Finite Group Databasebeta

← C29×#13390 #20308290

Subgroups — C29×#13390 #20308290

Order 7424.

382 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C29×#473C211yesmaximal, characteristic
2C29×#2161C211yesmaximal, characteristic, complemented
3C2×C29×#362C211yesmaximal, characteristic, complemented
4C2×C29×#362C211yesmaximal, characteristic, complemented
5C29×#2117C211yesmaximal, characteristic
6C29×#1813C211yesmaximal, characteristic
7C29×#1388C211yesmaximal, characteristic, complemented
8C2×C29×#137—21no—
9C22×Q16×C29C2211yescharacteristic
10C2×C29×#131C2211yescharacteristic
11C2×C29×M32C2211yescharacteristic
12C2×C29×M32C2211yescharacteristic
13C29×#473—22no—
14C29×#473—22no—
15C2×C29×#108C2211yescharacteristic
16C2×C29×#108C2211yescharacteristic
17C2×C29×#108C2211yescharacteristic
18C29×#413—21no—
19C2×C29×#101—21no—
20C29×#368—22no—
21C29×#362—22no—
22C29×#362—22no—
23C29×#350—22no—
24C29×#338—21no—
25C2×#41×C29D411yescharacteristic
26C22×Q8×C29—21no—
27C29×#137—24no—
28C29×#137—42no—
29C2×Q16×C29—21no—
30C2×Q16×C29—21no—
31C2×Q16×C29—21no—
32C2×Q16×C29—21no—
33C2×Q16×C29—21no—
34C2×Q16×C29—41no—
35C2×Q16×C29D412yes—
36C2×SD16×C29—41no—
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—24no—
61C29×#101—41no—
62C29×#100—41no—
63#41×C29—21no—
64#41×C29—21no—
65#41×C29—21no—
66#41×C29—21no—
67C2×Q8×C29—22no—
68C2×Q8×C29—41no—
69C2×Q8×C29—41no—
70C2×Q8×C29—41no—
71C2×Q8×C29—41no—
72C2×Q8×C29—41no—
73C2×Q8×C29D811yescharacteristic
74C2×D4×C29—21no—
75C2×D4×C29D811yescharacteristic
76C22×C4×C29—21no—
77C22×C4×C29—41no—
78C22×C4×C29C2×D411yescharacteristic
79Q16×C29—22no—
80Q16×C29—22no—
81Q16×C29—44no—
82Q16×C29—41no—
83Q16×C29—41no—
84SD16×C29—44no—
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#13390C2911yesmaximal, characteristic, direct product factor, Sylow
110C23×C29—21no—
111C23×C29#13711yescharacteristic
112Q8×C29—21no—
113Q8×C29—21no—
114Q8×C29—42no—
115Q8×C29—42no—
116Q8×C29—81no—
117Q8×C29—81no—
118D4×C29—21no—
119D4×C29—21no—
120D4×C29—41no—
121D4×C29—41no—
122C2×C4×C29—21no—
123C2×C4×C29—41no—
124C2×C4×C29—41no—
125C2×C4×C29—42no—
126C2×C4×C29—81no—
127C2×C4×C29—81no—
128C2×C4×C29#12011yescharacteristic
129C2×C4×C29#12111yescharacteristic
130C2×C4×C29#12311yescharacteristic
131C2×C4×C29C2×D811yescharacteristic
132C2×C4×C29#13511yescharacteristic
133C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
134C8×C29—41no—
135C8×C29—42no—
136C8×C29—81no—
137C8×C29—81no—
138C8×C29#12111yescharacteristic
139C8×C29#12111yescharacteristic
140C8×C29#12311yescharacteristic
141C8×C29#12411yescharacteristic
142C2×#473C2×C2911yescharacteristic
143#2161C2×C2911yescharacteristic, complemented
144C2×#362C2×C2911yescharacteristic, complemented
145C2×#362C2×C2911yescharacteristic, complemented
146#2117C2×C2911yescharacteristic
147#1813C2×C2911yescharacteristic
148#1388C2×C2911yescharacteristic, complemented
149C22×C29—41no—
150C22×C29—41no—
151C22×C29—81no—
152C22×C29#45211yescharacteristic
153C22×C29#46811yescharacteristic
154C22×C29#48011yescharacteristic
155C4×C29—41no—
156C4×C29—82no—
157C4×C29#39411yescharacteristic
158C4×C29#44711yescharacteristic
159C4×C29#46611yescharacteristic
160C4×C29#48211yescharacteristic
161C2×#137—21no—
162C22×Q16C22×C2911yescharacteristic
163C2×#131C22×C2911yescharacteristic
164C2×M32C22×C2911yescharacteristic
165C2×M32C22×C2911yescharacteristic
166#473—22no—
167#473—22no—
