Finite Group Databasebeta

← C29×#29425 #20324325

Subgroups — C29×#29425 #20324325

Order 7424.

724 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2323C211yesmaximal, characteristic
2C29×#2323C211yesmaximal, characteristic
3C29×#2077C211yesmaximal, characteristic
4C29×#2036C211yesmaximal, characteristic
5C29×#2035C211yesmaximal, characteristic
6C29×#2001C211yesmaximal, characteristic
7C29×#1928C211yesmaximal, characteristic, complemented
8C29×#1927C211yesmaximal, characteristic, complemented
9C29×#1921C211yesmaximal, characteristic, complemented
10C29×#1920C211yesmaximal, characteristic, complemented
11C29×#1878C211yesmaximal, characteristic, complemented
12C29×#1878C211yesmaximal, characteristic, complemented
13C29×#1865C211yesmaximal, characteristic, complemented
14C29×#1865C211yesmaximal, characteristic, complemented
15C29×#1818C211yesmaximal, characteristic
16C22×Q16×C29C2211yescharacteristic
17C2×C29×C22⋊Q8C2211yescharacteristic
18C2×C29×C22⋊Q8C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C2×C4×Q8×C29C2211yescharacteristic
21C2×C29×#117C2211yescharacteristic
22C2×C29×#107C2211yescharacteristic
23C2×C29×#106C2211yescharacteristic
24C2×C29×#106C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#103C2211yescharacteristic
27C2×C29×#103C2211yescharacteristic
28C2×C29×#103C2211yescharacteristic
29C2×C29×#103C2211yescharacteristic
30C2×C29×#103C2211yescharacteristic
31C2×C29×C22⋊C8C2211yescharacteristic
32C2×C29×C22⋊C8C2211yescharacteristic
33C29×#391C2211yescharacteristic
34C29×#391C2211yescharacteristic
35C29×#389—21no—
36C29×#389—21no—
37C29×#389C2211yescharacteristic
38C29×#389C2211yescharacteristic
39C29×#388—21no—
40C29×#388—21no—
41C29×#388—21no—
42C29×#388—21no—
43C29×#387—21no—
44C29×#387—21no—
45C29×#380C2211yescharacteristic
46C29×#380C2211yescharacteristic
47C4×C4⋊C4×C29C2211yescharacteristic
48C4×C4⋊C4×C29C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×Q8×C29C2311yescharacteristic
61C23×C4×C29C2311yescharacteristic
62C2×Q16×C29—22no—
63C2×Q16×C29—22no—
64C2×Q16×C29—41no—
65C22×C8×C29C2311yescharacteristic
66C22×C8×C29C2311yescharacteristic
67C22×C8×C29C2311yescharacteristic
68C22×C8×C29C2311yescharacteristic
69C29×C22⋊Q8—22no—
70C29×C22⋊Q8—22no—
71C29×C22⋊Q8—22no—
72C29×C22⋊Q8—22no—
73C4×Q8×C29—41no—
74C4×Q8×C29—41no—
75C4×Q8×C29—41no—
76C4×Q8×C29—41no—
77C29×#117—41no—
78C29×#117—41no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29D411yescharacteristic
86C2×C4⋊C4×C29D411yescharacteristic
87C2×C4⋊C4×C29C2311yescharacteristic
88C2×C4⋊C4×C29C2311yescharacteristic
89C2×C4⋊C4×C29C2311yescharacteristic
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2311yescharacteristic
92C2×C4⋊C4×C29C2311yescharacteristic
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29D411yescharacteristic
98C2×C22⋊C4×C29D411yescharacteristic
99C2×C42×C29—21no—
100C2×C42×C29—21no—
101C2×C42×C29—21no—
102C2×C42×C29—21no—
103C2×C42×C29C2311yescharacteristic
104C2×C42×C29C2311yescharacteristic
105C29×#107—22no—
106C29×#106—22no—
107C29×#106—41no—
108C29×#103—22no—
109C29×#103—22no—
110C29×#103—22no—
111C29×#103—22no—
112C29×#103—41no—
113C29×#103—41no—
114C29×C22⋊C8—41no—
115C29×C22⋊C8—41no—
