Finite Group Databasebeta

← C29×#60499 #20355399

Subgroups — C29×#60499 #20355399

Order 7424.

1970 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3504C211yesmaximal, characteristic, complemented
2C4×C29×2−1+4C211yesmaximal, characteristic
3C29×#3084C213yesmaximal, complemented
4C29×#3083C213yesmaximal, complemented
5C29×#3082C213yesmaximal, complemented
6C29×#3082C213yesmaximal, complemented
7C29×#3080C213yesmaximal, complemented
8C29×#3078C213yesmaximal, complemented
9C29×#3076C213yesmaximal, complemented
10C2×C29×#479C213yesmaximal, complemented
11C29×#2913C211yesmaximal, characteristic, complemented
12C29×#2912C211yesmaximal, characteristic, complemented
13C29×#2906C211yesmaximal, characteristic, complemented
14C29×#2898C211yesmaximal, characteristic
15C29×#2898C211yesmaximal, characteristic
16C2×C29×2−1+4C2211yescharacteristic
17C2×C29×#131C2211yescharacteristic
18C2×C29×#131C2211yescharacteristic
19C29×#557—21no—
20C29×#557—21no—
21C29×#554—23no—
22C29×#554—23no—
23C29×#544C2213yes—
24C29×#544C2213yes—
25C29×#533C2213yes—
26C2×C29×#125C2213yes—
27C29×#520—23no—
28C29×#520C2213yes—
29C29×#520C2211yescharacteristic
30C29×#520C2211yescharacteristic
31C29×#520C2211yescharacteristic
32C29×#519—21no—
33C29×#519C2213yes—
34C4×#41×C29—23no—
35C4×#41×C29C2213yes—
36C4×#41×C29C2211yescharacteristic
37C2×C4×Q8×C29—21no—
38C2×C4×Q8×C29C2213yes—
39C29×#479C2213yes—
40C29×#479C2216yes—
41C29×#479C2216yes—
42C29×#479C2216yes—
43C29×#479C2213yes—
44C29×#479C2216yes—
45C29×#478C2211yescharacteristic
46C29×#478C2213yes—
47C29×#478C2216yes—
48C29×#477C2213yes—
49C29×#477C2216yes—
50C29×#476C2213yes—
51C29×#475C2213yes—
52C29×#475C2216yes—
53C29×#474C2213yes—
54C29×#428C2213yes—
55C29×#428C2213yes—
56C29×#428C2213yes—
57C29×#428C2213yes—
58C29×#427C2213yes—
59C29×#427C2213yes—
60C2×C29×#107C2213yes—
61C2×C29×#106C2213yes—
62C29×#424C2213yes—
63C29×#424C2213yes—
64C29×#423C2213yes—
65C2×C29×C4⋊C8C2213yes—
66C29×#419C2213yes—
67C29×#419C2213yes—
68C29×#417C2213yes—
69C29×#417C2213yes—
70C29×#416C2213yes—
71C29×#416C2213yes—
72C2×C29×#103C2213yes—
73C2×C29×#103C2213yes—
74C29×2−1+4—24no—
75C29×2−1+4Q818yescomplemented
76C2×#41×C29—23no—
77C2×#41×C29C2313yes—
78C2×#41×C29C2311yescharacteristic
79C22×Q8×C29—21no—
80C22×Q8×C29C2313yes—
81C29×#131—24no—
82C29×#131—24no—
83C2×M16×C29C2313yes—
84C2×M16×C29C2313yes—
85C22×C8×C29C2313yes—
86C22×C8×C29C2313yes—
87C29×C4⋊Q8—23no—
88C29×C4⋊Q8—23no—
89C29×C4⋊Q8C2313yes—
90C29×C4⋊Q8C2313yes—
