Finite Group Databasebeta

← C149×#7345 #49186294

Subgroups — C149×#7345 #49186294

Order 38144.

342 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 50 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#1793×C149C211yesmaximal, characteristic
2#1319×C149C211yesmaximal, characteristic, complemented
3#1272×C149C211yesmaximal, characteristic, complemented
4C2×2−1+4×C149C411yescharacteristic
5C2×#104×C149—21no—
6#417×C149—21no—
7C2×#101×C149C411yescharacteristic
8#391×C149C2211yescharacteristic
9#336×C149—21no—
10#324×C149—21no—
112−1+4×C149—21no—
122−1+4×C149—41no—
132−1+4×C149—42no—
142−1+4×C149C812yescomplemented
15C2×#41×C149—21no—
16C2×#41×C149—41no—
17C2×#41×C149—41no—
18C22×Q8×C149—41no—
19C22×Q8×C149C2×C411yescharacteristic
20C2×M16×C149—21no—
21C22×C8×C149—41no—
22C2×C4⋊C4×C149D411yescharacteristic
23C2×C42×C149D411yescharacteristic
24#104×C149—42no—
25#103×C149—41no—
26#102×C149—41no—
27#101×C149—41no—
28C22⋊C8×C149—41no—
29#95×C149—41no—
30#41×C149—22no—
31#41×C149—22no—
32#41×C149—41no—
33#41×C149—42no—
34#41×C149—42no—
35#41×C149—42no—
36#41×C149—42no—
37#41×C149—44no—
38#41×C149—42no—
39#41×C149—42no—
40#41×C149—41no—
41C2×Q8×C149—21no—
42C2×Q8×C149—21no—
43C2×Q8×C149—41no—
44C2×Q8×C149—41no—
45C2×Q8×C149—42no—
46C2×Q8×C149—42no—
47C2×Q8×C149—44no—
48C2×Q8×C149—41no—
49C2×Q8×C149C2×C811yescharacteristic
50C2×Q8×C149M1611yescharacteristic
51C2×D4×C149—21no—
52C2×D4×C149—41no—
53C2×D4×C149—41no—
54C22×C4×C149—21no—
55C22×C4×C149—21no—
56C22×C4×C149—21no—
57C22×C4×C149—41no—
58C22×C4×C149—42no—
59C22×C4×C149C22⋊C411yescharacteristic
60M16×C149—41no—
61M16×C149—41no—
62C2×C8×C149—41no—
63C2×C8×C149—42no—
64C2×C8×C149—81no—
65C2×C8×C149—81no—
66C2×C8×C149—81no—
67C4⋊C4×C149—41no—
68C42×C149—41no—
69C23×C149—41no—
70C23×C149#9911yescharacteristic
71Q8×C149—22no—
72Q8×C149—41no—
73Q8×C149—41no—
74Q8×C149—42no—
75Q8×C149—41no—
76Q8×C149—42no—
77Q8×C149—42no—
78D4×C149—22no—
79D4×C149—41no—
80D4×C149—42no—
81D4×C149—42no—
82D4×C149—42no—
83D4×C149—42no—
84C2×C4×C149—21no—
85C2×C4×C149—21no—
86C2×C4×C149—21no—
87C2×C4×C149—21no—
88C2×C4×C149—21no—
89C2×C4×C149—21no—
90C2×C4×C149—42no—
91C2×C4×C149—42no—
92C2×C4×C149—41no—
93C2×C4×C149—44no—
94C2×C4×C149—44no—
95C2×C4×C149—41no—
96C2×C4×C149—41no—
97C2×C4×C149—41no—
98C2×C4×C149—41no—
99C2×C4×C149—41no—
100C2×C4×C149—81no—
101C2×C4×C149C22⋊C811yescharacteristic
102C2×C4×C149#10011yescharacteristic
103C8×C149—81no—
104C8×C149—82no—
105C8×C149—161no—
106C22×C149—21no—
107C22×C149—21no—
108C22×C149—42no—
109C22×C149—81no—
110C22×C149—81no—
111C22×C149#32311yescharacteristic
112C22×C149AΣL(1,𝔽16)11yescharacteristic
113C22×C149AΣL(1,𝔽16)11yescharacteristic
114C4×C149—21no—
115C4×C149—21no—
116C4×C149—41no—
117C4×C149—41no—
118C4×C149—41no—
119C4×C149—41no—
120C4×C149—42no—
121C4×C149—81no—
122C2×C149—21no—
123C2×C149—21no—
124C2×C149—82no—
125C2×C149#131611yescharacteristic
