Finite Group Databasebeta

← C29×#13396 #20308296

Subgroups — C29×#13396 #20308296

Order 7424.

422 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3058C211yesmaximal, characteristic
2C29×#2155C211yesmaximal, characteristic, complemented
3C2×C29×#361C211yesmaximal, characteristic, complemented
4C29×#2140C211yesmaximal, characteristic, complemented
5C29×#2117C211yesmaximal, characteristic, complemented
6C29×#1814C211yesmaximal, characteristic, complemented
7C29×#1384C211yesmaximal, characteristic, complemented
8C22×D8×C29C2211yescharacteristic
9C2×C29×#131C2211yescharacteristic
10C29×#535—21no—
11C2×C29×M32C2211yescharacteristic
12C2×C29×M32C2211yescharacteristic
13C29×#469—22no—
14C29×#466—22no—
15C2×C29×#108C2211yescharacteristic
16C29×#427C2211yescharacteristic
17C29×#427C2211yescharacteristic
18C29×#421—21no—
19C29×#418—21no—
20C29×#365—22no—
21C29×#361—22no—
22C29×#357—22no—
23C29×#350—22no—
24C29×#344—21no—
25C2×#41×C29D411yescharacteristic
26C22×D4×C29—21no—
27C2×D8×C29—21no—
28C2×D8×C29—21no—
29C2×D8×C29—21no—
30C2×D8×C29—21no—
31C2×D8×C29—21no—
32C2×D8×C29D412yes—
33C29×#131—21no—
34C29×#131—21no—
35C29×#131—21no—
36C29×#131—21no—
37C2×M16×C29—21no—
38C2×M16×C29—21no—
39C2×M16×C29D411yescharacteristic
40C22×C8×C29—21no—
41C22×C8×C29C2311yescharacteristic
42C29×#127—41no—
43C29×#124—41no—
44C29×#121—24no—
45C29×#120—42no—
46C29×#117—21no—
47C29×#117—21no—
48C29×M32—21no—
49C29×M32—21no—
50C29×M32—21no—
51C29×M32—21no—
52C2×C16×C29—21no—
53C2×C16×C29D412yescomplemented
54C29×#108—21no—
55C29×#108—21no—
56C29×#107—21no—
57C29×#107—21no—
58C29×#106—21no—
59C29×#106D412yes—
60C29×#104—42no—
61C29×#102—24no—
62C24×C29—41no—
63#41×C29—21no—
64#41×C29—21no—
65#41×C29—21no—
66#41×C29—21no—
67C2×Q8×C29SD1611yescharacteristic
68C2×D4×C29—21no—
69C2×D4×C29—22no—
70C2×D4×C29—44no—
71C2×D4×C29—41no—
72C2×D4×C29—41no—
73C2×D4×C29—41no—
74C2×D4×C29—41no—
75C2×D4×C29—41no—
76C2×D4×C29SD1611yescharacteristic
77C22×C4×C29—21no—
78C22×C4×C29C2×D411yescharacteristic
79D8×C29—22no—
80D8×C29—22no—
81D8×C29—41no—
82D8×C29—41no—
83M16×C29—21no—
84M16×C29—21no—
85M16×C29—41no—
86M16×C29—41no—
87M16×C29—41no—
88M16×C29—41no—
89C2×C8×C29—21no—
90C2×C8×C29—41no—
91C2×C8×C29—41no—
92C2×C8×C29—41no—
93C2×C8×C29C2×D411yescharacteristic
94C2×C8×C29C2×D411yescharacteristic
95C2×C8×C29C2×D411yescharacteristic
96C2×C8×C29#4111yescharacteristic
97C2×C8×C29#4111yescharacteristic
98C2×C8×C29#4111yescharacteristic
99C4⋊C4×C29—22no—
100C4⋊C4×C29—41no—
101C22⋊C4×C29—44no—
102C22⋊C4×C29—41no—
103C22⋊C4×C29—41no—
104C42×C29—41no—
105C42×C29—41no—
106C16×C29—22no—
107C16×C29—41no—
108#13396C2911yesmaximal, characteristic, direct product factor, Sylow
109C23×C29—21no—
110C23×C29—42no—
111C23×C29—81no—
112C23×C29—81no—
113C23×C29—162no—
114C23×C29AGL(1,ℤ/8)11yescharacteristic
115Q8×C29—21no—
116Q8×C29—21no—
117D4×C29—21no—
118D4×C29—21no—
119D4×C29—41no—
120D4×C29—41no—
121D4×C29—42no—
122D4×C29—42no—
123D4×C29—81no—
124D4×C29—81no—
125D4×C29—164no—
126C2×C4×C29—21no—
127C2×C4×C29—41no—
128C2×C4×C29—41no—
129C2×C4×C29—42no—
130C2×C4×C29—81no—
131C2×C4×C29#12011yescharacteristic
132C2×C4×C29#12111yescharacteristic
133C2×C4×C29#12311yescharacteristic
134C2×C4×C29C2×SD1611yescharacteristic
135C2×C4×C29#13511yescharacteristic
136C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
137C8×C29—41no—
138C8×C29—81no—
139C8×C29#12111yescharacteristic
140C8×C29#12111yescharacteristic
141C8×C29#12311yescharacteristic
142C8×C29#12411yescharacteristic
143#3058C2×C2911yescharacteristic
144#2155C2×C2911yescharacteristic, complemented
145C2×#361C2×C2911yescharacteristic, complemented
146#2140C2×C2911yescharacteristic, complemented
147#2117C2×C2911yescharacteristic, complemented
148#1814C2×C2911yescharacteristic, complemented
149#1384C2×C2911yescharacteristic, complemented
150C22×C29—41no—
151C22×C29—42no—
152C22×C29—41no—
153C22×C29—84no—
154C22×C29—82no—
155C22×C29—162no—
156C22×C29—162no—
157C22×C29#45011yescharacteristic
158C22×C29#46911yescharacteristic
159C22×C29#48211yescharacteristic
160C4×C29—41no—
