Finite Group Databasebeta

← C151×#10514 #50315439

Subgroups — C151×#10514 #50315439

Order 38656.

386 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 94 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#3246×C151C211yesmaximal, characteristic
2#1843×C151C211yesmaximal, characteristic, complemented
3#1552×C151C211yesmaximal, characteristic, complemented
4#1551×C151C211yesmaximal, characteristic
5#1506×C151C211yesmaximal, characteristic, complemented
6#1505×C151C211yesmaximal, characteristic
7#1290×C151C211yesmaximal, characteristic, complemented
8#533×C151C2211yescharacteristic
9#532×C151C2211yescharacteristic
10#476×C151—21no—
11#475×C151—21no—
12#465×C151—22no—
13#461×C151—21no—
14#460×C151—21no—
15#432×C151C2211yescharacteristic
16#432×C151C2211yescharacteristic
17C2×C4⋊C8×C151—22no—
18C2×C4⋊C8×C151C2211yescharacteristic
19C2×C4⋊C8×C151C2211yescharacteristic
20#376×C151C2211yescharacteristic
21#333×C151—21no—
22#332×C151—21no—
23#332×C151—21no—
24#331×C151—21no—
25#328×C151—22no—
26#327×C151—22no—
27C2×#41×C151—21no—
28C2×SD16×C151—22no—
29C22×C8×C151—21no—
30C22×C8×C151D412yes—
31C4⋊Q8×C151D411yescharacteristic
32C4⋊Q8×C151D411yescharacteristic
33C4⋊Q8×C151D411yescharacteristic
34#127×C151D411yescharacteristic
35#125×C151—21no—
36#124×C151—21no—
37C22⋊Q8×C151—21no—
38C22⋊Q8×C151—21no—
39#121×C151—21no—
40#121×C151—21no—
41C4×Q8×C151—21no—
42C4×Q8×C151—21no—
43C4×D4×C151—21no—
44C4×D4×C151—21no—
45#117×C151—21no—
46C2×C42×C151—21no—
47C2×C42×C151C2311yescharacteristic
48#106×C151—22no—
49C4⋊C8×C151—21no—
50C4⋊C8×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151—21no—
55C4⋊C8×C151—44no—
56#103×C151—22no—
57#102×C151—22no—
58C22⋊C8×C151—21no—
59C22⋊C8×C151—21no—
60#97×C151—21no—
61#97×C151—21no—
62#95×C151—21no—
63#95×C151D412yes—
64#41×C151—82no—
65C2×Q8×C151—21no—
66C2×Q8×C151—21no—
67C2×Q8×C151—21no—
68C2×D4×C151—21no—
69C2×D4×C151—21no—
70C2×D4×C151—21no—
71C2×D4×C151—41no—
72C22×C4×C151—22no—
73C22×C4×C151—41no—
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151C2×D411yescharacteristic
76C22×C4×C151#4111yescharacteristic
77SD16×C151—82no—
78C2×C8×C151—22no—
79C2×C8×C151—42no—
80C2×C8×C151—42no—
81C2×C8×C151—41no—
82C2×C8×C151—41no—
83C2×C8×C151—41no—
84C4⋊C4×C151—21no—
85C4⋊C4×C151—21no—
86C4⋊C4×C151—21no—
87C4⋊C4×C151—21no—
88C4⋊C4×C151—21no—
89C4⋊C4×C151—21no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—41no—
92C22⋊C4×C151—41no—
93C22⋊C4×C151—41no—
94C22⋊C4×C151—41no—
95C42×C151—22no—
96C42×C151—22no—
97C42×C151—41no—
98C42×C151C2×D411yescharacteristic
99C42×C151C2×D411yescharacteristic
100C42×C151#4111yescharacteristic
101C42×C151#4111yescharacteristic
102C23×C151—41no—
103C23×C151#12111yescharacteristic
104Q8×C151—41no—
105Q8×C151—41no—
106Q8×C151—81no—
107Q8×C151—81no—
108D4×C151—41no—
109D4×C151—41no—
110D4×C151—81no—
111D4×C151—81no—
112D4×C151—82no—
113C2×C4×C151—22no—
114C2×C4×C151—21no—
115C2×C4×C151—21no—
116C2×C4×C151—24no—
117C2×C4×C151—41no—
118C2×C4×C151—42no—
119C2×C4×C151—42no—
120C2×C4×C151—41no—
121C2×C4×C151—41no—
122C2×C4×C151—41no—
123C2×C4×C151—82no—
124C2×C4×C151#12011yescharacteristic
125C2×C4×C151#12111yescharacteristic
126C2×C4×C151#12111yescharacteristic
127C2×C4×C151#12311yescharacteristic
128C2×C4×C151#12311yescharacteristic
129C2×C4×C151#12411yescharacteristic
130C8×C151—42no—
131C8×C151—81no—
132C8×C151—81no—
133C8×C151—81no—
134C22×C151—21no—
135C22×C151—21no—
136C22×C151—81no—
137C22×C151—81no—
138C22×C151—81no—
139C22×C151#39411yescharacteristic
140C22×C151#47112yes—
141C4×C151—21no—
142C4×C151—21no—
143C4×C151—21no—
144C4×C151—21no—
145C4×C151—21no—
146C4×C151—44no—
147C4×C151—81no—
148C4×C151—81no—
149C4×C151—81no—
150C4×C151#45311yescharacteristic
151C4×C151#45611yescharacteristic
