Finite Group Databasebeta

← C151×#18186 #50323111

Subgroups — C151×#18186 #50323111

Order 38656.

1198 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3497×C151C211yesmaximal, characteristic, complemented
2#3109×C151C212yesmaximal, complemented
3#2398×C151C211yesmaximal, characteristic, complemented
4#1616×C151C214yesmaximal, complemented
5#1598×C151C214yesmaximal, complemented
6#1505×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×C4×Q8×C151C2211yescharacteristic
17C2×C4×D4×C151C2211yescharacteristic
18#481×C151C2214yes—
19#476×C151—22no—
20#459×C151—22no—
21#447×C151C2214yes—
22#442×C151—24no—
23#432×C151C2212yes—
24#400×C151C2212yes—
25#397×C151—21no—
26#394×C151C2212yes—
27#393×C151—21no—
28C4×C22⋊C4×C151—22no—
29#376×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
38C22×D4×C151C2311yescharacteristic
39C23×C4×C151—21no—
40C2×D8×C151—24no—
41C4⋊Q8×C151—22no—
42C4⋊Q8×C151D412yes—
43#127×C151—22no—
44#127×C151D412yes—
45#124×C151—24no—
46#124×C151—22no—
47C22⋊Q8×C151—24no—
48C22⋊Q8×C151—28no—
49#121×C151—24no—
50#121×C151—28no—
51#121×C151—22no—
52#121×C151—24no—
53#121×C151C2314yes—
54C4×Q8×C151—22no—
55C4×Q8×C151—22no—
56C4×D4×C151—24no—
57C4×D4×C151—24no—
58C4×D4×C151—22no—
59C4×D4×C151—22no—
60C4×D4×C151—22no—
61C4×D4×C151D414yes—
62C2×C4⋊C4×C151D411yescharacteristic
63C2×C4⋊C4×C151C2311yescharacteristic
64C2×C4⋊C4×C151C2312yes—
65C2×C22⋊C4×C151—22no—
66C2×C22⋊C4×C151—22no—
67C2×C22⋊C4×C151—21no—
68C2×C42×C151—21no—
69C2×C42×C151D412yes—
70C2×C42×C151C2311yescharacteristic
71#106×C151—24no—
72C4⋊C8×C151—22no—
73#102×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—21no—
82#41×C151—48no—
83#41×C151—48no—
84#41×C151—416no—
85#41×C151—48no—
86C2×Q8×C151—24no—
87C2×Q8×C151—22no—
88C2×Q8×C151—22no—
89C2×Q8×C151—24no—
90C2×Q8×C151—416no—
91C2×D4×C151—24no—
92C2×D4×C151—24no—
93C2×D4×C151—24no—
94C2×D4×C151—22no—
95C2×D4×C151—22no—
96C2×D4×C151—22no—
97C2×D4×C151—42no—
98C2×D4×C151C2×D414yes—
99C22×C4×C151—28no—
100C22×C4×C151—24no—
101C22×C4×C151—21no—
102C22×C4×C151—22no—
103C22×C4×C151—44no—
104C22×C4×C151—41no—
105C22×C4×C151—41no—
106C22×C4×C151C2×D411yescharacteristic
107C22×C4×C151C2×D411yescharacteristic
108C22×C4×C151C2×D412yes—
109C22×C4×C151C2×D412yes—
110C22×C4×C151C2411yescharacteristic
111D8×C151—48no—
112C2×C8×C151—24no—
113C4⋊C4×C151—24no—
114C4⋊C4×C151—22no—
115C4⋊C4×C151—22no—
116C4⋊C4×C151—24no—
117C4⋊C4×C151—22no—
118C4⋊C4×C151C2×D414yes—
119C22⋊C4×C151—28no—
120C22⋊C4×C151—24no—
121C22⋊C4×C151—24no—
122C22⋊C4×C151—44no—
123C22⋊C4×C151—42no—
124C22⋊C4×C151—44no—
125C42×C151—22no—
126C42×C151—22no—
127C42×C151—42no—
128C42×C151C2×D412yes—
129C42×C151C2×D412yes—
130C23×C151—22no—
131C23×C151—24no—
132C23×C151—42no—
133C23×C151—41no—
134C23×C151—41no—
135C23×C151—42no—
136C23×C151C22×D411yescharacteristic
137Q8×C151—28no—
138Q8×C151—44no—
139Q8×C151—48no—
