Finite Group Databasebeta

← C151×#11788 #50316713

Subgroups — C151×#11788 #50316713

Order 38656.

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

normal subgroups only

This group has 516 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#2542×C151C211yesmaximal, characteristic
2C4×#99×C151C211yesmaximal, characteristic
3#1465×C151C211yesmaximal, characteristic
4#1352×C151C214yesmaximal, complemented
5C2×C4⋊Q8×C151C411yescharacteristic, complemented
6C2×C22⋊Q8×C151—21no—
7C2×C22⋊Q8×C151—21no—
8C2×C4×D4×C151C2211yescharacteristic
9C2×#99×C151—21no—
10#407×C151—21no—
11#399×C151C412yescomplemented
12#399×C151C2212yes—
13#390×C151—21no—
14#384×C151—21no—
15C4×C4⋊C4×C151C411yescharacteristic, complemented
16C4×C22⋊C4×C151—21no—
17#342×C151C2212yes—
18#324×C151—21no—
19#323×C151C2212yes—
20C22×Q8×C151—21no—
21C22×D4×C151D411yescharacteristic
22C23×C4×C151D411yescharacteristic
23C23×C4×C151D411yescharacteristic
24C2×M16×C151—41no—
25C4⋊Q8×C151—41no—
26C4⋊Q8×C151—41no—
27C22⋊Q8×C151—44no—
28C22⋊Q8×C151—44no—
29C4×D4×C151—41no—
30C4×D4×C151—41no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151—22no—
34C2×C4⋊C4×C151—22no—
35C2×C4⋊C4×C151C2×C412yes—
36C2×C4⋊C4×C151D411yescharacteristic
37C2×C22⋊C4×C151—22no—
38C2×C22⋊C4×C151—22no—
39C2×C22⋊C4×C151—22no—
40C2×C22⋊C4×C151C2×C411yescharacteristic
41C2×C22⋊C4×C151C2311yescharacteristic
42C2×C42×C151—21no—
43C2×C42×C151—41no—
44C2×C42×C151C2×C411yescharacteristic
45#99×C151—24no—
46C22⋊C8×C151—22no—
47C22⋊C8×C151—41no—
48#95×C151—41no—
49#95×C151C2×C412yes—
50C24×C151C22⋊C411yescharacteristic
51C24×C151C2×D411yescharacteristic
52C2×Q8×C151—42no—
53C2×Q8×C151—42no—
54C2×Q8×C151—41no—
55C2×Q8×C151—41no—
56C2×D4×C151—22no—
57C2×D4×C151—22no—
58C2×D4×C151—41no—
59C22×C4×C151—22no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151—22no—
65C22×C4×C151—42no—
66C22×C4×C151—42no—
67C22×C4×C151—42no—
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151C22⋊C411yescharacteristic
71C22×C4×C151C22×C411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73M16×C151—82no—
74C2×C8×C151—42no—
75C4⋊C4×C151—24no—
76C4⋊C4×C151—41no—
77C4⋊C4×C151—42no—
78C4⋊C4×C151—44no—
79C4⋊C4×C151—44no—
80C4⋊C4×C151—42no—
81C22⋊C4×C151—24no—
82C22⋊C4×C151—41no—
83C22⋊C4×C151—41no—
84C22⋊C4×C151—44no—
85C22⋊C4×C151—44no—
86C22⋊C4×C151—42no—
87C42×C151—21no—
88C42×C151—21no—
89C42×C151—42no—
90C42×C151—82no—
91C23×C151—21no—
92C23×C151—21no—
93C23×C151—21no—
94C23×C151—21no—
95C23×C151—21no—
96C23×C151—41no—
97C23×C151—41no—
98C23×C151—41no—
99C23×C151—41no—
100C23×C151C2×C22⋊C411yescharacteristic
101C23×C151#13712yes—
102Q8×C151—82no—
103Q8×C151—82no—
104D4×C151—44no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—22no—
108C2×C4×C151—24no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—42no—
113C2×C4×C151—42no—
114C2×C4×C151—42no—
115C2×C4×C151—42no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151—41no—
119C2×C4×C151—42no—
120C2×C4×C151—42no—
121C2×C4×C151—44no—
122C2×C4×C151—42no—
123C2×C4×C151—81no—
124C2×C4×C151—81no—
125C2×C4×C151—82no—
126C2×C4×C151—82no—
127C2×C4×C151#9911yescharacteristic
128C2×C4×C151#9911yescharacteristic
129C2×C4×C151#10412yes—
130C8×C151—82no—
131C22×C151—21no—
132C22×C151—21no—
133C22×C151—22no—
134C22×C151—42no—
135C22×C151—42no—
136C22×C151—41no—
137C22×C151—41no—
138C22×C151—41no—
139C22×C151—41no—
140C22×C151—41no—
141C22×C151—81no—
142C22×C151—81no—
143C22×C151C2×#9911yescharacteristic
144C22×C151#41911yescharacteristic
145C22×C151C2×#10411yescharacteristic
146C4×C151—21no—
147C4×C151—22no—
148C4×C151—44no—
149C4×C151—41no—
150C4×C151—41no—
151C4×C151—41no—
