Finite Group Databasebeta

← C151×#18373 #50323298

Subgroups — C151×#18373 #50323298

Order 38656.

1102 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3497×C151C211yesmaximal, characteristic
2#3234×C151C212yesmaximal, complemented
3#2634×C151C211yesmaximal, characteristic, complemented
4#1616×C151C214yesmaximal, complemented
5#1610×C151C214yesmaximal, complemented
6#1514×C151C212yesmaximal, complemented
7#1467×C151C211yesmaximal, characteristic, complemented
8C2×2−1+4×C151—21no—
9#550×C151—22no—
10D4×Q8×C151—22no—
11#548×C151—24no—
12#537×C151—21no—
13#537×C151C2214yes—
14#532×C151—22no—
15#532×C151C2212yes—
16C2×#125×C151C2211yescharacteristic
17C2×C4×Q8×C151C2211yescharacteristic
18#501×C151—22no—
19#490×C151—22no—
20#481×C151C2214yes—
21#480×C151C2214yes—
22#478×C151—24no—
23#432×C151C2212yes—
24#400×C151—21no—
25#400×C151C2212yes—
26#398×C151C2212yes—
27#395×C151—21no—
28#387×C151—22no—
29#383×C151C2211yescharacteristic
30#327×C151C2218yes—
31#324×C151C2214yes—
322−1+4×C151—48no—
33C2×#41×C151—24no—
34C2×#41×C151—24no—
35C2×#41×C151—22no—
36C22×Q8×C151—24no—
37C22×Q8×C151D411yescharacteristic
38C4⋊Q8×C151—22no—
39C4⋊Q8×C151D412yes—
40#127×C151—22no—
41#127×C151D412yes—
42#125×C151—22no—
43#125×C151—22no—
44#124×C151—24no—
45#124×C151—22no—
46C22⋊Q8×C151—24no—
47C22⋊Q8×C151—28no—
48#121×C151—24no—
49#121×C151—28no—
50#121×C151—22no—
51#121×C151—24no—
52#121×C151C2314yes—
53C4×Q8×C151—22no—
54C4×Q8×C151—22no—
55C4×D4×C151—24no—
56C4×D4×C151—24no—
57C4×D4×C151—22no—
58C4×D4×C151D414yes—
59C2×C4⋊C4×C151—21no—
60C2×C4⋊C4×C151—22no—
61C2×C4⋊C4×C151—21no—
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2311yescharacteristic
65C2×C4⋊C4×C151C2312yes—
66C2×C42×C151D412yes—
67C2×C42×C151C2311yescharacteristic
68#107×C151—24no—
69#106×C151—24no—
70C4⋊C8×C151—22no—
71#102×C151—24no—
72#102×C151—24no—
73C22⋊C8×C151C2314yes—
74#97×C151—22no—
75#95×C151—21no—
76#95×C151—21no—
77#95×C151—22no—
78#95×C151—22no—
79#95×C151—22no—
80#95×C151C2312yes—
81#41×C151—48no—
82#41×C151—48no—
83#41×C151—416no—
84#41×C151—48no—
85C2×Q8×C151—24no—
86C2×Q8×C151—22no—
87C2×Q8×C151—22no—
88C2×Q8×C151—24no—
89C2×Q8×C151—416no—
90C2×D4×C151—24no—
91C2×D4×C151—24no—
92C2×D4×C151—24no—
93C2×D4×C151—22no—
94C2×D4×C151—22no—
95C2×D4×C151C2×D414yes—
96C22×C4×C151—28no—
97C22×C4×C151—24no—
98C22×C4×C151—22no—
99C22×C4×C151—21no—
100C22×C4×C151—21no—
101C22×C4×C151C2×D411yescharacteristic
102C22×C4×C151C2×D412yes—
103C22×C4×C151C2×D412yes—
104C22×C4×C151C2×D411yescharacteristic
105C22×C4×C151C2411yescharacteristic
106C2×C8×C151—24no—
107C4⋊C4×C151—24no—
108C4⋊C4×C151—22no—
109C4⋊C4×C151—22no—
110C4⋊C4×C151—24no—
111C4⋊C4×C151—22no—
112C4⋊C4×C151—22no—
113C4⋊C4×C151—42no—