91C29×#125—23no—
92C29×#125—23no—
93C29×#125—23no—
94C29×#125—23no—
95C29×#125C2313yes—
96C29×#125C2316yes—
97C29×#125C2311yescharacteristic
98C29×C22⋊Q8—23no—
99C29×C22⋊Q8—23no—
100C29×C22⋊Q8—26no—
101C29×C22⋊Q8—26no—
102C4×Q8×C29—21no—
103C4×Q8×C29—21no—
104C4×Q8×C29—21no—
105C4×Q8×C29—23no—
106C4×Q8×C29—23no—
107C4×Q8×C29—23no—
108C4×Q8×C29—23no—
109C4×Q8×C29—23no—
110C4×Q8×C29—23no—
111C4×Q8×C29D411yescharacteristic
112C4×Q8×C29D411yescharacteristic
113C4×Q8×C29C2316yes—
114C4×Q8×C29C2313yes—
115C4×Q8×C29C2313yes—
116C4×D4×C29—23no—
117C4×D4×C29—23no—
118C4×D4×C29—23no—
119C4×D4×C29—23no—
120C4×D4×C29—23no—
121C4×D4×C29—26no—
122C4×D4×C29D413yes—
123C4×D4×C29D413yes—
124C4×D4×C29C2313yes—
125C4×D4×C29C2311yescharacteristic
126C29×#117—23no—
127C29×#117—26no—
128C29×#117—23no—
129C29×#117C2313yes—
130C29×#117C2313yes—
131C29×#117C2313yes—
132C29×#117C2313yes—
133C2×C4⋊C4×C29—23no—
134C2×C4⋊C4×C29—23no—
135C2×C4⋊C4×C29—23no—
136C2×C4⋊C4×C29—23no—
137C2×C4⋊C4×C29C2313yes—
138C2×C4⋊C4×C29C2313yes—
139C2×C4⋊C4×C29C2313yes—
140C2×C42×C29—23no—
141C2×C42×C29—23no—
142C2×C42×C29C2313yes—
143C29×#107C2313yes—
144C29×#107C2316yes—
145C29×#107C2311yescharacteristic
146C29×#107C2313yes—
147C29×#107C2313yes—
148C29×#106C2313yes—
149C29×#106C2316yes—
150C29×#106C2311yescharacteristic
151C29×#106C2313yes—
152C29×#106C2313yes—
153C29×C4⋊C8C2313yes—
154C29×C4⋊C8C2313yes—
155C29×C4⋊C8C2316yes—
156C29×C4⋊C8C2311yescharacteristic
157C29×C4⋊C8C2313yes—
158C29×#103C2313yes—
159C29×#103C2313yes—
160C29×#103C2313yes—
161C29×#103C2316yes—
162C29×#103C2313yes—
163C29×#103C2316yes—
164C29×#102C2311yescharacteristic
165C29×#102C2313yes—
166C29×#102C2311yescharacteristic
167C29×#102C2313yes—
168#41×C29—224no—
169#41×C29—26no—
170#41×C29C2×Q8112yes—
171#41×C29C2×Q814yes—
172#41×C29#4114yes—
173C2×Q8×C29—28no—
174C2×Q8×C29—23no—
175C2×Q8×C29—23no—
176C2×Q8×C29—23no—
177C2×Q8×C29—26no—
178C2×Q8×C29C2×D411yescharacteristic
179C2×Q8×C29C2×Q8112yes—
180C2×Q8×C29C2413yes—
181C2×D4×C29—23no—
182C2×D4×C29C2×D413yes—
183C2×D4×C29C2411yescharacteristic
184C22×C4×C29—23no—
185C22×C4×C29—23no—
186C22×C4×C29—23no—
187C22×C4×C29—23no—
188C22×C4×C29—23no—
189C22×C4×C29—21no—
190C22×C4×C29—23no—
191C22×C4×C29C2×D413yes—
192C22×C4×C29C2×D413yes—
193C22×C4×C29C2413yes—
194M16×C29—26no—
195M16×C29—26no—
196C2×C8×C29—26no—
197C2×C8×C29—26no—
198C2×C8×C29C2411yescharacteristic
199C2×C8×C29C2411yescharacteristic
200C2×C8×C29C2413yes—
201C2×C8×C29C2413yes—
