Finite Group Databasebeta

← C29×#23767 #20318667

Subgroups — C29×#23767 #20318667

Order 7424.

750 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2324C211yesmaximal, characteristic
2C29×#2314C211yesmaximal, characteristic, complemented
3C29×#2101C211yesmaximal, characteristic, complemented
4C29×#2092C211yesmaximal, characteristic, complemented
5C29×#2083C211yesmaximal, characteristic, complemented
6C29×#2077C211yesmaximal, characteristic, complemented
7C29×#2076C211yesmaximal, characteristic, complemented
8C29×#2071C211yesmaximal, characteristic, complemented
9C29×#2033C211yesmaximal, characteristic
10C29×#2033C211yesmaximal, characteristic
11C29×#1776C211yesmaximal, characteristic, complemented
12C4×C29×#107C211yesmaximal, characteristic, complemented
13C29×#1762C211yesmaximal, characteristic, complemented
14C4×C29×#102C211yesmaximal, characteristic, complemented
15C29×#1750C211yesmaximal, characteristic, complemented
16C2×C29×#121C2211yescharacteristic
17C2×C4×D4×C29C2211yescharacteristic
18C2×C29×#117C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
21C2×C29×#107C2211yescharacteristic
22C2×C29×#106C2211yescharacteristic
23C2×C29×#102C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×C22⋊C8C2211yescharacteristic
28C2×C29×C22⋊C8C2211yescharacteristic
29C2×C29×#97C2211yescharacteristic
30C2×C4×C8×C29C2211yescharacteristic
31C29×#390—21no—
32C29×#390C2211yescharacteristic
33C29×#389C2211yescharacteristic
34C29×#388—21no—
35C29×#388—21no—
36C29×#388—21no—
37C29×#387—21no—
38C29×#387—21no—
39C29×#386—21no—
40C29×#385—21no—
41C29×#384C2211yescharacteristic
42C29×#382C2211yescharacteristic
43C29×#380C2211yescharacteristic
44C29×#380C2211yescharacteristic
45C29×#380C2211yescharacteristic
46C4×C4⋊C4×C29C2211yescharacteristic
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C4⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×D4×C29—21no—
60C22×D4×C29C2311yescharacteristic
61C23×C4×C29—21no—
62C23×C4×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C29×#121—22no—
68C29×#121—22no—
69C4×D4×C29—22no—
70C4×D4×C29—22no—
71C29×#117—22no—
72C29×#117—22no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29D411yescharacteristic
77C2×C4⋊C4×C29D411yescharacteristic
78C2×C4⋊C4×C29C2311yescharacteristic
79C2×C4⋊C4×C29C2311yescharacteristic
80C2×C4⋊C4×C29C2311yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C22⋊C4×C29—21no—
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29D411yescharacteristic
93C2×C22⋊C4×C29D411yescharacteristic
94C2×C42×C29—21no—
95C2×C42×C29—21no—
96C2×C42×C29—21no—
97C2×C42×C29C2311yescharacteristic
98C2×C42×C29C2311yescharacteristic
99C29×#107—22no—
100C29×#107—22no—
101C29×#107—22no—
102C29×#106—22no—
103C29×#102—22no—
104C29×#102—22no—
105C29×#102—22no—
106C29×#102—22no—
107C29×C22⋊C8—22no—
108C29×C22⋊C8—22no—
109C29×#97—22no—
110C4×C8×C29—22no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95—21no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C24×C29—21no—
121C24×C29C2×D411yescharacteristic
122C2×D4×C29—24no—
123C2×D4×C29—21no—
124C2×D4×C29—21no—
125C2×D4×C29—21no—
126C2×D4×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29—81no—
129C2×D4×C29—81no—
130C2×D4×C29#4112yes—
131C22×C4×C29—21no—
132C22×C4×C29—21no—
133C22×C4×C29—21no—
134C22×C4×C29—21no—
135C22×C4×C29—21no—
136C22×C4×C29—21no—
137C22×C4×C29—21no—
