Finite Group Databasebeta

← C29×#19482 #20314382

Subgroups — C29×#19482 #20314382

Order 7424.

626 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3206C211yesmaximal, characteristic, complemented
2C29×#3106C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic, complemented
4C29×#2990C211yesmaximal, characteristic, complemented
5C29×#1704C212yesmaximal, complemented
6C29×#1686C212yesmaximal, complemented
7C29×#1683C212yesmaximal, complemented
8C29×#1665C212yesmaximal, complemented
9C29×#1574C211yesmaximal, characteristic, complemented
10C29×#1560C211yesmaximal, characteristic, complemented
11C29×#1546C211yesmaximal, characteristic, complemented
12C29×#532C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C4×#41×C29C2211yescharacteristic
15C29×#492C2212yes—
16C29×#487C2212yes—
17C29×#482—21no—
18C29×#477—21no—
19C29×#477C2211yescharacteristic
20C29×#476—21no—
21C29×#476C2211yescharacteristic
22C29×#475C2212yes—
23C29×#474C2212yes—
24C29×#461—21no—
25C29×#461—21no—
26C29×#460C2211yescharacteristic
27C29×#459C2211yescharacteristic
28C29×#449—21no—
29C29×#448—22no—
30C29×#446C2212yes—
31C4×SD16×C29—21no—
32C4×D8×C29—21no—
33C29×#435—22no—
34C8×D4×C29C2212yes—
35C29×#432—21no—
36C29×#431C2211yescharacteristic
37C29×#431C2211yescharacteristic
38C29×#428—21no—
39C29×#423C2211yescharacteristic
40C29×#423C2211yescharacteristic
41C2×C29×C4⋊C8—21no—
42C29×#417—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#332C2212yes—
47C29×#332C2212yes—
48C29×#331C2212yes—
49C2×#41×C29—21no—
50C2×#41×C29D411yescharacteristic
51C22×Q8×C29—21no—
52C2×SD16×C29—21no—
53C2×SD16×C29—22no—
54C2×SD16×C29—22no—
55C2×D8×C29—21no—
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×#127C2311yescharacteristic
65C29×#124—21no—
66C29×#121—21no—
67C29×#121—21no—
68C4×Q8×C29D411yescharacteristic
69C4×Q8×C29C2311yescharacteristic
70C4×D4×C29—21no—
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29—21no—
74C4×D4×C29D411yescharacteristic
75C4×D4×C29C2311yescharacteristic
76C29×#117—21no—
77C29×#117D411yescharacteristic
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29—21no—
80C2×C42×C29—21no—
81C2×C42×C29C2311yescharacteristic
82C29×#107—22no—
83C29×#107—21no—
84C29×#106—22no—
85C29×#106—21no—
86C29×C4⋊C8—22no—
87C29×C4⋊C8—21no—
88C29×C4⋊C8—21no—
89C29×C4⋊C8D411yescharacteristic
90C29×C4⋊C8D411yescharacteristic
91C29×C4⋊C8C2311yescharacteristic
92C29×C4⋊C8C2311yescharacteristic
93C29×C4⋊C8C2312yes—
94C29×C4⋊C8C2312yes—
95C29×#103—21no—
96C29×#103—22no—
97C29×#103—22no—
98C29×#103—22no—
99C29×#102—21no—
100C29×#102—22no—
101C29×#102—21no—
102C29×#102—21no—
103C29×C22⋊C8—21no—
104C29×C22⋊C8—22no—
105C29×C22⋊C8D412yes—
106C29×#97—22no—
107C4×C8×C29—21no—
108C4×C8×C29C2312yes—
109#41×C29—22no—
110#41×C29—41no—
111#41×C29—82no—
112C2×Q8×C29—22no—
113C2×Q8×C29—21no—
114C2×Q8×C29—41no—
115C2×Q8×C29—81no—
116C2×Q8×C29—81no—
117C2×Q8×C29C2×D411yescharacteristic
118C2×D4×C29—21no—
119C2×D4×C29—21no—
120C2×D4×C29—21no—
121C2×D4×C29—21no—
122C2×D4×C29—41no—
123C2×D4×C29C2×D411yescharacteristic
124C22×C4×C29—21no—
125C22×C4×C29—21no—
126C22×C4×C29—21no—
127C22×C4×C29—41no—
128C22×C4×C29—41no—
129C22×C4×C29C2×D411yescharacteristic
130C22×C4×C29C2×D411yescharacteristic
131C22×C4×C29#4111yescharacteristic
132SD16×C29—42no—
133SD16×C29—82no—
134SD16×C29—82no—
135D8×C29—42no—
136M16×C29—42no—
137M16×C29—81no—
138C2×C8×C29—22no—
139C2×C8×C29—22no—
140C2×C8×C29—21no—
141C2×C8×C29—21no—
142C2×C8×C29—82no—
143C2×C8×C29C2×D412yes—
144C2×C8×C29C2×D412yes—
145C4⋊C4×C29—21no—
146C4⋊C4×C29—21no—
147C4⋊C4×C29—22no—
148C4⋊C4×C29—21no—
149C4⋊C4×C29—21no—
150C4⋊C4×C29—22no—
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—
159C22⋊C4×C29—41no—
160C42×C29—21no—
