Finite Group Databasebeta

← C29×#62153 #20357053

Subgroups — C29×#62153 #20357053

Order 7424.

1696 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3518C211yesmaximal, characteristic
2Q8×#41×C29C211yesmaximal, characteristic, complemented
3Q8×Q16×C29C211yesmaximal, characteristic, complemented
4Q8×SD16×C29C211yesmaximal, characteristic, complemented
5C29×#3363C211yesmaximal, characteristic, complemented
6C29×#3359C211yesmaximal, characteristic, complemented
7C29×#3357C213yesmaximal, complemented
8C29×#3356C213yesmaximal, complemented
9C29×#3329C213yesmaximal, complemented
10C29×#3328C213yesmaximal, complemented
11C29×#3252C213yesmaximal, complemented
12C29×#3231C213yesmaximal, complemented
13C29×#3108C213yesmaximal, complemented
14C29×#3078C213yesmaximal, complemented
15C29×#2991C211yesmaximal, characteristic, complemented
16Q82×C29C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18C29×#557—21no—
19C29×#557C2211yescharacteristic
20C29×#556—23no—
21C29×#556C2213yes—
22C29×#555C2213yes—
23C29×#554—23no—
24C29×#554C2213yes—
25D4×Q8×C29C2213yes—
26D4×Q8×C29C2211yescharacteristic
27C29×#548—21no—
28C29×#542—23no—
29C29×#533—23no—
30C29×#533C2213yes—
31C29×#533C2213yes—
32C29×#529C2213yes—
33C29×#519—21no—
34C4×#41×C29—21no—
35C4×#41×C29C2211yescharacteristic
36C2×C4×Q8×C29C2213yes—
37C29×#500C2213yes—
38C29×#498C2213yes—
39C29×#487C2213yes—
40C29×#487C2213yes—
41C29×#485C2216yes—
42C29×#485C2216yes—
43C29×#483C2213yes—
44C29×#480C2213yes—
45C29×#479C2213yes—
46C29×#479C2216yes—
47C29×#479C2213yes—
48C29×#477C2213yes—
49C29×#477C2213yes—
50C29×#477C2213yes—
51C29×#476C2213yes—
52C29×#475C2213yes—
53C29×#475C2213yes—
54C29×#470C2216yes—
55C29×#468C2216yes—
56C29×#464C2213yes—
57C29×#464C2211yescharacteristic
58C29×#462C2213yes—
59C29×#461C2213yes—
60C29×#451C2213yes—
61C29×#448C2213yes—
62C8×Q8×C29C2211yescharacteristic
63C8×Q8×C29C2211yescharacteristic
64C4×Q16×C29C2213yes—
65C4×Q16×C29C2213yes—
66C4×SD16×C29C2213yes—
67C4×SD16×C29C2213yes—
68C29×#436C2213yes—
69C29×#436C2213yes—
70C29×#431C2213yes—
71C29×#428C2216yes—
72C29×#423C2213yes—
73C29×#419C2216yes—
74C2×#41×C29D411yescharacteristic
75C22×Q8×C29—21no—
76C22×Q8×C29C2313yes—
77C2×Q16×C29C2311yescharacteristic
78C2×Q16×C29C2313yes—
79C2×SD16×C29C2311yescharacteristic
80C2×SD16×C29C2313yes—
81C2×M16×C29C2316yes—
82C29×C4⋊Q8—23no—
83C29×C4⋊Q8—23no—
84C29×C4⋊Q8—23no—
85C29×C4⋊Q8C2313yes—
86C29×C4⋊Q8C2313yes—
87C29×C4⋊Q8C2313yes—
88C29×C4⋊Q8C2313yes—
89C29×#126—26no—
90C29×#126—23no—
91C29×#125—23no—
92C29×#125—23no—
93C29×#125—23no—
94C29×#125C2313yes—
95C29×#124—23no—
96C29×#124—26no—
97C29×#124C2311yescharacteristic
98C29×#123—23no—
99C29×C22⋊Q8—23no—
100C29×C22⋊Q8—23no—
101C29×C22⋊Q8—23no—
102C29×C22⋊Q8—23no—
103C29×C22⋊Q8—26no—
104C29×C22⋊Q8—26no—
105C29×C22⋊Q8C2313yes—
106C29×C22⋊Q8C2316yes—
107C29×#121—23no—
108C29×#121C2313yes—
