Finite Group Databasebeta

← C29×#32753 #20327653

Subgroups — C29×#32753 #20327653

Order 7424.

614 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2628C211yesmaximal, characteristic
2C29×#2625C211yesmaximal, characteristic
3C29×#2087C211yesmaximal, characteristic, complemented
4C29×#2086C211yesmaximal, characteristic, complemented
5C29×#2085C211yesmaximal, characteristic, complemented
6C29×#2077C211yesmaximal, characteristic
7C29×#2075C211yesmaximal, characteristic
8C29×#2074C211yesmaximal, characteristic, complemented
9C29×#2068C211yesmaximal, characteristic, complemented
10C29×#2066C211yesmaximal, characteristic, complemented
11C29×#2057C211yesmaximal, characteristic, complemented
12C29×#2036C211yesmaximal, characteristic
13C29×#2036C211yesmaximal, characteristic
14C29×#2024C211yesmaximal, characteristic, complemented
15C29×#1798C211yesmaximal, characteristic
16C2×C29×C4⋊Q8C2211yescharacteristic
17C2×C29×C22⋊Q8C2211yescharacteristic
18C2×C29×#117C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
21C2×C29×#107C2211yescharacteristic
22C2×C29×#106C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×C4⋊C8C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#103C2211yescharacteristic
27C2×C29×#103C2211yescharacteristic
28C2×C29×#103C2211yescharacteristic
29C2×C29×C22⋊C8C2211yescharacteristic
30C2×C29×C22⋊C8C2211yescharacteristic
31C29×#400—21no—
32C29×#400—21no—
33C29×#399—21no—
34C29×#398—21no—
35C29×#397—21no—
36C29×#397—21no—
37C29×#395—21no—
38C29×#393—21no—
39C29×#391C2211yescharacteristic
40C29×#391C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#389C2211yescharacteristic
45C29×#382C2211yescharacteristic
46C29×#380C2211yescharacteristic
47C29×#380C2211yescharacteristic
48C29×#380C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29—21no—
60C22×Q8×C29C2311yescharacteristic
61C23×C4×C29C2311yescharacteristic
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C29×C4⋊Q8—41no—
67C29×C4⋊Q8—41no—
68C29×C22⋊Q8—41no—
69C29×C22⋊Q8—41no—
70C29×#117—41no—
71C29×#117—41no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29D411yescharacteristic
79C2×C4⋊C4×C29D411yescharacteristic
80C2×C4⋊C4×C29C2311yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C4⋊C4×C29C2311yescharacteristic
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29D411yescharacteristic
92C2×C22⋊C4×C29D411yescharacteristic
93C2×C42×C29C2311yescharacteristic
94C2×C42×C29C2311yescharacteristic
95C29×#107—41no—
96C29×#107—41no—
97C29×#107—41no—
98C29×#106—41no—
99C29×C4⋊C8—41no—
100C29×C4⋊C8—41no—
101C29×#103—41no—
102C29×#103—41no—
103C29×#103—41no—
104C29×#103—41no—
105C29×C22⋊C8—41no—
106C29×C22⋊C8—41no—
107C29×#95—21no—
108C29×#95—21no—
109C29×#95—21no—
110C29×#95—21no—
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×C29C2×D411yescharacteristic
121C2×Q8×C29—21no—
122C2×Q8×C29—21no—
123C2×Q8×C29—21no—
124C2×Q8×C29—21no—
125C2×Q8×C29—21no—
126C2×Q8×C29—21no—
127C2×Q8×C29—42no—
128C2×Q8×C29—81no—
129C2×Q8×C29—81no—
130C22×C4×C29—21no—
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×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—21no—
163C4⋊C4×C29—21no—
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—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—41no—
177C4⋊C4×C29—41no—
178C4⋊C4×C29—42no—
179C4⋊C4×C29—42no—
180C4⋊C4×C29—81no—
181C4⋊C4×C29—81no—
182C4⋊C4×C29—81no—
183C4⋊C4×C29—81no—
184C22⋊C4×C29—41no—
185C22⋊C4×C29—41no—
186C22⋊C4×C29—42no—
187C22⋊C4×C29—81no—
188C22⋊C4×C29—81no—
189C22⋊C4×C29—81no—
190C42×C29—21no—
191C42×C29—21no—
192C42×C29—21no—
193C42×C29—21no—
194#32753C2911yesmaximal, characteristic, direct product factor, Sylow
195C23×C29—21no—
196C23×C29—21no—
197C23×C29—21no—
198C23×C29—21no—