202C4⋊C4×C29—26no—
203C4⋊C4×C29—23no—
204C4⋊C4×C29—23no—
205C4⋊C4×C29—23no—
206C4⋊C4×C29—23no—
207C4⋊C4×C29—26no—
208C4⋊C4×C29—26no—
209C4⋊C4×C29—23no—
210C4⋊C4×C29—23no—
211C4⋊C4×C29—23no—
212C4⋊C4×C29—21no—
213C4⋊C4×C29—21no—
214C4⋊C4×C29—23no—
215C4⋊C4×C29—23no—
216C4⋊C4×C29C2×D413yes—
217C4⋊C4×C29C2×D413yes—
218C4⋊C4×C29C2413yes—
219C4⋊C4×C29C2413yes—
220C4⋊C4×C29C2413yes—
221C4⋊C4×C29C2411yescharacteristic
222C4⋊C4×C29C2411yescharacteristic
223C4⋊C4×C29C2411yescharacteristic
224C22⋊C4×C29—23no—
225C22⋊C4×C29—23no—
226C22⋊C4×C29—23no—
227C22⋊C4×C29—21no—
228C22⋊C4×C29—23no—
229C22⋊C4×C29C2×D416yes—
230C42×C29—23no—
231C42×C29—23no—
232C42×C29—26no—
233C42×C29—23no—
234C42×C29—23no—
235C42×C29—23no—
236C42×C29C2×D413yes—
237C42×C29C2×D413yes—
238C42×C29C2411yescharacteristic
239C42×C29C2413yes—
240#60499C2911yesmaximal, characteristic, direct product factor, Sylow
241C23×C29—21no—
242C23×C29C22×D413yes—
243Q8×C29—212no—
244Q8×C29—23no—
245Q8×C29—83no—
246Q8×C29—83no—
247Q8×C29C22⋊Q814yes—
248Q8×C29C22×Q816yes—
249D4×C29—212no—
250D4×C29—21no—
251D4×C29C22⋊Q8112yes—
252D4×C29C22×Q812yes—
253C2×C4×C29—212no—
254C2×C4×C29—23no—
255C2×C4×C29—212no—
256C2×C4×C29—21no—
257C2×C4×C29—23no—
258C2×C4×C29—21no—
259C2×C4×C29—21no—
260C2×C4×C29—23no—
261C2×C4×C29—23no—
262C2×C4×C29—43no—
263C2×C4×C29—43no—
264C2×C4×C29—42no—
265C2×C4×C29—83no—
266C2×C4×C29—83no—
267C2×C4×C29—83no—
268C2×C4×C29—83no—
269C2×C4×C29C22×D411yescharacteristic
270C2×C4×C29C22×D413yes—
271C2×C4×C29C22×D413yes—
272C2×C4×C29C22×D411yescharacteristic
273C2×C4×C29C22×D413yes—
274C2×C4×C29C22×Q816yes—
275C2×C4×C29C2×#4116yes—
276C2×C4×C29C2511yescharacteristic
277C8×C29—21no—
278C8×C29—21no—
279C8×C29—23no—
280C8×C29—23no—
281#3504C2×C2911yescharacteristic, complemented
282C4×2−1+4C2×C2911yescharacteristic
283#3084C2×C2913yescomplemented
284#3083C2×C2913yescomplemented
285#3082C2×C2913yescomplemented
286#3082C2×C2913yescomplemented
287#3080C2×C2913yescomplemented
288#3078C2×C2913yescomplemented
289#3076C2×C2913yescomplemented
290C2×#479C2×C2913yescomplemented
291#2913C2×C2911yescharacteristic, complemented
292#2912C2×C2911yescharacteristic, complemented
293#2906C2×C2911yescharacteristic, complemented
294#2898C2×C2911yescharacteristic
295#2898C2×C2911yescharacteristic
296C22×C29—23no—
297C22×C29—23no—
298C22×C29—22no—
299C22×C29—41no—
300C22×C29—41no—
301C22×C29C2×C22⋊Q816yes—
302C22×C29C23×D411yescharacteristic
303C4×C29—21no—
304C4×C29—23no—
305C4×C29—21no—