140D4×C151—24no—
141D4×C151—44no—
142D4×C151—44no—
143D4×C151—48no—
144D4×C151—42no—
145D4×C151—48no—
146D4×C151—44no—
147D4×C151—84no—
148C2×C4×C151—22no—
149C2×C4×C151—22no—
150C2×C4×C151—22no—
151C2×C4×C151—22no—
152C2×C4×C151—24no—
153C2×C4×C151—22no—
154C2×C4×C151—41no—
155C2×C4×C151—48no—
156C2×C4×C151—416no—
157C2×C4×C151—42no—
158C2×C4×C151—42no—
159C2×C4×C151—42no—
160C2×C4×C151—42no—
161C2×C4×C151—41no—
162C2×C4×C151—42no—
163C2×C4×C151—82no—
164C2×C4×C151—82no—
165C2×C4×C151#12012yes—
166C2×C4×C151#12011yescharacteristic
167C2×C4×C151#12011yescharacteristic
168C2×C4×C151AGL(1,ℤ/8)14yes—
169C2×C4×C151C22×D412yes—
170C8×C151—44no—
171C22×C151—21no—
172C22×C151—21no—
173C22×C151—44no—
174C22×C151—44no—
175C22×C151—44no—
176C22×C151—42no—
177C22×C151—44no—
178C22×C151—82no—
179C22×C151—81no—
180C22×C151—81no—
181C22×C151C2×#12011yescharacteristic
182C22×C151C2×AGL(1,ℤ/8)12yes—
183C4×C151—22no—
184C4×C151—24no—
185C4×C151—21no—
186C4×C151—22no—
187C4×C151—44no—
188C4×C151—42no—
189C4×C151—82no—
190C4×C151—81no—
191C4×C151#45412yes—
192C2×C151—22no—
193C2×C151—84no—
194C2×C151—82no—
195C2×C151#300311yescharacteristic
196C2×C151C2×#45411yescharacteristic
197C2×C151#302511yescharacteristic
198#18186C15111yesmaximal, characteristic, direct product factor, Sylow
199C151#1818611yescharacteristic, direct product factor, Sylow
200#3497C2×C15111yescharacteristic, complemented
201#3109C2×C15112yescomplemented
202#2398C2×C15111yescharacteristic, complemented
203#1616C2×C15114yescomplemented
204#1598C2×C15114yescomplemented
205#1505C2×C15112yescomplemented
206#1467C2×C15111yescharacteristic, complemented
207C2×2−1+4—21no—
208#550—22no—
209D4×Q8—22no—
210#548—24no—
211#537—21no—
212#537C22×C15114yes—
213#532—22no—
214#532C22×C15112yes—
215C2×C4×Q8C22×C15111yescharacteristic
216C2×C4×D4C22×C15111yescharacteristic
217#481C22×C15114yes—
218#476—22no—
219#459—22no—
220#447C22×C15114yes—
221#442—24no—
222#432C22×C15112yes—
223#400C22×C15112yes—
224#397—21no—
225#394C22×C15112yes—
226#393—21no—
227C4×C22⋊C4—22no—
228#376C22×C15111yescharacteristic
229#327C22×C15118yes—
230#324C22×C15114yes—
2312−1+4—48no—
232C2×#41—24no—
233C2×#41—24no—
234C2×#41—22no—
235C22×Q8—24no—
236C22×Q8D4×C15111yescharacteristic
237C22×D4C23×C15111yescharacteristic
238C23×C4—21no—
239C2×D8—24no—
240C4⋊Q8—22no—
241C4⋊Q8D4×C15112yes—
242#127—22no—
243#127D4×C15112yes—
244#124—24no—
245#124—22no—
246C22⋊Q8—24no—
247C22⋊Q8—28no—
248#121—24no—
249#121—28no—
250#121—22no—
251#121—24no—
252#121C23×C15114yes—
253C4×Q8—22no—
254C4×Q8—22no—
255C4×D4—24no—
256C4×D4—24no—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—22no—
260C4×D4D4×C15114yes—
261C2×C4⋊C4D4×C15111yescharacteristic
262C2×C4⋊C4C23×C15111yescharacteristic
263C2×C4⋊C4C23×C15112yes—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—22no—
266C2×C22⋊C4—22no—
267C2×C42—21no—
