Finite Group Databasebeta

← C29×#61846 #20356746

Subgroups — C29×#61846 #20356746

Order 7424.

1664 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×#3502C211yesmaximal, characteristic, complemented
2Q8×#41×C29C211yesmaximal, characteristic
3C29×#3387C213yesmaximal, complemented
4C29×#3385C213yesmaximal, complemented
5Q8×Q16×C29C211yesmaximal, characteristic, complemented
6Q8×SD16×C29C211yesmaximal, characteristic, complemented
7C29×#3374C213yesmaximal, complemented
8C29×#3372C213yesmaximal, complemented
9C29×#3363C211yesmaximal, characteristic, complemented
10C29×#3359C211yesmaximal, characteristic, complemented
11C29×#3237C213yesmaximal, complemented
12C29×#3231C213yesmaximal, complemented
13C29×#3116C213yesmaximal
14C29×#3107C213yesmaximal
15C29×#2984C211yesmaximal, characteristic, complemented
16Q82×C29C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18Q82×C29C2213yes—
19C29×#557—21no—
20C29×#557—23no—
21C29×#557C2211yescharacteristic
22C29×#557C2213yes—
23C29×#557C2213yes—
24C29×#554—23no—
25C29×#554C2213yes—
26D4×Q8×C29—21no—
27D4×Q8×C29C2211yescharacteristic
28C29×#544—23no—
29C29×#533—23no—
30C29×#533C2213yes—
31C29×#533C2213yes—
32C29×#533C2213yes—
33C29×#519—21no—
34C4×#41×C29C2213yes—
35C2×C4×Q8×C29—21no—
36C2×C4×Q8×C29C2211yescharacteristic
37C29×#501C2216yes—
38C29×#500C2213yes—
39C29×#498C2213yes—
40C29×#491C2216yes—
41C29×#487C2213yes—
42C29×#487C2213yes—
43C29×#485C2213yes—
44C29×#485C2216yes—
45C29×#485C2213yes—
46C29×#479C2216yes—
47C29×#479C2216yes—
48C29×#477C2213yes—
49C29×#477C2213yes—
50C29×#477C2213yes—
51C29×#476C2213yes—
52C29×#475C2213yes—
53C29×#475C2213yes—
54C29×#475C2213yes—
55C29×#474C2213yes—
56C29×#462C2213yes—
57C29×#462C2213yes—
58C29×#461C2213yes—
59C29×#461C2213yes—
60C29×#452C2211yescharacteristic
61C29×#452C2213yes—
62C29×#446C2213yes—
63C29×#446C2213yes—
64C8×Q8×C29C2211yescharacteristic
65C8×Q8×C29C2211yescharacteristic
66C29×#441C2216yes—
67C29×#440C2216yes—
68C4×Q16×C29C2213yes—
69C4×Q16×C29C2213yes—
70C4×SD16×C29C2213yes—
71C4×SD16×C29C2213yes—
72C29×#432C2213yes—
73C29×#431C2213yes—
74C2×#41×C29C2311yescharacteristic
75C22×Q8×C29—21no—
76C22×Q8×C29D411yescharacteristic
77C2×Q16×C29C2311yescharacteristic
78C2×Q16×C29C2313yes—
79C2×SD16×C29C2311yescharacteristic
80C2×SD16×C29C2313yes—
81C29×C4⋊Q8—23no—
82C29×C4⋊Q8—23no—
83C29×C4⋊Q8—23no—
84C29×C4⋊Q8—26no—
85C29×C4⋊Q8—23no—
86C29×C4⋊Q8C2313yes—
87C29×C4⋊Q8C2313yes—
88C29×C4⋊Q8C2313yes—
89C29×C4⋊Q8C2313yes—
90C29×C4⋊Q8C2313yes—
91C29×C4⋊Q8C2313yes—
92C29×#125—26no—
93C29×#125—23no—
94C29×#125—26no—
95C29×#125—23no—
96C29×#125—23no—
97C29×#125—23no—
98C29×#125C2316yes—
99C29×C22⋊Q8—23no—
100C29×C22⋊Q8—23no—
101C29×C22⋊Q8—23no—
102C29×C22⋊Q8—23no—
103C29×C22⋊Q8—23no—
104C29×C22⋊Q8—23no—
105C29×C22⋊Q8—26no—
106C29×C22⋊Q8C2311yescharacteristic
107C29×C22⋊Q8C2313yes—
108C4×Q8×C29—21no—
109C4×Q8×C29—23no—