114C4⋊C4×C151—41no—
115C4⋊C4×C151—41no—
116C4⋊C4×C151—44no—
117C4⋊C4×C151C2×D414yes—
118C22⋊C4×C151—28no—
119C22⋊C4×C151—24no—
120C22⋊C4×C151—24no—
121C42×C151—22no—
122C42×C151—22no—
123C42×C151C2×D412yes—
124C42×C151C2×D412yes—
125C23×C151—24no—
126C23×C151C22×D411yescharacteristic
127Q8×C151—28no—
128Q8×C151—44no—
129Q8×C151—48no—
130D4×C151—44no—
131D4×C151—44no—
132D4×C151—48no—
133D4×C151—44no—
134D4×C151—48no—
135D4×C151—84no—
136C2×C4×C151—22no—
137C2×C4×C151—22no—
138C2×C4×C151—22no—
139C2×C4×C151—24no—
140C2×C4×C151—22no—
141C2×C4×C151—41no—
142C2×C4×C151—41no—
143C2×C4×C151—48no—
144C2×C4×C151—416no—
145C2×C4×C151—42no—
146C2×C4×C151—42no—
147C2×C4×C151—42no—
148C2×C4×C151—42no—
149C2×C4×C151—41no—
150C2×C4×C151—41no—
151C2×C4×C151—42no—
152C2×C4×C151—42no—
153C2×C4×C151#12012yes—
154C2×C4×C151#12011yescharacteristic
155C2×C4×C151#12011yescharacteristic
156C2×C4×C151AGL(1,ℤ/8)14yes—
157C2×C4×C151C22×D412yes—
158C8×C151—44no—
159C22×C151—21no—
160C22×C151—21no—
161C22×C151—44no—
162C22×C151—44no—
163C22×C151—44no—
164C22×C151C2×#12011yescharacteristic
165C22×C151C2×AGL(1,ℤ/8)12yes—
166C4×C151—22no—
167C4×C151—24no—
168C4×C151—21no—
169C4×C151—21no—
170C4×C151—22no—
171C4×C151—44no—
172C4×C151—42no—
173C4×C151—82no—
174C4×C151—81no—
175C4×C151—81no—
176C2×C151—22no—
177C2×C151—84no—
178C2×C151#300311yescharacteristic
179C2×C151#302011yescharacteristic
180C2×C151#302811yescharacteristic
181#18373C15111yesmaximal, characteristic, direct product factor, Sylow
182C151#1837311yescharacteristic, direct product factor, Sylow
183#3497C2×C15111yescharacteristic
184#3234C2×C15112yescomplemented
185#2634C2×C15111yescharacteristic, complemented
186#1616C2×C15114yescomplemented
187#1610C2×C15114yescomplemented
188#1514C2×C15112yescomplemented
189#1467C2×C15111yescharacteristic, complemented
190C2×2−1+4—21no—
191#550—22no—
192D4×Q8—22no—
193#548—24no—
194#537—21no—
195#537C22×C15114yes—
196#532—22no—
197#532C22×C15112yes—
198C2×#125C22×C15111yescharacteristic
199C2×C4×Q8C22×C15111yescharacteristic
200#501—22no—
201#490—22no—
202#481C22×C15114yes—
203#480C22×C15114yes—
204#478—24no—
205#432C22×C15112yes—
206#400—21no—
207#400C22×C15112yes—
208#398C22×C15112yes—
209#395—21no—
210#387—22no—
211#383C22×C15111yescharacteristic
212#327C22×C15118yes—
213#324C22×C15114yes—
2142−1+4—48no—
215C2×#41—24no—
216C2×#41—24no—
217C2×#41—22no—
218C22×Q8—24no—
219C22×Q8D4×C15111yescharacteristic
220C4⋊Q8—22no—
221C4⋊Q8D4×C15112yes—
222#127—22no—
223#127D4×C15112yes—
224#125—22no—
225#125—22no—
226#124—24no—
227#124—22no—
228C22⋊Q8—24no—
229C22⋊Q8—28no—
230#121—24no—
231#121—28no—
232#121—22no—
233#121—24no—
234#121C23×C15114yes—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×D4—24no—
