Finite Group Databasebeta

← C29×#19488 #20314388

Subgroups — C29×#19488 #20314388

Order 7424.

592 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3229C211yesmaximal, characteristic, complemented
2C29×#3107C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic
4C29×#2990C211yesmaximal, characteristic
5C29×#1704C212yesmaximal, complemented
6C29×#1692C212yesmaximal, complemented
7C29×#1683C212yesmaximal, complemented
8C29×#1671C212yesmaximal, complemented
9C29×#1574C211yesmaximal, characteristic, complemented
10C29×#1561C211yesmaximal, characteristic, complemented
11C29×#1548C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C4×#41×C29C2211yescharacteristic
15C29×#498C2212yes—
16C29×#487C2212yes—
17C29×#485—21no—
18C29×#483—22no—
19C29×#477C2212yes—
20C29×#476C2212yes—
21C29×#475—21no—
22C29×#475—21no—
23C29×#475—21no—
24C29×#475C2211yescharacteristic
25C29×#474—21no—
26C29×#474C2211yescharacteristic
27C29×#462C2211yescharacteristic
28C29×#461C2211yescharacteristic
29C29×#452—21no—
30C29×#446C2212yes—
31C4×Q16×C29—21no—
32C4×SD16×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×#333C2212yes—
47C29×#332C2212yes—
48C29×#332C2212yes—
49C2×#41×C29D411yescharacteristic
50C22×Q8×C29—21no—
51C2×Q16×C29—21no—
52C2×SD16×C29—21no—
53C2×M16×C29—21no—
54C2×M16×C29—21no—
55C22×C8×C29—22no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8C2311yescharacteristic
60C29×C4⋊Q8C2311yescharacteristic
61C29×C4⋊Q8C2312yes—
62C29×#125—21no—
63C29×C22⋊Q8—21no—
64C29×C22⋊Q8—21no—
65C4×Q8×C29—21no—
66C4×Q8×C29—21no—
67C4×Q8×C29D411yescharacteristic
68C4×Q8×C29C2311yescharacteristic
69C4×D4×C29—21no—
70C4×D4×C29—21no—
71C4×D4×C29D411yescharacteristic
72C4×D4×C29C2311yescharacteristic
73C29×#117—21no—
74C29×#117—21no—
75C29×#117D411yescharacteristic
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C42×C29—21no—
79C2×C42×C29C2311yescharacteristic
80C29×#107—22no—
81C29×#107—21no—
82C29×#106—22no—
83C29×#106—22no—
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×#103—21no—
100C29×#103—21no—
101C29×#102—21no—
102C29×#102—22no—
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—
111C2×Q8×C29—21no—
112C2×Q8×C29—21no—
113C2×Q8×C29—22no—
114C2×Q8×C29—41no—
115C2×Q8×C29—82no—
116C2×Q8×C29C2×D411yescharacteristic
117C2×D4×C29—21no—
118C2×D4×C29C2×D411yescharacteristic
119C22×C4×C29—21no—
120C22×C4×C29—21no—
121C22×C4×C29—21no—
122C22×C4×C29—41no—
123C22×C4×C29C2×D411yescharacteristic
124C22×C4×C29C2×D411yescharacteristic
125C22×C4×C29#4111yescharacteristic
126Q16×C29—42no—
127SD16×C29—42no—
128M16×C29—42no—
129M16×C29—81no—
130C2×C8×C29—22no—
131C2×C8×C29—22no—
132C2×C8×C29—21no—
133C2×C8×C29—21no—
134C2×C8×C29—82no—
135C2×C8×C29C2×D412yes—
136C2×C8×C29C2×D412yes—
137C4⋊C4×C29—21no—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—22no—
140C4⋊C4×C29—22no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—21no—
143C4⋊C4×C29—21no—
144C4⋊C4×C29—21no—
145C4⋊C4×C29—41no—
146C4⋊C4×C29—41no—
147C4⋊C4×C29—41no—
148C4⋊C4×C29—41no—
149C4⋊C4×C29C2×D411yescharacteristic
150C4⋊C4×C29C2×D411yescharacteristic
151C22⋊C4×C29—21no—
152C22⋊C4×C29—21no—
153C22⋊C4×C29—21no—
154C22⋊C4×C29—41no—
155C42×C29—21no—
156C42×C29—21no—
157C42×C29—21no—
158C42×C29—41no—
159C42×C29C2×D411yescharacteristic
160C42×C29C2×D411yescharacteristic
161C42×C29#4111yescharacteristic
162C42×C29C2411yescharacteristic