110C4×Q8×C29—21no—
111C4×Q8×C29—23no—
112C4×Q8×C29—21no—
113C4×Q8×C29—23no—
114C4×Q8×C29—23no—
115C4×Q8×C29—23no—
116C4×Q8×C29—23no—
117C4×Q8×C29—23no—
118C4×Q8×C29D411yescharacteristic
119C4×Q8×C29D413yes—
120C4×Q8×C29C2313yes—
121C4×Q8×C29C2313yes—
122C4×Q8×C29C2313yes—
123C4×Q8×C29C2316yes—
124C4×Q8×C29C2313yes—
125C4×Q8×C29C2311yescharacteristic
126C4×Q8×C29C2313yes—
127C4×D4×C29—23no—
128C4×D4×C29—23no—
129C4×D4×C29C2313yes—
130C4×D4×C29C2313yes—
131C29×#117—23no—
132C29×#117—23no—
133C29×#117—23no—
134C29×#117C2313yes—
135C2×C4⋊C4×C29—23no—
136C2×C4⋊C4×C29D413yes—
137C2×C42×C29—23no—
138C2×C42×C29C2313yes—
139C29×#107C2313yes—
140C29×#107C2313yes—
141C29×#107C2316yes—
142C29×#106C2313yes—
143C29×#106C2313yes—
144C29×#106C2316yes—
145C29×C4⋊C8C2313yes—
146C29×C4⋊C8C2313yes—
147C29×C4⋊C8C2313yes—
148C29×C4⋊C8C2313yes—
149C29×#103C2313yes—
150C29×#103C2313yes—
151C29×#103C2311yescharacteristic
152C29×#103C2313yes—
153C29×#103C2313yes—
154C29×#103C2313yes—
155C29×#103C2316yes—
156C29×#103C2316yes—
157C29×#102C2311yescharacteristic
158C29×#102C2313yes—
159C29×C22⋊C8C2311yescharacteristic
160C29×C22⋊C8C2313yes—
161C29×#97C2316yes—
162C4×C8×C29C2313yes—
163C4×C8×C29C2313yes—
164#41×C29—22no—
165#41×C29—22no—
166C2×Q8×C29—24no—
167C2×Q8×C29—23no—
168C2×Q8×C29—23no—
169C2×Q8×C29—23no—
170C2×Q8×C29—23no—
171C2×Q8×C29—44no—
172C2×Q8×C29C2×D413yes—
173C2×Q8×C29C2×D411yescharacteristic
174C2×Q8×C29C2411yescharacteristic
175C2×Q8×C29C2413yes—
176C2×Q8×C29C2411yescharacteristic
177C2×D4×C29—21no—
178C2×D4×C29C2411yescharacteristic
179C22×C4×C29—21no—
180C22×C4×C29—23no—
181C22×C4×C29—23no—
182C22×C4×C29C2×D413yes—
183C22×C4×C29C2×D413yes—
184C22×C4×C29C2411yescharacteristic
185Q16×C29—22no—
186Q16×C29—26no—
187SD16×C29—22no—
188SD16×C29—26no—
189C2×C8×C29C2411yescharacteristic
190C2×C8×C29C2413yes—
191C2×C8×C29C2411yescharacteristic
192C2×C8×C29C2413yes—
193C4⋊C4×C29—26no—
194C4⋊C4×C29—23no—
195C4⋊C4×C29—23no—
196C4⋊C4×C29—23no—
197C4⋊C4×C29—23no—
198C4⋊C4×C29—23no—
199C4⋊C4×C29—23no—
200C4⋊C4×C29—23no—
201C4⋊C4×C29—21no—
202C4⋊C4×C29—23no—
203C4⋊C4×C29—23no—
204C4⋊C4×C29—26no—
205C4⋊C4×C29—23no—
206C4⋊C4×C29—23no—
207C4⋊C4×C29—26no—
208C4⋊C4×C29—23no—
209C4⋊C4×C29—23no—
210C4⋊C4×C29C2×D413yes—
211C4⋊C4×C29C2×D416yes—
212C4⋊C4×C29C2×D413yes—
213C4⋊C4×C29C2413yes—
214C4⋊C4×C29C2413yes—
215C4⋊C4×C29C2411yescharacteristic
216C4⋊C4×C29C2413yes—
217C22⋊C4×C29—23no—
218C22⋊C4×C29—21no—
219C22⋊C4×C29—23no—
220C22⋊C4×C29—23no—
221C22⋊C4×C29—23no—
222C42×C29—23no—
223C42×C29—23no—
224C42×C29—23no—
225C42×C29—26no—
226C42×C29—23no—
227C42×C29—23no—
228C42×C29C2×D413yes—
229C42×C29C2×D413yes—
230C42×C29C2413yes—
231C42×C29C2413yes—
232#61846C2911yesmaximal, characteristic, direct product factor, Sylow
233C23×C29—21no—
234C23×C29C22×D411yescharacteristic
235Q8×C29—26no—
236Q8×C29—21no—
237Q8×C29—21no—
238Q8×C29—23no—
