Finite Group Databasebeta

← C29×#11120 #20306020

Subgroups — C29×#11120 #20306020

Order 7424.

870 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#430C211yesmaximal, characteristic, complemented
2C2×C29×#421C211yesmaximal, characteristic
3C2×C29×#417C211yesmaximal, characteristic
4C2×C29×#413C211yesmaximal, characteristic
5C2×C29×#344C211yesmaximal, characteristic, complemented
6C2×C29×#343C211yesmaximal, characteristic, complemented
7C29×#1736C211yesmaximal, characteristic, complemented
8C22×#41×C29C2211yescharacteristic
9C22×M16×C29C2211yescharacteristic
10C22×M16×C29C2211yescharacteristic
11C22×M16×C29C2211yescharacteristic
12C22×M16×C29C2211yescharacteristic
13C2×C29×#117C2211yescharacteristic
14C22×C4⋊C4×C29C2211yescharacteristic
15C29×#430—22no—
16C29×#430—22no—
17C2×C29×#108—22no—
18C29×#421—22no—
19C29×#421C414yescomplemented
20C2×C29×#104—22no—
21C29×#417—22no—
22C29×#417—22no—
23C2×C29×#103—21no—
24C2×C29×#102—21no—
25C29×#413—22no—
26C29×#413—22no—
27C2×C29×#101—21no—
28C2×C29×#100—21no—
29C29×#344—22no—
30C29×#343—22no—
31C29×#340—22no—
32C2×#41×C29—21no—
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×C29C2×C412yes—
43C2×#41×C29Q812yes—
44C22×Q8×C29D411yescharacteristic
45C22×D4×C29—21no—
46C22×D4×C29D411yescharacteristic
47C23×C4×C29—21no—
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×C29—21no—
66C2×M16×C29—21no—
67C2×M16×C29—21no—
68C2×M16×C29C2×C412yes—
69C2×M16×C29D412yes—
70C2×M16×C29D412yes—
71C2×M16×C29D412yes—
72C2×M16×C29D412yes—
73C2×M16×C29D412yes—
74C22×C8×C29—21no—
75C22×C8×C29—21no—
76C22×C8×C29—21no—
77C22×C8×C29—21no—
78C29×#117—21no—
79C29×#117—21no—
80C29×#117—21no—
81C29×#117C2×C412yes—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29—21no—
85C2×C4⋊C4×C29—21no—
86C2×C4⋊C4×C29—21no—
87C2×C4⋊C4×C29—21no—
88C2×C4⋊C4×C29D412yes—
89C2×C22⋊C4×C29—21no—
90C2×C42×C29—21no—
91C29×#108—28no—
92C29×#104—28no—
93C29×#103—24no—
94C29×#102—24no—
95C29×#101—24no—
96C29×#100—24no—
97C24×C29—21no—
98C24×C29#4111yescharacteristic
99#41×C29—22no—
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—41no—
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—
115C2×Q8×C29—21no—
116C2×Q8×C29—21no—
117C2×Q8×C29—21no—
118C2×Q8×C29—21no—
119C2×Q8×C29—21no—
120C2×Q8×C29C4⋊C412yes—
121C2×D4×C29—22no—
122C2×D4×C29—22no—
123C2×D4×C29—21no—
124C2×D4×C29—21no—
125C2×D4×C29—21no—
126C2×D4×C29—21no—
127C2×D4×C29—21no—
128C2×D4×C29—41no—
129C2×D4×C29—41no—
130C2×D4×C29—41no—
131C2×D4×C29—41no—
132C2×D4×C29C4⋊C412yes—
133C22×C4×C29—21no—
134C22×C4×C29—22no—
135C22×C4×C29—22no—
136C22×C4×C29—22no—
137C22×C4×C29—41no—
138C22×C4×C29—41no—
139C22×C4×C29—41no—
140C22×C4×C29—41no—
141C22×C4×C29—41no—
142C22×C4×C29—41no—
143C22×C4×C29—41no—
144C22×C4×C29—82no—
145C22×C4×C29C22×C411yescharacteristic
146C22×C4×C29C2×D411yescharacteristic
147C22×C4×C29C2×D411yescharacteristic
148C22×C4×C29C2×D411yescharacteristic
149C22×C4×C29C2×D411yescharacteristic
150C22×C4×C29C2×D411yescharacteristic
151C22×C4×C29C2×D411yescharacteristic
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2×Q811yescharacteristic
154C22×C4×C29#4111yescharacteristic
155C22×C4×C29#4111yescharacteristic
156C22×C4×C29#4111yescharacteristic
157C22×C4×C29#4111yescharacteristic
158C22×C4×C29#4111yescharacteristic
159M16×C29—22no—
