Finite Group Databasebeta

← C29×#24471 #20319371

Subgroups — C29×#24471 #20319371

Order 7424.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 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
5C2×C29×#421C211yesmaximal, characteristic, complemented
6C29×#2620C211yesmaximal, characteristic, complemented
7C29×#2039C211yesmaximal, characteristic, complemented
8C29×#2037C211yesmaximal, characteristic, complemented
9C29×#2007C211yesmaximal, characteristic, complemented
10C29×#2004C211yesmaximal, characteristic, complemented
11C29×#1900C211yesmaximal, characteristic, complemented
12C29×#1897C211yesmaximal, characteristic, complemented
13C29×#1882C211yesmaximal, characteristic, complemented
14C29×#1859C211yesmaximal, 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
39C2×C29×#117C2211yescharacteristic, 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
50C29×#421—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×#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×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×C29C2311yescharacteristic
102C29×#137—22no—
103C29×#137—22no—
104C29×#137—22no—
105C29×#137—41no—
106C29×#137—41no—
107C29×#137—41no—
108C2×Q16×C29—21no—
109C2×Q16×C29—21no—
110C2×Q16×C29—21no—
111C2×SD16×C29—21no—
112C2×SD16×C29—21no—
113C2×SD16×C29—21no—
114C2×M16×C29—21no—
115C2×M16×C29—22no—
116C2×M16×C29—41no—
117C2×M16×C29C2311yescharacteristic
118C2×M16×C29C2311yescharacteristic
119C2×M16×C29C2311yescharacteristic
120C2×M16×C29C2311yescharacteristic
121C22×C8×C29—21no—
122C29×#127—22no—
123C29×#127—21no—
124C29×#124—22no—
125C29×#124—21no—
126C29×#124—22no—
127C29×#124—41no—
128C29×#123—22no—
129C29×#123—21no—
130C29×C22⋊Q8—22no—
131C29×C22⋊Q8—21no—
132C29×C22⋊Q8—21no—
133C29×C22⋊Q8—21no—
134C29×C22⋊Q8—21no—
135C29×C22⋊Q8—21no—
136C29×C22⋊Q8—21no—
137C29×C22⋊Q8D411yescharacteristic
138C29×C22⋊Q8D411yescharacteristic
139C29×#121—22no—
140C29×#121—22no—
141C29×#121—22no—
142C29×#121—22no—
143C29×#121—22no—
144C29×#121—21no—
145C29×#121—21no—
146C29×#121—21no—
147C29×#121—21no—
148C29×#121—21no—
149C29×#121—21no—
150C29×#121—22no—
151C29×#121—21no—
152C29×#121—21no—
153C29×#121D411yescharacteristic
154C29×#121D411yescharacteristic
155C29×#120—22no—
156C29×#120—22no—
157C29×#120—22no—
158C29×#120—21no—
159C29×#120—22no—
160C4×Q8×C29—21no—
161C4×D4×C29—22no—
162C4×D4×C29—22no—
163C4×D4×C29—21no—
164C4×D4×C29—22no—
165C4×D4×C29—21no—
166C4×D4×C29—21no—
167C29×#117—21no—
168C29×#117—22no—
169C29×#117—41no—
170C29×#117C2311yescharacteristic
171C2×C4⋊C4×C29—21no—
172C2×C4⋊C4×C29—21no—
173C2×C4⋊C4×C29—21no—
174C2×C4⋊C4×C29—22no—
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×#103—21no—
197C29×#103—21no—
198C29×#102—21no—
199C29×#102—21no—
200C29×#102—21no—
201C29×#100—22no—
202C29×#100—41no—
203C29×C22⋊C8—21no—
204C29×C22⋊C8—21no—
205C29×#95—22no—
206C24×C29—22no—
207C24×C29—21no—
208C24×C29C2×D412yes—
209C24×C29C2×D411yescharacteristic
