Finite Group Databasebeta

← C151×#10619 #50315544

Subgroups — C151×#10619 #50315544

Order 38656.

418 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#1954×C151C211yesmaximal, characteristic
2#1844×C151C211yesmaximal, characteristic, complemented
3#1802×C151C211yesmaximal, characteristic
4#1802×C151C211yesmaximal, characteristic
5#1296×C151C211yesmaximal, characteristic, complemented
6#1296×C151C211yesmaximal, characteristic, complemented
7#1277×C151C211yesmaximal, characteristic, complemented
8C2×C4×D4×C151C2211yescharacteristic
9C2×#106×C151—21no—
10C2×#106×C151—21no—
11C2×C4⋊C8×C151C2211yescharacteristic
12C2×C4⋊C8×C151C2211yescharacteristic
13C2×C4⋊C8×C151C2211yescharacteristic
14C2×#102×C151—21no—
15C2×#102×C151—21no—
16C2×C22⋊C8×C151—21no—
17C2×C22⋊C8×C151—21no—
18C2×C4×C8×C151C2211yescharacteristic
19#384×C151C2211yescharacteristic
20#384×C151C2211yescharacteristic
21#340×C151—21no—
22#340×C151—21no—
23C22×D4×C151D411yescharacteristic
24C23×C4×C151—21no—
25C22×C8×C151—21no—
26C22×C8×C151—21no—
27C22×C8×C151—21no—
28C22×C8×C151D411yescharacteristic
29C22×C8×C151D411yescharacteristic
30C4×D4×C151—21no—
31C4×D4×C151—21no—
32C4×D4×C151—21no—
33C4×D4×C151—21no—
34C2×C4⋊C4×C151—21no—
35C2×C4⋊C4×C151—21no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151—21no—
39C2×C4⋊C4×C151—21no—
40C2×C4⋊C4×C151D411yescharacteristic
41C2×C22⋊C4×C151—21no—
42C2×C42×C151C2311yescharacteristic
43#106×C151—42no—
44#106×C151—42no—
45C4⋊C8×C151—21no—
46C4⋊C8×C151—21no—
47C4⋊C8×C151—21no—
48C4⋊C8×C151—21no—
49C4⋊C8×C151—21no—
50C4⋊C8×C151—21no—
51#102×C151—42no—
52#102×C151—42no—
53C22⋊C8×C151—42no—
54C22⋊C8×C151—42no—
55C4×C8×C151—21no—
56C4×C8×C151—21no—
57C24×C151—21no—
58C2×D4×C151—21no—
59C2×D4×C151—21no—
60C2×D4×C151—21no—
61C2×D4×C151—21no—
62C2×D4×C151—21no—
63C2×D4×C151SD1612yes—
64C22×C4×C151—21no—
65C22×C4×C151—41no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151—41no—
69C22×C4×C151—41no—
70C22×C4×C151—41no—
71C22×C4×C151—41no—
72C22×C4×C151—41no—
73C22×C4×C151C2×D411yescharacteristic
74C22×C4×C151C2×D411yescharacteristic
75C22×C4×C151#4111yescharacteristic
76C2×C8×C151—21no—
77C2×C8×C151—21no—
78C2×C8×C151—21no—
79C2×C8×C151—21no—
80C2×C8×C151—41no—
81C2×C8×C151—41no—
82C2×C8×C151—41no—
83C2×C8×C151—41no—
84C2×C8×C151—41no—
85C2×C8×C151—41no—
86C2×C8×C151—41no—
87C2×C8×C151—41no—
88C2×C8×C151—41no—
89C2×C8×C151D812yes—
90C2×C8×C151SD1612yes—
91C4⋊C4×C151—21no—
92C4⋊C4×C151—21no—
93C4⋊C4×C151—41no—
94C4⋊C4×C151—41no—
95C4⋊C4×C151—41no—
96C4⋊C4×C151—41no—
97C4⋊C4×C151—41no—
98C4⋊C4×C151—41no—
99C4⋊C4×C151—41no—
100C4⋊C4×C151—41no—
101C4⋊C4×C151—81no—
102C4⋊C4×C151—81no—
103C22⋊C4×C151—41no—
104C22⋊C4×C151—41no—
105C42×C151#4111yescharacteristic
106C42×C151#4111yescharacteristic
107C42×C151#4111yescharacteristic
108C42×C151#4111yescharacteristic
109C23×C151—22no—
110C23×C151—41no—
111C23×C151—41no—
112C23×C151—41no—
113C23×C151—41no—
114C23×C151—41no—
115C23×C151—41no—
116C23×C151#12111yescharacteristic
117D4×C151—22no—
118D4×C151—22no—
119D4×C151—41no—
120D4×C151—41no—
121C2×C4×C151—21no—