238C4×D4—24no—
239C4×D4—22no—
240C4×D4D4×C15114yes—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—22no—
244C2×C4⋊C4D4×C15111yescharacteristic
245C2×C4⋊C4C23×C15111yescharacteristic
246C2×C4⋊C4C23×C15111yescharacteristic
247C2×C4⋊C4C23×C15112yes—
248C2×C42D4×C15112yes—
249C2×C42C23×C15111yescharacteristic
250#107—24no—
251#106—24no—
252C4⋊C8—22no—
253#102—24no—
254#102—24no—
255C22⋊C8C23×C15114yes—
256#97—22no—
257#95—21no—
258#95—21no—
259#95—22no—
260#95—22no—
261#95—22no—
262#95C23×C15112yes—
263#41—48no—
264#41—48no—
265#41—416no—
266#41—48no—
267C2×Q8—24no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—24no—
271C2×Q8—416no—
272C2×D4—24no—
273C2×D4—24no—
274C2×D4—24no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4C2×D4×C15114yes—
278C22×C4—28no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4C2×D4×C15111yescharacteristic
284C22×C4C2×D4×C15112yes—
285C22×C4C2×D4×C15112yes—
286C22×C4C2×D4×C15111yescharacteristic
287C22×C4C24×C15111yescharacteristic
288C2×C8—24no—
289C4⋊C4—24no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—42no—
298C4⋊C4—44no—
299C4⋊C4C2×D4×C15114yes—
300C22⋊C4—28no—
301C22⋊C4—24no—
302C22⋊C4—24no—
303C42—22no—
304C42—22no—
305C42C2×D4×C15112yes—
306C42C2×D4×C15112yes—
307C23—24no—
308C23C22×D4×C15111yescharacteristic
309Q8—28no—
310Q8—44no—
311Q8—48no—
312D4—44no—
313D4—44no—
314D4—48no—
315D4—44no—
316D4—48no—
317D4—84no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—48no—
326C2×C4—416no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4#120×C15111yescharacteristic
336C2×C4#120×C15111yescharacteristic
337C2×C4#120×C15112yes—
338C2×C4AGL(1,ℤ/8)×C15114yes—
339C2×C4C22×D4×C15112yes—
340C8—44no—
341C22—21no—
342C22—21no—
343C22—44no—
344C22—44no—
345C22—44no—
346C22C2×#120×C15111yescharacteristic
347C22C2×AGL(1,ℤ/8)×C15112yes—
348C4—22no—
349C4—24no—
350C4—21no—
351C4—21no—
352C4—22no—
353C4—44no—
354C4—42no—
355C4—82no—
356C4—81no—
357C4—81no—
358C2—22no—
359C2—84no—
360C2#3003×C15111yescharacteristic
361C2#3020×C15111yescharacteristic
362C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
prime radical#3497×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. #3234×C151C2semidirect
3. #2634×C151C2semidirect
4. #1616×C151C2semidirect
5. #1610×C151C2semidirect
6. #1514×C151C2semidirect
7. #1467×C151C2semidirect
181. #18373C151direct (N × H)
182. C151#18373direct (N × H)
184. #3234C2×C151semidirect
185. #2634C2×C151semidirect
186. #1616C2×C151semidirect
187. #1610C2×C151semidirect
188. #1514C2×C151semidirect
189. #1467C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3497×C1512
#3234×C1512
#2634×C1512
#1616×C1512
#1610×C1512
#1514×C1512
#1467×C1512
#18373151