Finite Group Databasebeta

← C29×#29401 #20324301

Subgroups — C29×#29401 #20324301

Order 7424.

672 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2331C211yesmaximal, characteristic, complemented
2C29×#2319C211yesmaximal, characteristic
3C29×#2085C211yesmaximal, characteristic, complemented
4C29×#2073C211yesmaximal, characteristic
5C29×#2057C211yesmaximal, characteristic, complemented
6C29×#2023C211yesmaximal, characteristic
7C29×#1925C211yesmaximal, characteristic
8C29×#1925C211yesmaximal, characteristic
9C29×#1921C211yesmaximal, characteristic, complemented
10C29×#1921C211yesmaximal, characteristic, complemented
11C29×#1919C211yesmaximal, characteristic, complemented
12C29×#1918C211yesmaximal, characteristic, complemented
13C29×#1864C211yesmaximal, characteristic
14C29×#1862C211yesmaximal, characteristic
15C29×#1840C211yesmaximal, characteristic, complemented
16C2×C29×C4⋊Q8C2211yescharacteristic
17C2×C4×D4×C29C2211yescharacteristic
18C2×C29×#107C2211yescharacteristic
19C2×C29×#107C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
21C2×C29×#106C2211yescharacteristic
22C2×C29×#102C2211yescharacteristic
23C2×C29×#102C2211yescharacteristic
24C2×C29×#102C2211yescharacteristic
25C2×C29×#102C2211yescharacteristic
26C29×#391—21no—
27C29×#391—21no—
28C29×#390C2211yescharacteristic
29C29×#390C2211yescharacteristic
30C29×#389C2211yescharacteristic
31C29×#389C2211yescharacteristic
32C29×#389C2211yescharacteristic
33C29×#389C2211yescharacteristic
34C29×#388—21no—
35C29×#388—21no—
36C29×#387—21no—
37C29×#387—21no—
38C29×#382C2211yescharacteristic
39C29×#381—21no—
40C29×#380—21no—
41C4×C4⋊C4×C29C2211yescharacteristic
42C4×C4⋊C4×C29C2211yescharacteristic
43C4×C4⋊C4×C29C2211yescharacteristic
44C29×#376C2211yescharacteristic
45C29×#340C2211yescharacteristic
46C29×#340C2211yescharacteristic
47C29×#340C2211yescharacteristic
48C29×#340C2211yescharacteristic
49C29×#340C2211yescharacteristic
50C29×#340C2211yescharacteristic
51C29×#340C2211yescharacteristic
52C29×#340C2211yescharacteristic
53C29×#336C2211yescharacteristic
54C29×#336C2211yescharacteristic
55C29×#336C2211yescharacteristic
56C29×#336C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29—21no—
60C22×D4×C29C2311yescharacteristic
61C23×C4×C29—21no—
62C22×C8×C29C2311yescharacteristic
63C22×C8×C29C2311yescharacteristic
64C22×C8×C29C2311yescharacteristic
65C22×C8×C29C2311yescharacteristic
66C29×C4⋊Q8—22no—
67C29×C4⋊Q8—22no—
68C4×D4×C29—22no—
69C4×D4×C29—22no—
70C2×C4⋊C4×C29—21no—
71C2×C4⋊C4×C29—21no—
72C2×C4⋊C4×C29—21no—
73C2×C4⋊C4×C29—21no—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29C2311yescharacteristic
76C2×C4⋊C4×C29C2311yescharacteristic
77C2×C4⋊C4×C29C2311yescharacteristic
78C2×C4⋊C4×C29C2311yescharacteristic
79C2×C4⋊C4×C29C2311yescharacteristic
80C2×C4⋊C4×C29C2311yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C22⋊C4×C29—21no—
83C2×C22⋊C4×C29—21no—
84C2×C22⋊C4×C29—21no—
85C2×C22⋊C4×C29—21no—
86C2×C22⋊C4×C29—21no—
87C2×C42×C29—21no—
88C2×C42×C29—21no—
89C2×C42×C29—21no—
90C2×C42×C29C2311yescharacteristic
91C2×C42×C29C2311yescharacteristic
92C2×C42×C29C2311yescharacteristic
93C29×#107—22no—
94C29×#107—22no—
95C29×#107—22no—
96C29×#106—22no—
97C29×#102—22no—
98C29×#102—22no—
99C29×#102—22no—
100C29×#102—22no—
101C29×#95—21no—
102C29×#95—21no—