109C4×Q8×C29—21no—
110C4×Q8×C29—21no—
111C4×Q8×C29—21no—
112C4×Q8×C29—23no—
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×C29C2313yes—
120C4×Q8×C29C2313yes—
121C4×Q8×C29C2313yes—
122C4×Q8×C29C2311yescharacteristic
123C4×Q8×C29C2313yes—
124C4×Q8×C29C2311yescharacteristic
125C4×D4×C29—23no—
126C4×D4×C29—23no—
127C4×D4×C29—23no—
128C4×D4×C29D413yes—
129C4×D4×C29C2313yes—
130C4×D4×C29C2313yes—
131C29×#117—23no—
132C29×#117—23no—
133C29×#117—23no—
134C29×#117D413yes—
135C29×#117C2316yes—
136C2×C4⋊C4×C29—23no—
137C2×C4⋊C4×C29C2313yes—
138C2×C42×C29—23no—
139C2×C42×C29C2313yes—
140C29×#107C2313yes—
141C29×#107C2316yes—
142C29×#107C2313yes—
143C29×#106C2313yes—
144C29×#106C2316yes—
145C29×#106C2313yes—
146C29×C4⋊C8C2311yescharacteristic
147C29×C4⋊C8C2313yes—
148C29×C4⋊C8C2313yes—
149C29×C4⋊C8C2313yes—
150C29×#103C2313yes—
151C29×#103C2313yes—
152C29×#103C2311yescharacteristic
153C29×#103C2313yes—
154C29×#103C2313yes—
155C29×#103C2313yes—
156C29×#103C2316yes—
157C29×#103C2316yes—
158C29×#102C2311yescharacteristic
159C29×#102C2313yes—
160C29×C22⋊C8C2313yes—
161C29×C22⋊C8C2313yes—
162C4×C8×C29C2313yes—
163C4×C8×C29C2313yes—
164#41×C29—24no—
165C2×Q8×C29—23no—
166C2×Q8×C29—23no—
167C2×Q8×C29—23no—
168C2×Q8×C29—23no—
169C2×Q8×C29—26no—
170C2×Q8×C29—43no—
171C2×Q8×C29—44no—
172C2×Q8×C29C2×D411yescharacteristic
173C2×Q8×C29C2411yescharacteristic
174C2×Q8×C29C2413yes—
175C2×Q8×C29C2411yescharacteristic
176C2×D4×C29—23no—
177C2×D4×C29C2×D413yes—
178C2×D4×C29C2411yescharacteristic
179C22×C4×C29—23no—
180C22×C4×C29—23no—
181C22×C4×C29—23no—
182C22×C4×C29C2×D413yes—
183C22×C4×C29C2×D413yes—
184C22×C4×C29C2413yes—
185Q16×C29—22no—
186Q16×C29—43no—
187SD16×C29—22no—
188SD16×C29—43no—
189M16×C29—46no—
190C2×C8×C29C2413yes—
191C2×C8×C29C2413yes—
192C2×C8×C29C2411yescharacteristic
193C2×C8×C29C2411yescharacteristic
194C4⋊C4×C29—21no—
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—23no—
202C4⋊C4×C29—23no—
203C4⋊C4×C29—23no—
204C4⋊C4×C29—23no—
205C4⋊C4×C29—23no—
206C4⋊C4×C29—23no—
207C4⋊C4×C29—26no—
208C4⋊C4×C29—23no—
209C4⋊C4×C29C2×D413yes—
210C4⋊C4×C29C2×D413yes—
211C4⋊C4×C29C2411yescharacteristic
212C4⋊C4×C29C2413yes—
213C4⋊C4×C29C2413yes—
214C4⋊C4×C29C2413yes—
215C22⋊C4×C29—26no—
216C22⋊C4×C29—26no—
217C22⋊C4×C29—23no—
218C22⋊C4×C29—23no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—21no—
221C22⋊C4×C29—23no—
222C22⋊C4×C29C2×D416yes—
223C42×C29—21no—
224C42×C29—23no—
225C42×C29—23no—
226C42×C29—23no—
227C42×C29—26no—
228C42×C29—23no—
229C42×C29C2×D413yes—
230C42×C29C2×D413yes—
231C42×C29C2411yescharacteristic
232C42×C29C2413yes—
233#62153C2911yesmaximal, characteristic, direct product factor, Sylow
234C23×C29—21no—
235C23×C29C22×D413yes—
236Q8×C29—21no—
237Q8×C29—21no—
238Q8×C29—23no—
239Q8×C29—23no—
240Q8×C29—21no—
241Q8×C29—46no—
242Q8×C29—46no—
243Q8×C29—83no—
244Q8×C29—83no—
245Q8×C29#13714yes—
