Finite Group Databasebeta

← C149×#13579 #49192528

Subgroups — C149×#13579 #49192528

Order 38144.

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

normal subgroups only

This group has 454 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#3151×C149C211yesmaximal, characteristic
2#2132×C149C211yesmaximal, characteristic, complemented
3#2126×C149C211yesmaximal, characteristic, complemented
4#1406×C149C214yesmaximal, complemented
5C2×AGL(1,ℤ/8)×C149—21no—
6C2×AGL(1,ℤ/8)×C149—21no—
7#532×C149C2211yescharacteristic
8C2×#127×C149C411yescharacteristic, complemented
9#496×C149C412yescomplemented
10#496×C149C2212yes—
11#493×C149—21no—
12#492×C149—21no—
13#413×C149—21no—
14#410×C149—21no—
15C4×M16×C149C411yescharacteristic, complemented
16#356×C149—21no—
17#355×C149C2212yescomplemented
18#354×C149C2212yescomplemented
19#353×C149—21no—
20C2×#41×C149D411yescharacteristic
21C2×#41×C149D411yescharacteristic
22C22×D4×C149—21no—
23C22×D4×C149—41no—
24AGL(1,ℤ/8)×C149—42no—
25AGL(1,ℤ/8)×C149—42no—
26AGL(1,ℤ/8)×C149—42no—
27AGL(1,ℤ/8)×C149—42no—
28C2×SD16×C149—22no—
29C2×SD16×C149—22no—
30C2×D8×C149—22no—
31C2×D8×C149—22no—
32C2×M16×C149—21no—
33C2×M16×C149—41no—
34C4⋊Q8×C149D411yescharacteristic
35#127×C149—21no—
36#127×C149—41no—
37#127×C149C2×C412yes—
38#127×C149D411yescharacteristic
39#124×C149C2×C411yescharacteristic
40#124×C149C2311yescharacteristic
41#121×C149—41no—
42C4×D4×C149—41no—
43#117×C149—41no—
44C2×C42×C149C2×C411yescharacteristic
45#101×C149—22no—
46#100×C149—41no—
47#99×C149—22no—
48#99×C149—41no—
49#97×C149C2×C412yes—
50C4×C8×C149—21no—
51C24×C149—41no—
52#41×C149—41no—
53#41×C149—41no—
54#41×C149—41no—
55#41×C149—41no—
56C2×Q8×C149C22⋊C411yescharacteristic
57C2×Q8×C149C2×D411yescharacteristic
58C2×D4×C149—21no—
59C2×D4×C149—21no—
60C2×D4×C149—22no—
61C2×D4×C149—41no—
62C2×D4×C149—41no—
63C2×D4×C149—41no—
64C2×D4×C149—41no—
65C2×D4×C149—41no—
66C2×D4×C149—42no—
67C2×D4×C149—42no—
68C2×D4×C149—41no—
69C2×D4×C149—84no—
70C2×D4×C149C22⋊C411yescharacteristic
71C2×D4×C149C2×D411yescharacteristic
72C22×C4×C149—21no—
73C22×C4×C149—21no—
74C22×C4×C149—21no—
75C22×C4×C149C22⋊C411yescharacteristic
76SD16×C149—44no—
77SD16×C149—44no—
78D8×C149—44no—
79D8×C149—44no—
80M16×C149—22no—
81M16×C149—22no—
82M16×C149—42no—
83M16×C149—81no—
84C2×C8×C149—22no—
85C2×C8×C149—81no—
86C4⋊C4×C149—41no—
87C4⋊C4×C149—81no—
88C22⋊C4×C149—41no—
89C22⋊C4×C149—41no—
90C22⋊C4×C149—42no—
91C42×C149—21no—
92C42×C149—81no—
93C42×C149C22⋊C411yescharacteristic
94C42×C149C22×C411yescharacteristic
95C23×C149—21no—
96C23×C149—21no—
97C23×C149—42no—
98C23×C149—81no—
99C23×C149—81no—
100C23×C149—84no—
101C23×C149#9911yescharacteristic
102Q8×C149—41no—
103Q8×C149—41no—
104D4×C149—41no—
105D4×C149—41no—
106D4×C149—42no—
107D4×C149—42no—
108D4×C149—82no—
109D4×C149—84no—
110D4×C149—81no—
111D4×C149—81no—
112D4×C149—84no—
113D4×C149—81no—
114D4×C149—81no—
115C2×C4×C149—21no—
116C2×C4×C149—21no—
117C2×C4×C149—21no—
118C2×C4×C149—21no—
119C2×C4×C149—21no—
120C2×C4×C149—21no—
121C2×C4×C149—42no—
122C2×C4×C149—41no—
123C2×C4×C149—41no—
124C2×C4×C149—41no—
125C2×C4×C149—41no—
126C2×C4×C149—82no—
127C2×C4×C149#9911yescharacteristic
128C2×C4×C149C2×C22⋊C411yescharacteristic
129C8×C149—24no—
130C8×C149—82no—
131C22×C149—21no—
132C22×C149—41no—
133C22×C149—41no—
134C22×C149—41no—
135C22×C149—81no—
136C22×C149—81no—
137C22×C149—84no—
138C22×C149—82no—
139C22×C149—162no—
140C22×C149—162no—
141C22×C149C2×#9911yescharacteristic
142C4×C149—22no—
143C4×C149—21no—
144C4×C149—41no—
145C4×C149—41no—
146C4×C149—41no—
147C4×C149—162no—
148C4×C149#35311yescharacteristic
149C4×C149#35311yescharacteristic
150C2×C149—21no—
151C2×C149—41no—
152C2×C149—81no—
153C2×C149—81no—
154C2×C149—162no—
155C2×C149C2×#35311yescharacteristic
156#13579C14911yesmaximal, characteristic, direct product factor, Sylow
