Finite Group Databasebeta

← C29×#34263 #20329163

Subgroups — C29×#34263 #20329163

Order 7424.

2390 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#520C211yesmaximal, characteristic
2C29×#2357C213yesmaximal, complemented
3C29×#2354C213yesmaximal, complemented
4C29×#2351C211yesmaximal, characteristic, complemented
5Q8×C4⋊C4×C29C211yesmaximal, characteristic, complemented
6C29×#2345C213yesmaximal, complemented
7C29×#2344C213yesmaximal, complemented
8C29×#2341C211yesmaximal, characteristic
9C29×#2341C211yesmaximal, characteristic
10C29×#2319C213yesmaximal, complemented
11C29×#2314C213yesmaximal, complemented
12C29×#2298C213yesmaximal, complemented
13C29×#2293C213yesmaximal, complemented
14C29×#2276C211yesmaximal, characteristic, complemented
15C42×Q8×C29C211yesmaximal, characteristic, complemented
16C22×#41×C29C2211yescharacteristic
17C29×#520C4116yescomplemented
18C2×C4×Q8×C29C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C2×C4×Q8×C29C2211yescharacteristic
21C2×C4×Q8×C29C2211yescharacteristic
22C2×C4×Q8×C29C2211yescharacteristic
23C2×C4×Q8×C29C2211yescharacteristic
24C2×C4×D4×C29C2213yes—
25C2×C4×D4×C29C2213yes—
26C2×C29×#117C2216yes—
27C2×C29×#117C2213yes—
28C22×C4⋊C4×C29C2213yes—
29C29×#390C2213yes—
30C29×#390C2213yes—
31C29×#390C2213yes—
32C29×#390C2213yes—
33C29×#389C2213yes—
34C29×#389C2213yes—
35C29×#389C2213yes—
36C29×#389C2213yes—
37C29×#388C2213yes—
38C29×#388C2216yes—
39C29×#388C2213yes—
40C29×#388C2213yes—
41C29×#388C2213yes—
42C29×#388C2216yes—
43C29×#387C2211yescharacteristic
44C29×#387C2213yes—
45C29×#387C2213yes—
46C29×#387C2213yes—
47C29×#387C2216yes—
48C29×#384C2213yes—
49C29×#382C2213yes—
50C29×#381C2216yes—
51C29×#380C2213yes—
52C29×#380C2213yes—
53C29×#380C2216yes—
54C4×C4⋊C4×C29C2213yes—
55C4×C4⋊C4×C29C2213yes—
56C4×C4⋊C4×C29C2213yes—
57C4×C4⋊C4×C29C2213yes—
58C4×C4⋊C4×C29C2213yes—
59C4×C4⋊C4×C29C2213yes—
60C4×C4⋊C4×C29C2213yes—
61C4×C4⋊C4×C29C2213yes—
62C4×C22⋊C4×C29C2216yes—
63C4×C22⋊C4×C29C2213yes—
64C4×C22⋊C4×C29C2213yes—
65C29×#376C2213yes—
66C43×C29C2213yes—
67C2×#41×C29—24no—
68C2×#41×C29—24no—
69C2×#41×C29C2×C418yes—
70C22×Q8×C29C2311yescharacteristic
71C22×D4×C29C2313yes—
72C23×C4×C29C2313yes—
73C23×C4×C29C2316yes—
74C4×Q8×C29—24no—
75C4×Q8×C29—24no—
76C4×Q8×C29—24no—
77C4×Q8×C29—24no—
78C4×Q8×C29C2×C418yes—
79C4×Q8×C29C2×C418yes—
80C4×D4×C29C2×C4124yes—
81C4×D4×C29C2×C4124yes—
82C29×#117—412no—
83C29×#117C2×C4124yes—
84C2×C4⋊C4×C29C2×C4124yes—
