Finite Group Databasebeta

← C29×#19408 #20314308

Subgroups — C29×#19408 #20314308

Order 7424.

674 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3206C211yesmaximal, characteristic, complemented
2C29×#3079C211yesmaximal, characteristic, complemented
3C29×#3035C211yesmaximal, characteristic
4C29×#2988C211yesmaximal, characteristic, complemented
5C29×#1680C212yesmaximal, complemented
6C29×#1679C212yesmaximal, complemented
7C29×#1666C212yesmaximal, complemented
8C29×#1665C212yesmaximal, complemented
9C29×#1570C211yesmaximal, characteristic, complemented
10C29×#1547C211yesmaximal, characteristic, complemented
11C2×C29×#332C211yesmaximal, characteristic, complemented
12C2×C29×#135—21no—
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#492C2212yes—
17C29×#487C2212yes—
18C29×#477—21no—
19C29×#476—21no—
20C29×#475C2212yes—
21C29×#474C2212yes—
22C29×#464—21no—
23C29×#463—21no—
24C29×#462C2211yescharacteristic
25C29×#461—21no—
26C29×#461—21no—
27C29×#461C2211yescharacteristic
28C29×#460C2211yescharacteristic
29C29×#459C2211yescharacteristic
30C29×#448—22no—
31C8×Q8×C29C2212yes—
32C8×D4×C29—22no—
33C8×D4×C29C2212yes—
34C29×#431—21no—
35C29×#431C2211yescharacteristic
36C29×#428—21no—
37C29×#423C2211yescharacteristic
38C2×C29×C4⋊C8—21no—
39C2×C29×C4⋊C8C2211yescharacteristic
40C2×C29×C4⋊C8C2211yescharacteristic
41C29×#417—21no—
42C29×#416—21no—
43C29×#334C2212yes—
44C29×#334C2212yes—
45C29×#332C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29D411yescharacteristic
51C22×Q8×C29—21no—
52C29×#135—44no—
53C2×Q16×C29—21no—
54C2×SD16×C29—21no—
55C2×SD16×C29—21no—
56C2×SD16×C29—22no—
57C2×SD16×C29—22no—
58C2×D8×C29—21no—
59C2×M16×C29—21no—
60C22×C8×C29—21no—
61C22×C8×C29—21no—
62C22×C8×C29—22no—
63C29×C4⋊Q8—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8C2311yescharacteristic
67C29×C4⋊Q8C2312yes—
68C29×#127C2311yescharacteristic
69C29×#124—21no—
70C29×#121—21no—
71C29×#121—21no—
72C4×Q8×C29D411yescharacteristic
73C4×Q8×C29C2311yescharacteristic
74C4×D4×C29—21no—
75C4×D4×C29—21no—
76C4×D4×C29—21no—
77C4×D4×C29—21no—
78C4×D4×C29D411yescharacteristic
79C4×D4×C29C2311yescharacteristic
80C29×#117—21no—
81C29×#117D411yescharacteristic
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C42×C29—21no—
85C2×C42×C29C2311yescharacteristic
86C29×#107—22no—
87C29×#106—22no—
88C29×C4⋊C8—22no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8—21no—
91C29×C4⋊C8—21no—
92C29×C4⋊C8D411yescharacteristic
93C29×C4⋊C8D411yescharacteristic
94C29×C4⋊C8C2312yes—
95C29×C4⋊C8C2311yescharacteristic
96C29×C4⋊C8C2311yescharacteristic
97C29×C4⋊C8C2312yes—
98C29×#103—22no—
99C29×#103—22no—
100C29×#103—22no—
101C29×#103—21no—
102C29×#103—21no—
103C29×#102—22no—
104C29×#102—21no—
105C29×#102—21no—
106C29×C22⋊C8—22no—
107C29×C22⋊C8D412yes—
108C4×C8×C29—22no—
109C4×C8×C29C2312yes—
110#41×C29—22no—
111#41×C29—42no—
112#41×C29—42no—
113#41×C29SD1614yescomplemented
