Finite Group Databasebeta

← C149×#9070 #49188019

Subgroups — C149×#9070 #49188019

Order 38144.

426 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 126 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#3131×C149C211yesmaximal, characteristic
2#2986×C149C211yesmaximal, characteristic, complemented
3#1526×C149C211yesmaximal, characteristic, complemented
4#1484×C149C212yesmaximal
5#1278×C149C212yesmaximal, complemented
6#533×C149C2211yescharacteristic
7#532×C149C2211yescharacteristic
8#488×C149—22no—
9#487×C149C412yes—
10#486×C149C412yes—
11#446×C149—22no—
12C8×Q8×C149—22no—
13#433×C149—22no—
14#431×C149C2212yes—
15#416×C149—22no—
16C4×M16×C149C2212yes—
17C2×C4×C8×C149C2211yescharacteristic
18#330×C149—22no—
19D4⋊C8×C149—22no—
20D4⋊C8×C149—22no—
21C2×#41×C149—21no—
22C2×M16×C149—22no—
23C22×C8×C149—21no—
24C4⋊Q8×C149C2×C411yescharacteristic
25C4⋊Q8×C149C2×C412yes—
26#127×C149C2×C411yescharacteristic
27#125×C149D412yes—
28#124×C149—21no—
29C22⋊Q8×C149—22no—
30#121×C149—22no—
31C4×Q8×C149—22no—
32C4×D4×C149—22no—
33#117×C149D412yes—
34C2×C42×C149C2311yescharacteristic
35C4⋊C8×C149—24no—
36C4⋊C8×C149D412yes—
37C4⋊C8×C149D412yes—
38#103×C149—24no—
39#102×C149—24no—
40C22⋊C8×C149—22no—
41#97×C149—22no—
42#97×C149—22no—
43C4×C8×C149—22no—
44C4×C8×C149—21no—
45C4×C8×C149—22no—
46C4×C8×C149—22no—
47C4×C8×C149C2×C412yes—
48#41×C149—44no—
49C2×Q8×C149—22no—
50C2×Q8×C149—21no—
51C2×D4×C149—21no—
52C2×D4×C149—22no—
53C2×D4×C149—41no—
54C22×C4×C149—41no—
55C22×C4×C149C2×D411yescharacteristic
56C22×C4×C149#4112yes—
57M16×C149—24no—
58M16×C149—42no—
59C2×C8×C149—22no—
60C2×C8×C149—22no—
61C2×C8×C149—22no—
62C2×C8×C149—42no—
63C2×C8×C149—42no—
64C4⋊C4×C149—22no—
65C4⋊C4×C149—24no—
66C4⋊C4×C149—22no—
67C4⋊C4×C149C22⋊C414yes—
68C22⋊C4×C149—22no—
69C22⋊C4×C149—42no—
70C42×C149—22no—
71C42×C149C22×C411yescharacteristic
72C42×C149C2×D411yescharacteristic
73C42×C149C2×D412yes—
74C23×C149—41no—
75C23×C149#12311yescharacteristic
76Q8×C149—42no—
77Q8×C149—42no—
78Q8×C149—42no—
79D4×C149—42no—
80D4×C149—42no—
81D4×C149—42no—
82D4×C149—82no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—24no—
87C2×C4×C149—41no—
88C2×C4×C149—82no—
89C2×C4×C149C2×C22⋊C411yescharacteristic
90C2×C4×C149C4×D412yes—
91C2×C4×C149#12011yescharacteristic
92C2×C4×C149#12112yes—
93C8×C149—42no—
94C8×C149—44no—
95C8×C149—42no—
96C8×C149—42no—
97C22×C149—22no—
98C22×C149—21no—
99C22×C149—82no—
100C22×C149—81no—
101C22×C149#38611yescharacteristic
102C4×C149—22no—
103C4×C149—21no—
104C4×C149—44no—
105C4×C149—81no—
106C4×C149#44312yes—
107C4×C149#44412yes—
108C4×C149#45412yes—
109C2×C149—41no—
110C2×C149—161no—
111C2×C149#187612yes—
112C2×C149#188811yescharacteristic
113#9070C14911yesmaximal, characteristic, direct product factor, Sylow
