Finite Group Databasebeta

← C29×#11885 #20306785

Subgroups — C29×#11885 #20306785

Order 7424.

422 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3050C211yesmaximal, characteristic
2C2×C29×C22⋊C16C211yesmaximal, characteristic, complemented
3C29×#1807C211yesmaximal, characteristic, complemented
4C29×#1348C212yesmaximal, complemented
5C29×#1347C212yesmaximal, complemented
6C2×C29×#135C411yescharacteristic, complemented
7C23×C8×C29C2211yescharacteristic
8C29×#525—21no—
9C22×C16×C29—21no—
10C29×#467C411yescharacteristic, complemented
11C29×#467C2211yescharacteristic
12C29×#466C411yescharacteristic, complemented
13C29×#466C2211yescharacteristic
14C29×#465—21no—
15C29×#465—21no—
16C29×#427C411yescharacteristic, complemented
17C2×C29×#106—21no—
18C29×#416—21no—
19C29×#380—21no—
20C29×C22⋊C16—21no—
21C29×C22⋊C16C2212yes—
22C29×#340C2212yes—
23C2×#41×C29—21no—
24C23×C4×C29D411yescharacteristic
25C29×#135—42no—
26C2×Q16×C29C2×C411yescharacteristic
27C2×SD16×C29—21no—
28C2×D8×C29C2×C411yescharacteristic
29C22×C8×C29—42no—
30C22×C8×C29C2×C411yescharacteristic
31C22×C8×C29C2×C411yescharacteristic
32C22×C8×C29D411yescharacteristic
33C22×C8×C29D411yescharacteristic
34C22×C8×C29D411yescharacteristic
35C22×C8×C29C2311yescharacteristic
36C29×#123—41no—
37C29×C22⋊Q8—21no—
38C29×C22⋊Q8—21no—
39C29×#121—21no—
40C29×#121—21no—
41C29×#120—41no—
42C4×D4×C29—41no—
43C4×D4×C29—41no—
44C29×#117—21no—
45C2×C4⋊C4×C29—22no—
46C2×C22⋊C4×C29—41no—
47C2×C16×C29—22no—
48C2×C16×C29—42no—
49C29×#107C2×C411yescharacteristic
50C29×#107C2×C411yescharacteristic
51C29×#106—21no—
52C29×#106—42no—
53C29×#103—21no—
54C29×#103—21no—
55C29×#102—21no—
56C29×#102—21no—
57C29×#95—41no—
58C24×C29D811yescharacteristic
59#41×C29—42no—
60#41×C29—42no—
61C2×Q8×C29—21no—
62C2×D4×C29—21no—
63C2×D4×C29—41no—
64C2×D4×C29—41no—
65C2×D4×C29—41no—
66C22×C4×C29—41no—
67C22×C4×C29—41no—
68C22×C4×C29—41no—
69C22×C4×C29—42no—
70C22×C4×C29C22⋊C411yescharacteristic
71C22×C4×C29C22⋊C411yescharacteristic
72C22×C4×C29D811yescharacteristic
73C22×C4×C29SD1611yescharacteristic
74C22×C4×C29SD1611yescharacteristic
75C22×C4×C29C2×D411yescharacteristic
76Q16×C29—41no—
77SD16×C29—42no—
78D8×C29—41no—
79C2×C8×C29—22no—
80C2×C8×C29—22no—
81C2×C8×C29—22no—
82C2×C8×C29—41no—
83C2×C8×C29—41no—
84C2×C8×C29—41no—
85C2×C8×C29C22⋊C411yescharacteristic
86C2×C8×C29C22⋊C411yescharacteristic
87C2×C8×C29C22×C411yescharacteristic
88C2×C8×C29C2×D411yescharacteristic
89C4⋊C4×C29—21no—
90C4⋊C4×C29—21no—
91C4⋊C4×C29—42no—
92C4⋊C4×C29—42no—
93C4⋊C4×C29—41no—
94C4⋊C4×C29—41no—
95C22⋊C4×C29—41no—
96C22⋊C4×C29—41no—
97C22⋊C4×C29—41no—
98C22⋊C4×C29—41no—
99C22⋊C4×C29—41no—
100C22⋊C4×C29—82no—
101C42×C29—41no—
102C16×C29—42no—
103#11885C2911yesmaximal, characteristic, direct product factor, Sylow
104C23×C29—22no—
105C23×C29—22no—
106C23×C29—41no—
107C23×C29—41no—
108C23×C29#10211yescharacteristic
109C23×C29#10211yescharacteristic
110C23×C29C2×D811yescharacteristic
111Q8×C29—41no—
112Q8×C29—41no—
113D4×C29—41no—
114D4×C29—41no—
115D4×C29—82no—
116D4×C29—82no—
117D4×C29—82no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—21no—
124C2×C4×C29—41no—
125C2×C4×C29—41no—
126C2×C4×C29—41no—
127C2×C4×C29—41no—
128C2×C4×C29—41no—
129C2×C4×C29—41no—
130C2×C4×C29—82no—
131C2×C4×C29—82no—
132C2×C4×C29—82no—
133C2×C4×C29—82no—
134C2×C4×C29#10211yescharacteristic
135C2×C4×C29#10211yescharacteristic
136C2×C4×C29C2×C22⋊C411yescharacteristic
137C2×C4×C29C2×SD1611yescharacteristic
138C8×C29—21no—
139C8×C29—21no—
140C8×C29—21no—
141C8×C29#9912yes—
142#3050C2×C2911yescharacteristic
143C2×C22⋊C16C2×C2911yescharacteristic, complemented
144#1807C2×C2911yescharacteristic, complemented
145#1348C2×C2912yescomplemented
146#1347C2×C2912yescomplemented
147C22×C29—21no—
148C22×C29—21no—
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—21no—
154C22×C29—44no—
155C22×C29—81no—
156C22×C29—81no—
157C22×C29—81no—
158C22×C29#36012yes—
159C22×C29C2×#10211yescharacteristic
160C22×C29#50812yes—
161C4×C29—21no—
162C4×C29—21no—
163C4×C29—21no—
164C4×C29—81no—