157C149#1357911yescharacteristic, direct product factor, Sylow
158#3151C2×C14911yescharacteristic
159#2132C2×C14911yescharacteristic, complemented
160#2126C2×C14911yescharacteristic, complemented
161#1406C2×C14914yescomplemented
162C2×AGL(1,ℤ/8)—21no—
163C2×AGL(1,ℤ/8)—21no—
164#532C22×C14911yescharacteristic
165C2×#127C4×C14911yescharacteristic, complemented
166#496C4×C14912yescomplemented
167#496C22×C14912yes—
168#493—21no—
169#492—21no—
170#413—21no—
171#410—21no—
172C4×M16C4×C14911yescharacteristic, complemented
173#356—21no—
174#355C22×C14912yescomplemented
175#354C22×C14912yescomplemented
176#353—21no—
177C2×#41D4×C14911yescharacteristic
178C2×#41D4×C14911yescharacteristic
179C22×D4—21no—
180C22×D4—41no—
181AGL(1,ℤ/8)—42no—
182AGL(1,ℤ/8)—42no—
183AGL(1,ℤ/8)—42no—
184AGL(1,ℤ/8)—42no—
185C2×SD16—22no—
186C2×SD16—22no—
187C2×D8—22no—
188C2×D8—22no—
189C2×M16—21no—
190C2×M16—41no—
191C4⋊Q8D4×C14911yescharacteristic
192#127—21no—
193#127—41no—
194#127C2×C4×C14912yes—
195#127D4×C14911yescharacteristic
196#124C2×C4×C14911yescharacteristic
197#124C23×C14911yescharacteristic
198#121—41no—
199C4×D4—41no—
200#117—41no—
201C2×C42C2×C4×C14911yescharacteristic
202#101—22no—
203#100—41no—
204#99—22no—
205#99—41no—
206#97C2×C4×C14912yes—
207C4×C8—21no—
208C24—41no—
209#41—41no—
210#41—41no—
211#41—41no—
212#41—41no—
213C2×Q8C22⋊C4×C14911yescharacteristic
214C2×Q8C2×D4×C14911yescharacteristic
215C2×D4—21no—
216C2×D4—21no—
217C2×D4—22no—
218C2×D4—41no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—84no—
227C2×D4C22⋊C4×C14911yescharacteristic
228C2×D4C2×D4×C14911yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4C22⋊C4×C14911yescharacteristic
233SD16—44no—
234SD16—44no—
235D8—44no—
236D8—44no—
237M16—22no—
238M16—22no—
239M16—42no—
240M16—81no—
241C2×C8—22no—
242C2×C8—81no—
243C4⋊C4—41no—
244C4⋊C4—81no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—42no—
248C42—21no—
249C42—81no—
250C42C22⋊C4×C14911yescharacteristic
251C42C22×C4×C14911yescharacteristic
252C23—21no—
253C23—21no—
254C23—42no—
255C23—81no—
256C23—81no—
257C23—84no—
258C23#99×C14911yescharacteristic
259Q8—41no—
260Q8—41no—
261D4—41no—
262D4—41no—
263D4—42no—
264D4—42no—
265D4—82no—
266D4—84no—
267D4—81no—
268D4—81no—
269D4—84no—
270D4—81no—
271D4—81no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—82no—
284C2×C4#99×C14911yescharacteristic
285C2×C4C2×C22⋊C4×C14911yescharacteristic
286C8—24no—
287C8—82no—
288C22—21no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22—81no—
294C22—84no—
295C22—82no—
296C22—162no—
297C22—162no—
298C22C2×#99×C14911yescharacteristic
299C4—22no—
300C4—21no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—162no—
305C4#353×C14911yescharacteristic
306C4#353×C14911yescharacteristic
307C2—21no—
308C2—41no—
309C2—81no—
310C2—81no—
311C2—162no—
312C2C2×#353×C14911yescharacteristic
subgroupG/H
center, socleC2×C149C2×#353
commutatorC42C22×C4×C149
Frattini, cosocle#124C23×C149
prime radical#3151×C149C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C149 ◁ C2×C4×C149 ◁ C22×C4×C149 ◁ #532×C149 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2132×C149C2semidirect
3. #2126×C149C2semidirect
4. #1406×C149C2semidirect
8. C2×#127×C149C4semidirect
9. #496×C149C4semidirect
15. C4×M16×C149C4semidirect
17. #355×C149C22semidirect
18. #354×C149C22semidirect
156. #13579C149direct (N × H)
157. C149#13579direct (N × H)
159. #2132C2×C149semidirect
160. #2126C2×C149semidirect
161. #1406C2×C149semidirect
165. C2×#127C4×C149semidirect
166. #496C4×C149semidirect
172. C4×M16C4×C149semidirect
174. #355C22×C149semidirect
175. #354C22×C149semidirect

Maximal subgroups

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

subgroupindex
#3151×C1492
#2132×C1492
#2126×C1492
#1406×C1492
#13579149