Finite Group Databasebeta

← C2×C29×#2080 #20318548

Subgroups — C2×C29×#2080 #20318548

Order 7424.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#424C211yesmaximal, characteristic, complemented
2C2×C29×#421C211yesmaximal, characteristic
3C2×C29×#416C211yesmaximal, characteristic
4C2×C29×#413C211yesmaximal, characteristic
5C29×#2080C218yesmaximal, direct product factor
6C2×C29×#344C211yesmaximal, characteristic, complemented
7C2×C29×#341C211yesmaximal, characteristic, complemented
8C2×C29×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#41×C29C2211yescharacteristic
10C22×M16×C29C2211yescharacteristic
11C22×M16×C29C2211yescharacteristic
12C22×M16×C29C2211yescharacteristic
13C23×C8×C29C2211yescharacteristic
14C2×C29×#117C2211yescharacteristic
15C2×C29×#117C2211yescharacteristic
16C29×#424—22no—
17C29×#424C2214yescomplemented
18C2×C29×C4⋊C8—22no—
19C29×#421—22no—
20C29×#421C2214yes—
21C2×C29×#104—22no—
22C29×#416—22no—
23C29×#416C2214yes—
24C2×C29×#103—21no—
25C2×C29×#102—21no—
26C29×#413—22no—
27C29×#413C2214yes—
28C2×C29×#101—21no—
29C2×C29×#100—21no—
30C29×#344C2214yescomplemented
31C29×#341C2214yescomplemented
32C29×H(3,ℤ/4)C2214yescomplemented
33C2×#41×C29—21no—
34C2×#41×C29—21no—
35C2×#41×C29—21no—
36C2×#41×C29—21no—
37C2×#41×C29—21no—
38C2×#41×C29—21no—
39C2×#41×C29—21no—
40C2×#41×C29—21no—
41C2×#41×C29—21no—
42C2×#41×C29—21no—
43C2×#41×C29D412yes—
44C2×#41×C29C2312yes—
45C22×Q8×C29D411yescharacteristic
46C22×D4×C29—21no—
47C22×D4×C29D411yescharacteristic
48C23×C4×C29—21no—
49C23×C4×C29C2311yescharacteristic
50C2×M16×C29—21no—
51C2×M16×C29—21no—
52C2×M16×C29—21no—
53C2×M16×C29—21no—
54C2×M16×C29—21no—
55C2×M16×C29—21no—
56C2×M16×C29—21no—
57C2×M16×C29—21no—
58C2×M16×C29—21no—
59C2×M16×C29—21no—
60C2×M16×C29—21no—
61C2×M16×C29—21no—
62C2×M16×C29—21no—
63C2×M16×C29—21no—
64C2×M16×C29—21no—
65C2×M16×C29C2312yes—
66C2×M16×C29C2312yes—
67C2×M16×C29C2312yes—
68C22×C8×C29—21no—
69C22×C8×C29—21no—
70C22×C8×C29—21no—
71C22×C8×C29—21no—
72C22×C8×C29—21no—
73C22×C8×C29—21no—
74C22×C8×C29—21no—
75C22×C8×C29—21no—
76C22×C8×C29—21no—
77C22×C8×C29C2312yes—
78C29×#117—21no—
79C29×#117—21no—
80C29×#117—21no—
81C29×#117—21no—
82C29×#117—21no—
83C29×#117D412yes—
84C29×#117C2312yes—
85C29×#117C2312yes—
86C2×C4⋊C4×C29—21no—
87C2×C4⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C42×C29—21no—
91C2×C42×C29D412yes—
92C29×C4⋊C8—28no—
93C29×#104—28no—
94C29×#103—24no—
95C29×#102—24no—
96C29×#101—24no—
97C29×#100—24no—
98C24×C29—21no—
99C24×C29#4111yescharacteristic
100#41×C29—22no—
101#41×C29—22no—
102#41×C29—22no—
103#41×C29—22no—
104#41×C29—22no—
105#41×C29—22no—
106#41×C29—22no—
107#41×C29—22no—
108#41×C29—41no—
109#41×C29—41no—
110#41×C29—41no—
111#41×C29—41no—
112#41×C29—41no—
113#41×C29—41no—
114#41×C29—41no—
115#41×C29—41no—
116C2×Q8×C29—21no—
117C2×Q8×C29—21no—
118C2×Q8×C29—21no—
119C2×Q8×C29—21no—
120C2×Q8×C29—21no—
121C2×Q8×C29C2×D412yes—
122C2×D4×C29—22no—
123C2×D4×C29—22no—
124C2×D4×C29—21no—
125C2×D4×C29—21no—
126C2×D4×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29—21no—
129C2×D4×C29—41no—
130C2×D4×C29—41no—
131C2×D4×C29—41no—
132C2×D4×C29—41no—
133C2×D4×C29C2×D412yes—
134C22×C4×C29—22no—
135C22×C4×C29—21no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—41no—
139C22×C4×C29—41no—
140C22×C4×C29—41no—
141C22×C4×C29—41no—
