Finite Group Databasebeta

← C149×#7759 #49186708

Subgroups — C149×#7759 #49186708

Order 38144.

456 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 106 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#2811×C149C211yesmaximal, characteristic
2#2024×C149C212yesmaximal
3#2016×C149C211yesmaximal, characteristic
4#1272×C149C211yesmaximal, characteristic
5#1272×C149C212yesmaximal
6C22×Q16×C149—21no—
7C2×C4⋊Q8×C149C2211yescharacteristic
8C2×#103×C149—22no—
9C2×#103×C149—21no—
10#395×C149—21no—
11#395×C149—22no—
12#391×C149—21no—
13#391×C149—22no—
14#391×C149C2211yescharacteristic
15#391×C149C2212yes—
16#340×C149—22no—
17#336×C149C2211yescharacteristic
18#336×C149C2212yes—
19C22×Q8×C149—21no—
20C22×Q8×C149—21no—
21C22×Q8×C149D411yescharacteristic
22C22×Q8×C149D412yes—
23C2×Q16×C149—42no—
24C2×Q16×C149—42no—
25C2×Q16×C149—42no—
26C22×C8×C149—21no—
27C22×C8×C149—22no—
28C4⋊Q8×C149—42no—
29C2×C4⋊C4×C149—22no—
30C2×C4⋊C4×C149—21no—
31C2×C4⋊C4×C149—22no—
32C2×C4⋊C4×C149D411yescharacteristic
33C2×C4⋊C4×C149D412yes—
34C2×C42×C149—21no—
35C2×C42×C149C2311yescharacteristic
36#103×C149—44no—
37#103×C149—42no—
38#95×C149—22no—
39#95×C149—21no—
40#95×C149—22no—
41#95×C149—22no—
42#95×C149—22no—
43C2×Q8×C149—21no—
44C2×Q8×C149—22no—
45C2×Q8×C149—22no—
46C2×Q8×C149—41no—
47C2×Q8×C149—42no—
48C2×Q8×C149—41no—
49C2×Q8×C149—41no—
50C2×Q8×C149—42no—
51C2×Q8×C149—41no—
52C2×Q8×C149—41no—
53C2×Q8×C149—41no—
54C2×Q8×C149—41no—
55C2×Q8×C149—81no—
56C2×Q8×C149—82no—
57C2×Q8×C149SD1612yes—
58C2×Q8×C149Q1614yescomplemented
59C22×C4×C149—21no—
60C22×C4×C149—22no—
61C22×C4×C149—21no—
62C22×C4×C149—22no—
63C22×C4×C149—41no—
64C22×C4×C149C2×D411yescharacteristic
65C22×C4×C149C2×D412yes—
66Q16×C149—48no—
67C2×C8×C149—22no—
68C2×C8×C149—41no—
69C2×C8×C149—41no—
70C2×C8×C149—42no—
71C2×C8×C149—42no—
72C2×C8×C149—42no—
73C4⋊C4×C149—24no—
74C4⋊C4×C149—42no—
75C4⋊C4×C149—41no—
76C4⋊C4×C149—42no—
77C4⋊C4×C149—81no—
78C4⋊C4×C149—82no—
79C42×C149—41no—
80C42×C149—81no—
81C23×C149#12011yescharacteristic
82Q8×C149—42no—
83Q8×C149—44no—
84Q8×C149—42no—
85Q8×C149—42no—
86Q8×C149—81no—
87Q8×C149—82no—
88Q8×C149—81no—
89Q8×C149—81no—
90Q8×C149—84no—
91C2×C4×C149—21no—
92C2×C4×C149—22no—
93C2×C4×C149—22no—
94C2×C4×C149—21no—
95C2×C4×C149—22no—
96C2×C4×C149—24no—
97C2×C4×C149—41no—
98C2×C4×C149—42no—
99C2×C4×C149—41no—
100C2×C4×C149—42no—
101C2×C4×C149—41no—
102C2×C4×C149—42no—
103C2×C4×C149—42no—
104C2×C4×C149—42no—
105C2×C4×C149—42no—
106C2×C4×C149—42no—
107C2×C4×C149—81no—
108C2×C4×C149—81no—
109C2×C4×C149C2×SD1611yescharacteristic
110C2×C4×C149C2×Q1612yes—
111C2×C4×C149#13711yescharacteristic
112C2×C4×C149#13712yes—
113C8×C149—42no—
114C8×C149—82no—
115C22×C149#44811yescharacteristic
116C22×C149#45112yes—
117C22×C149#45311yescharacteristic
118C22×C149#45512yes—
119C22×C149B(4,𝔽2)11yescharacteristic
120C4×C149—21no—
121C4×C149—21no—
122C4×C149—22no—
123C4×C149—22no—
124C4×C149—42no—
125C4×C149—44no—
126C4×C149—82no—
127C4×C149—81no—
128C4×C149—82no—
129C2×C149#159611yescharacteristic
130C2×C149#160212yes—
