Finite Group Databasebeta

← C151×#11806 #50316731

Subgroups — C151×#11806 #50316731

Order 38656.

488 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 98 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#2619×C151C211yesmaximal, characteristic
2#1822×C151C211yesmaximal, characteristic, complemented
3#1464×C151C211yesmaximal, characteristic, complemented
4#1345×C151C214yesmaximal, complemented
5C2×#127×C151C411yescharacteristic
6C2×#121×C151—21no—
7C2×#117×C151C2211yescharacteristic
8#432×C151—21no—
9#407×C151—21no—
10#394×C151—21no—
11#394×C151C2212yes—
12#392×C151—21no—
13#392×C151C412yes—
14#390×C151—21no—
15#382×C151C411yescharacteristic
16#343×C151—21no—
17#343×C151C2212yes—
18#324×C151C2212yes—
19#323×C151—21no—
20C22×D4×C151—21no—
21C22×D4×C151—21no—
22C22×D4×C151—22no—
23C22×D4×C151C2×C412yes—
24C23×C4×C151D411yescharacteristic
25C2×M16×C151—22no—
26#127×C151—41no—
27#127×C151—41no—
28#121×C151—44no—
29#117×C151—41no—
30#117×C151—41no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151D411yescharacteristic
33C2×C4⋊C4×C151C2311yescharacteristic
34C2×C22⋊C4×C151—22no—
35C2×C22⋊C4×C151—22no—
36C2×C22⋊C4×C151—22no—
37C2×C22⋊C4×C151C2×C411yescharacteristic
38C2×C22⋊C4×C151D411yescharacteristic
39C2×C42×C151C2×C411yescharacteristic
40C2×C42×C151D411yescharacteristic
41C4⋊C8×C151—41no—
42C22⋊C8×C151—22no—
43C22⋊C8×C151—41no—
44C22⋊C8×C151—41no—
45#97×C151—41no—
46#95×C151—21no—
47#95×C151C2×C412yes—
48C24×C151—22no—
49C24×C151C22⋊C411yescharacteristic
50C2×D4×C151—42no—
51C2×D4×C151—42no—
52C2×D4×C151—42no—
53C2×D4×C151—42no—
54C2×D4×C151—44no—
55C2×D4×C151—41no—
56C2×D4×C151—41no—
57C2×D4×C151—82no—
58C2×D4×C151—82no—
59C2×D4×C151—82no—
60C2×D4×C151—82no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—22no—
64C22×C4×C151—22no—
65C22×C4×C151—41no—
66C22×C4×C151C22⋊C411yescharacteristic
67C22×C4×C151C22⋊C411yescharacteristic
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22×C411yescharacteristic
70C22×C4×C151C2×D411yescharacteristic
71C22×C4×C151C2×D411yescharacteristic
72M16×C151—42no—
73M16×C151—42no—
74C2×C8×C151—42no—
75C2×C8×C151—42no—
76C4⋊C4×C151—41no—
77C4⋊C4×C151—41no—
78C4⋊C4×C151—42no—
79C22⋊C4×C151—41no—
80C22⋊C4×C151—41no—
81C22⋊C4×C151—44no—
82C22⋊C4×C151—82no—
83C22⋊C4×C151—82no—
84C42×C151—21no—
85C42×C151—21no—
86C42×C151—21no—
87C42×C151—21no—
88C23×C151—21no—
89C23×C151—21no—
90C23×C151—21no—
91C23×C151—41no—
92C23×C151—41no—
93C23×C151—42no—
94C23×C151—42no—
95C23×C151—42no—
96C23×C151—42no—
97C23×C151—42no—
98C23×C151—42no—
99C23×C151—42no—
100C23×C151C2×C22⋊C411yescharacteristic
101D4×C151—82no—
102D4×C151—82no—
103D4×C151—84no—
104D4×C151—84no—
105D4×C151—88no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—21no—
113C2×C4×C151—21no—
114C2×C4×C151—42no—
115C2×C4×C151—42no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—41no—
120C2×C4×C151—42no—
121C2×C4×C151—42no—
122C2×C4×C151—42no—
123C2×C4×C151#9911yescharacteristic
124C2×C4×C151#9911yescharacteristic
125C2×C4×C151AGL(1,ℤ/8)12yes—
126C8×C151—82no—
127C8×C151—82no—
128C22×C151—21no—
129C22×C151—21no—
130C22×C151—42no—
131C22×C151—41no—
132C22×C151—41no—
133C22×C151—41no—
134C22×C151—81no—
135C22×C151—82no—
136C22×C151—82no—
137C22×C151—82no—
138C22×C151—82no—
139C22×C151—82no—
140C22×C151—82no—
141C22×C151—82no—
142C22×C151C2×#9911yescharacteristic
143C22×C151#41811yescharacteristic
144C22×C151#42111yescharacteristic
145C4×C151—22no—
146C4×C151—21no—
147C4×C151—21no—
148C4×C151—41no—
149C4×C151—41no—
150C4×C151—41no—
151C4×C151—41no—