138C22×C4×C29—21no—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—42no—
145C22×C4×C29—81no—
146C22×C4×C29—81no—
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2411yescharacteristic
153C2×C8×C29—21no—
154C2×C8×C29—21no—
155C2×C8×C29—21no—
156C2×C8×C29—21no—
157C2×C8×C29—21no—
158C2×C8×C29—21no—
159C2×C8×C29—21no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29#4112yes—
164C2×C8×C29#4112yes—
165C4⋊C4×C29—22no—
166C4⋊C4×C29—22no—
167C4⋊C4×C29—21no—
168C4⋊C4×C29—21no—
169C4⋊C4×C29—21no—
170C4⋊C4×C29—21no—
171C4⋊C4×C29—21no—
172C4⋊C4×C29—21no—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—81no—
181C4⋊C4×C29—81no—
182C4⋊C4×C29—81no—
183C4⋊C4×C29#4112yes—
184C22⋊C4×C29—24no—
185C22⋊C4×C29—22no—
186C22⋊C4×C29—22no—
187C22⋊C4×C29—42no—
188C22⋊C4×C29—81no—
189C22⋊C4×C29—81no—
190C22⋊C4×C29—81no—
191C22⋊C4×C29—81no—
192C22⋊C4×C29—81no—
193C42×C29—21no—
194C42×C29—21no—
195C42×C29—81no—
196C42×C29—81no—
197C42×C29—81no—
198C42×C29#4112yes—
199C42×C29#4112yes—
200#23767C2911yesmaximal, characteristic, direct product factor, Sylow
201C23×C29—21no—
202C23×C29—22no—
203C23×C29—21no—
204C23×C29—21no—
205C23×C29—21no—
206C23×C29—21no—
207C23×C29—21no—
208C23×C29—21no—
209C23×C29—41no—
210C23×C29—41no—
211C23×C29—41no—
212C23×C29—41no—
213C23×C29—41no—
214C23×C29—41no—
215C23×C29C22×D411yescharacteristic
216D4×C29—22no—
217D4×C29—22no—
218D4×C29—41no—
219D4×C29—41no—
220D4×C29—84no—
221C2×C4×C29—21no—
222C2×C4×C29—21no—
223C2×C4×C29—21no—
224C2×C4×C29—21no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—22no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—21no—
234C2×C4×C29—21no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—41no—
240C2×C4×C29—41no—
241C2×C4×C29—41no—
242C2×C4×C29—41no—
243C2×C4×C29—41no—
244C2×C4×C29—41no—
245C2×C4×C29—41no—
246C2×C4×C29—41no—
247C2×C4×C29—41no—
248C2×C4×C29—41no—
249C2×C4×C29—41no—
250C2×C4×C29—41no—
251C2×C4×C29—41no—
252C2×C4×C29—41no—
253C2×C4×C29—41no—
254C2×C4×C29—41no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—84no—
260C2×C4×C29#12312yes—
261C2×C4×C29#12312yes—
262C2×C4×C29C2×#4111yescharacteristic
263C2×C4×C29C2×#4111yescharacteristic
264C2×C4×C29C2×#4111yescharacteristic
265C2×C4×C29C2×#4111yescharacteristic
266C2×C4×C29C2×#4111yescharacteristic
267C2×C4×C29C2×#4111yescharacteristic
268C8×C29—22no—
269C8×C29—22no—
270C8×C29—41no—
271C8×C29—41no—
272#2324C2×C2911yescharacteristic
273#2314C2×C2911yescharacteristic, complemented
274#2101C2×C2911yescharacteristic, complemented
275#2092C2×C2911yescharacteristic, complemented
276#2083C2×C2911yescharacteristic, complemented
277#2077C2×C2911yescharacteristic, complemented
278#2076C2×C2911yescharacteristic, complemented
279#2071C2×C2911yescharacteristic, complemented
280#2033C2×C2911yescharacteristic
281#2033C2×C2911yescharacteristic
282#1776C2×C2911yescharacteristic, complemented
283C4×#107C2×C2911yescharacteristic, complemented
284#1762C2×C2911yescharacteristic, complemented
285C4×#102C2×C2911yescharacteristic, complemented
286#1750C2×C2911yescharacteristic, complemented
287C22×C29—41no—
288C22×C29—41no—
289C22×C29—41no—
290C22×C29—42no—
291C22×C29—41no—
292C22×C29—42no—
293C22×C29—41no—
294C22×C29—42no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29—81no—
301C22×C29C2×#12311yescharacteristic
302C22×C29#52511yescharacteristic
303C22×C29#53211yescharacteristic
304C22×C29#57611yescharacteristic
