Finite Group Databasebeta

← C29×#28968 #20323868

Subgroups — C29×#28968 #20323868

Order 7424.

714 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2507C211yesmaximal, characteristic, complemented
2C29×#2452C211yesmaximal, characteristic
3C29×#2094C211yesmaximal, characteristic
4C29×#2088C211yesmaximal, characteristic, complemented
5C29×#2067C211yesmaximal, characteristic
6C29×#2057C211yesmaximal, characteristic, complemented
7C29×#1990C211yesmaximal, characteristic, complemented
8C29×#1944C211yesmaximal, characteristic, complemented
9C29×#1943C211yesmaximal, characteristic, complemented
10C29×#1936C211yesmaximal, characteristic
11C29×#1934C211yesmaximal, characteristic
12C29×#1920C211yesmaximal, characteristic, complemented
13C29×#1862C211yesmaximal, characteristic
14C29×#1771C211yesmaximal, characteristic, complemented
15C29×#1762C211yesmaximal, characteristic
16C2×C29×C4⋊Q8C2211yescharacteristic
17C2×C29×C22⋊Q8—21no—
18C2×C4×D4×C29C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
21C2×C29×#106C2211yescharacteristic
22C2×C29×#106C2211yescharacteristic
23C2×C29×C4⋊C8C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#97C2211yescharacteristic
29C2×C29×#97C2211yescharacteristic
30C2×C4×C8×C29C2211yescharacteristic
31C29×#398—21no—
32C29×#398—21no—
33C29×#396—21no—
34C29×#393—21no—
35C29×#390C2211yescharacteristic
36C29×#390C2211yescharacteristic
37C29×#389—21no—
38C29×#389C2211yescharacteristic
39C29×#389C2211yescharacteristic
40C29×#389C2211yescharacteristic
41C29×#389C2211yescharacteristic
42C29×#389C2211yescharacteristic
43C29×#389C2211yescharacteristic
44C29×#387—21no—
45C29×#385—21no—
46C29×#384C2211yescharacteristic
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×Q8×C29—21no—
60C22×D4×C29C2311yescharacteristic
61C23×C4×C29—21no—
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C29×C4⋊Q8—22no—
67C29×C4⋊Q8—41no—
68C29×C22⋊Q8—44no—
69C4×D4×C29—22no—
70C4×D4×C29—41no—
71C2×C4⋊C4×C29—21no—
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×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29D411yescharacteristic
81C2×C4⋊C4×C29D411yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
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×C29C2311yescharacteristic
96C2×C42×C29C2311yescharacteristic
97C2×C42×C29C2311yescharacteristic
98C29×#107—22no—
99C29×#107—41no—
100C29×#106—22no—
101C29×#106—22no—
102C29×C4⋊C8—22no—
103C29×#102—22no—
104C29×#102—22no—
105C29×#102—41no—
106C29×#102Q814yescomplemented
107C29×#97—22no—
108C29×#97—41no—
109C4×C8×C29—41no—
110C29×#95—21no—
111C29×#95—21no—
112C29×#95—21no—
113C29×#95—21no—
114C29×#95—21no—
115C29×#95—21no—
116C29×#95—21no—
117C29×#95D411yescharacteristic
118C29×#95D411yescharacteristic
119C24×C29—21no—
120C2×Q8×C29—42no—
121C2×Q8×C29—42no—
122C2×Q8×C29—81no—
123C2×D4×C29—21no—
124C2×D4×C29—21no—
125C2×D4×C29—21no—
126C2×D4×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29C2×Q812yes—
129C22×C4×C29—21no—
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—42no—
137C22×C4×C29—42no—
138C22×C4×C29—81no—
139C22×C4×C29C2×D411yescharacteristic
140C22×C4×C29C2×D411yescharacteristic
141C22×C4×C29C2×D411yescharacteristic
142C22×C4×C29C2×D411yescharacteristic
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2411yescharacteristic
146C2×C8×C29—21no—
147C2×C8×C29—21no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—21no—
153C2×C8×C29—21no—
154C2×C8×C29—21no—
155C2×C8×C29C2×Q812yes—
156C2×C8×C29#4112yes—
157C2×C8×C29#4112yes—
158C4⋊C4×C29—22no—
159C4⋊C4×C29—22no—
160C4⋊C4×C29—21no—
161C4⋊C4×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—42no—
173C4⋊C4×C29—42no—
174C4⋊C4×C29—42no—
175C4⋊C4×C29—42no—
176C4⋊C4×C29—81no—
177C4⋊C4×C29—81no—
178C4⋊C4×C29—81no—
179C4⋊C4×C29—81no—
180C4⋊C4×C29—81no—
181C4⋊C4×C29C2×Q812yes—
182C4⋊C4×C29#4112yes—
183C22⋊C4×C29—42no—
184C22⋊C4×C29—42no—
185C22⋊C4×C29—42no—
186C22⋊C4×C29—42no—
187C22⋊C4×C29—81no—
188C42×C29—21no—
189C42×C29—21no—
190C42×C29—21no—
191C42×C29—21no—
192C42×C29—21no—
