Finite Group Databasebeta

← C29×#2044 #16815758

Subgroups — C29×#2044 #16815758

Order 3712.

382 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 84 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×#534C211yesmaximal, characteristic
2C2×C29×#99C212yesmaximal, complemented
3C29×#386C212yesmaximal, complemented
4C29×#385C211yesmaximal, characteristic, complemented
5C29×#342C211yesmaximal, characteristic, complemented
6C22×D4×C29C2212yes—
7C23×C4×C29C2211yescharacteristic
8C29×#123—22no—
9C29×#121—21no—
10C29×#121—21no—
11C29×#120—22no—
12C2×C4⋊C4×C29—21no—
13C2×C22⋊C4×C29—22no—
14C2×C22⋊C4×C29C2212yes—
15C2×C22⋊C4×C29C2211yescharacteristic
16C2×C22⋊C4×C29C2211yescharacteristic
17C29×#99—24no—
18C29×#95—21no—
19C29×#95—22no—
20C24×C29D412yes—
21C24×C29C2311yescharacteristic
22C2×D4×C29—22no—
23C2×D4×C29—22no—
24C2×D4×C29—22no—
25C2×D4×C29—22no—
26C2×D4×C29—22no—
27C2×D4×C29—22no—
28C2×D4×C29—21no—
29C2×D4×C29—21no—
30C22×C4×C29—22no—
31C22×C4×C29—21no—
32C22×C4×C29—21no—
33C22×C4×C29—22no—
34C22×C4×C29—42no—
35C22×C4×C29D412yes—
36C22×C4×C29D411yescharacteristic
37C22×C4×C29D411yescharacteristic
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—42no—
41C22⋊C4×C29—22no—
42C22⋊C4×C29—22no—
43C22⋊C4×C29—22no—
44C22⋊C4×C29—21no—
45C22⋊C4×C29—22no—
46C22⋊C4×C29—22no—
47C22⋊C4×C29—44no—
48C22⋊C4×C29D412yescomplemented
49C23×C29—22no—
50C23×C29—22no—
51C23×C29—22no—
52C23×C29—41no—
53C23×C29—41no—
54C23×C29—42no—
55C23×C29—42no—
56C23×C29C2×D412yes—
57C23×C29C2×D411yescharacteristic
58C23×C29C2×D411yescharacteristic
59C23×C29#4111yescharacteristic
60C23×C29#4112yes—
61D4×C29—42no—
62D4×C29—42no—
63D4×C29—42no—
64D4×C29—42no—
65D4×C29—81no—
66D4×C29—81no—
67C2×C4×C29—24no—
68C2×C4×C29—22no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—22no—
72C2×C4×C29—22no—
73C2×C4×C29—22no—
74C2×C4×C29—22no—
75C2×C4×C29—41no—
76C2×C4×C29—41no—
77C2×C4×C29—41no—
78C2×C4×C29—42no—
79C2×C4×C29—41no—
80C2×C4×C29—41no—
81C2×C4×C29—41no—
82C2×C4×C29—42no—
83C2×C4×C29—42no—
84C2×C4×C29—42no—
85#2044C2911yesmaximal, characteristic, direct product factor, Sylow
86C22×C29—21no—
87C22×C29—22no—
88C22×C29—21no—
89C22×C29—22no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29—42no—
93C22×C29—44no—
94C22×C29—42no—
95C22×C29—42no—
96C22×C29—42no—
97C22×C29—82no—
98C22×C29#12011yescharacteristic
99C22×C29#12111yescharacteristic
100C22×C29#12112yes—
101C22×C29#12312yes—
102C22×C29#12411yescharacteristic
103C4×C29—42no—
104C4×C29—42no—
105C4×C29—42no—
106C4×C29—41no—
107C4×C29—41no—
108C4×C29—82no—
109#534C2×C2911yescharacteristic
110C2×#99C2×C2912yescomplemented
111#386C2×C2912yescomplemented
112#385C2×C2911yescharacteristic, complemented
113#342C2×C2911yescharacteristic, complemented
114C2×C29—21no—
115C2×C29—22no—
116C2×C29—22no—
117C2×C29—21no—
118C2×C29—82no—
119C2×C29#39411yescharacteristic
120C2×C29B(4,𝔽2)11yescharacteristic
121C2×C29#45811yescharacteristic
122C22×D4C22×C2912yes—
123C23×C4C22×C2911yescharacteristic
124#123—22no—
125#121—21no—
126#121—21no—
127#120—22no—
128C2×C4⋊C4—21no—
129C2×C22⋊C4—22no—
130C2×C22⋊C4C22×C2912yes—
131C2×C22⋊C4C22×C2911yescharacteristic
132C2×C22⋊C4C22×C2911yescharacteristic
133#99—24no—
134#95—21no—
135#95—22no—
136C29#204411yescharacteristic, direct product factor, Sylow
137C24D4×C2912yes—
138C24C23×C2911yescharacteristic
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—22no—
142C2×D4—22no—
143C2×D4—22no—
144C2×D4—22no—
145C2×D4—21no—
146C2×D4—21no—
147C22×C4—22no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—42no—
152C22×C4D4×C2912yes—
153C22×C4D4×C2911yescharacteristic
154C22×C4D4×C2911yescharacteristic
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—42no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—21no—
162C22⋊C4—22no—
163C22⋊C4—22no—
164C22⋊C4—44no—
165C22⋊C4D4×C2912yescomplemented
166C23—22no—
167C23—22no—
168C23—22no—
169C23—41no—
170C23—41no—
171C23—42no—
172C23—42no—
173C23C2×D4×C2912yes—
174C23C2×D4×C2911yescharacteristic
175C23C2×D4×C2911yescharacteristic
176C23#41×C2911yescharacteristic
177C23#41×C2912yes—
178D4—42no—
179D4—42no—
180D4—42no—
181D4—42no—
182D4—81no—
183D4—81no—
184C2×C4—24no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—41no—
207C22—41no—
208C22—42no—
209C22—44no—
210C22—42no—
211C22—42no—
212C22—42no—
213C22—82no—
214C22C29×#12011yescharacteristic
215C22C29×#12111yescharacteristic
216C22C29×#12112yes—
217C22C29×#12312yes—
218C22C29×#12411yescharacteristic
219C4—42no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—82no—
225C2—21no—
226C2—22no—
227C2—22no—
228C2—21no—
229C2—82no—
230C2C29×#39411yescharacteristic
231C2C29×B(4,𝔽2)11yescharacteristic
232C2C29×#45811yescharacteristic
subgroupG/H
center, socleC22×C29#120
commutator, Frattini, cosocleC24C23×C29
prime radicalC29×#534C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C24×C29 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C29×#99C2semidirect
3. C29×#386C2semidirect
4. C29×#385C2semidirect
5. C29×#342C2semidirect
48. C22⋊C4×C29D4semidirect
85. #2044C29direct (N × H)
110. C2×#99C2×C29semidirect
111. #386C2×C29semidirect
112. #385C2×C29semidirect
113. #342C2×C29semidirect
136. C29#2044direct (N × H)
165. C22⋊C4D4×C29semidirect

Maximal subgroups

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

subgroupindex
C29×#5342
C2×C29×#992
C29×#3862
C29×#3852
C29×#3422
#204429