Finite Group Databasebeta

← C29×#9200 #20304100

Subgroups — C29×#9200 #20304100

Order 7424.

560 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2627C211yesmaximal, characteristic
2C29×#2316C211yesmaximal, characteristic
3C29×#1520C212yesmaximal
4C2×C29×#324C211yesmaximal, characteristic
5C29×#1289C212yesmaximal
6C2×C29×C22⋊Q8C2211yescharacteristic
7C2×C29×#117—21no—
8C22×C4⋊C4×C29C2211yescharacteristic
9C2×C29×C22⋊C8C2212yes—
10C29×#400C412yescomplemented
11C29×#398—22no—
12C29×#395C412yescomplemented
13C29×#389—24no—
14C29×#385—21no—
15C29×#381—21no—
16C29×#380—21no—
17C29×#380C2211yescharacteristic
18C29×#380C2212yes—
19C29×#328—24no—
20C29×#324—22no—
21C22×Q8×C29C2×C411yescharacteristic
22C23×C4×C29D411yescharacteristic
23C23×C4×C29D411yescharacteristic
24C23×C4×C29C2311yescharacteristic
25C22×C8×C29—22no—
26C29×C22⋊Q8—22no—
27C29×C22⋊Q8—22no—
28C29×#117—42no—
29C29×#117—42no—
30C2×C4⋊C4×C29—22no—
31C2×C4⋊C4×C29—22no—
32C2×C4⋊C4×C29—22no—
33C2×C4⋊C4×C29—21no—
34C2×C4⋊C4×C29—22no—
35C2×C4⋊C4×C29—22no—
36C2×C4⋊C4×C29—22no—
37C2×C4⋊C4×C29—21no—
38C2×C4⋊C4×C29C2×C411yescharacteristic
39C2×C4⋊C4×C29C2×C412yes—
40C2×C4⋊C4×C29D412yes—
41C2×C22⋊C4×C29—22no—
42C2×C22⋊C4×C29—21no—
43C2×C22⋊C4×C29—21no—
44C2×C42×C29—22no—
45C29×C22⋊C8—22no—
46C29×C22⋊C8—22no—
47C29×#95—22no—
48C29×#95—22no—
49C29×#95—22no—
50C29×#95—22no—
51C29×#95C2×C412yes—
52C29×#95D414yes—
53C24×C29C2×D411yescharacteristic
54C2×Q8×C29—22no—
55C2×Q8×C29—81no—
56C22×C4×C29—21no—
57C22×C4×C29—21no—
58C22×C4×C29—21no—
59C22×C4×C29—21no—
60C22×C4×C29—21no—
61C22×C4×C29—21no—
62C22×C4×C29—21no—
63C22×C4×C29—22no—
64C22×C4×C29—21no—
65C22×C4×C29—24no—
66C22×C4×C29—81no—
67C22×C4×C29—81no—
68C22×C4×C29C22⋊C412yes—
69C22×C4×C29C22⋊C412yes—
70C22×C4×C29SD1612yes—
71C22×C4×C29Q1612yes—
72C22×C4×C29C22×C411yescharacteristic
73C22×C4×C29C2×D412yes—
74C22×C4×C29C2×D411yescharacteristic
75C22×C4×C29#4112yes—
76C2×C8×C29—42no—
77C2×C8×C29—82no—
78C4⋊C4×C29—24no—
79C4⋊C4×C29—24no—
80C4⋊C4×C29—22no—
81C4⋊C4×C29—44no—
82C4⋊C4×C29—42no—
83C4⋊C4×C29—82no—
84C4⋊C4×C29—81no—
85C4⋊C4×C29—82no—
86C4⋊C4×C29—82no—
87C22⋊C4×C29—41no—
88C22⋊C4×C29—41no—
89C22⋊C4×C29—42no—
90C22⋊C4×C29—41no—
91C22⋊C4×C29—42no—
92C22⋊C4×C29—41no—
93C42×C29—44no—
94#9200C2911yesmaximal, characteristic, direct product factor, Sylow
95C23×C29—41no—
96C23×C29—41no—
97C23×C29C2×C22⋊C411yescharacteristic
98C23×C29#12011yescharacteristic
99C23×C29#12311yescharacteristic
100C23×C29C2×SD1611yescharacteristic
101C23×C29C2×Q1611yescharacteristic
102C23×C29AGL(1,ℤ/8)11yescharacteristic
103C23×C29#13711yescharacteristic
104Q8×C29—82no—
105C2×C4×C29—22no—
106C2×C4×C29—22no—
107C2×C4×C29—22no—
108C2×C4×C29—22no—
109C2×C4×C29—22no—
110C2×C4×C29—22no—
111C2×C4×C29—22no—
112C2×C4×C29—41no—
113C2×C4×C29—42no—
114C2×C4×C29—42no—
115C2×C4×C29—41no—
116C2×C4×C29—42no—
117C2×C4×C29—42no—
118C2×C4×C29—42no—
119C2×C4×C29—44no—
120C2×C4×C29—42no—
121C2×C4×C29—42no—
122C2×C4×C29—44no—
123C2×C4×C29—42no—
124C2×C4×C29—41no—
125C2×C4×C29—41no—
126C2×C4×C29—42no—
127C2×C4×C29—44no—
128C2×C4×C29—81no—
129C2×C4×C29#10314yes—
130C2×C4×C29C4×D412yes—
131C2×C4×C29#12112yes—
132C8×C29—82no—
133#2627C2×C2911yescharacteristic
134#2316C2×C2911yescharacteristic
135#1520C2×C2912yes—
136C2×#324C2×C2911yescharacteristic
137#1289C2×C2912yes—
138C22×C29—21no—
139C22×C29—21no—
140C22×C29—21no—
141C22×C29—21no—
142C22×C29—21no—
143C22×C29—21no—
144C22×C29—41no—
145C22×C29—41no—
146C22×C29—41no—
147C22×C29—41no—
148C22×C29#38611yescharacteristic
149C22×C29C2×#10311yescharacteristic
150C22×C29#41711yescharacteristic
151C22×C29#45011yescharacteristic