160M16×C29—22no—
161M16×C29—22no—
162M16×C29—22no—
163M16×C29—22no—
164M16×C29—22no—
165M16×C29—22no—
166M16×C29—22no—
167M16×C29—22no—
168M16×C29—41no—
169M16×C29—41no—
170M16×C29—41no—
171M16×C29—41no—
172M16×C29—41no—
173M16×C29—41no—
174M16×C29C22⋊C414yes—
175C2×C8×C29—22no—
176C2×C8×C29—22no—
177C2×C8×C29—22no—
178C2×C8×C29—22no—
179C2×C8×C29—22no—
180C2×C8×C29—22no—
181C2×C8×C29—41no—
182C2×C8×C29—41no—
183C2×C8×C29—41no—
184C2×C8×C29—41no—
185C2×C8×C29—41no—
186C2×C8×C29—41no—
187C4⋊C4×C29—22no—
188C4⋊C4×C29—22no—
189C4⋊C4×C29—22no—
190C4⋊C4×C29—41no—
191C4⋊C4×C29—41no—
192C4⋊C4×C29—41no—
193C22⋊C4×C29—22no—
194C22⋊C4×C29—41no—
195C42×C29—22no—
196C42×C29—41no—
197#11120C2911yesmaximal, characteristic, direct product factor, Sylow
198C23×C29—22no—
199C23×C29—41no—
200C23×C29—41no—
201C23×C29—41no—
202C23×C29—41no—
203C23×C29—81no—
204C23×C29—81no—
205C23×C29C4×D411yescharacteristic
206C23×C29#12111yescharacteristic
207C23×C29C22⋊Q811yescharacteristic
208C23×C29#12311yescharacteristic
209C23×C29#12411yescharacteristic
210C23×C29#12411yescharacteristic
211C23×C29#12611yescharacteristic
212Q8×C29—22no—
213Q8×C29—22no—
214Q8×C29—41no—
215Q8×C29—41no—
216D4×C29—22no—
217D4×C29—22no—
218D4×C29—42no—
219D4×C29—42no—
220D4×C29—42no—
221D4×C29—42no—
222D4×C29—41no—
223D4×C29—41no—
224C2×C4×C29—22no—
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—42no—
233C2×C4×C29—81no—
234C2×C4×C29—81no—
235C2×C4×C29—82no—
236C2×C4×C29—82no—
237C2×C4×C29—82no—
238C2×C4×C29C2×C22⋊C411yescharacteristic
239C2×C4×C29C2×C4⋊C411yescharacteristic
240C2×C4×C29#11711yescharacteristic
241C2×C4×C29C4×D411yescharacteristic
242C2×C4×C29C4×D411yescharacteristic
243C2×C4×C29C4×D411yescharacteristic
244C2×C4×C29#12011yescharacteristic
245C2×C4×C29#12011yescharacteristic
246C2×C4×C29#12011yescharacteristic
247C2×C4×C29#12111yescharacteristic
248C2×C4×C29#12111yescharacteristic
249C2×C4×C29#12111yescharacteristic
250C2×C4×C29#12111yescharacteristic
251C2×C4×C29#12111yescharacteristic
252C2×C4×C29#12111yescharacteristic
253C2×C4×C29#12111yescharacteristic
254C2×C4×C29C22⋊Q811yescharacteristic
255C2×C4×C29C22⋊Q811yescharacteristic
256C2×C4×C29C22⋊Q811yescharacteristic
257C2×C4×C29C22⋊Q811yescharacteristic
258C2×C4×C29C22⋊Q811yescharacteristic
259C2×C4×C29#12311yescharacteristic
260C2×C4×C29#12311yescharacteristic
261C2×C4×C29#12311yescharacteristic
262C2×C4×C29#12311yescharacteristic
263C2×C4×C29#12411yescharacteristic
264C2×C4×C29#12611yescharacteristic
265C2×C4×C29#12711yescharacteristic
266C8×C29—24no—
267C8×C29—42no—
268C8×C29—42no—
269C8×C29—42no—
270C2×#430C2×C2911yescharacteristic, complemented
271C2×#421C2×C2911yescharacteristic
272C2×#417C2×C2911yescharacteristic
273C2×#413C2×C2911yescharacteristic
274C2×#344C2×C2911yescharacteristic, complemented
275C2×#343C2×C2911yescharacteristic, complemented
276#1736C2×C2911yescharacteristic, complemented
277C22×C29—21no—
278C22×C29—21no—
279C22×C29—21no—
280C22×C29—21no—
281C22×C29—21no—
282C22×C29—21no—
283C22×C29—41no—
284C22×C29—41no—
285C22×C29—41no—
286C22×C29—41no—
287C22×C29—42no—
288C22×C29—82no—
289C22×C29—82no—
290C22×C29—81no—
291C22×C29—81no—
292C22×C29#38511yescharacteristic
293C22×C29#38811yescharacteristic
294C22×C29#39011yescharacteristic
295C22×C29#39311yescharacteristic