85C2×C4⋊C4×C29C2313yes—
86C2×C4⋊C4×C29C2313yes—
87C2×C4⋊C4×C29C2313yes—
88C2×C4⋊C4×C29C2313yes—
89C2×C4⋊C4×C29C2313yes—
90C2×C4⋊C4×C29C2311yescharacteristic
91C2×C4⋊C4×C29C2316yes—
92C2×C4⋊C4×C29C2313yes—
93C2×C4⋊C4×C29C2313yes—
94C2×C4⋊C4×C29C2313yes—
95C2×C4⋊C4×C29C2313yes—
96C2×C4⋊C4×C29C2313yes—
97C2×C4⋊C4×C29C2311yescharacteristic
98C2×C22⋊C4×C29C2313yes—
99C2×C22⋊C4×C29C2313yes—
100C2×C22⋊C4×C29C2316yes—
101C2×C22⋊C4×C29C2316yes—
102C2×C22⋊C4×C29C2313yes—
103C2×C22⋊C4×C29C2313yes—
104C2×C22⋊C4×C29C2313yes—
105C2×C22⋊C4×C29C2313yes—
106C2×C42×C29C2313yes—
107C2×C42×C29C2313yes—
108C2×C42×C29C2313yes—
109C2×C42×C29C2313yes—
110C2×C42×C29C2313yes—
111C2×C42×C29C2311yescharacteristic
112C2×C42×C29C2316yes—
113C2×C42×C29C2313yes—
114C2×C42×C29C2313yes—
115C2×C42×C29C2313yes—
116C2×C42×C29C2313yes—
117C29×#95C2311yescharacteristic
118C29×#95C2313yes—
119C29×#95C2313yes—
120C29×#95C2313yes—
121C29×#95C2311yescharacteristic
122C29×#95C2311yescharacteristic
123C29×#95C2313yes—
124C29×#95C2313yes—
125C29×#95C2313yes—
126C29×#95C2316yes—
127C29×#95C2316yes—
128C29×#95C2311yescharacteristic
129C29×#95C2313yes—
130C29×#95C2313yes—
131C24×C29C2413yes—
132#41×C29—232no—
133C2×Q8×C29C22×C414yes—
134C2×Q8×C29#4114yes—
135C2×Q8×C29#4114yes—
136C2×D4×C29—26no—
137C2×D4×C29—26no—
138C2×D4×C29C22×C4112yes—
139C22×C4×C29—26no—
140C22×C4×C29—26no—
141C22×C4×C29—46no—
142C22×C4×C29—46no—
143C22×C4×C29C22×C4112yes—
144C22×C4×C29C22×C4124yes—
145C22×C4×C29C2413yes—
146C22×C4×C29C2413yes—
147C22×C4×C29C2411yescharacteristic
148C22×C4×C29C2413yes—
149C22×C4×C29C2413yes—
150C22×C4×C29C2411yescharacteristic
151C22×C4×C29C2411yescharacteristic
152C22×C4×C29C2413yes—
153C22×C4×C29C2411yescharacteristic
154C22×C4×C29C2413yes—
155C22×C4×C29C2411yescharacteristic
156C22×C4×C29C2411yescharacteristic
157C22×C4×C29C2411yescharacteristic
158C22×C4×C29C2413yes—
159C4⋊C4×C29—26no—
160C4⋊C4×C29—26no—
161C4⋊C4×C29—26no—
162C4⋊C4×C29—26no—
163C4⋊C4×C29—26no—
164C4⋊C4×C29—22no—
165C4⋊C4×C29—43no—
166C4⋊C4×C29—43no—
167C4⋊C4×C29—46no—
168C4⋊C4×C29C22×C4112yes—
169C4⋊C4×C29C22×C4112yes—
170C4⋊C4×C29C22×C4112yes—
171C4⋊C4×C29C22×C414yes—
172C22⋊C4×C29—26no—
173C22⋊C4×C29—26no—
174C22⋊C4×C29—46no—
175C22⋊C4×C29—43no—
176C22⋊C4×C29—43no—
177C22⋊C4×C29—46no—
178C22⋊C4×C29C22×C4112yes—
179C22⋊C4×C29C22×C4112yes—
180C42×C29—26no—
181C42×C29—26no—
182C42×C29—26no—
183C42×C29—26no—
184C42×C29—26no—
185C42×C29—22no—
186C42×C29—43no—
