Finite Group Databasebeta

← C149×#12153 #49191102

Subgroups — C149×#12153 #49191102

Order 38144.

424 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 74 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#2582×C149C211yesmaximal, characteristic, complemented
2#2039×C149C211yesmaximal, characteristic
3#1610×C149C212yesmaximal
4#1346×C149C212yesmaximal, complemented
5#1325×C149C211yesmaximal, characteristic, complemented
6#537×C149C2211yescharacteristic
7C2×C4×Q8×C149—21no—
8#480×C149—22no—
9C2×#104×C149—21no—
10#417×C149—21no—
11#398×C149—21no—
12#398×C149C2212yes—
13#391×C149—22no—
14#389×C149—22no—
15#384×C149C2211yescharacteristic
16#343×C149C2211yescharacteristic
17#327×C149—22no—
18#324×C149C2212yes—
19C2×#41×C149—21no—
20C22×Q8×C149—21no—
21C2×M16×C149—21no—
22C22⋊Q8×C149—41no—
23#121×C149—22no—
24#121×C149—41no—
25C4×Q8×C149—42no—
26C4×Q8×C149—42no—
27C2×C4⋊C4×C149—21no—
28C2×C4⋊C4×C149—22no—
29C2×C4⋊C4×C149—22no—
30C2×C4⋊C4×C149—21no—
31C2×C4⋊C4×C149D411yescharacteristic
32C2×C4⋊C4×C149D412yes—
33C2×C4⋊C4×C149C2311yescharacteristic
34C2×C42×C149—22no—
35C2×C42×C149D411yescharacteristic
36#107×C149—42no—
37#104×C149—42no—
38#103×C149—41no—
39#102×C149—41no—
40#102×C149—42no—
41C22⋊C8×C149—22no—
42#95×C149—22no—
43#95×C149—21no—
44#95×C149—22no—
45#95×C149D412yes—
46#41×C149—41no—
47#41×C149—41no—
48#41×C149—41no—
49#41×C149—41no—
50C2×Q8×C149—24no—
51C2×Q8×C149—21no—
52C2×Q8×C149—42no—
53C2×Q8×C149—42no—
54C2×D4×C149—21no—
55C2×D4×C149—22no—
56C2×D4×C149—41no—
57C22×C4×C149—21no—
58C22×C4×C149—22no—
59C22×C4×C149—21no—
60C22×C4×C149—22no—
61C22×C4×C149—41no—
62C22×C4×C149C2×D411yescharacteristic
63C22×C4×C149C2×D412yes—
64M16×C149—41no—
65M16×C149—41no—
66C2×C8×C149—42no—
67C2×C8×C149—41no—
68C4⋊C4×C149—22no—
69C4⋊C4×C149—41no—
70C4⋊C4×C149—44no—
71C4⋊C4×C149—42no—
72C4⋊C4×C149—41no—
73C4⋊C4×C149—42no—
74C4⋊C4×C149—42no—
75C4⋊C4×C149—42no—
76C4⋊C4×C149—81no—
77C22⋊C4×C149—42no—
78C42×C149—21no—
79C42×C149—44no—
80C42×C149D812yes—
81C23×C149—41no—
82C23×C149#12011yescharacteristic
83Q8×C149—48no—
84Q8×C149—41no—
85Q8×C149—41no—
86D4×C149—41no—
87D4×C149—41no—
88D4×C149—82no—
89D4×C149—81no—
90D4×C149—81no—
91C2×C4×C149—22no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—21no—
95C2×C4×C149—21no—
96C2×C4×C149—24no—
97C2×C4×C149—22no—
98C2×C4×C149—42no—
99C2×C4×C149—42no—
100C2×C4×C149—42no—
101C2×C4×C149—42no—
102C2×C4×C149—42no—
103C2×C4×C149—42no—
104C2×C4×C149—41no—
105C2×C4×C149—42no—
106C2×C4×C149—41no—
107C2×C4×C149—81no—
108C2×C4×C149—81no—
109C2×C4×C149C2×D811yescharacteristic
110C2×C4×C149AGL(1,ℤ/8)11yescharacteristic
111C8×C149—81no—
112C8×C149—82no—
113C22×C149—21no—
114C22×C149—21no—
115C22×C149—81no—
116C22×C149—81no—
117C22×C149—81no—
118C22×C149#44711yescharacteristic
119C22×C149#45411yescharacteristic
120C22×C149B(4,𝔽2)11yescharacteristic
121C4×C149—24no—
122C4×C149—21no—
123C4×C149—21no—
124C4×C149—44no—
125C4×C149—42no—
126C4×C149—82no—
127C4×C149—81no—
128C4×C149—81no—
129C2×C149—21no—
130C2×C149—21no—
131C2×C149—161no—
132C2×C149#159811yescharacteristic
