Finite Group Databasebeta

← C29×#13389 #20308289

Subgroups — C29×#13389 #20308289

Order 7424.

402 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#472C211yesmaximal, characteristic
2C29×#2161C211yesmaximal, characteristic, complemented
3C2×C29×#361C211yesmaximal, characteristic, complemented
4C2×C29×#361C211yesmaximal, characteristic, complemented
5C29×#2117C211yesmaximal, characteristic, complemented
6C29×#1813C211yesmaximal, characteristic, complemented
7C29×#1388C211yesmaximal, characteristic, complemented
8C2×C29×AGL(1,ℤ/8)—21no—
9C22×D8×C29C2211yescharacteristic
10C2×C29×#131C2211yescharacteristic
11C2×C29×M32C2211yescharacteristic
12C2×C29×M32C2211yescharacteristic
13C29×#472—22no—
14C29×#472—22no—
15C2×C29×#108C2211yescharacteristic
16C2×C29×#108C2211yescharacteristic
17C2×C29×#108C2211yescharacteristic
18C29×#413—21no—
19C2×C29×#100—21no—
20C29×#368—22no—
21C29×#361—22no—
22C29×#361—22no—
23C29×#350—22no—
24C29×#338—21no—
25C2×#41×C29D411yescharacteristic
26C22×D4×C29—21no—
27C29×AGL(1,ℤ/8)—24no—
28C29×AGL(1,ℤ/8)—42no—
29C2×SD16×C29—41no—
30C2×D8×C29—21no—
31C2×D8×C29—21no—
32C2×D8×C29—21no—
33C2×D8×C29—21no—
34C2×D8×C29—21no—
35C2×D8×C29—41no—
36C2×D8×C29D412yes—
37C29×#131—21no—
38C29×#131—21no—
39C29×#131—21no—
40C29×#131—21no—
41C2×M16×C29—21no—
42C2×M16×C29—21no—
43C2×M16×C29—21no—
44C2×M16×C29—21no—
45C2×M16×C29D411yescharacteristic
46C22×C8×C29—21no—
47C22×C8×C29C2311yescharacteristic
48C29×M32—21no—
49C29×M32—21no—
50C29×M32—21no—
51C29×M32D412yes—
52C2×C16×C29—21no—
53C2×C16×C29—21no—
54C29×#108—21no—
55C29×#108—21no—
56C29×#108—21no—
57C29×#108—21no—
58C29×#108—21no—
59C29×#108D412yes—
60C29×#101—41no—
61C29×#100—24no—
62C29×#100—41no—
63C24×C29—41no—
64#41×C29—21no—
65#41×C29—21no—
66#41×C29—21no—
67#41×C29—21no—
68C2×Q8×C29D811yescharacteristic
69C2×D4×C29—21no—
70C2×D4×C29—22no—
71C2×D4×C29—41no—
72C2×D4×C29—41no—
73C2×D4×C29—41no—
74C2×D4×C29—41no—
75C2×D4×C29—41no—
76C2×D4×C29D811yescharacteristic
77C22×C4×C29—21no—
78C22×C4×C29C2×D411yescharacteristic
79SD16×C29—44no—
80D8×C29—22no—
81D8×C29—22no—
82D8×C29—44no—
83D8×C29—41no—
84D8×C29—41no—
85M16×C29—22no—
86M16×C29—21no—
87M16×C29—21no—
88M16×C29—41no—
89M16×C29—41no—
90M16×C29—41no—
91M16×C29—41no—
92M16×C29—41no—
93M16×C29—41no—
94M16×C29—41no—
95C2×C8×C29—21no—
96C2×C8×C29—41no—
97C2×C8×C29—41no—
98C2×C8×C29—41no—
99C2×C8×C29—41no—
100C2×C8×C29—41no—
101C2×C8×C29C2×D411yescharacteristic
102C2×C8×C29C2×D411yescharacteristic
103C2×C8×C29C2×D411yescharacteristic
104C2×C8×C29#4111yescharacteristic
105C2×C8×C29#4111yescharacteristic
106C2×C8×C29#4111yescharacteristic
107C16×C29—22no—
108C16×C29—41no—
109#13389C2911yesmaximal, characteristic, direct product factor, Sylow
110C23×C29—21no—
111C23×C29—42no—
112C23×C29—81no—
113C23×C29—81no—
114C23×C29—162no—
115C23×C29#13711yescharacteristic
116Q8×C29—21no—
117Q8×C29—21no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—41no—
121D4×C29—41no—
122D4×C29—42no—
123D4×C29—42no—
124D4×C29—81no—
125D4×C29—81no—
126C2×C4×C29—21no—
127C2×C4×C29—41no—
128C2×C4×C29—41no—
129C2×C4×C29#12011yescharacteristic
130C2×C4×C29#12111yescharacteristic
131C2×C4×C29#12311yescharacteristic
132C2×C4×C29C2×D811yescharacteristic
133C2×C4×C29#13511yescharacteristic
134C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
135C8×C29—41no—
136C8×C29—42no—
137C8×C29—81no—
138C8×C29—81no—
139C8×C29#12111yescharacteristic
140C8×C29#12111yescharacteristic
141C8×C29#12311yescharacteristic
142C8×C29#12411yescharacteristic
143C2×#472C2×C2911yescharacteristic
144#2161C2×C2911yescharacteristic, complemented
145C2×#361C2×C2911yescharacteristic, complemented
146C2×#361C2×C2911yescharacteristic, complemented
147#2117C2×C2911yescharacteristic, complemented
148#1813C2×C2911yescharacteristic, complemented
149#1388C2×C2911yescharacteristic, complemented
150C22×C29—41no—
151C22×C29—41no—
152C22×C29—81no—
153C22×C29—82no—
154C22×C29—162no—
155C22×C29—162no—
156C22×C29—162no—
157C22×C29#45211yescharacteristic
158C22×C29#46811yescharacteristic