187C42×C29—43no—
188C42×C29—46no—
189C42×C29C22×C4112yes—
190C42×C29C22×C4112yes—
191#34263C2911yesmaximal, characteristic, direct product factor, Sylow
192C23×C29—23no—
193C23×C29—23no—
194C23×C29—23no—
195C23×C29—23no—
196C23×C29—23no—
197C23×C29—23no—
198C23×C29C23×C416yes—
199C23×C29C2511yescharacteristic
200Q8×C29#117116yescomplemented
201D4×C29—224no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—21no—
205C2×C4×C29—21no—
206C2×C4×C29—23no—
207C2×C4×C29—23no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—23no—
214C2×C4×C29—21no—
215C2×C4×C29—23no—
216C2×C4×C29—224no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—23no—
220C2×C4×C29—23no—
221C2×C4×C29—23no—
222C2×C4×C29—23no—
223C2×C4×C29—23no—
224C2×C4×C29—23no—
225C2×C4×C29—23no—
226C2×C4×C29—23no—
227C2×C4×C29—21no—
228C2×C4×C29—23no—
229C2×C4×C29—23no—
230C2×C4×C29—23no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
233C2×C4×C29—23no—
234C2×C4×C29—21no—
235C2×C4×C29—424no—
236C2×C4×C29C23×C412yes—
237C2×C4×C29C23×C412yes—
238C2×C4×C29C23×C416yes—
239C2×C4×C29C23×C416yes—
240C2×C4×C29C23×C412yes—
241C2×C4×C29C23×C416yes—
242C2×C4×C29C2×#4116yes—
243C2×C4×C29C2×#4116yes—
244C2×C4×C29H(5,𝔽2)12yes—
245C2×C4×C292−1+412yes—
246C2×#520C2×C2911yescharacteristic
247#2357C2×C2913yescomplemented
248#2354C2×C2913yescomplemented
249#2351C2×C2911yescharacteristic, complemented
250Q8×C4⋊C4C2×C2911yescharacteristic, complemented
251#2345C2×C2913yescomplemented
252#2344C2×C2913yescomplemented
253#2341C2×C2911yescharacteristic
254#2341C2×C2911yescharacteristic
255#2319C2×C2913yescomplemented
256#2314C2×C2913yescomplemented
257#2298C2×C2913yescomplemented
258#2293C2×C2913yescomplemented
259#2276C2×C2911yescharacteristic, complemented
260C42×Q8C2×C2911yescharacteristic, complemented
261C22×C29—26no—
262C22×C29—26no—
263C22×C29—26no—
264C22×C29—43no—
265C22×C29—43no—
266C22×C29—43no—
267C22×C29—43no—
268C22×C29C24×C411yescharacteristic
269C22×C29C22×#4111yescharacteristic
270C22×C29C22×#4111yescharacteristic
271C22×C29C2×H(5,𝔽2)11yescharacteristic
272C22×C29C2×2−1+411yescharacteristic
273C22×C29#58511yescharacteristic
274C22×C29#58511yescharacteristic
275C4×C29—22no—
276C4×C29—26no—
277C4×C29—26no—
278C4×C29—22no—
279C4×C29—22no—
280C4×C29—22no—
281C4×C29—22no—
282C4×C29—41no—
283C4×C29—43no—
284C4×C29—43no—
285C4×C29—43no—
286C4×C29—41no—
287C4×C29—43no—
288C4×C29C2×#117112yes—
289C22×#41C22×C2911yescharacteristic