142C22×C4×C29—41no—
143C22×C4×C29C2×D411yescharacteristic
144C22×C4×C29C2×D411yescharacteristic
145C22×C4×C29C2×D411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29#4111yescharacteristic
148C22×C4×C29#4111yescharacteristic
149C22×C4×C29#4111yescharacteristic
150C22×C4×C29#4111yescharacteristic
151C22×C4×C29#4111yescharacteristic
152C22×C4×C29#4111yescharacteristic
153C22×C4×C29#4111yescharacteristic
154C22×C4×C29#4111yescharacteristic
155C22×C4×C29#4111yescharacteristic
156C22×C4×C29C2411yescharacteristic
157M16×C29—22no—
158M16×C29—22no—
159M16×C29—22no—
160M16×C29—22no—
161M16×C29—22no—
162M16×C29—22no—
163M16×C29—41no—
164M16×C29—41no—
165M16×C29—41no—
166M16×C29—41no—
167M16×C29—41no—
168M16×C29—41no—
169C2×C8×C29—22no—
170C2×C8×C29—22no—
171C2×C8×C29—22no—
172C2×C8×C29—22no—
173C2×C8×C29—22no—
174C2×C8×C29—22no—
175C2×C8×C29—41no—
176C2×C8×C29—41no—
177C2×C8×C29—41no—
178C2×C8×C29—41no—
179C2×C8×C29—41no—
180C2×C8×C29—41no—
181C2×C8×C29—41no—
182C2×C8×C29—41no—
183C2×C8×C29—41no—
184C2×C8×C29—41no—
185C4⋊C4×C29—22no—
186C4⋊C4×C29—22no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—41no—
189C22⋊C4×C29—22no—
190C22⋊C4×C29—22no—
191C22⋊C4×C29—22no—
192C22⋊C4×C29—41no—
193C42×C29—22no—
194C42×C29—22no—
195C42×C29—41no—
196C42×C29C2×D414yes—
197C2×#2080C2911yesmaximal, characteristic, direct product factor, Sylow
198C23×C29—22no—
199C23×C29—42no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—82no—
203C23×C29#12311yescharacteristic
204C23×C29#12311yescharacteristic
205C23×C29#12311yescharacteristic
206C23×C29#12311yescharacteristic
207C23×C29#12611yescharacteristic
208C23×C29#12611yescharacteristic
209C23×C29C2×#4111yescharacteristic
210Q8×C29—22no—
211Q8×C29—22no—
212Q8×C29—41no—
213Q8×C29—41no—
214D4×C29—22no—
215D4×C29—22no—
216D4×C29—42no—
217D4×C29—42no—
218D4×C29—42no—
219D4×C29—42no—
220D4×C29—41no—
221D4×C29—41no—
222C2×C4×C29—24no—
223C2×C4×C29—22no—
224C2×C4×C29—44no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—42no—
228C2×C4×C29—42no—
229C2×C4×C29—42no—
230C2×C4×C29—42no—
231C2×C4×C29—42no—
232C2×C4×C29—82no—
233C2×C4×C29#12111yescharacteristic
234C2×C4×C29#12111yescharacteristic
235C2×C4×C29#12111yescharacteristic
236C2×C4×C29#12111yescharacteristic
237C2×C4×C29#12311yescharacteristic
238C2×C4×C29#12311yescharacteristic
239C2×C4×C29#12311yescharacteristic
240C2×C4×C29#12311yescharacteristic
241C2×C4×C29#12311yescharacteristic
242C2×C4×C29#12311yescharacteristic
243C2×C4×C29#12311yescharacteristic
244C2×C4×C29#12311yescharacteristic
245C2×C4×C29#12411yescharacteristic
246C2×C4×C29#12411yescharacteristic
247C2×C4×C29#12411yescharacteristic
248C2×C4×C29#12411yescharacteristic
249C2×C4×C29#12611yescharacteristic
250C2×C4×C29#12611yescharacteristic
251C2×C4×C29#12611yescharacteristic
252C2×C4×C29#12611yescharacteristic
253C2×C4×C29#12611yescharacteristic
254C2×C4×C29#12611yescharacteristic
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29C22×D411yescharacteristic
257C2×C4×C29C2×#4111yescharacteristic
258C2×C4×C29C2×#4111yescharacteristic
259C2×C4×C29C2×#4111yescharacteristic
260C2×C4×C29C2×#4111yescharacteristic
261C8×C29—42no—
262C8×C29—42no—
263C8×C29—42no—
264C8×C29—42no—
265C2×#424C2×C2911yescharacteristic, complemented
266C2×#421C2×C2911yescharacteristic
267C2×#416C2×C2911yescharacteristic
268C2×#413C2×C2911yescharacteristic
