Finite Group Databasebeta

← C149×#10393 #49189342

Subgroups — C149×#10393 #49189342

Order 38144.

526 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 90 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#2842×C149C211yesmaximal, characteristic
2#1819×C149C211yesmaximal, characteristic
3#1819×C149C212yesmaximal
4#1304×C149C211yesmaximal, characteristic
5#1304×C149C212yesmaximal
6C22×C22⋊C4×C149C2211yescharacteristic
7#399×C149—22no—
8#396×C149—24no—
9#379×C149C2212yes—
10#379×C149C2211yescharacteristic
11#379×C149C2211yescharacteristic
12#379×C149C2212yes—
13#342×C149—24no—
14#342×C149—22no—
15C25×C149C2311yescharacteristic
16C23×C4×C149Q812yes—
17C2×C4⋊C4×C149—24no—
18C2×C4⋊C4×C149—22no—
19C2×C22⋊C4×C149—22no—
20C2×C22⋊C4×C149—21no—
21C2×C22⋊C4×C149—21no—
22C2×C22⋊C4×C149—22no—
23C2×C22⋊C4×C149—22no—
24C2×C22⋊C4×C149—21no—
25C2×C22⋊C4×C149—22no—
26C2×C22⋊C4×C149—22no—
27C2×C22⋊C4×C149—22no—
28C2×C22⋊C4×C149—22no—
29C2×C22⋊C4×C149—22no—
30C2×C22⋊C4×C149—22no—
31C2×C22⋊C4×C149D414yes—
32C2×C22⋊C4×C149D412yes—
33#95×C149—22no—
34C24×C149—42no—
35C24×C149—82no—
36C24×C149C2×D412yes—
37C24×C149C2×D411yescharacteristic
38C24×C149C2×Q811yescharacteristic
39C24×C149#4112yes—
40C24×C149#4111yescharacteristic
41C22×C4×C149—22no—
42C22×C4×C149—24no—
43C22×C4×C149—22no—
44C22×C4×C149—22no—
45C22×C4×C149—22no—
46C22×C4×C149—42no—
47C22×C4×C149—41no—
48C22×C4×C149—82no—
49C4⋊C4×C149—84no—
50C4⋊C4×C149—82no—
51C22⋊C4×C149—41no—
52C22⋊C4×C149—42no—
53C22⋊C4×C149—41no—
54C22⋊C4×C149—44no—
55C22⋊C4×C149—42no—
56C22⋊C4×C149—44no—
57C22⋊C4×C149—42no—
58C22⋊C4×C149—82no—
59C22⋊C4×C149—82no—
60C22⋊C4×C149—82no—
61C22⋊C4×C149—82no—
62C22⋊C4×C149—82no—
63C22⋊C4×C149—82no—
64C23×C149—24no—
65C23×C149—22no—
66C23×C149—42no—
67C23×C149—41no—
68C23×C149—42no—
69C23×C149—42no—
70C23×C149—42no—
71C23×C149—42no—
72C23×C149—42no—
73C23×C149—42no—
74C23×C149—41no—
75C23×C149—42no—
76C23×C149—88no—
77C23×C149#12011yescharacteristic
78C23×C149C22⋊Q812yes—
79C23×C149C22⋊Q811yescharacteristic
80C23×C149#12412yes—
81C23×C149#12411yescharacteristic
82C2×C4×C149—44no—
83C2×C4×C149—44no—
84C2×C4×C149—44no—
85C2×C4×C149—42no—
86C2×C4×C149—44no—
87C2×C4×C149—42no—
88C2×C4×C149—82no—
89C2×C4×C149—82no—
90C2×C4×C149—82no—
91C2×C4×C149—82no—
92C2×C4×C149—81no—
93C2×C4×C149—82no—
94C2×C4×C149—82no—
95C2×C4×C149—82no—
96C22×C149—22no—
97C22×C149—22no—
98C22×C149—21no—
99C22×C149—22no—
100C22×C149—21no—
101C22×C149—22no—
102C22×C149—22no—
103C22×C149—22no—
104C22×C149—22no—
105C22×C149—22no—
106C22×C149—22no—
107C22×C149—44no—
108C22×C149—84no—
109C22×C149—82no—
110C22×C149—82no—
111C22×C149—84no—
112C22×C149#39311yescharacteristic
113C22×C149#45812yes—
114C4×C149—82no—
115C4×C149—84no—
116C4×C149—82no—
117C4×C149—162no—
118C4×C149—161no—
119C2×C149—22no—
120C2×C149—42no—
121C2×C149—41no—
122C2×C149—42no—
123C2×C149—41no—
124C2×C149#203011yescharacteristic
125C2×C149#203212yes—