290#520C4×C29116yescomplemented
291C2×C4×Q8C22×C2911yescharacteristic
292C2×C4×Q8C22×C2911yescharacteristic
293C2×C4×Q8C22×C2911yescharacteristic
294C2×C4×Q8C22×C2911yescharacteristic
295C2×C4×Q8C22×C2911yescharacteristic
296C2×C4×Q8C22×C2911yescharacteristic
297C2×C4×D4C22×C2913yes—
298C2×C4×D4C22×C2913yes—
299C2×#117C22×C2916yes—
300C2×#117C22×C2913yes—
301C22×C4⋊C4C22×C2913yes—
302#390C22×C2913yes—
303#390C22×C2913yes—
304#390C22×C2913yes—
305#390C22×C2913yes—
306#389C22×C2913yes—
307#389C22×C2913yes—
308#389C22×C2913yes—
309#389C22×C2913yes—
310#388C22×C2916yes—
311#388C22×C2916yes—
312#388C22×C2913yes—
313#388C22×C2913yes—
314#388C22×C2913yes—
315#388C22×C2913yes—
316#387C22×C2913yes—
317#387C22×C2916yes—
318#387C22×C2913yes—
319#387C22×C2913yes—
320#387C22×C2911yescharacteristic
321#384C22×C2913yes—
322#382C22×C2913yes—
323#381C22×C2916yes—
324#380C22×C2913yes—
325#380C22×C2913yes—
326#380C22×C2916yes—
327C4×C4⋊C4C22×C2913yes—
328C4×C4⋊C4C22×C2913yes—
329C4×C4⋊C4C22×C2913yes—
330C4×C4⋊C4C22×C2913yes—
331C4×C4⋊C4C22×C2913yes—
332C4×C4⋊C4C22×C2913yes—
333C4×C4⋊C4C22×C2913yes—
334C4×C4⋊C4C22×C2913yes—
335C4×C22⋊C4C22×C2913yes—
336C4×C22⋊C4C22×C2913yes—
337C4×C22⋊C4C22×C2916yes—
338#376C22×C2913yes—
339C43C22×C2913yes—
340C2×C29—46no—
341C2×C29C22×#11711yescharacteristic
342C2×C29C4×H(5,𝔽2)11yescharacteristic
343C2×C29C4×2−1+411yescharacteristic
344C2×C29#351611yescharacteristic
345C2×C29#351711yescharacteristic
346C2×C29#352211yescharacteristic
347C2×C29#352411yescharacteristic
348C2×#41—24no—
349C2×#41—24no—
350C2×#41C2×C4×C2918yes—
351C22×Q8C23×C2911yescharacteristic
352C22×D4C23×C2913yes—
353C23×C4C23×C2913yes—
354C23×C4C23×C2916yes—
355C4×Q8—24no—
356C4×Q8—24no—
357C4×Q8—24no—
358C4×Q8—24no—
359C4×Q8C2×C4×C2918yes—
360C4×Q8C2×C4×C2918yes—
361C4×D4C2×C4×C29124yes—
362C4×D4C2×C4×C29124yes—
363#117—412no—
364#117C2×C4×C29124yes—
365C2×C4⋊C4C2×C4×C29124yes—
366C2×C4⋊C4C23×C2913yes—
367C2×C4⋊C4C23×C2913yes—
368C2×C4⋊C4C23×C2913yes—
369C2×C4⋊C4C23×C2913yes—
370C2×C4⋊C4C23×C2913yes—
371C2×C4⋊C4C23×C2911yescharacteristic
372C2×C4⋊C4C23×C2916yes—
373C2×C4⋊C4C23×C2913yes—
374C2×C4⋊C4C23×C2913yes—
375C2×C4⋊C4C23×C2913yes—
376C2×C4⋊C4C23×C2913yes—
377C2×C4⋊C4C23×C2913yes—
378C2×C4⋊C4C23×C2911yescharacteristic
379C2×C22⋊C4C23×C2913yes—
380C2×C22⋊C4C23×C2913yes—
381C2×C22⋊C4C23×C2916yes—
382C2×C22⋊C4C23×C2913yes—
383C2×C22⋊C4C23×C2916yes—
384C2×C22⋊C4C23×C2913yes—
385C2×C22⋊C4C23×C2913yes—
