Finite Group Databasebeta

← C2×C29×#2033 #20318375

Subgroups — C2×C29×#2033 #20318375

Order 7424.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C29×#121C211yesmaximal, characteristic
2C22×C29×#107C211yesmaximal, characteristic, complemented
3C22×C29×#102C211yesmaximal, characteristic, complemented
4C22×C29×#102C211yesmaximal, characteristic, complemented
5C22×C29×C22⋊C8C211yesmaximal, characteristic, complemented
6C2×C29×#380C211yesmaximal, characteristic, complemented
7C29×#2033C218yesmaximal, direct product factor
8C2×C29×#340C211yesmaximal, characteristic, complemented
9C23×D4×C29—21no—
10C23×D4×C29C2211yescharacteristic
11C24×C4×C29C2211yescharacteristic
12C23×C8×C29C2211yescharacteristic
13C23×C8×C29C2211yescharacteristic
14C2×C29×#121—24no—
15C2×C29×#121—22no—
16C2×C29×#121—24no—
17C2×C29×#121C2214yes—
18C22×C4⋊C4×C29C2211yescharacteristic
19C22×C4⋊C4×C29C2211yescharacteristic
20C22×C4⋊C4×C29C2211yescharacteristic
21C22×C22⋊C4×C29—21no—
22C22×C22⋊C4×C29—21no—
23C2×C29×#107—24no—
24C2×C29×#107C2214yescomplemented
25C2×C29×#102—24no—
26C2×C29×#102—24no—
27C2×C29×#102C2214yescomplemented
28C2×C29×#102C2214yescomplemented
29C2×C29×C22⋊C8—24no—
30C2×C29×C22⋊C8C2214yescomplemented
31C29×#380—22no—
32C29×#380C2214yescomplemented
33C2×C29×#95—21no—
34C29×#340C2214yescomplemented
35C25×C29—21no—
36C25×C29D411yescharacteristic
37C22×D4×C29—28no—
38C22×D4×C29—24no—
39C22×D4×C29—22no—
40C22×D4×C29—21no—
41C22×D4×C29—22no—
42C22×D4×C29—22no—
43C22×D4×C29—22no—
44C22×D4×C29—22no—
45C22×D4×C29—44no—
46C22×D4×C29—44no—
47C22×D4×C29D414yes—
48C22×D4×C29C2312yes—
49C23×C4×C29—21no—
50C23×C4×C29—22no—
51C23×C4×C29—22no—
52C23×C4×C29—22no—
53C23×C4×C29—22no—
54C23×C4×C29—22no—
55C23×C4×C29—22no—
56C23×C4×C29—21no—
57C23×C4×C29—21no—
58C23×C4×C29D412yes—
59C23×C4×C29D411yescharacteristic
60C23×C4×C29C2312yes—
61C23×C4×C29C2311yescharacteristic
62C22×C8×C29—22no—
63C22×C8×C29—22no—
64C22×C8×C29—22no—
65C22×C8×C29—22no—
66C22×C8×C29—22no—
67C22×C8×C29D414yescomplemented
68C22×C8×C29C2312yes—
69C22×C8×C29C2312yes—
70C29×#121—216no—
71C29×#121—28no—
72C29×#121—28no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—22no—
75C2×C4⋊C4×C29—22no—
76C2×C4⋊C4×C29—22no—
77C2×C4⋊C4×C29—22no—
78C2×C4⋊C4×C29—22no—
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C4⋊C4×C29D414yes—
82C2×C4⋊C4×C29C2312yes—
83C2×C4⋊C4×C29C2312yes—
84C2×C4⋊C4×C29C2312yes—
85C2×C22⋊C4×C29—28no—
86C2×C22⋊C4×C29—24no—
87C2×C22⋊C4×C29—24no—
88C2×C22⋊C4×C29—44no—
89C29×#107—28no—
90C29×#102—28no—
91C29×#102—28no—
92C29×C22⋊C8—28no—
93C29×#95—24no—
94C24×C29—22no—
95C24×C29—22no—
96C24×C29—22no—
97C24×C29—22no—
98C24×C29—22no—
99C24×C29—22no—
100C24×C29—24no—
101C24×C29—22no—
102C24×C29—42no—
103C24×C29—42no—
104C24×C29—42no—
105C24×C29—42no—
106C24×C29—42no—
107C24×C29—42no—
108C24×C29D814yes—
109C24×C29C2×D412yes—