114C2×Q8×C29—21no—
115C2×Q8×C29—22no—
116C2×Q8×C29—41no—
117C2×Q8×C29—81no—
118C2×Q8×C29—81no—
119C2×Q8×C29C2×D411yescharacteristic
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—21no—
123C2×D4×C29—21no—
124C2×D4×C29—41no—
125C2×D4×C29C2×D411yescharacteristic
126C22×C4×C29—21no—
127C22×C4×C29—21no—
128C22×C4×C29—21no—
129C22×C4×C29—41no—
130C22×C4×C29—41no—
131C22×C4×C29C2×D411yescharacteristic
132C22×C4×C29C2×D411yescharacteristic
133C22×C4×C29#4111yescharacteristic
134Q16×C29—42no—
135SD16×C29—42no—
136SD16×C29—42no—
137SD16×C29—82no—
138SD16×C29—82no—
139D8×C29—42no—
140M16×C29—42no—
141C2×C8×C29—22no—
142C2×C8×C29—21no—
143C2×C8×C29—21no—
144C2×C8×C29—22no—
145C2×C8×C29—42no—
146C2×C8×C29—82no—
147C2×C8×C29—81no—
148C2×C8×C29C2×D412yes—
149C2×C8×C29C2×D412yes—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—22no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—22no—
155C4⋊C4×C29—21no—
156C4⋊C4×C29—41no—
157C4⋊C4×C29—41no—
158C4⋊C4×C29C2×D411yescharacteristic
159C4⋊C4×C29C2×D411yescharacteristic
160C22⋊C4×C29—21no—
161C22⋊C4×C29—21no—
162C22⋊C4×C29—21no—
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C42×C29—21no—
166C42×C29—21no—
167C42×C29—21no—
168C42×C29C2×D411yescharacteristic
169C42×C29C2×D411yescharacteristic
170C42×C29#4111yescharacteristic
171C42×C29C2411yescharacteristic
172#19408C2911yesmaximal, characteristic, direct product factor, Sylow
173C23×C29—21no—
174C23×C29—41no—
175C23×C29#12111yescharacteristic
176Q8×C29—21no—
177Q8×C29—41no—
178Q8×C29—41no—
179Q8×C29—42no—
180Q8×C29—42no—
181Q8×C29—82no—
182Q8×C29C2×SD1612yes—
183D4×C29—24no—
184D4×C29—21no—
185D4×C29—41no—
186D4×C29—41no—
187D4×C29—41no—
188D4×C29—41no—
189D4×C29—81no—
190D4×C29—82no—
191D4×C29C2×SD1612yes—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—24no—
196C2×C4×C29—21no—
197C2×C4×C29—21no—
198C2×C4×C29—41no—
199C2×C4×C29—41no—
200C2×C4×C29—41no—
201C2×C4×C29—41no—
202C2×C4×C29—42no—
203C2×C4×C29—81no—
204C2×C4×C29—82no—
205C2×C4×C29—82no—
206C2×C4×C29#12111yescharacteristic
207C2×C4×C29#12111yescharacteristic
208C2×C4×C29#12111yescharacteristic
209C2×C4×C29C2×SD1612yes—
210C2×C4×C29#13512yes—
211C2×C4×C29C22×D411yescharacteristic
212C2×C4×C29C22×D411yescharacteristic
213C2×C4×C29C2×#4111yescharacteristic
214C8×C29—22no—
215C8×C29—22no—
216C8×C29—41no—
217C8×C29—41no—
218C8×C29—42no—
219C8×C29—42no—
220#3206C2×C2911yescharacteristic, complemented
221#3079C2×C2911yescharacteristic, complemented
222#3035C2×C2911yescharacteristic
223#2988C2×C2911yescharacteristic, complemented
224#1680C2×C2912yescomplemented
225#1679C2×C2912yescomplemented
226#1666C2×C2912yescomplemented
227#1665C2×C2912yescomplemented
228#1570C2×C2911yescharacteristic, complemented
229#1547C2×C2911yescharacteristic, complemented
230C2×#332C2×C2911yescharacteristic, complemented
231C22×C29—21no—
232C22×C29—21no—
233C22×C29—22no—
234C22×C29—41no—
