Finite Group Databasebeta

← C29×#10212 #20305112

Subgroups — C29×#10212 #20305112

Order 7424.

536 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3253C211yesmaximal, characteristic, complemented
2C29×#3214C212yesmaximal, complemented
3C29×#1963C211yesmaximal, characteristic, complemented
4C29×#1505C212yesmaximal, complemented
5C29×#1307C211yesmaximal, characteristic, complemented
6C29×#532C2211yescharacteristic
7C29×#532C2212yes—
8C29×#496—22no—
9C29×#489—22no—
10C29×#476—22no—
11C29×#469—22no—
12C29×#461—22no—
13C29×#459—22no—
14C29×#459—22no—
15C29×#449—24no—
16C29×#432C2212yes—
17C29×#423C2211yescharacteristic
18C2×C29×#104—22no—
19C29×#376C2211yescharacteristic
20C29×#327—24no—
21C2×#41×C29—21no—
22C2×#41×C29—22no—
23C2×SD16×C29—24no—
24C2×D8×C29—24no—
25C2×D8×C29—22no—
26C2×M16×C29D412yes—
27C29×C4⋊Q8D412yes—
28C29×C4⋊Q8D411yescharacteristic
29C29×#127D412yes—
30C29×#127D411yescharacteristic
31C29×#124—22no—
32C29×#124—21no—
33C29×#121—22no—
34C29×#121—22no—
35C29×#121—22no—
36C4×D4×C29—22no—
37C4×D4×C29—22no—
38C4×D4×C29—22no—
39C2×C42×C29—21no—
40C2×C42×C29C2311yescharacteristic
41C29×#106—22no—
42C29×C4⋊C8—22no—
43C29×C4⋊C8—22no—
44C29×#104—44no—
45C29×#103—24no—
46C29×#102—24no—
47C29×#102—24no—
48C29×C22⋊C8D414yes—
49C29×#97—22no—
50C29×#95—22no—
51#41×C29—42no—
52#41×C29—42no—
53#41×C29—84no—
54C2×Q8×C29—22no—
55C2×Q8×C29—21no—
56C2×D4×C29—22no—
57C2×D4×C29—22no—
58C2×D4×C29—22no—
59C2×D4×C29—21no—
60C2×D4×C29—22no—
61C2×D4×C29—41no—
62C2×D4×C29—42no—
63C22×C4×C29—41no—
64C22×C4×C29—41no—
65C22×C4×C29—42no—
66C22×C4×C29C2×D411yescharacteristic
67C22×C4×C29C2×D412yes—
68SD16×C29—84no—
69D8×C29—84no—
70D8×C29—82no—
71M16×C29—42no—
72C2×C8×C29—22no—
73C2×C8×C29—24no—
74C4⋊C4×C29—22no—
75C4⋊C4×C29—22no—
76C4⋊C4×C29—22no—
77C22⋊C4×C29—42no—
78C22⋊C4×C29—42no—
79C22⋊C4×C29—42no—
80C42×C29—22no—
81C42×C29—41no—
82C42×C29C2×D412yes—
83C42×C29C2×D411yescharacteristic
84C42×C29#4111yescharacteristic
85#10212C2911yesmaximal, characteristic, direct product factor, Sylow
86C23×C29—41no—
87C23×C29—42no—
88C23×C29#12711yescharacteristic
89Q8×C29—44no—
90Q8×C29—42no—
91D4×C29—42no—
92D4×C29—44no—
93D4×C29—42no—
94D4×C29—42no—
95D4×C29—42no—
96D4×C29—42no—
97D4×C29—82no—
98D4×C29—82no—
99D4×C29—84no—
100C2×C4×C29—21no—
101C2×C4×C29—21no—
102C2×C4×C29—42no—
103C2×C4×C29—42no—
104C2×C4×C29—41no—
105C2×C4×C29—42no—
106C2×C4×C29—84no—
107C2×C4×C29—82no—
108C2×C4×C29—81no—
109C2×C4×C29—81no—
110C2×C4×C29#12012yes—
111C2×C4×C29#12011yescharacteristic
112C2×C4×C29#12111yescharacteristic
113C2×C4×C29#12112yes—
114C8×C29—44no—
115C8×C29—42no—
116#3253C2×C2911yescharacteristic, complemented
117#3214C2×C2912yescomplemented
118#1963C2×C2911yescharacteristic, complemented
119#1505C2×C2912yescomplemented
120#1307C2×C2911yescharacteristic, complemented
121C22×C29—21no—
122C22×C29—22no—
123C22×C29—81no—
124C22×C29—82no—
125C22×C29—82no—
126C22×C29—82no—
127C22×C29—82no—
128C22×C29#39211yescharacteristic
129C4×C29—21no—
130C4×C29—22no—
131C4×C29—22no—
132C4×C29—82no—