246Q8×C292−1+412yes—
247D4×C29—26no—
248D4×C29—21no—
249D4×C29—21no—
250D4×C29—83no—
251C2×C4×C29—21no—
252C2×C4×C29—26no—
253C2×C4×C29—23no—
254C2×C4×C29—23no—
255C2×C4×C29—21no—
256C2×C4×C29—21no—
257C2×C4×C29—23no—
258C2×C4×C29—23no—
259C2×C4×C29—23no—
260C2×C4×C29—23no—
261C2×C4×C29—43no—
262C2×C4×C29—46no—
263C2×C4×C29—46no—
264C2×C4×C29—83no—
265C2×C4×C29C22×D411yescharacteristic
266C2×C4×C29C22×D413yes—
267C2×C4×C29C22×D411yescharacteristic
268C2×C4×C29C22×D413yes—
269C2×C4×C29C22×D413yes—
270C2×C4×C29C2511yescharacteristic
271C8×C29—21no—
272C8×C29—21no—
273C8×C29—23no—
274C8×C29—23no—
275#3518C2×C2911yescharacteristic
276Q8×#41C2×C2911yescharacteristic, complemented
277Q8×Q16C2×C2911yescharacteristic, complemented
278Q8×SD16C2×C2911yescharacteristic, complemented
279#3363C2×C2911yescharacteristic, complemented
280#3359C2×C2911yescharacteristic, complemented
281#3357C2×C2913yescomplemented
282#3356C2×C2913yescomplemented
283#3329C2×C2913yescomplemented
284#3328C2×C2913yescomplemented
285#3252C2×C2913yescomplemented
286#3231C2×C2913yescomplemented
287#3108C2×C2913yescomplemented
288#3078C2×C2913yescomplemented
289#2991C2×C2911yescharacteristic, complemented
290C22×C29—23no—
291C22×C29—23no—
292C22×C29—23no—
293C22×C29—41no—
294C22×C29—41no—
295C22×C29—41no—
296C22×C29C23×D411yescharacteristic
297C4×C29—21no—
298C4×C29—23no—
299C4×C29—23no—
300C4×C29—22no—
301C4×C29—21no—
302C4×C29—41no—
303C4×C29—43no—
304C4×C29—43no—
305C4×C29—43no—
306C4×C29—41no—
307C4×C29—43no—
308C4×C29C2×#13716yes—
309C4×C29C2×2−1+411yescharacteristic
310C4×C29#58511yescharacteristic
311Q82C22×C2911yescharacteristic
312Q82C22×C2911yescharacteristic
313#557—21no—
314#557C22×C2911yescharacteristic
315#556—23no—
316#556C22×C2913yes—
317#555C22×C2913yes—
318#554—23no—
319#554C22×C2913yes—
320D4×Q8C22×C2913yes—
321D4×Q8C22×C2911yescharacteristic
322#548—21no—
323#542—23no—
324#533—23no—
325#533C22×C2913yes—
326#533C22×C2913yes—
327#529C22×C2913yes—
328#519—21no—
329C4×#41—21no—
330C4×#41C22×C2911yescharacteristic
331C2×C4×Q8C22×C2913yes—
332#500C22×C2913yes—
333#498C22×C2913yes—
334#487C22×C2913yes—
335#487C22×C2913yes—
336#485C22×C2916yes—
337#485C22×C2916yes—
338#483C22×C2913yes—
339#480C22×C2913yes—
340#479C22×C2913yes—
341#479C22×C2916yes—
342#479C22×C2913yes—
343#477C22×C2913yes—
344#477C22×C2913yes—
345#477C22×C2913yes—
346#476C22×C2913yes—
347#475C22×C2913yes—
348#475C22×C2913yes—
349#470C22×C2916yes—
350#468C22×C2916yes—
351#464C22×C2911yescharacteristic
352#464C22×C2913yes—
353#462C22×C2913yes—
354#461C22×C2913yes—
355#451C22×C2913yes—
356#448C22×C2913yes—
357C8×Q8C22×C2911yescharacteristic
358C8×Q8C22×C2911yescharacteristic
359C4×Q16C22×C2913yes—
360C4×Q16C22×C2913yes—
361C4×SD16C22×C2913yes—
362C4×SD16C22×C2913yes—
363#436C22×C2913yes—
364#436C22×C2913yes—
365#431C22×C2913yes—
366#428C22×C2916yes—