386C2×C22⋊C4C23×C2913yes—
387C2×C42C23×C2913yes—
388C2×C42C23×C2913yes—
389C2×C42C23×C2913yes—
390C2×C42C23×C2913yes—
391C2×C42C23×C2913yes—
392C2×C42C23×C2911yescharacteristic
393C2×C42C23×C2916yes—
394C2×C42C23×C2913yes—
395C2×C42C23×C2913yes—
396C2×C42C23×C2913yes—
397C2×C42C23×C2913yes—
398#95C23×C2911yescharacteristic
399#95C23×C2913yes—
400#95C23×C2913yes—
401#95C23×C2913yes—
402#95C23×C2911yescharacteristic
403#95C23×C2911yescharacteristic
404#95C23×C2913yes—
405#95C23×C2913yes—
406#95C23×C2913yes—
407#95C23×C2916yes—
408#95C23×C2916yes—
409#95C23×C2911yescharacteristic
410#95C23×C2913yes—
411#95C23×C2913yes—
412C29#3426311yescharacteristic, direct product factor, Sylow
413C24C24×C2913yes—
414#41—232no—
415C2×Q8C22×C4×C2914yes—
416C2×Q8#41×C2914yes—
417C2×Q8#41×C2914yes—
418C2×D4—26no—
419C2×D4—26no—
420C2×D4C22×C4×C29112yes—
421C22×C4—26no—
422C22×C4—26no—
423C22×C4—46no—
424C22×C4—46no—
425C22×C4C22×C4×C29112yes—
426C22×C4C22×C4×C29124yes—
427C22×C4C24×C2911yescharacteristic
428C22×C4C24×C2911yescharacteristic
429C22×C4C24×C2913yes—
430C22×C4C24×C2913yes—
431C22×C4C24×C2913yes—
432C22×C4C24×C2913yes—
433C22×C4C24×C2911yescharacteristic
434C22×C4C24×C2911yescharacteristic
435C22×C4C24×C2913yes—
436C22×C4C24×C2911yescharacteristic
437C22×C4C24×C2913yes—
438C22×C4C24×C2911yescharacteristic
439C22×C4C24×C2911yescharacteristic
440C22×C4C24×C2913yes—
441C4⋊C4—26no—
442C4⋊C4—26no—
443C4⋊C4—26no—
444C4⋊C4—26no—
445C4⋊C4—26no—
446C4⋊C4—22no—
447C4⋊C4—46no—
448C4⋊C4—43no—
449C4⋊C4—43no—
450C4⋊C4C22×C4×C29112yes—
451C4⋊C4C22×C4×C29112yes—
452C4⋊C4C22×C4×C29112yes—
453C4⋊C4C22×C4×C2914yes—
454C22⋊C4—26no—
455C22⋊C4—26no—
456C22⋊C4—46no—
457C22⋊C4—46no—
458C22⋊C4—43no—
459C22⋊C4—43no—
460C22⋊C4C22×C4×C29112yes—
461C22⋊C4C22×C4×C29112yes—
462C42—26no—
463C42—26no—
464C42—26no—
465C42—26no—
466C42—26no—
467C42—22no—
468C42—46no—
469C42—43no—
470C42—43no—
471C42C22×C4×C29112yes—
472C42C22×C4×C29112yes—
473C23—23no—
474C23—23no—
475C23—23no—
476C23—23no—
477C23—23no—
478C23—23no—
479C23C23×C4×C2916yes—
480C23C25×C2911yescharacteristic
481Q8C29×#117116yescomplemented
482D4—224no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—23no—
488C2×C4—23no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—23no—
495C2×C4—21no—
496C2×C4—23no—
497C2×C4—224no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—23no—
501C2×C4—23no—
502C2×C4—23no—
503C2×C4—23no—
504C2×C4—23no—
505C2×C4—23no—
