Finite Group Databasebeta

← C29×#19171 #20314071

Subgroups — C29×#19171 #20314071

Order 7424.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3152C211yesmaximal, characteristic
2C29×#3103C211yesmaximal, characteristic
3C2×C29×#475C211yesmaximal, characteristic, complemented
4Q8×M16×C29C211yesmaximal, characteristic, complemented
5C29×#1690C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1670C212yesmaximal, complemented
8C29×#1666C212yesmaximal, complemented
9C29×#1565C211yesmaximal, characteristic, complemented
10C29×#1547C211yesmaximal, characteristic
11C29×#1546C211yesmaximal, characteristic, complemented
12C2×C29×#137—21no—
13C2×C29×#137—21no—
14C29×#532C2211yescharacteristic
15C2×C29×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C29C2211yescharacteristic
17C29×#497—22no—
18C29×#494C2212yes—
19C29×#492C2212yes—
20C29×#481—21no—
21C29×#475—21no—
22C29×#475—21no—
23C29×#475C2212yes—
24C29×#475C2211yescharacteristic
25C29×#475C2212yes—
26C29×#475C2211yescharacteristic
27C29×#460C2211yescharacteristic
28C29×#460C2211yescharacteristic
29C29×#448—21no—
30C29×#446—22no—
31C29×#446C2212yes—
32C8×Q8×C29C2212yes—
33C4×SD16×C29—21no—
34C4×SD16×C29—21no—
35C29×#431C2211yescharacteristic
36C2×C29×#106—21no—
37C29×#423—21no—
38C29×#423C2211yescharacteristic
39C2×C29×C4⋊C8C2211yescharacteristic
40C2×C29×#103—21no—
41C4×M16×C29—21no—
42C4×M16×C29C2211yescharacteristic
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#332C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C22×Q8×C29—21no—
51C22×Q8×C29D411yescharacteristic
52C29×#137—44no—
53C29×#137—44no—
54C2×Q16×C29—22no—
55C2×Q16×C29—22no—
56C2×SD16×C29—21no—
57C2×SD16×C29—21no—
58C2×SD16×C29—22no—
59C2×SD16×C29—22no—
60C2×M16×C29—21no—
61C2×M16×C29D411yescharacteristic
62C2×M16×C29D411yescharacteristic
63C22×C8×C29—21no—
64C29×C4⋊Q8—21no—
65C29×C4⋊Q8—21no—
66C29×C4⋊Q8—21no—
67C29×C4⋊Q8C2312yes—
68C29×C4⋊Q8C2311yescharacteristic
69C29×#127C2311yescharacteristic
70C29×#124—21no—
71C29×#121—21no—
72C29×#121—21no—
73C4×Q8×C29—21no—
74C4×Q8×C29—21no—
75C4×Q8×C29D411yescharacteristic
76C4×Q8×C29D411yescharacteristic
77C4×Q8×C29C2311yescharacteristic
78C4×Q8×C29C2311yescharacteristic
79C4×D4×C29—21no—
80C4×D4×C29—21no—
81C2×C4⋊C4×C29—21no—
82C2×C4⋊C4×C29—21no—
83C2×C4⋊C4×C29—21no—
84C2×C4⋊C4×C29D411yescharacteristic
85C2×C42×C29—21no—
86C2×C42×C29C2311yescharacteristic
87C29×#106—22no—
88C29×#106—22no—
89C29×#106—21no—
90C29×#106—21no—
91C29×C4⋊C8—22no—
92C29×C4⋊C8—22no—
93C29×C4⋊C8—21no—
94C29×C4⋊C8—21no—
95C29×C4⋊C8C2311yescharacteristic
96C29×C4⋊C8C2311yescharacteristic
97C29×C4⋊C8C2312yes—
98C29×C4⋊C8C2312yes—
99C29×#103—21no—
100C29×#103—21no—
101C29×#103—22no—
102C29×#103—22no—
103C29×#102—21no—
104C29×#102—21no—
105C29×C22⋊C8—21no—
106C29×#97—22no—
107C29×#97D412yes—
108C4×C8×C29—22no—
109C4×C8×C29—21no—
110C4×C8×C29C2312yes—
111#41×C29—42no—
112#41×C29—42no—