110C24×C29C2×D411yescharacteristic
111C2×D4×C29—216no—
112C2×D4×C29—24no—
113C2×D4×C29—28no—
114C2×D4×C29—28no—
115C2×D4×C29—22no—
116C2×D4×C29—22no—
117C2×D4×C29—22no—
118C2×D4×C29—22no—
119C2×D4×C29—22no—
120C2×D4×C29—48no—
121C2×D4×C29—432no—
122C2×D4×C29—48no—
123C2×D4×C29—44no—
124C2×D4×C29—42no—
125C2×D4×C29—42no—
126C2×D4×C29—44no—
127C2×D4×C29C2×D414yes—
128C22×C4×C29—22no—
129C22×C4×C29—24no—
130C22×C4×C29—22no—
131C22×C4×C29—22no—
132C22×C4×C29—22no—
133C22×C4×C29—24no—
134C22×C4×C29—24no—
135C22×C4×C29—24no—
136C22×C4×C29—22no—
137C22×C4×C29—22no—
138C22×C4×C29—22no—
139C22×C4×C29—22no—
140C22×C4×C29—22no—
141C22×C4×C29—22no—
142C22×C4×C29—22no—
143C22×C4×C29—22no—
144C22×C4×C29—42no—
145C22×C4×C29—42no—
146C22×C4×C29—44no—
147C22×C4×C29—44no—
148C22×C4×C29—44no—
149C22×C4×C29—44no—
150C22×C4×C29—42no—
151C22×C4×C29—42no—
152C22×C4×C29—42no—
153C22×C4×C29—42no—
154C22×C4×C29—42no—
155C22×C4×C29—42no—
156C22×C4×C29C2×D412yes—
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2×D412yes—
159C22×C4×C29C2×D412yes—
160C22×C4×C29C2×D412yes—
161C22×C4×C29#4112yes—
162C22×C4×C29#4112yes—
163C22×C4×C29#4112yes—
164C22×C4×C29C2411yescharacteristic
165C2×C8×C29—28no—
166C2×C8×C29—22no—
167C2×C8×C29—22no—
168C2×C8×C29—22no—
169C2×C8×C29—22no—
170C2×C8×C29—22no—
171C2×C8×C29—44no—
172C2×C8×C29C2×D414yescomplemented
173C4⋊C4×C29—24no—
174C4⋊C4×C29—22no—
175C4⋊C4×C29—22no—
176C4⋊C4×C29—22no—
177C4⋊C4×C29—22no—
178C4⋊C4×C29—22no—
179C4⋊C4×C29—42no—
180C4⋊C4×C29—42no—
181C4⋊C4×C29C2×D414yes—
182C22⋊C4×C29—216no—
183C22⋊C4×C29—48no—
184C2×#2033C2911yesmaximal, characteristic, direct product factor, Sylow
185C23×C29—22no—
186C23×C29—22no—
187C23×C29—22no—
188C23×C29—22no—
189C23×C29—22no—
190C23×C29—22no—
191C23×C29—28no—
192C23×C29—28no—
193C23×C29—28no—
194C23×C29—24no—
195C23×C29—44no—
196C23×C29—44no—
197C23×C29—44no—
198C23×C29—44no—
199C23×C29—42no—
200C23×C29—42no—
201C23×C29—42no—
202C23×C29—42no—
203C23×C29—42no—
204C23×C29—42no—
205C23×C29—48no—
206C23×C29—48no—
207C23×C29—48no—
208C23×C29—84no—
209C23×C29—84no—
210C23×C29—84no—
211C23×C29—84no—
212C23×C29#12012yes—
213C23×C29#12112yes—
214C23×C29#12312yes—
215C23×C29C2×D814yes—
216C23×C29C2×D812yes—
217C23×C29#13512yes—
218C23×C29AGL(1,ℤ/8)12yes—
219C23×C29#13712yes—
220C23×C29C22×D411yescharacteristic
221D4×C29—24no—
222D4×C29—24no—
223D4×C29—432no—
224D4×C29—42no—
225D4×C29—42no—
226D4×C29—48no—
227C2×C4×C29—22no—
228C2×C4×C29—24no—
229C2×C4×C29—22no—
230C2×C4×C29—22no—
231C2×C4×C29—42no—
232C2×C4×C29—42no—
233C2×C4×C29—44no—
234C2×C4×C29—48no—
235C2×C4×C29—42no—
236C2×C4×C29—42no—
237C2×C4×C29—42no—
238C2×C4×C29—42no—
239C2×C4×C29—48no—
240C2×C4×C29—42no—
241C2×C4×C29—42no—
242C2×C4×C29—42no—
243C2×C4×C29—42no—
244C2×C4×C29—42no—
245C2×C4×C29—42no—
246C2×C4×C29—84no—
247C2×C4×C29—84no—
248C2×C4×C29#12012yes—
