Finite Group Databasebeta

← C29×#19378 #20314278

Subgroups — C29×#19378 #20314278

Order 7424.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3252C211yesmaximal, characteristic
2C29×#3218C211yesmaximal, characteristic
3C29×#3165C211yesmaximal, characteristic, complemented
4C29×#2969C211yesmaximal, characteristic
5C29×#1694C211yesmaximal, characteristic, complemented
6C29×#1693C211yesmaximal, characteristic, complemented
7C29×#1692C211yesmaximal, characteristic, complemented
8C29×#1691C211yesmaximal, characteristic, complemented
9C29×#1674C211yesmaximal, characteristic, complemented
10C29×#1673C211yesmaximal, characteristic, complemented
11C29×#1672C211yesmaximal, characteristic, complemented
12C29×#1671C211yesmaximal, characteristic, complemented
13C29×#1569C211yesmaximal, characteristic, complemented
14C29×#1554C211yesmaximal, characteristic, complemented
15C29×#1546C211yesmaximal, characteristic, complemented
16C29×#533C2211yescharacteristic
17C2×C29×C4⋊Q8C2211yescharacteristic
18C29×#529C2211yescharacteristic
19C29×#501—21no—
20C29×#501—21no—
21C29×#500C2211yescharacteristic
22C29×#500C2211yescharacteristic
23C29×#498C2211yescharacteristic
24C29×#498C2211yescharacteristic
25C29×#497—21no—
26C29×#491—21no—
27C29×#479—21no—
28C29×#477C2211yescharacteristic
29C29×#476C2211yescharacteristic
30C29×#470—21no—
31C29×#468—21no—
32C29×#464—21no—
33C29×#462C2211yescharacteristic
34C29×#462C2211yescharacteristic
35C29×#462C2211yescharacteristic
36C29×#461C2211yescharacteristic
37C29×#461C2211yescharacteristic
38C29×#461C2211yescharacteristic
39C29×#451—21no—
40C29×#448—21no—
41C29×#446C2211yescharacteristic
42C8×Q8×C29C2211yescharacteristic
43C29×#436—21no—
44C29×#436C2211yescharacteristic
45C29×#435—21no—
46C8×D4×C29C2211yescharacteristic
47C29×#433—21no—
48C29×#432C2211yescharacteristic
49C29×#431C2211yescharacteristic
50C29×#428—21no—
51C29×#428—21no—
52C29×#423C2211yescharacteristic
53C29×#405—21no—
54C4×M16×C29C2211yescharacteristic
55C29×#335C2211yescharacteristic
56C29×#335C2211yescharacteristic
57C29×#334C2211yescharacteristic
58C29×#334C2211yescharacteristic
59C29×#333C2211yescharacteristic
60C29×#333C2211yescharacteristic
61C29×#332C2211yescharacteristic
62C29×#332C2211yescharacteristic
63C29×#332C2211yescharacteristic
64C29×#332C2211yescharacteristic
65C29×#332C2211yescharacteristic
66C29×#332C2211yescharacteristic
67C22×Q8×C29—21no—
68C2×Q16×C29—21no—
69C2×Q16×C29—21no—
70C2×Q16×C29—21no—
71C2×SD16×C29—21no—
72C2×SD16×C29—21no—
73C2×SD16×C29—21no—
74C2×M16×C29—21no—
75C2×M16×C29—21no—
76C2×M16×C29D411yescharacteristic
77C2×M16×C29D411yescharacteristic
78C22×C8×C29—21no—
79C29×C4⋊Q8—21no—
80C29×C4⋊Q8—21no—
81C29×C4⋊Q8—21no—
82C29×C4⋊Q8C2311yescharacteristic
83C29×C4⋊Q8C2311yescharacteristic
84C29×C4⋊Q8C2311yescharacteristic
85C29×C4⋊Q8C2311yescharacteristic
86C29×#126—21no—
87C29×#125—21no—
88C29×#125D411yescharacteristic
89C29×#124D411yescharacteristic
90C29×#123—21no—
91C29×C22⋊Q8—21no—
92C29×C22⋊Q8—21no—
93C29×C22⋊Q8D411yescharacteristic
94C29×#121D411yescharacteristic
95C4×Q8×C29—21no—
96C4×Q8×C29—21no—
97C4×Q8×C29C2311yescharacteristic
98C4×D4×C29—21no—
99C4×D4×C29C2311yescharacteristic
100C29×#117—21no—
101C29×#117—21no—
102C2×C4⋊C4×C29—21no—
103C2×C4⋊C4×C29—21no—
104C2×C42×C29C2311yescharacteristic
105C29×#107—21no—
106C29×#107—21no—
107C29×#107—21no—
108C29×#107—21no—
109C29×#107—21no—
