Finite Group Databasebeta

← C2×#1339×C151 #50316608

Subgroups — C2×#1339×C151 #50316608

Order 38656.

496 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C151C211yesmaximal, characteristic
2C2×#349×C151C211yesmaximal, characteristic, complemented
3C2×H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
4#1339×C151C214yesmaximal, direct product factor
5C22×D8×C151C411yescharacteristic, complemented
6C22×M16×C151C2211yescharacteristic
7C2×#121×C151—21no—
8C2×#117×C151—21no—
9C2×M32×C151—21no—
10#469×C151—21no—
11#469×C151—21no—
12#469×C151C412yescomplemented
13#469×C151C2212yes—
14C2×#106×C151C411yescharacteristic, complemented
15C2×#102×C151—21no—
16#349×C151—21no—
17#349×C151C2212yescomplemented
18H(3,ℤ/4)×C151—21no—
19H(3,ℤ/4)×C151C2212yescomplemented
20C22×D4×C151—21no—
21C22×D4×C151—41no—
22C23×C4×C151D411yescharacteristic
23C2×D8×C151—21no—
24C2×D8×C151—41no—
25C2×D8×C151—41no—
26C2×D8×C151C2×C412yescomplemented
27C2×M16×C151—41no—
28C2×M16×C151—41no—
29C2×M16×C151C2×C411yescharacteristic
30C2×M16×C151D411yescharacteristic
31C2×M16×C151D411yescharacteristic
32C2×M16×C151C2311yescharacteristic
33C22×C8×C151C2×C411yescharacteristic
34C22×C8×C151D411yescharacteristic
35#121×C151—22no—
36#121×C151—22no—
37#121×C151—41no—
38#121×C151—41no—
39#117×C151—22no—
40#117×C151—22no—
41#117×C151—41no—
42#117×C151—41no—
43C2×C4⋊C4×C151—21no—
44C2×C4⋊C4×C151—41no—
45C2×C22⋊C4×C151—41no—
46C2×C22⋊C4×C151—41no—
47C2×C42×C151—22no—
48M32×C151—22no—
49M32×C151—41no—
50C2×C16×C151—41no—
51#106×C151—21no—
52#106×C151C2×C412yescomplemented
53#102×C151—22no—
54#102×C151—22no—
55C24×C151—41no—
56C24×C151D811yescharacteristic
57C2×D4×C151—22no—
58C2×D4×C151—42no—
59C2×D4×C151—42no—
60C2×D4×C151—41no—
61C2×D4×C151—41no—
62C2×D4×C151—41no—
63C2×D4×C151—41no—
64C2×D4×C151—41no—
65C2×D4×C151—84no—
66C22×C4×C151—21no—
67C22×C4×C151—21no—
68C22×C4×C151—21no—
69C22×C4×C151—21no—
70C22×C4×C151—42no—
71C22×C4×C151—41no—
72C22×C4×C151C22⋊C411yescharacteristic
73C22×C4×C151C22⋊C411yescharacteristic
74C22×C4×C151D811yescharacteristic
75C22×C4×C151SD1611yescharacteristic
76C22×C4×C151SD1611yescharacteristic
77C22×C4×C151C2×D411yescharacteristic
78D8×C151—42no—
79D8×C151—42no—
80M16×C151—41no—
81M16×C151—41no—
82M16×C151—41no—
83M16×C151—41no—
84C2×C8×C151—21no—
85C2×C8×C151—21no—
86C2×C8×C151—21no—
87C2×C8×C151—21no—
88C2×C8×C151C22⋊C411yescharacteristic
89C2×C8×C151C22⋊C411yescharacteristic
90C2×C8×C151C22×C411yescharacteristic
91C2×C8×C151C2×D411yescharacteristic
92C4⋊C4×C151—22no—
93C4⋊C4×C151—42no—
94C4⋊C4×C151—42no—
95C4⋊C4×C151—41no—
96C22⋊C4×C151—42no—
97C22⋊C4×C151—42no—
98C22⋊C4×C151—42no—
99C22⋊C4×C151—42no—
100C42×C151—24no—
101C42×C151—42no—
102C16×C151—42no—
103C23×C151—21no—
104C23×C151—21no—
105C23×C151—42no—
106C23×C151—42no—
107C23×C151—82no—
108C23×C151—82no—
109C23×C151—81no—
110C23×C151—81no—
111C23×C151#10211yescharacteristic
112C23×C151#10211yescharacteristic
113C23×C151C2×D811yescharacteristic
114D4×C151—42no—