306C4×C29—23no—
307C4×C29—26no—
308C4×C29—43no—
309C4×C29—43no—
310C4×C29—41no—
311C4×C29—41no—
312C4×C29—43no—
313C4×C29—41no—
314C4×C29C2×C22⋊Q816yes—
315C4×C29C23×Q811yescharacteristic
316C4×C29C22×#4111yescharacteristic
317C2×2−1+4C22×C2911yescharacteristic
318C2×#131C22×C2911yescharacteristic
319C2×#131C22×C2911yescharacteristic
320#557—21no—
321#557—21no—
322#554—23no—
323#554—23no—
324#544C22×C2913yes—
325#544C22×C2913yes—
326#533C22×C2913yes—
327C2×#125C22×C2913yes—
328#520—23no—
329#520C22×C2913yes—
330#520C22×C2911yescharacteristic
331#520C22×C2911yescharacteristic
332#520C22×C2911yescharacteristic
333#519—21no—
334#519C22×C2913yes—
335C4×#41—23no—
336C4×#41C22×C2913yes—
337C4×#41C22×C2911yescharacteristic
338C2×C4×Q8—21no—
339C2×C4×Q8C22×C2913yes—
340#479C22×C2913yes—
341#479C22×C2916yes—
342#479C22×C2916yes—
343#479C22×C2916yes—
344#479C22×C2913yes—
345#479C22×C2916yes—
346#478C22×C2911yescharacteristic
347#478C22×C2913yes—
348#478C22×C2916yes—
349#477C22×C2913yes—
350#477C22×C2916yes—
351#476C22×C2913yes—
352#475C22×C2913yes—
353#475C22×C2916yes—
354#474C22×C2913yes—
355#428C22×C2913yes—
356#428C22×C2913yes—
357#428C22×C2913yes—
358#428C22×C2913yes—
359#427C22×C2913yes—
360#427C22×C2913yes—
361C2×#107C22×C2913yes—
362C2×#106C22×C2913yes—
363#424C22×C2913yes—
364#424C22×C2913yes—
365#423C22×C2913yes—
366C2×C4⋊C8C22×C2913yes—
367#419C22×C2913yes—
368#419C22×C2913yes—
369#417C22×C2913yes—
370#417C22×C2913yes—
371#416C22×C2913yes—
372#416C22×C2913yes—
373C2×#103C22×C2913yes—
374C2×#103C22×C2913yes—
375C2×C29—26no—
376C2×C29—42no—
377C2×C29C22×C22⋊Q811yescharacteristic
378C2×C29#358411yescharacteristic
379C2×C29#358611yescharacteristic
3802−1+4—24no—
3812−1+4Q8×C2918yescomplemented
382C2×#41—23no—
383C2×#41C23×C2913yes—
384C2×#41C23×C2911yescharacteristic
385C22×Q8—21no—
386C22×Q8C23×C2913yes—
387#131—24no—
388#131—24no—
389C2×M16C23×C2913yes—
390C2×M16C23×C2913yes—
391C22×C8C23×C2913yes—
392C22×C8C23×C2913yes—
393C4⋊Q8—23no—
394C4⋊Q8—23no—
395C4⋊Q8C23×C2913yes—
396C4⋊Q8C23×C2913yes—
397#125—23no—
398#125—23no—
399#125—23no—
400#125—23no—
401#125C23×C2913yes—
402#125C23×C2916yes—
403#125C23×C2911yescharacteristic
404C22⋊Q8—23no—
405C22⋊Q8—23no—
406C22⋊Q8—26no—
407C22⋊Q8—26no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—23no—
412C4×Q8—23no—
413C4×Q8—23no—
414C4×Q8—23no—
415C4×Q8—23no—
416C4×Q8—23no—
417C4×Q8D4×C2911yescharacteristic
418C4×Q8D4×C2911yescharacteristic
419C4×Q8C23×C2913yes—
420C4×Q8C23×C2916yes—