133C2×C149#219811yescharacteristic
134C2×C149#220511yescharacteristic
135#12153C14911yesmaximal, characteristic, direct product factor, Sylow
136C149#1215311yescharacteristic, direct product factor, Sylow
137#2582C2×C14911yescharacteristic, complemented
138#2039C2×C14911yescharacteristic
139#1610C2×C14912yes—
140#1346C2×C14912yescomplemented
141#1325C2×C14911yescharacteristic, complemented
142#537C22×C14911yescharacteristic
143C2×C4×Q8—21no—
144#480—22no—
145C2×#104—21no—
146#417—21no—
147#398—21no—
148#398C22×C14912yes—
149#391—22no—
150#389—22no—
151#384C22×C14911yescharacteristic
152#343C22×C14911yescharacteristic
153#327—22no—
154#324C22×C14912yes—
155C2×#41—21no—
156C22×Q8—21no—
157C2×M16—21no—
158C22⋊Q8—41no—
159#121—22no—
160#121—41no—
161C4×Q8—42no—
162C4×Q8—42no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4D4×C14911yescharacteristic
168C2×C4⋊C4D4×C14912yes—
169C2×C4⋊C4C23×C14911yescharacteristic
170C2×C42—22no—
171C2×C42D4×C14911yescharacteristic
172#107—42no—
173#104—42no—
174#103—41no—
175#102—41no—
176#102—42no—
177C22⋊C8—22no—
178#95—22no—
179#95—21no—
180#95—22no—
181#95D4×C14912yes—
182#41—41no—
183#41—41no—
184#41—41no—
185#41—41no—
186C2×Q8—24no—
187C2×Q8—21no—
188C2×Q8—42no—
189C2×Q8—42no—
190C2×D4—21no—
191C2×D4—22no—
192C2×D4—41no—
193C22×C4—21no—
194C22×C4—22no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—41no—
198C22×C4C2×D4×C14911yescharacteristic
199C22×C4C2×D4×C14912yes—
200M16—41no—
201M16—41no—
202C2×C8—42no—
203C2×C8—41no—
204C4⋊C4—22no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—44no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—81no—
213C22⋊C4—42no—
214C42—21no—
215C42—44no—
216C42D8×C14912yes—
217C23—41no—
218C23#120×C14911yescharacteristic
219Q8—48no—
220Q8—41no—
221Q8—41no—
222D4—41no—
223D4—41no—
224D4—82no—
225D4—81no—
226D4—81no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—24no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4C2×D8×C14911yescharacteristic
246C2×C4AGL(1,ℤ/8)×C14911yescharacteristic
247C8—81no—
248C8—82no—
249C22—21no—
250C22—21no—
251C22—81no—
252C22—81no—
253C22—81no—
254C22#447×C14911yescharacteristic
255C22#454×C14911yescharacteristic
256C22B(4,𝔽2)×C14911yescharacteristic
257C4—24no—
258C4—21no—
259C4—21no—
260C4—44no—
261C4—42no—
262C4—81no—
263C4—82no—
264C4—81no—
265C2—21no—
266C2—21no—
267C2—161no—
268C2#1598×C14911yescharacteristic
269C2#2198×C14911yescharacteristic
270C2#2205×C14911yescharacteristic
subgroupG/H
center, socleC22×C149B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C149
prime radical#537×C149C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C23×C149 ◁ C2×C4⋊C4×C149 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2582×C149C2semidirect
4. #1346×C149C2semidirect
5. #1325×C149C2semidirect
135. #12153C149direct (N × H)
136. C149#12153direct (N × H)
137. #2582C2×C149semidirect
140. #1346C2×C149semidirect
141. #1325C2×C149semidirect

Maximal subgroups

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

subgroupindex
#2582×C1492
#2039×C1492
#1610×C1492
#1346×C1492
#1325×C1492
#12153149