235C22×C29—41no—
236C22×C29—81no—
237C22×C29—81no—
238C22×C29—81no—
239C22×C29#46512yes—
240C22×C29C2×#12111yescharacteristic
241C4×C29—21no—
242C4×C29—22no—
243C4×C29—21no—
244C4×C29—21no—
245C4×C29—41no—
246C4×C29—41no—
247C4×C29—82no—
248C4×C29—81no—
249C4×C29#46512yes—
250C4×C29C22×SD1611yescharacteristic
251C4×C29C2×#13511yescharacteristic
252C4×C29#57611yescharacteristic
253C4×C29#57711yescharacteristic
254C2×#135—21no—
255#532C22×C2911yescharacteristic
256C2×C4⋊Q8C22×C2911yescharacteristic
257C4×#41C22×C2911yescharacteristic
258#492C22×C2912yes—
259#487C22×C2912yes—
260#477—21no—
261#476—21no—
262#475C22×C2912yes—
263#474C22×C2912yes—
264#464—21no—
265#463—21no—
266#462C22×C2911yescharacteristic
267#461—21no—
268#461—21no—
269#461C22×C2911yescharacteristic
270#460C22×C2911yescharacteristic
271#459C22×C2911yescharacteristic
272#448—22no—
273C8×Q8C22×C2912yes—
274C8×D4—22no—
275C8×D4C22×C2912yes—
276#431—21no—
277#431C22×C2911yescharacteristic
278#428—21no—
279#423C22×C2911yescharacteristic
280C2×C4⋊C8—21no—
281C2×C4⋊C8C22×C2911yescharacteristic
282C2×C4⋊C8C22×C2911yescharacteristic
283#417—21no—
284#416—21no—
285#334C22×C2912yes—
286#334C22×C2912yes—
287#332C22×C2912yes—
288#332C22×C2912yes—
289#332C22×C2912yes—
290#331C22×C2912yes—
291C2×C29—22no—
292C2×C29—42no—
293C2×C29—161no—
294C2×C29#304511yescharacteristic
295C2×C29C2×#46511yescharacteristic
296C2×C29#306911yescharacteristic
297C2×#41—21no—
298C2×#41D4×C2911yescharacteristic
299C22×Q8—21no—
300#135—44no—
301C2×Q16—21no—
302C2×SD16—21no—
303C2×SD16—21no—
304C2×SD16—22no—
305C2×SD16—22no—
306C2×D8—21no—
307C2×M16—21no—
308C22×C8—21no—
309C22×C8—21no—
310C22×C8—22no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8C23×C2912yes—
315C4⋊Q8C23×C2911yescharacteristic
316#127C23×C2911yescharacteristic
317#124—21no—
318#121—21no—
319#121—21no—
320C4×Q8D4×C2911yescharacteristic
321C4×Q8C23×C2911yescharacteristic
322C4×D4—21no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4D4×C2911yescharacteristic
327C4×D4C23×C2911yescharacteristic
328#117—21no—
329#117D4×C2911yescharacteristic
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C42—21no—
333C2×C42C23×C2911yescharacteristic
334#107—22no—
335#106—22no—
336C4⋊C8—22no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8—21no—
340C4⋊C8D4×C2911yescharacteristic
341C4⋊C8D4×C2911yescharacteristic
342C4⋊C8C23×C2912yes—
343C4⋊C8C23×C2912yes—
344C4⋊C8C23×C2911yescharacteristic
345C4⋊C8C23×C2911yescharacteristic
346#103—22no—
347#103—22no—
348#103—22no—
349#103—21no—
350#103—21no—
351#102—22no—
352#102—21no—
353#102—21no—
354C22⋊C8—22no—
355C22⋊C8D4×C2912yes—
356C4×C8—22no—
357C4×C8C23×C2912yes—
358C29#1940811yescharacteristic, direct product factor, Sylow
359#41—22no—
360#41—42no—
361#41—42no—
362#41SD16×C2914yescomplemented
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—41no—
366C2×Q8—81no—
367C2×Q8—81no—
368C2×Q8C2×D4×C2911yescharacteristic
