Finite Group Databasebeta

← C149×#9144 #49188093

Subgroups — C149×#9144 #49188093

Order 38144.

738 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2855×C149C211yesmaximal, characteristic
2C2×C4×C4⋊C4×C149C211yesmaximal, characteristic
3#1817×C149C211yesmaximal, characteristic
4C2×#328×C149C212yesmaximal
5#1294×C149C212yesmaximal
6C2×C22⋊Q8×C149C2211yescharacteristic
7C22×C4⋊C4×C149—21no—
8C22×C42×C149—21no—
9C22×C42×C149C2211yescharacteristic
10C2×C22⋊C8×C149C2212yes—
11#391×C149C412yescomplemented
12#389×C149C412yescomplemented
13#387×C149—22no—
14#385×C149—21no—
15#381×C149—21no—
16#380×C149C2211yescharacteristic
17C4×C4⋊C4×C149—24no—
18C2×#95×C149C2212yes—
19#336×C149—22no—
20#328×C149—24no—
21C22×Q8×C149C2×C411yescharacteristic
22C23×C4×C149—22no—
23C23×C4×C149D411yescharacteristic
24C23×C4×C149D411yescharacteristic
25C23×C4×C149C2311yescharacteristic
26C22×C8×C149—22no—
27C22⋊Q8×C149—22no—
28C22⋊Q8×C149—22no—
29C2×C4⋊C4×C149—24no—
30C2×C4⋊C4×C149—28no—
31C2×C4⋊C4×C149—22no—
32C2×C4⋊C4×C149—21no—
33C2×C4⋊C4×C149C2×C411yescharacteristic
34C2×C4⋊C4×C149C2×C412yes—
35C2×C22⋊C4×C149—21no—
36C2×C22⋊C4×C149—21no—
37C2×C42×C149—22no—
38C2×C42×C149—22no—
39C2×C42×C149—24no—
40C2×C42×C149—42no—
41C2×C42×C149—42no—
42C2×C42×C149C2×C412yes—
43C2×C42×C149D412yes—
44C22⋊C8×C149—22no—
45C22⋊C8×C149—22no—
46#95×C149—22no—
47#95×C149—22no—
48#95×C149—22no—
49#95×C149—22no—
50#95×C149—21no—
51#95×C149D414yes—
52C24×C149C2×D411yescharacteristic
53C2×Q8×C149—22no—
54C2×Q8×C149—42no—
55C22×C4×C149—21no—
56C22×C4×C149—21no—
57C22×C4×C149—21no—
58C22×C4×C149—21no—
59C22×C4×C149—21no—
60C22×C4×C149—21no—
61C22×C4×C149—24no—
62C22×C4×C149—28no—
63C22×C4×C149—24no—
64C22×C4×C149—22no—
65C22×C4×C149—21no—
66C22×C4×C149—21no—
67C22×C4×C149—42no—
68C22×C4×C149—44no—
69C22×C4×C149—42no—
70C22×C4×C149—42no—
71C22×C4×C149C22⋊C412yes—
72C22×C4×C149C22⋊C412yes—
73C22×C4×C149SD1612yes—
74C22×C4×C149Q1612yes—
75C22×C4×C149C22×C411yescharacteristic
76C22×C4×C149C2×D411yescharacteristic
77C22×C4×C149C2×D412yes—
78C22×C4×C149#4112yes—
79C2×C8×C149—44no—
80C2×C8×C149—42no—
81C4⋊C4×C149—216no—
82C4⋊C4×C149—22no—
83C4⋊C4×C149—42no—
84C4⋊C4×C149—44no—
85C4⋊C4×C149—42no—
86C22⋊C4×C149—41no—
87C22⋊C4×C149—41no—
88C22⋊C4×C149—41no—
89C22⋊C4×C149—41no—
90C42×C149—24no—
91C42×C149—24no—
92C42×C149—48no—
93C23×C149—22no—
94C23×C149—22no—
95C23×C149C2×C22⋊C411yescharacteristic
96C23×C149#12011yescharacteristic
97C23×C149#12311yescharacteristic
98C23×C149C2×SD1611yescharacteristic
99C23×C149C2×Q1611yescharacteristic
100C23×C149AGL(1,ℤ/8)11yescharacteristic
101C23×C149#13711yescharacteristic
102Q8×C149—82no—
103C2×C4×C149—24no—
104C2×C4×C149—24no—
105C2×C4×C149—22no—
106C2×C4×C149—22no—
107C2×C4×C149—22no—
108C2×C4×C149—22no—
109C2×C4×C149—22no—
110C2×C4×C149—22no—
111C2×C4×C149—22no—
112C2×C4×C149—22no—
113C2×C4×C149—22no—
114C2×C4×C149—22no—
115C2×C4×C149—28no—
116C2×C4×C149—42no—
117C2×C4×C149—42no—
118C2×C4×C149—44no—
119C2×C4×C149—48no—
120C2×C4×C149—48no—
121C2×C4×C149—44no—
122C2×C4×C149—41no—
123C2×C4×C149—41no—
124C2×C4×C149—42no—
125C2×C4×C149—42no—
126C2×C4×C149—42no—
127C2×C4×C149—42no—
128C2×C4×C149—42no—
129C2×C4×C149#10314yes—
130C2×C4×C149#10414yes—
131C2×C4×C149C4×D412yes—
132C2×C4×C149#12112yes—
133C8×C149—82no—
134C22×C149—21no—
135C22×C149—21no—
136C22×C149—21no—
137C22×C149—21no—
138C22×C149—22no—
139C22×C149—22no—
140C22×C149—22no—
141C22×C149—22no—
142C22×C149#38611yescharacteristic
143C22×C149#41012yes—
144C22×C149C2×#10311yescharacteristic
145C22×C149#41711yescharacteristic
146C22×C149C2×#10412yes—
147C22×C149#45011yescharacteristic
148C22×C149#45111yescharacteristic
149C22×C149#48311yescharacteristic
150C22×C149#48411yescharacteristic
151C4×C149—24no—
152C4×C149—24no—
153C4×C149—22no—
154C4×C149—22no—
155C4×C149—48no—
156C4×C149—81no—
157C4×C149—81no—
158C4×C149—82no—
159C2×C149—21no—
160C2×C149—21no—
161C2×C149—21no—
162C2×C149—21no—
163C2×C149#150312yes—