159C22×C29#48011yescharacteristic
160C4×C29—41no—
161C4×C29#39411yescharacteristic
162C4×C29#44711yescharacteristic
163C4×C29#46611yescharacteristic
164C4×C29#48211yescharacteristic
165C2×AGL(1,ℤ/8)—21no—
166C22×D8C22×C2911yescharacteristic
167C2×#131C22×C2911yescharacteristic
168C2×M32C22×C2911yescharacteristic
169C2×M32C22×C2911yescharacteristic
170#472—22no—
171#472—22no—
172C2×#108C22×C2911yescharacteristic
173C2×#108C22×C2911yescharacteristic
174C2×#108C22×C2911yescharacteristic
175#413—21no—
176C2×#100—21no—
177#368—22no—
178#361—22no—
179#361—22no—
180#350—22no—
181#338—21no—
182C2×C29—21no—
183C2×C29—21no—
184C2×C29—21no—
185C2×C29—81no—
186C2×C29—162no—
187C2×C29#203311yescharacteristic
188C2×#41D4×C2911yescharacteristic
189C22×D4—21no—
190AGL(1,ℤ/8)—24no—
191AGL(1,ℤ/8)—42no—
192C2×SD16—41no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—41no—
199C2×D8D4×C2912yes—
200#131—21no—
201#131—21no—
202#131—21no—
203#131—21no—
204C2×M16—21no—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16—21no—
208C2×M16D4×C2911yescharacteristic
209C22×C8—21no—
210C22×C8C23×C2911yescharacteristic
211M32—21no—
212M32—21no—
213M32—21no—
214M32D4×C2912yes—
215C2×C16—21no—
216C2×C16—21no—
217#108—21no—
218#108—21no—
219#108—21no—
220#108—21no—
221#108—21no—
222#108D4×C2912yes—
223#101—41no—
224#100—24no—
225#100—41no—
226C29#1338911yescharacteristic, direct product factor, Sylow
227C24—41no—
228#41—21no—
229#41—21no—
230#41—21no—
231#41—21no—
232C2×Q8D8×C2911yescharacteristic
233C2×D4—21no—
234C2×D4—22no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4D8×C2911yescharacteristic
241C22×C4—21no—
242C22×C4C2×D4×C2911yescharacteristic
243SD16—44no—
244D8—22no—
245D8—22no—
246D8—44no—
247D8—41no—
248D8—41no—
249M16—21no—
250M16—22no—
251M16—21no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—41no—
257M16—41no—
258M16—41no—
259C2×C8—21no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8C2×D4×C2911yescharacteristic
266C2×C8C2×D4×C2911yescharacteristic
267C2×C8C2×D4×C2911yescharacteristic
268C2×C8#41×C2911yescharacteristic
269C2×C8#41×C2911yescharacteristic
270C2×C8#41×C2911yescharacteristic
271C16—22no—
272C16—41no—
273C23—21no—
274C23—42no—
275C23—81no—
276C23—81no—
277C23—162no—
278C23C29×#13711yescharacteristic
279Q8—21no—
280Q8—21no—
281D4—21no—
282D4—21no—
283D4—41no—
284D4—41no—
285D4—42no—
286D4—42no—
287D4—81no—
288D4—81no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4C29×#12011yescharacteristic
293C2×C4C29×#12111yescharacteristic
294C2×C4C29×#12311yescharacteristic
295C2×C4C2×D8×C2911yescharacteristic
296C2×C4C29×#13511yescharacteristic
297C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
298C8—42no—
299C8—41no—
300C8—81no—
301C8—81no—
302C8C29×#12111yescharacteristic
303C8C29×#12111yescharacteristic
304C8C29×#12311yescharacteristic
305C8C29×#12411yescharacteristic
306C22—41no—
307C22—41no—
308C22—81no—
309C22—82no—
310C22—162no—
311C22—162no—
312C22—162no—
313C22C29×#45211yescharacteristic
314C22C29×#46811yescharacteristic
315C22C29×#48011yescharacteristic
316C4—41no—
317C4C29×#39411yescharacteristic
318C4C29×#44711yescharacteristic
319C4C29×#46611yescharacteristic
320C4C29×#48211yescharacteristic
321C2—21no—
322C2—21no—
323C2—21no—
324C2—81no—
325C2—162no—
326C2C29×#203311yescharacteristic
subgroupG/H
center, socleC2×C29#2033
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC2×C29×#472C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C2×C29×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2161C2semidirect
3. C2×C29×#361C2semidirect
4. C2×C29×#361C2semidirect
5. C29×#2117C2semidirect
6. C29×#1813C2semidirect
7. C29×#1388C2semidirect
109. #13389C29direct (N × H)
144. #2161C2×C29semidirect
145. C2×#361C2×C29semidirect
146. C2×#361C2×C29semidirect
147. #2117C2×C29semidirect
148. #1813C2×C29semidirect
149. #1388C2×C29semidirect
226. C29#13389direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4722
C29×#21612
C2×C29×#3612
C29×#21172
C29×#18132
C29×#13882
#1338929