152C4×C151—84no—
153C4×C151—82no—
154C4×C151#35312yes—
155C2×C151—21no—
156C2×C151—21no—
157C2×C151—42no—
158C2×C151—81no—
159C2×C151#150811yescharacteristic
160C2×C151#212311yescharacteristic
161C2×C151C2×#35311yescharacteristic
162#11788C15111yesmaximal, characteristic, direct product factor, Sylow
163C151#1178811yescharacteristic, direct product factor, Sylow
164#2542C2×C15111yescharacteristic
165C4×#99C2×C15111yescharacteristic
166#1465C2×C15111yescharacteristic
167#1352C2×C15114yescomplemented
168C2×C4⋊Q8C4×C15111yescharacteristic, complemented
169C2×C22⋊Q8—21no—
170C2×C22⋊Q8—21no—
171C2×C4×D4C22×C15111yescharacteristic
172C2×#99—21no—
173#407—21no—
174#399C4×C15112yescomplemented
175#399C22×C15112yes—
176#390—21no—
177#384—21no—
178C4×C4⋊C4C4×C15111yescharacteristic, complemented
179C4×C22⋊C4—21no—
180#342C22×C15112yes—
181#324—21no—
182#323C22×C15112yes—
183C22×Q8—21no—
184C22×D4D4×C15111yescharacteristic
185C23×C4D4×C15111yescharacteristic
186C23×C4D4×C15111yescharacteristic
187C2×M16—41no—
188C4⋊Q8—41no—
189C4⋊Q8—41no—
190C22⋊Q8—44no—
191C22⋊Q8—44no—
192C4×D4—41no—
193C4×D4—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4C2×C4×C15112yes—
199C2×C4⋊C4D4×C15111yescharacteristic
200C2×C22⋊C4—22no—
201C2×C22⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4C2×C4×C15111yescharacteristic
204C2×C22⋊C4C23×C15111yescharacteristic
205C2×C42—21no—
206C2×C42—41no—
207C2×C42C2×C4×C15111yescharacteristic
208#99—24no—
209C22⋊C8—22no—
210C22⋊C8—41no—
211#95—41no—
212#95C2×C4×C15112yes—
213C24C22⋊C4×C15111yescharacteristic
214C24C2×D4×C15111yescharacteristic
215C2×Q8—42no—
216C2×Q8—42no—
217C2×Q8—41no—
218C2×Q8—41no—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—41no—
222C22×C4—22no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4C22⋊C4×C15111yescharacteristic
232C22×C4C22⋊C4×C15111yescharacteristic
233C22×C4C22⋊C4×C15111yescharacteristic
234C22×C4C22×C4×C15111yescharacteristic
235C22×C4C2×D4×C15111yescharacteristic
236M16—82no—
237C2×C8—42no—
238C4⋊C4—24no—
239C4⋊C4—41no—
240C4⋊C4—42no—
241C4⋊C4—44no—
242C4⋊C4—44no—
243C4⋊C4—42no—
244C22⋊C4—24no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C22⋊C4—44no—
248C22⋊C4—44no—
249C22⋊C4—42no—
250C42—21no—
251C42—21no—
252C42—42no—
253C42—82no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23C2×C22⋊C4×C15111yescharacteristic
264C23#137×C15112yes—
265Q8—82no—
266Q8—82no—
267D4—44no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—24no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—44no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4#99×C15111yescharacteristic
291C2×C4#99×C15111yescharacteristic
292C2×C4#104×C15112yes—
293C8—82no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—81no—
305C22—81no—
306C22C2×#99×C15111yescharacteristic
307C22#419×C15111yescharacteristic
308C22C2×#104×C15111yescharacteristic
309C4—21no—
310C4—22no—
311C4—44no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—84no—
316C4—82no—
317C4#353×C15112yes—
318C2—21no—
319C2—21no—
320C2—42no—
321C2—81no—
322C2#1508×C15111yescharacteristic
323C2#2123×C15111yescharacteristic
324C2C2×#353×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C22⋊C4C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1352×C151C2semidirect
5. C2×C4⋊Q8×C151C4semidirect
11. #399×C151C4semidirect
15. C4×C4⋊C4×C151C4semidirect
162. #11788C151direct (N × H)
163. C151#11788direct (N × H)
167. #1352C2×C151semidirect
168. C2×C4⋊Q8C4×C151semidirect
174. #399C4×C151semidirect
178. C4×C4⋊C4C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2542×C1512
C4×#99×C1512
#1465×C1512
#1352×C1512
#11788151