Finite Group Databasebeta

← C29×#62106 #20357006

Subgroups — C29×#62106 #20357006

Order 7424.

1782 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3518C211yesmaximal, characteristic, complemented
2C29×#3483C211yesmaximal, characteristic, complemented
3Q8×Q16×C29C211yesmaximal, characteristic, complemented
4Q8×SD16×C29C211yesmaximal, characteristic, complemented
5C29×#3362C211yesmaximal, characteristic, complemented
6C29×#3358C211yesmaximal, characteristic, complemented
7C29×#3341C213yesmaximal, complemented
8C29×#3340C213yesmaximal, complemented
9C29×#3305C213yesmaximal, complemented
10C29×#3304C213yesmaximal, complemented
11C29×#3247C213yesmaximal, complemented
12C29×#3228C213yesmaximal, complemented
13C29×#3102C213yesmaximal, complemented
14C29×#3076C213yesmaximal, complemented
15C29×#2988C211yesmaximal, characteristic, complemented
16Q82×C29C2211yescharacteristic
17Q82×C29C2211yescharacteristic
18C29×#556—23no—
19C29×#556C2213yes—
20C29×#555—23no—
21C29×#555C2213yes—
22C29×#555C2213yes—
23C29×#550—21no—
24C29×#550C2213yes—
25C29×#550C2211yescharacteristic
26D4×Q8×C29C2211yescharacteristic
27C29×#548—21no—
28C29×#542—23no—
29C29×#533C2213yes—
30C29×#532—23no—
31C29×#532C2213yes—
32C29×#529C2213yes—
33C29×#519—21no—
34C4×#41×C29—21no—
35C4×#41×C29C2213yes—
36C4×#41×C29C2211yescharacteristic
37C29×#500C2213yes—
38C29×#498C2213yes—
39C29×#486C2213yes—
40C29×#486C2213yes—
41C29×#485C2213yes—
42C29×#482C2216yes—
43C29×#482C2216yes—
44C29×#482C2213yes—
45C29×#479C2213yes—
46C29×#478C2213yes—
47C29×#478C2216yes—
48C29×#477C2213yes—
49C29×#477C2213yes—
50C29×#476C2213yes—
51C29×#476C2213yes—
52C29×#475C2213yes—
53C29×#474C2213yes—
54C29×#466C2216yes—
55C29×#465C2216yes—
56C29×#464C2211yescharacteristic
57C29×#463C2213yes—
58C29×#460C2213yes—
59C29×#459C2213yes—
60C29×#452C2213yes—
61C29×#449C2213yes—
62C8×Q8×C29C2211yescharacteristic
63C8×Q8×C29C2211yescharacteristic
64C4×Q16×C29C2213yes—
65C4×SD16×C29C2213yes—
66C4×SD16×C29C2213yes—
67C4×D8×C29C2213yes—
68C8×D4×C29C2213yes—
69C8×D4×C29C2213yes—
70C29×#431C2213yes—
71C29×#427C2216yes—
72C2×C29×C4⋊C8C2213yes—
73C29×#416C2216yes—
74C2×#41×C29—21no—
75C2×#41×C29—23no—
76C2×#41×C29D411yescharacteristic
77C2×#41×C29C2313yes—
78C22×Q8×C29—21no—
79C2×Q16×C29C2311yescharacteristic
80C2×SD16×C29C2311yescharacteristic
81C2×SD16×C29C2313yes—
82C2×D8×C29C2313yes—
83C22×C8×C29C2316yes—
84C29×C4⋊Q8—23no—
85C29×C4⋊Q8—23no—
86C29×C4⋊Q8C2313yes—
87C29×C4⋊Q8C2313yes—
88C29×C4⋊Q8C2313yes—
89C29×#127—23no—
90C29×#127C2313yes—
91C29×#126—26no—
92C29×#126—23no—
93C29×#125C2313yes—
94C29×#124—23no—
95C29×#124—26no—
96C29×#124—26no—
97C29×#124—23no—
98C29×#124C2311yescharacteristic
99C29×#123—23no—
100C29×C22⋊Q8—23no—
101C29×C22⋊Q8—23no—
102C29×C22⋊Q8—23no—
103C29×C22⋊Q8C2313yes—
104C29×#121—23no—
105C29×#121—23no—
106C29×#121—23no—
107C29×#121—23no—