116C29×#95—21no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95—21no—
125C29×#95—21no—
126C24×C29C2×D411yescharacteristic
127C2×Q8×C29—21no—
128C2×Q8×C29—21no—
129C2×Q8×C29—21no—
130C2×Q8×C29—21no—
131C2×Q8×C29—21no—
132C2×Q8×C29—21no—
133C2×Q8×C29—21no—
134C2×Q8×C29—21no—
135C2×Q8×C29—21no—
136C2×Q8×C29—21no—
137C2×Q8×C29#4112yes—
138C2×Q8×C29#4112yes—
139C22×C4×C29—21no—
140C22×C4×C29—21no—
141C22×C4×C29—21no—
142C22×C4×C29—21no—
143C22×C4×C29—21no—
144C22×C4×C29—21no—
145C22×C4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—21no—
150C22×C4×C29—21no—
151C22×C4×C29—21no—
152C22×C4×C29—21no—
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2411yescharacteristic
159Q16×C29—44no—
160C2×C8×C29—21no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C4⋊C4×C29—24no—
173C4⋊C4×C29—24no—
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—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—41no—
186C4⋊C4×C29—42no—
187C4⋊C4×C29—42no—
188C4⋊C4×C29—81no—
189C4⋊C4×C29—81no—
190C4⋊C4×C29#4112yes—
191C4⋊C4×C29#4112yes—
192C22⋊C4×C29—24no—
193C22⋊C4×C29—24no—
194C22⋊C4×C29—41no—
195C22⋊C4×C29—41no—
196C22⋊C4×C29—81no—
197C22⋊C4×C29—81no—
198C42×C29—21no—
199C42×C29—21no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—42no—
203C42×C29—42no—
204C42×C29—81no—
205C42×C29—81no—
206#29425C2911yesmaximal, characteristic, direct product factor, Sylow
207C23×C29—21no—
208C23×C29—21no—
209C23×C29—21no—
210C23×C29—21no—
211C23×C29—21no—
212C23×C29—21no—
213C23×C29—21no—
214C23×C29C22×D411yescharacteristic
215Q8×C29—22no—
216Q8×C29—22no—
217Q8×C29—22no—
218Q8×C29—22no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—41no—
222Q8×C29—41no—
223C2×C4×C29—22no—
224C2×C4×C29—22no—
225C2×C4×C29—22no—
226C2×C4×C29—22no—
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—21no—
234C2×C4×C29—21no—
235C2×C4×C29—21no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
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—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29C2×#4111yescharacteristic
267C2×C4×C29C2×#4111yescharacteristic
268C2×C4×C29C2×#4111yescharacteristic
269C2×C4×C29C2×#4111yescharacteristic
270C2×C4×C29H(5,𝔽2)11yescharacteristic
271C2×C4×C29H(5,𝔽2)11yescharacteristic
272C8×C29—41no—
273C8×C29—41no—
274C8×C29—41no—
275C8×C29—41no—
276#2323C2×C2911yescharacteristic
277#2323C2×C2911yescharacteristic
278#2077C2×C2911yescharacteristic
279#2036C2×C2911yescharacteristic
280#2035C2×C2911yescharacteristic
281#2001C2×C2911yescharacteristic
282#1928C2×C2911yescharacteristic, complemented
283#1927C2×C2911yescharacteristic, complemented
284#1921C2×C2911yescharacteristic, complemented
285#1920C2×C2911yescharacteristic, complemented
286#1878C2×C2911yescharacteristic, complemented
287#1878C2×C2911yescharacteristic, complemented
288#1865C2×C2911yescharacteristic, complemented
289#1865C2×C2911yescharacteristic, complemented
290#1818C2×C2911yescharacteristic
291C22×C29—41no—
292C22×C29—41no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29—41no—
297C22×C29—41no—
298C22×C29#52511yescharacteristic
299C22×C29#52511yescharacteristic
300C22×C29#53411yescharacteristic
301C22×C29#57711yescharacteristic
302C22×C29#57711yescharacteristic
