Finite Group Databasebeta

← C29×#24031 #20318931

Subgroups — C29×#24031 #20318931

Order 7424.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3488C211yesmaximal, characteristic
2C29×#3093C211yesmaximal, characteristic, complemented
3C29×#2896C211yesmaximal, characteristic, complemented
4C29×#2500C211yesmaximal, characteristic, complemented
5C29×#2040C211yesmaximal, characteristic, complemented
6C29×#2039C211yesmaximal, characteristic, complemented
7C29×#2037C211yesmaximal, characteristic, complemented
8C29×#2037C211yesmaximal, characteristic, complemented
9C29×#1900C211yesmaximal, characteristic, complemented
10C29×#1871C211yesmaximal, characteristic, complemented
11C29×#1860C211yesmaximal, characteristic, complemented
12C29×#1859C211yesmaximal, characteristic, complemented
13C29×#1792C211yesmaximal, characteristic, complemented
14C29×#1792C211yesmaximal, characteristic, complemented
15C29×#1789C211yesmaximal, characteristic, complemented
16C2×C29×H(5,𝔽2)C2211yescharacteristic
17C22×#41×C29C2211yescharacteristic
18C22×M16×C29C2211yescharacteristic, complemented
19C29×#550—21no—
20C29×#548—21no—
21C29×#546—21no—
22C29×#546—22no—
23D42×C29—22no—
24D42×C29—21no—
25C29×#537—21no—
26C29×#537C2211yescharacteristic
27C29×#535—21no—
28C29×#535C2211yescharacteristic
29C29×#525—21no—
30C29×#525C2211yescharacteristic
31C2×C29×#121—21no—
32C2×C29×#121C2211yescharacteristic
33C29×#520C2211yescharacteristic
34C2×C29×#117C2211yescharacteristic, complemented
35C29×#485—21no—
36C29×#485—21no—
37C29×#482—21no—
38C29×#482—21no—
39C29×#428C2211yescharacteristic, complemented
40C29×#428C2211yescharacteristic, complemented
41C2×C29×#104C2211yescharacteristic
42C2×C29×#104C2211yescharacteristic
43C2×C29×#104C2211yescharacteristic, complemented
44C2×C29×#104C2211yescharacteristic, complemented
45C2×C29×#104C2211yescharacteristic, complemented
46C2×C29×#104C2211yescharacteristic, complemented
47C29×#419—21no—
48C29×#418—21no—
49C29×#417C2211yescharacteristic
50C29×#417C2211yescharacteristic
51C29×#417C2211yescharacteristic, complemented
52C29×#417C2211yescharacteristic, complemented
53C29×#417C2211yescharacteristic, complemented
54C29×#417C2211yescharacteristic, complemented
55C29×#416—21no—
56C29×#416—21no—
57C2×C29×#100C2211yescharacteristic, complemented
58C2×C29×#100C2211yescharacteristic, complemented
59C29×#407C2211yescharacteristic, complemented
60C29×#394—22no—
61C29×#390C2211yescharacteristic, complemented
62C29×#390C2211yescharacteristic, complemented
63C29×#388—22no—
64C29×#384C2211yescharacteristic, complemented
65C29×#382C2211yescharacteristic, complemented
66C4×C22⋊C4×C29C2211yescharacteristic, complemented
67C29×#343C2211yescharacteristic, complemented
68C29×#343C2211yescharacteristic, complemented
69C29×#339C2211yescharacteristic, complemented
70C29×#339C2211yescharacteristic, complemented
71C29×H(5,𝔽2)—22no—
72C29×H(5,𝔽2)—22no—
73C29×H(5,𝔽2)—41no—
74C29×H(5,𝔽2)—41no—
75C2×#41×C29—21no—
76C2×#41×C29—21no—
77C2×#41×C29—21no—
78C2×#41×C29—21no—
79C2×#41×C29—22no—
80C2×#41×C29—22no—
81C2×#41×C29—41no—
82C2×#41×C29—41no—
83C2×#41×C29D411yescharacteristic