165C4×C29—81no—
166C4×C29—81no—
167C4×C29—162no—
168C4×C29C2×#9911yescharacteristic
169C4×C29#42111yescharacteristic
170C2×#135C4×C2911yescharacteristic, complemented
171C23×C8C22×C2911yescharacteristic
172#525—21no—
173C22×C16—21no—
174#467C4×C2911yescharacteristic, complemented
175#467C22×C2911yescharacteristic
176#466C4×C2911yescharacteristic, complemented
177#466C22×C2911yescharacteristic
178#465—21no—
179#465—21no—
180#427C4×C2911yescharacteristic, complemented
181C2×#106—21no—
182#416—21no—
183#380—21no—
184C22⋊C16—21no—
185C22⋊C16C22×C2912yes—
186#340C22×C2912yes—
187C2×C29—22no—
188C2×C29—22no—
189C2×C29—41no—
190C2×C29—161no—
191C2×C29#151911yescharacteristic
192C2×C29#213811yescharacteristic
193C2×C29C2×#36011yescharacteristic
194C2×#41—21no—
195C23×C4D4×C2911yescharacteristic
196#135—42no—
197C2×Q16C2×C4×C2911yescharacteristic
198C2×SD16—21no—
199C2×D8C2×C4×C2911yescharacteristic
200C22×C8—42no—
201C22×C8C2×C4×C2911yescharacteristic
202C22×C8C2×C4×C2911yescharacteristic
203C22×C8D4×C2911yescharacteristic
204C22×C8D4×C2911yescharacteristic
205C22×C8D4×C2911yescharacteristic
206C22×C8C23×C2911yescharacteristic
207#123—41no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210#121—21no—
211#121—21no—
212#120—41no—
213C4×D4—41no—
214C4×D4—41no—
215#117—21no—
216C2×C4⋊C4—22no—
217C2×C22⋊C4—41no—
218C2×C16—22no—
219C2×C16—42no—
220#107C2×C4×C2911yescharacteristic
221#107C2×C4×C2911yescharacteristic
222#106—21no—
223#106—42no—
224#103—21no—
225#103—21no—
226#102—21no—
227#102—21no—
228#95—41no—
229C29#1188511yescharacteristic, direct product factor, Sylow
230C24D8×C2911yescharacteristic
231#41—42no—
232#41—42no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—42no—
242C22×C4C22⋊C4×C2911yescharacteristic
243C22×C4C22⋊C4×C2911yescharacteristic
244C22×C4D8×C2911yescharacteristic
245C22×C4SD16×C2911yescharacteristic
246C22×C4SD16×C2911yescharacteristic
247C22×C4C2×D4×C2911yescharacteristic
248Q16—41no—
249SD16—42no—
250D8—41no—
251C2×C8—22no—
252C2×C8—22no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8C22⋊C4×C2911yescharacteristic
258C2×C8C22⋊C4×C2911yescharacteristic
259C2×C8C22×C4×C2911yescharacteristic
260C2×C8C2×D4×C2911yescharacteristic
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—82no—
273C42—41no—
274C16—42no—
275C23—22no—
276C23—22no—
277C23—41no—
278C23—41no—
279C23C29×#10211yescharacteristic
280C23C29×#10211yescharacteristic
281C23C2×D8×C2911yescharacteristic
282Q8—41no—
283Q8—41no—
284D4—41no—
285D4—41no—
286D4—82no—
287D4—82no—
288D4—82no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
304C2×C4—82no—
305C2×C4C29×#10211yescharacteristic
306C2×C4C29×#10211yescharacteristic
307C2×C4C2×C22⋊C4×C2911yescharacteristic
308C2×C4C2×SD16×C2911yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8C29×#9912yes—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—44no—
321C22—81no—
322C22—81no—
323C22—81no—
324C22C29×#36012yes—
325C22C2×C29×#10211yescharacteristic
326C22C29×#50812yes—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—81no—
333C4—162no—
334C4C2×C29×#9911yescharacteristic
335C4C29×#42111yescharacteristic
336C2—22no—
337C2—22no—
338C2—41no—
339C2—161no—
340C2C29×#151911yescharacteristic
341C2C29×#213811yescharacteristic
342C2C2×C29×#36011yescharacteristic
subgroupG/H
center, socleC22×C29C2×#102
commutatorC2×C8C22×C4×C29
Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3050C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×C22⋊C16C2semidirect
3. C29×#1807C2semidirect
4. C29×#1348C2semidirect
5. C29×#1347C2semidirect
6. C2×C29×#135C4semidirect
10. C29×#467C4semidirect
12. C29×#466C4semidirect
16. C29×#427C4semidirect
103. #11885C29direct (N × H)
143. C2×C22⋊C16C2×C29semidirect
144. #1807C2×C29semidirect
145. #1348C2×C29semidirect
146. #1347C2×C29semidirect
170. C2×#135C4×C29semidirect
174. #467C4×C29semidirect
176. #466C4×C29semidirect
180. #427C4×C29semidirect
229. C29#11885direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30502
C2×C29×C22⋊C162
C29×#18072
C29×#13482
C29×#13472
#1188529