108C29×#121—26no—
109C29×#121C2313yes—
110C29×#121C2316yes—
111C4×Q8×C29—21no—
112C4×Q8×C29—21no—
113C4×Q8×C29—23no—
114C4×Q8×C29—23no—
115C4×Q8×C29—23no—
116C4×Q8×C29D411yescharacteristic
117C4×Q8×C29C2313yes—
118C4×Q8×C29C2313yes—
119C4×Q8×C29C2311yescharacteristic
120C4×Q8×C29C2311yescharacteristic
121C4×D4×C29—23no—
122C4×D4×C29—23no—
123C4×D4×C29—23no—
124C4×D4×C29—23no—
125C4×D4×C29—23no—
126C4×D4×C29D413yes—
127C4×D4×C29C2313yes—
128C4×D4×C29C2313yes—
129C4×D4×C29C2313yes—
130C4×D4×C29C2313yes—
131C29×#117—23no—
132C29×#117—23no—
133C29×#117—23no—
134C29×#117—23no—
135C29×#117D413yes—
136C29×#117C2313yes—
137C29×#117C2316yes—
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×#103C2311yescharacteristic
151C29×#103C2313yes—
152C29×#103C2313yes—
153C29×#103C2313yes—
154C29×#102C2311yescharacteristic
155C29×#102C2313yes—
156C29×#102C2313yes—
157C29×#102C2313yes—
158C29×#102C2316yes—
159C29×#102C2316yes—
160C29×C22⋊C8C2313yes—
161C29×C22⋊C8C2313yes—
162C4×C8×C29C2313yes—
163C4×C8×C29C2313yes—
164#41×C29—24no—
165#41×C29—26no—
166#41×C29—43no—
167#41×C29—44no—
168#41×C29—86no—
169C2×Q8×C29—23no—
170C2×Q8×C29—23no—
171C2×Q8×C29—23no—
172C2×Q8×C29—44no—
173C2×Q8×C29C2×D411yescharacteristic
174C2×Q8×C29C2411yescharacteristic
175C2×Q8×C29C2411yescharacteristic
176C2×D4×C29—23no—
177C2×D4×C29—23no—
178C2×D4×C29—26no—
179C2×D4×C29—23no—
180C2×D4×C29—23no—
181C2×D4×C29C2×D413yes—
182C2×D4×C29C2411yescharacteristic
183C2×D4×C29C2413yes—
184C22×C4×C29—23no—
185C22×C4×C29—23no—
186C22×C4×C29—23no—
187C22×C4×C29—23no—
188C22×C4×C29C2×D413yes—
189C22×C4×C29C2×D413yes—
190C22×C4×C29C2413yes—
191Q16×C29—22no—
192SD16×C29—22no—
193SD16×C29—43no—
194D8×C29—43no—
195C2×C8×C29—46no—
196C2×C8×C29C2413yes—
197C2×C8×C29C2413yes—
198C2×C8×C29C2411yescharacteristic
199C2×C8×C29C2411yescharacteristic
200C4⋊C4×C29—21no—
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—23no—
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—23no—
216C22⋊C4×C29—26no—
217C22⋊C4×C29—23no—
218C22⋊C4×C29—23no—
219C22⋊C4×C29—21no—
220C22⋊C4×C29—26no—
221C22⋊C4×C29—23no—
222C22⋊C4×C29—23no—
223C22⋊C4×C29—21no—
224C22⋊C4×C29—23no—
225C22⋊C4×C29C2×D416yes—
226C42×C29—21no—
227C42×C29—23no—
228C42×C29—23no—
229C42×C29—26no—
230C42×C29—23no—
231C42×C29C2×D413yes—
232C42×C29C2×D413yes—
233C42×C29C2411yescharacteristic
234C42×C29C2413yes—
235#62106C2911yesmaximal, characteristic, direct product factor, Sylow
236C23×C29—21no—
237C23×C29—23no—
238C23×C29C22×D413yes—
239Q8×C29—21no—
240Q8×C29—21no—
241Q8×C29—21no—
242Q8×C29—46no—
243Q8×C29—83no—
244Q8×C29—83no—
245Q8×C29#13514yes—
246Q8×C292−1+412yes—
247D4×C29—26no—
248D4×C29—21no—
249D4×C29—23no—
250D4×C29—21no—
251D4×C29—23no—
252D4×C29—46no—
253D4×C29—46no—
254D4×C29—83no—
255D4×C29—83no—
256D4×C29—86no—
257C2×C4×C29—21no—
258C2×C4×C29—26no—
259C2×C4×C29—23no—
260C2×C4×C29—23no—