163#19488C2911yesmaximal, characteristic, direct product factor, Sylow
164C23×C29—21no—
165C23×C29#12111yescharacteristic
166Q8×C29—21no—
167Q8×C29—21no—
168Q8×C29—41no—
169Q8×C29—41no—
170Q8×C29—41no—
171Q8×C29—41no—
172Q8×C29—82no—
173Q8×C29—82no—
174D4×C29—21no—
175D4×C29—42no—
176D4×C29#13712yes—
177C2×C4×C29—21no—
178C2×C4×C29—21no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—22no—
182C2×C4×C29—21no—
183C2×C4×C29—21no—
184C2×C4×C29—21no—
185C2×C4×C29—42no—
186C2×C4×C29—41no—
187C2×C4×C29—41no—
188C2×C4×C29—42no—
189C2×C4×C29—41no—
190C2×C4×C29—41no—
191C2×C4×C29—42no—
192C2×C4×C29—82no—
193C2×C4×C29#12111yescharacteristic
194C2×C4×C29#12111yescharacteristic
195C2×C4×C29#12111yescharacteristic
196C2×C4×C29C22×D411yescharacteristic
197C2×C4×C29C22×D411yescharacteristic
198C2×C4×C29C2×#4111yescharacteristic
199C8×C29—22no—
200C8×C29—22no—
201C8×C29—41no—
202C8×C29—42no—
203C8×C29—41no—
204C8×C29—42no—
205#3229C2×C2911yescharacteristic, complemented
206#3107C2×C2911yescharacteristic
207#3079C2×C2911yescharacteristic
208#2990C2×C2911yescharacteristic
209#1704C2×C2912yescomplemented
210#1692C2×C2912yescomplemented
211#1683C2×C2912yescomplemented
212#1671C2×C2912yescomplemented
213#1574C2×C2911yescharacteristic, complemented
214#1561C2×C2911yescharacteristic, complemented
215#1548C2×C2911yescharacteristic, complemented
216C22×C29—21no—
217C22×C29—21no—
218C22×C29—22no—
219C22×C29—21no—
220C22×C29—41no—
221C22×C29—41no—
222C22×C29C2×#12111yescharacteristic
223C4×C29—21no—
224C4×C29—21no—
225C4×C29—21no—
226C4×C29—41no—
227C4×C29—41no—
228C4×C29—41no—
229C4×C29—81no—
230C4×C29—81no—
231C4×C29—82no—
232C4×C29#47112yes—
233C4×C29C2×#13711yescharacteristic
234C4×C29#57511yescharacteristic
235C4×C29#57711yescharacteristic
236C4×C29#57811yescharacteristic
237#533C22×C2911yescharacteristic
238C2×C4⋊Q8C22×C2911yescharacteristic
239C4×#41C22×C2911yescharacteristic
240#498C22×C2912yes—
241#487C22×C2912yes—
242#485—21no—
243#483—22no—
244#477C22×C2912yes—
245#476C22×C2912yes—
246#475—21no—
247#475—21no—
248#475—21no—
249#475C22×C2911yescharacteristic
250#474—21no—
251#474C22×C2911yescharacteristic
252#462C22×C2911yescharacteristic
253#461C22×C2911yescharacteristic
254#452—21no—
255#446C22×C2912yes—
256C4×Q16—21no—
257C4×SD16—21no—
258#435—22no—
259C8×D4C22×C2912yes—
260#432—21no—
261#431C22×C2911yescharacteristic
262#431C22×C2911yescharacteristic
263#428—21no—
264#423C22×C2911yescharacteristic
265#423C22×C2911yescharacteristic
266C2×C4⋊C8—21no—
267#417—21no—
268#335C22×C2912yes—
269#334C22×C2912yes—
270#333C22×C2912yes—
271#333C22×C2912yes—
272#332C22×C2912yes—
273#332C22×C2912yes—
274C2×C29—41no—
275C2×C29—42no—
276C2×C29#304611yescharacteristic
277C2×C29#305611yescharacteristic
278C2×C29C2×#47111yescharacteristic
279C2×#41D4×C2911yescharacteristic
280C22×Q8—21no—
281C2×Q16—21no—
282C2×SD16—21no—
283C2×M16—21no—
284C2×M16—21no—
285C22×C8—22no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8C23×C2912yes—
290C4⋊Q8C23×C2911yescharacteristic
291C4⋊Q8C23×C2911yescharacteristic
292#125—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C4×Q8—21no—
296C4×Q8—21no—
297C4×Q8D4×C2911yescharacteristic
298C4×Q8C23×C2911yescharacteristic
299C4×D4—21no—
300C4×D4—21no—
301C4×D4D4×C2911yescharacteristic
302C4×D4C23×C2911yescharacteristic
303#117—21no—
304#117—21no—
305#117D4×C2911yescharacteristic
