Finite Group Databasebeta

← C151×#11688 #50316613

Subgroups — C151×#11688 #50316613

Order 38656.

432 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#3054×C151C211yesmaximal, characteristic
2C2×#349×C151C211yesmaximal, characteristic, complemented
3C2×#338×C151C211yesmaximal, characteristic, complemented
4#1342×C151C212yesmaximal, complemented
5#1341×C151C212yesmaximal, complemented
6C2×#135×C151C411yescharacteristic
7C22×M16×C151—21no—
8C22×M16×C151C2211yescharacteristic
9#525×C151—21no—
10C2×M32×C151—21no—
11#470×C151C411yescharacteristic
12#470×C151C2211yescharacteristic
13#469×C151C411yescharacteristic
14#469×C151C2211yescharacteristic
15#468×C151—21no—
16#468×C151—21no—
17#427×C151C411yescharacteristic
18#416×C151—21no—
19#349×C151—21no—
20#349×C151C2212yes—
21#338×C151—21no—
22#338×C151C2212yes—
23C2×#41×C151—21no—
24C23×C4×C151D411yescharacteristic
25#135×C151—41no—
26#135×C151—41no—
27C2×Q16×C151C2×C411yescharacteristic
28C2×SD16×C151—21no—
29C2×D8×C151C2×C411yescharacteristic
30C2×M16×C151—22no—
31C2×M16×C151—22no—
32C2×M16×C151—41no—
33C2×M16×C151—41no—
34C2×M16×C151—41no—
35C2×M16×C151—41no—
36C2×M16×C151—41no—
37C2×M16×C151—41no—
38C2×M16×C151C2×C411yescharacteristic
39C2×M16×C151D411yescharacteristic
40C2×M16×C151D411yescharacteristic
41C2×M16×C151C2311yescharacteristic
42C22×C8×C151—22no—
43C22×C8×C151C2×C411yescharacteristic
44C22×C8×C151D411yescharacteristic
45#123×C151—41no—
46C22⋊Q8×C151—21no—
47C22⋊Q8×C151—21no—
48#121×C151—21no—
49#121×C151—21no—
50#120×C151—41no—
51C4×D4×C151—41no—
52C4×D4×C151—41no—
53#117×C151—21no—
54M32×C151—22no—
55M32×C151—41no—
56C2×C16×C151—41no—
57#107×C151—21no—
58#106×C151C2×C411yescharacteristic
59#106×C151C2×C411yescharacteristic
60#103×C151—21no—
61#103×C151—21no—
62#102×C151—21no—
63#102×C151—21no—
64C24×C151SD1611yescharacteristic
65#41×C151—41no—
66#41×C151—41no—
67#41×C151—41no—
68#41×C151—41no—
69C2×Q8×C151—21no—
70C2×D4×C151—21no—
71C2×D4×C151—41no—
72C2×D4×C151—41no—
73C2×D4×C151—41no—
74C22×C4×C151—21no—
75C22×C4×C151—21no—
76C22×C4×C151—21no—
77C22×C4×C151—21no—
78C22×C4×C151—41no—
79C22×C4×C151C22⋊C411yescharacteristic
80C22×C4×C151C22⋊C411yescharacteristic
81C22×C4×C151D811yescharacteristic
82C22×C4×C151D811yescharacteristic
83C22×C4×C151SD1611yescharacteristic
84C22×C4×C151C2×D411yescharacteristic
85Q16×C151—41no—
86SD16×C151—42no—
87D8×C151—41no—
88M16×C151—41no—
89M16×C151—41no—
90M16×C151—41no—
91M16×C151—41no—
92M16×C151—42no—
93M16×C151—42no—
94M16×C151—42no—
95M16×C151—42no—
96C2×C8×C151—21no—
97C2×C8×C151—21no—
98C2×C8×C151—21no—
99C2×C8×C151—21no—
100C2×C8×C151—24no—
101C2×C8×C151—42no—
102C2×C8×C151—42no—
103C2×C8×C151C22⋊C411yescharacteristic
104C2×C8×C151C22⋊C411yescharacteristic
105C2×C8×C151C22×C411yescharacteristic
106C2×C8×C151C2×D411yescharacteristic
107C4⋊C4×C151—21no—
108C4⋊C4×C151—21no—
109C4⋊C4×C151—41no—
110C4⋊C4×C151—41no—
111C22⋊C4×C151—41no—
112C22⋊C4×C151—41no—
113C22⋊C4×C151—41no—
114C22⋊C4×C151—41no—
115C22⋊C4×C151—41no—
