Finite Group Databasebeta

← C29×#19558 #20314458

Subgroups — C29×#19558 #20314458

Order 7424.

624 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3253C211yesmaximal, characteristic
2C29×#3227C211yesmaximal, characteristic, complemented
3C29×#3206C211yesmaximal, characteristic, complemented
4C29×#2979C211yesmaximal, characteristic, complemented
5C29×#1701C212yesmaximal, complemented
6C29×#1691C212yesmaximal, complemented
7C29×#1681C212yesmaximal, complemented
8C29×#1671C212yesmaximal, complemented
9C29×#1574C211yesmaximal, characteristic, complemented
10C29×#1546C211yesmaximal, characteristic, complemented
11C29×#1543C211yesmaximal, characteristic, complemented
12C29×#532C2211yescharacteristic
13C29×#532C2211yescharacteristic
14C2×C29×C4⋊Q8C2211yescharacteristic
15C29×#498C2212yes—
16C29×#492—21no—
17C29×#487—21no—
18C29×#486C2212yes—
19C29×#481—22no—
20C29×#476—21no—
21C29×#476—21no—
22C29×#476—21no—
23C29×#476C2212yes—
24C29×#469—22no—
25C29×#461C2212yes—
26C29×#461C2212yes—
27C29×#459—21no—
28C29×#459C2212yes—
29C29×#448—22no—
30C29×#436—21no—
31C29×#436C2212yes—
32C8×D4×C29—21no—
33C8×D4×C29C2212yes—
34C29×#431C2211yescharacteristic
35C29×#431C2211yescharacteristic
36C29×#431C2211yescharacteristic
37C29×#423C2211yescharacteristic
38C29×#408—22no—
39C29×#335C2212yes—
40C29×#334C2212yes—
41C29×#333C2211yescharacteristic
42C29×#333C2211yescharacteristic
43C29×#332C2212yes—
44C29×#332C2212yes—
45C29×#331C2211yescharacteristic
46C29×#331C2211yescharacteristic
47C2×#41×C29—21no—
48C2×#41×C29—21no—
49C22×Q8×C29—21no—
50C2×SD16×C29—22no—
51C2×SD16×C29—22no—
52C2×D8×C29—22no—
53C2×M16×C29—21no—
54C2×M16×C29—22no—
55C22×C8×C29—22no—
56C29×C4⋊Q8—21no—
57C29×C4⋊Q8—21no—
58C29×C4⋊Q8—21no—
59C29×C4⋊Q8D411yescharacteristic
60C29×C4⋊Q8C2312yes—
61C29×C4⋊Q8C2311yescharacteristic
62C29×#127D411yescharacteristic
63C29×#127C2311yescharacteristic
64C29×#124—21no—
65C29×#124—21no—
66C29×#121—21no—
67C29×#121—21no—
68C29×#121—21no—
69C29×#121D412yes—
70C4×D4×C29—21no—
71C4×D4×C29—21no—
72C4×D4×C29—21no—
73C4×D4×C29C2312yes—
74C2×C4⋊C4×C29—21no—
75C2×C4⋊C4×C29—21no—
76C2×C42×C29C2311yescharacteristic
77C29×#106—22no—
78C29×#106—22no—
79C29×#106—22no—
80C29×C4⋊C8—21no—
81C29×C4⋊C8D411yescharacteristic
82C29×C4⋊C8D411yescharacteristic
83C29×C4⋊C8C2311yescharacteristic
84C29×C4⋊C8C2311yescharacteristic
85C29×C4⋊C8C2311yescharacteristic
86C29×C4⋊C8C2311yescharacteristic
87C29×C4⋊C8C2312yes—
88C29×#103—22no—
89C29×#103—22no—
90C29×#102—22no—
91C29×#102—22no—
92C29×#102—22no—
93C29×#102—22no—
94C29×C22⋊C8—21no—
95C29×C22⋊C8—21no—
96C29×C22⋊C8—22no—
97C29×C22⋊C8—22no—
98C29×C22⋊C8D412yes—
99C4×C8×C29—21no—
100C4×C8×C29—21no—
101C4×C8×C29C2312yes—