113C2×Q8×C29—21no—
114C2×Q8×C29—22no—
115C2×Q8×C29—21no—
116C2×Q8×C29—22no—
117C2×Q8×C29—41no—
118C2×Q8×C29—41no—
119C2×Q8×C29—42no—
120C2×Q8×C29—42no—
121C2×Q8×C29C2×D411yescharacteristic
122C2×Q8×C29C2×D411yescharacteristic
123C2×D4×C29—21no—
124C2×D4×C29—21no—
125C2×D4×C29—21no—
126C2×D4×C29—41no—
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—44no—
135Q16×C29—44no—
136SD16×C29—44no—
137SD16×C29—42no—
138SD16×C29—42no—
139SD16×C29—44no—
140M16×C29—22no—
141M16×C29—42no—
142M16×C29SD1614yescomplemented
143C2×C8×C29—22no—
144C2×C8×C29—22no—
145C2×C8×C29—21no—
146C2×C8×C29—21no—
147C2×C8×C29—42no—
148C2×C8×C29C2×D412yes—
149C2×C8×C29C2×D412yes—
150C4⋊C4×C29—21no—
151C4⋊C4×C29—21no—
152C4⋊C4×C29—21no—
153C4⋊C4×C29—21no—
154C4⋊C4×C29—21no—
155C4⋊C4×C29—22no—
156C4⋊C4×C29—21no—
157C4⋊C4×C29—22no—
158C4⋊C4×C29—21no—
159C4⋊C4×C29—41no—
160C4⋊C4×C29—41no—
161C4⋊C4×C29C2×D411yescharacteristic
162C4⋊C4×C29C2×D411yescharacteristic
163C22⋊C4×C29—41no—
164C22⋊C4×C29—41no—
165C42×C29—21no—
166C42×C29—21no—
167C42×C29—21no—
168C42×C29—21no—
169C42×C29C2×D411yescharacteristic
170C42×C29C2×D411yescharacteristic
171C42×C29#4111yescharacteristic
172C42×C29C2411yescharacteristic
173#19171C2911yesmaximal, characteristic, direct product factor, Sylow
174C23×C29—41no—
175C23×C29#12111yescharacteristic
176Q8×C29—21no—
177Q8×C29—21no—
178Q8×C29—21no—
179Q8×C29—42no—
180Q8×C29—42no—
181Q8×C29—41no—
182Q8×C29—42no—
183Q8×C29—41no—
184Q8×C29—82no—
185Q8×C29#13712yescomplemented
186D4×C29—41no—
187D4×C29—41no—
188D4×C29—41no—
189D4×C29—41no—
190D4×C29—81no—
191D4×C29—82no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—21no—
195C2×C4×C29—21no—
196C2×C4×C29—21no—
197C2×C4×C29—21no—
198C2×C4×C29—41no—
199C2×C4×C29—42no—
200C2×C4×C29—41no—
201C2×C4×C29—42no—
202C2×C4×C29—81no—
203C2×C4×C29—82no—
204C2×C4×C29—82no—
205C2×C4×C29#12111yescharacteristic
206C2×C4×C29#12111yescharacteristic
207C2×C4×C29#12111yescharacteristic
208C2×C4×C29C2×SD1612yes—
209C2×C4×C29AGL(1,ℤ/8)12yes—
210C2×C4×C29C22×D411yescharacteristic
211C2×C4×C29C22×D411yescharacteristic
212C2×C4×C29C2×#4111yescharacteristic
213C8×C29—22no—
214C8×C29—42no—
215C8×C29—41no—
216C8×C29—42no—
217C8×C29—41no—
218C8×C29C2×SD1614yes—
219#3152C2×C2911yescharacteristic
220#3103C2×C2911yescharacteristic
221C2×#475C2×C2911yescharacteristic, complemented
222Q8×M16C2×C2911yescharacteristic, complemented
223#1690C2×C2912yescomplemented
224#1686C2×C2912yescomplemented
225#1670C2×C2912yescomplemented
226#1666C2×C2912yescomplemented
227#1565C2×C2911yescharacteristic, complemented
228#1547C2×C2911yescharacteristic
229#1546C2×C2911yescharacteristic, complemented
230C22×C29—21no—
231C22×C29—21no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29—81no—
235C22×C29#46012yes—
236C22×C29C2×#12111yescharacteristic
237C4×C29—21no—
238C4×C29—22no—
239C4×C29—21no—
240C4×C29—21no—
241C4×C29—41no—
242C4×C29—41no—