115D4×C151—42no—
116D4×C151—84no—
117D4×C151—84no—
118D4×C151—81no—
119D4×C151—81no—
120C2×C4×C151—21no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—21no—
124C2×C4×C151—21no—
125C2×C4×C151—21no—
126C2×C4×C151—21no—
127C2×C4×C151—21no—
128C2×C4×C151—21no—
129C2×C4×C151—21no—
130C2×C4×C151—44no—
131C2×C4×C151—42no—
132C2×C4×C151—82no—
133C2×C4×C151—84no—
134C2×C4×C151#9911yescharacteristic
135C2×C4×C151#9911yescharacteristic
136C2×C4×C151#10211yescharacteristic
137C2×C4×C151#10211yescharacteristic
138C2×C4×C151#10411yescharacteristic
139C2×C4×C151#10411yescharacteristic
140C2×C4×C151C2×C22⋊C411yescharacteristic
141C2×C4×C151C2×SD1611yescharacteristic
142C8×C151—21no—
143C8×C151—21no—
144C8×C151—21no—
145C8×C151—21no—
146C22×C151—22no—
147C22×C151—21no—
148C22×C151—21no—
149C22×C151—41no—
150C22×C151—41no—
151C22×C151—42no—
152C22×C151—81no—
153C22×C151—82no—
154C22×C151—82no—
155C22×C151—82no—
156C22×C151—162no—
157C22×C151—162no—
158C22×C151#32711yescharacteristic
159C22×C151#32711yescharacteristic
160C22×C151C2×#10211yescharacteristic
161C4×C151—21no—
162C4×C151—21no—
163C4×C151—82no—
164C4×C151—84no—
165C4×C151#32711yescharacteristic
166C4×C151#32711yescharacteristic
167C4×C151C2×#9911yescharacteristic
168C4×C151C2×#10411yescharacteristic
169C2×C151—21no—
170C2×C151—21no—
171C2×C151—41no—
172C2×C151—41no—
173C2×C151—162no—
174C2×C151#133912yesdirect product factor
175C2×C151C2×#32711yescharacteristic
176C2×#1339C15111yesmaximal, characteristic, direct product factor, Sylow
177C151C2×#133911yescharacteristic, direct product factor, Sylow
178C2×#469C2×C15111yescharacteristic
179C2×#349C2×C15111yescharacteristic, complemented
180C2×H(3,ℤ/4)C2×C15111yescharacteristic, complemented
181#1339C2×C15114yesdirect product factor
182C22×D8C4×C15111yescharacteristic, complemented
183C22×M16C22×C15111yescharacteristic
184C2×#121—21no—
185C2×#117—21no—
186C2×M32—21no—
187#469—21no—
188#469—21no—
189#469C4×C15112yescomplemented
190#469C22×C15112yes—
191C2×#106C4×C15111yescharacteristic, complemented
192C2×#102—21no—
193#349—21no—
194#349C22×C15112yescomplemented
195H(3,ℤ/4)—21no—
196H(3,ℤ/4)C22×C15112yescomplemented
197C22×D4—21no—
198C22×D4—41no—
199C23×C4D4×C15111yescharacteristic
200C2×D8—21no—
201C2×D8—41no—
202C2×D8—41no—
203C2×D8C2×C4×C15112yescomplemented
204C2×M16—41no—
205C2×M16—41no—
206C2×M16C2×C4×C15111yescharacteristic
207C2×M16D4×C15111yescharacteristic
208C2×M16D4×C15111yescharacteristic
209C2×M16C23×C15111yescharacteristic
210C22×C8C2×C4×C15111yescharacteristic
211C22×C8D4×C15111yescharacteristic
212#121—22no—
213#121—22no—
214#121—41no—
215#121—41no—
216#117—22no—
217#117—22no—
218#117—41no—
219#117—41no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—41no—
222C2×C22⋊C4—41no—
223C2×C22⋊C4—41no—
224C2×C42—22no—
225M32—22no—
226M32—41no—
227C2×C16—41no—
228#106—21no—
229#106C2×C4×C15112yescomplemented
230#102—22no—
231#102—22no—
232C24—41no—
233C24D8×C15111yescharacteristic
234C2×D4—22no—
235C2×D4—42no—
