Finite Group Databasebeta

← C151×#12114 #50317039

Subgroups — C151×#12114 #50317039

Order 38656.

474 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 474 conjugacy classes of subgroups — too many to draw. Only its 70 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#3192×C151C211yesmaximal, characteristic, complemented
2#2190×C151C212yesmaximal, complemented
3#2010×C151C211yesmaximal, characteristic, complemented
4#1339×C151C212yesmaximal, complemented
5#1320×C151C211yesmaximal, characteristic, complemented
6#575×C151C2211yescharacteristic, complemented
7#525×C151—21no—
8C2×#121×C151—21no—
9#509×C151—22no—
10#481×C151—22no—
11#469×C151—21no—
12#469×C151C2212yes—
13#447×C151—22no—
14#421×C151—21no—
15#407×C151C2211yescharacteristic
16#360×C151—22no—
17#349×C151C2212yescomplemented
18H(3,ℤ/4)×C151C2211yescharacteristic, complemented
19C2×#41×C151—21no—
20C22×D4×C151—21no—
21C22×D4×C151—41no—
22C23×C4×C151D411yescharacteristic
23#137×C151—41no—
24AGL(1,ℤ/8)×C151—41no—
25#135×C151—22no—
26C2×D8×C151—21no—
27C2×D8×C151D412yescomplemented
28C2×M16×C151D411yescharacteristic
29C2×M16×C151C2311yescharacteristic
30#123×C151—41no—
31C22⋊Q8×C151—41no—
32#121×C151—22no—
33#121×C151—22no—
34#121×C151—41no—
35#121×C151—41no—
36#121×C151—41no—
37#120×C151—41no—
38C4×D4×C151—42no—
39#117×C151—21no—
40C2×C4⋊C4×C151—21no—
41C2×C22⋊C4×C151—41no—
42SD32×C151—42no—
43D16×C151—42no—
44M32×C151—22no—
45#106×C151—21no—
46#106×C151D412yescomplemented
47#104×C151—42no—
48#102×C151—22no—
49#102×C151—22no—
50C22⋊C8×C151—22no—
51C24×C151—41no—
52C24×C151D811yescharacteristic
53#41×C151—41no—
54#41×C151—41no—
55#41×C151—41no—
56#41×C151—41no—
57C2×Q8×C151—21no—
58C2×D4×C151—21no—
59C2×D4×C151—22no—
60C2×D4×C151—41no—
61C2×D4×C151—42no—
62C2×D4×C151—42no—
63C2×D4×C151—41no—
64C2×D4×C151—42no—
65C2×D4×C151—81no—
66C2×D4×C151—81no—
67C2×D4×C151—84no—
68C22×C4×C151—21no—
69C22×C4×C151—21no—
70C22×C4×C151—41no—
71C22×C4×C151—41no—
72C22×C4×C151—41no—
73C22×C4×C151—41no—
74C22×C4×C151D811yescharacteristic
75C22×C4×C151C2×D411yescharacteristic
76Q16×C151—22no—
77SD16×C151—42no—
78D8×C151—22no—
79D8×C151—42no—
80D8×C151—81no—
81M16×C151—41no—
82M16×C151—41no—
83C2×C8×C151—21no—
84C2×C8×C151C2×D412yes—
85C4⋊C4×C151—22no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151—41no—
88C4⋊C4×C151—42no—
89C22⋊C4×C151—42no—
90C22⋊C4×C151—42no—
91C22⋊C4×C151—42no—
92C22⋊C4×C151—41no—
93C22⋊C4×C151—42no—
94C42×C151—22no—
95C16×C151—42no—
96C23×C151—21no—
97C23×C151—41no—
98C23×C151—42no—
99C23×C151—41no—
100C23×C151—42no—
101C23×C151—82no—
102C23×C151—82no—
103C23×C151—82no—
104C23×C151C2×D811yescharacteristic
105Q8×C151—41no—
106Q8×C151—41no—
107D4×C151—41no—
108D4×C151—42no—
109D4×C151—41no—
110D4×C151—42no—
111D4×C151—82no—
112D4×C151—81no—
113D4×C151—84no—
114D4×C151—84no—
115D4×C151—84no—
116D4×C151—81no—
117C2×C4×C151—21no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—41no—
121C2×C4×C151—41no—
122C2×C4×C151—41no—
123C2×C4×C151—41no—
124C2×C4×C151—42no—
125C2×C4×C151—42no—
126C2×C4×C151—81no—
127C2×C4×C151—81no—
128C2×C4×C151—82no—
129C2×C4×C151—81no—
130C2×C4×C151#12011yescharacteristic
131C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
132C8×C151—22no—
133C8×C151—41no—
134C22×C151—22no—
135C22×C151—21no—
136C22×C151—41no—
137C22×C151—41no—
138C22×C151—42no—
139C22×C151—41no—
140C22×C151—82no—
141C22×C151—82no—
142C22×C151—81no—
143C22×C151—82no—
144C22×C151—81no—
145C22×C151—82no—
146C22×C151—164no—
147C22×C151#44711yescharacteristic
148C4×C151—21no—
149C4×C151—41no—
150C4×C151—82no—
151C4×C151—82no—
152C4×C151—81no—
153C4×C151#45311yescharacteristic
154C4×C151B(4,𝔽2)11yescharacteristic
155C2×C151—21no—
156C2×C151—41no—
157C2×C151—42no—
158C2×C151—161no—
159C2×C151—162no—