199C23×C29—21no—
200C23×C29—21no—
201C23×C29—21no—
202C23×C29C22×D411yescharacteristic
203Q8×C29—41no—
204Q8×C29—41no—
205Q8×C29—41no—
206Q8×C29—41no—
207Q8×C29—84no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
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—21no—
223C2×C4×C29—41no—
224C2×C4×C29—41no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
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×C29H(5,𝔽2)11yescharacteristic
252C2×C4×C29H(5,𝔽2)11yescharacteristic
253C2×C4×C29H(5,𝔽2)11yescharacteristic
254C2×C4×C292−1+411yescharacteristic
255C2×C4×C292−1+411yescharacteristic
256C2×C4×C292−1+411yescharacteristic
257C8×C29—41no—
258C8×C29—41no—
259C8×C29—41no—
260C8×C29—41no—
261#2628C2×C2911yescharacteristic
262#2625C2×C2911yescharacteristic
263#2087C2×C2911yescharacteristic, complemented
264#2086C2×C2911yescharacteristic, complemented
265#2085C2×C2911yescharacteristic, complemented
266#2077C2×C2911yescharacteristic
267#2075C2×C2911yescharacteristic
268#2074C2×C2911yescharacteristic, complemented
269#2068C2×C2911yescharacteristic, complemented
270#2066C2×C2911yescharacteristic, complemented
271#2057C2×C2911yescharacteristic, complemented
272#2036C2×C2911yescharacteristic
273#2036C2×C2911yescharacteristic
274#2024C2×C2911yescharacteristic, complemented
275#1798C2×C2911yescharacteristic
276C22×C29—41no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29—41no—
281C22×C29—41no—
282C22×C29—41no—
283C22×C29#53411yescharacteristic
284C22×C29#53611yescharacteristic
285C22×C29#53711yescharacteristic
286C22×C29#57611yescharacteristic
287C22×C29#57711yescharacteristic
288C22×C29#57811yescharacteristic
289C22×C29#57811yescharacteristic
290C4×C29—41no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—81no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29—81no—
299C4×C29—81no—
300C4×C29—81no—
301C4×C29—81no—
302C4×C29—81no—
303C4×C29#56211yescharacteristic
304C4×C29#56211yescharacteristic
305C4×C29#56311yescharacteristic
306C4×C29#56311yescharacteristic
307C2×C4⋊Q8C22×C2911yescharacteristic
308C2×C22⋊Q8C22×C2911yescharacteristic
309C2×#117C22×C2911yescharacteristic
310C2×#107C22×C2911yescharacteristic
311C2×#107C22×C2911yescharacteristic
312C2×#107C22×C2911yescharacteristic
313C2×#106C22×C2911yescharacteristic
314C2×C4⋊C8C22×C2911yescharacteristic
315C2×C4⋊C8C22×C2911yescharacteristic
316C2×#103C22×C2911yescharacteristic
317C2×#103C22×C2911yescharacteristic
318C2×#103C22×C2911yescharacteristic
319C2×#103C22×C2911yescharacteristic
320C2×C22⋊C8C22×C2911yescharacteristic
321C2×C22⋊C8C22×C2911yescharacteristic
322#400—21no—
323#400—21no—
324#399—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#395—21no—
329#393—21no—
330#391C22×C2911yescharacteristic
331#391C22×C2911yescharacteristic
332#389C22×C2911yescharacteristic
333#389C22×C2911yescharacteristic
334#389C22×C2911yescharacteristic
335#389C22×C2911yescharacteristic
336#382C22×C2911yescharacteristic
337#380C22×C2911yescharacteristic
338#380C22×C2911yescharacteristic
339#380C22×C2911yescharacteristic
340#340C22×C2911yescharacteristic
341#340C22×C2911yescharacteristic
342#340C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#340C22×C2911yescharacteristic
346#340C22×C2911yescharacteristic
347#340C22×C2911yescharacteristic
348#336C22×C2911yescharacteristic
349#336C22×C2911yescharacteristic
350C2×C29—81no—
351C2×C29#281411yescharacteristic
352C2×C29#319811yescharacteristic
353C2×C29#320211yescharacteristic
354C2×C29#324211yescharacteristic
355C2×C29#324311yescharacteristic
356C2×C29#325811yescharacteristic
357C2×C29#326211yescharacteristic
358C22×Q8—21no—
359C22×Q8C23×C2911yescharacteristic
360C23×C4C23×C2911yescharacteristic