131C2×C149#163311yescharacteristic
132C2×C149#164512yes—
133C2×C149#165911yescharacteristic
134#7759C14911yesmaximal, characteristic, direct product factor, Sylow
135C149#775911yescharacteristic, direct product factor, Sylow
136#2811C2×C14911yescharacteristic
137#2024C2×C14912yes—
138#2016C2×C14911yescharacteristic
139#1272C2×C14912yes—
140#1272C2×C14911yescharacteristic
141C22×Q16—21no—
142C2×C4⋊Q8C22×C14911yescharacteristic
143C2×#103—22no—
144C2×#103—21no—
145#395—22no—
146#395—21no—
147#391—21no—
148#391—22no—
149#391C22×C14911yescharacteristic
150#391C22×C14912yes—
151#340—22no—
152#336C22×C14911yescharacteristic
153#336C22×C14912yes—
154C22×Q8—21no—
155C22×Q8—21no—
156C22×Q8D4×C14911yescharacteristic
157C22×Q8D4×C14912yes—
158C2×Q16—42no—
159C2×Q16—42no—
160C2×Q16—42no—
161C22×C8—21no—
162C22×C8—22no—
163C4⋊Q8—42no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4D4×C14912yes—
168C2×C4⋊C4D4×C14911yescharacteristic
169C2×C42—21no—
170C2×C42C23×C14911yescharacteristic
171#103—44no—
172#103—42no—
173#95—22no—
174#95—21no—
175#95—22no—
176#95—22no—
177#95—22no—
178C2×Q8—21no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—41no—
182C2×Q8—42no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—42no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×Q8—41no—
189C2×Q8—41no—
190C2×Q8—81no—
191C2×Q8—82no—
192C2×Q8SD16×C14912yes—
193C2×Q8Q16×C14914yescomplemented
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—21no—
197C22×C4—22no—
198C22×C4—41no—
199C22×C4C2×D4×C14911yescharacteristic
200C22×C4C2×D4×C14912yes—
201Q16—48no—
202C2×C8—22no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—42no—
208C4⋊C4—24no—
209C4⋊C4—41no—
210C4⋊C4—42no—
211C4⋊C4—42no—
212C4⋊C4—81no—
213C4⋊C4—82no—
214C42—41no—
215C42—81no—
216C23#120×C14911yescharacteristic
217Q8—42no—
218Q8—44no—
219Q8—42no—
220Q8—42no—
221Q8—81no—
222Q8—82no—
223Q8—81no—
224Q8—81no—
225Q8—84no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—24no—
232C2×C4—41no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4C2×SD16×C14911yescharacteristic
245C2×C4C2×Q16×C14912yes—
246C2×C4#137×C14911yescharacteristic
247C2×C4#137×C14912yes—
248C8—42no—
249C8—82no—
250C22#448×C14911yescharacteristic
251C22#451×C14912yes—
252C22#453×C14911yescharacteristic
253C22#455×C14912yes—
254C22B(4,𝔽2)×C14911yescharacteristic
255C4—21no—
256C4—21no—
257C4—22no—
258C4—22no—
259C4—42no—
260C4—44no—
261C4—82no—
262C4—81no—
263C4—82no—
264C2#1596×C14911yescharacteristic
265C2#1602×C14912yes—
266C2#1633×C14911yescharacteristic
267C2#1645×C14912yes—
268C2#1659×C14911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C149#120
commutator, Frattini, cosocleC2×C42C23×C149
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C149 ◁ C2×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
58. C2×Q8×C149Q16semidirect
134. #7759C149direct (N × H)
135. C149#7759direct (N × H)
193. C2×Q8Q16×C149semidirect

Maximal subgroups

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

subgroupindex
#2811×C1492
#2024×C1492
#2016×C1492
#1272×C1492
#7759149