268C2×C42D4×C15112yes—
269C2×C42C23×C15111yescharacteristic
270#106—24no—
271C4⋊C8—22no—
272#102—24no—
273#102—24no—
274C22⋊C8C23×C15114yes—
275#97—22no—
276#95—21no—
277#95—22no—
278#95—22no—
279#95C23×C15112yes—
280C24—21no—
281#41—48no—
282#41—48no—
283#41—416no—
284#41—48no—
285C2×Q8—24no—
286C2×Q8—22no—
287C2×Q8—22no—
288C2×Q8—24no—
289C2×Q8—416no—
290C2×D4—24no—
291C2×D4—24no—
292C2×D4—24no—
293C2×D4—22no—
294C2×D4—22no—
295C2×D4—22no—
296C2×D4—42no—
297C2×D4C2×D4×C15114yes—
298C22×C4—28no—
299C22×C4—24no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—44no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C2×D4×C15111yescharacteristic
306C22×C4C2×D4×C15111yescharacteristic
307C22×C4C2×D4×C15112yes—
308C22×C4C2×D4×C15112yes—
309C22×C4C24×C15111yescharacteristic
310D8—48no—
311C2×C8—24no—
312C4⋊C4—24no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—24no—
316C4⋊C4—22no—
317C4⋊C4C2×D4×C15114yes—
318C22⋊C4—28no—
319C22⋊C4—24no—
320C22⋊C4—24no—
321C22⋊C4—44no—
322C22⋊C4—42no—
323C22⋊C4—44no—
324C42—22no—
325C42—22no—
326C42—42no—
327C42C2×D4×C15112yes—
328C42C2×D4×C15112yes—
329C23—22no—
330C23—24no—
331C23—42no—
332C23—41no—
333C23—41no—
334C23—42no—
335C23C22×D4×C15111yescharacteristic
336Q8—28no—
337Q8—44no—
338Q8—48no—
339D4—24no—
340D4—44no—
341D4—42no—
342D4—44no—
343D4—48no—
344D4—48no—
345D4—44no—
346D4—84no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—22no—
351C2×C4—22no—
352C2×C4—24no—
353C2×C4—41no—
354C2×C4—48no—
355C2×C4—416no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—82no—
363C2×C4—82no—
364C2×C4#120×C15111yescharacteristic
365C2×C4#120×C15112yes—
366C2×C4#120×C15111yescharacteristic
367C2×C4AGL(1,ℤ/8)×C15114yes—
368C2×C4C22×D4×C15112yes—
369C8—44no—
370C22—21no—
371C22—21no—
372C22—44no—
373C22—44no—
374C22—44no—
375C22—42no—
376C22—44no—
377C22—82no—
378C22—81no—
379C22—81no—
380C22C2×#120×C15111yescharacteristic
381C22C2×AGL(1,ℤ/8)×C15112yes—
382C4—22no—
383C4—24no—
384C4—21no—
385C4—22no—
386C4—44no—
387C4—42no—
388C4—82no—
389C4—81no—
390C4#454×C15112yes—
391C2—22no—
392C2—82no—
393C2—84no—
394C2#3003×C15111yescharacteristic
395C2C2×#454×C15111yescharacteristic
396C2#3025×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC22×C4C24×C151
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
1. #3497×C151C2semidirect
2. #3109×C151C2semidirect
3. #2398×C151C2semidirect
4. #1616×C151C2semidirect
5. #1598×C151C2semidirect
6. #1505×C151C2semidirect
7. #1467×C151C2semidirect
198. #18186C151direct (N × H)
199. C151#18186direct (N × H)
200. #3497C2×C151semidirect
201. #3109C2×C151semidirect
202. #2398C2×C151semidirect
203. #1616C2×C151semidirect
204. #1598C2×C151semidirect
205. #1505C2×C151semidirect
206. #1467C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3497×C1512
#3109×C1512
#2398×C1512
#1616×C1512
#1598×C1512
#1505×C1512
#1467×C1512
#18186151