Finite Group Databasebeta

← C149×#10217 #49189166

Subgroups — C149×#10217 #49189166

Order 38144.

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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#3255×C149C211yesmaximal, characteristic
2#3237×C149C212yesmaximal
3#1995×C149C211yesmaximal, characteristic
4#1506×C149C212yesmaximal
5#1307×C149C211yesmaximal, characteristic
6#533×C149C2211yescharacteristic
7#533×C149C2212yes—
8#501×C149—22no—
9#491×C149—22no—
10#485×C149—24no—
11#477×C149—22no—
12#475×C149—22no—
13#475×C149—22no—
14#470×C149—22no—
15#462×C149—22no—
16#432×C149C2212yes—
17#423×C149C2211yescharacteristic
18#376×C149C2211yescharacteristic
19#339×C149—22no—
20#328×C149—24no—
21C2×Q16×C149—22no—
22C2×M16×C149D412yes—
23C4⋊Q8×C149D412yes—
24C4⋊Q8×C149D412yes—
25C4⋊Q8×C149D412yes—
26#125×C149—22no—
27#125×C149—21no—
28C22⋊Q8×C149—22no—
29C22⋊Q8×C149—22no—
30C22⋊Q8×C149—22no—
31C4×Q8×C149—22no—
32C4×Q8×C149—22no—
33C4×Q8×C149—22no—
34#117×C149—22no—
35#117×C149—21no—
36C2×C42×C149—21no—
37C2×C42×C149C2311yescharacteristic
38#107×C149—24no—
39#106×C149—22no—
40#106×C149—24no—
41C4⋊C8×C149—22no—
42C4⋊C8×C149—22no—
43#103×C149—24no—
44#103×C149—24no—
45#103×C149—24no—
46C22⋊C8×C149D414yes—
47#97×C149—22no—
48#95×C149—22no—
49C2×Q8×C149—22no—
50C2×Q8×C149—22no—
51C2×Q8×C149—22no—
52C22×C4×C149—41no—
53C22×C4×C149C2×D411yescharacteristic
54C22×C4×C149C2×D412yes—
55Q16×C149—82no—
56M16×C149—42no—
57C2×C8×C149—24no—
58C2×C8×C149—22no—
59C4⋊C4×C149—22no—
60C4⋊C4×C149—22no—
61C4⋊C4×C149—22no—
62C4⋊C4×C149—22no—
63C4⋊C4×C149—22no—
64C4⋊C4×C149—22no—
65C4⋊C4×C149—42no—
66C4⋊C4×C149—42no—
67C4⋊C4×C149—42no—
68C22⋊C4×C149—42no—
69C22⋊C4×C149—41no—
70C42×C149—22no—
71C42×C149—41no—
72C42×C149—41no—
73C42×C149—42no—
74C42×C149C2×D411yescharacteristic
75C42×C149C2×D412yes—
76C42×C149#4111yescharacteristic
77C23×C149#12711yescharacteristic
78Q8×C149—44no—
79Q8×C149—42no—
80Q8×C149—42no—
81Q8×C149—82no—
82C2×C4×C149—21no—
83C2×C4×C149—21no—
84C2×C4×C149—42no—
85C2×C4×C149—42no—
86C2×C4×C149—42no—
87C2×C4×C149—42no—
88C2×C4×C149—42no—
89C2×C4×C149—82no—
90C2×C4×C149#12012yes—
91C2×C4×C149#12011yescharacteristic
92C2×C4×C149#12112yes—
93C2×C4×C149#12111yescharacteristic
94C8×C149—44no—
95C8×C149—42no—
96C22×C149—21no—
97C22×C149—22no—
98C22×C149#39211yescharacteristic
99C4×C149—21no—
100C4×C149—22no—
101C4×C149—22no—
102C4×C149—82no—
103C4×C149—82no—
104C4×C149—82no—
105C4×C149—82no—
106C4×C149#45511yescharacteristic
107C4×C149#45611yescharacteristic
108C2×C149—41no—
109C2×C149#200711yescharacteristic
110C2×C149#200912yes—
111#10217C14911yesmaximal, characteristic, direct product factor, Sylow
112C149#1021711yescharacteristic, direct product factor, Sylow
113#3255C2×C14911yescharacteristic
114#3237C2×C14912yes—
115#1995C2×C14911yescharacteristic
116#1506C2×C14912yes—
117#1307C2×C14911yescharacteristic
118#533C22×C14911yescharacteristic
119#533C22×C14912yes—
120#501—22no—
121#491—22no—
122#485—24no—
123#477—22no—
124#475—22no—
125#475—22no—
126#470—22no—
127#462—22no—
128#432C22×C14912yes—
129#423C22×C14911yescharacteristic
130#376C22×C14911yescharacteristic
131#339—22no—
132#328—24no—
133C2×Q16—22no—
134C2×M16D4×C14912yes—
135C4⋊Q8D4×C14912yes—
136C4⋊Q8D4×C14912yes—
137C4⋊Q8D4×C14912yes—
138#125—22no—
139#125—21no—
140C22⋊Q8—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145C4×Q8—22no—
146#117—21no—
147#117—22no—
148C2×C42—21no—
149C2×C42C23×C14911yescharacteristic
150#107—24no—
151#106—22no—
152#106—24no—
153C4⋊C8—22no—
154C4⋊C8—22no—
155#103—24no—
156#103—24no—
157#103—24no—
158C22⋊C8D4×C14914yes—
159#97—22no—
160#95—22no—
161C2×Q8—22no—
162C2×Q8—22no—
163C2×Q8—22no—
164C22×C4—41no—
165C22×C4C2×D4×C14911yescharacteristic
166C22×C4C2×D4×C14912yes—
167Q16—82no—
168M16—42no—
169C2×C8—24no—
170C2×C8—22no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—42no—
182C42—22no—
183C42—41no—
184C42—41no—
185C42—42no—
186C42C2×D4×C14911yescharacteristic
187C42C2×D4×C14912yes—
188C42#41×C14911yescharacteristic
189C23#127×C14911yescharacteristic
190Q8—44no—
191Q8—42no—
192Q8—42no—
193Q8—82no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—82no—
202C2×C4#120×C14912yes—
203C2×C4#120×C14911yescharacteristic
204C2×C4#121×C14912yes—
205C2×C4#121×C14911yescharacteristic
206C8—44no—
207C8—42no—
208C22—21no—
209C22—22no—
210C22#392×C14911yescharacteristic
211C4—21no—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—82no—
216C4—82no—
217C4—82no—
218C4#455×C14911yescharacteristic
219C4#456×C14911yescharacteristic
220C2—41no—
221C2#2007×C14911yescharacteristic
222C2#2009×C14912yes—
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC23×C149#127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
111. #10217C149direct (N × H)
112. C149#10217direct (N × H)

Maximal subgroups

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

subgroupindex
#3255×C1492
#3237×C1492
#1995×C1492
#1506×C1492
#1307×C1492
#10217149