Finite Group Databasebeta

← C149×#11694 #49190643

Subgroups — C149×#11694 #49190643

Order 38144.

468 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 126 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#2621×C149C211yesmaximal, characteristic
2#1740×C149C211yesmaximal, characteristic
3#1458×C149C211yesmaximal, characteristic
4#1344×C149C214yesmaximal
5C2×C4⋊Q8×C149C411yescharacteristic, complemented
6C2×C22⋊Q8×C149—21no—
7C2×#117×C149—21no—
8C2×#117×C149C2211yescharacteristic
9#431×C149—21no—
10#398×C149—21no—
11#398×C149C412yescomplemented
12#397×C149—21no—
13#397×C149C2212yes—
14#391×C149—21no—
15#382×C149C411yescharacteristic, complemented
16#342×C149—21no—
17#342×C149C2212yes—
18#324×C149—21no—
19#323×C149C2212yes—
20C22×Q8×C149—21no—
21C23×C4×C149D411yescharacteristic
22C4⋊Q8×C149—41no—
23C4⋊Q8×C149—41no—
24C22⋊Q8×C149—42no—
25C22⋊Q8×C149—42no—
26#117×C149—24no—
27#117×C149—41no—
28#117×C149—41no—
29#117×C149—42no—
30C2×C4⋊C4×C149—21no—
31C2×C4⋊C4×C149—22no—
32C2×C4⋊C4×C149—21no—
33C2×C4⋊C4×C149—41no—
34C2×C4⋊C4×C149C2×C412yes—
35C2×C4⋊C4×C149C2×C411yescharacteristic
36C2×C4⋊C4×C149D411yescharacteristic
37C2×C22⋊C4×C149—22no—
38C2×C22⋊C4×C149—22no—
39C2×C22⋊C4×C149D411yescharacteristic
40C2×C22⋊C4×C149C2311yescharacteristic
41C2×C42×C149—41no—
42C2×C42×C149C2×C411yescharacteristic
43C2×C42×C149D411yescharacteristic
44C4⋊C8×C149—41no—
45C22⋊C8×C149—22no—
46C4×C8×C149—41no—
47#95×C149—21no—
48#95×C149—22no—
49#95×C149—22no—
50#95×C149C2×C412yes—
51C24×C149C2×D411yescharacteristic
52C2×Q8×C149—41no—
53C2×Q8×C149—41no—
54C2×Q8×C149—42no—
55C2×Q8×C149—42no—
56C22×C4×C149—21no—
57C22×C4×C149—21no—
58C22×C4×C149—22no—
59C22×C4×C149—22no—
60C22×C4×C149—22no—
61C22×C4×C149—42no—
62C22×C4×C149C22⋊C411yescharacteristic
63C22×C4×C149C22⋊C411yescharacteristic
64C22×C4×C149C22⋊C411yescharacteristic
65C22×C4×C149C22⋊C411yescharacteristic
66C22×C4×C149D812yes—
67C22×C4×C149SD1612yes—
68C22×C4×C149C22×C411yescharacteristic
69C22×C4×C149C2×D411yescharacteristic
70C2×C8×C149—42no—
71C4⋊C4×C149—41no—
72C4⋊C4×C149—41no—
73C4⋊C4×C149—42no—
74C4⋊C4×C149—44no—
75C4⋊C4×C149—42no—
76C4⋊C4×C149—42no—
77C4⋊C4×C149—44no—
78C22⋊C4×C149—24no—
79C22⋊C4×C149—41no—
80C22⋊C4×C149—41no—
81C22⋊C4×C149—42no—
82C22⋊C4×C149—42no—
83C22⋊C4×C149—42no—
84C42×C149—21no—
85C42×C149—21no—
86C42×C149—21no—
87C42×C149—21no—
88C42×C149—44no—
89C23×C149—21no—
90C23×C149—21no—
91C23×C149—41no—
92C23×C149—41no—
93C23×C149C2×C22⋊C411yescharacteristic
94C23×C149C2×D811yescharacteristic
95C23×C149C2×SD1611yescharacteristic
96Q8×C149—82no—
97Q8×C149—82no—
98C2×C4×C149—21no—
99C2×C4×C149—21no—
100C2×C4×C149—22no—
101C2×C4×C149—22no—
102C2×C4×C149—22no—
103C2×C4×C149—22no—
104C2×C4×C149—21no—
105C2×C4×C149—21no—
106C2×C4×C149—21no—
107C2×C4×C149—21no—
108C2×C4×C149—41no—
109C2×C4×C149—41no—
110C2×C4×C149—41no—
111C2×C4×C149—41no—
112C2×C4×C149—44no—
113C2×C4×C149—42no—
114C2×C4×C149—42no—
115C2×C4×C149—42no—
116C2×C4×C149—42no—
117C2×C4×C149—42no—
118C2×C4×C149—42no—
119C2×C4×C149—82no—
120C2×C4×C149—82no—
121C2×C4×C149#9911yescharacteristic
122C2×C4×C149#9911yescharacteristic
123C2×C4×C149#10212yes—
124C2×C4×C149#10212yes—
125C2×C4×C149#10412yes—
126C8×C149—82no—
127C22×C149—21no—
128C22×C149—21no—
129C22×C149—21no—
130C22×C149—21no—
131C22×C149—41no—
132C22×C149—41no—
133C22×C149—41no—
134C22×C149—41no—
135C22×C149—81no—
136C22×C149C2×#9911yescharacteristic
137C22×C149C2×#10211yescharacteristic
138C22×C149C2×#10411yescharacteristic
139C4×C149—22no—
140C4×C149—41no—
141C4×C149—41no—
142C4×C149—41no—
143C4×C149—41no—
144C4×C149—82no—
145C4×C149—84no—
146C4×C149—82no—
147C4×C149#32712yes—
148C4×C149#32712yes—
149C2×C149—21no—
150C2×C149—21no—