367#423C22×C2913yes—
368#419C22×C2916yes—
369C2×C29—43no—
370C2×C29—81no—
371C2×C29#348911yescharacteristic
372C2×C29C22×#13711yescharacteristic
373C2×C29#358411yescharacteristic
374C2×#41D4×C2911yescharacteristic
375C22×Q8—21no—
376C22×Q8C23×C2913yes—
377C2×Q16C23×C2911yescharacteristic
378C2×Q16C23×C2913yes—
379C2×SD16C23×C2911yescharacteristic
380C2×SD16C23×C2913yes—
381C2×M16C23×C2916yes—
382C4⋊Q8—23no—
383C4⋊Q8—23no—
384C4⋊Q8—23no—
385C4⋊Q8C23×C2913yes—
386C4⋊Q8C23×C2913yes—
387C4⋊Q8C23×C2913yes—
388C4⋊Q8C23×C2913yes—
389#126—26no—
390#126—23no—
391#125—23no—
392#125—23no—
393#125—23no—
394#125C23×C2913yes—
395#124—23no—
396#124—26no—
397#124C23×C2911yescharacteristic
398#123—23no—
399C22⋊Q8—23no—
400C22⋊Q8—23no—
401C22⋊Q8—23no—
402C22⋊Q8—23no—
403C22⋊Q8—26no—
404C22⋊Q8—26no—
405C22⋊Q8C23×C2913yes—
406C22⋊Q8C23×C2916yes—
407#121—23no—
408#121C23×C2913yes—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8—23no—
418C4×Q8D4×C2911yescharacteristic
419C4×Q8C23×C2911yescharacteristic
420C4×Q8C23×C2913yes—
421C4×Q8C23×C2913yes—
422C4×Q8C23×C2913yes—
423C4×Q8C23×C2913yes—
424C4×Q8C23×C2911yescharacteristic
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—23no—
428C4×D4D4×C2913yes—
429C4×D4C23×C2913yes—
430C4×D4C23×C2913yes—
431#117—23no—
432#117—23no—
433#117—23no—
434#117D4×C2913yes—
435#117C23×C2916yes—
436C2×C4⋊C4—23no—
437C2×C4⋊C4C23×C2913yes—
438C2×C42—23no—
439C2×C42C23×C2913yes—
440#107C23×C2913yes—
441#107C23×C2916yes—
442#107C23×C2913yes—
443#106C23×C2913yes—
444#106C23×C2916yes—
445#106C23×C2913yes—
446C4⋊C8C23×C2913yes—
447C4⋊C8C23×C2913yes—
448C4⋊C8C23×C2913yes—
449C4⋊C8C23×C2911yescharacteristic
450#103C23×C2913yes—
451#103C23×C2913yes—
452#103C23×C2916yes—
453#103C23×C2916yes—
454#103C23×C2913yes—
455#103C23×C2911yescharacteristic
456#103C23×C2913yes—
457#103C23×C2913yes—
458#102C23×C2911yescharacteristic
459#102C23×C2913yes—
460C22⋊C8C23×C2913yes—
461C22⋊C8C23×C2913yes—
462C4×C8C23×C2913yes—
463C4×C8C23×C2913yes—
464C29#6215311yescharacteristic, direct product factor, Sylow
465#41—24no—
466C2×Q8—23no—
467C2×Q8—23no—
468C2×Q8—23no—
469C2×Q8—23no—
470C2×Q8—26no—
471C2×Q8—43no—
472C2×Q8—44no—
473C2×Q8C2×D4×C2911yescharacteristic
474C2×Q8C24×C2913yes—
475C2×Q8C24×C2911yescharacteristic
476C2×Q8C24×C2911yescharacteristic
477C2×D4—23no—
478C2×D4C2×D4×C2913yes—
479C2×D4C24×C2911yescharacteristic
480C22×C4—23no—
481C22×C4—23no—
482C22×C4—23no—
483C22×C4C2×D4×C2913yes—
484C22×C4C2×D4×C2913yes—
485C22×C4C24×C2913yes—
486Q16—22no—
487Q16—43no—
488SD16—22no—
489SD16—43no—
490M16—46no—
491C2×C8C24×C2911yescharacteristic
492C2×C8C24×C2911yescharacteristic
493C2×C8C24×C2913yes—
494C2×C8C24×C2913yes—
495C4⋊C4—21no—
496C4⋊C4—23no—
497C4⋊C4—23no—
498C4⋊C4—23no—
499C4⋊C4—23no—
500C4⋊C4—23no—
501C4⋊C4—23no—
502C4⋊C4—23no—
503C4⋊C4—23no—
504C4⋊C4—23no—
505C4⋊C4—23no—
506C4⋊C4—23no—
507C4⋊C4—23no—