164C2×C149#150912yes—
165C2×C149#187211yescharacteristic
166C2×C149#189611yescharacteristic
167C2×C149#189911yescharacteristic
168#9144C14911yesmaximal, characteristic, direct product factor, Sylow
169C149#914411yescharacteristic, direct product factor, Sylow
170#2855C2×C14911yescharacteristic
171C2×C4×C4⋊C4C2×C14911yescharacteristic
172#1817C2×C14911yescharacteristic
173C2×#328C2×C14912yes—
174#1294C2×C14912yes—
175C2×C22⋊Q8C22×C14911yescharacteristic
176C22×C4⋊C4—21no—
177C22×C42—21no—
178C22×C42C22×C14911yescharacteristic
179C2×C22⋊C8C22×C14912yes—
180#391C4×C14912yescomplemented
181#389C4×C14912yescomplemented
182#387—22no—
183#385—21no—
184#381—21no—
185#380C22×C14911yescharacteristic
186C4×C4⋊C4—24no—
187C2×#95C22×C14912yes—
188#336—22no—
189#328—24no—
190C22×Q8C2×C4×C14911yescharacteristic
191C23×C4—22no—
192C23×C4D4×C14911yescharacteristic
193C23×C4D4×C14911yescharacteristic
194C23×C4C23×C14911yescharacteristic
195C22×C8—22no—
196C22⋊Q8—22no—
197C22⋊Q8—22no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—28no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4C2×C4×C14911yescharacteristic
203C2×C4⋊C4C2×C4×C14912yes—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C42—22no—
207C2×C42—22no—
208C2×C42—24no—
209C2×C42—42no—
210C2×C42—42no—
211C2×C42C2×C4×C14912yes—
212C2×C42D4×C14912yes—
213C22⋊C8—22no—
214C22⋊C8—22no—
215#95—22no—
216#95—22no—
217#95—22no—
218#95—22no—
219#95—21no—
220#95D4×C14914yes—
221C24C2×D4×C14911yescharacteristic
222C2×Q8—22no—
223C2×Q8—42no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—24no—
231C22×C4—28no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4—44no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4C22⋊C4×C14912yes—
241C22×C4C22⋊C4×C14912yes—
242C22×C4SD16×C14912yes—
243C22×C4Q16×C14912yes—
244C22×C4C22×C4×C14911yescharacteristic
245C22×C4C2×D4×C14911yescharacteristic
246C22×C4C2×D4×C14912yes—
247C22×C4#41×C14912yes—
248C2×C8—44no—
249C2×C8—42no—
250C4⋊C4—216no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—44no—
254C4⋊C4—42no—
255C22⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C42—24no—
260C42—24no—
261C42—48no—
262C23—22no—
263C23—22no—
264C23C2×C22⋊C4×C14911yescharacteristic
265C23#120×C14911yescharacteristic
266C23#123×C14911yescharacteristic
267C23C2×SD16×C14911yescharacteristic
268C23C2×Q16×C14911yescharacteristic
269C23AGL(1,ℤ/8)×C14911yescharacteristic
270C23#137×C14911yescharacteristic
271Q8—82no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—28no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—48no—
288C2×C4—48no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4#103×C14914yes—
299C2×C4#104×C14914yes—
300C2×C4C4×D4×C14912yes—
301C2×C4#121×C14912yes—
302C8—82no—
303C22—22no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22#386×C14911yescharacteristic
312C22#410×C14912yes—
313C22C2×#103×C14911yescharacteristic
314C22#417×C14911yescharacteristic
315C22C2×#104×C14912yes—
316C22#450×C14911yescharacteristic
317C22#451×C14911yescharacteristic
318C22#483×C14911yescharacteristic
319C22#484×C14911yescharacteristic
320C4—24no—
321C4—24no—
322C4—22no—
323C4—22no—
324C4—48no—
325C4—82no—
326C4—81no—
327C4—81no—
328C2—21no—
329C2—21no—
330C2—21no—
331C2—21no—
332C2#1503×C14912yes—
333C2#1509×C14912yes—
334C2#1872×C14911yescharacteristic
335C2#1896×C14911yescharacteristic
336C2#1899×C14911yescharacteristic
subgroupG/H
center, socleC23×C149C2×C22⋊C4
commutatorC22×C4C22×C4×C149
Frattini, cosocleC23×C4C23×C149
prime radicalC24×C149C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C149 ◁ C22×C42×C149 ◁ G

Complements

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

NH ≅ G/Ntype
11. #391×C149C4semidirect
12. #389×C149C4semidirect
168. #9144C149direct (N × H)
169. C149#9144direct (N × H)
180. #391C4×C149semidirect
181. #389C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2855×C1492
C2×C4×C4⋊C4×C1492
#1817×C1492
C2×#328×C1492
#1294×C1492
#9144149