84C2×#41×C29D411yescharacteristic
85C2×#41×C29C2311yescharacteristic
86C2×#41×C29C2311yescharacteristic
87C2×#41×C29C2311yescharacteristic
88C22×Q8×C29D411yescharacteristic
89C22×D4×C29—21no—
90C22×D4×C29—22no—
91C22×D4×C29—22no—
92C22×D4×C29—21no—
93C22×D4×C29—21no—
94C22×D4×C29D411yescharacteristic
95C22×D4×C29D412yes—
96C22×D4×C29C2311yescharacteristic
97C23×C4×C29—21no—
98C23×C4×C29C2311yescharacteristic
99C2×M16×C29—21no—
100C2×M16×C29—41no—
101C2×M16×C29—41no—
102C2×M16×C29C2311yescharacteristic
103C2×M16×C29C2311yescharacteristic
104C2×M16×C29C2311yescharacteristic
105C2×M16×C29C2311yescharacteristic
106C22×C8×C29—21no—
107C29×#127—22no—
108C29×#127—21no—
109C29×#124—22no—
110C29×#124—21no—
111C29×#123—22no—
112C29×#123—21no—
113C29×C22⋊Q8—22no—
114C29×C22⋊Q8—21no—
115C29×C22⋊Q8—21no—
116C29×C22⋊Q8D411yescharacteristic
117C29×C22⋊Q8D411yescharacteristic
118C29×#121—22no—
119C29×#121—22no—
120C29×#121—22no—
121C29×#121—22no—
122C29×#121—22no—
123C29×#121—21no—
124C29×#121—21no—
125C29×#121—21no—
126C29×#121—21no—
127C29×#121—21no—
128C29×#121—21no—
129C29×#121—22no—
130C29×#121—21no—
131C29×#121—21no—
132C29×#121D411yescharacteristic
133C29×#121D411yescharacteristic
134C29×#120—22no—
135C29×#120—22no—
136C29×#120—22no—
137C29×#120—21no—
138C29×#120—22no—
139C4×Q8×C29—21no—
140C4×D4×C29—22no—
141C4×D4×C29—22no—
142C4×D4×C29—21no—
143C4×D4×C29—22no—
144C4×D4×C29—21no—
145C4×D4×C29—21no—
146C29×#117—21no—
147C29×#117—21no—
148C29×#117—21no—
149C29×#117—21no—
150C29×#117—21no—
151C29×#117C2311yescharacteristic
152C2×C4⋊C4×C29—21no—
153C2×C4⋊C4×C29—22no—
154C2×C4⋊C4×C29C2311yescharacteristic
155C2×C4⋊C4×C29C2311yescharacteristic
156C2×C4⋊C4×C29C2311yescharacteristic
157C2×C22⋊C4×C29—22no—
158C2×C22⋊C4×C29—21no—
159C2×C22⋊C4×C29—21no—
160C2×C22⋊C4×C29—22no—
161C2×C22⋊C4×C29—22no—
162C2×C22⋊C4×C29D412yes—
163C2×C42×C29—21no—
164C2×C42×C29C2311yescharacteristic
165C2×C42×C29C2311yescharacteristic
166C29×#107—21no—
167C29×#107—21no—
168C29×#106—21no—
169C29×#106—21no—
170C29×#104—22no—
171C29×#104—22no—
172C29×#104—41no—
173C29×#104—41no—
174C29×#104—41no—
175C29×#104—41no—
176C29×#103—21no—
177C29×#103—21no—
178C29×#103—21no—
179C29×#103—21no—
180C29×#103—21no—
181C29×#103—21no—
182C29×#102—21no—
183C29×#102—21no—
184C29×#102—21no—
185C29×#102—21no—
186C29×#102—21no—
187C29×#102—21no—
188C29×#100—41no—
189C29×#100—41no—
190C29×C22⋊C8—21no—
191C29×C22⋊C8—21no—
192C29×#95—21no—
193C29×#95—22no—
194C24×C29—22no—
195C24×C29—21no—
196C24×C29C2×D412yes—
197C24×C29C2×D411yescharacteristic
198#41×C29—21no—
199#41×C29—21no—
200#41×C29—22no—
201#41×C29—22no—
202#41×C29—21no—
203#41×C29—21no—
204#41×C29—21no—
205#41×C29—21no—
206#41×C29—21no—
207#41×C29—21no—
208#41×C29—21no—
209#41×C29—21no—
210#41×C29—42no—
211#41×C29—42no—
212#41×C29—41no—
213#41×C29—41no—
214#41×C29—42no—
215#41×C29—42no—
216#41×C29—42no—
217#41×C29—42no—
218#41×C29—42no—
219#41×C29—42no—
220#41×C29#4112yes—
221#41×C29#4112yes—
222C2×Q8×C29—21no—
223C2×Q8×C29—22no—
224C2×Q8×C29—41no—
225C2×Q8×C29C2×D411yescharacteristic
226C2×Q8×C29C2×D411yescharacteristic
