Finite Group Databasebeta

← C149×#11911 #49190860

Subgroups — C149×#11911 #49190860

Order 38144.

318 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 106 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#3135×C149C211yesmaximal, characteristic
2C2×#347×C149C212yesmaximal, complemented
3#1356×C149C212yesmaximal, complemented
4#1355×C149C212yesmaximal, complemented
5#533×C149C411yescharacteristic
6#532×C149C411yescharacteristic
7C2×M32×C149—22no—
8#491×C149C411yescharacteristic
9#491×C149C2211yescharacteristic
10#490×C149C411yescharacteristic
11#490×C149C2211yescharacteristic
12#489×C149—22no—
13#416×C149—22no—
14C2×#97×C149C2211yescharacteristic
15#347×C149—22no—
16#347×C149C2214yes—
17C2×#41×C149—21no—
18C22×C8×C149D412yes—
19C4⋊Q8×C149—21no—
20C4⋊Q8×C149C2×C411yescharacteristic
21#127×C149C2×C411yescharacteristic
22#125×C149C2×C411yescharacteristic
23#125×C149C2×C411yescharacteristic
24#124×C149—21no—
25C22⋊Q8×C149—41no—
26#121×C149—41no—
27C4×Q8×C149—41no—
28C4×D4×C149—41no—
29#117×C149—21no—
30C2×C42×C149C2×C411yescharacteristic
31M32×C149—24no—
32M32×C149—24no—
33C2×C16×C149—24no—
34#103×C149—22no—
35#103×C149—22no—
36#102×C149—22no—
37#102×C149—22no—
38#97×C149C2×C411yescharacteristic
39#97×C149D412yes—
40#97×C149C2311yescharacteristic
41#41×C149—42no—
42#41×C149—42no—
43C2×Q8×C149—21no—
44C2×Q8×C149—41no—
45C2×D4×C149—21no—
46C2×D4×C149—41no—
47C2×D4×C149—41no—
48C22×C4×C149—21no—
49C22×C4×C149—41no—
50C22×C4×C149C22⋊C411yescharacteristic
51C2×C8×C149—22no—
52C2×C8×C149—22no—
53C2×C8×C149C22⋊C412yes—
54C2×C8×C149C2×D412yes—
55C4⋊C4×C149—21no—
56C4⋊C4×C149—21no—
57C4⋊C4×C149—41no—
58C4⋊C4×C149—41no—
59C4⋊C4×C149—41no—
60C4⋊C4×C149—41no—
61C22⋊C4×C149—42no—
62C22⋊C4×C149—41no—
63C42×C149—21no—
64C42×C149—41no—
65C42×C149C22⋊C411yescharacteristic
66C42×C149C22×C411yescharacteristic
67C16×C149—28no—
68C23×C149—41no—
69C23×C149#10011yescharacteristic
70Q8×C149—42no—
71Q8×C149—82no—
72D4×C149—42no—
73D4×C149—82no—
74D4×C149—82no—
75C2×C4×C149—21no—
76C2×C4×C149—21no—
77C2×C4×C149—41no—
78C2×C4×C149—41no—
79C2×C4×C149—41no—
80C2×C4×C149—81no—
81C2×C4×C149—81no—
82C2×C4×C149—81no—
83C2×C4×C149#10011yescharacteristic
84C2×C4×C149#10412yes—
85C2×C4×C149#10412yes—
86C2×C4×C149C2×C22⋊C411yescharacteristic
87C8×C149—22no—
88C8×C149—22no—
89C22×C149—41no—
90C22×C149—82no—
91C22×C149—81no—
92C22×C149#32912yes—
93C22×C149C2×#10011yescharacteristic
94C4×C149—41no—
95C4×C149—41no—
96C4×C149—81no—
97C4×C149—81no—
98C4×C149—81no—
99C4×C149#32911yescharacteristic
100C4×C149#32911yescharacteristic
101C4×C149C2×#10412yes—
102C2×C149—21no—
103C2×C149—22no—
104C2×C149—161no—
105C2×C149C2×#32911yescharacteristic
106#11911C14911yesmaximal, characteristic, direct product factor, Sylow