122C2×C4×C151—21no—
123C2×C4×C151—41no—
124C2×C4×C151—41no—
125C2×C4×C151—41no—
126C2×C4×C151—81no—
127C2×C4×C151—81no—
128C2×C4×C151—81no—
129C2×C4×C151—81no—
130C2×C4×C151—81no—
131C2×C4×C151—81no—
132C2×C4×C151—81no—
133C2×C4×C151—81no—
134C2×C4×C151—81no—
135C2×C4×C151—81no—
136C2×C4×C151#12311yescharacteristic
137C2×C4×C151#12311yescharacteristic
138C2×C4×C151#12311yescharacteristic
139C2×C4×C151#12411yescharacteristic
140C2×C4×C151#12611yescharacteristic
141C2×C4×C151#12611yescharacteristic
142C2×C4×C151C2×D811yescharacteristic
143C2×C4×C151C2×SD1611yescharacteristic
144C2×C4×C151C2×SD1611yescharacteristic
145C2×C4×C151#13511yescharacteristic
146C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C151#13711yescharacteristic
149C2×C4×C151#13711yescharacteristic
150C8×C151—22no—
151C8×C151—22no—
152C8×C151—81no—
153C8×C151—81no—
154C8×C151—81no—
155C22×C151—42no—
156C22×C151—42no—
157C22×C151—42no—
158C22×C151—81no—
159C22×C151—81no—
160C22×C151—81no—
161C22×C151—81no—
162C22×C151#39711yescharacteristic
163C22×C151#45911yescharacteristic
164C22×C151#46111yescharacteristic
165C22×C151#46511yescharacteristic
166C22×C151#46811yescharacteristic
167C22×C151#47111yescharacteristic
168C22×C151#47111yescharacteristic
169C4×C151—21no—
170C4×C151—21no—
171C4×C151—81no—
172C4×C151—161no—
173C4×C151—161no—
174C4×C151#48011yescharacteristic
175C4×C151#48111yescharacteristic
176C4×C151#48111yescharacteristic
177C4×C151#48211yescharacteristic
178C4×C151#48311yescharacteristic
179C4×C151#48511yescharacteristic
180C4×C151#48611yescharacteristic
181C4×C151#48911yescharacteristic
182C2×C151—82no—
183C2×C151#166511yescharacteristic
184C2×C151#167111yescharacteristic
185C2×C151#168511yescharacteristic
186C2×C151#169111yescharacteristic
187C2×C151#207111yescharacteristic
188C2×C151#207711yescharacteristic
189C2×C151#207911yescharacteristic
190#10619C15111yesmaximal, characteristic, direct product factor, Sylow
191C151#1061911yescharacteristic, direct product factor, Sylow
192#1954C2×C15111yescharacteristic
193#1844C2×C15111yescharacteristic, complemented
194#1802C2×C15111yescharacteristic
195#1802C2×C15111yescharacteristic
196#1296C2×C15111yescharacteristic, complemented
197#1296C2×C15111yescharacteristic, complemented
198#1277C2×C15111yescharacteristic, complemented
199C2×C4×D4C22×C15111yescharacteristic
200C2×#106—21no—
201C2×#106—21no—
202C2×C4⋊C8C22×C15111yescharacteristic
203C2×C4⋊C8C22×C15111yescharacteristic
204C2×C4⋊C8C22×C15111yescharacteristic
205C2×#102—21no—
206C2×#102—21no—
207C2×C22⋊C8—21no—
208C2×C22⋊C8—21no—
209C2×C4×C8C22×C15111yescharacteristic
210#384C22×C15111yescharacteristic
211#384C22×C15111yescharacteristic
212#340—21no—
213#340—21no—
214C22×D4D4×C15111yescharacteristic
215C23×C4—21no—
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8D4×C15111yescharacteristic
220C22×C8D4×C15111yescharacteristic
221C4×D4—21no—
222C4×D4—21no—
223C4×D4—21no—
224C4×D4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4D4×C15111yescharacteristic
232C2×C22⋊C4—21no—
233C2×C42C23×C15111yescharacteristic