296C22×C29#39411yescharacteristic
297C22×C29#39611yescharacteristic
298C22×C29#39711yescharacteristic
299C4×C29—42no—
300C4×C29—82no—
301C4×C29—82no—
302C4×C29#38011yescharacteristic
303C4×C29#38511yescharacteristic
304C4×C29#38611yescharacteristic
305C4×C29#38811yescharacteristic
306C4×C29#39211yescharacteristic
307C4×C29#39411yescharacteristic
308C4×C29#39611yescharacteristic
309C4×C29#39911yescharacteristic
310C22×#41C22×C2911yescharacteristic
311C22×M16C22×C2911yescharacteristic
312C22×M16C22×C2911yescharacteristic
313C22×M16C22×C2911yescharacteristic
314C22×M16C22×C2911yescharacteristic
315C2×#117C22×C2911yescharacteristic
316C22×C4⋊C4C22×C2911yescharacteristic
317#430—22no—
318#430—22no—
319C2×#108—22no—
320#421—22no—
321#421C4×C2914yescomplemented
322C2×#104—22no—
323#417—22no—
324#417—22no—
325C2×#103—21no—
326C2×#102—21no—
327#413—22no—
328#413—22no—
329C2×#101—21no—
330C2×#100—21no—
331#344—22no—
332#343—22no—
333#340—22no—
334C2×C29—21no—
335C2×C29—21no—
336C2×C29—21no—
337C2×C29—21no—
338C2×C29—21no—
339C2×C29—21no—
340C2×C29—82no—
341C2×C29#143911yescharacteristic
342C2×C29#204811yescharacteristic
343C2×C29#204911yescharacteristic
344C2×#41—21no—
345C2×#41—21no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—21no—
349C2×#41—21no—
350C2×#41—21no—
351C2×#41—21no—
352C2×#41—21no—
353C2×#41—21no—
354C2×#41C2×C4×C2912yes—
355C2×#41Q8×C2912yes—
356C22×Q8D4×C2911yescharacteristic
357C22×D4—21no—
358C22×D4D4×C2911yescharacteristic
359C23×C4—21no—
360C23×C4—21no—
361C23×C4C23×C2911yescharacteristic
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—21no—
376C2×M16—21no—
377C2×M16—21no—
378C2×M16—21no—
379C2×M16—21no—
380C2×M16C2×C4×C2912yes—
381C2×M16D4×C2912yes—
382C2×M16D4×C2912yes—
383C2×M16D4×C2912yes—
384C2×M16D4×C2912yes—
385C2×M16D4×C2912yes—
386C22×C8—21no—
387C22×C8—21no—
388C22×C8—21no—
389C22×C8—21no—
390#117—21no—
391#117—21no—
392#117—21no—
393#117C2×C4×C2912yes—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4D4×C2912yes—
401C2×C22⋊C4—21no—
402C2×C42—21no—
403#108—28no—
404#104—28no—
405#103—24no—
406#102—24no—
407#101—24no—
408#100—24no—
409C29#1112011yescharacteristic, direct product factor, Sylow
410C24—21no—
411C24#41×C2911yescharacteristic
412#41—22no—
413#41—22no—
414#41—22no—
415#41—22no—
416#41—22no—
417#41—22no—
418#41—22no—
419#41—22no—
420#41—41no—
421#41—41no—
422#41—41no—
423#41—41no—
424#41—41no—
425#41—41no—
426#41—41no—
427#41—41no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8C4⋊C4×C2912yes—
434C2×D4—22no—
435C2×D4—22no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4C4⋊C4×C2912yes—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—82no—
458C22×C4C22×C4×C2911yescharacteristic
459C22×C4C2×D4×C2911yescharacteristic
460C22×C4C2×D4×C2911yescharacteristic
461C22×C4C2×D4×C2911yescharacteristic
462C22×C4C2×D4×C2911yescharacteristic
463C22×C4C2×D4×C2911yescharacteristic
464C22×C4C2×D4×C2911yescharacteristic
465C22×C4C2×D4×C2911yescharacteristic
466C22×C4C2×Q8×C2911yescharacteristic
467C22×C4#41×C2911yescharacteristic
468C22×C4#41×C2911yescharacteristic
469C22×C4#41×C2911yescharacteristic
470C22×C4#41×C2911yescharacteristic
471C22×C4#41×C2911yescharacteristic
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—22no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486M16—41no—
