Finite Group Databasebeta

← C29×#19315 #20314215

Subgroups — C29×#19315 #20314215

Order 7424.

598 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3165C211yesmaximal, characteristic, complemented
2C29×#3116C211yesmaximal, characteristic
3C29×#3079C211yesmaximal, characteristic
4C29×#2970C211yesmaximal, characteristic
5C29×#1696C212yesmaximal, complemented
6C29×#1692C212yesmaximal, complemented
7C29×#1675C212yesmaximal, complemented
8C29×#1671C212yesmaximal, complemented
9C29×#1569C211yesmaximal, characteristic, complemented
10C29×#1559C211yesmaximal, characteristic, complemented
11C29×#1558C211yesmaximal, characteristic, complemented
12C29×#533C2211yescharacteristic
13C2×C29×C4⋊Q8C2211yescharacteristic
14C4×#41×C29C2211yescharacteristic
15C29×#501—21no—
16C29×#501—21no—
17C29×#500C2212yes—
18C29×#498C2212yes—
19C29×#485—21no—
20C29×#477C2212yes—
21C29×#477C2211yescharacteristic
22C29×#476C2212yes—
23C29×#476C2211yescharacteristic
24C29×#475—21no—
25C29×#474—21no—
26C29×#462C2211yescharacteristic
27C29×#461C2211yescharacteristic
28C29×#452—21no—
29C29×#446C2212yes—
30C29×#441—21no—
31C29×#440—21no—
32C29×#435—22no—
33C8×D4×C29C2212yes—
34C29×#432—21no—
35C29×#432C2211yescharacteristic
36C29×#432C2211yescharacteristic
37C29×#428—22no—
38C29×#428—21no—
39C29×#423C2211yescharacteristic
40C29×#417—21no—
41C4×M16×C29C2211yescharacteristic
42C2×C29×#97—21no—
43C29×#335C2212yes—
44C29×#334C2212yes—
45C29×#333C2212yes—
46C29×#333C2212yes—
47C29×#333C2212yes—
48C29×#332C2212yes—
49C2×#41×C29D411yescharacteristic
50C22×Q8×C29—21no—
51C2×Q16×C29—21no—
52C2×SD16×C29—21no—
53C2×M16×C29—21no—
54C2×M16×C29D412yes—
55C22×C8×C29—22no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8C2311yescharacteristic
60C29×C4⋊Q8C2312yes—
61C29×C4⋊Q8C2311yescharacteristic
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—22no—
82C29×#107—22no—
83C29×#107—21no—
84C29×#106—22no—
85C29×#106—22no—
86C29×#106—22no—
87C29×#106—21no—
88C29×C4⋊C8—22no—
89C29×C4⋊C8—21no—
90C29×C4⋊C8C2312yes—
91C29×C4⋊C8C2311yescharacteristic
92C29×C4⋊C8C2311yescharacteristic
93C29×C4⋊C8C2312yes—
94C29×#103—21no—
95C29×#103—22no—
96C29×#103—21no—
97C29×#103—21no—
98C29×#102—21no—
99C29×#102—22no—
100C29×C22⋊C8—21no—
101C29×C22⋊C8—21no—
102C29×C22⋊C8—22no—
103C29×#97—22no—
104C29×#97—21no—
105C29×#97—21no—
106C29×#97D411yescharacteristic
107C29×#97D411yescharacteristic
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—24no—
129M16×C29—42no—
130C2×C8×C29—22no—
131C2×C8×C29—22no—
132C2×C8×C29—21no—
133C2×C8×C29—21no—
134C2×C8×C29—44no—
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#19315C2911yesmaximal, 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—81no—
171Q8×C29—82no—
172Q8×C29—82no—
173D4×C29—21no—
174D4×C29—42no—
175D4×C29#13712yes—
176C2×C4×C29—22no—
177C2×C4×C29—21no—
178C2×C4×C29—21no—
179C2×C4×C29—21no—
180C2×C4×C29—21no—
181C2×C4×C29—21no—
182C2×C4×C29—41no—
183C2×C4×C29—42no—
184C2×C4×C29—42no—
185C2×C4×C29—41no—
186C2×C4×C29—41no—
187C2×C4×C29—42no—
188C2×C4×C29—81no—