421C4×Q8C23×C2913yes—
422C4×D4—23no—
423C4×D4—23no—
424C4×D4—23no—
425C4×D4—23no—
426C4×D4—23no—
427C4×D4—26no—
428C4×D4D4×C2913yes—
429C4×D4D4×C2913yes—
430C4×D4C23×C2911yescharacteristic
431C4×D4C23×C2913yes—
432#117—23no—
433#117—26no—
434#117—23no—
435#117C23×C2913yes—
436#117C23×C2913yes—
437#117C23×C2913yes—
438#117C23×C2913yes—
439C2×C4⋊C4—23no—
440C2×C4⋊C4—23no—
441C2×C4⋊C4—23no—
442C2×C4⋊C4—23no—
443C2×C4⋊C4C23×C2913yes—
444C2×C4⋊C4C23×C2913yes—
445C2×C4⋊C4C23×C2913yes—
446C2×C42—23no—
447C2×C42—23no—
448C2×C42C23×C2913yes—
449#107C23×C2913yes—
450#107C23×C2916yes—
451#107C23×C2911yescharacteristic
452#107C23×C2913yes—
453#107C23×C2913yes—
454#106C23×C2913yes—
455#106C23×C2916yes—
456#106C23×C2911yescharacteristic
457#106C23×C2913yes—
458#106C23×C2913yes—
459C4⋊C8C23×C2911yescharacteristic
460C4⋊C8C23×C2913yes—
461C4⋊C8C23×C2913yes—
462C4⋊C8C23×C2913yes—
463C4⋊C8C23×C2916yes—
464#103C23×C2913yes—
465#103C23×C2913yes—
466#103C23×C2916yes—
467#103C23×C2916yes—
468#103C23×C2913yes—
469#103C23×C2913yes—
470#102C23×C2911yescharacteristic
471#102C23×C2911yescharacteristic
472#102C23×C2913yes—
473#102C23×C2913yes—
474C29#6049911yescharacteristic, direct product factor, Sylow
475#41—224no—
476#41—26no—
477#41C2×Q8×C29112yes—
478#41C2×Q8×C2914yes—
479#41#41×C2914yes—
480C2×Q8—28no—
481C2×Q8—23no—
482C2×Q8—23no—
483C2×Q8—23no—
484C2×Q8—26no—
485C2×Q8C2×D4×C2911yescharacteristic
486C2×Q8C2×Q8×C29112yes—
487C2×Q8C24×C2913yes—
488C2×D4—23no—
489C2×D4C2×D4×C2913yes—
490C2×D4C24×C2911yescharacteristic
491C22×C4—23no—
492C22×C4—23no—
493C22×C4—23no—
494C22×C4—23no—
495C22×C4—23no—
496C22×C4—21no—
497C22×C4—23no—
498C22×C4C2×D4×C2913yes—
499C22×C4C2×D4×C2913yes—
500C22×C4C24×C2913yes—
501M16—26no—
502M16—26no—
503C2×C8—26no—
504C2×C8—26no—
505C2×C8C24×C2911yescharacteristic
506C2×C8C24×C2913yes—
507C2×C8C24×C2913yes—
508C2×C8C24×C2911yescharacteristic
509C4⋊C4—26no—
510C4⋊C4—23no—
511C4⋊C4—23no—
512C4⋊C4—23no—
513C4⋊C4—23no—
514C4⋊C4—26no—
515C4⋊C4—26no—
516C4⋊C4—23no—
517C4⋊C4—23no—
518C4⋊C4—23no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—23no—
522C4⋊C4—23no—
523C4⋊C4C2×D4×C2913yes—
524C4⋊C4C2×D4×C2913yes—
525C4⋊C4C24×C2913yes—
526C4⋊C4C24×C2911yescharacteristic
527C4⋊C4C24×C2913yes—
528C4⋊C4C24×C2911yescharacteristic
529C4⋊C4C24×C2913yes—
530C4⋊C4C24×C2911yescharacteristic
531C22⋊C4—23no—
532C22⋊C4—23no—
533C22⋊C4—23no—
534C22⋊C4—21no—
535C22⋊C4—23no—
536C22⋊C4C2×D4×C2916yes—
537C42—23no—
538C42—23no—
