Finite Group Databasebeta

← C149×#10080 #49189029

Subgroups — C149×#10080 #49189029

Order 38144.

552 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×#490×C149C212yesmaximal
2#2822×C149C211yesmaximal, characteristic, complemented
3#1961×C149C211yesmaximal, characteristic
4C2×#330×C149C212yesmaximal, complemented
5#1295×C149C211yesmaximal, characteristic, complemented
6C2×#127×C149C2211yescharacteristic
7C2×#125×C149C2212yes—
8#490×C149—24no—
9#490×C149—24no—
10C2×#102×C149—22no—
11C2×#102×C149—22no—
12C2×#102×C149—22no—
13C2×#97×C149C2211yescharacteristic
14C2×#97×C149C2212yes—
15#400×C149—22no—
16#398×C149—22no—
17#398×C149—22no—
18#382×C149C2211yescharacteristic
19#330×C149—24no—
20C22×D4×C149—22no—
21C22×D4×C149—21no—
22C22×C8×C149—21no—
23C22×C8×C149—22no—
24#127×C149—22no—
25#127×C149—21no—
26#127×C149D412yes—
27#125×C149—22no—
28#125×C149—22no—
29#125×C149—22no—
30#125×C149—22no—
31C2×C4⋊C4×C149—22no—
32C2×C4⋊C4×C149—22no—
33C2×C4⋊C4×C149—22no—
34C2×C4⋊C4×C149D412yes—
35C2×C4⋊C4×C149D412yes—
36C2×C4⋊C4×C149D412yes—
37C2×C42×C149C2311yescharacteristic
38#102×C149—28no—
39#102×C149—28no—
40#102×C149—44no—
41#97×C149—22no—
42#97×C149—22no—
43#97×C149D414yes—
44#95×C149—24no—
45#95×C149—22no—
46#95×C149—22no—
47C24×C149—41no—
48C2×D4×C149—24no—
49C2×D4×C149—22no—
50C2×D4×C149—42no—
51C2×D4×C149—48no—
52C2×D4×C149—42no—
53C2×D4×C149—42no—
54C2×D4×C149—41no—
55C22×C4×C149—22no—
56C22×C4×C149—22no—
57C22×C4×C149—22no—
58C22×C4×C149C2×D412yes—
59C22×C4×C149C2×D411yescharacteristic
60C2×C8×C149—22no—
61C2×C8×C149—24no—
62C2×C8×C149—44no—
63C2×C8×C149—41no—
64C2×C8×C149—41no—
65C4⋊C4×C149—22no—
66C4⋊C4×C149—22no—
67C4⋊C4×C149—22no—
68C4⋊C4×C149—22no—
69C4⋊C4×C149—42no—
70C4⋊C4×C149—42no—
71C4⋊C4×C149—42no—
72C4⋊C4×C149—42no—
73C4⋊C4×C149—42no—
74C4⋊C4×C149—82no—
75C42×C149C2×D411yescharacteristic
76C42×C149C2×D412yes—
77C42×C149#4111yescharacteristic
78C23×C149—42no—
79C23×C149—81no—
80C23×C149—84no—
81C23×C149—81no—
82C23×C149#12011yescharacteristic
83D4×C149—48no—
84D4×C149—44no—
85D4×C149—84no—
86D4×C149—82no—
87C2×C4×C149—21no—
88C2×C4×C149—24no—
89C2×C4×C149—21no—
90C2×C4×C149—42no—
91C2×C4×C149—42no—
92C2×C4×C149—42no—
93C2×C4×C149—42no—
94C2×C4×C149—44no—
95C2×C4×C149—44no—
96C2×C4×C149—42no—
97C2×C4×C149#12012yes—
98C2×C4×C149#12112yes—
99C2×C4×C149#12111yescharacteristic
100C2×C4×C149#12711yescharacteristic
101C8×C149—44no—
102C8×C149—42no—
103C22×C149—84no—
104C22×C149—82no—
105C22×C149—162no—
106C22×C149—162no—
107C22×C149#39211yescharacteristic
108C22×C149#45311yescharacteristic
109C22×C149#45414yes—
110C22×C149#45411yescharacteristic
111C4×C149—22no—
112C4×C149—22no—
113C4×C149—21no—
114C4×C149—21no—
115C4×C149—82no—
116C4×C149—82no—
117C4×C149—82no—
118C2×C149—162no—
119C2×C149#165712yes—
120C2×C149#165812yes—
121C2×C149#200312yes—
122C2×C149#200611yescharacteristic