110C29×#106—21no—
111C29×#106—21no—
112C29×#106—21no—
113C29×#106—21no—
114C29×#106—21no—
115C29×C4⋊C8—21no—
116C29×C4⋊C8—21no—
117C29×C4⋊C8—21no—
118C29×C4⋊C8C2311yescharacteristic
119C29×C4⋊C8C2311yescharacteristic
120C29×C4⋊C8C2311yescharacteristic
121C29×C4⋊C8C2311yescharacteristic
122C29×C4⋊C8C2311yescharacteristic
123C29×C4⋊C8C2311yescharacteristic
124C29×#103—21no—
125C29×#103—21no—
126C29×#103—21no—
127C29×#103—21no—
128C29×#103—21no—
129C29×#103—21no—
130C29×#103—21no—
131C29×#102—21no—
132C29×C22⋊C8—21no—
133C29×C22⋊C8—21no—
134C29×C22⋊C8—21no—
135C29×C22⋊C8—21no—
136C29×#97—21no—
137C29×#97—21no—
138C29×#97D411yescharacteristic
139C29×#97D411yescharacteristic
140C4×C8×C29—21no—
141C4×C8×C29—21no—
142C4×C8×C29C2311yescharacteristic
143C4×C8×C29C2311yescharacteristic
144C2×Q8×C29—21no—
145C2×Q8×C29—21no—
146C2×Q8×C29—21no—
147C2×Q8×C29—21no—
148C2×Q8×C29—41no—
149C2×Q8×C29—81no—
150C2×Q8×C29—81no—
151C2×Q8×C29C2×D411yescharacteristic
152C2×D4×C29—21no—
153C2×D4×C29C2×D411yescharacteristic
154C22×C4×C29—21no—
155C22×C4×C29—41no—
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29#4111yescharacteristic
159Q16×C29—81no—
160Q16×C29—81no—
161Q16×C29—81no—
162SD16×C29—81no—
163SD16×C29—81no—
164SD16×C29—81no—
165M16×C29—22no—
166M16×C29—22no—
167M16×C29—42no—
168M16×C29—81no—
169C2×C8×C29—21no—
170C2×C8×C29—21no—
171C2×C8×C29—21no—
172C2×C8×C29—21no—
173C2×C8×C29—21no—
174C2×C8×C29—21no—
175C2×C8×C29—42no—
176C2×C8×C29C2×D411yescharacteristic
177C2×C8×C29C2×D411yescharacteristic
178C2×C8×C29C2×D411yescharacteristic
179C2×C8×C29C2×D411yescharacteristic
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—21no—
184C4⋊C4×C29—21no—
185C4⋊C4×C29—21no—
186C4⋊C4×C29—21no—
187C4⋊C4×C29—21no—
188C4⋊C4×C29—21no—
189C4⋊C4×C29—21no—
190C4⋊C4×C29—21no—
191C4⋊C4×C29—21no—
192C4⋊C4×C29—41no—
193C4⋊C4×C29—41no—
194C4⋊C4×C29—41no—
195C4⋊C4×C29—41no—
196C4⋊C4×C29C2×D411yescharacteristic
197C4⋊C4×C29C2×D411yescharacteristic
198C22⋊C4×C29—21no—
199C22⋊C4×C29—21no—
200C22⋊C4×C29—21no—
201C22⋊C4×C29—21no—
202C22⋊C4×C29—21no—
203C22⋊C4×C29—41no—
204C42×C29—21no—
205C42×C29—41no—
206C42×C29C2×D411yescharacteristic
207C42×C29C2×D411yescharacteristic
208C42×C29#4111yescharacteristic
209C42×C29C2411yescharacteristic
210#19378C2911yesmaximal, characteristic, direct product factor, Sylow
211C23×C29—21no—
212C23×C29#12111yescharacteristic
213Q8×C29—21no—
214Q8×C29—21no—
215Q8×C29—41no—
216Q8×C29—41no—
217Q8×C29—41no—
218Q8×C29—41no—
219Q8×C29—41no—
220Q8×C29—41no—
221Q8×C29—81no—
222Q8×C29—82no—
223D4×C29—21no—
224D4×C29—21no—
225D4×C29—81no—
226C2×C4×C29—21no—
227C2×C4×C29—21no—
228C2×C4×C29—21no—
229C2×C4×C29—21no—
230C2×C4×C29—21no—
231C2×C4×C29—21no—
232C2×C4×C29—21no—
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—41no—
240C2×C4×C29—82no—
241C2×C4×C29#12111yescharacteristic
242C2×C4×C29#12111yescharacteristic
243C2×C4×C29#12111yescharacteristic
244C2×C4×C29C22×D411yescharacteristic
245C2×C4×C29C22×D411yescharacteristic
246C2×C4×C29C2×#4111yescharacteristic
247C8×C29—21no—
248C8×C29—21no—
249C8×C29—41no—
250C8×C29—41no—
251C8×C29—41no—
252C8×C29—41no—
253C8×C29—41no—
254C8×C29—41no—
255C8×C29#13712yes—
256C8×C29#13712yes—
257#3252C2×C2911yescharacteristic
258#3218C2×C2911yescharacteristic
259#3165C2×C2911yescharacteristic, complemented
260#2969C2×C2911yescharacteristic
261#1694C2×C2911yescharacteristic, complemented