234#106—42no—
235#106—42no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242#102—42no—
243#102—42no—
244C22⋊C8—42no—
245C22⋊C8—42no—
246C4×C8—21no—
247C4×C8—21no—
248C24—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4SD16×C15112yes—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4C2×D4×C15111yescharacteristic
265C22×C4C2×D4×C15111yescharacteristic
266C22×C4#41×C15111yescharacteristic
267C2×C8—21no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8D8×C15112yes—
281C2×C8SD16×C15112yes—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—81no—
293C4⋊C4—81no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42#41×C15111yescharacteristic
297C42#41×C15111yescharacteristic
298C42#41×C15111yescharacteristic
299C42#41×C15111yescharacteristic
300C23—22no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23#121×C15111yescharacteristic
308D4—22no—
309D4—22no—
310D4—41no—
311D4—41no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4#123×C15111yescharacteristic
328C2×C4#123×C15111yescharacteristic
329C2×C4#123×C15111yescharacteristic
330C2×C4#124×C15111yescharacteristic
331C2×C4#126×C15111yescharacteristic
332C2×C4#126×C15111yescharacteristic
333C2×C4C2×D8×C15111yescharacteristic
334C2×C4C2×SD16×C15111yescharacteristic
335C2×C4C2×SD16×C15111yescharacteristic
336C2×C4#135×C15111yescharacteristic
337C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
338C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
339C2×C4#137×C15111yescharacteristic
340C2×C4#137×C15111yescharacteristic
341C8—22no—
342C8—22no—
343C8—81no—
344C8—81no—
345C8—81no—
346C22—42no—
347C22—42no—
348C22—42no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22—81no—
353C22#397×C15111yescharacteristic
354C22#459×C15111yescharacteristic
355C22#461×C15111yescharacteristic
356C22#465×C15111yescharacteristic
357C22#468×C15111yescharacteristic
358C22#471×C15111yescharacteristic
359C22#471×C15111yescharacteristic
360C4—21no—
361C4—21no—
362C4—81no—
363C4—161no—
364C4—161no—
365C4#480×C15111yescharacteristic
366C4#481×C15111yescharacteristic
367C4#481×C15111yescharacteristic
368C4#482×C15111yescharacteristic
369C4#483×C15111yescharacteristic
370C4#485×C15111yescharacteristic
371C4#486×C15111yescharacteristic
372C4#489×C15111yescharacteristic
373C2—82no—
374C2#1665×C15111yescharacteristic
375C2#1671×C15111yescharacteristic
376C2#1685×C15111yescharacteristic
377C2#1691×C15111yescharacteristic
378C2#2071×C15111yescharacteristic
379C2#2077×C15111yescharacteristic
380C2#2079×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#121
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1844×C151C2semidirect
5. #1296×C151C2semidirect
6. #1296×C151C2semidirect
7. #1277×C151C2semidirect
190. #10619C151direct (N × H)
191. C151#10619direct (N × H)
193. #1844C2×C151semidirect
196. #1296C2×C151semidirect
197. #1296C2×C151semidirect
198. #1277C2×C151semidirect

Maximal subgroups

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

subgroupindex
#1954×C1512
#1844×C1512
#1802×C1512
#1296×C1512
#1277×C1512
#10619151