107C149#1191111yescharacteristic, direct product factor, Sylow
108#3135C2×C14911yescharacteristic
109C2×#347C2×C14912yescomplemented
110#1356C2×C14912yescomplemented
111#1355C2×C14912yescomplemented
112#533C4×C14911yescharacteristic
113#532C4×C14911yescharacteristic
114C2×M32—22no—
115#491C4×C14911yescharacteristic
116#491C22×C14911yescharacteristic
117#490C4×C14911yescharacteristic
118#490C22×C14911yescharacteristic
119#489—22no—
120#416—22no—
121C2×#97C22×C14911yescharacteristic
122#347—22no—
123#347C22×C14914yes—
124C2×#41—21no—
125C22×C8D4×C14912yes—
126C4⋊Q8—21no—
127C4⋊Q8C2×C4×C14911yescharacteristic
128#127C2×C4×C14911yescharacteristic
129#125C2×C4×C14911yescharacteristic
130#125C2×C4×C14911yescharacteristic
131#124—21no—
132C22⋊Q8—41no—
133#121—41no—
134C4×Q8—41no—
135C4×D4—41no—
136#117—21no—
137C2×C42C2×C4×C14911yescharacteristic
138M32—24no—
139M32—24no—
140C2×C16—24no—
141#103—22no—
142#103—22no—
143#102—22no—
144#102—22no—
145#97C2×C4×C14911yescharacteristic
146#97D4×C14912yes—
147#97C23×C14911yescharacteristic
148#41—42no—
149#41—42no—
150C2×Q8—21no—
151C2×Q8—41no—
152C2×D4—21no—
153C2×D4—41no—
154C2×D4—41no—
155C22×C4—21no—
156C22×C4—41no—
157C22×C4C22⋊C4×C14911yescharacteristic
158C2×C8—22no—
159C2×C8—22no—
160C2×C8C22⋊C4×C14912yes—
161C2×C8C2×D4×C14912yes—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C22⋊C4—42no—
169C22⋊C4—41no—
170C42—21no—
171C42—41no—
172C42C22⋊C4×C14911yescharacteristic
173C42C22×C4×C14911yescharacteristic
174C16—28no—
175C23—41no—
176C23#100×C14911yescharacteristic
177Q8—42no—
178Q8—82no—
179D4—42no—
180D4—82no—
181D4—82no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4#100×C14911yescharacteristic
191C2×C4#104×C14912yes—
192C2×C4#104×C14912yes—
193C2×C4C2×C22⋊C4×C14911yescharacteristic
194C8—22no—
195C8—22no—
196C22—41no—
197C22—82no—
198C22—81no—
199C22#329×C14912yes—
200C22C2×#100×C14911yescharacteristic
201C4—41no—
202C4—41no—
203C4—81no—
204C4—81no—
205C4—81no—
206C4#329×C14911yescharacteristic
207C4#329×C14911yescharacteristic
208C4C2×#104×C14912yes—
209C2—21no—
210C2—22no—
211C2—161no—
212C2C2×#329×C14911yescharacteristic
subgroupG/H
centerC4×C149#329
commutatorC42C22×C4×C149
Frattini, cosocle#97C23×C149
socleC2×C149C2×#329
prime radical#532×C149C4
LCSG ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C149 ◁ C22×C4×C149 ◁ C2×#97×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#347×C149C2semidirect
3. #1356×C149C2semidirect
4. #1355×C149C2semidirect
106. #11911C149direct (N × H)
107. C149#11911direct (N × H)
109. C2×#347C2×C149semidirect
110. #1356C2×C149semidirect
111. #1355C2×C149semidirect

Maximal subgroups

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

subgroupindex
#3135×C1492
C2×#347×C1492
#1356×C1492
#1355×C1492
#11911149