303C22×C29#57811yescharacteristic
304C22×C29#57811yescharacteristic
305C4×C29—41no—
306C4×C29—42no—
307C4×C29—42no—
308C4×C29—42no—
309C4×C29—42no—
310C4×C29—41no—
311C4×C29—41no—
312C4×C29—41no—
313C4×C29—41no—
314C4×C29—81no—
315C4×C29—81no—
316C4×C29—81no—
317C4×C29—81no—
318C4×C29#55111yescharacteristic
319C4×C29#55311yescharacteristic
320C4×C29#55311yescharacteristic
321C4×C29#55911yescharacteristic
322C22×Q16C22×C2911yescharacteristic
323C2×C22⋊Q8C22×C2911yescharacteristic
324C2×C22⋊Q8C22×C2911yescharacteristic
325C2×C4×Q8C22×C2911yescharacteristic
326C2×C4×Q8C22×C2911yescharacteristic
327C2×#117C22×C2911yescharacteristic
328C2×#107C22×C2911yescharacteristic
329C2×#106C22×C2911yescharacteristic
330C2×#106C22×C2911yescharacteristic
331C2×#103C22×C2911yescharacteristic
332C2×#103C22×C2911yescharacteristic
333C2×#103C22×C2911yescharacteristic
334C2×#103C22×C2911yescharacteristic
335C2×#103C22×C2911yescharacteristic
336C2×#103C22×C2911yescharacteristic
337C2×C22⋊C8C22×C2911yescharacteristic
338C2×C22⋊C8C22×C2911yescharacteristic
339#391C22×C2911yescharacteristic
340#391C22×C2911yescharacteristic
341#389—21no—
342#389—21no—
343#389C22×C2911yescharacteristic
344#389C22×C2911yescharacteristic
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#387—21no—
350#387—21no—
351#380C22×C2911yescharacteristic
352#380C22×C2911yescharacteristic
353C4×C4⋊C4C22×C2911yescharacteristic
354C4×C4⋊C4C22×C2911yescharacteristic
355#340C22×C2911yescharacteristic
356#340C22×C2911yescharacteristic
357#340C22×C2911yescharacteristic
358#340C22×C2911yescharacteristic
359#340C22×C2911yescharacteristic
360#340C22×C2911yescharacteristic
361#336C22×C2911yescharacteristic
362#336C22×C2911yescharacteristic
363#336C22×C2911yescharacteristic
364#336C22×C2911yescharacteristic
365C2×C29—81no—
366C2×C29#260011yescharacteristic
367C2×C29#312011yescharacteristic
368C2×C29#312111yescharacteristic
369C2×C29#312511yescharacteristic
370C2×C29#312711yescharacteristic
371C2×C29#320111yescharacteristic
372C2×C29#320111yescharacteristic
373C22×Q8C23×C2911yescharacteristic
374C22×Q8C23×C2911yescharacteristic
375C23×C4C23×C2911yescharacteristic
376C2×Q16—22no—
377C2×Q16—22no—
378C2×Q16—41no—
379C22×C8C23×C2911yescharacteristic
380C22×C8C23×C2911yescharacteristic
381C22×C8C23×C2911yescharacteristic
382C22×C8C23×C2911yescharacteristic
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—22no—
386C22⋊Q8—22no—
387C4×Q8—41no—
388C4×Q8—41no—
389C4×Q8—41no—
390C4×Q8—41no—
391#117—41no—
392#117—41no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4D4×C2911yescharacteristic
400C2×C4⋊C4D4×C2911yescharacteristic
401C2×C4⋊C4C23×C2911yescharacteristic
402C2×C4⋊C4C23×C2911yescharacteristic
403C2×C4⋊C4C23×C2911yescharacteristic
404C2×C4⋊C4C23×C2911yescharacteristic
405C2×C4⋊C4C23×C2911yescharacteristic
406C2×C4⋊C4C23×C2911yescharacteristic
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4D4×C2911yescharacteristic
412C2×C22⋊C4D4×C2911yescharacteristic
413C2×C42—21no—
414C2×C42—21no—
415C2×C42—21no—
416C2×C42—21no—
417C2×C42C23×C2911yescharacteristic
418C2×C42C23×C2911yescharacteristic
419#107—22no—
420#106—22no—
421#106—41no—
422#103—22no—
423#103—22no—