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—82no—
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—22no—
291C22×C4×C29—21no—
292C22×C4×C29—21no—
293C22×C4×C29—21no—
294C22×C4×C29—21no—
295C22×C4×C29—21no—
296C22×C4×C29—21no—
297C22×C4×C29—21no—
298C22×C4×C29—42no—
299C22×C4×C29—42no—
300C22×C4×C29C2×D411yescharacteristic
301C22×C4×C29C2×D411yescharacteristic
302C22×C4×C29C2×D411yescharacteristic
303C22×C4×C29C2×D411yescharacteristic
304C22×C4×C29C2×D411yescharacteristic
305C22×C4×C29C2×D412yes—
306C22×C4×C29C2411yescharacteristic
307Q16×C29—42no—
308Q16×C29—42no—
309Q16×C29—42no—
310SD16×C29—42no—
311SD16×C29—42no—
312SD16×C29—42no—
313M16×C29—21no—
314M16×C29—21no—
315M16×C29—21no—
316M16×C29—21no—
317M16×C29—21no—
318M16×C29—21no—
319M16×C29—21no—
320M16×C29—42no—
321M16×C29C2×D412yescomplemented
322C2×C8×C29—21no—
323C2×C8×C29—21no—
324C2×C8×C29—21no—
325C2×C8×C29—21no—
326C2×C8×C29—42no—
327C4⋊C4×C29—22no—
328C4⋊C4×C29—22no—
329C4⋊C4×C29—21no—
330C4⋊C4×C29—21no—
331C4⋊C4×C29—21no—
332C4⋊C4×C29—21no—
333C4⋊C4×C29—21no—
334C4⋊C4×C29—21no—
335C4⋊C4×C29—42no—
336C4⋊C4×C29—41no—
337C4⋊C4×C29—41no—
338C4⋊C4×C29—82no—
339C4⋊C4×C29C2×D411yescharacteristic
340C4⋊C4×C29C2×D411yescharacteristic
341C22⋊C4×C29—22no—
342C22⋊C4×C29—22no—
343C22⋊C4×C29—22no—
344C22⋊C4×C29—22no—
345C22⋊C4×C29—22no—
346C22⋊C4×C29—21no—
347C22⋊C4×C29—21no—
348C22⋊C4×C29—21no—
349C22⋊C4×C29—21no—
350C22⋊C4×C29—22no—
351C22⋊C4×C29—22no—
352C22⋊C4×C29—21no—
353C22⋊C4×C29—42no—
354C22⋊C4×C29—44no—
355C22⋊C4×C29—41no—
356C22⋊C4×C29—41no—
357C22⋊C4×C29—82no—
358C42×C29—22no—
359C42×C29—21no—
360C42×C29—21no—
361C42×C29—21no—
362C42×C29—21no—
363C42×C29C2×D412yescomplemented
364#24471C2911yesmaximal, characteristic, direct product factor, Sylow
365C23×C29—21no—
366C23×C29—21no—
367C23×C29—21no—
368C23×C29—22no—
369C23×C29—21no—
370C23×C29—21no—
371C23×C29—22no—
372C23×C29—22no—
373C23×C29—41no—
374C23×C29—41no—
375C23×C29—42no—
376C23×C29—42no—
377C23×C29—44no—
378C23×C29—42no—
379C23×C29—42no—
380C23×C29—81no—
381C23×C29—82no—
382C23×C29—82no—
383C23×C29#12011yescharacteristic
384C23×C29#12011yescharacteristic
385C23×C29C22×D411yescharacteristic
386Q8×C29—21no—
387Q8×C29—21no—
388Q8×C29—21no—
389Q8×C29—21no—
390Q8×C29—21no—
391Q8×C29—42no—
392Q8×C29—41no—
393Q8×C29—41no—
394Q8×C29—41no—
395Q8×C29—41no—
396Q8×C29#12112yes—
397D4×C29—22no—
398D4×C29—22no—
399D4×C29—21no—
400D4×C29—21no—
401D4×C29—21no—
402D4×C29—21no—
403D4×C29—21no—
404D4×C29—42no—
405D4×C29—42no—
406D4×C29—44no—
407D4×C29—42no—
408D4×C29—44no—
409D4×C29—44no—
410D4×C29—42no—
411D4×C29—41no—
412D4×C29—41no—
413D4×C29—41no—
414D4×C29—41no—
415D4×C29—41no—
416D4×C29—41no—
417D4×C29—41no—
418D4×C29—41no—
419D4×C29—81no—
420D4×C29—82no—
421D4×C29—82no—
422D4×C29—82no—
423D4×C29—82no—
424D4×C29#12112yes—
425C2×C4×C29—21no—
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—22no—
435C2×C4×C29—21no—
436C2×C4×C29—21no—
437C2×C4×C29—22no—