152C22×C29#45111yescharacteristic
153C22×C29#48311yescharacteristic
154C22×C29#48411yescharacteristic
155C4×C29—24no—
156C4×C29—22no—
157C4×C29—22no—
158C4×C29—42no—
159C4×C29—84no—
160C4×C29—82no—
161C4×C29—81no—
162C4×C29—81no—
163C2×C22⋊Q8C22×C2911yescharacteristic
164C2×#117—21no—
165C22×C4⋊C4C22×C2911yescharacteristic
166C2×C22⋊C8C22×C2912yes—
167#400C4×C2912yescomplemented
168#398—22no—
169#395C4×C2912yescomplemented
170#389—24no—
171#385—21no—
172#381—21no—
173#380—21no—
174#380C22×C2911yescharacteristic
175#380C22×C2912yes—
176#328—24no—
177#324—22no—
178C2×C29—21no—
179C2×C29—21no—
180C2×C29—21no—
181C2×C29—21no—
182C2×C29—21no—
183C2×C29—21no—
184C2×C29#187211yescharacteristic
185C2×C29#191211yescharacteristic
186C2×C29#191311yescharacteristic
187C22×Q8C2×C4×C2911yescharacteristic
188C23×C4D4×C2911yescharacteristic
189C23×C4D4×C2911yescharacteristic
190C23×C4C23×C2911yescharacteristic
191C22×C8—22no—
192C22⋊Q8—22no—
193C22⋊Q8—22no—
194#117—42no—
195#117—42no—
196C2×C4⋊C4—22no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—22no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4C2×C4×C2911yescharacteristic
205C2×C4⋊C4C2×C4×C2912yes—
206C2×C4⋊C4D4×C2912yes—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C42—22no—
211C22⋊C8—22no—
212C22⋊C8—22no—
213#95—22no—
214#95—22no—
215#95—22no—
216#95—22no—
217#95C2×C4×C2912yes—
218#95D4×C2914yes—
219C29#920011yescharacteristic, direct product factor, Sylow
220C24C2×D4×C2911yescharacteristic
221C2×Q8—22no—
222C2×Q8—81no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—21no—
232C22×C4—24no—
233C22×C4—81no—
234C22×C4—81no—
235C22×C4C22⋊C4×C2912yes—
236C22×C4C22⋊C4×C2912yes—
237C22×C4SD16×C2912yes—
238C22×C4Q16×C2912yes—
239C22×C4C22×C4×C2911yescharacteristic
240C22×C4C2×D4×C2912yes—
241C22×C4C2×D4×C2911yescharacteristic
242C22×C4#41×C2912yes—
243C2×C8—42no—
244C2×C8—82no—
245C4⋊C4—24no—
246C4⋊C4—24no—
247C4⋊C4—22no—
248C4⋊C4—44no—
249C4⋊C4—42no—
250C4⋊C4—82no—
251C4⋊C4—81no—
252C4⋊C4—82no—
253C4⋊C4—82no—
254C22⋊C4—41no—
255C22⋊C4—41no—
256C22⋊C4—42no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C42—44no—
261C23—41no—
262C23—41no—
263C23C2×C22⋊C4×C2911yescharacteristic
264C23C29×#12011yescharacteristic
265C23C29×#12311yescharacteristic
266C23C2×SD16×C2911yescharacteristic
267C23C2×Q16×C2911yescharacteristic
268C23C29×AGL(1,ℤ/8)11yescharacteristic
269C23C29×#13711yescharacteristic
270Q8—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—44no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—44no—
289C2×C4—42no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C29×#10314yes—
296C2×C4C4×D4×C2912yes—
297C2×C4C29×#12112yes—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C29×#38611yescharacteristic
310C22C2×C29×#10311yescharacteristic
311C22C29×#41711yescharacteristic
312C22C29×#45011yescharacteristic
313C22C29×#45111yescharacteristic
314C22C29×#48311yescharacteristic
315C22C29×#48411yescharacteristic
316C4—22no—
317C4—22no—
318C4—24no—
319C4—42no—
320C4—84no—
321C4—82no—
322C4—81no—
323C4—81no—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2C29×#187211yescharacteristic
331C2C29×#191211yescharacteristic
332C2C29×#191311yescharacteristic
subgroupG/H
center, socleC22×C29#386
commutatorC22×C4C22×C4×C29
Frattini, cosocleC23×C4C23×C29
prime radicalC24×C29C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
10. C29×#400C4semidirect
12. C29×#395C4semidirect
94. #9200C29direct (N × H)
167. #400C4×C29semidirect
169. #395C4×C29semidirect
219. C29#9200direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#26272
C29×#23162
C29×#15202
C2×C29×#3242
C29×#12892
#920029