487M16C22⋊C4×C2914yes—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C22⋊C4—22no—
507C22⋊C4—41no—
508C42—22no—
509C42—41no—
510C23—22no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—81no—
516C23—81no—
517C23C4×D4×C2911yescharacteristic
518C23C29×#12111yescharacteristic
519C23C29×C22⋊Q811yescharacteristic
520C23C29×#12311yescharacteristic
521C23C29×#12411yescharacteristic
522C23C29×#12411yescharacteristic
523C23C29×#12611yescharacteristic
524Q8—22no—
525Q8—22no—
526Q8—41no—
527Q8—41no—
528D4—22no—
529D4—22no—
530D4—42no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—41no—
535D4—41no—
536C2×C4—22no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—82no—
546C2×C4—82no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—82no—
550C2×C4C2×C22⋊C4×C2911yescharacteristic
551C2×C4C2×C4⋊C4×C2911yescharacteristic
552C2×C4C29×#11711yescharacteristic
553C2×C4C4×D4×C2911yescharacteristic
554C2×C4C4×D4×C2911yescharacteristic
555C2×C4C4×D4×C2911yescharacteristic
556C2×C4C29×#12011yescharacteristic
557C2×C4C29×#12011yescharacteristic
558C2×C4C29×#12011yescharacteristic
559C2×C4C29×#12111yescharacteristic
560C2×C4C29×#12111yescharacteristic
561C2×C4C29×#12111yescharacteristic
562C2×C4C29×#12111yescharacteristic
563C2×C4C29×#12111yescharacteristic
564C2×C4C29×#12111yescharacteristic
565C2×C4C29×#12111yescharacteristic
566C2×C4C29×C22⋊Q811yescharacteristic
567C2×C4C29×C22⋊Q811yescharacteristic
568C2×C4C29×C22⋊Q811yescharacteristic
569C2×C4C29×C22⋊Q811yescharacteristic
570C2×C4C29×C22⋊Q811yescharacteristic
571C2×C4C29×#12311yescharacteristic
572C2×C4C29×#12311yescharacteristic
573C2×C4C29×#12311yescharacteristic
574C2×C4C29×#12311yescharacteristic
575C2×C4C29×#12411yescharacteristic
576C2×C4C29×#12611yescharacteristic
577C2×C4C29×#12711yescharacteristic
578C8—24no—
579C8—42no—
580C8—42no—
581C8—42no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—81no—
596C22—81no—
597C22C29×#38511yescharacteristic
598C22C29×#38811yescharacteristic
599C22C29×#39011yescharacteristic
600C22C29×#39311yescharacteristic
601C22C29×#39411yescharacteristic
602C22C29×#39611yescharacteristic
603C22C29×#39711yescharacteristic
604C4—42no—
605C4—82no—
606C4—82no—
607C4C29×#38011yescharacteristic
608C4C29×#38511yescharacteristic
609C4C29×#38611yescharacteristic
610C4C29×#38811yescharacteristic
611C4C29×#39211yescharacteristic
612C4C29×#39411yescharacteristic
613C4C29×#39611yescharacteristic
614C4C29×#39911yescharacteristic
615C2—21no—
616C2—21no—
617C2—21no—
618C2—21no—
619C2—21no—
620C2—21no—
621C2—82no—
622C2C29×#143911yescharacteristic
623C2C29×#204811yescharacteristic
624C2C29×#204911yescharacteristic
subgroupG/H
center, socleC22×C29#394
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC22×#41×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C29×#430C2semidirect
5. C2×C29×#344C2semidirect
6. C2×C29×#343C2semidirect
7. C29×#1736C2semidirect
19. C29×#421C4semidirect
197. #11120C29direct (N × H)
270. C2×#430C2×C29semidirect
274. C2×#344C2×C29semidirect
275. C2×#343C2×C29semidirect
276. #1736C2×C29semidirect
321. #421C4×C29semidirect
409. C29#11120direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4302
C2×C29×#4212
C2×C29×#4172
C2×C29×#4132
C2×C29×#3442
C2×C29×#3432
C29×#17362
#1112029