506C2×C4—23no—
507C2×C4—23no—
508C2×C4—21no—
509C2×C4—23no—
510C2×C4—23no—
511C2×C4—23no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—23no—
515C2×C4—21no—
516C2×C4—424no—
517C2×C4C23×C4×C2912yes—
518C2×C4C23×C4×C2912yes—
519C2×C4C23×C4×C2916yes—
520C2×C4C23×C4×C2916yes—
521C2×C4C23×C4×C2912yes—
522C2×C4C23×C4×C2916yes—
523C2×C4C2×#41×C2916yes—
524C2×C4C2×#41×C2916yes—
525C2×C4C29×H(5,𝔽2)12yes—
526C2×C4C29×2−1+412yes—
527C22—26no—
528C22—26no—
529C22—26no—
530C22—43no—
531C22—43no—
532C22—43no—
533C22—43no—
534C22C24×C4×C2911yescharacteristic
535C22C22×#41×C2911yescharacteristic
536C22C22×#41×C2911yescharacteristic
537C22C2×C29×H(5,𝔽2)11yescharacteristic
538C22C2×C29×2−1+411yescharacteristic
539C22C29×#58511yescharacteristic
540C22C29×#58511yescharacteristic
541C4—22no—
542C4—22no—
543C4—22no—
544C4—26no—
545C4—26no—
546C4—22no—
547C4—22no—
548C4—41no—
549C4—43no—
550C4—43no—
551C4—43no—
552C4—41no—
553C4—43no—
554C4C2×C29×#117112yes—
555C2—46no—
556C2C22×C29×#11711yescharacteristic
557C2C4×C29×H(5,𝔽2)11yescharacteristic
558C2C4×C29×2−1+411yescharacteristic
559C2C29×#351611yescharacteristic
560C2C29×#351711yescharacteristic
561C2C29×#352211yescharacteristic
562C2C29×#352411yescharacteristic
subgroupG/H
center, socleC23×C29C25
commutatorC22C24×C4×C29
Frattini, cosocleC23C25×C29
prime radicalC22×#41×C29C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2357C2semidirect
3. C29×#2354C2semidirect
4. C29×#2351C2semidirect
5. Q8×C4⋊C4×C29C2semidirect
6. C29×#2345C2semidirect
7. C29×#2344C2semidirect
10. C29×#2319C2semidirect
11. C29×#2314C2semidirect
12. C29×#2298C2semidirect
13. C29×#2293C2semidirect
14. C29×#2276C2semidirect
15. C42×Q8×C29C2semidirect
17. C29×#520C4semidirect
191. #34263C29direct (N × H)
200. Q8×C29#117semidirect
247. #2357C2×C29semidirect
248. #2354C2×C29semidirect
249. #2351C2×C29semidirect
250. Q8×C4⋊C4C2×C29semidirect
251. #2345C2×C29semidirect
252. #2344C2×C29semidirect
255. #2319C2×C29semidirect
256. #2314C2×C29semidirect
257. #2298C2×C29semidirect
258. #2293C2×C29semidirect
259. #2276C2×C29semidirect
260. C42×Q8C2×C29semidirect
290. #520C4×C29semidirect
412. C29#34263direct (N × H)
481. Q8C29×#117semidirect

Maximal subgroups

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

subgroupindex
C2×C29×#5202
C29×#23572
C29×#23542
C29×#23512
Q8×C4⋊C4×C292
C29×#23452
C29×#23442
C29×#23412
C29×#23192
C29×#23142
C29×#22982
C29×#22932
C29×#22762
C42×Q8×C292
#3426329