269#2080C2×C2918yesdirect product factor
270C2×#344C2×C2911yescharacteristic, complemented
271C2×#341C2×C2911yescharacteristic, complemented
272C2×H(3,ℤ/4)C2×C2911yescharacteristic, complemented
273C22×C29—22no—
274C22×C29—22no—
275C22×C29—22no—
276C22×C29—41no—
277C22×C29—41no—
278C22×C29—41no—
279C22×C29—41no—
280C22×C29—42no—
281C22×C29—82no—
282C22×C29—82no—
283C22×C29—82no—
284C22×C29#39711yescharacteristic
285C22×C29#39711yescharacteristic
286C22×C29#39711yescharacteristic
287C22×C29#39711yescharacteristic
288C22×C29C2×#12311yescharacteristic
289C22×C29C2×#12311yescharacteristic
290C22×C29C2×#12611yescharacteristic
291C4×C29—44no—
292C4×C29—42no—
293C4×C29—82no—
294C4×C29#39711yescharacteristic
295C4×C29#39711yescharacteristic
296C4×C29#39711yescharacteristic
297C4×C29#39711yescharacteristic
298C4×C29C2×#12111yescharacteristic
299C4×C29C2×#12311yescharacteristic
300C4×C29C2×#12411yescharacteristic
301C4×C29C2×#12611yescharacteristic
302C22×#41C22×C2911yescharacteristic
303C22×M16C22×C2911yescharacteristic
304C22×M16C22×C2911yescharacteristic
305C22×M16C22×C2911yescharacteristic
306C23×C8C22×C2911yescharacteristic
307C2×#117C22×C2911yescharacteristic
308C2×#117C22×C2911yescharacteristic
309#424—22no—
310#424C22×C2914yescomplemented
311C2×C4⋊C8—22no—
312#421—22no—
313#421C22×C2914yes—
314C2×#104—22no—
315#416—22no—
316#416C22×C2914yes—
317C2×#103—21no—
318C2×#102—21no—
319#413—22no—
320#413C22×C2914yes—
321C2×#101—21no—
322C2×#100—21no—
323#344C22×C2914yescomplemented
324#341C22×C2914yescomplemented
325H(3,ℤ/4)C22×C2914yescomplemented
326C2×C29—21no—
327C2×C29—21no—
328C2×C29—21no—
329C2×C29—21no—
330C2×C29—21no—
331C2×C29—21no—
332C2×C29—82no—
333C2×C29#208012yesdirect product factor
334C2×C29C2×#39711yescharacteristic
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41D4×C2912yes—
346C2×#41C23×C2912yes—
347C22×Q8D4×C2911yescharacteristic
348C22×D4—21no—
349C22×D4D4×C2911yescharacteristic
350C23×C4—21no—
351C23×C4C23×C2911yescharacteristic
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16C23×C2912yes—
368C2×M16C23×C2912yes—
369C2×M16C23×C2912yes—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8C23×C2912yes—
380#117—21no—
381#117—21no—
382#117—21no—
383#117—21no—
384#117—21no—
385#117D4×C2912yes—
386#117C23×C2912yes—
387#117C23×C2912yes—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C42—21no—
393C2×C42D4×C2912yes—
394C4⋊C8—28no—
395#104—28no—
396#103—24no—
397#102—24no—
398#101—24no—
399#100—24no—
400C29C2×#208011yescharacteristic, direct product factor, Sylow
401C24—21no—
402C24#41×C2911yescharacteristic
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×D4×C2912yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4C2×D4×C2912yes—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4C2×D4×C2911yescharacteristic
447C22×C4C2×D4×C2911yescharacteristic
448C22×C4C2×D4×C2911yescharacteristic
449C22×C4C2×D4×C2911yescharacteristic
450C22×C4#41×C2911yescharacteristic
451C22×C4#41×C2911yescharacteristic
452C22×C4#41×C2911yescharacteristic
453C22×C4#41×C2911yescharacteristic
454C22×C4#41×C2911yescharacteristic
455C22×C4#41×C2911yescharacteristic
456C22×C4#41×C2911yescharacteristic
457C22×C4#41×C2911yescharacteristic
458C22×C4#41×C2911yescharacteristic
459C22×C4C24×C2911yescharacteristic
460M16—22no—
461M16—22no—
462M16—22no—