114C149#907011yescharacteristic, direct product factor, Sylow
115#3131C2×C14911yescharacteristic
116#2986C2×C14911yescharacteristic, complemented
117#1526C2×C14911yescharacteristic, complemented
118#1484C2×C14912yes—
119#1278C2×C14912yescomplemented
120#533C22×C14911yescharacteristic
121#532C22×C14911yescharacteristic
122#488—22no—
123#487C4×C14912yes—
124#486C4×C14912yes—
125#446—22no—
126C8×Q8—22no—
127#433—22no—
128#431C22×C14912yes—
129#416—22no—
130C4×M16C22×C14912yes—
131C2×C4×C8C22×C14911yescharacteristic
132#330—22no—
133D4⋊C8—22no—
134D4⋊C8—22no—
135C2×#41—21no—
136C2×M16—22no—
137C22×C8—21no—
138C4⋊Q8C2×C4×C14911yescharacteristic
139C4⋊Q8C2×C4×C14912yes—
140#127C2×C4×C14911yescharacteristic
141#125D4×C14912yes—
142#124—21no—
143C22⋊Q8—22no—
144#121—22no—
145C4×Q8—22no—
146C4×D4—22no—
147#117D4×C14912yes—
148C2×C42C23×C14911yescharacteristic
149C4⋊C8—24no—
150C4⋊C8D4×C14912yes—
151C4⋊C8D4×C14912yes—
152#103—24no—
153#102—24no—
154C22⋊C8—22no—
155#97—22no—
156#97—22no—
157C4×C8—22no—
158C4×C8—21no—
159C4×C8—22no—
160C4×C8—22no—
161C4×C8C2×C4×C14912yes—
162#41—44no—
163C2×Q8—22no—
164C2×Q8—21no—
165C2×D4—21no—
166C2×D4—22no—
167C2×D4—41no—
168C22×C4—41no—
169C22×C4C2×D4×C14911yescharacteristic
170C22×C4#41×C14912yes—
171M16—24no—
172M16—42no—
173C2×C8—22no—
174C2×C8—22no—
175C2×C8—22no—
176C2×C8—42no—
177C2×C8—42no—
178C4⋊C4—22no—
179C4⋊C4—24no—
180C4⋊C4—22no—
181C4⋊C4C22⋊C4×C14914yes—
182C22⋊C4—22no—
183C22⋊C4—42no—
184C42—22no—
185C42C22×C4×C14911yescharacteristic
186C42C2×D4×C14911yescharacteristic
187C42C2×D4×C14912yes—
188C23—41no—
189C23#123×C14911yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—42no—
193D4—42no—
194D4—42no—
195D4—42no—
196D4—82no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—41no—
202C2×C4—82no—
203C2×C4C2×C22⋊C4×C14911yescharacteristic
204C2×C4C4×D4×C14912yes—
205C2×C4#120×C14911yescharacteristic
206C2×C4#121×C14912yes—
207C8—42no—
208C8—44no—
209C8—42no—
210C8—42no—
211C22—22no—
212C22—21no—
213C22—82no—
214C22—81no—
215C22#386×C14911yescharacteristic
216C4—22no—
217C4—21no—
218C4—44no—
219C4—81no—
220C4#443×C14912yes—
221C4#444×C14912yes—
222C4#454×C14912yes—
223C2—41no—
224C2—161no—
225C2#1876×C14912yes—
226C2#1888×C14911yescharacteristic
subgroupG/H
centerC2×C4×C149#120
commutatorC42C22×C4×C149
Frattini, cosocleC2×C42C23×C149
socleC22×C149#386
prime radical#532×C149C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2986×C149C2semidirect
3. #1526×C149C2semidirect
5. #1278×C149C2semidirect
113. #9070C149direct (N × H)
114. C149#9070direct (N × H)
116. #2986C2×C149semidirect
117. #1526C2×C149semidirect
119. #1278C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3131×C1492
#2986×C1492
#1526×C1492
#1484×C1492
#1278×C1492
#9070149