Finite Group Databasebeta

← C29×#23832 #20318732

Subgroups — C29×#23832 #20318732

Order 7424.

730 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2330C211yesmaximal, characteristic, complemented
2C29×#2326C211yesmaximal, characteristic
3C29×#2100C211yesmaximal, characteristic, complemented
4C29×#2099C211yesmaximal, characteristic, complemented
5C29×#2072C211yesmaximal, characteristic, complemented
6C29×#2071C211yesmaximal, characteristic
7C29×#2042C211yesmaximal, characteristic
8C29×#2042C211yesmaximal, characteristic
9C29×#2026C211yesmaximal, characteristic, complemented
10C29×#2025C211yesmaximal, characteristic
11C29×#1763C211yesmaximal, characteristic, complemented
12C29×#1762C211yesmaximal, characteristic
13C4×C29×#103C211yesmaximal, characteristic, complemented
14C4×C29×#102C211yesmaximal, characteristic
15C29×#1746C211yesmaximal, characteristic, complemented
16C2×C29×#125C2211yescharacteristic
17C2×C29×#124C2211yescharacteristic
18C2×C4×Q8×C29C2211yescharacteristic
19C2×C4×D4×C29C2211yescharacteristic
20C2×C29×#103C2211yescharacteristic
21C2×C29×#103C2211yescharacteristic
22C2×C29×#103C2211yescharacteristic
23C2×C29×#103C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C2×C4×C8×C29C2211yescharacteristic
30C29×#391C2211yescharacteristic
31C29×#390C2211yescharacteristic
32C29×#389—21no—
33C29×#389—21no—
34C29×#389C2211yescharacteristic
35C29×#389C2211yescharacteristic
36C29×#388—21no—
37C29×#388—21no—
38C29×#387—21no—
39C29×#387—21no—
40C29×#385—21no—
41C29×#385—21no—
42C29×#384C2211yescharacteristic
43C29×#384C2211yescharacteristic
44C4×C4⋊C4×C29C2211yescharacteristic
45C4×C4⋊C4×C29C2211yescharacteristic
46C29×#376C2211yescharacteristic
47C29×#340C2211yescharacteristic
48C29×#340C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×D4×C29C2311yescharacteristic
61C23×C4×C29—21no—
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C29×#125—22no—
67C29×#125—22no—
68C29×#124—22no—
69C29×#124—22no—
70C4×Q8×C29—22no—
71C4×Q8×C29—22no—
72C4×D4×C29—22no—
73C4×D4×C29—22no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—21no—
94C2×C42×C29—21no—
95C2×C42×C29—21no—
96C2×C42×C29—21no—
97C2×C42×C29C2311yescharacteristic
98C2×C42×C29C2311yescharacteristic
99C2×C42×C29C2311yescharacteristic
100C29×#103—22no—
101C29×#103—22no—
102C29×#103—22no—
103C29×#103—22no—
104C29×#102—22no—
105C29×#102—22no—
106C29×#102—22no—
107C29×#102—22no—
108C29×#97—22no—
109C4×C8×C29—22no—
110C29×#95—21no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95D411yescharacteristic
117C29×#95D411yescharacteristic
118C29×#95D411yescharacteristic
119C29×#95D411yescharacteristic
120C24×C29—21no—
121C2×Q8×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—21no—
126C2×Q8×C29#4112yes—
127C2×D4×C29—21no—
128C2×D4×C29—21no—
129C2×D4×C29—21no—
130C2×D4×C29—21no—
131C2×D4×C29—21no—
132C2×D4×C29#4112yes—
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—42no—
141C22×C4×C29—81no—
142C22×C4×C29—81no—
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2411yescharacteristic
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—21no—
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—
162C4⋊C4×C29—24no—
163C4⋊C4×C29—24no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—21no—
166C4⋊C4×C29—21no—
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—42no—
175C4⋊C4×C29—81no—
176C4⋊C4×C29—81no—
177C4⋊C4×C29—81no—
178C4⋊C4×C29—81no—
179C4⋊C4×C29—81no—
180C4⋊C4×C29—81no—
181C4⋊C4×C29#4112yes—
182C4⋊C4×C29#4112yes—
183C22⋊C4×C29—24no—
184C22⋊C4×C29—24no—
185C22⋊C4×C29—42no—
186C22⋊C4×C29—81no—
187C22⋊C4×C29—81no—
188C42×C29—21no—
189C42×C29—21no—
190C42×C29—21no—
191C42×C29—21no—
192C42×C29—42no—
193C42×C29—81no—
194C42×C29—81no—
195C42×C29#4112yes—
196C42×C29#4112yes—
197#23832C2911yesmaximal, characteristic, direct product factor, Sylow
