Finite Group Databasebeta

← #2021×C149 #34040934

Subgroups — #2021×C149 #34040934

Order 19072.

638 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 92 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
1#534×C149C211yesmaximal, characteristic, complemented
2C2×#120×C149C212yesmaximal, complemented
3C2×#99×C149C212yesmaximal, complemented
4#379×C149C211yesmaximal, characteristic, complemented
5#342×C149C211yesmaximal, characteristic, complemented
6C25×C149C2211yescharacteristic
7C22×D4×C149—22no—
8C22×D4×C149C2212yes—
9#123×C149—22no—
10#121×C149—22no—
11#120×C149—24no—
12#120×C149—22no—
13#120×C149—24no—
14C2×C22⋊C4×C149—22no—
15C2×C22⋊C4×C149—22no—
16C2×C22⋊C4×C149C2211yescharacteristic
17C2×C22⋊C4×C149C2211yescharacteristic
18C2×C22⋊C4×C149C2212yes—
19#99×C149—24no—
20C24×C149—21no—
21C24×C149—22no—
22C24×C149—22no—
23C24×C149—21no—
24C24×C149—44no—
25C24×C149D412yescomplemented
26C24×C149D412yescomplemented
27C24×C149C2311yescharacteristic
28C2×D4×C149—28no—
29C2×D4×C149—22no—
30C2×D4×C149—22no—
31C2×D4×C149—22no—
32C2×D4×C149—22no—
33C2×D4×C149—22no—
34C2×D4×C149—22no—
35C2×D4×C149—22no—
36C2×D4×C149—48no—
37C22×C4×C149—22no—
38C22×C4×C149—21no—
39C22×C4×C149D412yescomplemented
40C22×C4×C149D412yescomplemented
41C4⋊C4×C149—22no—
42C22⋊C4×C149—28no—
43C22⋊C4×C149—24no—
44C22⋊C4×C149—22no—
45C22⋊C4×C149—22no—
46C22⋊C4×C149—22no—
47C22⋊C4×C149—44no—
48C22⋊C4×C149D414yescomplemented
49C23×C149—24no—
50C23×C149—28no—
51C23×C149—24no—
52C23×C149—22no—
53C23×C149—22no—
54C23×C149—22no—
55C23×C149—22no—
56C23×C149—44no—
57C23×C149—42no—
58C23×C149—42no—
59C23×C149—44no—
60C23×C149—48no—
61C23×C149—44no—
62C23×C149—44no—
63C23×C149—41no—
64C23×C149—42no—
65C23×C149—41no—
66C23×C149C2×D412yes—
67C23×C149C2×D411yescharacteristic
68C23×C149C2×D411yescharacteristic
69C23×C149C2×D412yes—
70C23×C149#4111yescharacteristic
71D4×C149—416no—
72D4×C149—42no—
73D4×C149—42no—
74D4×C149—42no—
75D4×C149—42no—
76D4×C149—82no—
77C2×C4×C149—22no—
78C2×C4×C149—24no—
79C2×C4×C149—22no—
80C2×C4×C149—22no—
81C2×C4×C149—22no—
82C2×C4×C149—44no—
83C2×C4×C149—42no—
84C2×C4×C149—42no—
85C2×C4×C149—41no—
86C22×C149—22no—
87C22×C149—24no—
88C22×C149—28no—
89C22×C149—24no—
90C22×C149—41no—
91C22×C149—42no—
92C22×C149—41no—
93C22×C149—44no—
94C22×C149—44no—
95C22×C149—42no—
96C22×C149—48no—
97C22×C149—44no—
98C22×C149—42no—
99C22×C149—44no—
100C22×C149—42no—
101C22×C149—44no—
102C22×C149—82no—
103C22×C149#12012yes—
104C22×C149#12011yescharacteristic
105C22×C149#12112yes—
106C22×C149#12111yescharacteristic
107C22×C149#12711yescharacteristic
108C4×C149—44no—
109C4×C149—42no—
110C4×C149—42no—
111C4×C149—81no—
112C2×C149—22no—
113C2×C149—21no—
114C2×C149—21no—
115C2×C149—22no—
116C2×C149—44no—
117C2×C149—82no—
118C2×C149#39211yescharacteristic
119C2×C149B(4,𝔽2)12yes—
120C149#202111yescharacteristic, direct product factor, Sylow
121#2021C14911yesmaximal, characteristic, direct product factor, Sylow
122#534C2×C14911yescharacteristic, complemented
123C2×#120C2×C14912yescomplemented
