Finite Group Databasebeta

← C151×#11867 #50316792

Subgroups — C151×#11867 #50316792

Order 38656.

376 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3060×C151C211yesmaximal, characteristic
2#2115×C151C211yesmaximal, characteristic, complemented
3#1812×C151C211yesmaximal, characteristic, complemented
4#1340×C151C212yesmaximal, complemented
5#1339×C151C212yesmaximal, complemented
6C2×#135×C151C411yescharacteristic, complemented
7C2×#131×C151C2211yescharacteristic
8#537×C151—21no—
9C2×M32×C151—21no—
10#470×C151C411yescharacteristic, complemented
11#470×C151C2211yescharacteristic
12#469×C151C411yescharacteristic, complemented
13#469×C151C2211yescharacteristic
14#465×C151—21no—
15#465×C151—21no—
16#427×C151—21no—
17C2×#106×C151C411yescharacteristic, complemented
18#417×C151—21no—
19#410×C151—21no—
20#349×C151—21no—
21#349×C151C2212yes—
22H(3,ℤ/4)×C151C2212yes—
23C2×#41×C151—21no—
24C2×#41×C151D411yescharacteristic
25#135×C151—41no—
26#135×C151—41no—
27C2×Q16×C151C2×C411yescharacteristic
28C2×SD16×C151—21no—
29C2×D8×C151C2×C411yescharacteristic
30#131×C151—41no—
31#131×C151—41no—
32C2×M16×C151C2×C411yescharacteristic
33C2×M16×C151D411yescharacteristic
34C2×M16×C151C2311yescharacteristic
35C22×C8×C151C2×C411yescharacteristic
36C22×C8×C151D411yescharacteristic
37C22×C8×C151D411yescharacteristic
38C22⋊Q8×C151—21no—
39C22⋊Q8×C151—21no—
40C22⋊Q8×C151—41no—
41#121×C151—21no—
42#121×C151—21no—
43#121×C151—41no—
44#121×C151—41no—
45#121×C151—41no—
46#117×C151—22no—
47C2×C4⋊C4×C151—21no—
48M32×C151—22no—
49M32×C151—41no—
50C2×C16×C151—41no—
51#107×C151—41no—
52#106×C151—21no—
53#106×C151—41no—
54#106×C151C2×C411yescharacteristic
55#106×C151C2×C411yescharacteristic
56#103×C151—21no—
57#103×C151—21no—
58#102×C151—21no—
59#102×C151—21no—
60#99×C151—41no—
61#99×C151—41no—
62#41×C151—41no—
63#41×C151—41no—
64#41×C151—42no—
65#41×C151—42no—
66C2×Q8×C151—21no—
67C2×Q8×C151SD1611yescharacteristic
68C2×D4×C151—21no—
69C2×D4×C151—41no—
70C2×D4×C151—41no—
71C2×D4×C151—41no—
72C2×D4×C151D811yescharacteristic
73C2×D4×C151D811yescharacteristic
74C2×D4×C151SD1611yescharacteristic
75C22×C4×C151—41no—
76C22×C4×C151—41no—
77C22×C4×C151C22⋊C411yescharacteristic
78C22×C4×C151C22⋊C411yescharacteristic
79C22×C4×C151C2×D411yescharacteristic
80Q16×C151—41no—
81SD16×C151—41no—
82SD16×C151—41no—
83D8×C151—41no—
84M16×C151—41no—
85M16×C151—41no—
86M16×C151—41no—
87C2×C8×C151—21no—
88C2×C8×C151—21no—
89C2×C8×C151—21no—
90C2×C8×C151—21no—
91C2×C8×C151—21no—
92C2×C8×C151—21no—
93C2×C8×C151C22⋊C411yescharacteristic
94C2×C8×C151C22⋊C411yescharacteristic
95C2×C8×C151C22×C411yescharacteristic
96C2×C8×C151C2×D411yescharacteristic
97C4⋊C4×C151—21no—
98C4⋊C4×C151—21no—
99C4⋊C4×C151—42no—
100C4⋊C4×C151—41no—
101C4⋊C4×C151—41no—
102C4⋊C4×C151—41no—
103C22⋊C4×C151—41no—
104C22⋊C4×C151—41no—
105C22⋊C4×C151—41no—
106C22⋊C4×C151—41no—
107C22⋊C4×C151—42no—
108C42×C151—42no—
109C16×C151—42no—
110C23×C151—41no—
111C23×C151#10211yescharacteristic
112C23×C151#10211yescharacteristic
113C23×C151C2×D811yescharacteristic
114Q8×C151—41no—
115Q8×C151—41no—
116Q8×C151—41no—
117D4×C151—41no—
118D4×C151—41no—
119D4×C151—41no—
120D4×C151—41no—
121D4×C151—41no—
122D4×C151—82no—
123D4×C151—161no—
124D4×C151—161no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—21no—
131C2×C4×C151—41no—
132C2×C4×C151—41no—
133C2×C4×C151—41no—
134C2×C4×C151—82no—
135C2×C4×C151—82no—
136C2×C4×C151—161no—
137C2×C4×C151#10211yescharacteristic
138C2×C4×C151#10211yescharacteristic
139C2×C4×C151C2×C22⋊C411yescharacteristic
140C2×C4×C151C2×SD1611yescharacteristic
141C8×C151—21no—
142C8×C151—21no—
143C8×C151—21no—
144C8×C151#9911yescharacteristic
145C8×C151#9911yescharacteristic
146C22×C151—21no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—41no—
152C22×C151—81no—
153C22×C151—81no—
154C22×C151—81no—
155C22×C151C2×#10211yescharacteristic
156C4×C151—21no—
157C4×C151—21no—
158C4×C151—21no—
159C4×C151—81no—
160C4×C151—81no—
161C4×C151—81no—
162C4×C151—162no—
163C4×C151C2×#9911yescharacteristic
164C4×C151#42111yescharacteristic
165C2×C151—21no—
166C2×C151—41no—
167C2×C151—41no—
168C2×C151—41no—
169C2×C151—161no—