102#41×C29—81no—
103#41×C29—81no—
104#41×C29—82no—
105C2×Q8×C29—21no—
106C2×Q8×C29—22no—
107C2×Q8×C29—21no—
108C2×Q8×C29—41no—
109C2×Q8×C29—81no—
110C2×Q8×C29—81no—
111C2×D4×C29—22no—
112C2×D4×C29—21no—
113C2×D4×C29—21no—
114C2×D4×C29—21no—
115C2×D4×C29—21no—
116C2×D4×C29—21no—
117C2×D4×C29—41no—
118C2×D4×C29C2×D412yes—
119C22×C4×C29—22no—
120C22×C4×C29—41no—
121C22×C4×C29—41no—
122C22×C4×C29C2×D411yescharacteristic
123C22×C4×C29C2×D411yescharacteristic
124C22×C4×C29#4111yescharacteristic
125SD16×C29—82no—
126SD16×C29—82no—
127D8×C29—82no—
128M16×C29—82no—
129M16×C29—81no—
130C2×C8×C29—21no—
131C2×C8×C29—21no—
132C2×C8×C29—22no—
133C2×C8×C29—21no—
134C2×C8×C29—21no—
135C2×C8×C29—82no—
136C2×C8×C29C2×D412yes—
137C2×C8×C29C2×D412yes—
138C4⋊C4×C29—21no—
139C4⋊C4×C29—22no—
140C4⋊C4×C29—21no—
141C4⋊C4×C29—21no—
142C4⋊C4×C29—22no—
143C4⋊C4×C29—41no—
144C4⋊C4×C29—41no—
145C4⋊C4×C29C2×D412yes—
146C22⋊C4×C29—22no—
147C22⋊C4×C29—22no—
148C22⋊C4×C29—41no—
149C22⋊C4×C29—41no—
150C42×C29C2×D411yescharacteristic
151C42×C29C2×D411yescharacteristic
152C42×C29#4111yescharacteristic
153C42×C29C2411yescharacteristic
154#19558C2911yesmaximal, characteristic, direct product factor, Sylow
155C23×C29—22no—
156C23×C29—41no—
157C23×C29#12111yescharacteristic
158Q8×C29—42no—
159Q8×C29—42no—
160Q8×C29—81no—
161Q8×C29—81no—
162Q8×C29—82no—
163D4×C29—22no—
164D4×C29—22no—
165D4×C29—41no—
166D4×C29—41no—
167D4×C29—41no—
168D4×C29—41no—
169D4×C29—42no—
170D4×C29—81no—
171D4×C29—81no—
172D4×C29—82no—
173D4×C29—82no—
174C2×C4×C29—21no—
175C2×C4×C29—21no—
176C2×C4×C29—21no—
177C2×C4×C29—21no—
178C2×C4×C29—22no—
179C2×C4×C29—22no—
180C2×C4×C29—42no—
181C2×C4×C29—42no—
182C2×C4×C29—41no—
183C2×C4×C29—42no—
184C2×C4×C29—82no—
185C2×C4×C29—82no—
186C2×C4×C29#12111yescharacteristic
187C2×C4×C29#12111yescharacteristic
188C2×C4×C29#12111yescharacteristic
189C2×C4×C29C22×D411yescharacteristic
190C2×C4×C29C22×D411yescharacteristic
191C2×C4×C29C2×#4111yescharacteristic
192C8×C29—22no—
193C8×C29—22no—
194C8×C29—42no—
195C8×C29—41no—
196C8×C29—41no—
197C8×C29—41no—
198C8×C29—41no—
199#3253C2×C2911yescharacteristic
200#3227C2×C2911yescharacteristic, complemented
201#3206C2×C2911yescharacteristic, complemented
202#2979C2×C2911yescharacteristic, complemented
203#1701C2×C2912yescomplemented
204#1691C2×C2912yescomplemented
205#1681C2×C2912yescomplemented
206#1671C2×C2912yescomplemented
207#1574C2×C2911yescharacteristic, complemented
208#1546C2×C2911yescharacteristic, complemented
209#1543C2×C2911yescharacteristic, complemented
210C22×C29—21no—
211C22×C29—21no—
212C22×C29—21no—
213C22×C29—42no—
214C22×C29—42no—
215C22×C29—42no—
216C22×C29—81no—
217C22×C29—81no—
218C22×C29—81no—