261C2×C4×C29—21no—
262C2×C4×C29—21no—
263C2×C4×C29—23no—
264C2×C4×C29—23no—
265C2×C4×C29—23no—
266C2×C4×C29—43no—
267C2×C4×C29—46no—
268C2×C4×C29—46no—
269C2×C4×C29—46no—
270C2×C4×C29—46no—
271C2×C4×C29C22×D413yes—
272C2×C4×C29C22×D411yescharacteristic
273C2×C4×C29C22×D411yescharacteristic
274C2×C4×C29C22×D413yes—
275C2×C4×C29C22×D413yes—
276C2×C4×C29C2511yescharacteristic
277C8×C29—21no—
278C8×C29—21no—
279C8×C29—23no—
280C8×C29—23no—
281#3518C2×C2911yescharacteristic, complemented
282#3483C2×C2911yescharacteristic, complemented
283Q8×Q16C2×C2911yescharacteristic, complemented
284Q8×SD16C2×C2911yescharacteristic, complemented
285#3362C2×C2911yescharacteristic, complemented
286#3358C2×C2911yescharacteristic, complemented
287#3341C2×C2913yescomplemented
288#3340C2×C2913yescomplemented
289#3305C2×C2913yescomplemented
290#3304C2×C2913yescomplemented
291#3247C2×C2913yescomplemented
292#3228C2×C2913yescomplemented
293#3102C2×C2913yescomplemented
294#3076C2×C2913yescomplemented
295#2988C2×C2911yescharacteristic, complemented
296C22×C29—23no—
297C22×C29—23no—
298C22×C29—23no—
299C22×C29—43no—
300C22×C29—41no—
301C22×C29—43no—
302C22×C29—41no—
303C22×C29—41no—
304C22×C29—43no—
305C22×C29C23×D411yescharacteristic
306C4×C29—21no—
307C4×C29—23no—
308C4×C29—23no—
309C4×C29—22no—
310C4×C29—21no—
311C4×C29—43no—
312C4×C29—43no—
313C4×C29—41no—
314C4×C29—41no—
315C4×C29—43no—
316C4×C29C2×#13516yes—
317C4×C29C2×2−1+411yescharacteristic
318C4×C29#58511yescharacteristic
319Q82C22×C2911yescharacteristic
320Q82C22×C2911yescharacteristic
321#556—23no—
322#556C22×C2913yes—
323#555—23no—
324#555C22×C2913yes—
325#555C22×C2913yes—
326#550—21no—
327#550C22×C2913yes—
328#550C22×C2911yescharacteristic
329D4×Q8C22×C2911yescharacteristic
330#548—21no—
331#542—23no—
332#533C22×C2913yes—
333#532—23no—
334#532C22×C2913yes—
335#529C22×C2913yes—
336#519—21no—
337C4×#41—21no—
338C4×#41C22×C2913yes—
339C4×#41C22×C2911yescharacteristic
340#500C22×C2913yes—
341#498C22×C2913yes—
342#486C22×C2913yes—
343#486C22×C2913yes—
344#485C22×C2913yes—
345#482C22×C2916yes—
346#482C22×C2913yes—
347#482C22×C2916yes—
348#479C22×C2913yes—
349#478C22×C2916yes—
350#478C22×C2913yes—
351#477C22×C2913yes—
352#477C22×C2913yes—
353#476C22×C2913yes—
354#476C22×C2913yes—
355#475C22×C2913yes—
356#474C22×C2913yes—
357#466C22×C2916yes—
358#465C22×C2916yes—
359#464C22×C2911yescharacteristic
360#463C22×C2913yes—
361#460C22×C2913yes—
362#459C22×C2913yes—
363#452C22×C2913yes—
364#449C22×C2913yes—
365C8×Q8C22×C2911yescharacteristic
366C8×Q8C22×C2911yescharacteristic
367C4×Q16C22×C2913yes—
368C4×SD16C22×C2913yes—
369C4×SD16C22×C2913yes—
370C4×D8C22×C2913yes—
371C8×D4C22×C2913yes—
372C8×D4C22×C2913yes—
373#431C22×C2913yes—
374#427C22×C2916yes—
375C2×C4⋊C8C22×C2913yes—
376#416C22×C2916yes—
377C2×C29—43no—
378C2×C29—83no—
379C2×C29—81no—
380C2×C29#348911yescharacteristic
