Finite Group Databasebeta

← C29×#13674 #20308574

Subgroups — C29×#13674 #20308574

Order 7424.

454 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#3291C211yesmaximal, characteristic, complemented
2C29×#2196C212yesmaximal, complemented
3C29×#1629C211yesmaximal, characteristic, complemented
4C29×#1409C211yesmaximal, characteristic, complemented
5C29×#1402C212yesmaximal, complemented
6C29×#577—22no—
7D42×C29C2211yescharacteristic
8C29×#492C2211yescharacteristic
9C29×#476—21no—
10C29×#471—22no—
11C29×B(4,𝔽2)—22no—
12C29×#456—21no—
13C29×#453C2212yes—
14C29×#443—21no—
15C29×#353C2212yes—
16C29×AΣL(1,𝔽16)—22no—
17C29×#331C2211yescharacteristic
18C29×D4⋊C8—21no—
19C29×2−1+4—21no—
20C29×H(5,𝔽2)D412yescomplemented
21C22×D4×C29—41no—
22C29×#137—22no—
23C29×#137—42no—
24C29×AGL(1,ℤ/8)—22no—
25C29×AGL(1,ℤ/8)—42no—
26C29×#135—21no—
27C29×#135—42no—
28C2×SD16×C29—22no—
29C2×SD16×C29—42no—
30C29×#131—22no—
31C29×C4⋊Q8D411yescharacteristic, complemented
32C29×#127C2311yescharacteristic
33C29×#121—41no—
34C29×#120—22no—
35C29×#120—42no—
36C4×D4×C29—21no—
37C29×#108—21no—
38C29×#106—41no—
39C29×C4⋊C8—21no—
40C29×#104—22no—
41C29×#102—41no—
42C29×#101—21no—
43C29×#100D412yescomplemented
44C29×#99—22no—
45C29×#99—42no—
46C4×C8×C29D411yescharacteristic, complemented
47C24×C29—22no—
48#41×C29—22no—
49#41×C29—42no—
50#41×C29—42no—
51#41×C29—81no—
52C2×Q8×C29—21no—
53C2×Q8×C29—42no—
54C2×D4×C29—21no—
55C2×D4×C29—41no—
56C2×D4×C29—42no—
57C2×D4×C29—42no—
58C2×D4×C29—42no—
59C2×D4×C29—82no—
60C2×D4×C29—82no—
61C2×D4×C29—82no—
62C2×D4×C29C2×D412yes—
63C22×C4×C29—41no—
64Q16×C29—21no—
65Q16×C29—42no—
66SD16×C29—22no—
67SD16×C29—42no—
68SD16×C29—42no—
69SD16×C29—42no—
70SD16×C29—42no—
71D8×C29—21no—
72D8×C29—42no—
73M16×C29—22no—
74M16×C29—42no—
75C2×C8×C29—21no—
76C2×C8×C29—42no—
77C2×C8×C29—41no—
78C4⋊C4×C29—21no—
79C4⋊C4×C29—41no—
80C22⋊C4×C29—22no—
81C22⋊C4×C29—41no—
82C22⋊C4×C29—42no—
83C22⋊C4×C29—82no—
84C42×C29C2×D411yescharacteristic
85#13674C2911yesmaximal, characteristic, direct product factor, Sylow
86C23×C29—22no—
87C23×C29—41no—
88C23×C29—42no—
89C23×C29—82no—
90C23×C29—84no—
91Q8×C29—22no—
92Q8×C29—42no—
93Q8×C29—81no—
94D4×C29—22no—
95D4×C29—22no—
96D4×C29—42no—
97D4×C29—41no—
98D4×C29—42no—
99D4×C29—81no—
100D4×C29—81no—
101D4×C29—82no—
102D4×C29—81no—
103D4×C29—84no—
104D4×C29—164no—
105C2×C4×C29—21no—
106C2×C4×C29—42no—
107C2×C4×C29—42no—
108C2×C4×C29—41no—
109C2×C4×C29—41no—
110C2×C4×C29—81no—
111C2×C4×C29—81no—
112C2×C4×C29—82no—
113C2×C4×C29—82no—
114C2×C4×C29#12011yescharacteristic
115C8×C29—21no—
116C8×C29—21no—
117C8×C29—42no—
118C8×C29—81no—
119#3291C2×C2911yescharacteristic, complemented
120#2196C2×C2912yescomplemented
121#1629C2×C2911yescharacteristic, complemented
122#1409C2×C2911yescharacteristic, complemented
123#1402C2×C2912yescomplemented
124C22×C29—42no—
125C22×C29—42no—
126C22×C29—42no—
127C22×C29—82no—
128C22×C29—81no—
129C22×C29—84no—
130C22×C29—81no—
131C22×C29—162no—
132C22×C29—162no—
133C22×C29B(4,𝔽2)11yescharacteristic
134C4×C29—21no—
135C4×C29—21no—
136C4×C29—21no—
137C4×C29—42no—
138C4×C29—81no—
139C4×C29—81no—
140C4×C29—162no—