262#1693C2×C2911yescharacteristic, complemented
263#1692C2×C2911yescharacteristic, complemented
264#1691C2×C2911yescharacteristic, complemented
265#1674C2×C2911yescharacteristic, complemented
266#1673C2×C2911yescharacteristic, complemented
267#1672C2×C2911yescharacteristic, complemented
268#1671C2×C2911yescharacteristic, complemented
269#1569C2×C2911yescharacteristic, complemented
270#1554C2×C2911yescharacteristic, complemented
271#1546C2×C2911yescharacteristic, complemented
272C22×C29—21no—
273C22×C29—21no—
274C22×C29—21no—
275C22×C29—41no—
276C22×C29—41no—
277C22×C29—41no—
278C22×C29C2×#12111yescharacteristic
279C4×C29—21no—
280C4×C29—21no—
281C4×C29—21no—
282C4×C29—21no—
283C4×C29—41no—
284C4×C29—41no—
285C4×C29—41no—
286C4×C29—81no—
287C4×C29—81no—
288C4×C29—81no—
289C4×C29—81no—
290C4×C29C2×#13711yescharacteristic
291C4×C29C2×#13711yescharacteristic
292C4×C29#57611yescharacteristic
293C4×C29#57711yescharacteristic
294#533C22×C2911yescharacteristic
295C2×C4⋊Q8C22×C2911yescharacteristic
296#529C22×C2911yescharacteristic
297#501—21no—
298#501—21no—
299#500C22×C2911yescharacteristic
300#500C22×C2911yescharacteristic
301#498C22×C2911yescharacteristic
302#498C22×C2911yescharacteristic
303#497—21no—
304#491—21no—
305#479—21no—
306#477C22×C2911yescharacteristic
307#476C22×C2911yescharacteristic
308#470—21no—
309#468—21no—
310#464—21no—
311#462C22×C2911yescharacteristic
312#462C22×C2911yescharacteristic
313#462C22×C2911yescharacteristic
314#461C22×C2911yescharacteristic
315#461C22×C2911yescharacteristic
316#461C22×C2911yescharacteristic
317#451—21no—
318#448—21no—
319#446C22×C2911yescharacteristic
320C8×Q8C22×C2911yescharacteristic
321#436—21no—
322#436C22×C2911yescharacteristic
323#435—21no—
324C8×D4C22×C2911yescharacteristic
325#433—21no—
326#432C22×C2911yescharacteristic
327#431C22×C2911yescharacteristic
328#428—21no—
329#428—21no—
330#423C22×C2911yescharacteristic
331#405—21no—
332C4×M16C22×C2911yescharacteristic
333#335C22×C2911yescharacteristic
334#335C22×C2911yescharacteristic
335#334C22×C2911yescharacteristic
336#334C22×C2911yescharacteristic
337#333C22×C2911yescharacteristic
338#333C22×C2911yescharacteristic
339#332C22×C2911yescharacteristic
340#332C22×C2911yescharacteristic
341#332C22×C2911yescharacteristic
342#332C22×C2911yescharacteristic
343#332C22×C2911yescharacteristic
344#332C22×C2911yescharacteristic
345C2×C29—41no—
346C2×C29—81no—
347C2×C29#303911yescharacteristic
348C2×C29#306211yescharacteristic
349C2×C29#306911yescharacteristic
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16D4×C2911yescharacteristic
360C2×M16D4×C2911yescharacteristic
361C22×C8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8C23×C2911yescharacteristic
366C4⋊Q8C23×C2911yescharacteristic
367C4⋊Q8C23×C2911yescharacteristic
368C4⋊Q8C23×C2911yescharacteristic
369#126—21no—
370#125—21no—
371#125D4×C2911yescharacteristic
372#124D4×C2911yescharacteristic
373#123—21no—
374C22⋊Q8—21no—
375C22⋊Q8—21no—
376C22⋊Q8D4×C2911yescharacteristic
377#121D4×C2911yescharacteristic
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8C23×C2911yescharacteristic
381C4×D4—21no—
382C4×D4C23×C2911yescharacteristic
383#117—21no—
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C23×C2911yescharacteristic
388#107—21no—
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C2911yescharacteristic
402C4⋊C8C23×C2911yescharacteristic