103C29×#95—21no—
104C29×#95—21no—
105C29×#95—21no—
106C29×#95—21no—
107C29×#95—21no—
108C29×#95—21no—
109C29×#95—21no—
110C29×#95D411yescharacteristic
111C29×#95D411yescharacteristic
112C29×#95D411yescharacteristic
113C29×#95D411yescharacteristic
114C24×C29—21no—
115C2×Q8×C29—24no—
116C2×Q8×C29—81no—
117C2×Q8×C29—81no—
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29#4112yes—
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—24no—
128C22×C4×C29—21no—
129C22×C4×C29—21no—
130C22×C4×C29—21no—
131C22×C4×C29—21no—
132C22×C4×C29—81no—
133C22×C4×C29—81no—
134C22×C4×C29C2×D411yescharacteristic
135C22×C4×C29C2×D411yescharacteristic
136C22×C4×C29C2×D411yescharacteristic
137C22×C4×C29C2×D411yescharacteristic
138C22×C4×C29C2×D411yescharacteristic
139C22×C4×C29C2×D411yescharacteristic
140C22×C4×C29C2411yescharacteristic
141C2×C8×C29—21no—
142C2×C8×C29—21no—
143C2×C8×C29—21no—
144C2×C8×C29—21no—
145C2×C8×C29—21no—
146C2×C8×C29—21no—
147C2×C8×C29—21no—
148C2×C8×C29—21no—
149C2×C8×C29—21no—
150C2×C8×C29—21no—
151C2×C8×C29—21no—
152C2×C8×C29—21no—
153C4⋊C4×C29—24no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—21no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—21no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—21no—
160C4⋊C4×C29—21no—
161C4⋊C4×C29—21no—
162C4⋊C4×C29—21no—
163C4⋊C4×C29—21no—
164C4⋊C4×C29—21no—
165C4⋊C4×C29—81no—
166C4⋊C4×C29—81no—
167C4⋊C4×C29—81no—
168C4⋊C4×C29—81no—
169C4⋊C4×C29#4112yes—
170C4⋊C4×C29#4112yes—
171C4⋊C4×C29#4112yes—
172C22⋊C4×C29—24no—
173C22⋊C4×C29—81no—
174C22⋊C4×C29—81no—
175C22⋊C4×C29—81no—
176C22⋊C4×C29—81no—
177C42×C29—21no—
178C42×C29—21no—
179C42×C29—21no—
180C42×C29—21no—
181C42×C29—21no—
182C42×C29—21no—
183C42×C29—81no—
184C42×C29—81no—
185C42×C29—81no—
186#29401C2911yesmaximal, characteristic, direct product factor, Sylow
187C23×C29—22no—
188C23×C29—41no—
189C23×C29—41no—
190C23×C29—41no—
191C23×C29—41no—
192C23×C29—41no—
193C23×C29—41no—
194C23×C29C22×D411yescharacteristic
195Q8×C29—84no—
196D4×C29—22no—
197D4×C29—22no—
198D4×C29—41no—
199D4×C29—41no—
200C2×C4×C29—21no—
201C2×C4×C29—21no—
202C2×C4×C29—21no—
203C2×C4×C29—21no—
204C2×C4×C29—22no—
205C2×C4×C29—22no—
206C2×C4×C29—22no—
207C2×C4×C29—21no—
208C2×C4×C29—21no—
209C2×C4×C29—21no—
210C2×C4×C29—21no—
211C2×C4×C29—21no—
212C2×C4×C29—21no—
213C2×C4×C29—21no—
214C2×C4×C29—21no—
215C2×C4×C29—21no—
216C2×C4×C29—21no—
217C2×C4×C29—21no—
218C2×C4×C29—21no—
219C2×C4×C29—21no—
220C2×C4×C29—21no—
221C2×C4×C29—41no—
222C2×C4×C29—41no—
223C2×C4×C29—41no—
224C2×C4×C29—41no—
225C2×C4×C29—41no—
226C2×C4×C29—41no—
227C2×C4×C29—41no—
228C2×C4×C29—41no—
229C2×C4×C29—41no—
230C2×C4×C29—41no—
231C2×C4×C29—41no—
232C2×C4×C29—41no—
233C2×C4×C29—41no—
234C2×C4×C29—41no—
235C2×C4×C29—41no—
236C2×C4×C29—41no—
237C2×C4×C29—41no—
238C2×C4×C29—41no—
239C2×C4×C29—84no—
240C2×C4×C29C2×#4111yescharacteristic
241C2×C4×C29C2×#4111yescharacteristic
242C2×C4×C29C2×#4111yescharacteristic
243C2×C4×C29C2×#4111yescharacteristic
244C2×C4×C292−1+411yescharacteristic
245C2×C4×C292−1+411yescharacteristic
246C8×C29—41no—
247C8×C29—41no—
248C8×C29—41no—
249C8×C29—41no—
250#2331C2×C2911yescharacteristic, complemented
251#2319C2×C2911yescharacteristic
252#2085C2×C2911yescharacteristic, complemented
253#2073C2×C2911yescharacteristic
