Finite Group Databasebeta

← C29×#19490 #20314390

Subgroups — C29×#19490 #20314390

Order 7424.

624 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3230C211yesmaximal, characteristic, complemented
2C29×#3107C211yesmaximal, characteristic
3C29×#3039C211yesmaximal, characteristic
4C29×#2990C211yesmaximal, characteristic
5C29×#1700C212yesmaximal, complemented
6C29×#1694C212yesmaximal, complemented
7C29×#1679C212yesmaximal, complemented
8C29×#1673C212yesmaximal, complemented
9C29×#1574C211yesmaximal, characteristic, complemented
10C29×#1561C211yesmaximal, characteristic, complemented
11C29×#1549C211yesmaximal, characteristic, complemented
12C2×C29×#137—21no—
13C29×#533C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C4×#41×C29C2211yescharacteristic
16C29×#500C2212yes—
17C29×#487C2212yes—
18C29×#485—21no—
19C29×#484—22no—
20C29×#477—21no—
21C29×#477—21no—
22C29×#475C2211yescharacteristic
23C29×#474C2211yescharacteristic
24C29×#462—21no—
25C29×#462C2211yescharacteristic
26C29×#462C2212yes—
27C29×#461—21no—
28C29×#461C2211yescharacteristic
29C29×#461C2212yes—
30C29×#452—21no—
31C29×#446C2212yes—
32C4×Q16×C29—21no—
33C4×SD16×C29—21no—
34C29×#435—22no—
35C8×D4×C29C2212yes—
36C29×#432—21no—
37C29×#431C2211yescharacteristic
38C29×#431C2211yescharacteristic
39C29×#423C2211yescharacteristic
40C29×#423C2211yescharacteristic
41C2×C29×C4⋊C8—21no—
42C29×#419—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#332C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#332C2212yes—
49C2×#41×C29D411yescharacteristic
50C22×Q8×C29—21no—
51C29×#137—44no—
52C2×Q16×C29—21no—
53C2×Q16×C29—22no—
54C2×SD16×C29—21no—
55C2×SD16×C29—22no—
56C2×M16×C29—21no—
57C2×M16×C29—21no—
58C22×C8×C29—22no—
59C29×C4⋊Q8—21no—
60C29×C4⋊Q8—21no—
61C29×C4⋊Q8—21no—
62C29×C4⋊Q8C2312yes—
63C29×C4⋊Q8C2311yescharacteristic
64C29×C4⋊Q8C2311yescharacteristic
65C29×#125—21no—
66C29×C22⋊Q8—21no—
67C29×C22⋊Q8—21no—
68C4×Q8×C29—21no—
69C4×Q8×C29—21no—
70C4×Q8×C29D411yescharacteristic
71C4×Q8×C29C2311yescharacteristic
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C4×D4×C29D411yescharacteristic
75C4×D4×C29C2311yescharacteristic
76C29×#117—21no—
77C29×#117—21no—
78C29×#117D411yescharacteristic
79C2×C4⋊C4×C29—21no—
80C2×C4⋊C4×C29—21no—
81C2×C42×C29—21no—
82C2×C42×C29C2311yescharacteristic
83C29×#107—22no—
84C29×#107—22no—
85C29×#107—21no—
86C29×#106—21no—
87C29×C4⋊C8—22no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8D411yescharacteristic
91C29×C4⋊C8D411yescharacteristic
92C29×C4⋊C8C2311yescharacteristic
93C29×C4⋊C8C2311yescharacteristic
94C29×C4⋊C8C2312yes—
95C29×C4⋊C8C2312yes—
96C29×#103—21no—
97C29×#103—22no—
98C29×#103—22no—
99C29×#103—21no—
100C29×#103—21no—
101C29×#103—22no—
102C29×#103—22no—
103C29×#102—21no—
104C29×C22⋊C8—21no—
105C29×C22⋊C8—22no—
106C29×C22⋊C8D412yes—
107C29×#97—22no—
108C4×C8×C29—21no—
109C4×C8×C29C2312yes—
110#41×C29—22no—
111#41×C29—41no—
112C2×Q8×C29—21no—
113C2×Q8×C29—21no—
114C2×Q8×C29—22no—
115C2×Q8×C29—42no—
116C2×Q8×C29—42no—
117C2×Q8×C29—41no—
118C2×Q8×C29C2×D411yescharacteristic
119C2×D4×C29—21no—
120C2×D4×C29C2×D411yescharacteristic
121C22×C4×C29—21no—
122C22×C4×C29—21no—
123C22×C4×C29—21no—
124C22×C4×C29—41no—
125C22×C4×C29C2×D411yescharacteristic
126C22×C4×C29C2×D411yescharacteristic
127C22×C4×C29#4111yescharacteristic
128Q16×C29—42no—
129Q16×C29—44no—
130SD16×C29—42no—
131SD16×C29—44no—
132M16×C29—42no—
133M16×C29—81no—
134C2×C8×C29—22no—
135C2×C8×C29—22no—
136C2×C8×C29—21no—
137C2×C8×C29—21no—
138C2×C8×C29—82no—
139C2×C8×C29C2×D412yes—
140C2×C8×C29C2×D412yes—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—22no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—22no—