243C4×C29—41no—
244C4×C29—81no—
245C4×C29—82no—
246C4×C29#46012yes—
247C4×C29C22×SD1611yescharacteristic
248C4×C29C2×AGL(1,ℤ/8)11yescharacteristic
249C4×C29C2×#13711yescharacteristic
250C4×C29#57511yescharacteristic
251C2×#137—21no—
252C2×#137—21no—
253#532C22×C2911yescharacteristic
254C2×C4⋊Q8C22×C2911yescharacteristic
255C2×C4×Q8C22×C2911yescharacteristic
256#497—22no—
257#494C22×C2912yes—
258#492C22×C2912yes—
259#481—21no—
260#475—21no—
261#475—21no—
262#475C22×C2912yes—
263#475C22×C2912yes—
264#475C22×C2911yescharacteristic
265#475C22×C2911yescharacteristic
266#460C22×C2911yescharacteristic
267#460C22×C2911yescharacteristic
268#448—21no—
269#446—22no—
270#446C22×C2912yes—
271C8×Q8C22×C2912yes—
272C4×SD16—21no—
273C4×SD16—21no—
274#431C22×C2911yescharacteristic
275C2×#106—21no—
276#423—21no—
277#423C22×C2911yescharacteristic
278C2×C4⋊C8C22×C2911yescharacteristic
279C2×#103—21no—
280C4×M16—21no—
281C4×M16C22×C2911yescharacteristic
282#335C22×C2912yes—
283#334C22×C2912yes—
284#332C22×C2912yes—
285#332C22×C2912yes—
286#332C22×C2912yes—
287#331C22×C2912yes—
288C2×C29—22no—
289C2×C29—161no—
290C2×C29C2×#46011yescharacteristic
291C2×C29#305611yescharacteristic
292C2×C29#306911yescharacteristic
293C2×#41—21no—
294C22×Q8—21no—
295C22×Q8D4×C2911yescharacteristic
296#137—44no—
297#137—44no—
298C2×Q16—22no—
299C2×Q16—22no—
300C2×SD16—21no—
301C2×SD16—21no—
302C2×SD16—22no—
303C2×SD16—22no—
304C2×M16—21no—
305C2×M16D4×C2911yescharacteristic
306C2×M16D4×C2911yescharacteristic
307C22×C8—21no—
308C4⋊Q8—21no—
309C4⋊Q8—21no—
310C4⋊Q8—21no—
311C4⋊Q8C23×C2912yes—
312C4⋊Q8C23×C2911yescharacteristic
313#127C23×C2911yescharacteristic
314#124—21no—
315#121—21no—
316#121—21no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×Q8D4×C2911yescharacteristic
320C4×Q8D4×C2911yescharacteristic
321C4×Q8C23×C2911yescharacteristic
322C4×Q8C23×C2911yescharacteristic
323C4×D4—21no—
324C4×D4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4D4×C2911yescharacteristic
329C2×C42—21no—
330C2×C42C23×C2911yescharacteristic
331#106—22no—
332#106—22no—
333#106—21no—
334#106—21no—
335C4⋊C8—22no—
336C4⋊C8—22no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8C23×C2912yes—
340C4⋊C8C23×C2912yes—
341C4⋊C8C23×C2911yescharacteristic
342C4⋊C8C23×C2911yescharacteristic
343#103—22no—
344#103—22no—
345#103—21no—
346#103—21no—
347#102—21no—
348#102—21no—
349C22⋊C8—21no—
350#97—22no—
351#97D4×C2912yes—
352C4×C8—22no—
353C4×C8—21no—
354C4×C8C23×C2912yes—
355C29#1917111yescharacteristic, direct product factor, Sylow
356#41—42no—
357#41—42no—
358C2×Q8—21no—
359C2×Q8—22no—
360C2×Q8—21no—
361C2×Q8—22no—
362C2×Q8—41no—
363C2×Q8—41no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8C2×D4×C2911yescharacteristic
367C2×Q8C2×D4×C2911yescharacteristic
368C2×D4—21no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—41no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4C2×D4×C2911yescharacteristic
