Finite Group Databasebeta

← C149×#10259 #49189208

Subgroups — C149×#10259 #49189208

Order 38144.

474 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 122 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#3249×C149C211yesmaximal, characteristic
2#3078×C149C212yesmaximal
3#1984×C149C211yesmaximal, characteristic
4#1493×C149C212yesmaximal
5#1292×C149C211yesmaximal, characteristic
6#533×C149C2212yes—
7C2×C4×Q8×C149C2211yescharacteristic
8#479×C149—24no—
9#477×C149—22no—
10#477×C149—22no—
11#475×C149—22no—
12#467×C149—22no—
13#462×C149—22no—
14#428×C149—22no—
15#423×C149C2212yes—
16C2×C4⋊C8×C149C2211yescharacteristic
17#419×C149—22no—
18C2×C4×C8×C149C2211yescharacteristic
19#336×C149—22no—
20Q8⋊C8×C149—24no—
21C22×Q8×C149D411yescharacteristic
22C2×Q16×C149—22no—
23C2×M16×C149—22no—
24C22×C8×C149—21no—
25C22×C8×C149D412yes—
26C4⋊Q8×C149D412yes—
27C4⋊Q8×C149D412yes—
28#125×C149—22no—
29C22⋊Q8×C149—22no—
30C22⋊Q8×C149—22no—
31C4×Q8×C149—22no—
32C4×Q8×C149—22no—
33C4×Q8×C149—22no—
34C4×Q8×C149—22no—
35#117×C149—22no—
36C2×C4⋊C4×C149—21no—
37C2×C4⋊C4×C149D411yescharacteristic
38C2×C42×C149—21no—
39C2×C42×C149C2311yescharacteristic
40#107×C149—24no—
41#107×C149—22no—
42#106×C149—24no—
43C4⋊C8×C149—22no—
44C4⋊C8×C149—22no—
45C4⋊C8×C149D414yes—
46#103×C149—24no—
47#103×C149—24no—
48#103×C149—24no—
49C4×C8×C149—22no—
50C2×Q8×C149—21no—
51C2×Q8×C149—22no—
52C2×Q8×C149—22no—
53C2×Q8×C149—22no—
54C2×Q8×C149—22no—
55C2×Q8×C149Q1612yescomplemented
56C22×C4×C149—21no—
57C22×C4×C149—21no—
58C22×C4×C149C2×D411yescharacteristic
59C22×C4×C149C2×D411yescharacteristic
60C22×C4×C149#4111yescharacteristic
61Q16×C149—82no—
62M16×C149—42no—
63M16×C149—42no—
64C2×C8×C149—22no—
65C2×C8×C149—22no—
66C2×C8×C149—24no—
67C2×C8×C149—41no—
68C2×C8×C149—41no—
69C2×C8×C149—42no—
70C4⋊C4×C149—22no—
71C4⋊C4×C149—22no—
72C4⋊C4×C149—22no—
73C4⋊C4×C149—22no—
74C4⋊C4×C149—22no—
75C4⋊C4×C149—42no—
76C4⋊C4×C149—42no—
77C4⋊C4×C149—42no—
78C22⋊C4×C149—42no—
79C42×C149—41no—
80C42×C149—42no—
81C42×C149—41no—
82C42×C149C2×D412yes—
83C42×C149C2×D412yes—
84C23×C149#12111yescharacteristic
85Q8×C149—24no—
86Q8×C149—44no—
87Q8×C149—42no—
88Q8×C149—42no—
89Q8×C149—42no—
90C2×C4×C149—21no—
91C2×C4×C149—21no—
92C2×C4×C149—22no—
93C2×C4×C149—41no—
94C2×C4×C149—41no—
95C2×C4×C149—41no—
96C2×C4×C149—42no—
97C2×C4×C149—41no—
98C2×C4×C149—42no—
99C2×C4×C149—42no—
100C2×C4×C149#12012yes—
101C2×C4×C149#12011yescharacteristic
102C2×C4×C149#12112yes—
103C2×C4×C149#12711yescharacteristic
104C2×C4×C149C2×Q1611yescharacteristic
105C2×C4×C149#13511yescharacteristic
106C2×C4×C149#13712yes—
107C8×C149—42no—
108C8×C149—44no—
109C8×C149—42no—
110C22×C149—21no—
111C22×C149—21no—
112C22×C149#39211yescharacteristic
113C22×C149#46711yescharacteristic
114C22×C149#47011yescharacteristic
115C4×C149—21no—
116C4×C149—22no—
117C4×C149—42no—
118C4×C149—82no—
119C4×C149—81no—
120C4×C149—82no—
121C4×C149#45112yes—
122C4×C149#45212yes—
123C4×C149#45511yescharacteristic
124C4×C149#45611yescharacteristic
125C2×C149—21no—
126C2×C149—21no—