227C2×Q8×C29C2×D411yescharacteristic
228C2×D4×C29—21no—
229C2×D4×C29—22no—
230C2×D4×C29—22no—
231C2×D4×C29—22no—
232C2×D4×C29—22no—
233C2×D4×C29—21no—
234C2×D4×C29—21no—
235C2×D4×C29—21no—
236C2×D4×C29—21no—
237C2×D4×C29—21no—
238C2×D4×C29—22no—
239C2×D4×C29—22no—
240C2×D4×C29—22no—
241C2×D4×C29—21no—
242C2×D4×C29—22no—
243C2×D4×C29—21no—
244C2×D4×C29—21no—
245C2×D4×C29—21no—
246C2×D4×C29—21no—
247C2×D4×C29—21no—
248C2×D4×C29—21no—
249C2×D4×C29—21no—
250C2×D4×C29—41no—
251C2×D4×C29—42no—
252C2×D4×C29—42no—
253C2×D4×C29—42no—
254C2×D4×C29—42no—
255C2×D4×C29—44no—
256C2×D4×C29—44no—
257C2×D4×C29—42no—
258C2×D4×C29—42no—
259C2×D4×C29—82no—
260C2×D4×C29—84no—
261C2×D4×C29C2×D411yescharacteristic
262C2×D4×C29C2×D411yescharacteristic
263C2×D4×C29C2×D411yescharacteristic
264C22×C4×C29—21no—
265C22×C4×C29—21no—
266C22×C4×C29—21no—
267C22×C4×C29—21no—
268C22×C4×C29—21no—
269C22×C4×C29—22no—
270C22×C4×C29—21no—
271C22×C4×C29—21no—
272C22×C4×C29—22no—
273C22×C4×C29—21no—
274C22×C4×C29—21no—
275C22×C4×C29—21no—
276C22×C4×C29—21no—
277C22×C4×C29—21no—
278C22×C4×C29—21no—
279C22×C4×C29—21no—
280C22×C4×C29—42no—
281C22×C4×C29—42no—
282C22×C4×C29C2×D411yescharacteristic
283C22×C4×C29C2×D411yescharacteristic
284C22×C4×C29C2×D411yescharacteristic
285C22×C4×C29C2×D411yescharacteristic
286C22×C4×C29C2×D411yescharacteristic
287C22×C4×C29C2×D412yes—
288C22×C4×C29C2411yescharacteristic
289M16×C29—21no—
290M16×C29—21no—
291M16×C29—21no—
292M16×C29—21no—
293M16×C29—21no—
294M16×C29—21no—
295M16×C29—21no—
296M16×C29—21no—
297M16×C29—42no—
298C2×C8×C29—21no—
299C2×C8×C29—21no—
300C2×C8×C29—21no—
301C2×C8×C29—21no—
302C2×C8×C29—42no—
303C4⋊C4×C29—22no—
304C4⋊C4×C29—22no—
305C4⋊C4×C29—21no—
306C4⋊C4×C29—21no—
307C4⋊C4×C29—21no—
308C4⋊C4×C29—21no—
309C4⋊C4×C29—21no—
310C4⋊C4×C29—21no—
311C4⋊C4×C29—21no—
312C4⋊C4×C29—21no—
313C4⋊C4×C29—82no—
314C4⋊C4×C29C2×D411yescharacteristic
315C4⋊C4×C29C2×D411yescharacteristic
316C22⋊C4×C29—22no—
317C22⋊C4×C29—22no—
318C22⋊C4×C29—22no—
319C22⋊C4×C29—22no—
320C22⋊C4×C29—22no—
321C22⋊C4×C29—21no—
322C22⋊C4×C29—21no—
323C22⋊C4×C29—21no—
324C22⋊C4×C29—21no—
325C22⋊C4×C29—22no—
326C22⋊C4×C29—22no—
327C22⋊C4×C29—21no—
328C22⋊C4×C29—42no—
329C22⋊C4×C29—44no—
330C22⋊C4×C29—41no—
331C22⋊C4×C29—41no—
332C22⋊C4×C29—82no—
333C42×C29—22no—
334C42×C29—21no—
335C42×C29—21no—
336C42×C29—21no—
337C42×C29—21no—
338C42×C29—21no—
339C42×C29—41no—
340C42×C29—41no—
341#24031C2911yesmaximal, characteristic, direct product factor, Sylow
342C23×C29—21no—
343C23×C29—21no—
344C23×C29—21no—
345C23×C29—22no—
346C23×C29—21no—
347C23×C29—21no—
348C23×C29—22no—
349C23×C29—22no—
350C23×C29—41no—
351C23×C29—41no—
352C23×C29—42no—
353C23×C29—42no—
354C23×C29—44no—
355C23×C29—42no—
356C23×C29—42no—
357C23×C29—81no—
358C23×C29—82no—
359C23×C29—82no—
360C23×C29#12011yescharacteristic
361C23×C29#12011yescharacteristic
362C23×C29C22×D411yescharacteristic
363Q8×C29—21no—
364Q8×C29—21no—
365Q8×C29—21no—
366Q8×C29—21no—
367Q8×C29—21no—
368Q8×C29—42no—
369Q8×C29#12312yes—
370D4×C29—22no—
371D4×C29—22no—
372D4×C29—21no—
373D4×C29—21no—
374D4×C29—21no—
375D4×C29—21no—