305C22×C29#57611yescharacteristic
306C22×C29#57711yescharacteristic
307C22×C29#57811yescharacteristic
308C4×C29—22no—
309C4×C29—22no—
310C4×C29—41no—
311C4×C29—41no—
312C4×C29—42no—
313C4×C29—41no—
314C4×C29—81no—
315C4×C29—81no—
316C4×C29—81no—
317C4×C29—81no—
318C4×C29—81no—
319C4×C29—81no—
320C4×C29#52911yescharacteristic
321C4×C29#52911yescharacteristic
322C4×C29#52911yescharacteristic
323C4×C29#52911yescharacteristic
324C2×#121C22×C2911yescharacteristic
325C2×C4×D4C22×C2911yescharacteristic
326C2×#117C22×C2911yescharacteristic
327C2×#107C22×C2911yescharacteristic
328C2×#107C22×C2911yescharacteristic
329C2×#107C22×C2911yescharacteristic
330C2×#106C22×C2911yescharacteristic
331C2×#102C22×C2911yescharacteristic
332C2×#102C22×C2911yescharacteristic
333C2×#102C22×C2911yescharacteristic
334C2×#102C22×C2911yescharacteristic
335C2×C22⋊C8C22×C2911yescharacteristic
336C2×C22⋊C8C22×C2911yescharacteristic
337C2×#97C22×C2911yescharacteristic
338C2×C4×C8C22×C2911yescharacteristic
339#390—21no—
340#390C22×C2911yescharacteristic
341#389C22×C2911yescharacteristic
342#388—21no—
343#388—21no—
344#388—21no—
345#387—21no—
346#387—21no—
347#386—21no—
348#385—21no—
349#384C22×C2911yescharacteristic
350#382C22×C2911yescharacteristic
351#380C22×C2911yescharacteristic
352#380C22×C2911yescharacteristic
353#380C22×C2911yescharacteristic
354C4×C4⋊C4C22×C2911yescharacteristic
355C4×C4⋊C4C22×C2911yescharacteristic
356C4×C4⋊C4C22×C2911yescharacteristic
357#340C22×C2911yescharacteristic
358#340C22×C2911yescharacteristic
359#340C22×C2911yescharacteristic
360#340C22×C2911yescharacteristic
361#340C22×C2911yescharacteristic
362#340C22×C2911yescharacteristic
363#340C22×C2911yescharacteristic
364#340C22×C2911yescharacteristic
365#336C22×C2911yescharacteristic
366#336C22×C2911yescharacteristic
367C2×C29—81no—
368C2×C29—82no—
369C2×C29#239511yescharacteristic
370C2×C29#309611yescharacteristic
371C2×C29#309811yescharacteristic
372C2×C29#312011yescharacteristic
373C2×C29#312211yescharacteristic
374C2×C29#317511yescharacteristic
375C2×C29#317911yescharacteristic
376C22×D4—21no—
377C22×D4C23×C2911yescharacteristic
378C23×C4—21no—
379C23×C4C23×C2911yescharacteristic
380C22×C8C23×C2911yescharacteristic
381C22×C8C23×C2911yescharacteristic
382C22×C8C23×C2911yescharacteristic
383C22×C8C23×C2911yescharacteristic
384#121—22no—
385#121—22no—
386C4×D4—22no—
387C4×D4—22no—
388#117—22no—
389#117—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4D4×C2911yescharacteristic
394C2×C4⋊C4D4×C2911yescharacteristic
395C2×C4⋊C4C23×C2911yescharacteristic
396C2×C4⋊C4C23×C2911yescharacteristic
397C2×C4⋊C4C23×C2911yescharacteristic
398C2×C4⋊C4C23×C2911yescharacteristic
399C2×C4⋊C4C23×C2911yescharacteristic
400C2×C4⋊C4C23×C2911yescharacteristic
401C2×C4⋊C4C23×C2911yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4D4×C2911yescharacteristic
410C2×C22⋊C4D4×C2911yescharacteristic
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C23×C2911yescharacteristic
415C2×C42C23×C2911yescharacteristic
416#107—22no—
417#107—22no—
418#107—22no—
419#106—22no—
420#102—22no—
421#102—22no—
422#102—22no—
423#102—22no—
424C22⋊C8—22no—
425C22⋊C8—22no—
426#97—22no—
427C4×C8—22no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437C29#2376711yescharacteristic, direct product factor, Sylow
438C24—21no—
439C24C2×D4×C2911yescharacteristic