160C2×C151#159511yescharacteristic
161#12114C15111yesmaximal, characteristic, direct product factor, Sylow
162C151#1211411yescharacteristic, direct product factor, Sylow
163#3192C2×C15111yescharacteristic, complemented
164#2190C2×C15112yescomplemented
165#2010C2×C15111yescharacteristic, complemented
166#1339C2×C15112yescomplemented
167#1320C2×C15111yescharacteristic, complemented
168#575C22×C15111yescharacteristic, complemented
169#525—21no—
170C2×#121—21no—
171#509—22no—
172#481—22no—
173#469—21no—
174#469C22×C15112yes—
175#447—22no—
176#421—21no—
177#407C22×C15111yescharacteristic
178#360—22no—
179#349C22×C15112yescomplemented
180H(3,ℤ/4)C22×C15111yescharacteristic, complemented
181C2×#41—21no—
182C22×D4—21no—
183C22×D4—41no—
184C23×C4D4×C15111yescharacteristic
185#137—41no—
186AGL(1,ℤ/8)—41no—
187#135—22no—
188C2×D8—21no—
189C2×D8D4×C15112yescomplemented
190C2×M16D4×C15111yescharacteristic
191C2×M16C23×C15111yescharacteristic
192#123—41no—
193C22⋊Q8—41no—
194#121—22no—
195#121—22no—
196#121—41no—
197#121—41no—
198#121—41no—
199#120—41no—
200C4×D4—42no—
201#117—21no—
202C2×C4⋊C4—21no—
203C2×C22⋊C4—41no—
204SD32—42no—
205D16—42no—
206M32—22no—
207#106—21no—
208#106D4×C15112yescomplemented
209#104—42no—
210#102—22no—
211#102—22no—
212C22⋊C8—22no—
213C24—41no—
214C24D8×C15111yescharacteristic
215#41—41no—
216#41—41no—
217#41—41no—
218#41—41no—
219C2×Q8—21no—
220C2×D4—21no—
221C2×D4—22no—
222C2×D4—41no—
223C2×D4—42no—
224C2×D4—42no—
225C2×D4—41no—
226C2×D4—42no—
227C2×D4—81no—
228C2×D4—81no—
229C2×D4—84no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4D8×C15111yescharacteristic
237C22×C4C2×D4×C15111yescharacteristic
238Q16—22no—
239SD16—42no—
240D8—22no—
241D8—42no—
242D8—81no—
243M16—41no—
244M16—41no—
245C2×C8—21no—
246C2×C8C2×D4×C15112yes—
247C4⋊C4—22no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C22⋊C4—42no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C42—22no—
257C16—42no—
258C23—21no—
259C23—41no—
260C23—42no—
261C23—41no—
262C23—42no—
263C23—82no—
264C23—82no—
265C23—82no—
266C23C2×D8×C15111yescharacteristic
267Q8—41no—
268Q8—41no—
269D4—41no—
270D4—42no—
271D4—41no—
272D4—42no—
273D4—82no—
274D4—84no—
275D4—81no—
276D4—84no—
277D4—84no—
278D4—81no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—82no—
291C2×C4—81no—
292C2×C4#120×C15111yescharacteristic
293C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
294C8—22no—
295C8—41no—
296C22—22no—
297C22—21no—
298C22—41no—
299C22—41no—
300C22—42no—
301C22—41no—
302C22—82no—
303C22—82no—
304C22—81no—
305C22—82no—
306C22—81no—
307C22—82no—
308C22—164no—
309C22#447×C15111yescharacteristic
310C4—21no—
311C4—41no—
312C4—82no—
313C4—82no—
314C4—81no—
315C4#453×C15111yescharacteristic
316C4B(4,𝔽2)×C15111yescharacteristic
317C2—21no—
318C2—41no—
319C2—42no—
320C2—162no—
321C2—161no—
322C2#1595×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#1595
commutator, Frattini, cosocleC2×M16C23×C151
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3192×C151C2semidirect
2. #2190×C151C2semidirect
3. #2010×C151C2semidirect
4. #1339×C151C2semidirect
5. #1320×C151C2semidirect
6. #575×C151C22semidirect
17. #349×C151C22semidirect
18. H(3,ℤ/4)×C151C22semidirect
27. C2×D8×C151D4semidirect
46. #106×C151D4semidirect
161. #12114C151direct (N × H)
162. C151#12114direct (N × H)
163. #3192C2×C151semidirect
164. #2190C2×C151semidirect
165. #2010C2×C151semidirect
166. #1339C2×C151semidirect
167. #1320C2×C151semidirect
168. #575C22×C151semidirect
179. #349C22×C151semidirect
180. H(3,ℤ/4)C22×C151semidirect
189. C2×D8D4×C151semidirect
208. #106D4×C151semidirect

Maximal subgroups

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

subgroupindex
#3192×C1512
#2190×C1512
#2010×C1512
#1339×C1512
#1320×C1512
#12114151