381C2×C29C22×#13511yescharacteristic
382C2×C29#358511yescharacteristic
383C2×#41—21no—
384C2×#41—23no—
385C2×#41D4×C2911yescharacteristic
386C2×#41C23×C2913yes—
387C22×Q8—21no—
388C2×Q16C23×C2911yescharacteristic
389C2×SD16C23×C2911yescharacteristic
390C2×SD16C23×C2913yes—
391C2×D8C23×C2913yes—
392C22×C8C23×C2916yes—
393C4⋊Q8—23no—
394C4⋊Q8—23no—
395C4⋊Q8C23×C2913yes—
396C4⋊Q8C23×C2913yes—
397C4⋊Q8C23×C2913yes—
398#127—23no—
399#127C23×C2913yes—
400#126—26no—
401#126—23no—
402#125C23×C2913yes—
403#124—23no—
404#124—26no—
405#124—26no—
406#124—23no—
407#124C23×C2911yescharacteristic
408#123—23no—
409C22⋊Q8—23no—
410C22⋊Q8—23no—
411C22⋊Q8—23no—
412C22⋊Q8C23×C2913yes—
413#121—23no—
414#121—23no—
415#121—23no—
416#121—23no—
417#121—26no—
418#121C23×C2913yes—
419#121C23×C2916yes—
420C4×Q8—21no—
421C4×Q8—21no—
422C4×Q8—23no—
423C4×Q8—23no—
424C4×Q8—23no—
425C4×Q8D4×C2911yescharacteristic
426C4×Q8C23×C2911yescharacteristic
427C4×Q8C23×C2913yes—
428C4×Q8C23×C2913yes—
429C4×Q8C23×C2911yescharacteristic
430C4×D4—23no—
431C4×D4—23no—
432C4×D4—23no—
433C4×D4—23no—
434C4×D4—23no—
435C4×D4D4×C2913yes—
436C4×D4C23×C2913yes—
437C4×D4C23×C2913yes—
438C4×D4C23×C2913yes—
439C4×D4C23×C2913yes—
440#117—23no—
441#117—23no—
442#117—23no—
443#117—23no—
444#117D4×C2913yes—
445#117C23×C2913yes—
446#117C23×C2916yes—
447C2×C42—23no—
448C2×C42C23×C2913yes—
449#107C23×C2913yes—
450#107C23×C2916yes—
451#107C23×C2913yes—
452#106C23×C2913yes—
453#106C23×C2916yes—
454#106C23×C2913yes—
455C4⋊C8C23×C2913yes—
456C4⋊C8C23×C2913yes—
457C4⋊C8C23×C2913yes—
458C4⋊C8C23×C2911yescharacteristic
459#103C23×C2913yes—
460#103C23×C2913yes—
461#103C23×C2911yescharacteristic
462#103C23×C2913yes—
463#102C23×C2916yes—
464#102C23×C2916yes—
465#102C23×C2911yescharacteristic
466#102C23×C2913yes—
467#102C23×C2913yes—
468#102C23×C2913yes—
469C22⋊C8C23×C2913yes—
470C22⋊C8C23×C2913yes—
471C4×C8C23×C2913yes—
472C4×C8C23×C2913yes—
473C29#6210611yescharacteristic, direct product factor, Sylow
474#41—24no—
475#41—26no—
476#41—43no—
477#41—44no—
478#41—86no—
479C2×Q8—23no—
480C2×Q8—23no—
481C2×Q8—23no—
482C2×Q8—44no—
483C2×Q8C2×D4×C2911yescharacteristic
484C2×Q8C24×C2911yescharacteristic
485C2×Q8C24×C2911yescharacteristic
486C2×D4—23no—
487C2×D4—23no—
488C2×D4—26no—
489C2×D4—23no—
490C2×D4—23no—
491C2×D4C2×D4×C2913yes—
492C2×D4C24×C2913yes—
493C2×D4C24×C2911yescharacteristic
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—23no—
497C22×C4—23no—
498C22×C4C2×D4×C2913yes—
499C22×C4C2×D4×C2913yes—
500C22×C4C24×C2913yes—
501Q16—22no—
502SD16—22no—
503SD16—43no—
504D8—43no—
505C2×C8—46no—
506C2×C8C24×C2911yescharacteristic
507C2×C8C24×C2911yescharacteristic
508C2×C8C24×C2913yes—
509C2×C8C24×C2913yes—
510C4⋊C4—21no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—23no—
515C4⋊C4—23no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4C2×D4×C2913yes—
