Finite Group Databasebeta

← C151×#19214 #50324139

Subgroups — C151×#19214 #50324139

Order 38656.

658 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3209×C151C211yesmaximal, characteristic, complemented
2#3208×C151C211yesmaximal, characteristic
3C2×#486×C151C211yesmaximal, characteristic
4#2960×C151C211yesmaximal, characteristic, complemented
5#1702×C151C214yesmaximal, complemented
6#1682×C151C214yesmaximal, complemented
7#1564×C151C211yesmaximal, characteristic, complemented
8#1549×C151C211yesmaximal, characteristic, complemented
9#1545×C151C211yesmaximal, characteristic
10#533×C151C2211yescharacteristic
11C2×C4⋊Q8×C151C2211yescharacteristic
12C2×#127×C151C2211yescharacteristic
13#494×C151—21no—
14#492×C151—21no—
15#487×C151—21no—
16#486×C151—21no—
17#486×C151—21no—
18#486×C151—21no—
19#486×C151C2212yes—
20#486×C151C2212yes—
21#462×C151C2214yescomplemented
22#460×C151C2214yes—
23#451×C151—22no—
24#450×C151—22no—
25#446×C151—21no—
26#446×C151C2212yescomplemented
27C8×Q8×C151—21no—
28C8×Q8×C151C2212yescomplemented
29#431×C151C2211yescharacteristic
30#431×C151C2211yescharacteristic
31#424×C151—21no—
32#423×C151C2211yescharacteristic
33C2×#102×C151—21no—
34C2×#102×C151—21no—
35#405×C151—21no—
36C2×C4×C8×C151C2211yescharacteristic
37#335×C151C2212yescomplemented
38#334×C151C2212yescomplemented
39#332×C151C2214yescomplemented
40#331×C151C2214yes—
41C22×Q8×C151—21no—
42C22×D4×C151—21no—
43C22×D4×C151—21no—
44C22×D4×C151—21no—
45C2×Q16×C151—24no—
46C2×SD16×C151—24no—
47C2×M16×C151—21no—
48C22×C8×C151D411yescharacteristic
49C22×C8×C151D411yescharacteristic
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151—21no—
53C4⋊Q8×C151D411yescharacteristic
54C4⋊Q8×C151D411yescharacteristic
55C4⋊Q8×C151C2312yes—
56#127×C151—21no—
57#127×C151—21no—
58#127×C151—21no—
59#127×C151C2312yes—
60#125×C151—21no—
61C22⋊Q8×C151—21no—
62C22⋊Q8×C151D412yes—
63C4×Q8×C151—21no—
64C4×Q8×C151C2312yes—
65#117×C151—21no—
66C2×C4⋊C4×C151—21no—
67C2×C4⋊C4×C151—21no—
68C2×C42×C151C2311yescharacteristic
69C4⋊C8×C151—22no—
70C4⋊C8×C151—22no—
71C4⋊C8×C151—21no—
72C4⋊C8×C151C2312yes—
73C4⋊C8×C151C2312yes—
74C4⋊C8×C151C2312yes—
75#103×C151—24no—
76#102×C151—22no—
77#102×C151—22no—
78#102×C151—22no—
79#102×C151—22no—
80#102×C151—24no—
81C22⋊C8×C151—21no—
82C22⋊C8×C151—21no—
83#97×C151—22no—
84C4×C8×C151—22no—
85C4×C8×C151—21no—
86C4×C8×C151—21no—
87C4×C8×C151D411yescharacteristic
88C4×C8×C151D411yescharacteristic
89C4×C8×C151C2311yescharacteristic
90C4×C8×C151C2311yescharacteristic
91C24×C151—41no—
92C2×Q8×C151—21no—
93C2×Q8×C151—22no—
94C2×Q8×C151—41no—
95C2×Q8×C151—82no—
96C2×Q8×C151C2×D412yes—
97C2×D4×C151—22no—
98C2×D4×C151—22no—
99C2×D4×C151—22no—
100C2×D4×C151—41no—
101C2×D4×C151—41no—
102C2×D4×C151—41no—
103C2×D4×C151—42no—
104C2×D4×C151—42no—
105C2×D4×C151—82no—
106C2×D4×C151—82no—
107C22×C4×C151—41no—
108C22×C4×C151C2×D411yescharacteristic
109C22×C4×C151C2×D411yescharacteristic
110C22×C4×C151#4111yescharacteristic
111Q16×C151—84no—
112SD16×C151—84no—
113M16×C151—42no—
114C2×C8×C151—22no—
115C2×C8×C151—22no—
116C2×C8×C151—22no—
117C2×C8×C151—22no—
118C2×C8×C151—22no—
119C2×C8×C151C2×D411yescharacteristic
120C2×C8×C151C2×D411yescharacteristic
121C2×C8×C151C2×D411yescharacteristic
122C2×C8×C151C2×D411yescharacteristic
123C4⋊C4×C151—21no—
124C4⋊C4×C151—21no—
125C4⋊C4×C151—21no—
126C4⋊C4×C151—22no—
127C4⋊C4×C151—22no—
128C4⋊C4×C151—22no—
129C4⋊C4×C151—22no—
130C4⋊C4×C151—41no—
131C4⋊C4×C151—41no—
132C4⋊C4×C151C2×D412yes—
133C22⋊C4×C151—22no—
134C42×C151—22no—
135C42×C151C2×D411yescharacteristic
136C42×C151C2×D411yescharacteristic
137C42×C151#4111yescharacteristic
138C42×C151C2411yescharacteristic
139C23×C151—42no—
140C23×C151—82no—
141C23×C151—82no—
142C23×C151—82no—