161C42×C29—21no—
162C42×C29—21no—
163C42×C29C2×D411yescharacteristic
164C42×C29C2×D411yescharacteristic
165C42×C29#4111yescharacteristic
166C42×C29C2411yescharacteristic
167#19482C2911yesmaximal, characteristic, direct product factor, Sylow
168C23×C29—21no—
169C23×C29—41no—
170C23×C29#12111yescharacteristic
171Q8×C29—21no—
172Q8×C29—21no—
173Q8×C29—42no—
174Q8×C29—42no—
175Q8×C29—81no—
176Q8×C29—82no—
177D4×C29—21no—
178D4×C29—42no—
179D4×C29—41no—
180D4×C29—41no—
181D4×C29—41no—
182D4×C29—41no—
183D4×C29—81no—
184D4×C29—82no—
185D4×C29#13712yes—
186C2×C4×C29—21no—
187C2×C4×C29—21no—
188C2×C4×C29—21no—
189C2×C4×C29—21no—
190C2×C4×C29—22no—
191C2×C4×C29—21no—
192C2×C4×C29—21no—
193C2×C4×C29—21no—
194C2×C4×C29—42no—
195C2×C4×C29—41no—
196C2×C4×C29—41no—
197C2×C4×C29—42no—
198C2×C4×C29—41no—
199C2×C4×C29—42no—
200C2×C4×C29—82no—
201C2×C4×C29—82no—
202C2×C4×C29#12111yescharacteristic
203C2×C4×C29#12111yescharacteristic
204C2×C4×C29#12111yescharacteristic
205C2×C4×C29C22×D411yescharacteristic
206C2×C4×C29C22×D411yescharacteristic
207C2×C4×C29C2×#4111yescharacteristic
208C8×C29—22no—
209C8×C29—22no—
210C8×C29—41no—
211C8×C29—42no—
212C8×C29—41no—
213C8×C29—42no—
214#3206C2×C2911yescharacteristic, complemented
215#3106C2×C2911yescharacteristic
216#3079C2×C2911yescharacteristic, complemented
217#2990C2×C2911yescharacteristic, complemented
218#1704C2×C2912yescomplemented
219#1686C2×C2912yescomplemented
220#1683C2×C2912yescomplemented
221#1665C2×C2912yescomplemented
222#1574C2×C2911yescharacteristic, complemented
223#1560C2×C2911yescharacteristic, complemented
224#1546C2×C2911yescharacteristic, complemented
225C22×C29—21no—
226C22×C29—21no—
227C22×C29—22no—
228C22×C29—21no—
229C22×C29—41no—
230C22×C29—41no—
231C22×C29—81no—
232C22×C29—81no—
233C22×C29—81no—
234C22×C29C2×#12111yescharacteristic
235C4×C29—21no—
236C4×C29—21no—
237C4×C29—21no—
238C4×C29—41no—
239C4×C29—41no—
240C4×C29—41no—
241C4×C29—82no—
242C4×C29—81no—
243C4×C29#47112yes—
244C4×C29C2×#13711yescharacteristic
245C4×C29#57511yescharacteristic
246C4×C29#57611yescharacteristic
247C4×C29#57711yescharacteristic
248#532C22×C2911yescharacteristic
249C2×C4⋊Q8C22×C2911yescharacteristic
250C4×#41C22×C2911yescharacteristic
251#492C22×C2912yes—
252#487C22×C2912yes—
253#482—21no—
254#477—21no—
255#477C22×C2911yescharacteristic
256#476—21no—
257#476C22×C2911yescharacteristic
258#475C22×C2912yes—
259#474C22×C2912yes—
260#461—21no—
261#461—21no—
262#460C22×C2911yescharacteristic
263#459C22×C2911yescharacteristic
264#449—21no—
265#448—22no—
266#446C22×C2912yes—
267C4×SD16—21no—
268C4×D8—21no—
269#435—22no—
270C8×D4C22×C2912yes—
271#432—21no—
272#431C22×C2911yescharacteristic
273#431C22×C2911yescharacteristic
274#428—21no—
275#423C22×C2911yescharacteristic
276#423C22×C2911yescharacteristic
277C2×C4⋊C8—21no—
278#417—21no—
279#335C22×C2912yes—
280#334C22×C2912yes—
281#333C22×C2912yes—
282#332C22×C2912yes—
283#332C22×C2912yes—
284#331C22×C2912yes—
285C2×C29—41no—
286C2×C29—42no—
287C2×C29—161no—
288C2×C29#304511yescharacteristic
289C2×C29#305611yescharacteristic
290C2×C29C2×#47111yescharacteristic
291C2×#41—21no—
292C2×#41D4×C2911yescharacteristic
293C22×Q8—21no—
294C2×SD16—21no—
295C2×SD16—22no—
296C2×SD16—22no—
297C2×D8—21no—
298C2×M16—21no—
299C2×M16—21no—
300C22×C8—22no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8C23×C2912yes—
305C4⋊Q8C23×C2911yescharacteristic
306#127C23×C2911yescharacteristic
307#124—21no—
308#121—21no—
309#121—21no—
310C4×Q8D4×C2911yescharacteristic
311C4×Q8C23×C2911yescharacteristic
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—21no—
316C4×D4D4×C2911yescharacteristic
317C4×D4C23×C2911yescharacteristic
318#117—21no—
319#117D4×C2911yescharacteristic
