Finite Group Databasebeta

← C29×#12246 #20307146

Subgroups — C29×#12246 #20307146

Order 7424.

558 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2537C211yesmaximal, characteristic
2C29×#2060C211yesmaximal, characteristic, complemented
3C29×#1599C212yesmaximal, complemented
4C29×#1345C212yesmaximal, complemented
5C29×#1325C211yesmaximal, characteristic, complemented
6C29×#544C2211yescharacteristic
7C2×C29×#121—22no—
8C2×C4×D4×C29—21no—
9C29×#450—22no—
10C29×#428—21no—
11C29×#394—21no—
12C29×#394C2212yes—
13C29×#384C2211yescharacteristic
14C29×#380—22no—
15C29×#343C2211yescharacteristic
16C29×#339—21no—
17C29×#328—22no—
18C29×#324C2212yes—
19C22×D4×C29—21no—
20C22×D4×C29—21no—
21C22×D4×C29D412yes—
22C23×C4×C29—22no—
23C2×SD16×C29—42no—
24C2×M16×C29—21no—
25C29×C4⋊Q8—41no—
26C29×#125—41no—
27C29×C22⋊Q8—22no—
28C29×#121—48no—
29C4×D4×C29—42no—
30C4×D4×C29—42no—
31C29×#117—21no—
32C2×C4⋊C4×C29—21no—
33C2×C4⋊C4×C29—22no—
34C2×C4⋊C4×C29D411yescharacteristic
35C2×C4⋊C4×C29C2311yescharacteristic
36C2×C22⋊C4×C29—22no—
37C2×C22⋊C4×C29—22no—
38C2×C22⋊C4×C29—22no—
39C2×C42×C29D411yescharacteristic
40C29×#107—41no—
41C29×#106—41no—
42C29×#102—42no—
43C29×C22⋊C8—22no—
44C29×#95—21no—
45C29×#95D412yes—
46C24×C29—22no—
47C2×Q8×C29—22no—
48C2×D4×C29—24no—
49C2×D4×C29—42no—
50C2×D4×C29—42no—
51C2×D4×C29—42no—
52C2×D4×C29—44no—
53C2×D4×C29—44no—
54C2×D4×C29—81no—
55C22×C4×C29—21no—
56C22×C4×C29—22no—
57C22×C4×C29—21no—
58C22×C4×C29—44no—
59C22×C4×C29—44no—
60C22×C4×C29—44no—
61C22×C4×C29C2×D411yescharacteristic
62C22×C4×C29C2×D412yes—
63SD16×C29—84no—
64M16×C29—22no—
65M16×C29—41no—
66C2×C8×C29—41no—
67C2×C8×C29—42no—
68C4⋊C4×C29—21no—
69C4⋊C4×C29—21no—
70C4⋊C4×C29—22no—
71C4⋊C4×C29—41no—
72C4⋊C4×C29—41no—
73C4⋊C4×C29—42no—
74C4⋊C4×C29—44no—
75C4⋊C4×C29—42no—
76C22⋊C4×C29—44no—
77C22⋊C4×C29—44no—
78C22⋊C4×C29—41no—
79C22⋊C4×C29—42no—
80C22⋊C4×C29—42no—
81C42×C29—21no—
82C42×C29—41no—
83C42×C29SD1612yescomplemented
84#12246C2911yesmaximal, characteristic, direct product factor, Sylow
85C23×C29—24no—
86C23×C29—42no—
87C23×C29—42no—
88C23×C29—42no—
89C23×C29—42no—
90C23×C29—42no—
91C23×C29—42no—
92C23×C29#12011yescharacteristic
93Q8×C29—82no—
94D4×C29—48no—
95D4×C29—44no—
96D4×C29—82no—
97D4×C29—84no—
98C2×C4×C29—22no—
99C2×C4×C29—22no—
100C2×C4×C29—22no—
101C2×C4×C29—21no—
102C2×C4×C29—21no—
103C2×C4×C29—22no—
104C2×C4×C29—42no—
105C2×C4×C29—42no—
106C2×C4×C29—42no—
107C2×C4×C29—42no—
108C2×C4×C29—42no—
109C2×C4×C29—41no—
110C2×C4×C29—41no—
111C2×C4×C29—41no—
112C2×C4×C29—88no—
113C2×C4×C29C2×SD1611yescharacteristic
114C2×C4×C29AGL(1,ℤ/8)11yescharacteristic
115C8×C29—42no—
116C8×C29—82no—
117#2537C2×C2911yescharacteristic
118#2060C2×C2911yescharacteristic, complemented
119#1599C2×C2912yescomplemented
120#1345C2×C2912yescomplemented
121#1325C2×C2911yescharacteristic, complemented
122C22×C29—21no—
123C22×C29—21no—
124C22×C29—44no—
125C22×C29—44no—
126C22×C29—44no—
127C22×C29—82no—
128C22×C29—82no—
129C22×C29—82no—
130C22×C29—82no—
131C22×C29#45011yescharacteristic
132C22×C29#45611yescharacteristic
133C22×C29B(4,𝔽2)11yescharacteristic
134C4×C29—24no—
135C4×C29—21no—