193C42×C29—21no—
194C42×C29—81no—
195#28968C2911yesmaximal, characteristic, direct product factor, Sylow
196C23×C29—22no—
197C23×C29—41no—
198C23×C29—41no—
199C23×C29—41no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29C22×D411yescharacteristic
204Q8×C29—84no—
205D4×C29—22no—
206D4×C29—22no—
207D4×C29—41no—
208D4×C29—41no—
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—22no—
218C2×C4×C29—22no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
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—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—84no—
247C2×C4×C29AGL(1,ℤ/8)12yes—
248C2×C4×C29#13712yes—
249C2×C4×C29C22×Q811yescharacteristic
250C2×C4×C29C2×#4111yescharacteristic
251C2×C4×C29C2×#4111yescharacteristic
252C2×C4×C29C2×#4111yescharacteristic
253C2×C4×C29H(5,𝔽2)11yescharacteristic
254C2×C4×C292−1+411yescharacteristic
255C8×C29—22no—
256C8×C29—22no—
257C8×C29—22no—
258C8×C29—41no—
259#2507C2×C2911yescharacteristic, complemented
260#2452C2×C2911yescharacteristic
261#2094C2×C2911yescharacteristic
262#2088C2×C2911yescharacteristic, complemented
263#2067C2×C2911yescharacteristic
264#2057C2×C2911yescharacteristic, complemented
265#1990C2×C2911yescharacteristic, complemented
266#1944C2×C2911yescharacteristic, complemented
267#1943C2×C2911yescharacteristic, complemented
268#1936C2×C2911yescharacteristic
269#1934C2×C2911yescharacteristic
270#1920C2×C2911yescharacteristic, complemented
271#1862C2×C2911yescharacteristic
272#1771C2×C2911yescharacteristic, complemented
273#1762C2×C2911yescharacteristic
274C22×C29—42no—
275C22×C29—42no—
276C22×C29—42no—
277C22×C29—81no—
278C22×C29—81no—
279C22×C29—81no—
280C22×C29—81no—
281C22×C29#53211yescharacteristic
282C22×C29#54611yescharacteristic
283C22×C29D4×Q811yescharacteristic
284C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C29C2×#13711yescharacteristic
286C22×C29#57611yescharacteristic
287C22×C29#57711yescharacteristic
288C4×C29—22no—
289C4×C29—22no—
290C4×C29—42no—
291C4×C29—41no—
292C4×C29—41no—
293C4×C29—41no—
294C4×C29—41no—
295C4×C29—42no—
296C4×C29—81no—
297C4×C29—81no—
298C4×C29—81no—
299C4×C29—81no—
300C4×C29—81no—
301C4×C29#53311yescharacteristic
302C4×C29#53911yescharacteristic
303C4×C29#55211yescharacteristic
304C4×C29#55411yescharacteristic
305C2×C4⋊Q8C22×C2911yescharacteristic
306C2×C22⋊Q8—21no—
307C2×C4×D4C22×C2911yescharacteristic
308C2×#107C22×C2911yescharacteristic
309C2×#107C22×C2911yescharacteristic
310C2×#106C22×C2911yescharacteristic
311C2×#106C22×C2911yescharacteristic
312C2×C4⋊C8C22×C2911yescharacteristic
313C2×#102C22×C2911yescharacteristic
314C2×#102C22×C2911yescharacteristic
315C2×#102C22×C2911yescharacteristic
316C2×#102C22×C2911yescharacteristic
317C2×#97C22×C2911yescharacteristic
318C2×#97C22×C2911yescharacteristic
319C2×C4×C8C22×C2911yescharacteristic
320#398—21no—
321#398—21no—
322#396—21no—
323#393—21no—
324#390C22×C2911yescharacteristic
325#390C22×C2911yescharacteristic
326#389—21no—
327#389C22×C2911yescharacteristic
328#389C22×C2911yescharacteristic
329#389C22×C2911yescharacteristic
330#389C22×C2911yescharacteristic
331#389C22×C2911yescharacteristic
332#389C22×C2911yescharacteristic
333#387—21no—
334#385—21no—
335#384C22×C2911yescharacteristic
336C4×C4⋊C4C22×C2911yescharacteristic
337C4×C4⋊C4C22×C2911yescharacteristic
338#340C22×C2911yescharacteristic
339#340C22×C2911yescharacteristic
340#340C22×C2911yescharacteristic
341#340C22×C2911yescharacteristic
342#340C22×C2911yescharacteristic
343#340C22×C2911yescharacteristic
344#340C22×C2911yescharacteristic
345#340C22×C2911yescharacteristic
346#336C22×C2911yescharacteristic
347#336C22×C2911yescharacteristic
348C2×C29—82no—
349C2×C29#255611yescharacteristic
350C2×C29#317911yescharacteristic
351C2×C29#318211yescharacteristic
352C2×C29#331611yescharacteristic
353C2×C29#331811yescharacteristic
354C2×C29#338411yescharacteristic
355C2×C29#338511yescharacteristic
356C22×Q8—21no—
357C22×D4C23×C2911yescharacteristic
358C23×C4—21no—
359C22×C8C23×C2911yescharacteristic