147C4⋊C4×C29—21no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—41no—
150C4⋊C4×C29—41no—
151C4⋊C4×C29—41no—
152C4⋊C4×C29—41no—
153C4⋊C4×C29C2×D411yescharacteristic
154C4⋊C4×C29C2×D411yescharacteristic
155C22⋊C4×C29—21no—
156C22⋊C4×C29—21no—
157C22⋊C4×C29—21no—
158C22⋊C4×C29—41no—
159C42×C29—21no—
160C42×C29—21no—
161C42×C29—21no—
162C42×C29—41no—
163C42×C29C2×D411yescharacteristic
164C42×C29C2×D411yescharacteristic
165C42×C29#4111yescharacteristic
166C42×C29C2411yescharacteristic
167#19490C2911yesmaximal, characteristic, direct product factor, Sylow
168C23×C29—21no—
169C23×C29#12111yescharacteristic
170Q8×C29—21no—
171Q8×C29—21no—
172Q8×C29—42no—
173Q8×C29—41no—
174Q8×C29—41no—
175Q8×C29—42no—
176Q8×C29—41no—
177Q8×C29—41no—
178Q8×C29—82no—
179D4×C29—21no—
180D4×C29—42no—
181D4×C29AGL(1,ℤ/8)12yes—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—21no—
186C2×C4×C29—22no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—42no—
191C2×C4×C29—41no—
192C2×C4×C29—41no—
193C2×C4×C29—42no—
194C2×C4×C29—41no—
195C2×C4×C29—41no—
196C2×C4×C29—42no—
197C2×C4×C29—82no—
198C2×C4×C29#12111yescharacteristic
199C2×C4×C29#12111yescharacteristic
200C2×C4×C29#12111yescharacteristic
201C2×C4×C29C22×D411yescharacteristic
202C2×C4×C29C22×D411yescharacteristic
203C2×C4×C29C2×#4111yescharacteristic
204C8×C29—22no—
205C8×C29—22no—
206C8×C29—42no—
207C8×C29—41no—
208C8×C29—41no—
209C8×C29—42no—
210#3230C2×C2911yescharacteristic, complemented
211#3107C2×C2911yescharacteristic
212#3039C2×C2911yescharacteristic
213#2990C2×C2911yescharacteristic
214#1700C2×C2912yescomplemented
215#1694C2×C2912yescomplemented
216#1679C2×C2912yescomplemented
217#1673C2×C2912yescomplemented
218#1574C2×C2911yescharacteristic, complemented
219#1561C2×C2911yescharacteristic, complemented
220#1549C2×C2911yescharacteristic, complemented
221C22×C29—21no—
222C22×C29—21no—
223C22×C29—22no—
224C22×C29—21no—
225C22×C29—41no—
226C22×C29—41no—
227C22×C29C2×#12111yescharacteristic
228C4×C29—21no—
229C4×C29—21no—
230C4×C29—21no—
231C4×C29—41no—
232C4×C29—41no—
233C4×C29—41no—
234C4×C29—81no—
235C4×C29—82no—
236C4×C29—81no—
237C4×C29#47312yes—
238C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C29#57511yescharacteristic
240C4×C29#57711yescharacteristic
241C4×C29#57811yescharacteristic
242C2×#137—21no—
243#533C22×C2911yescharacteristic
244C2×C4⋊Q8C22×C2911yescharacteristic
245C4×#41C22×C2911yescharacteristic
246#500C22×C2912yes—
247#487C22×C2912yes—
248#485—21no—
249#484—22no—
250#477—21no—
251#477—21no—
252#475C22×C2911yescharacteristic
253#474C22×C2911yescharacteristic
254#462—21no—
255#462C22×C2911yescharacteristic
256#462C22×C2912yes—
257#461—21no—
258#461C22×C2911yescharacteristic
259#461C22×C2912yes—
260#452—21no—
261#446C22×C2912yes—
262C4×Q16—21no—
263C4×SD16—21no—
264#435—22no—
265C8×D4C22×C2912yes—
266#432—21no—
267#431C22×C2911yescharacteristic
268#431C22×C2911yescharacteristic
269#423C22×C2911yescharacteristic
270#423C22×C2911yescharacteristic
271C2×C4⋊C8—21no—
272#419—21no—
273#335C22×C2912yes—
274#334C22×C2912yes—
275#332C22×C2912yes—
276#332C22×C2912yes—
277#332C22×C2912yes—
278#332C22×C2912yes—
279C2×C29—41no—
280C2×C29—42no—
281C2×C29#304611yescharacteristic
282C2×C29#305511yescharacteristic
283C2×C29C2×#47311yescharacteristic
284C2×#41D4×C2911yescharacteristic
285C22×Q8—21no—
286#137—44no—
287C2×Q16—22no—
288C2×Q16—21no—
289C2×SD16—22no—
290C2×SD16—21no—
291C2×M16—21no—
292C2×M16—21no—
293C22×C8—22no—
294C4⋊Q8—21no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8C23×C2912yes—
298C4⋊Q8C23×C2911yescharacteristic
299C4⋊Q8C23×C2911yescharacteristic
300#125—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×Q8D4×C2911yescharacteristic
