Finite Group Databasebeta

← C151×#10489 #50315414

Subgroups — C151×#10489 #50315414

Order 38656.

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

normal subgroups only

This group has 394 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#3206×C151C211yesmaximal, characteristic
2#1966×C151C211yesmaximal, characteristic, complemented
3#1574×C151C211yesmaximal, characteristic, complemented
4#1560×C151C211yesmaximal, characteristic
5#1548×C151C211yesmaximal, characteristic, complemented
6#1484×C151C211yesmaximal, characteristic
7#1299×C151C211yesmaximal, characteristic, complemented
8#532×C151C2211yescharacteristic
9C2×C4⋊Q8×C151C2211yescharacteristic
10#492×C151—21no—
11#487×C151—21no—
12#461×C151—21no—
13#461×C151—21no—
14#448×C151—22no—
15#431×C151C2211yescharacteristic
16#431×C151C2211yescharacteristic
17#423×C151C2211yescharacteristic
18#423×C151C2211yescharacteristic
19C2×#101×C151—22no—
20C4×M16×C151C2211yescharacteristic
21#335×C151—21no—
22#334×C151—21no—
23#333×C151—21no—
24#333×C151—22no—
25#331×C151—21no—
26D4⋊C8×C151—22no—
27C2×#41×C151—21no—
28C22×Q8×C151D412yes—
29C2×SD16×C151—22no—
30C2×SD16×C151—22no—
31C2×M16×C151—21no—
32C2×M16×C151—21no—
33C2×M16×C151—21no—
34C4⋊Q8×C151—21no—
35C4⋊Q8×C151—21no—
36C4⋊Q8×C151—21no—
37C4⋊Q8×C151—21no—
38C4⋊Q8×C151D411yescharacteristic
39#127×C151D411yescharacteristic
40#124×C151—21no—
41#121×C151—21no—
42#121×C151—21no—
43C4×D4×C151—21no—
44C4×D4×C151—21no—
45C2×C4⋊C4×C151—21no—
46C2×C4⋊C4×C151—21no—
47C2×C42×C151C2311yescharacteristic
48C4⋊C8×C151—21no—
49C4⋊C8×C151—21no—
50C4⋊C8×C151—21no—
51C4⋊C8×C151—21no—
52C4⋊C8×C151D411yescharacteristic
53C4⋊C8×C151D411yescharacteristic
54C4⋊C8×C151D412yes—
55#103×C151—22no—
56#103×C151—22no—
57#101×C151—44no—
58C22⋊C8×C151—21no—
59C22⋊C8×C151—21no—
60#97×C151—21no—
61C4×C8×C151—21no—
62C4×C8×C151—21no—
63C4×C8×C151—21no—
64#41×C151—82no—
65C2×Q8×C151—22no—
66C2×Q8×C151—22no—
67C2×Q8×C151—21no—
68C2×Q8×C151—42no—
69C2×Q8×C151—42no—
70C2×D4×C151—21no—
71C2×D4×C151—21no—
72C2×D4×C151—21no—
73C2×D4×C151—41no—
74C22×C4×C151—22no—
75C22×C4×C151—41no—
76C22×C4×C151C2×D411yescharacteristic
77C22×C4×C151#4111yescharacteristic
78C22×C4×C151#4111yescharacteristic
79SD16×C151—82no—
80SD16×C151—82no—
81M16×C151—22no—
82M16×C151—41no—
83M16×C151—42no—
84M16×C151—81no—
85C2×C8×C151—21no—
86C2×C8×C151—21no—
87C2×C8×C151—22no—
88C2×C8×C151—41no—
89C2×C8×C151—41no—
90C2×C8×C151—41no—
91C4⋊C4×C151—21no—
92C4⋊C4×C151—21no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—41no—
95C4⋊C4×C151—41no—
96C4⋊C4×C151—41no—
97C22⋊C4×C151—41no—
98C22⋊C4×C151—41no—
99C42×C151C2×D411yescharacteristic
100C42×C151C2×D411yescharacteristic
101C42×C151C2×D411yescharacteristic
102C42×C151#4111yescharacteristic
103C23×C151—41no—
104C23×C151#12311yescharacteristic
105Q8×C151—42no—
106Q8×C151—42no—
107Q8×C151—82no—
108Q8×C151—81no—
109D4×C151—41no—
110D4×C151—41no—
111D4×C151—41no—
112D4×C151—41no—
113D4×C151—81no—
114D4×C151—82no—
115C2×C4×C151—21no—
116C2×C4×C151—21no—
117C2×C4×C151—22no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—44no—
121C2×C4×C151—42no—
122C2×C4×C151—41no—
123C2×C4×C151—82no—
124C2×C4×C151#12011yescharacteristic
125C2×C4×C151#12111yescharacteristic
126C2×C4×C151#12111yescharacteristic
127C2×C4×C151#12111yescharacteristic
128C2×C4×C151#12311yescharacteristic
129C2×C4×C151#12411yescharacteristic
130C8×C151—42no—
131C8×C151—41no—
132C8×C151—41no—
133C8×C151—42no—
134C8×C151—81no—
135C8×C151—81no—
136C22×C151—21no—
137C22×C151—21no—
138C22×C151—21no—
139C22×C151—81no—
140C22×C151—81no—
141C22×C151—81no—
142C22×C151#39411yescharacteristic
143C4×C151—21no—
144C4×C151—21no—
145C4×C151—21no—
146C4×C151—82no—
147C4×C151—81no—
148C4×C151#45311yescharacteristic
149C4×C151#45511yescharacteristic
150C4×C151#47111yescharacteristic
151C4×C151#47112yes—