152C4×C151—82no—
153C2×C151—21no—
154C2×C151—21no—
155C2×C151—81no—
156C2×C151—162no—
157C2×C151#151011yescharacteristic
158C2×C151#212211yescharacteristic
159C2×C151#213411yescharacteristic
160#11806C15111yesmaximal, characteristic, direct product factor, Sylow
161C151#1180611yescharacteristic, direct product factor, Sylow
162#2619C2×C15111yescharacteristic
163#1822C2×C15111yescharacteristic, complemented
164#1464C2×C15111yescharacteristic, complemented
165#1345C2×C15114yescomplemented
166C2×#127C4×C15111yescharacteristic
167C2×#121—21no—
168C2×#117C22×C15111yescharacteristic
169#432—21no—
170#407—21no—
171#394—21no—
172#394C22×C15112yes—
173#392—21no—
174#392C4×C15112yes—
175#390—21no—
176#382C4×C15111yescharacteristic
177#343—21no—
178#343C22×C15112yes—
179#324C22×C15112yes—
180#323—21no—
181C22×D4—22no—
182C22×D4—21no—
183C22×D4—21no—
184C22×D4C2×C4×C15112yes—
185C23×C4D4×C15111yescharacteristic
186C2×M16—22no—
187#127—41no—
188#127—41no—
189#121—44no—
190#117—41no—
191#117—41no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4D4×C15111yescharacteristic
194C2×C4⋊C4C23×C15111yescharacteristic
195C2×C22⋊C4—22no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4C2×C4×C15111yescharacteristic
199C2×C22⋊C4D4×C15111yescharacteristic
200C2×C42C2×C4×C15111yescharacteristic
201C2×C42D4×C15111yescharacteristic
202C4⋊C8—41no—
203C22⋊C8—22no—
204C22⋊C8—41no—
205C22⋊C8—41no—
206#97—41no—
207#95—21no—
208#95C2×C4×C15112yes—
209C24—22no—
210C24C22⋊C4×C15111yescharacteristic
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—44no—
216C2×D4—41no—
217C2×D4—41no—
218C2×D4—82no—
219C2×D4—82no—
220C2×D4—82no—
221C2×D4—82no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4C22⋊C4×C15111yescharacteristic
228C22×C4C22⋊C4×C15111yescharacteristic
229C22×C4C22⋊C4×C15111yescharacteristic
230C22×C4C22×C4×C15111yescharacteristic
231C22×C4C2×D4×C15111yescharacteristic
232C22×C4C2×D4×C15111yescharacteristic
233M16—42no—
234M16—42no—
235C2×C8—42no—
236C2×C8—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—42no—
240C22⋊C4—41no—
241C22⋊C4—41no—
242C22⋊C4—44no—
243C22⋊C4—82no—
244C22⋊C4—82no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C23—21no—
250C23—21no—
251C23—21no—
252C23—41no—
253C23—41no—
254C23—42no—
255C23—42no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—42no—
261C23C2×C22⋊C4×C15111yescharacteristic
262D4—82no—
263D4—82no—
264D4—84no—
265D4—84no—
266D4—88no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4#99×C15111yescharacteristic
285C2×C4#99×C15111yescharacteristic
286C2×C4AGL(1,ℤ/8)×C15112yes—
287C8—82no—
288C8—82no—
289C22—21no—
290C22—21no—
291C22—42no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22—82no—
297C22—82no—
298C22—82no—
299C22—82no—
300C22—82no—
301C22—82no—
302C22—82no—
303C22C2×#99×C15111yescharacteristic
304C22#418×C15111yescharacteristic
305C22#421×C15111yescharacteristic
306C4—22no—
307C4—21no—
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—82no—
314C2—21no—
315C2—21no—
316C2—81no—
317C2—162no—
318C2#1510×C15111yescharacteristic
319C2#2122×C15111yescharacteristic
320C2#2134×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radical#2619×C151C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1822×C151C2semidirect
3. #1464×C151C2semidirect
4. #1345×C151C2semidirect
160. #11806C151direct (N × H)
161. C151#11806direct (N × H)
163. #1822C2×C151semidirect
164. #1464C2×C151semidirect
165. #1345C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2619×C1512
#1822×C1512
#1464×C1512
#1345×C1512
#11806151