236C2×D4—42no—
237C2×D4—41no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—84no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4C22⋊C4×C15111yescharacteristic
250C22×C4C22⋊C4×C15111yescharacteristic
251C22×C4D8×C15111yescharacteristic
252C22×C4SD16×C15111yescharacteristic
253C22×C4SD16×C15111yescharacteristic
254C22×C4C2×D4×C15111yescharacteristic
255D8—42no—
256D8—42no—
257M16—41no—
258M16—41no—
259M16—41no—
260M16—41no—
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—22no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—42no—
277C42—24no—
278C42—42no—
279C16—42no—
280C23—21no—
281C23—21no—
282C23—42no—
283C23—42no—
284C23—82no—
285C23—82no—
286C23—81no—
287C23—81no—
288C23#102×C15111yescharacteristic
289C23#102×C15111yescharacteristic
290C23C2×D8×C15111yescharacteristic
291D4—42no—
292D4—42no—
293D4—84no—
294D4—84no—
295D4—81no—
296D4—81no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—44no—
308C2×C4—42no—
309C2×C4—82no—
310C2×C4—84no—
311C2×C4#99×C15111yescharacteristic
312C2×C4#99×C15111yescharacteristic
313C2×C4#102×C15111yescharacteristic
314C2×C4#102×C15111yescharacteristic
315C2×C4#104×C15111yescharacteristic
316C2×C4#104×C15111yescharacteristic
317C2×C4C2×C22⋊C4×C15111yescharacteristic
318C2×C4C2×SD16×C15111yescharacteristic
319C8—21no—
320C8—21no—
321C8—21no—
322C8—21no—
323C22—22no—
324C22—21no—
325C22—21no—
326C22—41no—
327C22—41no—
328C22—42no—
329C22—81no—
330C22—82no—
331C22—82no—
332C22—82no—
333C22—162no—
334C22—162no—
335C22#327×C15111yescharacteristic
336C22#327×C15111yescharacteristic
337C22C2×#102×C15111yescharacteristic
338C4—21no—
339C4—21no—
340C4—82no—
341C4—84no—
342C4#327×C15111yescharacteristic
343C4#327×C15111yescharacteristic
344C4C2×#99×C15111yescharacteristic
345C4C2×#104×C15111yescharacteristic
346C2—21no—
347C2—21no—
348C2—41no—
349C2—41no—
350C2—162no—
351C2#1339×C15112yesdirect product factor
352C2C2×#327×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#327
commutatorC2×C8C22×C4×C151
Frattini, cosocleC2×M16C23×C151
prime radicalC2×#469×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C22×M16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#349×C151C2semidirect
3. C2×H(3,ℤ/4)×C151C2semidirect
4. #1339×C151C2direct (N × H)
5. C22×D8×C151C4semidirect
12. #469×C151C4semidirect
14. C2×#106×C151C4semidirect
17. #349×C151C22semidirect
19. H(3,ℤ/4)×C151C22semidirect
26. C2×D8×C151C2×C4semidirect
52. #106×C151C2×C4semidirect
174. C2×C151#1339direct (N × H)
176. C2×#1339C151direct (N × H)
177. C151C2×#1339direct (N × H)
179. C2×#349C2×C151semidirect
180. C2×H(3,ℤ/4)C2×C151semidirect
181. #1339C2×C151direct (N × H)
182. C22×D8C4×C151semidirect
189. #469C4×C151semidirect
191. C2×#106C4×C151semidirect
194. #349C22×C151semidirect
196. H(3,ℤ/4)C22×C151semidirect
203. C2×D8C2×C4×C151semidirect
229. #106C2×C4×C151semidirect
351. C2#1339×C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#469×C1512
C2×#349×C1512
C2×H(3,ℤ/4)×C1512
#1339×C1512
C2×#1339151