239Q8×C29—21no—
240Q8×C29—23no—
241Q8×C29—46no—
242Q8×C29—83no—
243Q8×C29—83no—
244Q8×C29—83no—
245Q8×C29#13714yes—
246Q8×C292−1+412yes—
247D4×C29—24no—
248D4×C29—21no—
249D4×C292−1+412yes—
250C2×C4×C29—24no—
251C2×C4×C29—21no—
252C2×C4×C29—26no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—23no—
256C2×C4×C29—21no—
257C2×C4×C29—23no—
258C2×C4×C29—21no—
259C2×C4×C29—23no—
260C2×C4×C29—23no—
261C2×C4×C29—43no—
262C2×C4×C29—46no—
263C2×C4×C29—83no—
264C2×C4×C29C22×D411yescharacteristic
265C2×C4×C29C22×D413yes—
266C2×C4×C29C22×D413yes—
267C2×C4×C29C22×D413yes—
268C2×C4×C29C22×D413yes—
269C2×C4×C29C2511yescharacteristic
270C8×C29—21no—
271C8×C29—23no—
272C8×C29—21no—
273C8×C29—23no—
274#3502C2×C2911yescharacteristic, complemented
275Q8×#41C2×C2911yescharacteristic
276#3387C2×C2913yescomplemented
277#3385C2×C2913yescomplemented
278Q8×Q16C2×C2911yescharacteristic, complemented
279Q8×SD16C2×C2911yescharacteristic, complemented
280#3374C2×C2913yescomplemented
281#3372C2×C2913yescomplemented
282#3363C2×C2911yescharacteristic, complemented
283#3359C2×C2911yescharacteristic, complemented
284#3237C2×C2913yescomplemented
285#3231C2×C2913yescomplemented
286#3116C2×C2913yes—
287#3107C2×C2913yes—
288#2984C2×C2911yescharacteristic, complemented
289C22×C29—21no—
290C22×C29—21no—
291C22×C29—22no—
292C22×C29—21no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29C23×D411yescharacteristic
296C4×C29—23no—
297C4×C29—23no—
298C4×C29—21no—
299C4×C29—22no—
300C4×C29—23no—
301C4×C29—43no—
302C4×C29—41no—
303C4×C29—43no—
304C4×C29—43no—
305C4×C29—41no—
306C4×C29—43no—
307C4×C29C2×#13716yes—
308C4×C29C2×2−1+411yescharacteristic
309C4×C29C2×2−1+411yescharacteristic
310Q82C22×C2911yescharacteristic
311Q82C22×C2911yescharacteristic
312Q82C22×C2913yes—
313#557—21no—
314#557—23no—
315#557C22×C2911yescharacteristic
316#557C22×C2913yes—
317#557C22×C2913yes—
318#554—23no—
319#554C22×C2913yes—
320D4×Q8—21no—
321D4×Q8C22×C2911yescharacteristic
322#544—23no—
323#533—23no—
324#533C22×C2913yes—
325#533C22×C2913yes—
326#533C22×C2913yes—
327#519—21no—
328C4×#41C22×C2913yes—
329C2×C4×Q8—21no—
330C2×C4×Q8C22×C2911yescharacteristic
331#501C22×C2916yes—
332#500C22×C2913yes—
333#498C22×C2913yes—
334#491C22×C2916yes—
335#487C22×C2913yes—
336#487C22×C2913yes—
337#485C22×C2913yes—
338#485C22×C2913yes—
339#485C22×C2916yes—
340#479C22×C2916yes—
341#479C22×C2916yes—
342#477C22×C2913yes—
343#477C22×C2913yes—
344#477C22×C2913yes—
345#476C22×C2913yes—
346#475C22×C2913yes—
347#475C22×C2913yes—
348#475C22×C2913yes—
349#474C22×C2913yes—
350#462C22×C2913yes—
351#462C22×C2913yes—
352#461C22×C2913yes—
353#461C22×C2913yes—
354#452C22×C2911yescharacteristic
355#452C22×C2913yes—
356#446C22×C2913yes—
357#446C22×C2913yes—
358C8×Q8C22×C2911yescharacteristic
359C8×Q8C22×C2911yescharacteristic
360#441C22×C2916yes—
361#440C22×C2916yes—
362C4×Q16C22×C2913yes—