438C2×C4×C29—21no—
439C2×C4×C29—22no—
440C2×C4×C29—21no—
441C2×C4×C29—21no—
442C2×C4×C29—21no—
443C2×C4×C29—22no—
444C2×C4×C29—42no—
445C2×C4×C29—42no—
446C2×C4×C29—42no—
447C2×C4×C29—44no—
448C2×C4×C29—41no—
449C2×C4×C29—41no—
450C2×C4×C29—41no—
451C2×C4×C29—41no—
452C2×C4×C29—41no—
453C2×C4×C29—41no—
454C2×C4×C29—42no—
455C2×C4×C29—41no—
456C2×C4×C29—42no—
457C2×C4×C29—41no—
458C2×C4×C29—41no—
459C2×C4×C29—41no—
460C2×C4×C29—41no—
461C2×C4×C29—41no—
462C2×C4×C29—41no—
463C2×C4×C29—82no—
464C2×C4×C29#12011yescharacteristic
465C2×C4×C29#12011yescharacteristic
466C2×C4×C29C22×D411yescharacteristic
467C2×C4×C29C22×D411yescharacteristic
468C2×C4×C29C22×D411yescharacteristic
469C2×C4×C29C2×#4111yescharacteristic
470C2×C4×C29H(5,𝔽2)11yescharacteristic
471C2×C4×C29H(5,𝔽2)11yescharacteristic
472C8×C29—22no—
473C8×C29—41no—
474C8×C29—41no—
475C8×C29—41no—
476#3488C2×C2911yescharacteristic
477#3056C2×C2911yescharacteristic, complemented
478C2×#455C2×C2911yescharacteristic, complemented
479#3007C2×C2911yescharacteristic, complemented
480C2×#421C2×C2911yescharacteristic, complemented
481#2620C2×C2911yescharacteristic, complemented
482#2039C2×C2911yescharacteristic, complemented
483#2037C2×C2911yescharacteristic, complemented
484#2007C2×C2911yescharacteristic, complemented
485#2004C2×C2911yescharacteristic, complemented
486#1900C2×C2911yescharacteristic, complemented
487#1897C2×C2911yescharacteristic, complemented
488#1882C2×C2911yescharacteristic, complemented
489#1859C2×C2911yescharacteristic, complemented
490#1792C2×C2911yescharacteristic, complemented
491C22×C29—21no—
492C22×C29—21no—
493C22×C29—21no—
494C22×C29—21no—
495C22×C29—22no—
496C22×C29—21no—
497C22×C29—21no—
498C22×C29—21no—
499C22×C29—21no—
500C22×C29—41no—
501C22×C29—41no—
502C22×C29—41no—
503C22×C29—41no—
504C22×C29—42no—
505C22×C29—42no—
506C22×C29—41no—
507C22×C29—41no—
508C22×C29—41no—
509C22×C29—42no—
510C22×C29—41no—
511C22×C29—81no—
512C22×C29—81no—
513C22×C29—82no—
514C22×C29—82no—
515C22×C29—84no—
516C22×C29—164no—
517C22×C29C2×#12011yescharacteristic
518C22×C29D4211yescharacteristic
519C22×C29#54611yescharacteristic
520C4×C29—21no—
521C4×C29—21no—
522C4×C29—22no—
523C4×C29—42no—
524C4×C29—41no—
525C4×C29—41no—
526C4×C29—42no—
527C4×C29—41no—
528C4×C29—41no—
529C4×C29—81no—
530C4×C29—81no—
531C4×C29—81no—
532C4×C29C2×#12111yescharacteristic
533C4×C29#53411yescharacteristic
534C4×C29D4211yescharacteristic
535C4×C29#54611yescharacteristic
536C2×H(5,𝔽2)C22×C2911yescharacteristic
537C22×#41C22×C2911yescharacteristic
538C2×#137C22×C2911yescharacteristic
539C2×#137C22×C2911yescharacteristic, complemented
540C2×#137C22×C2911yescharacteristic, complemented
541C22×M16C22×C2911yescharacteristic, complemented
542#550—21no—
543#548—21no—
544#546—21no—
545#546—22no—
546D42—22no—
547D42—21no—
548#537—21no—
549#537C22×C2911yescharacteristic
550#535—21no—
551#535C22×C2911yescharacteristic
552C2×#124C22×C2911yescharacteristic, complemented