161C4×C29—82no—
162C4×C29—161no—
163C4×C29#39411yescharacteristic
164C4×C29#44911yescharacteristic
165C4×C29#46511yescharacteristic
166C4×C29#48111yescharacteristic
167C22×D8C22×C2911yescharacteristic
168C2×#131C22×C2911yescharacteristic
169#535—21no—
170C2×M32C22×C2911yescharacteristic
171C2×M32C22×C2911yescharacteristic
172#469—22no—
173#466—22no—
174C2×#108C22×C2911yescharacteristic
175#427C22×C2911yescharacteristic
176#427C22×C2911yescharacteristic
177#421—21no—
178#418—21no—
179#365—22no—
180#361—22no—
181#357—22no—
182#350—22no—
183#344—21no—
184C2×C29—21no—
185C2×C29—21no—
186C2×C29—21no—
187C2×C29—81no—
188C2×C29—162no—
189C2×C29#203411yescharacteristic
190C2×#41D4×C2911yescharacteristic
191C22×D4—21no—
192C2×D8—21no—
193C2×D8—21no—
194C2×D8—21no—
195C2×D8—21no—
196C2×D8—21no—
197C2×D8D4×C2912yes—
198#131—21no—
199#131—21no—
200#131—21no—
201#131—21no—
202C2×M16—21no—
203C2×M16—21no—
204C2×M16D4×C2911yescharacteristic
205C22×C8—21no—
206C22×C8C23×C2911yescharacteristic
207#127—41no—
208#124—41no—
209#121—24no—
210#120—42no—
211#117—21no—
212#117—21no—
213M32—21no—
214M32—21no—
215M32—21no—
216M32—21no—
217C2×C16—21no—
218C2×C16D4×C2912yescomplemented
219#108—21no—
220#108—21no—
221#107—21no—
222#107—21no—
223#106—21no—
224#106D4×C2912yes—
225#104—42no—
226#102—24no—
227C29#1339611yescharacteristic, direct product factor, Sylow
228C24—41no—
229#41—21no—
230#41—21no—
231#41—21no—
232#41—21no—
233C2×Q8SD16×C2911yescharacteristic
234C2×D4—21no—
235C2×D4—22no—
236C2×D4—44no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4SD16×C2911yescharacteristic
243C22×C4—21no—
244C22×C4C2×D4×C2911yescharacteristic
245D8—22no—
246D8—22no—
247D8—41no—
248D8—41no—
249M16—21no—
250M16—21no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255C2×C8—21no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—41no—
259C2×C8C2×D4×C2911yescharacteristic
260C2×C8C2×D4×C2911yescharacteristic
261C2×C8C2×D4×C2911yescharacteristic
262C2×C8#41×C2911yescharacteristic
263C2×C8#41×C2911yescharacteristic
264C2×C8#41×C2911yescharacteristic
265C4⋊C4—22no—
266C4⋊C4—41no—
267C22⋊C4—44no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C42—41no—
271C42—41no—
272C16—22no—
273C16—41no—
274C23—21no—
275C23—42no—
276C23—81no—
277C23—81no—
278C23—162no—
279C23C29×AGL(1,ℤ/8)11yescharacteristic
280Q8—21no—
281Q8—21no—
282D4—21no—
283D4—21no—
284D4—41no—
285D4—41no—
286D4—42no—
287D4—42no—
288D4—81no—
289D4—81no—
290D4—164no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4C29×#12011yescharacteristic
297C2×C4C29×#12111yescharacteristic
298C2×C4C29×#12311yescharacteristic
299C2×C4C2×SD16×C2911yescharacteristic
300C2×C4C29×#13511yescharacteristic
301C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
302C8—41no—
303C8—81no—
304C8C29×#12111yescharacteristic
305C8C29×#12111yescharacteristic
306C8C29×#12311yescharacteristic
307C8C29×#12411yescharacteristic
308C22—41no—
309C22—42no—
310C22—41no—
311C22—84no—
312C22—82no—
313C22—162no—
314C22—162no—
315C22C29×#45011yescharacteristic
316C22C29×#46911yescharacteristic
317C22C29×#48211yescharacteristic
318C4—41no—
319C4—82no—
320C4—161no—
321C4C29×#39411yescharacteristic
322C4C29×#44911yescharacteristic
323C4C29×#46511yescharacteristic
324C4C29×#48111yescharacteristic
325C2—21no—
326C2—21no—
327C2—21no—
328C2—81no—
329C2—162no—
330C2C29×#203411yescharacteristic
subgroupG/H
center, socleC2×C29#2034
commutator, Frattini, cosocleC22×C8C23×C29
prime radicalC29×#3058C2
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×#2155C2semidirect
3. C2×C29×#361C2semidirect
4. C29×#2140C2semidirect
5. C29×#2117C2semidirect
6. C29×#1814C2semidirect
7. C29×#1384C2semidirect
53. C2×C16×C29D4semidirect
108. #13396C29direct (N × H)
144. #2155C2×C29semidirect
145. C2×#361C2×C29semidirect
146. #2140C2×C29semidirect
147. #2117C2×C29semidirect
148. #1814C2×C29semidirect
149. #1384C2×C29semidirect
218. C2×C16D4×C29semidirect
227. C29#13396direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#30582
C29×#21552
C2×C29×#3612
C29×#21402
C29×#21172
C29×#18142
C29×#13842
#1339629