376D4×C29—21no—
377D4×C29—42no—
378D4×C29—42no—
379D4×C29—44no—
380D4×C29—42no—
381D4×C29—44no—
382D4×C29—44no—
383D4×C29—42no—
384D4×C29—41no—
385D4×C29—41no—
386D4×C29—41no—
387D4×C29—41no—
388D4×C29—41no—
389D4×C29—41no—
390D4×C29—41no—
391D4×C29—41no—
392D4×C29—81no—
393D4×C29—82no—
394D4×C29—82no—
395D4×C29—82no—
396D4×C29—82no—
397D4×C29#12312yes—
398C2×C4×C29—21no—
399C2×C4×C29—21no—
400C2×C4×C29—21no—
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—22no—
410C2×C4×C29—22no—
411C2×C4×C29—22no—
412C2×C4×C29—21no—
413C2×C4×C29—22no—
414C2×C4×C29—21no—
415C2×C4×C29—21no—
416C2×C4×C29—21no—
417C2×C4×C29—42no—
418C2×C4×C29—42no—
419C2×C4×C29—42no—
420C2×C4×C29—44no—
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—42no—
428C2×C4×C29—41no—
429C2×C4×C29—42no—
430C2×C4×C29—41no—
431C2×C4×C29—42no—
432C2×C4×C29—41no—
433C2×C4×C29—41no—
434C2×C4×C29—41no—
435C2×C4×C29—82no—
436C2×C4×C29#12011yescharacteristic
437C2×C4×C29#12011yescharacteristic
438C2×C4×C29C22×D411yescharacteristic
439C2×C4×C29C22×D411yescharacteristic
440C2×C4×C29C2×#4111yescharacteristic
441C2×C4×C29C2×#4111yescharacteristic
442C2×C4×C29H(5,𝔽2)11yescharacteristic
443C2×C4×C29H(5,𝔽2)11yescharacteristic
444C8×C29—41no—
445C8×C29—41no—
446C8×C29—41no—
447C8×C29—41no—
448#3488C2×C2911yescharacteristic
449#3093C2×C2911yescharacteristic, complemented
450#2896C2×C2911yescharacteristic, complemented
451#2500C2×C2911yescharacteristic, complemented
452#2040C2×C2911yescharacteristic, complemented
453#2039C2×C2911yescharacteristic, complemented
454#2037C2×C2911yescharacteristic, complemented
455#2037C2×C2911yescharacteristic, complemented
456#1900C2×C2911yescharacteristic, complemented
457#1871C2×C2911yescharacteristic, complemented
458#1860C2×C2911yescharacteristic, complemented
459#1859C2×C2911yescharacteristic, complemented
460#1792C2×C2911yescharacteristic, complemented
461#1792C2×C2911yescharacteristic, complemented
462#1789C2×C2911yescharacteristic, complemented
463C22×C29—21no—
464C22×C29—21no—
465C22×C29—21no—
466C22×C29—21no—
467C22×C29—22no—
468C22×C29—21no—
469C22×C29—21no—
470C22×C29—21no—
471C22×C29—21no—
472C22×C29—41no—
473C22×C29—41no—
474C22×C29—41no—
475C22×C29—41no—
476C22×C29—42no—
477C22×C29—41no—
478C22×C29—42no—
479C22×C29—41no—
480C22×C29—42no—
481C22×C29—41no—
482C22×C29—41no—
483C22×C29—81no—
484C22×C29—81no—
485C22×C29—82no—
486C22×C29—82no—
487C22×C29—84no—
488C22×C29—164no—
489C22×C29C2×#12011yescharacteristic
490C22×C29#54611yescharacteristic
491C22×C29#54611yescharacteristic
492C4×C29—21no—
493C4×C29—21no—
494C4×C29—22no—
495C4×C29—42no—
496C4×C29—41no—
497C4×C29—41no—
498C4×C29—41no—
499C4×C29—42no—
500C4×C29—41no—
501C4×C29—81no—
502C4×C29—81no—
503C4×C29—81no—
504C4×C29C2×#12311yescharacteristic
505C4×C29#53411yescharacteristic
506C4×C29#54611yescharacteristic
507C4×C29#54611yescharacteristic
508C2×H(5,𝔽2)C22×C2911yescharacteristic
509C22×#41C22×C2911yescharacteristic
510C22×M16C22×C2911yescharacteristic, complemented
511#550—21no—
512#548—21no—
513#546—21no—
514#546—22no—
515D42—22no—
516D42—21no—
517#537—21no—
518#537C22×C2911yescharacteristic