249C2×C4×C29#12114yes—
250C2×C4×C29#12114yes—
251C2×C4×C29#12112yes—
252C2×C4×C29#12314yes—
253C2×C4×C29#12312yes—
254C2×C4×C29#12414yes—
255C2×C4×C29C22×D411yescharacteristic
256C2×C4×C29C22×D411yescharacteristic
257C2×C4×C29C22×D411yescharacteristic
258C2×C4×C29C2×#4111yescharacteristic
259C2×C4×C29C2×#4111yescharacteristic
260C2×C4×C29C2×#4111yescharacteristic
261C8×C29—24no—
262C8×C29—42no—
263C22×#121C2×C2911yescharacteristic
264C22×#107C2×C2911yescharacteristic, complemented
265C22×#102C2×C2911yescharacteristic, complemented
266C22×#102C2×C2911yescharacteristic, complemented
267C22×C22⋊C8C2×C2911yescharacteristic, complemented
268C2×#380C2×C2911yescharacteristic, complemented
269#2033C2×C2918yesdirect product factor
270C2×#340C2×C2911yescharacteristic, complemented
271C22×C29—24no—
272C22×C29—24no—
273C22×C29—24no—
274C22×C29—42no—
275C22×C29—42no—
276C22×C29—42no—
277C22×C29—42no—
278C22×C29—416no—
279C22×C29—44no—
280C22×C29—44no—
281C22×C29—44no—
282C22×C29—82no—
283C22×C29—82no—
284C22×C29—82no—
285C22×C29—82no—
286C22×C29—816no—
287C22×C29#39414yes—
288C22×C29#44714yes—
289C22×C29#45214yes—
290C22×C29#46614yes—
291C22×C29#46814yes—
292C22×C29#48014yes—
293C22×C29#48214yes—
294C22×C29C2×#12011yescharacteristic
295C22×C29C2×#12111yescharacteristic
296C22×C29C2×#12311yescharacteristic
297C22×C29C22×D811yescharacteristic
298C22×C29C2×#13511yescharacteristic
299C22×C29C2×AGL(1,ℤ/8)11yescharacteristic
300C22×C29C2×#13711yescharacteristic
301C4×C29—42no—
302C4×C29—44no—
303C4×C29—82no—
304C4×C29—82no—
305C4×C29#39414yes—
306C4×C29C2×#12111yescharacteristic
307C4×C29C2×#12111yescharacteristic
308C4×C29C2×#12311yescharacteristic
309C4×C29C2×#12411yescharacteristic
310C23×D4—21no—
311C23×D4C22×C2911yescharacteristic
312C24×C4C22×C2911yescharacteristic
313C23×C8C22×C2911yescharacteristic
314C23×C8C22×C2911yescharacteristic
315C2×#121—24no—
316C2×#121—22no—
317C2×#121—24no—
318C2×#121C22×C2914yes—
319C22×C4⋊C4C22×C2911yescharacteristic
320C22×C4⋊C4C22×C2911yescharacteristic
321C22×C4⋊C4C22×C2911yescharacteristic
322C22×C22⋊C4—21no—
323C22×C22⋊C4—21no—
324C2×#107—24no—
325C2×#107C22×C2914yescomplemented
326C2×#102—24no—
327C2×#102—24no—
328C2×#102C22×C2914yescomplemented
329C2×#102C22×C2914yescomplemented
330C2×C22⋊C8—24no—
331C2×C22⋊C8C22×C2914yescomplemented
332#380—22no—
333#380C22×C2914yescomplemented
334C2×#95—21no—
335#340C22×C2914yescomplemented
336C2×C29—44no—
337C2×C29—84no—
338C2×C29#203318yesdirect product factor
339C2×C29C2×#39411yescharacteristic
340C2×C29C2×#44711yescharacteristic
341C2×C29C2×#45211yescharacteristic
342C2×C29C2×#46611yescharacteristic
343C2×C29C2×#46811yescharacteristic
344C2×C29C2×#48011yescharacteristic
345C2×C29C2×#48211yescharacteristic
346C25—21no—
347C25D4×C2911yescharacteristic