136C4×C29—21no—
137C4×C29—42no—
138C4×C29—82no—
139C4×C29—81no—
140C4×C29—81no—
141C4×C29—81no—
142#544C22×C2911yescharacteristic
143C2×#121—22no—
144C2×C4×D4—21no—
145#450—22no—
146#428—21no—
147#394—21no—
148#394C22×C2912yes—
149#384C22×C2911yescharacteristic
150#380—22no—
151#343C22×C2911yescharacteristic
152#339—21no—
153#328—22no—
154#324C22×C2912yes—
155C2×C29—21no—
156C2×C29—21no—
157C2×C29—84no—
158C2×C29#160411yescharacteristic
159C2×C29#219611yescharacteristic
160C2×C29#220411yescharacteristic
161C22×D4—21no—
162C22×D4—21no—
163C22×D4D4×C2912yes—
164C23×C4—22no—
165C2×SD16—42no—
166C2×M16—21no—
167C4⋊Q8—41no—
168#125—41no—
169C22⋊Q8—22no—
170#121—48no—
171C4×D4—42no—
172C4×D4—42no—
173#117—21no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4D4×C2911yescharacteristic
177C2×C4⋊C4C23×C2911yescharacteristic
178C2×C22⋊C4—22no—
179C2×C22⋊C4—22no—
180C2×C22⋊C4—22no—
181C2×C42D4×C2911yescharacteristic
182#107—41no—
183#106—41no—
184#102—42no—
185C22⋊C8—22no—
186#95—21no—
187#95D4×C2912yes—
188C29#1224611yescharacteristic, direct product factor, Sylow
189C24—22no—
190C2×Q8—22no—
191C2×D4—24no—
192C2×D4—42no—
193C2×D4—42no—
194C2×D4—42no—
195C2×D4—44no—
196C2×D4—44no—
197C2×D4—81no—
198C22×C4—21no—
199C22×C4—22no—
200C22×C4—21no—
201C22×C4—44no—
202C22×C4—44no—
203C22×C4—44no—
204C22×C4C2×D4×C2911yescharacteristic
205C22×C4C2×D4×C2912yes—
206SD16—84no—
207M16—22no—
208M16—41no—
209C2×C8—41no—
210C2×C8—42no—
211C4⋊C4—22no—
212C4⋊C4—21no—
213C4⋊C4—21no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C22⋊C4—44no—
220C22⋊C4—44no—
221C22⋊C4—41no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C42—21no—
225C42—41no—
226C42SD16×C2912yescomplemented
227C23—24no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23C29×#12011yescharacteristic
235Q8—82no—
236D4—48no—
237D4—44no—
238D4—82no—
239D4—84no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—88no—
255C2×C4C2×SD16×C2911yescharacteristic
256C2×C4C29×AGL(1,ℤ/8)11yescharacteristic
257C8—42no—
258C8—82no—
259C22—21no—
260C22—21no—
261C22—44no—
262C22—44no—
263C22—44no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22C29×#45011yescharacteristic
269C22C29×#45611yescharacteristic
270C22C29×B(4,𝔽2)11yescharacteristic
271C4—24no—
272C4—21no—
273C4—21no—
274C4—42no—
275C4—82no—
276C4—81no—
277C4—81no—
278C4—81no—
279C2—21no—
280C2—21no—
281C2—84no—
282C2C29×#160411yescharacteristic
283C2C29×#219611yescharacteristic
284C2C29×#220411yescharacteristic
subgroupG/H
center, socleC22×C29B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C29
prime radicalC29×#2537C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C23×C29 ◁ C2×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C29×#2060C2semidirect
3. C29×#1599C2semidirect
4. C29×#1345C2semidirect
5. C29×#1325C2semidirect
83. C42×C29SD16semidirect
84. #12246C29direct (N × H)
118. #2060C2×C29semidirect
119. #1599C2×C29semidirect
120. #1345C2×C29semidirect
121. #1325C2×C29semidirect
188. C29#12246direct (N × H)
226. C42SD16×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#25372
C29×#20602
C29×#15992
C29×#13452
C29×#13252
#1224629