219C22×C29C2×#12111yescharacteristic
220C4×C29—21no—
221C4×C29—21no—
222C4×C29—21no—
223C4×C29—42no—
224C4×C29—82no—
225C4×C29—81no—
226C4×C29#47112yes—
227C4×C29#57611yescharacteristic
228C4×C29#57711yescharacteristic
229C4×C29#57711yescharacteristic
230C4×C29#57711yescharacteristic
231#532C22×C2911yescharacteristic
232#532C22×C2911yescharacteristic
233C2×C4⋊Q8C22×C2911yescharacteristic
234#498C22×C2912yes—
235#492—21no—
236#487—21no—
237#486C22×C2912yes—
238#481—22no—
239#476—21no—
240#476—21no—
241#476—21no—
242#476C22×C2912yes—
243#469—22no—
244#461C22×C2912yes—
245#461C22×C2912yes—
246#459—21no—
247#459C22×C2912yes—
248#448—22no—
249#436—21no—
250#436C22×C2912yes—
251C8×D4—21no—
252C8×D4C22×C2912yes—
253#431C22×C2911yescharacteristic
254#431C22×C2911yescharacteristic
255#431C22×C2911yescharacteristic
256#423C22×C2911yescharacteristic
257#408—22no—
258#335C22×C2912yes—
259#334C22×C2912yes—
260#333C22×C2911yescharacteristic
261#333C22×C2911yescharacteristic
262#332C22×C2912yes—
263#332C22×C2912yes—
264#331C22×C2911yescharacteristic
265#331C22×C2911yescharacteristic
266C2×C29—41no—
267C2×C29—82no—
268C2×C29—161no—
269C2×C29#304211yescharacteristic
270C2×C29#306211yescharacteristic
271C2×C29C2×#47111yescharacteristic
272C2×#41—21no—
273C2×#41—21no—
274C22×Q8—21no—
275C2×SD16—22no—
276C2×SD16—22no—
277C2×D8—22no—
278C2×M16—21no—
279C2×M16—22no—
280C22×C8—22no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8—21no—
284C4⋊Q8D4×C2911yescharacteristic
285C4⋊Q8C23×C2912yes—
286C4⋊Q8C23×C2911yescharacteristic
287#127D4×C2911yescharacteristic
288#127C23×C2911yescharacteristic
289#124—21no—
290#124—21no—
291#121—21no—
292#121—21no—
293#121—21no—
294#121D4×C2912yes—
295C4×D4—21no—
296C4×D4—21no—
297C4×D4—21no—
298C4×D4C23×C2912yes—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C42C23×C2911yescharacteristic
302#106—22no—
303#106—22no—
304#106—22no—
305C4⋊C8—21no—
306C4⋊C8D4×C2911yescharacteristic
307C4⋊C8D4×C2911yescharacteristic
308C4⋊C8C23×C2911yescharacteristic
309C4⋊C8C23×C2911yescharacteristic
310C4⋊C8C23×C2911yescharacteristic
311C4⋊C8C23×C2911yescharacteristic
312C4⋊C8C23×C2912yes—
313#103—22no—
314#103—22no—
315#102—22no—
316#102—22no—
317#102—22no—
318#102—22no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—22no—
322C22⋊C8—22no—
323C22⋊C8D4×C2912yes—
324C4×C8—21no—
325C4×C8—21no—
326C4×C8C23×C2912yes—
327C29#1955811yescharacteristic, direct product factor, Sylow
328#41—81no—
329#41—81no—
330#41—82no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—21no—
334C2×Q8—41no—
335C2×Q8—81no—
336C2×Q8—81no—
337C2×D4—22no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—41no—
344C2×D4C2×D4×C2912yes—