141#577—22no—
142D42C22×C2911yescharacteristic
143#492C22×C2911yescharacteristic
144#476—21no—
145#471—22no—
146B(4,𝔽2)—22no—
147#456—21no—
148#453C22×C2912yes—
149#443—21no—
150#353C22×C2912yes—
151AΣL(1,𝔽16)—22no—
152#331C22×C2911yescharacteristic
153D4⋊C8—21no—
154C2×C29—21no—
155C2×C29—82no—
156C2×C29—82no—
157C2×C29—82no—
158C2×C29#219611yescharacteristic
1592−1+4—21no—
160H(5,𝔽2)D4×C2912yescomplemented
161C22×D4—41no—
162#137—22no—
163#137—42no—
164AGL(1,ℤ/8)—22no—
165AGL(1,ℤ/8)—42no—
166#135—21no—
167#135—42no—
168C2×SD16—22no—
169C2×SD16—42no—
170#131—22no—
171C4⋊Q8D4×C2911yescharacteristic, complemented
172#127C23×C2911yescharacteristic
173#121—41no—
174#120—22no—
175#120—42no—
176C4×D4—21no—
177#108—21no—
178#106—41no—
179C4⋊C8—21no—
180#104—22no—
181#102—41no—
182#101—21no—
183#100D4×C2912yescomplemented
184#99—22no—
185#99—42no—
186C4×C8D4×C2911yescharacteristic, complemented
187C29#1367411yescharacteristic, direct product factor, Sylow
188C24—22no—
189#41—22no—
190#41—42no—
191#41—42no—
192#41—81no—
193C2×Q8—21no—
194C2×Q8—42no—
195C2×D4—21no—
196C2×D4—41no—
197C2×D4—42no—
198C2×D4—42no—
199C2×D4—42no—
200C2×D4—82no—
201C2×D4—82no—
202C2×D4—82no—
203C2×D4C2×D4×C2912yes—
204C22×C4—41no—
205Q16—21no—
206Q16—42no—
207SD16—22no—
208SD16—42no—
209SD16—42no—
210SD16—42no—
211SD16—42no—
212D8—21no—
213D8—42no—
214M16—22no—
215M16—42no—
216C2×C8—21no—
217C2×C8—42no—
218C2×C8—41no—
219C4⋊C4—21no—
220C4⋊C4—41no—
221C22⋊C4—22no—
222C22⋊C4—41no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C42C2×D4×C2911yescharacteristic
226C23—22no—
227C23—41no—
228C23—42no—
229C23—82no—
230C23—84no—
231Q8—22no—
232Q8—42no—
233Q8—81no—
234D4—22no—
235D4—22no—
236D4—42no—
237D4—41no—
238D4—42no—
239D4—81no—
240D4—81no—
241D4—82no—
242D4—81no—
243D4—84no—
244D4—164no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4C29×#12011yescharacteristic
255C8—21no—
256C8—21no—
257C8—42no—
258C8—81no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—82no—
263C22—81no—
264C22—84no—
265C22—81no—
266C22—162no—
267C22—162no—
268C22C29×B(4,𝔽2)11yescharacteristic
269C4—21no—
270C4—21no—
271C4—21no—
272C4—42no—
273C4—81no—
274C4—81no—
275C4—162no—
276C2—21no—
277C2—82no—
278C2—82no—
279C2—82no—
280C2C29×#219611yescharacteristic
subgroupG/H
center, socleC2×C29#2196
commutator, Frattini, cosocle#127C23×C29
LCSG ▷ #127 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C29 ◁ C22×C29 ◁ C2×C4×C29 ◁ C29×#127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3291C2semidirect
2. C29×#2196C2semidirect
3. C29×#1629C2semidirect
4. C29×#1409C2semidirect
5. C29×#1402C2semidirect
20. C29×H(5,𝔽2)D4semidirect
31. C29×C4⋊Q8D4semidirect
43. C29×#100D4semidirect
46. C4×C8×C29D4semidirect
85. #13674C29direct (N × H)
119. #3291C2×C29semidirect
120. #2196C2×C29semidirect
121. #1629C2×C29semidirect
122. #1409C2×C29semidirect
123. #1402C2×C29semidirect
160. H(5,𝔽2)D4×C29semidirect
171. C4⋊Q8D4×C29semidirect
183. #100D4×C29semidirect
186. C4×C8D4×C29semidirect
187. C29#13674direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32912
C29×#21962
C29×#16292
C29×#14092
C29×#14022
#1367429