Finite Group Databasebeta

← C29×#11894 #20306794

Subgroups — C29×#11894 #20306794

Order 7424.

394 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3050C211yesmaximal, characteristic
2C29×#2112C211yesmaximal, characteristic, complemented
3C29×#1810C211yesmaximal, characteristic, complemented
4C29×#1350C212yesmaximal, complemented
5C29×#1349C212yesmaximal, complemented
6C2×C29×#135C411yescharacteristic
7C23×C8×C29C2211yescharacteristic
8C29×#525—21no—
9C2×C29×M32—21no—
10C29×#467C411yescharacteristic
11C29×#467C2211yescharacteristic
12C29×#466C411yescharacteristic
13C29×#466C2211yescharacteristic
14C29×#465—21no—
15C29×#465—21no—
16C2×C29×#108—21no—
17C29×#427C411yescharacteristic
18C29×#416—21no—
19C29×#407—21no—
20C29×C22⋊C16—21no—
21C29×C22⋊C16C2212yes—
22C29×#341C2212yes—
23C2×#41×C29—21no—
24C23×C4×C29D411yescharacteristic
25C29×#135—42no—
26C2×Q16×C29C2×C411yescharacteristic
27C2×SD16×C29—21no—
28C2×D8×C29C2×C411yescharacteristic
29C2×M16×C29—22no—
30C22×C8×C29—42no—
31C22×C8×C29C2×C411yescharacteristic
32C22×C8×C29C2×C411yescharacteristic
33C22×C8×C29D411yescharacteristic
34C22×C8×C29D411yescharacteristic
35C22×C8×C29D411yescharacteristic
36C22×C8×C29C2311yescharacteristic
37C29×#123—41no—
38C29×C22⋊Q8—21no—
39C29×C22⋊Q8—21no—
40C29×#121—21no—
41C29×#121—21no—
42C29×#120—41no—
43C4×D4×C29—41no—
44C4×D4×C29—41no—
45C29×#117—21no—
46C29×M32—42no—
47C2×C16×C29—22no—
48C29×#108—42no—
49C29×#107C2×C411yescharacteristic
50C29×#107C2×C411yescharacteristic
51C29×#106—21no—
52C29×#103—21no—
53C29×#103—21no—
54C29×#102—21no—
55C29×#102—21no—
56C29×C22⋊C8—41no—
57C29×C22⋊C8—41no—
58C24×C29SD1611yescharacteristic
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×C29C22⋊C411yescharacteristic
70C22×C4×C29C22⋊C411yescharacteristic
71C22×C4×C29D811yescharacteristic
72C22×C4×C29D811yescharacteristic
73C22×C4×C29SD1611yescharacteristic
74C22×C4×C29C2×D411yescharacteristic
75Q16×C29—41no—
76SD16×C29—42no—
77D8×C29—41no—
78M16×C29—42no—
79M16×C29—42no—
80C2×C8×C29—22no—
81C2×C8×C29—22no—
82C2×C8×C29—22no—
83C2×C8×C29—41no—
84C2×C8×C29—41no—
85C2×C8×C29—41no—
86C2×C8×C29—42no—
87C2×C8×C29C22⋊C411yescharacteristic
88C2×C8×C29C22⋊C411yescharacteristic
89C2×C8×C29C22×C411yescharacteristic
90C2×C8×C29C2×D411yescharacteristic
91C4⋊C4×C29—21no—
92C4⋊C4×C29—21no—
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—
100C42×C29—41no—
101C16×C29—42no—
102#11894C2911yesmaximal, characteristic, direct product factor, Sylow
103C23×C29—41no—
104C23×C29—41no—
105C23×C29—41no—
106C23×C29—41no—
107C23×C29#10211yescharacteristic
108C23×C29#10211yescharacteristic
109C23×C29C2×SD1611yescharacteristic
110Q8×C29—41no—
111Q8×C29—41no—
112D4×C29—41no—
113D4×C29—41no—
114D4×C29—82no—
115D4×C29—82no—
116D4×C29—82no—
117C2×C4×C29—21no—
118C2×C4×C29—21no—
119C2×C4×C29—21no—
120C2×C4×C29—21no—
121C2×C4×C29—21no—
122C2×C4×C29—21no—
123C2×C4×C29—41no—
124C2×C4×C29—41no—
125C2×C4×C29—41no—
126C2×C4×C29—41no—
127C2×C4×C29—41no—
128C2×C4×C29—41no—
129C2×C4×C29—82no—
130C2×C4×C29#10211yescharacteristic
131C2×C4×C29#10211yescharacteristic
132C2×C4×C29C2×C22⋊C411yescharacteristic
133C2×C4×C29C2×D811yescharacteristic
134C8×C29—21no—
135C8×C29—21no—
136C8×C29—21no—
137C8×C29—82no—
138C8×C29#9912yes—
139#3050C2×C2911yescharacteristic
140#2112C2×C2911yescharacteristic, complemented
141#1810C2×C2911yescharacteristic, complemented
142#1350C2×C2912yescomplemented
143#1349C2×C2912yescomplemented
144C22×C29—21no—
145C22×C29—21no—
146C22×C29—21no—
147C22×C29—21no—
148C22×C29—21no—
149C22×C29—21no—
150C22×C29—21no—
151C22×C29—21no—
152C22×C29—21no—
153C22×C29—44no—
154C22×C29—81no—
155C22×C29—81no—
156C22×C29—81no—
