Finite Group Databasebeta

← C29×#9056 #20303956

Subgroups — C29×#9056 #20303956

Order 7424.

432 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3170C211yesmaximal, characteristic
2C29×#2962C211yesmaximal, characteristic
3C29×#1986C211yesmaximal, characteristic
4C29×#1503C211yesmaximal, characteristic
5C29×#1481C211yesmaximal, characteristic
6C29×#1279C211yesmaximal, characteristic
7C29×#1278C211yesmaximal, characteristic
8C29×#533C2211yescharacteristic
9C29×#533C2211yescharacteristic
10C29×#500C411yescharacteristic, complemented
11C29×#494C411yescharacteristic, complemented
12C29×#487C411yescharacteristic, complemented
13C29×#487C411yescharacteristic, complemented
14C29×#467—22no—
15C29×#446—21no—
16C29×#446—22no—
17C8×Q8×C29—21no—
18C4×Q16×C29—22no—
19C29×#431C2211yescharacteristic
20C29×#424—21no—
21C2×C29×C4⋊C8C2211yescharacteristic
22C29×#405—21no—
23C4×M16×C29C2211yescharacteristic
24C2×C4×C8×C29C2211yescharacteristic
25C4×C4⋊C4×C29C2211yescharacteristic
26C29×#339—21no—
27C29×#339—21no—
28C29×#328—22no—
29C29×Q8⋊C8—21no—
30C29×Q8⋊C8—21no—
31C2×Q16×C29—22no—
32C2×M16×C29D411yescharacteristic
33C2×M16×C29D411yescharacteristic
34C22×C8×C29—21no—
35C22×C8×C29—21no—
36C29×C4⋊Q8C2×C411yescharacteristic
37C29×C4⋊Q8C2×C411yescharacteristic
38C29×C4⋊Q8C2×C411yescharacteristic
39C29×C4⋊Q8C2×C411yescharacteristic
40C29×#125—21no—
41C29×#125—21no—
42C29×C22⋊Q8—21no—
43C29×C22⋊Q8—21no—
44C29×C22⋊Q8—21no—
45C29×C22⋊Q8D412yes—
46C4×Q8×C29—21no—
47C4×Q8×C29—21no—
48C4×Q8×C29—21no—
49C4×Q8×C29D412yes—
50C29×#117—21no—
51C29×#117—21no—
52C2×C4⋊C4×C29—21no—
53C2×C42×C29—21no—
54C2×C42×C29C2311yescharacteristic
55C29×#107—22no—
56C29×C4⋊C8—22no—
57C29×C4⋊C8—22no—
58C29×C4⋊C8—21no—
59C29×C4⋊C8—21no—
60C29×C4⋊C8D411yescharacteristic
61C29×C4⋊C8D411yescharacteristic
62C29×#103—22no—
63C29×#103—22no—
64C29×C22⋊C8—21no—
65C29×#97—22no—
66C29×#97—21no—
67C4×C8×C29—22no—
68C4×C8×C29—21no—
69C4×C8×C29—21no—
70C4×C8×C29—21no—
71C4×C8×C29C2×C411yescharacteristic
72C4×C8×C29C2×C411yescharacteristic
73C29×#95—21no—
74C2×Q8×C29—21no—
75C2×Q8×C29—21no—
76C2×Q8×C29—21no—
77C2×Q8×C29C22⋊C412yes—
78C22×C4×C29—41no—
79C22×C4×C29C2×D411yescharacteristic
80C22×C4×C29C2×D411yescharacteristic
81C22×C4×C29#4111yescharacteristic
82Q16×C29—44no—
83M16×C29—21no—
84M16×C29—21no—
85M16×C29—21no—
86M16×C29Q1612yescomplemented
87C2×C8×C29—21no—
88C2×C8×C29—21no—
89C2×C8×C29—21no—
90C2×C8×C29—21no—
91C2×C8×C29—21no—
92C2×C8×C29—21no—
93C2×C8×C29—42no—
94C2×C8×C29—41no—
95C2×C8×C29—41no—
96C2×C8×C29—41no—
97C4⋊C4×C29—21no—
98C4⋊C4×C29—21no—
99C4⋊C4×C29—21no—
100C4⋊C4×C29—22no—
101C4⋊C4×C29—22no—
102C4⋊C4×C29—22no—
103C4⋊C4×C29—21no—
104C4⋊C4×C29—21no—
105C4⋊C4×C29—21no—
106C4⋊C4×C29—21no—
107C4⋊C4×C29—41no—
108C4⋊C4×C29—41no—
109C4⋊C4×C29—41no—
110C4⋊C4×C29C22⋊C412yes—
111C22⋊C4×C29—22no—
112C22⋊C4×C29—41no—
113C42×C29—22no—
114C42×C29—41no—
115C42×C29—41no—
116C42×C29—41no—
117C42×C29C22×C411yescharacteristic
118C42×C29C2×D411yescharacteristic