424#103—22no—
425#103—22no—
426#103—41no—
427#103—41no—
428C22⋊C8—41no—
429C22⋊C8—41no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436#95—21no—
437#95—21no—
438#95—21no—
439#95—21no—
440C29#2942511yescharacteristic, direct product factor, Sylow
441C24C2×D4×C2911yescharacteristic
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8#41×C2912yes—
453C2×Q8#41×C2912yes—
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—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4C2×D4×C2911yescharacteristic
469C22×C4C2×D4×C2911yescharacteristic
470C22×C4C2×D4×C2911yescharacteristic
471C22×C4C2×D4×C2911yescharacteristic
472C22×C4C2×D4×C2911yescharacteristic
473C22×C4C24×C2911yescharacteristic
474Q16—44no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C4⋊C4—24no—
488C4⋊C4—24no—
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—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—81no—
504C4⋊C4—81no—
505C4⋊C4#41×C2912yes—
506C4⋊C4#41×C2912yes—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—81no—
512C22⋊C4—81no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—42no—
518C42—42no—
519C42—81no—
520C42—81no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23C22×D4×C2911yescharacteristic
529Q8—22no—
530Q8—22no—
531Q8—22no—
532Q8—22no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
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—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4C2×#41×C2911yescharacteristic
581C2×C4C2×#41×C2911yescharacteristic
582C2×C4C2×#41×C2911yescharacteristic
583C2×C4C2×#41×C2911yescharacteristic
584C2×C4C29×H(5,𝔽2)11yescharacteristic
585C2×C4C29×H(5,𝔽2)11yescharacteristic
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22C29×#52511yescharacteristic
598C22C29×#52511yescharacteristic
599C22C29×#53411yescharacteristic
600C22C29×#57711yescharacteristic
601C22C29×#57711yescharacteristic
602C22C29×#57811yescharacteristic
603C22C29×#57811yescharacteristic
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—42no—
610C4—42no—
611C4—42no—
612C4—42no—
613C4—81no—
614C4—81no—
615C4—81no—
616C4—81no—
617C4C29×#55111yescharacteristic
618C4C29×#55311yescharacteristic
619C4C29×#55311yescharacteristic
620C4C29×#55911yescharacteristic
621C2—81no—
622C2C29×#260011yescharacteristic
623C2C29×#312011yescharacteristic
624C2C29×#312111yescharacteristic
625C2C29×#312511yescharacteristic
626C2C29×#312711yescharacteristic
627C2C29×#320111yescharacteristic
628C2C29×#320111yescharacteristic
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
7. C29×#1928C2semidirect
8. C29×#1927C2semidirect
9. C29×#1921C2semidirect
10. C29×#1920C2semidirect
11. C29×#1878C2semidirect
12. C29×#1878C2semidirect
13. C29×#1865C2semidirect
14. C29×#1865C2semidirect
206. #29425C29direct (N × H)
282. #1928C2×C29semidirect
283. #1927C2×C29semidirect
284. #1921C2×C29semidirect
285. #1920C2×C29semidirect
286. #1878C2×C29semidirect
287. #1878C2×C29semidirect
288. #1865C2×C29semidirect
289. #1865C2×C29semidirect
440. C29#29425direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23232
C29×#20772
C29×#20362
C29×#20352
C29×#20012
C29×#19282
C29×#19272
C29×#19212
C29×#19202
C29×#18782
C29×#18652
C29×#18182
#2942529