345C22×C4—22no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4C2×D4×C2911yescharacteristic
349C22×C4C2×D4×C2911yescharacteristic
350C22×C4#41×C2911yescharacteristic
351SD16—82no—
352SD16—82no—
353D8—82no—
354M16—82no—
355M16—81no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—22no—
361C2×C8—82no—
362C2×C8C2×D4×C2912yes—
363C2×C8C2×D4×C2912yes—
364C4⋊C4—21no—
365C4⋊C4—22no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4C2×D4×C2912yes—
372C22⋊C4—22no—
373C22⋊C4—22no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C42C2×D4×C2911yescharacteristic
377C42C2×D4×C2911yescharacteristic
378C42#41×C2911yescharacteristic
379C42C24×C2911yescharacteristic
380C23—22no—
381C23—41no—
382C23C29×#12111yescharacteristic
383Q8—42no—
384Q8—42no—
385Q8—81no—
386Q8—81no—
387Q8—82no—
388D4—22no—
389D4—22no—
390D4—42no—
391D4—41no—
392D4—41no—
393D4—41no—
394D4—41no—
395D4—81no—
396D4—81no—
397D4—82no—
398D4—82no—
399C2×C4—22no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—22no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—82no—
410C2×C4—82no—
411C2×C4C29×#12111yescharacteristic
412C2×C4C29×#12111yescharacteristic
413C2×C4C29×#12111yescharacteristic
414C2×C4C22×D4×C2911yescharacteristic
415C2×C4C22×D4×C2911yescharacteristic
416C2×C4C2×#41×C2911yescharacteristic
417C8—22no—
418C8—22no—
419C8—42no—
420C8—41no—
421C8—41no—
422C8—41no—
423C8—41no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22C2×C29×#12111yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—42no—
438C4—82no—
439C4—81no—
440C4C29×#47112yes—
441C4C29×#57611yescharacteristic
442C4C29×#57711yescharacteristic
443C4C29×#57711yescharacteristic
444C4C29×#57711yescharacteristic
445C2—41no—
446C2—82no—
447C2—161no—
448C2C29×#304211yescharacteristic
449C2C29×#306211yescharacteristic
450C2C2×C29×#47111yescharacteristic
subgroupG/H
center, socleC22×C29C2×#121
commutator, Frattini, cosocleC42C24×C29
prime radicalC29×#3253C2
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
2. C29×#3227C2semidirect
3. C29×#3206C2semidirect
4. C29×#2979C2semidirect
5. C29×#1701C2semidirect
6. C29×#1691C2semidirect
7. C29×#1681C2semidirect
8. C29×#1671C2semidirect
9. C29×#1574C2semidirect
10. C29×#1546C2semidirect
11. C29×#1543C2semidirect
154. #19558C29direct (N × H)
200. #3227C2×C29semidirect
201. #3206C2×C29semidirect
202. #2979C2×C29semidirect
203. #1701C2×C29semidirect
204. #1691C2×C29semidirect
205. #1681C2×C29semidirect
206. #1671C2×C29semidirect
207. #1574C2×C29semidirect
208. #1546C2×C29semidirect
209. #1543C2×C29semidirect
327. C29#19558direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32532
C29×#32272
C29×#32062
C29×#29792
C29×#17012
C29×#16912
C29×#16812
C29×#16712
C29×#15742
C29×#15462
C29×#15432
#1955829