127C2×C149#200111yescharacteristic
128C2×C149#200711yescharacteristic
129C2×C149#201711yescharacteristic
130#10259C14911yesmaximal, characteristic, direct product factor, Sylow
131C149#1025911yescharacteristic, direct product factor, Sylow
132#3249C2×C14911yescharacteristic
133#3078C2×C14912yes—
134#1984C2×C14911yescharacteristic
135#1493C2×C14912yes—
136#1292C2×C14911yescharacteristic
137#533C22×C14912yes—
138C2×C4×Q8C22×C14911yescharacteristic
139#479—24no—
140#477—22no—
141#477—22no—
142#475—22no—
143#467—22no—
144#462—22no—
145#428—22no—
146#423C22×C14912yes—
147C2×C4⋊C8C22×C14911yescharacteristic
148#419—22no—
149C2×C4×C8C22×C14911yescharacteristic
150#336—22no—
151Q8⋊C8—24no—
152C22×Q8D4×C14911yescharacteristic
153C2×Q16—22no—
154C2×M16—22no—
155C22×C8—21no—
156C22×C8D4×C14912yes—
157C4⋊Q8D4×C14912yes—
158C4⋊Q8D4×C14912yes—
159#125—22no—
160C22⋊Q8—22no—
161C22⋊Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—22no—
166#117—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4D4×C14911yescharacteristic
169C2×C42—21no—
170C2×C42C23×C14911yescharacteristic
171#107—24no—
172#107—22no—
173#106—24no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8D4×C14914yes—
177#103—24no—
178#103—24no—
179#103—24no—
180C4×C8—22no—
181C2×Q8—21no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—22no—
186C2×Q8Q16×C14912yescomplemented
187C22×C4—21no—
188C22×C4—21no—
189C22×C4C2×D4×C14911yescharacteristic
190C22×C4C2×D4×C14911yescharacteristic
191C22×C4#41×C14911yescharacteristic
192Q16—82no—
193M16—42no—
194M16—42no—
195C2×C8—22no—
196C2×C8—22no—
197C2×C8—24no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—42no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C22⋊C4—42no—
210C42—41no—
211C42—42no—
212C42—41no—
213C42C2×D4×C14912yes—
214C42C2×D4×C14912yes—
215C23#121×C14911yescharacteristic
216Q8—24no—
217Q8—44no—
218Q8—42no—
219Q8—42no—
220Q8—42no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4#120×C14912yes—
232C2×C4#120×C14911yescharacteristic
233C2×C4#121×C14912yes—
234C2×C4#127×C14911yescharacteristic
235C2×C4C2×Q16×C14911yescharacteristic
236C2×C4#135×C14911yescharacteristic
237C2×C4#137×C14912yes—
238C8—42no—
239C8—44no—
240C8—42no—
241C22—21no—
242C22—21no—
243C22#392×C14911yescharacteristic
244C22#467×C14911yescharacteristic
245C22#470×C14911yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4#451×C14912yes—
253C4#452×C14912yes—
254C4#455×C14911yescharacteristic
255C4#456×C14911yescharacteristic
256C2—21no—
257C2—21no—
258C2#2001×C14911yescharacteristic
259C2#2007×C14911yescharacteristic
260C2#2017×C14911yescharacteristic
subgroupG/H
center, socleC22×C149#392
commutator, Frattini, cosocleC2×C42C23×C149
prime radicalC23×C149#121
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
55. C2×Q8×C149Q16semidirect
130. #10259C149direct (N × H)
131. C149#10259direct (N × H)
186. C2×Q8Q16×C149semidirect

Maximal subgroups

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

subgroupindex
#3249×C1492
#3078×C1492
#1984×C1492
#1493×C1492
#1292×C1492
#10259149