361C22×C8C23×C2911yescharacteristic
362C22×C8C23×C2911yescharacteristic
363C22×C8C23×C2911yescharacteristic
364C22×C8C23×C2911yescharacteristic
365C4⋊Q8—41no—
366C4⋊Q8—41no—
367C22⋊Q8—41no—
368C22⋊Q8—41no—
369#117—41no—
370#117—41no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4D4×C2911yescharacteristic
378C2×C4⋊C4D4×C2911yescharacteristic
379C2×C4⋊C4C23×C2911yescharacteristic
380C2×C4⋊C4C23×C2911yescharacteristic
381C2×C4⋊C4C23×C2911yescharacteristic
382C2×C4⋊C4C23×C2911yescharacteristic
383C2×C4⋊C4C23×C2911yescharacteristic
384C2×C4⋊C4C23×C2911yescharacteristic
385C2×C4⋊C4C23×C2911yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4D4×C2911yescharacteristic
391C2×C22⋊C4D4×C2911yescharacteristic
392C2×C42C23×C2911yescharacteristic
393C2×C42C23×C2911yescharacteristic
394#107—41no—
395#107—41no—
396#107—41no—
397#106—41no—
398C4⋊C8—41no—
399C4⋊C8—41no—
400#103—41no—
401#103—41no—
402#103—41no—
403#103—41no—
404C22⋊C8—41no—
405C22⋊C8—41no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419C29#3275311yescharacteristic, direct product factor, Sylow
420C24C2×D4×C2911yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—42no—
428C2×Q8—81no—
429C2×Q8—81no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4C2×D4×C2911yescharacteristic
445C22×C4C2×D4×C2911yescharacteristic
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4C24×C2911yescharacteristic
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
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—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
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—41no—
477C4⋊C4—41no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—81no—
481C4⋊C4—81no—
482C4⋊C4—81no—
483C4⋊C4—81no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C22⋊C4—81no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23C22×D4×C2911yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—84no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
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×C4C29×H(5,𝔽2)11yescharacteristic
551C2×C4C29×H(5,𝔽2)11yescharacteristic
552C2×C4C29×H(5,𝔽2)11yescharacteristic
553C2×C4C29×2−1+411yescharacteristic
554C2×C4C29×2−1+411yescharacteristic
555C2×C4C29×2−1+411yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C29×#53411yescharacteristic
568C22C29×#53611yescharacteristic
569C22C29×#53711yescharacteristic
570C22C29×#57611yescharacteristic
571C22C29×#57711yescharacteristic
572C22C29×#57811yescharacteristic
573C22C29×#57811yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C29×#56211yescharacteristic
588C4C29×#56211yescharacteristic
589C4C29×#56311yescharacteristic
590C4C29×#56311yescharacteristic
591C2—81no—
592C2C29×#281411yescharacteristic
593C2C29×#319811yescharacteristic
594C2C29×#320211yescharacteristic
595C2C29×#324211yescharacteristic
596C2C29×#324311yescharacteristic
597C2C29×#325811yescharacteristic
598C2C29×#326211yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC24×C29C2×D4
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
3. C29×#2087C2semidirect
4. C29×#2086C2semidirect
5. C29×#2085C2semidirect
8. C29×#2074C2semidirect
9. C29×#2068C2semidirect
10. C29×#2066C2semidirect
11. C29×#2057C2semidirect
14. C29×#2024C2semidirect
194. #32753C29direct (N × H)
263. #2087C2×C29semidirect
264. #2086C2×C29semidirect
265. #2085C2×C29semidirect
268. #2074C2×C29semidirect
269. #2068C2×C29semidirect
270. #2066C2×C29semidirect
271. #2057C2×C29semidirect
274. #2024C2×C29semidirect
419. C29#32753direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26282
C29×#26252
C29×#20872
C29×#20862
C29×#20852
C29×#20772
C29×#20752
C29×#20742
C29×#20682
C29×#20662
C29×#20572
C29×#20362
C29×#20242
C29×#17982
#3275329