553#525—21no—
554#525C22×C2911yescharacteristic
555C2×C22⋊Q8C22×C2911yescharacteristic, complemented
556C2×#121—21no—
557C2×#121C22×C2911yescharacteristic
558#520C22×C2911yescharacteristic
559C2×#117C22×C2911yescharacteristic, complemented
560#470—21no—
561#468—21no—
562#467—21no—
563#465—21no—
564#455—24no—
565#452—21no—
566#452—21no—
567#451—21no—
568#450—21no—
569#428C22×C2911yescharacteristic, complemented
570#421—24no—
571C2×#104C22×C2911yescharacteristic
572C2×#104C22×C2911yescharacteristic
573C2×#104C22×C2911yescharacteristic, complemented
574C2×#104C22×C2911yescharacteristic, complemented
575C2×#104C22×C2911yescharacteristic, complemented
576C2×#104C22×C2911yescharacteristic, complemented
577#419C22×C2911yescharacteristic, complemented
578#417C22×C2911yescharacteristic
579#417C22×C2911yescharacteristic, complemented
580#417C22×C2911yescharacteristic, complemented
581C2×#100C22×C2911yescharacteristic, complemented
582C2×#100C22×C2911yescharacteristic, complemented
583#407C22×C2911yescharacteristic, complemented
584#396—22no—
585#394—22no—
586#391C22×C2911yescharacteristic, complemented
587#390C22×C2911yescharacteristic, complemented
588#384C22×C2911yescharacteristic, complemented
589#343C22×C2911yescharacteristic, complemented
590#343C22×C2911yescharacteristic, complemented
591#339C22×C2911yescharacteristic, complemented
592#339C22×C2911yescharacteristic, complemented
593C2×C29—21no—
594C2×C29—21no—
595C2×C29—41no—
596C2×C29—41no—
597C2×C29—42no—
598C2×C29—81no—
599C2×C29—82no—
600C2×C29—81no—
601C2×C29#241011yescharacteristic
602C2×C29#301911yescharacteristic
603C2×C29#302211yescharacteristic
604H(5,𝔽2)—22no—
605H(5,𝔽2)—22no—
606H(5,𝔽2)—41no—
607H(5,𝔽2)—41no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—22no—
613C2×#41—22no—
614C2×#41—41no—
615C2×#41—41no—
616C2×#41D4×C2911yescharacteristic
617C2×#41D4×C2911yescharacteristic
618C2×#41C23×C2911yescharacteristic
619C2×#41C23×C2911yescharacteristic
620C2×#41C23×C2911yescharacteristic
621C22×Q8D4×C2911yescharacteristic
622C22×Q8C23×C2911yescharacteristic
623C22×D4—21no—
624C22×D4—22no—
625C22×D4—22no—
626C22×D4—21no—
627C22×D4—21no—
628C22×D4D4×C2911yescharacteristic
629C22×D4D4×C2912yes—
630C22×D4C23×C2911yescharacteristic
631C23×C4—21no—
632C23×C4C23×C2911yescharacteristic
633#137—22no—
634#137—22no—
635#137—22no—
636#137—41no—
637#137—41no—
638#137—41no—
639C2×Q16—21no—
640C2×Q16—21no—
641C2×Q16—21no—
642C2×SD16—21no—
643C2×SD16—21no—
644C2×SD16—21no—
645C2×M16—21no—
646C2×M16—22no—
647C2×M16—41no—
648C2×M16C23×C2911yescharacteristic
649C2×M16C23×C2911yescharacteristic
650C2×M16C23×C2911yescharacteristic
651C2×M16C23×C2911yescharacteristic
652C22×C8—21no—
653#127—22no—
654#127—21no—
655#124—22no—
656#124—21no—
657#124—22no—
658#124—41no—
659#123—22no—
660#123—21no—
661C22⋊Q8—22no—
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—22no—
674#121—22no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—22no—