151C2×C149—41no—
152C2×C149—41no—
153C2×C149C2×#32711yescharacteristic
154C2×C149#212311yescharacteristic
155C2×C149#212911yescharacteristic
156#11694C14911yesmaximal, characteristic, direct product factor, Sylow
157C149#1169411yescharacteristic, direct product factor, Sylow
158#2621C2×C14911yescharacteristic
159#1740C2×C14911yescharacteristic
160#1458C2×C14911yescharacteristic
161#1344C2×C14914yes—
162C2×C4⋊Q8C4×C14911yescharacteristic, complemented
163C2×C22⋊Q8—21no—
164C2×#117—21no—
165C2×#117C22×C14911yescharacteristic
166#431—21no—
167#398—21no—
168#398C4×C14912yescomplemented
169#397—21no—
170#397C22×C14912yes—
171#391—21no—
172#382C4×C14911yescharacteristic, complemented
173#342—21no—
174#342C22×C14912yes—
175#324—21no—
176#323C22×C14912yes—
177C22×Q8—21no—
178C23×C4D4×C14911yescharacteristic
179C4⋊Q8—41no—
180C4⋊Q8—41no—
181C22⋊Q8—42no—
182C22⋊Q8—42no—
183#117—24no—
184#117—41no—
185#117—41no—
186#117—42no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—41no—
191C2×C4⋊C4C2×C4×C14912yes—
192C2×C4⋊C4C2×C4×C14911yescharacteristic
193C2×C4⋊C4D4×C14911yescharacteristic
194C2×C22⋊C4—22no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4D4×C14911yescharacteristic
197C2×C22⋊C4C23×C14911yescharacteristic
198C2×C42—41no—
199C2×C42C2×C4×C14911yescharacteristic
200C2×C42D4×C14911yescharacteristic
201C4⋊C8—41no—
202C22⋊C8—22no—
203C4×C8—41no—
204#95—21no—
205#95—22no—
206#95—22no—
207#95C2×C4×C14912yes—
208C24C2×D4×C14911yescharacteristic
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8—42no—
212C2×Q8—42no—
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—42no—
219C22×C4C22⋊C4×C14911yescharacteristic
220C22×C4C22⋊C4×C14911yescharacteristic
221C22×C4C22⋊C4×C14911yescharacteristic
222C22×C4C22⋊C4×C14911yescharacteristic
223C22×C4D8×C14912yes—
224C22×C4SD16×C14912yes—
225C22×C4C22×C4×C14911yescharacteristic
226C22×C4C2×D4×C14911yescharacteristic
227C2×C8—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—44no—
233C4⋊C4—42no—
234C4⋊C4—44no—
235C22⋊C4—24no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—44no—
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23C2×C22⋊C4×C14911yescharacteristic
251C23C2×D8×C14911yescharacteristic
252C23C2×SD16×C14911yescharacteristic
253Q8—82no—
254Q8—82no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—44no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—42no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—82no—
277C2×C4—82no—
278C2×C4#99×C14911yescharacteristic
279C2×C4#99×C14911yescharacteristic
280C2×C4#102×C14912yes—
281C2×C4#102×C14912yes—
282C2×C4#104×C14912yes—
283C8—82no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22C2×#99×C14911yescharacteristic
294C22C2×#102×C14911yescharacteristic
295C22C2×#104×C14911yescharacteristic
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—82no—
302C4—84no—
303C4—82no—
304C4#327×C14912yes—
305C4#327×C14912yes—
306C2—21no—
307C2—21no—
308C2—41no—
309C2—41no—
310C2C2×#327×C14911yescharacteristic
311C2#2123×C14911yescharacteristic
312C2#2129×C14911yescharacteristic
subgroupG/H
center, socleC22×C149C2×#99
commutatorC22×C4C22×C4×C149
Frattini, cosocleC2×C22⋊C4C23×C149
prime radicalC24×C149C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C149 ◁ C22×C4×C149 ◁ C2×#117×C149 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×C4⋊Q8×C149C4semidirect
11. #398×C149C4semidirect
15. #382×C149C4semidirect
156. #11694C149direct (N × H)
157. C149#11694direct (N × H)
162. C2×C4⋊Q8C4×C149semidirect
168. #398C4×C149semidirect
172. #382C4×C149semidirect

Maximal subgroups

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

subgroupindex
#2621×C1492
#1740×C1492
#1458×C1492
#1344×C1492
#11694149