152C4×C151#47311yescharacteristic
153C2×C151—41no—
154C2×C151—161no—
155C2×C151#203711yescharacteristic
156C2×C151#204611yescharacteristic
157C2×C151#205211yescharacteristic
158#10489C15111yesmaximal, characteristic, direct product factor, Sylow
159C151#1048911yescharacteristic, direct product factor, Sylow
160#3206C2×C15111yescharacteristic
161#1966C2×C15111yescharacteristic, complemented
162#1574C2×C15111yescharacteristic, complemented
163#1560C2×C15111yescharacteristic
164#1548C2×C15111yescharacteristic, complemented
165#1484C2×C15111yescharacteristic
166#1299C2×C15111yescharacteristic, complemented
167#532C22×C15111yescharacteristic
168C2×C4⋊Q8C22×C15111yescharacteristic
169#492—21no—
170#487—21no—
171#461—21no—
172#461—21no—
173#448—22no—
174#431C22×C15111yescharacteristic
175#431C22×C15111yescharacteristic
176#423C22×C15111yescharacteristic
177#423C22×C15111yescharacteristic
178C2×#101—22no—
179C4×M16C22×C15111yescharacteristic
180#335—21no—
181#334—21no—
182#333—21no—
183#333—22no—
184#331—21no—
185D4⋊C8—22no—
186C2×#41—21no—
187C22×Q8D4×C15112yes—
188C2×SD16—22no—
189C2×SD16—22no—
190C2×M16—21no—
191C2×M16—21no—
192C2×M16—21no—
193C4⋊Q8—21no—
194C4⋊Q8—21no—
195C4⋊Q8—21no—
196C4⋊Q8—21no—
197C4⋊Q8D4×C15111yescharacteristic
198#127D4×C15111yescharacteristic
199#124—21no—
200#121—21no—
201#121—21no—
202C4×D4—21no—
203C4×D4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C42C23×C15111yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8D4×C15112yes—
212C4⋊C8D4×C15111yescharacteristic
213C4⋊C8D4×C15111yescharacteristic
214#103—22no—
215#103—22no—
216#101—44no—
217C22⋊C8—21no—
218C22⋊C8—21no—
219#97—21no—
220C4×C8—21no—
221C4×C8—21no—
222C4×C8—21no—
223#41—82no—
224C2×Q8—22no—
225C2×Q8—22no—
226C2×Q8—21no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4—21no—
232C2×D4—41no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4C2×D4×C15111yescharacteristic
236C22×C4#41×C15111yescharacteristic
237C22×C4#41×C15111yescharacteristic
238SD16—82no—
239SD16—82no—
240M16—22no—
241M16—41no—
242M16—42no—
243M16—81no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—22no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C22⋊C4—41no—
257C22⋊C4—41no—
258C42C2×D4×C15111yescharacteristic
259C42C2×D4×C15111yescharacteristic
260C42C2×D4×C15111yescharacteristic
261C42#41×C15111yescharacteristic
262C23—41no—
263C23#123×C15111yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—82no—
267Q8—81no—
268D4—41no—
269D4—41no—
270D4—41no—
271D4—41no—
272D4—81no—
273D4—82no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—22no—
278C2×C4—21no—
279C2×C4—44no—
280C2×C4—41no—
281C2×C4—42no—
282C2×C4—82no—
283C2×C4#120×C15111yescharacteristic
284C2×C4#121×C15111yescharacteristic
285C2×C4#121×C15111yescharacteristic
286C2×C4#121×C15111yescharacteristic
287C2×C4#123×C15111yescharacteristic
288C2×C4#124×C15111yescharacteristic
289C8—42no—
290C8—41no—
291C8—41no—
292C8—42no—
293C8—81no—
294C8—81no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—81no—
299C22—81no—
300C22—81no—
301C22#394×C15111yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—82no—
306C4—81no—
307C4#453×C15111yescharacteristic
308C4#455×C15111yescharacteristic
309C4#471×C15112yes—
310C4#471×C15111yescharacteristic
311C4#473×C15111yescharacteristic
312C2—41no—
313C2—161no—
314C2#2037×C15111yescharacteristic
315C2#2046×C15111yescharacteristic
316C2#2052×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. #1966×C151C2semidirect
3. #1574×C151C2semidirect
5. #1548×C151C2semidirect
7. #1299×C151C2semidirect
158. #10489C151direct (N × H)
159. C151#10489direct (N × H)
161. #1966C2×C151semidirect
162. #1574C2×C151semidirect
164. #1548C2×C151semidirect
166. #1299C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3206×C1512
#1966×C1512
#1574×C1512
#1560×C1512
#1548×C1512
#1484×C1512
#1299×C1512
#10489151