126#10393C14911yesmaximal, characteristic, direct product factor, Sylow
127C149#1039311yescharacteristic, direct product factor, Sylow
128#2842C2×C14911yescharacteristic
129#1819C2×C14912yes—
130#1819C2×C14911yescharacteristic
131#1304C2×C14911yescharacteristic
132#1304C2×C14912yes—
133C22×C22⋊C4C22×C14911yescharacteristic
134#399—22no—
135#396—24no—
136#379C22×C14912yes—
137#379C22×C14911yescharacteristic
138#379C22×C14911yescharacteristic
139#379C22×C14912yes—
140#342—24no—
141#342—22no—
142C25C23×C14911yescharacteristic
143C23×C4Q8×C14912yes—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—22no—
146C2×C22⋊C4—22no—
147C2×C22⋊C4—21no—
148C2×C22⋊C4—21no—
149C2×C22⋊C4—22no—
150C2×C22⋊C4—22no—
151C2×C22⋊C4—21no—
152C2×C22⋊C4—22no—
153C2×C22⋊C4—22no—
154C2×C22⋊C4—22no—
155C2×C22⋊C4—22no—
156C2×C22⋊C4—22no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4D4×C14914yes—
159C2×C22⋊C4D4×C14912yes—
160#95—22no—
161C24—42no—
162C24—82no—
163C24C2×D4×C14912yes—
164C24C2×D4×C14911yescharacteristic
165C24C2×Q8×C14911yescharacteristic
166C24#41×C14912yes—
167C24#41×C14911yescharacteristic
168C22×C4—22no—
169C22×C4—24no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—41no—
175C22×C4—82no—
176C4⋊C4—84no—
177C4⋊C4—82no—
178C22⋊C4—41no—
179C22⋊C4—42no—
180C22⋊C4—41no—
181C22⋊C4—44no—
182C22⋊C4—42no—
183C22⋊C4—44no—
184C22⋊C4—42no—
185C22⋊C4—82no—
186C22⋊C4—82no—
187C22⋊C4—82no—
188C22⋊C4—82no—
189C22⋊C4—82no—
190C22⋊C4—82no—
191C23—24no—
192C23—22no—
193C23—42no—
194C23—41no—
195C23—42no—
196C23—42no—
197C23—42no—
198C23—42no—
199C23—42no—
200C23—42no—
201C23—41no—
202C23—42no—
203C23—88no—
204C23#120×C14911yescharacteristic
205C23C22⋊Q8×C14912yes—
206C23C22⋊Q8×C14911yescharacteristic
207C23#124×C14912yes—
208C23#124×C14911yescharacteristic
209C2×C4—44no—
210C2×C4—44no—
211C2×C4—44no—
212C2×C4—42no—
213C2×C4—44no—
214C2×C4—42no—
215C2×C4—82no—
216C2×C4—82no—
217C2×C4—82no—
218C2×C4—82no—
219C2×C4—81no—
220C2×C4—82no—
221C2×C4—82no—
222C2×C4—82no—
223C22—22no—
224C22—22no—
225C22—21no—
226C22—22no—
227C22—21no—
228C22—22no—
229C22—22no—
230C22—22no—
231C22—22no—
232C22—22no—
233C22—22no—
234C22—44no—
235C22—84no—
236C22—82no—
237C22—82no—
238C22—84no—
239C22#393×C14911yescharacteristic
240C22#458×C14912yes—
241C4—82no—
242C4—84no—
243C4—82no—
244C4—162no—
245C4—161no—
246C2—22no—
247C2—42no—
248C2—41no—
249C2—42no—
250C2—41no—
251C2#2030×C14911yescharacteristic
252C2#2032×C14912yes—
subgroupG/H
center, socleC22×C149#393
commutator, Frattini, cosocleC25C23×C149
prime radicalC25×C149C23
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C22×C149 ◁ C25×C149 ◁ G

Complements

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

NH ≅ G/Ntype
126. #10393C149direct (N × H)
127. C149#10393direct (N × H)

Maximal subgroups

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

subgroupindex
#2842×C1492
#1819×C1492
#1304×C1492
#10393149