119C42×C29C2×D411yescharacteristic
120C42×C29#4111yescharacteristic
121#9056C2911yesmaximal, characteristic, direct product factor, Sylow
122C23×C29#12111yescharacteristic
123Q8×C29—42no—
124Q8×C29—42no—
125Q8×C29—41no—
126Q8×C29—41no—
127Q8×C29—41no—
128Q8×C29—41no—
129C2×C4×C29—21no—
130C2×C4×C29—21no—
131C2×C4×C29—22no—
132C2×C4×C29—22no—
133C2×C4×C29—41no—
134C2×C4×C29—42no—
135C2×C4×C29—41no—
136C2×C4×C29—41no—
137C2×C4×C29—81no—
138C2×C4×C29—81no—
139C2×C4×C29C2×C22⋊C411yescharacteristic
140C2×C4×C29C4×D411yescharacteristic
141C2×C4×C29C4×D411yescharacteristic
142C2×C4×C29#12011yescharacteristic
143C2×C4×C29#12111yescharacteristic
144C2×C4×C29#12311yescharacteristic
145C2×C4×C29C2×Q1611yescharacteristic
146C2×C4×C29#13511yescharacteristic
147C2×C4×C29#13711yescharacteristic
148C2×C4×C29#13711yescharacteristic
149C8×C29—22no—
150C8×C29—22no—
151C8×C29—41no—
152C8×C29—41no—
153C8×C29—41no—
154C8×C29—41no—
155C8×C29—81no—
156#3170C2×C2911yescharacteristic
157#2962C2×C2911yescharacteristic
158#1986C2×C2911yescharacteristic
159#1503C2×C2911yescharacteristic
160#1481C2×C2911yescharacteristic
161#1279C2×C2911yescharacteristic
162#1278C2×C2911yescharacteristic
163C22×C29—21no—
164C22×C29—21no—
165C22×C29#38611yescharacteristic
166C22×C29#46211yescharacteristic
167C22×C29#46411yescharacteristic
168C4×C29—21no—
169C4×C29—21no—
170C4×C29—21no—
171C4×C29—42no—
172C4×C29—42no—
173C4×C29—82no—
174C4×C29—81no—
175C4×C29—81no—
176C4×C29C4×Q1611yescharacteristic
177C4×C29#44111yescharacteristic
178C4×C29#44311yescharacteristic
179C4×C29#44411yescharacteristic
180C4×C29#45111yescharacteristic
181C4×C29#45211yescharacteristic
182#533C22×C2911yescharacteristic
183#533C22×C2911yescharacteristic
184#500C4×C2911yescharacteristic, complemented
185#494C4×C2911yescharacteristic, complemented
186#487C4×C2911yescharacteristic, complemented
187#487C4×C2911yescharacteristic, complemented
188#467—22no—
189#446—22no—
190#446—21no—
191C8×Q8—21no—
192C4×Q16—22no—
193#431C22×C2911yescharacteristic
194#424—21no—
195C2×C4⋊C8C22×C2911yescharacteristic
196#405—21no—
197C4×M16C22×C2911yescharacteristic
198C2×C4×C8C22×C2911yescharacteristic
199C4×C4⋊C4C22×C2911yescharacteristic
200#339—21no—
201#339—21no—
202#328—22no—
203Q8⋊C8—21no—
204Q8⋊C8—21no—
205C2×C29—21no—
206C2×C29—21no—
207C2×C29#187611yescharacteristic
208C2×C29#187811yescharacteristic
209C2×C29#188411yescharacteristic
210C2×Q16—22no—
211C2×M16D4×C2911yescharacteristic
212C2×M16D4×C2911yescharacteristic
213C22×C8—21no—
214C22×C8—21no—
215C4⋊Q8C2×C4×C2911yescharacteristic
216C4⋊Q8C2×C4×C2911yescharacteristic
217C4⋊Q8C2×C4×C2911yescharacteristic
218C4⋊Q8C2×C4×C2911yescharacteristic
219#125—21no—
220#125—21no—
221C22⋊Q8—21no—
222C22⋊Q8—21no—
223C22⋊Q8—21no—
224C22⋊Q8D4×C2912yes—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8—21no—
228C4×Q8D4×C2912yes—
229#117—21no—
230#117—21no—
231C2×C4⋊C4—21no—
232C2×C42—21no—
233C2×C42C23×C2911yescharacteristic
234#107—22no—