403C4⋊C8C23×C2911yescharacteristic
404C4⋊C8C23×C2911yescharacteristic
405C4⋊C8C23×C2911yescharacteristic
406C4⋊C8C23×C2911yescharacteristic
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415C22⋊C8—21no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—21no—
419#97—21no—
420#97—21no—
421#97D4×C2911yescharacteristic
422#97D4×C2911yescharacteristic
423C4×C8—21no—
424C4×C8—21no—
425C4×C8C23×C2911yescharacteristic
426C4×C8C23×C2911yescharacteristic
427C29#1937811yescharacteristic, direct product factor, Sylow
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×Q8C2×D4×C2911yescharacteristic
436C2×D4—21no—
437C2×D4C2×D4×C2911yescharacteristic
438C22×C4—21no—
439C22×C4—41no—
440C22×C4C2×D4×C2911yescharacteristic
441C22×C4C2×D4×C2911yescharacteristic
442C22×C4#41×C2911yescharacteristic
443Q16—81no—
444Q16—81no—
445Q16—81no—
446SD16—81no—
447SD16—81no—
448SD16—81no—
449M16—22no—
450M16—22no—
451M16—42no—
452M16—81no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—42no—
460C2×C8C2×D4×C2911yescharacteristic
461C2×C8C2×D4×C2911yescharacteristic
462C2×C8C2×D4×C2911yescharacteristic
463C2×C8C2×D4×C2911yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4C2×D4×C2911yescharacteristic
481C4⋊C4C2×D4×C2911yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—41no—
488C42—21no—
489C42—41no—
490C42C2×D4×C2911yescharacteristic
491C42C2×D4×C2911yescharacteristic
492C42#41×C2911yescharacteristic
493C42C24×C2911yescharacteristic
494C23—21no—
495C23C29×#12111yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—82no—
506D4—21no—
507D4—21no—
508D4—81no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—82no—
524C2×C4C29×#12111yescharacteristic
525C2×C4C29×#12111yescharacteristic
526C2×C4C29×#12111yescharacteristic
527C2×C4C22×D4×C2911yescharacteristic
528C2×C4C22×D4×C2911yescharacteristic
529C2×C4C2×#41×C2911yescharacteristic
530C8—21no—
531C8—21no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8C29×#13712yes—
539C8C29×#13712yes—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22C2×C29×#12111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—81no—
557C4—81no—
558C4C2×C29×#13711yescharacteristic
559C4C2×C29×#13711yescharacteristic
560C4C29×#57611yescharacteristic
561C4C29×#57711yescharacteristic
562C2—41no—
563C2—81no—
564C2C29×#303911yescharacteristic
565C2C29×#306211yescharacteristic
566C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#121D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
3. C29×#3165C2semidirect
5. C29×#1694C2semidirect
6. C29×#1693C2semidirect
7. C29×#1692C2semidirect
8. C29×#1691C2semidirect
9. C29×#1674C2semidirect
10. C29×#1673C2semidirect
11. C29×#1672C2semidirect
12. C29×#1671C2semidirect
13. C29×#1569C2semidirect
14. C29×#1554C2semidirect
15. C29×#1546C2semidirect
210. #19378C29direct (N × H)
259. #3165C2×C29semidirect
261. #1694C2×C29semidirect
262. #1693C2×C29semidirect
263. #1692C2×C29semidirect
264. #1691C2×C29semidirect
265. #1674C2×C29semidirect
266. #1673C2×C29semidirect
267. #1672C2×C29semidirect
268. #1671C2×C29semidirect
269. #1569C2×C29semidirect
270. #1554C2×C29semidirect
271. #1546C2×C29semidirect
427. C29#19378direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32522
C29×#32182
C29×#31652
C29×#29692
C29×#16942
C29×#16932
C29×#16922
C29×#16912
C29×#16742
C29×#16732
C29×#16722
C29×#16712
C29×#15692
C29×#15542
C29×#15462
#1937829