198C23×C29—22no—
199C23×C29—41no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29—41no—
204C23×C29—41no—
205C23×C29C22×D411yescharacteristic
206Q8×C29—22no—
207Q8×C29—22no—
208Q8×C29—41no—
209Q8×C29—41no—
210D4×C29—22no—
211D4×C29—22no—
212D4×C29—41no—
213D4×C29—41no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—21no—
222C2×C4×C29—22no—
223C2×C4×C29—22no—
224C2×C4×C29—22no—
225C2×C4×C29—21no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
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—84no—
252C2×C4×C29#12412yes—
253C2×C4×C29#12412yes—
254C2×C4×C29C2×#4111yescharacteristic
255C2×C4×C29C2×#4111yescharacteristic
256C2×C4×C29C2×#4111yescharacteristic
257C2×C4×C29C2×#4111yescharacteristic
258C2×C4×C29C2×#4111yescharacteristic
259C2×C4×C29C2×#4111yescharacteristic
260C8×C29—41no—
261C8×C29—41no—
262C8×C29—41no—
263C8×C29—41no—
264#2330C2×C2911yescharacteristic, complemented
265#2326C2×C2911yescharacteristic
266#2100C2×C2911yescharacteristic, complemented
267#2099C2×C2911yescharacteristic, complemented
268#2072C2×C2911yescharacteristic, complemented
269#2071C2×C2911yescharacteristic
270#2042C2×C2911yescharacteristic
271#2042C2×C2911yescharacteristic
272#2026C2×C2911yescharacteristic, complemented
273#2025C2×C2911yescharacteristic
274#1763C2×C2911yescharacteristic, complemented
275#1762C2×C2911yescharacteristic
276C4×#103C2×C2911yescharacteristic, complemented
277C4×#102C2×C2911yescharacteristic
278#1746C2×C2911yescharacteristic, complemented
279C22×C29—42no—
280C22×C29—42no—
281C22×C29—42no—
282C22×C29—81no—
283C22×C29—81no—
284C22×C29—81no—
285C22×C29—81no—
286C22×C29#52511yescharacteristic
287C22×C29#52511yescharacteristic
288C22×C29C2×#12411yescharacteristic
289C22×C29#57611yescharacteristic
290C22×C29#57711yescharacteristic
291C22×C29#57711yescharacteristic
292C22×C29#57811yescharacteristic
293C4×C29—22no—
294C4×C29—22no—
295C4×C29—41no—
296C4×C29—41no—
297C4×C29—41no—
298C4×C29—42no—
299C4×C29—41no—
300C4×C29—42no—
301C4×C29—42no—
302C4×C29—81no—
303C4×C29—81no—
304C4×C29—81no—
305C4×C29—81no—
306C4×C29#52911yescharacteristic
307C4×C29#52911yescharacteristic
308C4×C29#52911yescharacteristic
309C4×C29#52911yescharacteristic
310C2×#125C22×C2911yescharacteristic
311C2×#124C22×C2911yescharacteristic
312C2×C4×Q8C22×C2911yescharacteristic
313C2×C4×D4C22×C2911yescharacteristic
314C2×#103C22×C2911yescharacteristic
315C2×#103C22×C2911yescharacteristic
316C2×#103C22×C2911yescharacteristic
317C2×#103C22×C2911yescharacteristic
318C2×#102C22×C2911yescharacteristic
319C2×#102C22×C2911yescharacteristic
320C2×#102C22×C2911yescharacteristic
321C2×#102C22×C2911yescharacteristic
322C2×#97C22×C2911yescharacteristic
323C2×C4×C8C22×C2911yescharacteristic
324#391C22×C2911yescharacteristic
325#390C22×C2911yescharacteristic
326#389—21no—
327#389—21no—
328#389C22×C2911yescharacteristic
329#389C22×C2911yescharacteristic
330#388—21no—
331#388—21no—
332#387—21no—
333#387—21no—
334#385—21no—
335#385—21no—
336#384C22×C2911yescharacteristic
337#384C22×C2911yescharacteristic
338C4×C4⋊C4C22×C2911yescharacteristic
339C4×C4⋊C4C22×C2911yescharacteristic
340#376C22×C2911yescharacteristic
341#340C22×C2911yescharacteristic
342#340C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#340C22×C2911yescharacteristic
346#340C22×C2911yescharacteristic
347#340C22×C2911yescharacteristic
348#340C22×C2911yescharacteristic
349#336C22×C2911yescharacteristic
350#336C22×C2911yescharacteristic
351#336C22×C2911yescharacteristic
352#336C22×C2911yescharacteristic
353C2×C29—82no—
354C2×C29#239811yescharacteristic
355C2×C29#311911yescharacteristic
356C2×C29#312011yescharacteristic
357C2×C29#312411yescharacteristic
358C2×C29#312511yescharacteristic
359C2×C29#313611yescharacteristic
360C2×C29#313711yescharacteristic