235C4⋊C8—22no—
236C4⋊C8—22no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8D4×C2911yescharacteristic
240C4⋊C8D4×C2911yescharacteristic
241#103—22no—
242#103—22no—
243C22⋊C8—21no—
244#97—22no—
245#97—21no—
246C4×C8—22no—
247C4×C8—21no—
248C4×C8—21no—
249C4×C8—21no—
250C4×C8C2×C4×C2911yescharacteristic
251C4×C8C2×C4×C2911yescharacteristic
252#95—21no—
253C29#905611yescharacteristic, direct product factor, Sylow
254C2×Q8—21no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8C22⋊C4×C2912yes—
258C22×C4—41no—
259C22×C4C2×D4×C2911yescharacteristic
260C22×C4C2×D4×C2911yescharacteristic
261C22×C4#41×C2911yescharacteristic
262Q16—44no—
263M16—21no—
264M16—21no—
265M16—21no—
266M16Q16×C2912yescomplemented
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—42no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C4⋊C4—21no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—22no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4C22⋊C4×C2912yes—
291C22⋊C4—22no—
292C22⋊C4—41no—
293C42—22no—
294C42—41no—
295C42—41no—
296C42—41no—
297C42C22×C4×C2911yescharacteristic
298C42C2×D4×C2911yescharacteristic
299C42C2×D4×C2911yescharacteristic
300C42#41×C2911yescharacteristic
301C23C29×#12111yescharacteristic
302Q8—42no—
303Q8—42no—
304Q8—41no—
305Q8—41no—
306Q8—41no—
307Q8—41no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4C2×C22⋊C4×C2911yescharacteristic
319C2×C4C4×D4×C2911yescharacteristic
320C2×C4C4×D4×C2911yescharacteristic
321C2×C4C29×#12011yescharacteristic
322C2×C4C29×#12111yescharacteristic
323C2×C4C29×#12311yescharacteristic
324C2×C4C2×Q16×C2911yescharacteristic
325C2×C4C29×#13511yescharacteristic
326C2×C4C29×#13711yescharacteristic
327C2×C4C29×#13711yescharacteristic
328C8—22no—
329C8—22no—
330C8—41no—
331C8—41no—
332C8—41no—
333C8—41no—
334C8—81no—
335C22—21no—
336C22—21no—
337C22C29×#38611yescharacteristic
338C22C29×#46211yescharacteristic
339C22C29×#46411yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—42no—
344C4—42no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4C4×Q16×C2911yescharacteristic
349C4C29×#44111yescharacteristic
350C4C29×#44311yescharacteristic
351C4C29×#44411yescharacteristic
352C4C29×#45111yescharacteristic
353C4C29×#45211yescharacteristic
354C2—21no—
355C2—21no—
356C2C29×#187611yescharacteristic
357C2C29×#187811yescharacteristic
358C2C29×#188411yescharacteristic
subgroupG/H
centerC2×C4×C29#120
commutatorC42C22×C4×C29
Frattini, cosocleC2×C42C23×C29
socleC22×C29#386
prime radicalC23×C29#121
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
10. C29×#500C4semidirect
11. C29×#494C4semidirect
12. C29×#487C4semidirect
13. C29×#487C4semidirect
86. M16×C29Q16semidirect
121. #9056C29direct (N × H)
184. #500C4×C29semidirect
185. #494C4×C29semidirect
186. #487C4×C29semidirect
187. #487C4×C29semidirect
253. C29#9056direct (N × H)
266. M16Q16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#31702
C29×#29622
C29×#19862
C29×#15032
C29×#14812
C29×#12792
C29×#12782
#905629