124C2×#99C2×C14912yescomplemented
125#379C2×C14911yescharacteristic, complemented
126#342C2×C14911yescharacteristic, complemented
127C25C22×C14911yescharacteristic
128C22×D4—22no—
129C22×D4C22×C14912yes—
130#123—22no—
131#121—22no—
132#120—24no—
133#120—22no—
134#120—24no—
135C2×C22⋊C4—22no—
136C2×C22⋊C4—22no—
137C2×C22⋊C4C22×C14911yescharacteristic
138C2×C22⋊C4C22×C14911yescharacteristic
139C2×C22⋊C4C22×C14912yes—
140#99—24no—
141C24—21no—
142C24—22no—
143C24—22no—
144C24—21no—
145C24—44no—
146C24D4×C14912yescomplemented
147C24D4×C14912yescomplemented
148C24C23×C14911yescharacteristic
149C2×D4—28no—
150C2×D4—22no—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—48no—
158C22×C4—22no—
159C22×C4—21no—
160C22×C4D4×C14912yescomplemented
161C22×C4D4×C14912yescomplemented
162C4⋊C4—22no—
163C22⋊C4—28no—
164C22⋊C4—24no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4—22no—
168C22⋊C4—44no—
169C22⋊C4D4×C14914yescomplemented
170C23—24no—
171C23—28no—
172C23—24no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—44no—
178C23—42no—
179C23—42no—
180C23—44no—
181C23—48no—
182C23—44no—
183C23—44no—
184C23—41no—
185C23—42no—
186C23—41no—
187C23C2×D4×C14912yes—
188C23C2×D4×C14911yescharacteristic
189C23C2×D4×C14911yescharacteristic
190C23C2×D4×C14912yes—
191C23#41×C14911yescharacteristic
192D4—416no—
193D4—42no—
194D4—42no—
195D4—42no—
196D4—42no—
197D4—82no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—44no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—41no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—41no—
212C22—42no—
213C22—41no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—44no—
219C22—42no—
220C22—44no—
221C22—42no—
222C22—44no—
223C22—82no—
224C22#120×C14912yes—
225C22#120×C14911yescharacteristic
226C22#121×C14912yes—
227C22#121×C14911yescharacteristic
228C22#127×C14911yescharacteristic
229C4—44no—
230C4—42no—
231C4—42no—
232C4—81no—
233C2—22no—
234C2—21no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—82no—
239C2#392×C14911yescharacteristic
240C2B(4,𝔽2)×C14912yes—
subgroupG/H
center, socleC22×C149#120
commutator, Frattini, cosocleC24C23×C149
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C24×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #534×C149C2semidirect
2. C2×#120×C149C2semidirect
3. C2×#99×C149C2semidirect
4. #379×C149C2semidirect
5. #342×C149C2semidirect
25. C24×C149D4semidirect
26. C24×C149D4semidirect
39. C22×C4×C149D4semidirect
40. C22×C4×C149D4semidirect
48. C22⋊C4×C149D4semidirect
120. C149#2021direct (N × H)
121. #2021C149direct (N × H)
122. #534C2×C149semidirect
123. C2×#120C2×C149semidirect
124. C2×#99C2×C149semidirect
125. #379C2×C149semidirect
126. #342C2×C149semidirect
146. C24D4×C149semidirect
147. C24D4×C149semidirect
160. C22×C4D4×C149semidirect
161. C22×C4D4×C149semidirect
169. C22⋊C4D4×C149semidirect

Maximal subgroups

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

subgroupindex
#534×C1492
C2×#120×C1492
C2×#99×C1492
#379×C1492
#342×C1492
#2021149