348C22×D4—28no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—21no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—44no—
357C22×D4—44no—
358C22×D4D4×C2914yes—
359C22×D4C23×C2912yes—
360C23×C4—21no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4D4×C2911yescharacteristic
370C23×C4D4×C2912yes—
371C23×C4C23×C2912yes—
372C23×C4C23×C2911yescharacteristic
373C22×C8—22no—
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—22no—
378C22×C8D4×C2914yescomplemented
379C22×C8C23×C2912yes—
380C22×C8C23×C2912yes—
381#121—216no—
382#121—28no—
383#121—28no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4D4×C2914yes—
393C2×C4⋊C4C23×C2912yes—
394C2×C4⋊C4C23×C2912yes—
395C2×C4⋊C4C23×C2912yes—
396C2×C22⋊C4—28no—
397C2×C22⋊C4—24no—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—44no—
400#107—28no—
401#102—28no—
402#102—28no—
403C22⋊C8—28no—
404#95—24no—
405C29C2×#203311yescharacteristic, direct product factor, Sylow
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—22no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24—42no—
419C24—42no—
420C24D8×C2914yes—
421C24C2×D4×C2912yes—
422C24C2×D4×C2911yescharacteristic
423C2×D4—216no—
424C2×D4—24no—
425C2×D4—28no—
426C2×D4—28no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—432no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—44no—
439C2×D4C2×D4×C2914yes—
440C22×C4—22no—
441C22×C4—24no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—44no—
459C22×C4—44no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4C2×D4×C2912yes—
469C22×C4C2×D4×C2911yescharacteristic
470C22×C4C2×D4×C2912yes—
471C22×C4C2×D4×C2912yes—
472C22×C4C2×D4×C2912yes—
473C22×C4#41×C2912yes—
474C22×C4#41×C2912yes—
475C22×C4#41×C2912yes—
476C22×C4C24×C2911yescharacteristic
477C2×C8—28no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—44no—
484C2×C8C2×D4×C2914yescomplemented
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4C2×D4×C2914yes—
494C22⋊C4—216no—
495C22⋊C4—48no—
496C23—28no—
497C23—28no—
498C23—28no—
499C23—22no—
500C23—22no—
501C23—22no—
502C23—22no—
503C23—22no—
504C23—22no—
505C23—24no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—44no—
510C23—48no—
511C23—48no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—42no—
517C23—42no—
518C23—48no—
519C23—84no—
520C23—84no—
521C23—84no—
522C23—84no—
523C23C29×#12012yes—
524C23C29×#12112yes—
525C23C29×#12312yes—
526C23C2×D8×C2914yes—
527C23C2×D8×C2912yes—
528C23C29×#13512yes—
529C23C29×AGL(1,ℤ/8)12yes—
530C23C29×#13712yes—
531C23C22×D4×C2911yescharacteristic
532D4—24no—
533D4—24no—
534D4—432no—
535D4—42no—
536D4—42no—
537D4—48no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—48no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—48no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—84no—
558C2×C4—84no—
559C2×C4C29×#12012yes—
560C2×C4C29×#12114yes—
561C2×C4C29×#12114yes—
562C2×C4C29×#12112yes—