152C2×C151—22no—
153C2×C151—161no—
154C2×C151#203911yescharacteristic
155C2×C151#204611yescharacteristic
156C2×C151#205311yescharacteristic
157#10514C15111yesmaximal, characteristic, direct product factor, Sylow
158C151#1051411yescharacteristic, direct product factor, Sylow
159#3246C2×C15111yescharacteristic
160#1843C2×C15111yescharacteristic, complemented
161#1552C2×C15111yescharacteristic, complemented
162#1551C2×C15111yescharacteristic
163#1506C2×C15111yescharacteristic, complemented
164#1505C2×C15111yescharacteristic
165#1290C2×C15111yescharacteristic, complemented
166#533C22×C15111yescharacteristic
167#532C22×C15111yescharacteristic
168#476—21no—
169#475—21no—
170#465—22no—
171#461—21no—
172#460—21no—
173#432C22×C15111yescharacteristic
174#432C22×C15111yescharacteristic
175C2×C4⋊C8—22no—
176C2×C4⋊C8C22×C15111yescharacteristic
177C2×C4⋊C8C22×C15111yescharacteristic
178#376C22×C15111yescharacteristic
179#333—21no—
180#332—21no—
181#332—21no—
182#331—21no—
183#328—22no—
184#327—22no—
185C2×#41—21no—
186C2×SD16—22no—
187C22×C8—21no—
188C22×C8D4×C15112yes—
189C4⋊Q8D4×C15111yescharacteristic
190C4⋊Q8D4×C15111yescharacteristic
191C4⋊Q8D4×C15111yescharacteristic
192#127D4×C15111yescharacteristic
193#125—21no—
194#124—21no—
195C22⋊Q8—21no—
196C22⋊Q8—21no—
197#121—21no—
198#121—21no—
199C4×Q8—21no—
200C4×Q8—21no—
201C4×D4—21no—
202C4×D4—21no—
203#117—21no—
204C2×C42—21no—
205C2×C42C23×C15111yescharacteristic
206#106—22no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—44no—
214#103—22no—
215#102—22no—
216C22⋊C8—21no—
217C22⋊C8—21no—
218#97—21no—
219#97—21no—
220#95—21no—
221#95D4×C15112yes—
222#41—82no—
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—21no—
226C2×D4—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—41no—
230C22×C4—22no—
231C22×C4—41no—
232C22×C4C2×D4×C15111yescharacteristic
233C22×C4C2×D4×C15111yescharacteristic
234C22×C4#41×C15111yescharacteristic
235SD16—82no—
236C2×C8—22no—
237C2×C8—42no—
238C2×C8—42no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C42—22no—
254C42—22no—
255C42—41no—
256C42C2×D4×C15111yescharacteristic
257C42C2×D4×C15111yescharacteristic
258C42#41×C15111yescharacteristic
259C42#41×C15111yescharacteristic
260C23—41no—
261C23#121×C15111yescharacteristic
262Q8—41no—
263Q8—41no—
264Q8—81no—
265Q8—81no—
266D4—41no—
267D4—41no—
268D4—81no—
269D4—81no—
270D4—82no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—24no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—82no—
282C2×C4#120×C15111yescharacteristic
283C2×C4#121×C15111yescharacteristic
284C2×C4#121×C15111yescharacteristic
285C2×C4#123×C15111yescharacteristic
286C2×C4#123×C15111yescharacteristic
287C2×C4#124×C15111yescharacteristic
288C8—42no—
289C8—81no—
290C8—81no—
291C8—81no—
292C22—21no—
293C22—21no—
294C22—81no—
295C22—81no—
296C22—81no—
297C22#394×C15111yescharacteristic
298C22#471×C15112yes—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—44no—
305C4—81no—
306C4—81no—
307C4—81no—
308C4#453×C15111yescharacteristic
309C4#456×C15111yescharacteristic
310C2—22no—
311C2—161no—
312C2#2039×C15111yescharacteristic
313C2#2046×C15111yescharacteristic
314C2#2053×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#394
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#532×C151C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1843×C151C2semidirect
3. #1552×C151C2semidirect
5. #1506×C151C2semidirect
7. #1290×C151C2semidirect
157. #10514C151direct (N × H)
158. C151#10514direct (N × H)
160. #1843C2×C151semidirect
161. #1552C2×C151semidirect
163. #1506C2×C151semidirect
165. #1290C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3246×C1512
#1843×C1512
#1552×C1512
#1551×C1512
#1506×C1512
#1505×C1512
#1290×C1512
#10514151