254#2057C2×C2911yescharacteristic, complemented
255#2023C2×C2911yescharacteristic
256#1925C2×C2911yescharacteristic
257#1925C2×C2911yescharacteristic
258#1921C2×C2911yescharacteristic, complemented
259#1921C2×C2911yescharacteristic, complemented
260#1919C2×C2911yescharacteristic, complemented
261#1918C2×C2911yescharacteristic, complemented
262#1864C2×C2911yescharacteristic
263#1862C2×C2911yescharacteristic
264#1840C2×C2911yescharacteristic, complemented
265C22×C29—42no—
266C22×C29—42no—
267C22×C29—42no—
268C22×C29—81no—
269C22×C29—81no—
270C22×C29—81no—
271C22×C29—81no—
272C22×C29#52511yescharacteristic
273C22×C29#52511yescharacteristic
274C22×C29#53611yescharacteristic
275C22×C29#57611yescharacteristic
276C22×C29#57611yescharacteristic
277C22×C29#57711yescharacteristic
278C22×C29#57811yescharacteristic
279C4×C29—41no—
280C4×C29—42no—
281C4×C29—41no—
282C4×C29—41no—
283C4×C29—42no—
284C4×C29—42no—
285C4×C29—41no—
286C4×C29—41no—
287C4×C29—41no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29—81no—
291C4×C29—81no—
292C4×C29#55211yescharacteristic
293C4×C29#55211yescharacteristic
294C4×C29#55611yescharacteristic
295C4×C29#55611yescharacteristic
296C2×C4⋊Q8C22×C2911yescharacteristic
297C2×C4×D4C22×C2911yescharacteristic
298C2×#107C22×C2911yescharacteristic
299C2×#107C22×C2911yescharacteristic
300C2×#107C22×C2911yescharacteristic
301C2×#106C22×C2911yescharacteristic
302C2×#102C22×C2911yescharacteristic
303C2×#102C22×C2911yescharacteristic
304C2×#102C22×C2911yescharacteristic
305C2×#102C22×C2911yescharacteristic
306#391—21no—
307#391—21no—
308#390C22×C2911yescharacteristic
309#390C22×C2911yescharacteristic
310#389C22×C2911yescharacteristic
311#389C22×C2911yescharacteristic
312#389C22×C2911yescharacteristic
313#389C22×C2911yescharacteristic
314#388—21no—
315#388—21no—
316#387—21no—
317#387—21no—
318#382C22×C2911yescharacteristic
319#381—21no—
320#380—21no—
321C4×C4⋊C4C22×C2911yescharacteristic
322C4×C4⋊C4C22×C2911yescharacteristic
323C4×C4⋊C4C22×C2911yescharacteristic
324#376C22×C2911yescharacteristic
325#340C22×C2911yescharacteristic
326#340C22×C2911yescharacteristic
327#340C22×C2911yescharacteristic
328#340C22×C2911yescharacteristic
329#340C22×C2911yescharacteristic
330#340C22×C2911yescharacteristic
331#340C22×C2911yescharacteristic
332#340C22×C2911yescharacteristic
333#336C22×C2911yescharacteristic
334#336C22×C2911yescharacteristic
335#336C22×C2911yescharacteristic
336#336C22×C2911yescharacteristic
337#336C22×C2911yescharacteristic
338#336C22×C2911yescharacteristic
339C2×C29—82no—
340C2×C29#259911yescharacteristic
341C2×C29#311811yescharacteristic
342C2×C29#312111yescharacteristic
343C2×C29#312211yescharacteristic
344C2×C29#312411yescharacteristic
345C2×C29#324111yescharacteristic
346C2×C29#324311yescharacteristic
347C22×Q8—21no—
348C22×D4C23×C2911yescharacteristic
349C23×C4—21no—
350C22×C8C23×C2911yescharacteristic
351C22×C8C23×C2911yescharacteristic
352C22×C8C23×C2911yescharacteristic
353C22×C8C23×C2911yescharacteristic
354C4⋊Q8—22no—
355C4⋊Q8—22no—
356C4×D4—22no—
357C4×D4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C23×C2911yescharacteristic
364C2×C4⋊C4C23×C2911yescharacteristic
365C2×C4⋊C4C23×C2911yescharacteristic
366C2×C4⋊C4C23×C2911yescharacteristic
367C2×C4⋊C4C23×C2911yescharacteristic
368C2×C4⋊C4C23×C2911yescharacteristic