306C4×Q8C23×C2911yescharacteristic
307C4×D4—21no—
308C4×D4—21no—
309C4×D4D4×C2911yescharacteristic
310C4×D4C23×C2911yescharacteristic
311#117—21no—
312#117—21no—
313#117D4×C2911yescharacteristic
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C42—21no—
317C2×C42C23×C2911yescharacteristic
318#107—22no—
319#107—22no—
320#107—21no—
321#106—21no—
322C4⋊C8—22no—
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8D4×C2911yescharacteristic
326C4⋊C8D4×C2911yescharacteristic
327C4⋊C8C23×C2912yes—
328C4⋊C8C23×C2911yescharacteristic
329C4⋊C8C23×C2912yes—
330C4⋊C8C23×C2911yescharacteristic
331#103—21no—
332#103—22no—
333#103—22no—
334#103—22no—
335#103—22no—
336#103—21no—
337#103—21no—
338#102—21no—
339C22⋊C8—21no—
340C22⋊C8—22no—
341C22⋊C8D4×C2912yes—
342#97—22no—
343C4×C8—21no—
344C4×C8C23×C2912yes—
345C29#1949011yescharacteristic, direct product factor, Sylow
346#41—22no—
347#41—41no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8—22no—
351C2×Q8—42no—
352C2×Q8—42no—
353C2×Q8—41no—
354C2×Q8C2×D4×C2911yescharacteristic
355C2×D4—21no—
356C2×D4C2×D4×C2911yescharacteristic
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4C2×D4×C2911yescharacteristic
362C22×C4C2×D4×C2911yescharacteristic
363C22×C4#41×C2911yescharacteristic
364Q16—44no—
365Q16—42no—
366SD16—44no—
367SD16—42no—
368M16—42no—
369M16—81no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—82no—
375C2×C8C2×D4×C2912yes—
376C2×C8C2×D4×C2912yes—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4C2×D4×C2911yescharacteristic
390C4⋊C4C2×D4×C2911yescharacteristic
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—41no—
395C42—21no—
396C42—21no—
397C42—21no—
398C42—41no—
399C42C2×D4×C2911yescharacteristic
400C42C2×D4×C2911yescharacteristic
401C42#41×C2911yescharacteristic
402C42C24×C2911yescharacteristic
403C23—21no—
404C23C29×#12111yescharacteristic
405Q8—21no—
406Q8—21no—
407Q8—42no—
408Q8—41no—
409Q8—41no—
410Q8—42no—
411Q8—41no—
412Q8—41no—
413Q8—82no—
414D4—21no—
415D4—42no—
416D4C29×AGL(1,ℤ/8)12yes—
417C2×C4—22no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—82no—
433C2×C4C29×#12111yescharacteristic
434C2×C4C29×#12111yescharacteristic
435C2×C4C29×#12111yescharacteristic
436C2×C4C22×D4×C2911yescharacteristic
437C2×C4C22×D4×C2911yescharacteristic
438C2×C4C2×#41×C2911yescharacteristic
439C8—22no—
440C8—22no—
441C8—42no—
442C8—41no—
443C8—41no—
444C8—42no—
445C22—21no—
446C22—21no—
447C22—22no—
448C22—21no—
449C22—41no—
450C22—41no—
451C22C2×C29×#12111yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—81no—
459C4—82no—
460C4—81no—
461C4C29×#47312yes—
462C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
463C4C29×#57511yescharacteristic
464C4C29×#57711yescharacteristic
465C4C29×#57811yescharacteristic
466C2—41no—
467C2—42no—
468C2C29×#304611yescharacteristic
469C2C29×#305511yescharacteristic
470C2C2×C29×#47311yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC2×#41×C29D4
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×#3230C2semidirect
5. C29×#1700C2semidirect
6. C29×#1694C2semidirect
7. C29×#1679C2semidirect
8. C29×#1673C2semidirect
9. C29×#1574C2semidirect
10. C29×#1561C2semidirect
11. C29×#1549C2semidirect
167. #19490C29direct (N × H)
210. #3230C2×C29semidirect
214. #1700C2×C29semidirect
215. #1694C2×C29semidirect
216. #1679C2×C29semidirect
217. #1673C2×C29semidirect
218. #1574C2×C29semidirect
219. #1561C2×C29semidirect
220. #1549C2×C29semidirect
345. C29#19490direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32302
C29×#31072
C29×#30392
C29×#29902
C29×#17002
C29×#16942
C29×#16792
C29×#16732
C29×#15742
C29×#15612
C29×#15492
#1949029