Finite Group Databasebeta

← C151×#18179 #50323104

Subgroups — C151×#18179 #50323104

Order 38656.

1250 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3496×C151C211yesmaximal, characteristic
2#3112×C151C212yesmaximal, complemented
3#2398×C151C211yesmaximal, characteristic, complemented
4#1607×C151C214yesmaximal, complemented
5#1601×C151C214yesmaximal, complemented
6#1505×C151C212yesmaximal, complemented
7#1466×C151C211yesmaximal, characteristic, complemented
8C2×H(5,𝔽2)×C151—21no—
9#547×C151—22no—
10#546×C151—24no—
11D42×C151—22no—
12#537×C151—21no—
13#534×C151C2214yes—
14#532×C151C2212yes—
15C2×#121×C151—22no—
16C2×C4×Q8×C151C2211yescharacteristic, complemented
17C2×C4×D4×C151C2211yescharacteristic
18#480×C151C2214yescomplemented
19#477×C151—22no—
20#460×C151—22no—
21#448×C151C2214yescomplemented
22#440×C151—24no—
23#432×C151C2212yescomplemented
24#400×C151—21no—
25#397×C151C2212yescomplemented
26#394×C151—21no—
27#393×C151C2212yescomplemented
28C4×C22⋊C4×C151—22no—
29#376×C151C2211yescharacteristic, complemented
30#327×C151C2218yescomplemented
31#323×C151C2214yescomplemented
32H(5,𝔽2)×C151—48no—
33C2×#41×C151—24no—
34C2×#41×C151—22no—
35C22×Q8×C151C2311yescharacteristic
36C22×D4×C151—24no—
37C22×D4×C151—22no—
38C22×D4×C151—24no—
39C22×D4×C151D411yescharacteristic
40C23×C4×C151D412yes—
41C2×SD16×C151—24no—
42C4⋊Q8×C151D412yes—
43#127×C151D412yes—
44#124×C151—22no—
45#123×C151—28no—
46C22⋊Q8×C151—24no—
47#121×C151—24no—
48#121×C151—24no—
49#121×C151—24no—
50#121×C151—22no—
51#121×C151—24no—
52#121×C151C2314yes—
53#120×C151—28no—
54C4×Q8×C151—22no—
55C4×Q8×C151—22no—
56C4×D4×C151—22no—
57C4×D4×C151—22no—
58C4×D4×C151—22no—
59C4×D4×C151D414yes—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C22⋊C4×C151—24no—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151C2312yes—
68C2×C42×C151—21no—
69C2×C42×C151—21no—
70C2×C42×C151C2311yescharacteristic
71#107×C151—24no—
72C4⋊C8×C151—22no—
73#103×C151—24no—
74#102×C151—24no—
75C22⋊C8×C151C2314yes—
76#97×C151—22no—
77#95×C151—21no—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151C2312yes—
81C24×C151—24no—
82C24×C151C2×D412yes—
83#41×C151—48no—
84#41×C151—416no—
85C2×Q8×C151—22no—
86C2×Q8×C151—22no—
87C2×Q8×C151—42no—
88C2×D4×C151—24no—
89C2×D4×C151—28no—
90C2×D4×C151—24no—
91C2×D4×C151—24no—
92C2×D4×C151—22no—
93C2×D4×C151—22no—
94C2×D4×C151—22no—
95C2×D4×C151—416no—
96C2×D4×C151—48no—
97C2×D4×C151—48no—
98C2×D4×C151—84no—
99C2×D4×C151C2×D414yes—
100C22×C4×C151—24no—
101C22×C4×C151—21no—
102C22×C4×C151—22no—
103C22×C4×C151—24no—
104C22×C4×C151—22no—
105C22×C4×C151—22no—
106C22×C4×C151—21no—
107C22×C4×C151—44no—
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151C2×D412yes—
111C22×C4×C151C2411yescharacteristic
112SD16×C151—48no—
113C2×C8×C151—24no—
114C4⋊C4×C151—24no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—22no—
117C4⋊C4×C151—22no—
118C4⋊C4×C151—42no—
119C4⋊C4×C151C2×D414yes—
120C22⋊C4×C151—28no—
121C22⋊C4×C151—24no—
122C22⋊C4×C151—24no—
123C22⋊C4×C151—24no—
124C22⋊C4×C151—44no—
125C22⋊C4×C151—44no—
126C42×C151—42no—
127C42×C151—41no—
128C42×C151—41no—
129C42×C151C2×D412yes—
130C42×C151C2×D412yes—
131C23×C151—22no—
132C23×C151—22no—
133C23×C151—24no—
134C23×C151—42no—
135C23×C151—42no—