563C2×C4C29×#12314yes—
564C2×C4C29×#12312yes—
565C2×C4C29×#12414yes—
566C2×C4C22×D4×C2911yescharacteristic
567C2×C4C22×D4×C2911yescharacteristic
568C2×C4C22×D4×C2911yescharacteristic
569C2×C4C2×#41×C2911yescharacteristic
570C2×C4C2×#41×C2911yescharacteristic
571C2×C4C2×#41×C2911yescharacteristic
572C8—24no—
573C8—42no—
574C22—24no—
575C22—24no—
576C22—24no—
577C22—42no—
578C22—42no—
579C22—416no—
580C22—42no—
581C22—42no—
582C22—44no—
583C22—44no—
584C22—44no—
585C22—82no—
586C22—82no—
587C22—816no—
588C22—82no—
589C22—82no—
590C22C29×#39414yes—
591C22C29×#44714yes—
592C22C29×#45214yes—
593C22C29×#46614yes—
594C22C29×#46814yes—
595C22C29×#48014yes—
596C22C29×#48214yes—
597C22C2×C29×#12011yescharacteristic
598C22C2×C29×#12111yescharacteristic
599C22C2×C29×#12311yescharacteristic
600C22C22×D8×C2911yescharacteristic
601C22C2×C29×#13511yescharacteristic
602C22C2×C29×AGL(1,ℤ/8)11yescharacteristic
603C22C2×C29×#13711yescharacteristic
604C4—44no—
605C4—42no—
606C4—82no—
607C4—82no—
608C4C29×#39414yes—
609C4C2×C29×#12111yescharacteristic
610C4C2×C29×#12111yescharacteristic
611C4C2×C29×#12311yescharacteristic
612C4C2×C29×#12411yescharacteristic
613C2—44no—
614C2—84no—
615C2C29×#203318yesdirect product factor
616C2C2×C29×#39411yescharacteristic
617C2C2×C29×#44711yescharacteristic
618C2C2×C29×#45211yescharacteristic
619C2C2×C29×#46611yescharacteristic
620C2C2×C29×#46811yescharacteristic
621C2C2×C29×#48011yescharacteristic
622C2C2×C29×#48211yescharacteristic
subgroupG/H
center, socleC24×C29C2×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×C29×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C29 ◁ C24×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C29×#107C2semidirect
3. C22×C29×#102C2semidirect
4. C22×C29×#102C2semidirect
5. C22×C29×C22⋊C8C2semidirect
6. C2×C29×#380C2semidirect
7. C29×#2033C2direct (N × H)
8. C2×C29×#340C2semidirect
24. C2×C29×#107C22semidirect
27. C2×C29×#102C22semidirect
28. C2×C29×#102C22semidirect
30. C2×C29×C22⋊C8C22semidirect
32. C29×#380C22semidirect
34. C29×#340C22semidirect
67. C22×C8×C29D4semidirect
172. C2×C8×C29C2×D4semidirect
184. C2×#2033C29direct (N × H)
264. C22×#107C2×C29semidirect
265. C22×#102C2×C29semidirect
266. C22×#102C2×C29semidirect
267. C22×C22⋊C8C2×C29semidirect
268. C2×#380C2×C29semidirect
269. #2033C2×C29direct (N × H)
270. C2×#340C2×C29semidirect
325. C2×#107C22×C29semidirect
328. C2×#102C22×C29semidirect
329. C2×#102C22×C29semidirect
331. C2×C22⋊C8C22×C29semidirect
333. #380C22×C29semidirect
335. #340C22×C29semidirect
338. C2×C29#2033direct (N × H)
378. C22×C8D4×C29semidirect
405. C29C2×#2033direct (N × H)
484. C2×C8C2×D4×C29semidirect
615. C2C29×#2033direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C29×#1212
C22×C29×#1072
C22×C29×#1022
C22×C29×C22⋊C82
C2×C29×#3802
C29×#20332
C2×C29×#3402
C2×#203329