126C2×C149#140411yescharacteristic
127C2×C149#140511yescharacteristic
128#7345C14911yesmaximal, characteristic, direct product factor, Sylow
129C149#734511yescharacteristic, direct product factor, Sylow
130#1793C2×C14911yescharacteristic
131#1319C2×C14911yescharacteristic, complemented
132#1272C2×C14911yescharacteristic, complemented
133C2×2−1+4C4×C14911yescharacteristic
134C2×#104—21no—
135#417—21no—
136C2×#101C4×C14911yescharacteristic
137#391C22×C14911yescharacteristic
138#336—21no—
139#324—21no—
1402−1+4—21no—
1412−1+4—41no—
1422−1+4—42no—
1432−1+4C8×C14912yescomplemented
144C2×#41—21no—
145C2×#41—41no—
146C2×#41—41no—
147C22×Q8—41no—
148C22×Q8C2×C4×C14911yescharacteristic
149C2×M16—21no—
150C22×C8—41no—
151C2×C4⋊C4D4×C14911yescharacteristic
152C2×C42D4×C14911yescharacteristic
153#104—42no—
154#103—41no—
155#102—41no—
156#101—41no—
157C22⋊C8—41no—
158#95—41no—
159#41—22no—
160#41—22no—
161#41—41no—
162#41—42no—
163#41—42no—
164#41—42no—
165#41—42no—
166#41—44no—
167#41—42no—
168#41—42no—
169#41—41no—
170C2×Q8—21no—
171C2×Q8—21no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—44no—
177C2×Q8—41no—
178C2×Q8C2×C8×C14911yescharacteristic
179C2×Q8M16×C14911yescharacteristic
180C2×D4—21no—
181C2×D4—41no—
182C2×D4—41no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—41no—
187C22×C4—42no—
188C22×C4C22⋊C4×C14911yescharacteristic
189M16—41no—
190M16—41no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C4⋊C4—41no—
197C42—41no—
198C23—41no—
199C23#99×C14911yescharacteristic
200Q8—22no—
201Q8—41no—
202Q8—41no—
203Q8—42no—
204Q8—41no—
205Q8—42no—
206Q8—42no—
207D4—22no—
208D4—41no—
209D4—42no—
210D4—42no—
211D4—42no—
212D4—42no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—44no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—81no—
230C2×C4C22⋊C8×C14911yescharacteristic
231C2×C4#100×C14911yescharacteristic
232C8—81no—
233C8—82no—
234C8—161no—
235C22—21no—
236C22—21no—
237C22—42no—
238C22—81no—
239C22—81no—
240C22#323×C14911yescharacteristic
241C22AΣL(1,𝔽16)×C14911yescharacteristic
242C22AΣL(1,𝔽16)×C14911yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—42no—
250C4—81no—
251C2—21no—
252C2—21no—
253C2—82no—
254C2#1316×C14911yescharacteristic
255C2#1404×C14911yescharacteristic
256C2#1405×C14911yescharacteristic
subgroupG/H
center, socleC22×C149AΣL(1,𝔽16)
commutatorC2×Q8C2×C8×C149
Frattini, cosocle#391C22×C149
prime radicalC2×2−1+4×C149C4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C149 ◁ C22×C4×C149 ◁ #391×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1319×C149C2semidirect
3. #1272×C149C2semidirect
14. 2−1+4×C149C8semidirect
128. #7345C149direct (N × H)
129. C149#7345direct (N × H)
131. #1319C2×C149semidirect
132. #1272C2×C149semidirect
143. 2−1+4C8×C149semidirect

Maximal subgroups

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

subgroupindex
#1793×C1492
#1319×C1492
#1272×C1492
#7345149