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4C2×D4×C2911yescharacteristic
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4C2×D4×C2911yescharacteristic
381C22×C4C2×D4×C2911yescharacteristic
382C22×C4#41×C2911yescharacteristic
383Q16—42no—
384SD16—42no—
385SD16—42no—
386SD16—82no—
387SD16—82no—
388D8—42no—
389M16—42no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—21no—
393C2×C8—21no—
394C2×C8—42no—
395C2×C8—82no—
396C2×C8—81no—
397C2×C8C2×D4×C2912yes—
398C2×C8C2×D4×C2912yes—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4C2×D4×C2911yescharacteristic
408C4⋊C4C2×D4×C2911yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42C2×D4×C2911yescharacteristic
418C42C2×D4×C2911yescharacteristic
419C42#41×C2911yescharacteristic
420C42C24×C2911yescharacteristic
421C23—21no—
422C23—41no—
423C23C29×#12111yescharacteristic
424Q8—21no—
425Q8—41no—
426Q8—41no—
427Q8—42no—
428Q8—42no—
429Q8—82no—
430Q8C2×SD16×C2912yes—
431D4—24no—
432D4—21no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4C2×SD16×C2912yes—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—81no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4C29×#12111yescharacteristic
455C2×C4C29×#12111yescharacteristic
456C2×C4C29×#12111yescharacteristic
457C2×C4C2×SD16×C2912yes—
458C2×C4C29×#13512yes—
459C2×C4C22×D4×C2911yescharacteristic
460C2×C4C22×D4×C2911yescharacteristic
461C2×C4C2×#41×C2911yescharacteristic
462C8—22no—
463C8—22no—
464C8—41no—
465C8—41no—
466C8—42no—
467C8—42no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22C29×#46512yes—
477C22C2×C29×#12111yescharacteristic
478C4—21no—
479C4—22no—
480C4—21no—
481C4—21no—
482C4—41no—
483C4—41no—
484C4—82no—
485C4—81no—
486C4C29×#46512yes—
487C4C22×SD16×C2911yescharacteristic
488C4C2×C29×#13511yescharacteristic
489C4C29×#57611yescharacteristic
490C4C29×#57711yescharacteristic
491C2—22no—
492C2—42no—
493C2—161no—
494C2C29×#304511yescharacteristic
495C2C2×C29×#46511yescharacteristic
496C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3035C2
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
1. C29×#3206C2semidirect
2. C29×#3079C2semidirect
4. C29×#2988C2semidirect
5. C29×#1680C2semidirect
6. C29×#1679C2semidirect
7. C29×#1666C2semidirect
8. C29×#1665C2semidirect
9. C29×#1570C2semidirect
10. C29×#1547C2semidirect
11. C2×C29×#332C2semidirect
113. #41×C29SD16semidirect
172. #19408C29direct (N × H)
220. #3206C2×C29semidirect
221. #3079C2×C29semidirect
223. #2988C2×C29semidirect
224. #1680C2×C29semidirect
225. #1679C2×C29semidirect
226. #1666C2×C29semidirect
227. #1665C2×C29semidirect
228. #1570C2×C29semidirect
229. #1547C2×C29semidirect
230. C2×#332C2×C29semidirect
358. C29#19408direct (N × H)
362. #41SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#32062
C29×#30792
C29×#30352
C29×#29882
C29×#16802
C29×#16792
C29×#16662
C29×#16652
C29×#15702
C29×#15472
C2×C29×#3322
#1940829