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C42—21no—
323C2×C42C23×C2911yescharacteristic
324#107—22no—
325#107—21no—
326#106—22no—
327#106—21no—
328C4⋊C8—22no—
329C4⋊C8—21no—
330C4⋊C8—21no—
331C4⋊C8D4×C2911yescharacteristic
332C4⋊C8D4×C2911yescharacteristic
333C4⋊C8C23×C2912yes—
334C4⋊C8C23×C2912yes—
335C4⋊C8C23×C2911yescharacteristic
336C4⋊C8C23×C2911yescharacteristic
337#103—22no—
338#103—21no—
339#103—22no—
340#103—22no—
341#102—22no—
342#102—21no—
343#102—21no—
344#102—21no—
345C22⋊C8—21no—
346C22⋊C8—22no—
347C22⋊C8D4×C2912yes—
348#97—22no—
349C4×C8—21no—
350C4×C8C23×C2912yes—
351C29#1948211yescharacteristic, direct product factor, Sylow
352#41—22no—
353#41—41no—
354#41—82no—
355C2×Q8—22no—
356C2×Q8—21no—
357C2×Q8—41no—
358C2×Q8—81no—
359C2×Q8—81no—
360C2×Q8C2×D4×C2911yescharacteristic
361C2×D4—21no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—41no—
366C2×D4C2×D4×C2911yescharacteristic
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4C2×D4×C2911yescharacteristic
373C22×C4C2×D4×C2911yescharacteristic
374C22×C4#41×C2911yescharacteristic
375SD16—42no—
376SD16—82no—
377SD16—82no—
378D8—42no—
379M16—42no—
380M16—81no—
381C2×C8—21no—
382C2×C8—21no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—82no—
386C2×C8C2×D4×C2912yes—
387C2×C8C2×D4×C2912yes—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4C2×D4×C2911yescharacteristic
397C4⋊C4C2×D4×C2911yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—21no—
400C22⋊C4—21no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C42—21no—
404C42—21no—
405C42—21no—
406C42C2×D4×C2911yescharacteristic
407C42C2×D4×C2911yescharacteristic
408C42#41×C2911yescharacteristic
409C42C24×C2911yescharacteristic
410C23—21no—
411C23—41no—
412C23C29×#12111yescharacteristic
413Q8—21no—
414Q8—21no—
415Q8—42no—
416Q8—42no—
417Q8—81no—
418Q8—82no—
419D4—21no—
420D4—42no—
421D4—41no—
422D4—41no—
423D4—41no—
424D4—41no—
425D4—81no—
426D4—82no—
427D4C29×#13712yes—
428C2×C4—22no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—82no—
443C2×C4—82no—
444C2×C4C29×#12111yescharacteristic
445C2×C4C29×#12111yescharacteristic
446C2×C4C29×#12111yescharacteristic
447C2×C4C22×D4×C2911yescharacteristic
448C2×C4C22×D4×C2911yescharacteristic
449C2×C4C2×#41×C2911yescharacteristic
450C8—22no—
451C8—22no—
452C8—41no—
453C8—42no—
454C8—41no—
455C8—42no—
456C22—21no—
457C22—21no—
458C22—22no—
459C22—21no—
460C22—41no—
461C22—41no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22C2×C29×#12111yescharacteristic
466C4—21no—
467C4—21no—
468C4—21no—
469C4—41no—
470C4—41no—
471C4—41no—
472C4—82no—
473C4—81no—
474C4C29×#47112yes—
475C4C2×C29×#13711yescharacteristic
476C4C29×#57511yescharacteristic
477C4C29×#57611yescharacteristic
478C4C29×#57711yescharacteristic
479C2—41no—
480C2—42no—
481C2—161no—
482C2C29×#304511yescharacteristic
483C2C29×#305611yescharacteristic
484C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3106C2
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
3. C29×#3079C2semidirect
4. C29×#2990C2semidirect
5. C29×#1704C2semidirect
6. C29×#1686C2semidirect
7. C29×#1683C2semidirect
8. C29×#1665C2semidirect
9. C29×#1574C2semidirect
10. C29×#1560C2semidirect
11. C29×#1546C2semidirect
167. #19482C29direct (N × H)
214. #3206C2×C29semidirect
216. #3079C2×C29semidirect
217. #2990C2×C29semidirect
218. #1704C2×C29semidirect
219. #1686C2×C29semidirect
220. #1683C2×C29semidirect
221. #1665C2×C29semidirect
222. #1574C2×C29semidirect
223. #1560C2×C29semidirect
224. #1546C2×C29semidirect
351. C29#19482direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32062
C29×#31062
C29×#30792
C29×#29902
C29×#17042
C29×#16862
C29×#16832
C29×#16652
C29×#15742
C29×#15602
C29×#15462
#1948229