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—81no—
447C2×D4—81no—
448C2×D4#41×C2912yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—42no—
463C22×C4—81no—
464C22×C4—81no—
465C22×C4C2×D4×C2911yescharacteristic
466C22×C4C2×D4×C2911yescharacteristic
467C22×C4C2×D4×C2911yescharacteristic
468C22×C4C2×D4×C2911yescharacteristic
469C22×C4C2×D4×C2911yescharacteristic
470C22×C4C24×C2911yescharacteristic
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8#41×C2912yes—
482C2×C8#41×C2912yes—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4#41×C2912yes—
502C22⋊C4—24no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—42no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C22⋊C4—81no—
509C22⋊C4—81no—
510C22⋊C4—81no—
511C42—21no—
512C42—21no—
513C42—81no—
514C42—81no—
515C42—81no—
516C42#41×C2912yes—
517C42#41×C2912yes—
518C23—21no—
519C23—22no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23C22×D4×C2911yescharacteristic
533D4—22no—
534D4—22no—
535D4—41no—
536D4—41no—
537D4—84no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4C29×#12312yes—
578C2×C4C29×#12312yes—
579C2×C4C2×#41×C2911yescharacteristic
580C2×C4C2×#41×C2911yescharacteristic
581C2×C4C2×#41×C2911yescharacteristic
582C2×C4C2×#41×C2911yescharacteristic
583C2×C4C2×#41×C2911yescharacteristic
584C2×C4C2×#41×C2911yescharacteristic
585C8—22no—
586C8—22no—
587C8—41no—
588C8—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—41no—
594C22—42no—
595C22—41no—
596C22—42no—
597C22—41no—
598C22—41no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22C2×C29×#12311yescharacteristic
604C22C29×#52511yescharacteristic
605C22C29×#53211yescharacteristic
606C22C29×#57611yescharacteristic
607C22C29×#57611yescharacteristic
608C22C29×#57711yescharacteristic
609C22C29×#57811yescharacteristic
610C4—22no—
611C4—22no—
612C4—41no—
613C4—41no—
614C4—42no—
615C4—41no—
616C4—81no—
617C4—81no—
618C4—81no—
619C4—81no—
620C4—81no—
621C4—81no—
622C4C29×#52911yescharacteristic
623C4C29×#52911yescharacteristic
624C4C29×#52911yescharacteristic
625C4C29×#52911yescharacteristic
626C2—81no—
627C2—82no—
628C2C29×#239511yescharacteristic
629C2C29×#309611yescharacteristic
630C2C29×#309811yescharacteristic
631C2C29×#312011yescharacteristic
632C2C29×#312211yescharacteristic
633C2C29×#317511yescharacteristic
634C2C29×#317911yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC2×C29×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C2×C29×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2314C2semidirect
3. C29×#2101C2semidirect
4. C29×#2092C2semidirect
5. C29×#2083C2semidirect
6. C29×#2077C2semidirect
7. C29×#2076C2semidirect
8. C29×#2071C2semidirect
11. C29×#1776C2semidirect
12. C4×C29×#107C2semidirect
13. C29×#1762C2semidirect
14. C4×C29×#102C2semidirect
15. C29×#1750C2semidirect
200. #23767C29direct (N × H)
273. #2314C2×C29semidirect
274. #2101C2×C29semidirect
275. #2092C2×C29semidirect
276. #2083C2×C29semidirect
277. #2077C2×C29semidirect
278. #2076C2×C29semidirect
279. #2071C2×C29semidirect
282. #1776C2×C29semidirect
283. C4×#107C2×C29semidirect
284. #1762C2×C29semidirect
285. C4×#102C2×C29semidirect
286. #1750C2×C29semidirect
437. C29#23767direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23242
C29×#23142
C29×#21012
C29×#20922
C29×#20832
C29×#20772
C29×#20762
C29×#20712
C29×#20332
C29×#17762
C4×C29×#1072
C29×#17622
C4×C29×#1022
C29×#17502
#2376729