136C23×C151—48no—
137C23×C151—84no—
138C23×C151—84no—
139C23×C151AGL(1,ℤ/8)14yes—
140C23×C151C22×D411yescharacteristic
141Q8×C151—24no—
142Q8×C151—42no—
143Q8×C151—44no—
144D4×C151—28no—
145D4×C151—44no—
146D4×C151—44no—
147D4×C151—416no—
148D4×C151—48no—
149D4×C151—44no—
150D4×C151—84no—
151C2×C4×C151—22no—
152C2×C4×C151—22no—
153C2×C4×C151—22no—
154C2×C4×C151—24no—
155C2×C4×C151—22no—
156C2×C4×C151—41no—
157C2×C4×C151—48no—
158C2×C4×C151—41no—
159C2×C4×C151—48no—
160C2×C4×C151—41no—
161C2×C4×C151—44no—
162C2×C4×C151—42no—
163C2×C4×C151—42no—
164C2×C4×C151—42no—
165C2×C4×C151—41no—
166C2×C4×C151—42no—
167C2×C4×C151—42no—
168C2×C4×C151—82no—
169C2×C4×C151#12012yes—
170C2×C4×C151#12011yescharacteristic
171C2×C4×C151#12011yescharacteristic
172C2×C4×C151C22×D412yes—
173C8×C151—44no—
174C22×C151—21no—
175C22×C151—21no—
176C22×C151—24no—
177C22×C151—44no—
178C22×C151—42no—
179C22×C151—42no—
180C22×C151—44no—
181C22×C151—44no—
182C22×C151—44no—
183C22×C151—82no—
184C22×C151—168no—
185C22×C151C2×#12011yescharacteristic
186C22×C151C2×AGL(1,ℤ/8)12yes—
187C4×C151—22no—
188C4×C151—21no—
189C4×C151—22no—
190C4×C151—44no—
191C4×C151—42no—
192C4×C151—42no—
193C4×C151—82no—
194C4×C151—81no—
195C4×C151#45512yes—
196C2×C151—22no—
197C2×C151—44no—
198C2×C151—84no—
199C2×C151#300311yescharacteristic
200C2×C151C2×#45511yescharacteristic
201C2×C151#302511yescharacteristic
202#18179C15111yesmaximal, characteristic, direct product factor, Sylow
203C151#1817911yescharacteristic, direct product factor, Sylow
204#3496C2×C15111yescharacteristic
205#3112C2×C15112yescomplemented
206#2398C2×C15111yescharacteristic, complemented
207#1607C2×C15114yescomplemented
208#1601C2×C15114yescomplemented
209#1505C2×C15112yescomplemented
210#1466C2×C15111yescharacteristic, complemented
211C2×H(5,𝔽2)—21no—
212#547—22no—
213#546—24no—
214D42—22no—
215#537—21no—
216#534C22×C15114yes—
217#532C22×C15112yes—
218C2×#121—22no—
219C2×C4×Q8C22×C15111yescharacteristic, complemented
220C2×C4×D4C22×C15111yescharacteristic
221#480C22×C15114yescomplemented
222#477—22no—
223#460—22no—
224#448C22×C15114yescomplemented
225#440—24no—
226#432C22×C15112yescomplemented
227#400—21no—
228#397C22×C15112yescomplemented
229#394—21no—
230#393C22×C15112yescomplemented
231C4×C22⋊C4—22no—
232#376C22×C15111yescharacteristic, complemented
233#327C22×C15118yescomplemented
234#323C22×C15114yescomplemented
235H(5,𝔽2)—48no—
236C2×#41—24no—
237C2×#41—22no—
238C22×Q8C23×C15111yescharacteristic
239C22×D4—24no—
240C22×D4—24no—
241C22×D4—22no—
242C22×D4D4×C15111yescharacteristic
243C23×C4D4×C15112yes—
244C2×SD16—24no—
245C4⋊Q8D4×C15112yes—
246#127D4×C15112yes—
247#124—22no—
248#123—28no—
249C22⋊Q8—24no—
250#121—24no—
251#121—24no—
252#121—24no—
253#121—22no—
254#121—24no—
255#121C23×C15114yes—
256#120—28no—
257C4×Q8—22no—
258C4×Q8—22no—
259C4×D4—22no—
260C4×D4—22no—
261C4×D4—22no—
262C4×D4D4×C15114yes—
263C2×C4⋊C4—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4D4×C15111yescharacteristic
266C2×C4⋊C4C23×C15111yescharacteristic
267C2×C22⋊C4—24no—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—22no—
270C2×C22⋊C4C23×C15112yes—
271C2×C42—21no—
272C2×C42—21no—
273C2×C42C23×C15111yescharacteristic
274#107—24no—
275C4⋊C8—22no—
276#103—24no—