123#10080C14911yesmaximal, characteristic, direct product factor, Sylow
124C149#1008011yescharacteristic, direct product factor, Sylow
125C2×#490C2×C14912yes—
126#2822C2×C14911yescharacteristic, complemented
127#1961C2×C14911yescharacteristic
128C2×#330C2×C14912yescomplemented
129#1295C2×C14911yescharacteristic, complemented
130C2×#127C22×C14911yescharacteristic
131C2×#125C22×C14912yes—
132#490—24no—
133#490—24no—
134C2×#102—22no—
135C2×#102—22no—
136C2×#102—22no—
137C2×#97C22×C14911yescharacteristic
138C2×#97C22×C14912yes—
139#400—22no—
140#398—22no—
141#398—22no—
142#382C22×C14911yescharacteristic
143#330—24no—
144C22×D4—22no—
145C22×D4—21no—
146C22×C8—21no—
147C22×C8—22no—
148#127—22no—
149#127—21no—
150#127D4×C14912yes—
151#125—22no—
152#125—22no—
153#125—22no—
154#125—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4D4×C14912yes—
159C2×C4⋊C4D4×C14912yes—
160C2×C4⋊C4D4×C14912yes—
161C2×C42C23×C14911yescharacteristic
162#102—28no—
163#102—28no—
164#102—44no—
165#97—22no—
166#97—22no—
167#97D4×C14914yes—
168#95—24no—
169#95—22no—
170#95—22no—
171C24—41no—
172C2×D4—24no—
173C2×D4—22no—
174C2×D4—42no—
175C2×D4—48no—
176C2×D4—42no—
177C2×D4—42no—
178C2×D4—41no—
179C22×C4—22no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4C2×D4×C14912yes—
183C22×C4C2×D4×C14911yescharacteristic
184C2×C8—22no—
185C2×C8—24no—
186C2×C8—44no—
187C2×C8—41no—
188C2×C8—41no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—82no—
199C42C2×D4×C14911yescharacteristic
200C42C2×D4×C14912yes—
201C42#41×C14911yescharacteristic
202C23—42no—
203C23—81no—
204C23—84no—
205C23—81no—
206C23#120×C14911yescharacteristic
207D4—48no—
208D4—44no—
209D4—84no—
210D4—82no—
211C2×C4—21no—
212C2×C4—24no—
213C2×C4—21no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—44no—
219C2×C4—42no—
220C2×C4—44no—
221C2×C4#120×C14912yes—
222C2×C4#121×C14912yes—
223C2×C4#121×C14911yescharacteristic
224C2×C4#127×C14911yescharacteristic
225C8—44no—
226C8—42no—
227C22—84no—
228C22—82no—
229C22—162no—
230C22—162no—
231C22#392×C14911yescharacteristic
232C22#453×C14911yescharacteristic
233C22#454×C14914yes—
234C22#454×C14911yescharacteristic
235C4—22no—
236C4—22no—
237C4—21no—
238C4—21no—
239C4—82no—
240C4—82no—
241C4—82no—
242C2—162no—
243C2#1657×C14912yes—
244C2#1658×C14912yes—
245C2#2003×C14912yes—
246C2#2006×C14911yescharacteristic
subgroupG/H
center, socleC23×C149#120
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC2×#127×C149C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2822×C149C2semidirect
4. C2×#330×C149C2semidirect
5. #1295×C149C2semidirect
123. #10080C149direct (N × H)
124. C149#10080direct (N × H)
126. #2822C2×C149semidirect
128. C2×#330C2×C149semidirect
129. #1295C2×C149semidirect

Maximal subgroups

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

subgroupindex
C2×#490×C1492
#2822×C1492
#1961×C1492
C2×#330×C1492
#1295×C1492
#10080149