189C2×C4×C29—82no—
190C2×C4×C29#12111yescharacteristic
191C2×C4×C29#12111yescharacteristic
192C2×C4×C29#12111yescharacteristic
193C2×C4×C29C22×D411yescharacteristic
194C2×C4×C29C22×D411yescharacteristic
195C2×C4×C29C2×#4111yescharacteristic
196C8×C29—22no—
197C8×C29—42no—
198C8×C29—41no—
199C8×C29—42no—
200C8×C29—41no—
201C8×C29#13714yes—
202#3165C2×C2911yescharacteristic, complemented
203#3116C2×C2911yescharacteristic
204#3079C2×C2911yescharacteristic
205#2970C2×C2911yescharacteristic
206#1696C2×C2912yescomplemented
207#1692C2×C2912yescomplemented
208#1675C2×C2912yescomplemented
209#1671C2×C2912yescomplemented
210#1569C2×C2911yescharacteristic, complemented
211#1559C2×C2911yescharacteristic, complemented
212#1558C2×C2911yescharacteristic, complemented
213C22×C29—21no—
214C22×C29—21no—
215C22×C29—22no—
216C22×C29—21no—
217C22×C29—41no—
218C22×C29—41no—
219C22×C29C2×#12111yescharacteristic
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—21no—
224C4×C29—41no—
225C4×C29—41no—
226C4×C29—41no—
227C4×C29—81no—
228C4×C29—82no—
229C4×C29—81no—
230C4×C29C2×#13712yes—
231C4×C29C2×#13711yescharacteristic
232C4×C29#57511yescharacteristic
233#533C22×C2911yescharacteristic
234C2×C4⋊Q8C22×C2911yescharacteristic
235C4×#41C22×C2911yescharacteristic
236#501—21no—
237#501—21no—
238#500C22×C2912yes—
239#498C22×C2912yes—
240#485—21no—
241#477C22×C2912yes—
242#477C22×C2911yescharacteristic
243#476C22×C2912yes—
244#476C22×C2911yescharacteristic
245#475—21no—
246#474—21no—
247#462C22×C2911yescharacteristic
248#461C22×C2911yescharacteristic
249#452—21no—
250#446C22×C2912yes—
251#441—21no—
252#440—21no—
253#435—22no—
254C8×D4C22×C2912yes—
255#432—21no—
256#432C22×C2911yescharacteristic
257#432C22×C2911yescharacteristic
258#428—22no—
259#428—21no—
260#423C22×C2911yescharacteristic
261#417—21no—
262C4×M16C22×C2911yescharacteristic
263C2×#97—21no—
264#335C22×C2912yes—
265#334C22×C2912yes—
266#333C22×C2912yes—
267#333C22×C2912yes—
268#333C22×C2912yes—
269#332C22×C2912yes—
270C2×C29—41no—
271C2×C29—42no—
272C2×C29#303911yescharacteristic
273C2×C29#305611yescharacteristic
274C2×C29#306811yescharacteristic
275C2×#41D4×C2911yescharacteristic
276C22×Q8—21no—
277C2×Q16—21no—
278C2×SD16—21no—
279C2×M16—21no—
280C2×M16D4×C2912yes—
281C22×C8—22no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8C23×C2912yes—
286C4⋊Q8C23×C2911yescharacteristic
287C4⋊Q8C23×C2911yescharacteristic
288#125—21no—
289C22⋊Q8—21no—
290C22⋊Q8—21no—
291C4×Q8—21no—
292C4×Q8—21no—
293C4×Q8D4×C2911yescharacteristic
294C4×Q8C23×C2911yescharacteristic
295C4×D4—21no—
296C4×D4—21no—
297C4×D4D4×C2911yescharacteristic
298C4×D4C23×C2911yescharacteristic
299#117—21no—
300#117—21no—
301#117D4×C2911yescharacteristic
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C42—21no—
305C2×C42C23×C2911yescharacteristic
306#107—22no—
307#107—22no—
308#107—22no—
309#107—21no—
310#106—22no—
311#106—22no—
312#106—22no—
313#106—21no—
314C4⋊C8—22no—
315C4⋊C8—21no—
316C4⋊C8C23×C2912yes—
317C4⋊C8C23×C2912yes—
318C4⋊C8C23×C2911yescharacteristic