519#535—21no—
520#535C22×C2911yescharacteristic
521#525—21no—
522#525C22×C2911yescharacteristic
523C2×#121—21no—
524C2×#121C22×C2911yescharacteristic
525#520C22×C2911yescharacteristic
526C2×#117C22×C2911yescharacteristic, complemented
527#485—21no—
528#485—21no—
529#482—21no—
530#482—21no—
531#428C22×C2911yescharacteristic, complemented
532#428C22×C2911yescharacteristic, complemented
533C2×#104C22×C2911yescharacteristic
534C2×#104C22×C2911yescharacteristic
535C2×#104C22×C2911yescharacteristic, complemented
536C2×#104C22×C2911yescharacteristic, complemented
537C2×#104C22×C2911yescharacteristic, complemented
538C2×#104C22×C2911yescharacteristic, complemented
539#419—21no—
540#418—21no—
541#417C22×C2911yescharacteristic
542#417C22×C2911yescharacteristic
543#417C22×C2911yescharacteristic, complemented
544#417C22×C2911yescharacteristic, complemented
545#417C22×C2911yescharacteristic, complemented
546#417C22×C2911yescharacteristic, complemented
547#416—21no—
548#416—21no—
549C2×#100C22×C2911yescharacteristic, complemented
550C2×#100C22×C2911yescharacteristic, complemented
551#407C22×C2911yescharacteristic, complemented
552#394—22no—
553#390C22×C2911yescharacteristic, complemented
554#390C22×C2911yescharacteristic, complemented
555#388—22no—
556#384C22×C2911yescharacteristic, complemented
557#382C22×C2911yescharacteristic, complemented
558C4×C22⋊C4C22×C2911yescharacteristic, complemented
559#343C22×C2911yescharacteristic, complemented
560#343C22×C2911yescharacteristic, complemented
561#339C22×C2911yescharacteristic, complemented
562#339C22×C2911yescharacteristic, complemented
563C2×C29—21no—
564C2×C29—21no—
565C2×C29—41no—
566C2×C29—41no—
567C2×C29—42no—
568C2×C29—81no—
569C2×C29—82no—
570C2×C29—81no—
571C2×C29#240511yescharacteristic
572C2×C29#301811yescharacteristic
573C2×C29#301911yescharacteristic
574H(5,𝔽2)—22no—
575H(5,𝔽2)—22no—
576H(5,𝔽2)—41no—
577H(5,𝔽2)—41no—
578C2×#41—21no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—22no—
583C2×#41—22no—
584C2×#41—41no—
585C2×#41—41no—
586C2×#41D4×C2911yescharacteristic
587C2×#41D4×C2911yescharacteristic
588C2×#41C23×C2911yescharacteristic
589C2×#41C23×C2911yescharacteristic
590C2×#41C23×C2911yescharacteristic
591C22×Q8D4×C2911yescharacteristic
592C22×D4—21no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4D4×C2911yescharacteristic
598C22×D4D4×C2912yes—
599C22×D4C23×C2911yescharacteristic
600C23×C4—21no—
601C23×C4C23×C2911yescharacteristic
602C2×M16—21no—
603C2×M16—41no—
604C2×M16—41no—
605C2×M16C23×C2911yescharacteristic
606C2×M16C23×C2911yescharacteristic
607C2×M16C23×C2911yescharacteristic
608C2×M16C23×C2911yescharacteristic
609C22×C8—21no—
610#127—22no—
611#127—21no—
612#124—22no—
613#124—21no—
614#123—22no—
615#123—21no—
616C22⋊Q8—22no—
617C22⋊Q8—21no—
618C22⋊Q8—21no—
619C22⋊Q8D4×C2911yescharacteristic
620C22⋊Q8D4×C2911yescharacteristic
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—21no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—22no—
633#121—21no—
634#121—21no—
635#121D4×C2911yescharacteristic
636#121D4×C2911yescharacteristic
637#120—22no—
638#120—22no—