682#121—21no—
683#121—21no—
684#121D4×C2911yescharacteristic
685#121D4×C2911yescharacteristic
686#120—22no—
687#120—22no—
688#120—22no—
689#120—21no—
690#120—22no—
691C4×Q8—21no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—21no—
695C4×D4—22no—
696C4×D4—21no—
697C4×D4—21no—
698#117—21no—
699#117—22no—
700#117—41no—
701#117C23×C2911yescharacteristic
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4C23×C2911yescharacteristic
707C2×C4⋊C4C23×C2911yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4D4×C2912yes—
714C2×C42C23×C2911yescharacteristic
715C2×C42C23×C2911yescharacteristic
716#107—21no—
717#106—21no—
718#104—22no—
719#104—22no—
720#104—22no—
721#104—22no—
722#104—41no—
723#104D4×C2914yescomplemented
724#103—21no—
725#103—21no—
726#103—21no—
727#103—21no—
728#103—21no—
729#102—21no—
730#102—21no—
731#102—21no—
732#100—22no—
733#100—41no—
734C22⋊C8—21no—
735C22⋊C8—21no—
736#95—22no—
737C29#2447111yescharacteristic, direct product factor, Sylow
738C24—22no—
739C24—21no—
740C24C2×D4×C2912yes—
741C24C2×D4×C2911yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41C2×D4×C2912yes—
765#41#41×C2912yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8C2×D4×C2911yescharacteristic
776C2×Q8C2×D4×C2911yescharacteristic
777C2×Q8C2×D4×C2911yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×D4×C2911yescharacteristic
812C2×D4C2×D4×C2911yescharacteristic
813C2×D4C2×D4×C2911yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4C2×D4×C2911yescharacteristic
833C22×C4C2×D4×C2911yescharacteristic
834C22×C4C2×D4×C2911yescharacteristic
835C22×C4C2×D4×C2911yescharacteristic
836C22×C4C2×D4×C2911yescharacteristic
837C22×C4C2×D4×C2912yes—
838C22×C4C24×C2911yescharacteristic
839Q16—42no—
840Q16—42no—
841Q16—42no—
842SD16—42no—
843SD16—42no—
844SD16—42no—
845M16—21no—
846M16—21no—
847M16—21no—
848M16—21no—
849M16—21no—
850M16—21no—
851M16—21no—
852M16—42no—
853M16C2×D4×C2912yescomplemented
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—42no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—42no—
868C4⋊C4—41no—
869C4⋊C4—41no—
870C4⋊C4—82no—
871C4⋊C4C2×D4×C2911yescharacteristic
872C4⋊C4C2×D4×C2911yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—42no—
886C22⋊C4—44no—
887C22⋊C4—41no—
888C22⋊C4—41no—
889C22⋊C4—82no—
890C42—22no—
891C42—21no—
892C42—21no—
893C42—21no—
894C42—21no—
895C42C2×D4×C2912yescomplemented
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23C29×#12011yescharacteristic
915C23C29×#12011yescharacteristic
916C23C22×D4×C2911yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—41no—
924Q8—41no—
925Q8—41no—
926Q8—41no—
927Q8C29×#12112yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—82no—
951D4—81no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4C29×#12112yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—22no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—44no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—82no—