319C4⋊C8C23×C2911yescharacteristic
320#103—22no—
321#103—21no—
322#103—21no—
323#103—21no—
324#102—22no—
325#102—21no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—22no—
329#97—22no—
330#97—21no—
331#97—21no—
332#97D4×C2911yescharacteristic
333#97D4×C2911yescharacteristic
334C4×C8C23×C2912yes—
335C29#1931511yescharacteristic, direct product factor, Sylow
336#41—22no—
337#41—41no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—22no—
341C2×Q8—41no—
342C2×Q8—82no—
343C2×Q8C2×D4×C2911yescharacteristic
344C2×D4—21no—
345C2×D4C2×D4×C2911yescharacteristic
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—41no—
350C22×C4C2×D4×C2911yescharacteristic
351C22×C4C2×D4×C2911yescharacteristic
352C22×C4#41×C2911yescharacteristic
353Q16—42no—
354SD16—42no—
355M16—24no—
356M16—42no—
357C2×C8—22no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—44no—
362C2×C8C2×D4×C2912yes—
363C2×C8C2×D4×C2912yes—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4C2×D4×C2911yescharacteristic
377C4⋊C4C2×D4×C2911yescharacteristic
378C22⋊C4—21no—
379C22⋊C4—21no—
380C22⋊C4—21no—
381C22⋊C4—41no—
382C42—21no—
383C42—21no—
384C42—21no—
385C42—41no—
386C42C2×D4×C2911yescharacteristic
387C42C2×D4×C2911yescharacteristic
388C42#41×C2911yescharacteristic
389C42C24×C2911yescharacteristic
390C23—21no—
391C23C29×#12111yescharacteristic
392Q8—21no—
393Q8—21no—
394Q8—41no—
395Q8—41no—
396Q8—82no—
397Q8—81no—
398Q8—82no—
399D4—21no—
400D4—42no—
401D4C29×#13712yes—
402C2×C4—22no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—42no—
414C2×C4—81no—
415C2×C4—82no—
416C2×C4C29×#12111yescharacteristic
417C2×C4C29×#12111yescharacteristic
418C2×C4C29×#12111yescharacteristic
419C2×C4C22×D4×C2911yescharacteristic
420C2×C4C22×D4×C2911yescharacteristic
421C2×C4C2×#41×C2911yescharacteristic
422C8—22no—
423C8—42no—
424C8—41no—
425C8—42no—
426C8—41no—
427C8C29×#13714yes—
428C22—21no—
429C22—21no—
430C22—22no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22C2×C29×#12111yescharacteristic
435C4—21no—
436C4—21no—
437C4—21no—
438C4—21no—
439C4—41no—
440C4—41no—
441C4—41no—
442C4—81no—
443C4—82no—
444C4—81no—
445C4C2×C29×#13712yes—
446C4C2×C29×#13711yescharacteristic
447C4C29×#57511yescharacteristic
448C2—41no—
449C2—42no—
450C2C29×#303911yescharacteristic
451C2C29×#305611yescharacteristic
452C2C29×#306811yescharacteristic
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×#3165C2semidirect
5. C29×#1696C2semidirect
6. C29×#1692C2semidirect
7. C29×#1675C2semidirect
8. C29×#1671C2semidirect
9. C29×#1569C2semidirect
10. C29×#1559C2semidirect
11. C29×#1558C2semidirect
163. #19315C29direct (N × H)
202. #3165C2×C29semidirect
206. #1696C2×C29semidirect
207. #1692C2×C29semidirect
208. #1675C2×C29semidirect
209. #1671C2×C29semidirect
210. #1569C2×C29semidirect
211. #1559C2×C29semidirect
212. #1558C2×C29semidirect
335. C29#19315direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#31652
C29×#31162
C29×#30792
C29×#29702
C29×#16962
C29×#16922
C29×#16752
C29×#16712
C29×#15692
C29×#15592
C29×#15582
#1931529