116C42×C151—41no—
117C16×C151—42no—
118C23×C151—21no—
119C23×C151—21no—
120C23×C151—41no—
121C23×C151—81no—
122C23×C151#10211yescharacteristic
123C23×C151#10211yescharacteristic
124C23×C151C2×SD1611yescharacteristic
125Q8×C151—41no—
126Q8×C151—41no—
127D4×C151—41no—
128D4×C151—41no—
129D4×C151—82no—
130D4×C151—82no—
131D4×C151—81no—
132D4×C151—81no—
133C2×C4×C151—21no—
134C2×C4×C151—21no—
135C2×C4×C151—21no—
136C2×C4×C151—21no—
137C2×C4×C151—21no—
138C2×C4×C151—21no—
139C2×C4×C151—21no—
140C2×C4×C151—21no—
141C2×C4×C151—21no—
142C2×C4×C151—21no—
143C2×C4×C151—41no—
144C2×C4×C151—41no—
145C2×C4×C151—41no—
146C2×C4×C151—81no—
147C2×C4×C151—81no—
148C2×C4×C151#9911yescharacteristic
149C2×C4×C151#9911yescharacteristic
150C2×C4×C151#10211yescharacteristic
151C2×C4×C151#10211yescharacteristic
152C2×C4×C151#10411yescharacteristic
153C2×C4×C151#10411yescharacteristic
154C2×C4×C151C2×C22⋊C411yescharacteristic
155C2×C4×C151C2×D811yescharacteristic
156C8×C151—21no—
157C8×C151—21no—
158C8×C151—21no—
159C8×C151—21no—
160C8×C151—44no—
161C22×C151—21no—
162C22×C151—21no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—42no—
167C22×C151—81no—
168C22×C151—81no—
169C22×C151—81no—
170C22×C151—81no—
171C22×C151#32711yescharacteristic
172C22×C151#32711yescharacteristic
173C22×C151C2×#10211yescharacteristic
174C4×C151—21no—
175C4×C151—21no—
176C4×C151—81no—
177C4×C151—81no—
178C4×C151—81no—
179C4×C151#32711yescharacteristic
180C4×C151#32711yescharacteristic
181C4×C151C2×#9911yescharacteristic
182C4×C151C2×#10411yescharacteristic
183C2×C151—21no—
184C2×C151—21no—
185C2×C151—21no—
186C2×C151—41no—
187C2×C151—41no—
188C2×C151—161no—
189C2×C151C2×#32711yescharacteristic
190#11688C15111yesmaximal, characteristic, direct product factor, Sylow
191C151#1168811yescharacteristic, direct product factor, Sylow
192#3054C2×C15111yescharacteristic
193C2×#349C2×C15111yescharacteristic, complemented
194C2×#338C2×C15111yescharacteristic, complemented
195#1342C2×C15112yescomplemented
196#1341C2×C15112yescomplemented
197C2×#135C4×C15111yescharacteristic
198C22×M16—21no—
199C22×M16C22×C15111yescharacteristic
200#525—21no—
201C2×M32—21no—
202#470C4×C15111yescharacteristic
203#470C22×C15111yescharacteristic
204#469C4×C15111yescharacteristic
205#469C22×C15111yescharacteristic
206#468—21no—
207#468—21no—
208#427C4×C15111yescharacteristic
209#416—21no—
210#349—21no—
211#349C22×C15112yes—
212#338—21no—
213#338C22×C15112yes—
214C2×#41—21no—
215C23×C4D4×C15111yescharacteristic
216#135—41no—
217#135—41no—
218C2×Q16C2×C4×C15111yescharacteristic
219C2×SD16—21no—
220C2×D8C2×C4×C15111yescharacteristic
221C2×M16—22no—
222C2×M16—22no—
223C2×M16—41no—
224C2×M16—41no—
225C2×M16—41no—
226C2×M16—41no—
227C2×M16—41no—
228C2×M16—41no—
229C2×M16C2×C4×C15111yescharacteristic
230C2×M16D4×C15111yescharacteristic
231C2×M16D4×C15111yescharacteristic
232C2×M16C23×C15111yescharacteristic
233C22×C8—22no—
234C22×C8C2×C4×C15111yescharacteristic
235C22×C8D4×C15111yescharacteristic