639#120—22no—
640#120—21no—
641#120—22no—
642C4×Q8—21no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—21no—
646C4×D4—22no—
647C4×D4—21no—
648C4×D4—21no—
649#117—21no—
650#117—21no—
651#117—21no—
652#117—21no—
653#117—21no—
654#117C23×C2911yescharacteristic
655C2×C4⋊C4—21no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4C23×C2911yescharacteristic
658C2×C4⋊C4C23×C2911yescharacteristic
659C2×C4⋊C4C23×C2911yescharacteristic
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4D4×C2912yes—
666C2×C42—21no—
667C2×C42C23×C2911yescharacteristic
668C2×C42C23×C2911yescharacteristic
669#107—21no—
670#107—21no—
671#106—21no—
672#106—21no—
673#104—22no—
674#104—22no—
675#104—41no—
676#104—41no—
677#104—41no—
678#104—41no—
679#103—21no—
680#103—21no—
681#103—21no—
682#103—21no—
683#103—21no—
684#103—21no—
685#102—21no—
686#102—21no—
687#102—21no—
688#102—21no—
689#102—21no—
690#102—21no—
691#100—41no—
692#100—41no—
693C22⋊C8—21no—
694C22⋊C8—21no—
695#95—21no—
696#95—22no—
697C29#2403111yescharacteristic, direct product factor, Sylow
698C24—22no—
699C24—21no—
700C24C2×D4×C2912yes—
701C24C2×D4×C2911yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#41×C2912yes—
725#41#41×C2912yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×D4×C2911yescharacteristic
730C2×Q8C2×D4×C2911yescharacteristic
731C2×Q8C2×D4×C2911yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×D4×C2911yescharacteristic
766C2×D4C2×D4×C2911yescharacteristic
767C2×D4C2×D4×C2911yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4C2×D4×C2911yescharacteristic
787C22×C4C2×D4×C2911yescharacteristic
788C22×C4C2×D4×C2911yescharacteristic
789C22×C4C2×D4×C2911yescharacteristic
790C22×C4C2×D4×C2911yescharacteristic
791C22×C4C2×D4×C2912yes—
792C22×C4C24×C2911yescharacteristic
793M16—21no—
794M16—21no—
795M16—21no—
796M16—21no—
797M16—21no—
798M16—21no—
799M16—21no—
800M16—21no—
801M16—42no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—42no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—82no—
818C4⋊C4C2×D4×C2911yescharacteristic
819C4⋊C4C2×D4×C2911yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—42no—
833C22⋊C4—44no—
834C22⋊C4—41no—
835C22⋊C4—41no—
836C22⋊C4—82no—
837C42—22no—
838C42—21no—
839C42—21no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—41no—
844C42—41no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23C29×#12011yescharacteristic
864C23C29×#12011yescharacteristic
865C23C22×D4×C2911yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8C29×#12312yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—82no—
896D4—81no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4C29×#12312yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—21no—
916C2×C4—22no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—21no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—44no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—42no—
931C2×C4—41no—
932C2×C4—42no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—82no—
939C2×C4C29×#12011yescharacteristic
940C2×C4C29×#12011yescharacteristic
941C2×C4C22×D4×C2911yescharacteristic