539C42—26no—
540C42—23no—
541C42—23no—
542C42—23no—
543C42C2×D4×C2913yes—
544C42C2×D4×C2913yes—
545C42C24×C2911yescharacteristic
546C42C24×C2913yes—
547C23—21no—
548C23C22×D4×C2913yes—
549Q8—212no—
550Q8—23no—
551Q8—83no—
552Q8—83no—
553Q8C29×C22⋊Q814yes—
554Q8C22×Q8×C2916yes—
555D4—212no—
556D4—21no—
557D4C29×C22⋊Q8112yes—
558D4C22×Q8×C2912yes—
559C2×C4—212no—
560C2×C4—23no—
561C2×C4—212no—
562C2×C4—21no—
563C2×C4—23no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—23no—
567C2×C4—23no—
568C2×C4—43no—
569C2×C4—43no—
570C2×C4—42no—
571C2×C4—83no—
572C2×C4—83no—
573C2×C4—83no—
574C2×C4—83no—
575C2×C4C22×D4×C2911yescharacteristic
576C2×C4C22×D4×C2913yes—
577C2×C4C22×D4×C2913yes—
578C2×C4C22×D4×C2911yescharacteristic
579C2×C4C22×D4×C2913yes—
580C2×C4C22×Q8×C2916yes—
581C2×C4C2×#41×C2916yes—
582C2×C4C25×C2911yescharacteristic
583C8—21no—
584C8—21no—
585C8—23no—
586C8—23no—
587C22—23no—
588C22—23no—
589C22—22no—
590C22—41no—
591C22—41no—
592C22C2×C29×C22⋊Q816yes—
593C22C23×D4×C2911yescharacteristic
594C4—21no—
595C4—23no—
596C4—21no—
597C4—23no—
598C4—26no—
599C4—43no—
600C4—43no—
601C4—41no—
602C4—41no—
603C4—43no—
604C4—41no—
605C4C2×C29×C22⋊Q816yes—
606C4C23×Q8×C2911yescharacteristic
607C4C22×#41×C2911yescharacteristic
608C2—26no—
609C2—42no—
610C2C22×C29×C22⋊Q811yescharacteristic
611C2C29×#358411yescharacteristic
612C2C29×#358611yescharacteristic
subgroupG/H
center, socleC22×C29C23×D4
commutator, Frattini, cosocleC2×C4C25×C29
prime radicalC2×C29×2−1+4C22
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×#3504C2semidirect
3. C29×#3084C2semidirect
4. C29×#3083C2semidirect
5. C29×#3082C2semidirect
6. C29×#3082C2semidirect
7. C29×#3080C2semidirect
8. C29×#3078C2semidirect
9. C29×#3076C2semidirect
10. C2×C29×#479C2semidirect
11. C29×#2913C2semidirect
12. C29×#2912C2semidirect
13. C29×#2906C2semidirect
75. C29×2−1+4Q8semidirect
240. #60499C29direct (N × H)
281. #3504C2×C29semidirect
283. #3084C2×C29semidirect
284. #3083C2×C29semidirect
285. #3082C2×C29semidirect
286. #3082C2×C29semidirect
287. #3080C2×C29semidirect
288. #3078C2×C29semidirect
289. #3076C2×C29semidirect
290. C2×#479C2×C29semidirect
291. #2913C2×C29semidirect
292. #2912C2×C29semidirect
293. #2906C2×C29semidirect
381. 2−1+4Q8×C29semidirect
474. C29#60499direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#35042
C4×C29×2−1+42
C29×#30842
C29×#30832
C29×#30822
C29×#30802
C29×#30782
C29×#30762
C2×C29×#4792
C29×#29132
C29×#29122
C29×#29062
C29×#28982
#6049929