360C22×C8C23×C2911yescharacteristic
361C22×C8C23×C2911yescharacteristic
362C22×C8C23×C2911yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—41no—
365C22⋊Q8—44no—
366C4×D4—22no—
367C4×D4—41no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
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⋊C4—21no—
391C2×C42—21no—
392C2×C42C23×C2911yescharacteristic
393C2×C42C23×C2911yescharacteristic
394C2×C42C23×C2911yescharacteristic
395#107—22no—
396#107—41no—
397#106—22no—
398#106—22no—
399C4⋊C8—22no—
400#102—22no—
401#102—22no—
402#102—41no—
403#102Q8×C2914yescomplemented
404#97—22no—
405#97—41no—
406C4×C8—41no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95D4×C2911yescharacteristic
415#95D4×C2911yescharacteristic
416C29#2896811yescharacteristic, direct product factor, Sylow
417C24—21no—
418C2×Q8—42no—
419C2×Q8—42no—
420C2×Q8—81no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×Q8×C2912yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—81no—
437C22×C4C2×D4×C2911yescharacteristic
438C22×C4C2×D4×C2911yescharacteristic
439C22×C4C2×D4×C2911yescharacteristic
440C22×C4C2×D4×C2911yescharacteristic
441C22×C4C2×D4×C2911yescharacteristic
442C22×C4C2×D4×C2911yescharacteristic
443C22×C4C24×C2911yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8C2×Q8×C2912yes—
454C2×C8#41×C2912yes—
455C2×C8#41×C2912yes—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—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—42no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—81no—
475C4⋊C4—81no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4—81no—
479C4⋊C4C2×Q8×C2912yes—
480C4⋊C4#41×C2912yes—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—81no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—81no—
493C23—22no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23C22×D4×C2911yescharacteristic
501Q8—84no—
502D4—22no—
503D4—22no—
504D4—41no—
505D4—41no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
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—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—84no—
544C2×C4C29×AGL(1,ℤ/8)12yes—
545C2×C4C29×#13712yes—
546C2×C4C22×Q8×C2911yescharacteristic
547C2×C4C2×#41×C2911yescharacteristic
548C2×C4C2×#41×C2911yescharacteristic
549C2×C4C2×#41×C2911yescharacteristic
550C2×C4C29×H(5,𝔽2)11yescharacteristic
551C2×C4C29×2−1+411yescharacteristic
552C8—22no—
553C8—22no—
554C8—22no—
555C8—41no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22C29×#53211yescharacteristic
564C22C29×#54611yescharacteristic
565C22D4×Q8×C2911yescharacteristic
566C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
567C22C2×C29×#13711yescharacteristic
568C22C29×#57611yescharacteristic
569C22C29×#57711yescharacteristic
570C4—22no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—42no—
576C4—42no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4C29×#53311yescharacteristic
584C4C29×#53911yescharacteristic
585C4C29×#55211yescharacteristic
586C4C29×#55411yescharacteristic
587C2—82no—
588C2C29×#255611yescharacteristic
589C2C29×#317911yescharacteristic
590C2C29×#318211yescharacteristic
591C2C29×#331611yescharacteristic
592C2C29×#331811yescharacteristic
593C2C29×#338411yescharacteristic
594C2C29×#338511yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2507C2semidirect
4. C29×#2088C2semidirect
6. C29×#2057C2semidirect
7. C29×#1990C2semidirect
8. C29×#1944C2semidirect
9. C29×#1943C2semidirect
12. C29×#1920C2semidirect
14. C29×#1771C2semidirect
106. C29×#102Q8semidirect
195. #28968C29direct (N × H)
259. #2507C2×C29semidirect
262. #2088C2×C29semidirect
264. #2057C2×C29semidirect
265. #1990C2×C29semidirect
266. #1944C2×C29semidirect
267. #1943C2×C29semidirect
270. #1920C2×C29semidirect
272. #1771C2×C29semidirect
403. #102Q8×C29semidirect
416. C29#28968direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25072
C29×#24522
C29×#20942
C29×#20882
C29×#20672
C29×#20572
C29×#19902
C29×#19442
C29×#19432
C29×#19362
C29×#19342
C29×#19202
C29×#18622
C29×#17712
C29×#17622
#2896829