520C4⋊C4C2×D4×C2913yes—
521C4⋊C4C24×C2913yes—
522C4⋊C4C24×C2913yes—
523C4⋊C4C24×C2911yescharacteristic
524C4⋊C4C24×C2913yes—
525C22⋊C4—23no—
526C22⋊C4—26no—
527C22⋊C4—23no—
528C22⋊C4—23no—
529C22⋊C4—21no—
530C22⋊C4—26no—
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—21no—
534C22⋊C4—23no—
535C22⋊C4C2×D4×C2916yes—
536C42—21no—
537C42—23no—
538C42—23no—
539C42—26no—
540C42—23no—
541C42C2×D4×C2913yes—
542C42C2×D4×C2913yes—
543C42C24×C2913yes—
544C42C24×C2911yescharacteristic
545C23—21no—
546C23—23no—
547C23C22×D4×C2913yes—
548Q8—21no—
549Q8—21no—
550Q8—21no—
551Q8—46no—
552Q8—83no—
553Q8—83no—
554Q8C29×#13514yes—
555Q8C29×2−1+412yes—
556D4—26no—
557D4—21no—
558D4—23no—
559D4—21no—
560D4—23no—
561D4—46no—
562D4—46no—
563D4—83no—
564D4—86no—
565D4—83no—
566C2×C4—21no—
567C2×C4—26no—
568C2×C4—23no—
569C2×C4—23no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—43no—
576C2×C4—46no—
577C2×C4—46no—
578C2×C4—46no—
579C2×C4—46no—
580C2×C4C22×D4×C2913yes—
581C2×C4C22×D4×C2911yescharacteristic
582C2×C4C22×D4×C2911yescharacteristic
583C2×C4C22×D4×C2913yes—
584C2×C4C22×D4×C2913yes—
585C2×C4C25×C2911yescharacteristic
586C8—21no—
587C8—21no—
588C8—23no—
589C8—23no—
590C22—23no—
591C22—23no—
592C22—23no—
593C22—43no—
594C22—41no—
595C22—41no—
596C22—43no—
597C22—43no—
598C22—41no—
599C22C23×D4×C2911yescharacteristic
600C4—23no—
601C4—22no—
602C4—21no—
603C4—21no—
604C4—23no—
605C4—41no—
606C4—41no—
607C4—43no—
608C4—43no—
609C4—43no—
610C4C2×C29×#13516yes—
611C4C2×C29×2−1+411yescharacteristic
612C4C29×#58511yescharacteristic
613C2—43no—
614C2—83no—
615C2—81no—
616C2C29×#348911yescharacteristic
617C2C22×C29×#13511yescharacteristic
618C2C29×#358511yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
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
1. C29×#3518C2semidirect
2. C29×#3483C2semidirect
3. Q8×Q16×C29C2semidirect
4. Q8×SD16×C29C2semidirect
5. C29×#3362C2semidirect
6. C29×#3358C2semidirect
7. C29×#3341C2semidirect
8. C29×#3340C2semidirect
9. C29×#3305C2semidirect
10. C29×#3304C2semidirect
11. C29×#3247C2semidirect
12. C29×#3228C2semidirect
13. C29×#3102C2semidirect
14. C29×#3076C2semidirect
15. C29×#2988C2semidirect
235. #62106C29direct (N × H)
281. #3518C2×C29semidirect
282. #3483C2×C29semidirect
283. Q8×Q16C2×C29semidirect
284. Q8×SD16C2×C29semidirect
285. #3362C2×C29semidirect
286. #3358C2×C29semidirect
287. #3341C2×C29semidirect
288. #3340C2×C29semidirect
289. #3305C2×C29semidirect
290. #3304C2×C29semidirect
291. #3247C2×C29semidirect
292. #3228C2×C29semidirect
293. #3102C2×C29semidirect
294. #3076C2×C29semidirect
295. #2988C2×C29semidirect
473. C29#62106direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35182
C29×#34832
Q8×Q16×C292
Q8×SD16×C292
C29×#33622
C29×#33582
C29×#33412
C29×#33402
C29×#33052
C29×#33042
C29×#32472
C29×#32282
C29×#31022
C29×#30762
C29×#29882
#6210629