363C4×Q16C22×C2913yes—
364C4×SD16C22×C2913yes—
365C4×SD16C22×C2913yes—
366#432C22×C2913yes—
367#431C22×C2913yes—
368C2×C29—41no—
369C2×C29—42no—
370C2×C29#348611yescharacteristic
371C2×C29C22×#13711yescharacteristic
372C2×C29#358411yescharacteristic
373C2×#41C23×C2911yescharacteristic
374C22×Q8—21no—
375C22×Q8D4×C2911yescharacteristic
376C2×Q16C23×C2911yescharacteristic
377C2×Q16C23×C2913yes—
378C2×SD16C23×C2911yescharacteristic
379C2×SD16C23×C2913yes—
380C4⋊Q8—23no—
381C4⋊Q8—23no—
382C4⋊Q8—23no—
383C4⋊Q8—26no—
384C4⋊Q8—23no—
385C4⋊Q8C23×C2913yes—
386C4⋊Q8C23×C2913yes—
387C4⋊Q8C23×C2913yes—
388C4⋊Q8C23×C2913yes—
389C4⋊Q8C23×C2913yes—
390C4⋊Q8C23×C2913yes—
391#125—26no—
392#125—23no—
393#125—26no—
394#125—23no—
395#125—23no—
396#125—23no—
397#125C23×C2916yes—
398C22⋊Q8—23no—
399C22⋊Q8—23no—
400C22⋊Q8—23no—
401C22⋊Q8—23no—
402C22⋊Q8—23no—
403C22⋊Q8—23no—
404C22⋊Q8—26no—
405C22⋊Q8C23×C2911yescharacteristic
406C22⋊Q8C23×C2913yes—
407C4×Q8—21no—
408C4×Q8—23no—
409C4×Q8—21no—
410C4×Q8—23no—
411C4×Q8—21no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8D4×C2911yescharacteristic
418C4×Q8D4×C2913yes—
419C4×Q8C23×C2913yes—
420C4×Q8C23×C2913yes—
421C4×Q8C23×C2913yes—
422C4×Q8C23×C2913yes—
423C4×Q8C23×C2916yes—
424C4×Q8C23×C2911yescharacteristic
425C4×Q8C23×C2913yes—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4C23×C2913yes—
429C4×D4C23×C2913yes—
430#117—23no—
431#117—23no—
432#117—23no—
433#117C23×C2913yes—
434C2×C4⋊C4—23no—
435C2×C4⋊C4D4×C2913yes—
436C2×C42—23no—
437C2×C42C23×C2913yes—
438#107C23×C2913yes—
439#107C23×C2913yes—
440#107C23×C2916yes—
441#106C23×C2913yes—
442#106C23×C2913yes—
443#106C23×C2916yes—
444C4⋊C8C23×C2913yes—
445C4⋊C8C23×C2913yes—
446C4⋊C8C23×C2913yes—
447C4⋊C8C23×C2913yes—
448#103C23×C2913yes—
449#103C23×C2913yes—
450#103C23×C2911yescharacteristic
451#103C23×C2913yes—
452#103C23×C2913yes—
453#103C23×C2913yes—
454#103C23×C2916yes—
455#103C23×C2916yes—
456#102C23×C2911yescharacteristic
457#102C23×C2913yes—
458C22⋊C8C23×C2911yescharacteristic
459C22⋊C8C23×C2913yes—
460#97C23×C2916yes—
461C4×C8C23×C2913yes—
462C4×C8C23×C2913yes—
463C29#6184611yescharacteristic, direct product factor, Sylow
464#41—22no—
465#41—22no—
466C2×Q8—24no—
467C2×Q8—23no—
468C2×Q8—23no—
469C2×Q8—23no—
470C2×Q8—23no—
471C2×Q8—44no—
472C2×Q8C2×D4×C2913yes—
473C2×Q8C2×D4×C2911yescharacteristic
474C2×Q8C24×C2911yescharacteristic
475C2×Q8C24×C2913yes—
476C2×Q8C24×C2911yescharacteristic
477C2×D4—21no—
478C2×D4C24×C2911yescharacteristic
479C22×C4—21no—
480C22×C4—23no—
481C22×C4—23no—
482C22×C4C2×D4×C2913yes—
483C22×C4C2×D4×C2913yes—
484C22×C4C24×C2911yescharacteristic
485Q16—22no—
486Q16—26no—
487SD16—22no—
488SD16—26no—
489C2×C8C24×C2911yescharacteristic
490C2×C8C24×C2911yescharacteristic
491C2×C8C24×C2913yes—
492C2×C8C24×C2913yes—
493C4⋊C4—26no—
494C4⋊C4—23no—
495C4⋊C4—23no—
496C4⋊C4—23no—
497C4⋊C4—23no—