170C2×C151#151911yescharacteristic
171#11867C15111yesmaximal, characteristic, direct product factor, Sylow
172C151#1186711yescharacteristic, direct product factor, Sylow
173#3060C2×C15111yescharacteristic
174#2115C2×C15111yescharacteristic, complemented
175#1812C2×C15111yescharacteristic, complemented
176#1340C2×C15112yescomplemented
177#1339C2×C15112yescomplemented
178C2×#135C4×C15111yescharacteristic, complemented
179C2×#131C22×C15111yescharacteristic
180#537—21no—
181C2×M32—21no—
182#470C4×C15111yescharacteristic, complemented
183#470C22×C15111yescharacteristic
184#469C4×C15111yescharacteristic, complemented
185#469C22×C15111yescharacteristic
186#465—21no—
187#465—21no—
188#427—21no—
189C2×#106C4×C15111yescharacteristic, complemented
190#417—21no—
191#410—21no—
192#349—21no—
193#349C22×C15112yes—
194H(3,ℤ/4)C22×C15112yes—
195C2×#41—21no—
196C2×#41D4×C15111yescharacteristic
197#135—41no—
198#135—41no—
199C2×Q16C2×C4×C15111yescharacteristic
200C2×SD16—21no—
201C2×D8C2×C4×C15111yescharacteristic
202#131—41no—
203#131—41no—
204C2×M16C2×C4×C15111yescharacteristic
205C2×M16D4×C15111yescharacteristic
206C2×M16C23×C15111yescharacteristic
207C22×C8C2×C4×C15111yescharacteristic
208C22×C8D4×C15111yescharacteristic
209C22×C8D4×C15111yescharacteristic
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—41no—
213#121—21no—
214#121—21no—
215#121—41no—
216#121—41no—
217#121—41no—
218#117—22no—
219C2×C4⋊C4—21no—
220M32—22no—
221M32—41no—
222C2×C16—41no—
223#107—41no—
224#106—21no—
225#106—41no—
226#106C2×C4×C15111yescharacteristic
227#106C2×C4×C15111yescharacteristic
228#103—21no—
229#103—21no—
230#102—21no—
231#102—21no—
232#99—41no—
233#99—41no—
234#41—41no—
235#41—41no—
236#41—42no—
237#41—42no—
238C2×Q8—21no—
239C2×Q8SD16×C15111yescharacteristic
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4D8×C15111yescharacteristic
245C2×D4D8×C15111yescharacteristic
246C2×D4SD16×C15111yescharacteristic
247C22×C4—41no—
248C22×C4—41no—
249C22×C4C22⋊C4×C15111yescharacteristic
250C22×C4C22⋊C4×C15111yescharacteristic
251C22×C4C2×D4×C15111yescharacteristic
252Q16—41no—
253SD16—41no—
254SD16—41no—
255D8—41no—
256M16—41no—
257M16—41no—
258M16—41no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8C22⋊C4×C15111yescharacteristic
266C2×C8C22⋊C4×C15111yescharacteristic
267C2×C8C22×C4×C15111yescharacteristic
268C2×C8C2×D4×C15111yescharacteristic
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—42no—
280C42—42no—
281C16—42no—
282C23—41no—
283C23#102×C15111yescharacteristic
284C23#102×C15111yescharacteristic
285C23C2×D8×C15111yescharacteristic
286Q8—41no—
287Q8—41no—
288Q8—41no—
289D4—41no—
290D4—41no—
291D4—41no—
292D4—41no—
293D4—41no—
294D4—82no—
295D4—161no—
296D4—161no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—161no—
309C2×C4#102×C15111yescharacteristic
310C2×C4#102×C15111yescharacteristic
311C2×C4C2×C22⋊C4×C15111yescharacteristic
312C2×C4C2×SD16×C15111yescharacteristic
313C8—21no—
314C8—21no—
315C8—21no—
316C8#99×C15111yescharacteristic
317C8#99×C15111yescharacteristic
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#102×C15111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—162no—
335C4C2×#99×C15111yescharacteristic
336C4#421×C15111yescharacteristic
337C2—21no—
338C2—41no—
339C2—41no—
340C2—41no—
341C2—161no—
342C2#1519×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#1519
commutatorC2×C8C22×C4×C151
Frattini, cosocleC2×M16C23×C151
prime radical#3060×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2115×C151C2semidirect
3. #1812×C151C2semidirect
4. #1340×C151C2semidirect
5. #1339×C151C2semidirect
6. C2×#135×C151C4semidirect
10. #470×C151C4semidirect
12. #469×C151C4semidirect
17. C2×#106×C151C4semidirect
171. #11867C151direct (N × H)
172. C151#11867direct (N × H)
174. #2115C2×C151semidirect
175. #1812C2×C151semidirect
176. #1340C2×C151semidirect
177. #1339C2×C151semidirect
178. C2×#135C4×C151semidirect
182. #470C4×C151semidirect
184. #469C4×C151semidirect
189. C2×#106C4×C151semidirect

Maximal subgroups

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

subgroupindex
#3060×C1512
#2115×C1512
#1812×C1512
#1340×C1512
#1339×C1512
#11867151