157C22×C29C2×#10211yescharacteristic
158C4×C29—21no—
159C4×C29—21no—
160C4×C29—21no—
161C4×C29—81no—
162C4×C29—81no—
163C4×C29—81no—
164C4×C29C2×#9911yescharacteristic
165C4×C29#42111yescharacteristic
166C2×#135C4×C2911yescharacteristic
167C23×C8C22×C2911yescharacteristic
168#525—21no—
169C2×M32—21no—
170#467C4×C2911yescharacteristic
171#467C22×C2911yescharacteristic
172#466C4×C2911yescharacteristic
173#466C22×C2911yescharacteristic
174#465—21no—
175#465—21no—
176C2×#108—21no—
177#427C4×C2911yescharacteristic
178#416—21no—
179#407—21no—
180C22⋊C16—21no—
181C22⋊C16C22×C2912yes—
182#341C22×C2912yes—
183C2×C29—41no—
184C2×C29—41no—
185C2×C29—41no—
186C2×C29—161no—
187C2×C29#151911yescharacteristic
188C2×C29#214311yescharacteristic
189C2×C29#214811yescharacteristic
190C2×#41—21no—
191C23×C4D4×C2911yescharacteristic
192#135—42no—
193C2×Q16C2×C4×C2911yescharacteristic
194C2×SD16—21no—
195C2×D8C2×C4×C2911yescharacteristic
196C2×M16—22no—
197C22×C8—42no—
198C22×C8C2×C4×C2911yescharacteristic
199C22×C8C2×C4×C2911yescharacteristic
200C22×C8D4×C2911yescharacteristic
201C22×C8D4×C2911yescharacteristic
202C22×C8D4×C2911yescharacteristic
203C22×C8C23×C2911yescharacteristic
204#123—41no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207#121—21no—
208#121—21no—
209#120—41no—
210C4×D4—41no—
211C4×D4—41no—
212#117—21no—
213M32—42no—
214C2×C16—22no—
215#108—42no—
216#107C2×C4×C2911yescharacteristic
217#107C2×C4×C2911yescharacteristic
218#106—21no—
219#103—21no—
220#103—21no—
221#102—21no—
222#102—21no—
223C22⋊C8—41no—
224C22⋊C8—41no—
225C29#1189411yescharacteristic, direct product factor, Sylow
226C24SD16×C2911yescharacteristic
227#41—42no—
228#41—42no—
229C2×Q8—21no—
230C2×D4—21no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4C22⋊C4×C2911yescharacteristic
238C22×C4C22⋊C4×C2911yescharacteristic
239C22×C4D8×C2911yescharacteristic
240C22×C4D8×C2911yescharacteristic
241C22×C4SD16×C2911yescharacteristic
242C22×C4C2×D4×C2911yescharacteristic
243Q16—41no—
244SD16—42no—
245D8—41no—
246M16—42no—
247M16—42no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—42no—
255C2×C8C22⋊C4×C2911yescharacteristic
256C2×C8C22⋊C4×C2911yescharacteristic
257C2×C8C22×C4×C2911yescharacteristic
258C2×C8C2×D4×C2911yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—41no—
269C16—42no—
270C23—41no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23C29×#10211yescharacteristic
275C23C29×#10211yescharacteristic
276C23C2×SD16×C2911yescharacteristic
277Q8—41no—
278Q8—41no—
279D4—41no—
280D4—41no—
281D4—82no—
282D4—82no—
283D4—82no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—82no—
297C2×C4C29×#10211yescharacteristic
298C2×C4C29×#10211yescharacteristic
299C2×C4C2×C22⋊C4×C2911yescharacteristic
300C2×C4C2×D8×C2911yescharacteristic
301C8—21no—
302C8—21no—
303C8—21no—
304C8—82no—
305C8C29×#9912yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—44no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22C2×C29×#10211yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—81no—
326C4C2×C29×#9911yescharacteristic
327C4C29×#42111yescharacteristic
328C2—41no—
329C2—41no—
330C2—41no—
331C2—161no—
332C2C29×#151911yescharacteristic
333C2C29×#214311yescharacteristic
334C2C29×#214811yescharacteristic
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. C29×#2112C2semidirect
3. C29×#1810C2semidirect
4. C29×#1350C2semidirect
5. C29×#1349C2semidirect
102. #11894C29direct (N × H)
140. #2112C2×C29semidirect
141. #1810C2×C29semidirect
142. #1350C2×C29semidirect
143. #1349C2×C29semidirect
225. C29#11894direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30502
C29×#21122
C29×#18102
C29×#13502
C29×#13492
#1189429