942C2×C4C22×D4×C2911yescharacteristic
943C2×C4C2×#41×C2911yescharacteristic
944C2×C4C2×#41×C2911yescharacteristic
945C2×C4C29×H(5,𝔽2)11yescharacteristic
946C2×C4C29×H(5,𝔽2)11yescharacteristic
947C8—41no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×C29×#12011yescharacteristic
978C22C29×#54611yescharacteristic
979C22C29×#54611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—42no—
984C4—41no—
985C4—42no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—81no—
992C4C2×C29×#12311yescharacteristic
993C4C29×#53411yescharacteristic
994C4C29×#54611yescharacteristic
995C4C29×#54611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2C29×#240511yescharacteristic
1005C2C29×#301811yescharacteristic
1006C2C29×#301911yescharacteristic
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×#3093C2semidirect
3. C29×#2896C2semidirect
4. C29×#2500C2semidirect
5. C29×#2040C2semidirect
6. C29×#2039C2semidirect
7. C29×#2037C2semidirect
8. C29×#2037C2semidirect
9. C29×#1900C2semidirect
10. C29×#1871C2semidirect
11. C29×#1860C2semidirect
12. C29×#1859C2semidirect
13. C29×#1792C2semidirect
14. C29×#1792C2semidirect
15. C29×#1789C2semidirect
18. C22×M16×C29C22semidirect
34. C2×C29×#117C22semidirect
39. C29×#428C22semidirect
40. C29×#428C22semidirect
43. C2×C29×#104C22semidirect
44. C2×C29×#104C22semidirect
45. C2×C29×#104C22semidirect
46. C2×C29×#104C22semidirect
51. C29×#417C22semidirect
52. C29×#417C22semidirect
53. C29×#417C22semidirect
54. C29×#417C22semidirect
57. C2×C29×#100C22semidirect
58. C2×C29×#100C22semidirect
59. C29×#407C22semidirect
61. C29×#390C22semidirect
62. C29×#390C22semidirect
64. C29×#384C22semidirect
65. C29×#382C22semidirect
66. C4×C22⋊C4×C29C22semidirect
67. C29×#343C22semidirect
68. C29×#343C22semidirect
69. C29×#339C22semidirect
70. C29×#339C22semidirect
341. #24031C29direct (N × H)
449. #3093C2×C29semidirect
450. #2896C2×C29semidirect
451. #2500C2×C29semidirect
452. #2040C2×C29semidirect
453. #2039C2×C29semidirect
454. #2037C2×C29semidirect
455. #2037C2×C29semidirect
456. #1900C2×C29semidirect
457. #1871C2×C29semidirect
458. #1860C2×C29semidirect
459. #1859C2×C29semidirect
460. #1792C2×C29semidirect
461. #1792C2×C29semidirect
462. #1789C2×C29semidirect
510. C22×M16C22×C29semidirect
526. C2×#117C22×C29semidirect
531. #428C22×C29semidirect
532. #428C22×C29semidirect
535. C2×#104C22×C29semidirect
536. C2×#104C22×C29semidirect
537. C2×#104C22×C29semidirect
538. C2×#104C22×C29semidirect
543. #417C22×C29semidirect
544. #417C22×C29semidirect
545. #417C22×C29semidirect
546. #417C22×C29semidirect
549. C2×#100C22×C29semidirect
550. C2×#100C22×C29semidirect
551. #407C22×C29semidirect
553. #390C22×C29semidirect
554. #390C22×C29semidirect
556. #384C22×C29semidirect
557. #382C22×C29semidirect
558. C4×C22⋊C4C22×C29semidirect
559. #343C22×C29semidirect
560. #343C22×C29semidirect
561. #339C22×C29semidirect
562. #339C22×C29semidirect
697. C29#24031direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#34882
C29×#30932
C29×#28962
C29×#25002
C29×#20402
C29×#20392
C29×#20372
C29×#19002
C29×#18712
C29×#18602
C29×#18592
C29×#17922
C29×#17892
#2403129