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C42—21no—
309C2×C42C23×C2911yescharacteristic
310#107—22no—
311#107—21no—
312#106—22no—
313#106—22no—
314#106—22no—
315#106—21no—
316C4⋊C8—22no—
317C4⋊C8—21no—
318C4⋊C8—21no—
319C4⋊C8D4×C2911yescharacteristic
320C4⋊C8D4×C2911yescharacteristic
321C4⋊C8C23×C2912yes—
322C4⋊C8C23×C2912yes—
323C4⋊C8C23×C2911yescharacteristic
324C4⋊C8C23×C2911yescharacteristic
325#103—22no—
326#103—21no—
327#103—22no—
328#103—22no—
329#103—21no—
330#103—21no—
331#102—22no—
332#102—21no—
333C22⋊C8—21no—
334C22⋊C8—22no—
335C22⋊C8D4×C2912yes—
336#97—22no—
337C4×C8—21no—
338C4×C8C23×C2912yes—
339C29#1948811yescharacteristic, direct product factor, Sylow
340#41—22no—
341#41—41no—
342C2×Q8—21no—
343C2×Q8—21no—
344C2×Q8—22no—
345C2×Q8—41no—
346C2×Q8—82no—
347C2×Q8C2×D4×C2911yescharacteristic
348C2×D4—21no—
349C2×D4C2×D4×C2911yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—41no—
354C22×C4C2×D4×C2911yescharacteristic
355C22×C4C2×D4×C2911yescharacteristic
356C22×C4#41×C2911yescharacteristic
357Q16—42no—
358SD16—42no—
359M16—42no—
360M16—81no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—82no—
366C2×C8C2×D4×C2912yes—
367C2×C8C2×D4×C2912yes—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—21no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4C2×D4×C2911yescharacteristic
381C4⋊C4C2×D4×C2911yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C22⋊C4—41no—
386C42—21no—
387C42—21no—
388C42—21no—
389C42—41no—
390C42C2×D4×C2911yescharacteristic
391C42C2×D4×C2911yescharacteristic
392C42#41×C2911yescharacteristic
393C42C24×C2911yescharacteristic
394C23—21no—
395C23C29×#12111yescharacteristic
396Q8—21no—
397Q8—21no—
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—82no—
403Q8—82no—
404D4—21no—
405D4—42no—
406D4C29×#13712yes—
407C2×C4—22no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—82no—
423C2×C4C29×#12111yescharacteristic
424C2×C4C29×#12111yescharacteristic
425C2×C4C29×#12111yescharacteristic
426C2×C4C22×D4×C2911yescharacteristic
427C2×C4C22×D4×C2911yescharacteristic
428C2×C4C2×#41×C2911yescharacteristic
429C8—22no—
430C8—22no—
431C8—41no—
432C8—42no—
433C8—41no—
434C8—42no—
435C22—21no—
436C22—21no—
437C22—22no—
438C22—21no—
439C22—41no—
440C22—41no—
441C22C2×C29×#12111yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—41no—
448C4—81no—
449C4—81no—
450C4—82no—
451C4C29×#47112yes—
452C4C2×C29×#13711yescharacteristic
453C4C29×#57511yescharacteristic
454C4C29×#57711yescharacteristic
455C4C29×#57811yescharacteristic
456C2—41no—
457C2—42no—
458C2C29×#304611yescharacteristic
459C2C29×#305611yescharacteristic
460C2C2×C29×#47111yescharacteristic
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×#3229C2semidirect
5. C29×#1704C2semidirect
6. C29×#1692C2semidirect
7. C29×#1683C2semidirect
8. C29×#1671C2semidirect
9. C29×#1574C2semidirect
10. C29×#1561C2semidirect
11. C29×#1548C2semidirect
163. #19488C29direct (N × H)
205. #3229C2×C29semidirect
209. #1704C2×C29semidirect
210. #1692C2×C29semidirect
211. #1683C2×C29semidirect
212. #1671C2×C29semidirect
213. #1574C2×C29semidirect
214. #1561C2×C29semidirect
215. #1548C2×C29semidirect
339. C29#19488direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32292
C29×#31072
C29×#30792
C29×#29902
C29×#17042
C29×#16922
C29×#16832
C29×#16712
C29×#15742
C29×#15612
C29×#15482
#1948829