498C4⋊C4—23no—
499C4⋊C4—23no—
500C4⋊C4—23no—
501C4⋊C4—21no—
502C4⋊C4—23no—
503C4⋊C4—23no—
504C4⋊C4—26no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—26no—
508C4⋊C4—23no—
509C4⋊C4—23no—
510C4⋊C4C2×D4×C2913yes—
511C4⋊C4C2×D4×C2916yes—
512C4⋊C4C2×D4×C2913yes—
513C4⋊C4C24×C2911yescharacteristic
514C4⋊C4C24×C2913yes—
515C4⋊C4C24×C2913yes—
516C4⋊C4C24×C2913yes—
517C22⋊C4—21no—
518C22⋊C4—23no—
519C22⋊C4—23no—
520C22⋊C4—23no—
521C22⋊C4—23no—
522C42—23no—
523C42—23no—
524C42—23no—
525C42—26no—
526C42—23no—
527C42—23no—
528C42C2×D4×C2913yes—
529C42C2×D4×C2913yes—
530C42C24×C2913yes—
531C42C24×C2913yes—
532C23—21no—
533C23C22×D4×C2911yescharacteristic
534Q8—26no—
535Q8—21no—
536Q8—21no—
537Q8—23no—
538Q8—21no—
539Q8—23no—
540Q8—46no—
541Q8—83no—
542Q8—83no—
543Q8—83no—
544Q8C29×#13714yes—
545Q8C29×2−1+412yes—
546D4—24no—
547D4—21no—
548D4C29×2−1+412yes—
549C2×C4—24no—
550C2×C4—21no—
551C2×C4—26no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—23no—
555C2×C4—21no—
556C2×C4—23no—
557C2×C4—21no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—43no—
561C2×C4—46no—
562C2×C4—83no—
563C2×C4C22×D4×C2911yescharacteristic
564C2×C4C22×D4×C2913yes—
565C2×C4C22×D4×C2913yes—
566C2×C4C22×D4×C2913yes—
567C2×C4C22×D4×C2913yes—
568C2×C4C25×C2911yescharacteristic
569C8—21no—
570C8—23no—
571C8—21no—
572C8—23no—
573C22—21no—
574C22—22no—
575C22—21no—
576C22—21no—
577C22—41no—
578C22—41no—
579C22C23×D4×C2911yescharacteristic
580C4—21no—
581C4—22no—
582C4—23no—
583C4—23no—
584C4—23no—
585C4—43no—
586C4—41no—
587C4—43no—
588C4—43no—
589C4—41no—
590C4—43no—
591C4C2×C29×#13716yes—
592C4C2×C29×2−1+411yescharacteristic
593C4C2×C29×2−1+411yescharacteristic
594C2—41no—
595C2—42no—
596C2C29×#348611yescharacteristic
597C2C22×C29×#13711yescharacteristic
598C2C29×#358411yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC2×#41×C29C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C4×Q8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3502C2semidirect
3. C29×#3387C2semidirect
4. C29×#3385C2semidirect
5. Q8×Q16×C29C2semidirect
6. Q8×SD16×C29C2semidirect
7. C29×#3374C2semidirect
8. C29×#3372C2semidirect
9. C29×#3363C2semidirect
10. C29×#3359C2semidirect
11. C29×#3237C2semidirect
12. C29×#3231C2semidirect
15. C29×#2984C2semidirect
232. #61846C29direct (N × H)
274. #3502C2×C29semidirect
276. #3387C2×C29semidirect
277. #3385C2×C29semidirect
278. Q8×Q16C2×C29semidirect
279. Q8×SD16C2×C29semidirect
280. #3374C2×C29semidirect
281. #3372C2×C29semidirect
282. #3363C2×C29semidirect
283. #3359C2×C29semidirect
284. #3237C2×C29semidirect
285. #3231C2×C29semidirect
288. #2984C2×C29semidirect
463. C29#61846direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35022
Q8×#41×C292
C29×#33872
C29×#33852
Q8×Q16×C292
Q8×SD16×C292
C29×#33742
C29×#33722
C29×#33632
C29×#33592
C29×#32372
C29×#32312
C29×#31162
C29×#31072
C29×#29842
#6184629