995C2×C4C29×#12011yescharacteristic
996C2×C4C29×#12011yescharacteristic
997C2×C4C22×D4×C2911yescharacteristic
998C2×C4C22×D4×C2911yescharacteristic
999C2×C4C22×D4×C2911yescharacteristic
1000C2×C4C2×#41×C2911yescharacteristic
1001C2×C4C29×H(5,𝔽2)11yescharacteristic
1002C2×C4C29×H(5,𝔽2)11yescharacteristic
1003C8—22no—
1004C8—41no—
1005C8—41no—
1006C8—41no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×C29×#12011yescharacteristic
1034C22D42×C2911yescharacteristic
1035C22C29×#54611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—81no—
1046C4—81no—
1047C4—81no—
1048C4C2×C29×#12111yescharacteristic
1049C4C29×#53411yescharacteristic
1050C4D42×C2911yescharacteristic
1051C4C29×#54611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2C29×#241011yescharacteristic
1061C2C29×#301911yescharacteristic
1062C2C29×#302211yescharacteristic
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. C2×C29×#421C2semidirect
6. C29×#2620C2semidirect
7. C29×#2039C2semidirect
8. C29×#2037C2semidirect
9. C29×#2007C2semidirect
10. C29×#2004C2semidirect
11. C29×#1900C2semidirect
12. C29×#1897C2semidirect
13. C29×#1882C2semidirect
14. C29×#1859C2semidirect
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. C2×C29×#117C22semidirect
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
66. C29×#391C22semidirect
67. C29×#390C22semidirect
68. C29×#384C22semidirect
69. C29×#343C22semidirect
70. C29×#343C22semidirect
71. C29×#339C22semidirect
72. C29×#339C22semidirect
192. C29×#104D4semidirect
321. M16×C29C2×D4semidirect
363. C42×C29C2×D4semidirect
364. #24471C29direct (N × H)
477. #3056C2×C29semidirect
478. C2×#455C2×C29semidirect
479. #3007C2×C29semidirect
480. C2×#421C2×C29semidirect
481. #2620C2×C29semidirect
482. #2039C2×C29semidirect
483. #2037C2×C29semidirect
484. #2007C2×C29semidirect
485. #2004C2×C29semidirect
486. #1900C2×C29semidirect
487. #1897C2×C29semidirect
488. #1882C2×C29semidirect
489. #1859C2×C29semidirect
490. #1792C2×C29semidirect
539. C2×#137C22×C29semidirect
540. C2×#137C22×C29semidirect
541. C22×M16C22×C29semidirect
552. C2×#124C22×C29semidirect
555. C2×C22⋊Q8C22×C29semidirect
559. C2×#117C22×C29semidirect
569. #428C22×C29semidirect
573. C2×#104C22×C29semidirect
574. C2×#104C22×C29semidirect
575. C2×#104C22×C29semidirect
576. C2×#104C22×C29semidirect
577. #419C22×C29semidirect
579. #417C22×C29semidirect
580. #417C22×C29semidirect
581. C2×#100C22×C29semidirect
582. C2×#100C22×C29semidirect
583. #407C22×C29semidirect
586. #391C22×C29semidirect
587. #390C22×C29semidirect
588. #384C22×C29semidirect
589. #343C22×C29semidirect
590. #343C22×C29semidirect
591. #339C22×C29semidirect
592. #339C22×C29semidirect
723. #104D4×C29semidirect
737. C29#24471direct (N × H)
853. M16C2×D4×C29semidirect
895. C42C2×D4×C29semidirect

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
C2×C29×#4212
C29×#26202
C29×#20392
C29×#20372
C29×#20072
C29×#20042
C29×#19002
C29×#18972
C29×#18822
C29×#18592
C29×#17922
#2447129