277#102—24no—
278C22⋊C8C23×C15114yes—
279#97—22no—
280#95—21no—
281#95—22no—
282#95—22no—
283#95C23×C15112yes—
284C24—24no—
285C24C2×D4×C15112yes—
286#41—48no—
287#41—416no—
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—42no—
291C2×D4—24no—
292C2×D4—28no—
293C2×D4—24no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—416no—
299C2×D4—48no—
300C2×D4—48no—
301C2×D4—84no—
302C2×D4C2×D4×C15114yes—
303C22×C4—24no—
304C22×C4—21no—
305C22×C4—22no—
306C22×C4—24no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—44no—
311C22×C4C2×D4×C15111yescharacteristic
312C22×C4C2×D4×C15111yescharacteristic
313C22×C4C2×D4×C15112yes—
314C22×C4C24×C15111yescharacteristic
315SD16—48no—
316C2×C8—24no—
317C4⋊C4—24no—
318C4⋊C4—22no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—42no—
322C4⋊C4C2×D4×C15114yes—
323C22⋊C4—28no—
324C22⋊C4—24no—
325C22⋊C4—24no—
326C22⋊C4—24no—
327C22⋊C4—44no—
328C22⋊C4—44no—
329C42—42no—
330C42—41no—
331C42—41no—
332C42C2×D4×C15112yes—
333C42C2×D4×C15112yes—
334C23—22no—
335C23—22no—
336C23—24no—
337C23—42no—
338C23—42no—
339C23—48no—
340C23—84no—
341C23—84no—
342C23AGL(1,ℤ/8)×C15114yes—
343C23C22×D4×C15111yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—44no—
347D4—28no—
348D4—44no—
349D4—44no—
350D4—416no—
351D4—48no—
352D4—44no—
353D4—84no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—24no—
359C2×C4—41no—
360C2×C4—48no—
361C2×C4—48no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—44no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—82no—
372C2×C4#120×C15111yescharacteristic
373C2×C4#120×C15112yes—
374C2×C4#120×C15111yescharacteristic
375C2×C4C22×D4×C15112yes—
376C8—44no—
377C22—21no—
378C22—21no—
379C22—24no—
380C22—44no—
381C22—42no—
382C22—42no—
383C22—44no—
384C22—44no—
385C22—44no—
386C22—82no—
387C22—168no—
388C22C2×#120×C15111yescharacteristic
389C22C2×AGL(1,ℤ/8)×C15112yes—
390C4—22no—
391C4—21no—
392C4—22no—
393C4—44no—
394C4—42no—
395C4—42no—
396C4—82no—
397C4—81no—
398C4#455×C15112yes—
399C2—22no—
400C2—44no—
401C2—84no—
402C2#3003×C15111yescharacteristic
403C2C2×#455×C15111yescharacteristic
404C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3496×C151C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3112×C151C2semidirect
3. #2398×C151C2semidirect
4. #1607×C151C2semidirect
5. #1601×C151C2semidirect
6. #1505×C151C2semidirect
7. #1466×C151C2semidirect
16. C2×C4×Q8×C151C22semidirect
18. #480×C151C22semidirect
21. #448×C151C22semidirect
23. #432×C151C22semidirect
25. #397×C151C22semidirect
27. #393×C151C22semidirect
29. #376×C151C22semidirect
30. #327×C151C22semidirect
31. #323×C151C22semidirect
202. #18179C151direct (N × H)
203. C151#18179direct (N × H)
205. #3112C2×C151semidirect
206. #2398C2×C151semidirect
207. #1607C2×C151semidirect
208. #1601C2×C151semidirect
209. #1505C2×C151semidirect
210. #1466C2×C151semidirect
219. C2×C4×Q8C22×C151semidirect
221. #480C22×C151semidirect
224. #448C22×C151semidirect
226. #432C22×C151semidirect
228. #397C22×C151semidirect
230. #393C22×C151semidirect
232. #376C22×C151semidirect
233. #327C22×C151semidirect
234. #323C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3496×C1512
#3112×C1512
#2398×C1512
#1607×C1512
#1601×C1512
#1505×C1512
#1466×C1512
#18179151