369C2×C4⋊C4C23×C2911yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C42—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42C23×C2911yescharacteristic
379C2×C42C23×C2911yescharacteristic
380C2×C42C23×C2911yescharacteristic
381#107—22no—
382#107—22no—
383#107—22no—
384#106—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95D4×C2911yescharacteristic
399#95D4×C2911yescharacteristic
400#95D4×C2911yescharacteristic
401#95D4×C2911yescharacteristic
402C29#2940111yescharacteristic, direct product factor, Sylow
403C24—21no—
404C2×Q8—24no—
405C2×Q8—81no—
406C2×Q8—81no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4#41×C2912yes—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4C2×D4×C2911yescharacteristic
424C22×C4C2×D4×C2911yescharacteristic
425C22×C4C2×D4×C2911yescharacteristic
426C22×C4C2×D4×C2911yescharacteristic
427C22×C4C2×D4×C2911yescharacteristic
428C22×C4C2×D4×C2911yescharacteristic
429C22×C4C24×C2911yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—81no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4#41×C2912yes—
459C4⋊C4#41×C2912yes—
460C4⋊C4#41×C2912yes—
461C22⋊C4—24no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—81no—
473C42—81no—
474C42—81no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23C22×D4×C2911yescharacteristic
483Q8—84no—
484D4—22no—
485D4—22no—
486D4—41no—
487D4—41no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—84no—
528C2×C4C2×#41×C2911yescharacteristic
529C2×C4C2×#41×C2911yescharacteristic
530C2×C4C2×#41×C2911yescharacteristic
531C2×C4C2×#41×C2911yescharacteristic
532C2×C4C29×2−1+411yescharacteristic
533C2×C4C29×2−1+411yescharacteristic
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22C29×#52511yescharacteristic
546C22C29×#52511yescharacteristic
547C22C29×#53611yescharacteristic
548C22C29×#57611yescharacteristic
549C22C29×#57611yescharacteristic
550C22C29×#57711yescharacteristic
551C22C29×#57811yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—42no—
556C4—41no—
557C4—41no—
558C4—42no—
559C4—42no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4C29×#55211yescharacteristic
566C4C29×#55211yescharacteristic
567C4C29×#55611yescharacteristic
568C4C29×#55611yescharacteristic
569C2—82no—
570C2C29×#259911yescharacteristic
571C2C29×#311811yescharacteristic
572C2C29×#312111yescharacteristic
573C2C29×#312211yescharacteristic
574C2C29×#312411yescharacteristic
575C2C29×#324111yescharacteristic
576C2C29×#324311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D4×C29C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C29×#376 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2331C2semidirect
3. C29×#2085C2semidirect
5. C29×#2057C2semidirect
9. C29×#1921C2semidirect
10. C29×#1921C2semidirect
11. C29×#1919C2semidirect
12. C29×#1918C2semidirect
15. C29×#1840C2semidirect
186. #29401C29direct (N × H)
250. #2331C2×C29semidirect
252. #2085C2×C29semidirect
254. #2057C2×C29semidirect
258. #1921C2×C29semidirect
259. #1921C2×C29semidirect
260. #1919C2×C29semidirect
261. #1918C2×C29semidirect
264. #1840C2×C29semidirect
402. C29#29401direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#23312
C29×#23192
C29×#20852
C29×#20732
C29×#20572
C29×#20232
C29×#19252
C29×#19212
C29×#19192
C29×#19182
C29×#18642
C29×#18622
C29×#18402
#2940129