508C4⋊C4—26no—
509C4⋊C4—23no—
510C4⋊C4C2×D4×C2913yes—
511C4⋊C4C2×D4×C2913yes—
512C4⋊C4C24×C2911yescharacteristic
513C4⋊C4C24×C2913yes—
514C4⋊C4C24×C2913yes—
515C4⋊C4C24×C2913yes—
516C22⋊C4—26no—
517C22⋊C4—26no—
518C22⋊C4—23no—
519C22⋊C4—23no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—23no—
523C22⋊C4C2×D4×C2916yes—
524C42—21no—
525C42—23no—
526C42—23no—
527C42—23no—
528C42—26no—
529C42—23no—
530C42C2×D4×C2913yes—
531C42C2×D4×C2913yes—
532C42C24×C2913yes—
533C42C24×C2911yescharacteristic
534C23—21no—
535C23C22×D4×C2913yes—
536Q8—21no—
537Q8—21no—
538Q8—23no—
539Q8—23no—
540Q8—21no—
541Q8—46no—
542Q8—46no—
543Q8—83no—
544Q8—83no—
545Q8C29×#13714yes—
546Q8C29×2−1+412yes—
547D4—26no—
548D4—21no—
549D4—21no—
550D4—83no—
551C2×C4—21no—
552C2×C4—26no—
553C2×C4—23no—
554C2×C4—23no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—23no—
558C2×C4—23no—
559C2×C4—23no—
560C2×C4—23no—
561C2×C4—43no—
562C2×C4—46no—
563C2×C4—46no—
564C2×C4—83no—
565C2×C4C22×D4×C2911yescharacteristic
566C2×C4C22×D4×C2913yes—
567C2×C4C22×D4×C2911yescharacteristic
568C2×C4C22×D4×C2913yes—
569C2×C4C22×D4×C2913yes—
570C2×C4C25×C2911yescharacteristic
571C8—21no—
572C8—21no—
573C8—23no—
574C8—23no—
575C22—23no—
576C22—23no—
577C22—23no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22C23×D4×C2911yescharacteristic
582C4—23no—
583C4—22no—
584C4—21no—
585C4—21no—
586C4—23no—
587C4—43no—
588C4—41no—
589C4—43no—
590C4—41no—
591C4—43no—
592C4—43no—
593C4C2×C29×#13716yes—
594C4C2×C29×2−1+411yescharacteristic
595C4C29×#58511yescharacteristic
596C2—43no—
597C2—81no—
598C2C29×#348911yescharacteristic
599C2C22×C29×#13711yescharacteristic
600C2C29×#358411yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC29×#3518C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C4×#41×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. Q8×#41×C29C2semidirect
3. Q8×Q16×C29C2semidirect
4. Q8×SD16×C29C2semidirect
5. C29×#3363C2semidirect
6. C29×#3359C2semidirect
7. C29×#3357C2semidirect
8. C29×#3356C2semidirect
9. C29×#3329C2semidirect
10. C29×#3328C2semidirect
11. C29×#3252C2semidirect
12. C29×#3231C2semidirect
13. C29×#3108C2semidirect
14. C29×#3078C2semidirect
15. C29×#2991C2semidirect
233. #62153C29direct (N × H)
276. Q8×#41C2×C29semidirect
277. Q8×Q16C2×C29semidirect
278. Q8×SD16C2×C29semidirect
279. #3363C2×C29semidirect
280. #3359C2×C29semidirect
281. #3357C2×C29semidirect
282. #3356C2×C29semidirect
283. #3329C2×C29semidirect
284. #3328C2×C29semidirect
285. #3252C2×C29semidirect
286. #3231C2×C29semidirect
287. #3108C2×C29semidirect
288. #3078C2×C29semidirect
289. #2991C2×C29semidirect
464. C29#62153direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35182
Q8×#41×C292
Q8×Q16×C292
Q8×SD16×C292
C29×#33632
C29×#33592
C29×#33572
C29×#33562
C29×#33292
C29×#33282
C29×#32522
C29×#32312
C29×#31082
C29×#30782
C29×#29912
#6215329