168C2×#108C22×C2911yescharacteristic
169C2×#108C22×C2911yescharacteristic
170C2×#108C22×C2911yescharacteristic
171#413—21no—
172C2×#101—21no—
173#368—22no—
174#362—22no—
175#362—22no—
176#350—22no—
177#338—21no—
178C2×C29—21no—
179C2×C29—21no—
180C2×C29—21no—
181C2×C29—81no—
182C2×C29#203311yescharacteristic
183C2×#41D4×C2911yescharacteristic
184C22×Q8—21no—
185#137—24no—
186#137—42no—
187C2×Q16—21no—
188C2×Q16—21no—
189C2×Q16—21no—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—41no—
193C2×Q16D4×C2912yes—
194C2×SD16—41no—
195#131—21no—
196#131—21no—
197#131—21no—
198#131—21no—
199C2×M16—21no—
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C2×M16D4×C2911yescharacteristic
204C22×C8—21no—
205C22×C8C23×C2911yescharacteristic
206M32—21no—
207M32—21no—
208M32—21no—
209M32D4×C2912yes—
210C2×C16—21no—
211C2×C16—21no—
212#108—21no—
213#108—21no—
214#108—21no—
215#108—21no—
216#108—21no—
217#108D4×C2912yes—
218#101—24no—
219#101—41no—
220#100—41no—
221C29#1339011yescharacteristic, direct product factor, Sylow
222#41—21no—
223#41—21no—
224#41—21no—
225#41—21no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8D8×C2911yescharacteristic
233C2×D4—21no—
234C2×D4D8×C2911yescharacteristic
235C22×C4—21no—
236C22×C4—41no—
237C22×C4C2×D4×C2911yescharacteristic
238Q16—22no—
239Q16—22no—
240Q16—44no—
241Q16—41no—
242Q16—41no—
243SD16—44no—
244M16—21no—
245M16—22no—
246M16—21no—
247M16—41no—
248M16—41no—
249M16—41no—
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254C2×C8—21no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8C2×D4×C2911yescharacteristic
261C2×C8C2×D4×C2911yescharacteristic
262C2×C8C2×D4×C2911yescharacteristic
263C2×C8#41×C2911yescharacteristic
264C2×C8#41×C2911yescharacteristic
265C2×C8#41×C2911yescharacteristic
266C16—22no—
267C16—41no—
268C23—21no—
269C23C29×#13711yescharacteristic
270Q8—21no—
271Q8—21no—
272Q8—42no—
273Q8—42no—
274Q8—81no—
275Q8—81no—
276D4—21no—
277D4—21no—
278D4—41no—
279D4—41no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—42no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4C29×#12011yescharacteristic
287C2×C4C29×#12111yescharacteristic
288C2×C4C29×#12311yescharacteristic
289C2×C4C2×D8×C2911yescharacteristic
290C2×C4C29×#13511yescharacteristic
291C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
292C8—42no—
293C8—41no—
294C8—81no—
295C8—81no—
296C8C29×#12111yescharacteristic
297C8C29×#12111yescharacteristic
298C8C29×#12311yescharacteristic
299C8C29×#12411yescharacteristic
300C22—41no—
301C22—41no—
302C22—81no—
303C22C29×#45211yescharacteristic
304C22C29×#46811yescharacteristic
305C22C29×#48011yescharacteristic
306C4—41no—
307C4—82no—
308C4C29×#39411yescharacteristic
309C4C29×#44711yescharacteristic
310C4C29×#46611yescharacteristic
311C4C29×#48211yescharacteristic
312C2—21no—
313C2—21no—
314C2—21no—
315C2—81no—
316C2C29×#203311yescharacteristic
subgroupG/H
center, socleC2×C29#2033
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC2×#41×C29D4
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×#362C2semidirect
4. C2×C29×#362C2semidirect
7. C29×#1388C2semidirect
109. #13390C29direct (N × H)
143. #2161C2×C29semidirect
144. C2×#362C2×C29semidirect
145. C2×#362C2×C29semidirect
148. #1388C2×C29semidirect
221. C29#13390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C29×#4732
C29×#21612
C2×C29×#3622
C29×#21172
C29×#18132
C29×#13882
#1339029