377C22×C4C2×D4×C2911yescharacteristic
378C22×C4#41×C2911yescharacteristic
379Q16—44no—
380Q16—44no—
381SD16—44no—
382SD16—42no—
383SD16—42no—
384SD16—44no—
385M16—22no—
386M16—42no—
387M16SD16×C2914yescomplemented
388C2×C8—22no—
389C2×C8—21no—
390C2×C8—21no—
391C2×C8—22no—
392C2×C8—42no—
393C2×C8C2×D4×C2912yes—
394C2×C8C2×D4×C2912yes—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—21no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4C2×D4×C2911yescharacteristic
407C4⋊C4C2×D4×C2911yescharacteristic
408C22⋊C4—41no—
409C22⋊C4—41no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42C2×D4×C2911yescharacteristic
415C42C2×D4×C2911yescharacteristic
416C42#41×C2911yescharacteristic
417C42C24×C2911yescharacteristic
418C23—41no—
419C23C29×#12111yescharacteristic
420Q8—21no—
421Q8—21no—
422Q8—21no—
423Q8—42no—
424Q8—42no—
425Q8—41no—
426Q8—42no—
427Q8—41no—
428Q8—82no—
429Q8C29×#13712yescomplemented
430D4—41no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—81no—
435D4—82no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—82no—
448C2×C4—82no—
449C2×C4C29×#12111yescharacteristic
450C2×C4C29×#12111yescharacteristic
451C2×C4C29×#12111yescharacteristic
452C2×C4C2×SD16×C2912yes—
453C2×C4C29×AGL(1,ℤ/8)12yes—
454C2×C4C22×D4×C2911yescharacteristic
455C2×C4C22×D4×C2911yescharacteristic
456C2×C4C2×#41×C2911yescharacteristic
457C8—22no—
458C8—42no—
459C8—41no—
460C8—42no—
461C8—41no—
462C8C2×SD16×C2914yes—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—81no—
468C22C29×#46012yes—
469C22C2×C29×#12111yescharacteristic
470C4—21no—
471C4—22no—
472C4—21no—
473C4—21no—
474C4—41no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—82no—
479C4C29×#46012yes—
480C4C22×SD16×C2911yescharacteristic
481C4C2×C29×AGL(1,ℤ/8)11yescharacteristic
482C4C2×C29×#13711yescharacteristic
483C4C29×#57511yescharacteristic
484C2—22no—
485C2—161no—
486C2C2×C29×#46011yescharacteristic
487C2C29×#305611yescharacteristic
488C2C29×#306911yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#532C22
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. C2×C29×#475C2semidirect
4. Q8×M16×C29C2semidirect
5. C29×#1690C2semidirect
6. C29×#1686C2semidirect
7. C29×#1670C2semidirect
8. C29×#1666C2semidirect
9. C29×#1565C2semidirect
11. C29×#1546C2semidirect
142. M16×C29SD16semidirect
173. #19171C29direct (N × H)
185. Q8×C29#137semidirect
221. C2×#475C2×C29semidirect
222. Q8×M16C2×C29semidirect
223. #1690C2×C29semidirect
224. #1686C2×C29semidirect
225. #1670C2×C29semidirect
226. #1666C2×C29semidirect
227. #1565C2×C29semidirect
229. #1546C2×C29semidirect
355. C29#19171direct (N × H)
387. M16SD16×C29semidirect
429. Q8C29×#137semidirect

Maximal subgroups

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

subgroupindex
C29×#31522
C29×#31032
C2×C29×#4752
Q8×M16×C292
C29×#16902
C29×#16862
C29×#16702
C29×#16662
C29×#15652
C29×#15472
C29×#15462
#1917129