133C4×C29—81no—
134C4×C29—82no—
135C4×C29#45311yescharacteristic
136C4×C29#45411yescharacteristic
137#532C22×C2911yescharacteristic
138#532C22×C2912yes—
139#496—22no—
140#489—22no—
141#476—22no—
142#469—22no—
143#461—22no—
144#459—22no—
145#459—22no—
146#449—24no—
147#432C22×C2912yes—
148#423C22×C2911yescharacteristic
149C2×#104—22no—
150#376C22×C2911yescharacteristic
151#327—24no—
152C2×C29—41no—
153C2×C29—161no—
154C2×C29—162no—
155C2×C29#200611yescharacteristic
156C2×C29#200812yes—
157C2×#41—21no—
158C2×#41—22no—
159C2×SD16—24no—
160C2×D8—24no—
161C2×D8—22no—
162C2×M16D4×C2912yes—
163C4⋊Q8D4×C2912yes—
164C4⋊Q8D4×C2911yescharacteristic
165#127D4×C2912yes—
166#127D4×C2911yescharacteristic
167#124—22no—
168#124—21no—
169#121—22no—
170#121—22no—
171#121—22no—
172C4×D4—22no—
173C4×D4—22no—
174C4×D4—22no—
175C2×C42—21no—
176C2×C42C23×C2911yescharacteristic
177#106—22no—
178C4⋊C8—22no—
179C4⋊C8—22no—
180#104—44no—
181#103—24no—
182#102—24no—
183#102—24no—
184C22⋊C8D4×C2914yes—
185#97—22no—
186#95—22no—
187C29#1021211yescharacteristic, direct product factor, Sylow
188#41—42no—
189#41—42no—
190#41—84no—
191C2×Q8—22no—
192C2×Q8—21no—
193C2×D4—22no—
194C2×D4—22no—
195C2×D4—22no—
196C2×D4—21no—
197C2×D4—22no—
198C2×D4—41no—
199C2×D4—42no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—42no—
203C22×C4C2×D4×C2911yescharacteristic
204C22×C4C2×D4×C2912yes—
205SD16—84no—
206D8—84no—
207D8—82no—
208M16—42no—
209C2×C8—24no—
210C2×C8—22no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C22⋊C4—42no—
215C22⋊C4—42no—
216C22⋊C4—42no—
217C42—22no—
218C42—41no—
219C42C2×D4×C2911yescharacteristic
220C42C2×D4×C2912yes—
221C42#41×C2911yescharacteristic
222C23—41no—
223C23—42no—
224C23C29×#12711yescharacteristic
225Q8—44no—
226Q8—42no—
227D4—42no—
228D4—44no—
229D4—42no—
230D4—42no—
231D4—42no—
232D4—42no—
233D4—82no—
234D4—82no—
235D4—84no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—84no—
243C2×C4—82no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4C29×#12012yes—
247C2×C4C29×#12011yescharacteristic
248C2×C4C29×#12111yescharacteristic
249C2×C4C29×#12112yes—
250C8—44no—
251C8—42no—
252C22—21no—
253C22—22no—
254C22—81no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—82no—
259C22C29×#39211yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—82no—
264C4—81no—
265C4—82no—
266C4C29×#45311yescharacteristic
267C4C29×#45411yescharacteristic
268C2—41no—
269C2—161no—
270C2—162no—
271C2C29×#200611yescharacteristic
272C2C29×#200812yes—
subgroupG/H
center, socleC22×C29#392
commutator, Frattini, cosocleC2×C42C23×C29
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#3253C2semidirect
2. C29×#3214C2semidirect
3. C29×#1963C2semidirect
4. C29×#1505C2semidirect
5. C29×#1307C2semidirect
85. #10212C29direct (N × H)
116. #3253C2×C29semidirect
117. #3214C2×C29semidirect
118. #1963C2×C29semidirect
119. #1505C2×C29semidirect
120. #1307C2×C29semidirect
187. C29#10212direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#32532
C29×#32142
C29×#19632
C29×#15052
C29×#13072
#1021229