361C22×Q8C23×C2911yescharacteristic
362C22×D4C23×C2911yescharacteristic
363C23×C4—21no—
364C22×C8C23×C2911yescharacteristic
365C22×C8C23×C2911yescharacteristic
366C22×C8C23×C2911yescharacteristic
367C22×C8C23×C2911yescharacteristic
368#125—22no—
369#125—22no—
370#124—22no—
371#124—22no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C23×C2911yescharacteristic
386C2×C4⋊C4C23×C2911yescharacteristic
387C2×C4⋊C4C23×C2911yescharacteristic
388C2×C4⋊C4C23×C2911yescharacteristic
389C2×C4⋊C4C23×C2911yescharacteristic
390C2×C4⋊C4C23×C2911yescharacteristic
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42C23×C2911yescharacteristic
400C2×C42C23×C2911yescharacteristic
401C2×C42C23×C2911yescharacteristic
402#103—22no—
403#103—22no—
404#103—22no—
405#103—22no—
406#102—22no—
407#102—22no—
408#102—22no—
409#102—22no—
410#97—22no—
411C4×C8—22no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95D4×C2911yescharacteristic
419#95D4×C2911yescharacteristic
420#95D4×C2911yescharacteristic
421#95D4×C2911yescharacteristic
422C29#2383211yescharacteristic, direct product factor, Sylow
423C24—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8#41×C2912yes—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4#41×C2912yes—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—42no—
444C22×C4—81no—
445C22×C4—81no—
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4C2×D4×C2911yescharacteristic
451C22×C4C2×D4×C2911yescharacteristic
452C22×C4C24×C2911yescharacteristic
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—81no—
479C4⋊C4—81no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C4⋊C4#41×C2912yes—
485C4⋊C4#41×C2912yes—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—42no—
489C22⋊C4—81no—
490C22⋊C4—81no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—81no—
497C42—81no—
498C42#41×C2912yes—
499C42#41×C2912yes—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×D4×C2911yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—84no—
554C2×C4C29×#12412yes—
555C2×C4C29×#12412yes—
556C2×C4C2×#41×C2911yescharacteristic
557C2×C4C2×#41×C2911yescharacteristic
558C2×C4C2×#41×C2911yescharacteristic
559C2×C4C2×#41×C2911yescharacteristic
560C2×C4C2×#41×C2911yescharacteristic
561C2×C4C2×#41×C2911yescharacteristic
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22C29×#52511yescharacteristic
574C22C29×#52511yescharacteristic
575C22C2×C29×#12411yescharacteristic
576C22C29×#57611yescharacteristic
577C22C29×#57711yescharacteristic
578C22C29×#57711yescharacteristic
579C22C29×#57811yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—42no—
588C4—42no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4C29×#52911yescharacteristic
594C4C29×#52911yescharacteristic
595C4C29×#52911yescharacteristic
596C4C29×#52911yescharacteristic
597C2—82no—
598C2C29×#239811yescharacteristic
599C2C29×#311911yescharacteristic
600C2C29×#312011yescharacteristic
601C2C29×#312411yescharacteristic
602C2C29×#312511yescharacteristic
603C2C29×#313611yescharacteristic
604C2C29×#313711yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C29×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2330C2semidirect
3. C29×#2100C2semidirect
4. C29×#2099C2semidirect
5. C29×#2072C2semidirect
9. C29×#2026C2semidirect
11. C29×#1763C2semidirect
13. C4×C29×#103C2semidirect
15. C29×#1746C2semidirect
197. #23832C29direct (N × H)
264. #2330C2×C29semidirect
266. #2100C2×C29semidirect
267. #2099C2×C29semidirect
268. #2072C2×C29semidirect
272. #2026C2×C29semidirect
274. #1763C2×C29semidirect
276. C4×#103C2×C29semidirect
278. #1746C2×C29semidirect
422. C29#23832direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23302
C29×#23262
C29×#21002
C29×#20992
C29×#20722
C29×#20712
C29×#20422
C29×#20262
C29×#20252
C29×#17632
C29×#17622
C4×C29×#1032
C4×C29×#1022
C29×#17462
#2383229