463M16—22no—
464M16—22no—
465M16—22no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—41no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—41no—
496C42—22no—
497C42—22no—
498C42—41no—
499C42C2×D4×C2914yes—
500C23—22no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—82no—
505C23C29×#12311yescharacteristic
506C23C29×#12311yescharacteristic
507C23C29×#12311yescharacteristic
508C23C29×#12311yescharacteristic
509C23C29×#12611yescharacteristic
510C23C29×#12611yescharacteristic
511C23C2×#41×C2911yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—82no—
535C2×C4C29×#12111yescharacteristic
536C2×C4C29×#12111yescharacteristic
537C2×C4C29×#12111yescharacteristic
538C2×C4C29×#12111yescharacteristic
539C2×C4C29×#12311yescharacteristic
540C2×C4C29×#12311yescharacteristic
541C2×C4C29×#12311yescharacteristic
542C2×C4C29×#12311yescharacteristic
543C2×C4C29×#12311yescharacteristic
544C2×C4C29×#12311yescharacteristic
545C2×C4C29×#12311yescharacteristic
546C2×C4C29×#12311yescharacteristic
547C2×C4C29×#12411yescharacteristic
548C2×C4C29×#12411yescharacteristic
549C2×C4C29×#12411yescharacteristic
550C2×C4C29×#12411yescharacteristic
551C2×C4C29×#12611yescharacteristic
552C2×C4C29×#12611yescharacteristic
553C2×C4C29×#12611yescharacteristic
554C2×C4C29×#12611yescharacteristic
555C2×C4C29×#12611yescharacteristic
556C2×C4C29×#12611yescharacteristic
557C2×C4C22×D4×C2911yescharacteristic
558C2×C4C22×D4×C2911yescharacteristic
559C2×C4C2×#41×C2911yescharacteristic
560C2×C4C2×#41×C2911yescharacteristic
561C2×C4C2×#41×C2911yescharacteristic
562C2×C4C2×#41×C2911yescharacteristic
563C8—42no—
564C8—42no—
565C8—42no—
566C8—42no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22C29×#39711yescharacteristic
579C22C29×#39711yescharacteristic
580C22C29×#39711yescharacteristic
581C22C29×#39711yescharacteristic
582C22C2×C29×#12311yescharacteristic
583C22C2×C29×#12311yescharacteristic
584C22C2×C29×#12611yescharacteristic
585C4—44no—
586C4—42no—
587C4—82no—
588C4C29×#39711yescharacteristic
589C4C29×#39711yescharacteristic
590C4C29×#39711yescharacteristic
591C4C29×#39711yescharacteristic
592C4C2×C29×#12111yescharacteristic
593C4C2×C29×#12311yescharacteristic
594C4C2×C29×#12411yescharacteristic
595C4C2×C29×#12611yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—82no—
603C2C29×#208012yesdirect product factor
604C2C2×C29×#39711yescharacteristic
subgroupG/H
centerC2×C4×C29#124
commutator, Frattini, cosocleC22×C4C24×C29
socleC22×C29#397
prime radicalC22×#41×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#424C2semidirect
5. C29×#2080C2direct (N × H)
6. C2×C29×#344C2semidirect
7. C2×C29×#341C2semidirect
8. C2×C29×H(3,ℤ/4)C2semidirect
17. C29×#424C22semidirect
30. C29×#344C22semidirect
31. C29×#341C22semidirect
32. C29×H(3,ℤ/4)C22semidirect
197. C2×#2080C29direct (N × H)
265. C2×#424C2×C29semidirect
269. #2080C2×C29direct (N × H)
270. C2×#344C2×C29semidirect
271. C2×#341C2×C29semidirect
272. C2×H(3,ℤ/4)C2×C29semidirect
310. #424C22×C29semidirect
323. #344C22×C29semidirect
324. #341C22×C29semidirect
325. H(3,ℤ/4)C22×C29semidirect
333. C2×C29#2080direct (N × H)
400. C29C2×#2080direct (N × H)
603. C2C29×#2080direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4242
C2×C29×#4212
C2×C29×#4162
C2×C29×#4132
C29×#20802
C2×C29×#3442
C2×C29×#3412
C2×C29×H(3,ℤ/4)2
C2×#208029