236#123—41no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239#121—21no—
240#121—21no—
241#120—41no—
242C4×D4—41no—
243C4×D4—41no—
244#117—21no—
245M32—22no—
246M32—41no—
247C2×C16—41no—
248#107—21no—
249#106C2×C4×C15111yescharacteristic
250#106C2×C4×C15111yescharacteristic
251#103—21no—
252#103—21no—
253#102—21no—
254#102—21no—
255C24SD16×C15111yescharacteristic
256#41—41no—
257#41—41no—
258#41—41no—
259#41—41no—
260C2×Q8—21no—
261C2×D4—21no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—41no—
270C22×C4C22⋊C4×C15111yescharacteristic
271C22×C4C22⋊C4×C15111yescharacteristic
272C22×C4D8×C15111yescharacteristic
273C22×C4D8×C15111yescharacteristic
274C22×C4SD16×C15111yescharacteristic
275C22×C4C2×D4×C15111yescharacteristic
276Q16—41no—
277SD16—42no—
278D8—41no—
279M16—41no—
280M16—41no—
281M16—41no—
282M16—41no—
283M16—42no—
284M16—42no—
285M16—42no—
286M16—42no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—21no—
291C2×C8—24no—
292C2×C8—42no—
293C2×C8—42no—
294C2×C8C22⋊C4×C15111yescharacteristic
295C2×C8C22⋊C4×C15111yescharacteristic
296C2×C8C22×C4×C15111yescharacteristic
297C2×C8C2×D4×C15111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C42—41no—
308C16—42no—
309C23—21no—
310C23—21no—
311C23—41no—
312C23—81no—
313C23#102×C15111yescharacteristic
314C23#102×C15111yescharacteristic
315C23C2×SD16×C15111yescharacteristic
316Q8—41no—
317Q8—41no—
318D4—41no—
319D4—41no—
320D4—82no—
321D4—82no—
322D4—81no—
323D4—81no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4#99×C15111yescharacteristic
340C2×C4#99×C15111yescharacteristic
341C2×C4#102×C15111yescharacteristic
342C2×C4#102×C15111yescharacteristic
343C2×C4#104×C15111yescharacteristic
344C2×C4#104×C15111yescharacteristic
345C2×C4C2×C22⋊C4×C15111yescharacteristic
346C2×C4C2×D8×C15111yescharacteristic
347C8—21no—
348C8—21no—
349C8—21no—
350C8—21no—
351C8—44no—
352C22—21no—
353C22—21no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—42no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22#327×C15111yescharacteristic
363C22#327×C15111yescharacteristic
364C22C2×#102×C15111yescharacteristic
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4—81no—
370C4#327×C15111yescharacteristic
371C4#327×C15111yescharacteristic
372C4C2×#99×C15111yescharacteristic
373C4C2×#104×C15111yescharacteristic
374C2—21no—
375C2—21no—
376C2—21no—
377C2—41no—
378C2—41no—
379C2—161no—
380C2C2×#327×C15111yescharacteristic
subgroupG/H
centerC4×C151#327
commutatorC2×C8C22×C4×C151
Frattini, cosocleC2×M16C23×C151
socleC2×C151C2×#327
prime radical#3054×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×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×#338×C151C2semidirect
4. #1342×C151C2semidirect
5. #1341×C151C2semidirect
190. #11688C151direct (N × H)
191. C151#11688direct (N × H)
193. C2×#349C2×C151semidirect
194. C2×#338C2×C151semidirect
195. #1342C2×C151semidirect
196. #1341C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3054×C1512
C2×#349×C1512
C2×#338×C1512
#1342×C1512
#1341×C1512
#11688151