054C4D42×C2911yescharacteristic
1055C4C29×#54611yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2C29×#241011yescharacteristic
1065C2C2×C29×#45511yescharacteristic
1066C2C29×#301811yescharacteristic
subgroupG/H
center, socleC22×C29C2×#120
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC29×#3488C2
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
2. C29×#3056C2semidirect
3. C2×C29×#455C2semidirect
4. C29×#3007C2semidirect
5. C22×C29×#104C2semidirect
6. C29×#2850C2semidirect
7. C29×#2040C2semidirect
8. C29×#2037C2semidirect
9. C29×#2007C2semidirect
10. C29×#2004C2semidirect
11. C29×#1900C2semidirect
12. C29×#1896C2semidirect
13. C29×#1882C2semidirect
14. C29×#1860C2semidirect
15. C29×#1792C2semidirect
19. C2×C29×#137C22semidirect
20. C2×C29×#137C22semidirect
21. C22×M16×C29C22semidirect
32. C2×C29×#124C22semidirect
35. C2×C29×C22⋊Q8C22semidirect
39. C22×C42×C29C22semidirect
49. C29×#428C22semidirect
53. C2×C29×#104C22semidirect
54. C2×C29×#104C22semidirect
55. C2×C29×#104C22semidirect
56. C2×C29×#104C22semidirect
57. C29×#419C22semidirect
59. C29×#417C22semidirect
60. C29×#417C22semidirect
61. C2×C29×#100C22semidirect
62. C2×C29×#100C22semidirect
63. C29×#407C22semidirect
64. C29×#391C22semidirect
65. C29×#390C22semidirect
68. C29×#382C22semidirect
69. C29×#343C22semidirect
70. C29×#343C22semidirect
71. C29×#339C22semidirect
72. C29×#339C22semidirect
191. C29×#104D4semidirect
324. M16×C29C2×D4semidirect
364. C42×C29C2×D4semidirect
365. #24467C29direct (N × H)
479. #3056C2×C29semidirect
480. C2×#455C2×C29semidirect
481. #3007C2×C29semidirect
482. C22×#104C2×C29semidirect
483. #2850C2×C29semidirect
484. #2040C2×C29semidirect
485. #2037C2×C29semidirect
486. #2007C2×C29semidirect
487. #2004C2×C29semidirect
488. #1900C2×C29semidirect
489. #1896C2×C29semidirect
490. #1882C2×C29semidirect
491. #1860C2×C29semidirect
492. #1792C2×C29semidirect
518. C22×C29#455semidirect
541. C2×#137C22×C29semidirect
542. C2×#137C22×C29semidirect
543. C22×M16C22×C29semidirect
554. C2×#124C22×C29semidirect
557. C2×C22⋊Q8C22×C29semidirect
561. C22×C42C22×C29semidirect
571. #428C22×C29semidirect
575. C2×#104C22×C29semidirect
576. C2×#104C22×C29semidirect
577. C2×#104C22×C29semidirect
578. C2×#104C22×C29semidirect
579. #419C22×C29semidirect
581. #417C22×C29semidirect
582. #417C22×C29semidirect
583. C2×#100C22×C29semidirect
584. C2×#100C22×C29semidirect
585. #407C22×C29semidirect
586. #391C22×C29semidirect
587. #390C22×C29semidirect
590. #382C22×C29semidirect
591. #343C22×C29semidirect
592. #343C22×C29semidirect
593. #339C22×C29semidirect
594. #339C22×C29semidirect
724. #104D4×C29semidirect
739. C29#24467direct (N × H)
858. M16C2×D4×C29semidirect
898. C42C2×D4×C29semidirect
1036. C22C29×#455semidirect

Maximal subgroups

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

subgroupindex
C29×#34882
C29×#30562
C2×C29×#4552
C29×#30072
C22×C29×#1042
C29×#28502
C29×#20402
C29×#20372
C29×#20072
C29×#20042
C29×#19002
C29×#18962
C29×#18822
C29×#18602
C29×#17922
#2446729