143C23×C151#12111yescharacteristic
144Q8×C151—24no—
145Q8×C151—42no—
146Q8×C151—44no—
147Q8×C151—82no—
148D4×C151—42no—
149D4×C151—42no—
150D4×C151—44no—
151D4×C151—82no—
152D4×C151—82no—
153D4×C151—82no—
154D4×C151—82no—
155C2×C4×C151—22no—
156C2×C4×C151—22no—
157C2×C4×C151—22no—
158C2×C4×C151—22no—
159C2×C4×C151—42no—
160C2×C4×C151—82no—
161C2×C4×C151#12111yescharacteristic
162C2×C4×C151#12111yescharacteristic
163C2×C4×C151#12111yescharacteristic
164C2×C4×C151#13512yes—
165C2×C4×C151#13712yes—
166C2×C4×C151C22×D411yescharacteristic
167C2×C4×C151C22×D411yescharacteristic
168C2×C4×C151C2×#4111yescharacteristic
169C8×C151—21no—
170C8×C151—21no—
171C8×C151—21no—
172C8×C151—21no—
173C8×C151—42no—
174C8×C151—42no—
175C8×C151—42no—
176C22×C151—21no—
177C22×C151—21no—
178C22×C151—82no—
179C22×C151—82no—
180C22×C151—82no—
181C22×C151—164no—
182C22×C151#46412yes—
183C22×C151C2×#12111yescharacteristic
184C4×C151—21no—
185C4×C151—21no—
186C4×C151—42no—
187C4×C151—42no—
188C4×C151—82no—
189C4×C151#46412yes—
190C4×C151#47112yes—
191C4×C151C2×#13511yescharacteristic
192C4×C151C2×#13711yescharacteristic
193C4×C151#57612yes—
194C2×C151—22no—
195C2×C151—162no—
196C2×C151C2×#46411yescharacteristic
197C2×C151#305811yescharacteristic
198C2×C151C2×#47111yescharacteristic
199#19214C15111yesmaximal, characteristic, direct product factor, Sylow
200C151#1921411yescharacteristic, direct product factor, Sylow
201#3209C2×C15111yescharacteristic, complemented
202#3208C2×C15111yescharacteristic
203C2×#486C2×C15111yescharacteristic
204#2960C2×C15111yescharacteristic, complemented
205#1702C2×C15114yescomplemented
206#1682C2×C15114yescomplemented
207#1564C2×C15111yescharacteristic, complemented
208#1549C2×C15111yescharacteristic, complemented
209#1545C2×C15111yescharacteristic
210#533C22×C15111yescharacteristic
211C2×C4⋊Q8C22×C15111yescharacteristic
212C2×#127C22×C15111yescharacteristic
213#494—21no—
214#492—21no—
215#487—21no—
216#486—21no—
217#486—21no—
218#486—21no—
219#486C22×C15112yes—
220#486C22×C15112yes—
221#462C22×C15114yescomplemented
222#460C22×C15114yes—
223#451—22no—
224#450—22no—
225#446—21no—
226#446C22×C15112yescomplemented
227C8×Q8—21no—
228C8×Q8C22×C15112yescomplemented
229#431C22×C15111yescharacteristic
230#431C22×C15111yescharacteristic
231#424—21no—
232#423C22×C15111yescharacteristic
233C2×#102—21no—
234C2×#102—21no—
235#405—21no—
236C2×C4×C8C22×C15111yescharacteristic
237#335C22×C15112yescomplemented
238#334C22×C15112yescomplemented
239#332C22×C15114yescomplemented
240#331C22×C15114yes—
241C22×Q8—21no—
242C22×D4—21no—
243C22×D4—21no—
244C22×D4—21no—
245C2×Q16—24no—
246C2×SD16—24no—
247C2×M16—21no—
248C22×C8D4×C15111yescharacteristic
249C22×C8D4×C15111yescharacteristic
250C4⋊Q8—21no—
251C4⋊Q8—21no—
252C4⋊Q8—21no—
253C4⋊Q8D4×C15111yescharacteristic
254C4⋊Q8D4×C15111yescharacteristic
255C4⋊Q8C23×C15112yes—
256#127—21no—
257#127—21no—
258#127—21no—
259#127C23×C15112yes—
260#125—21no—
261C22⋊Q8—21no—
262C22⋊Q8D4×C15112yes—
263C4×Q8—21no—
264C4×Q8C23×C15112yes—
265#117—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C42C23×C15111yescharacteristic
269C4⋊C8—22no—
270C4⋊C8—22no—
271C4⋊C8—21no—
272C4⋊C8C23×C15112yes—
273C4⋊C8C23×C15112yes—
274C4⋊C8C23×C15112yes—
275#103—24no—
276#102—22no—
277#102—22no—
278#102—22no—
279#102—22no—
280#102—24no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283#97—22no—
284C4×C8—22no—
285C4×C8—21no—
286C4×C8—21no—
287C4×C8D4×C15111yescharacteristic
288C4×C8D4×C15111yescharacteristic
289C4×C8C23×C15111yescharacteristic
290C4×C8C23×C15111yescharacteristic
291C24—41no—
292C2×Q8—21no—
293C2×Q8—22no—
294C2×Q8—41no—
295C2×Q8—82no—
296C2×Q8C2×D4×C15112yes—
297C2×D4—22no—
298C2×D4—22no—
299C2×D4—22no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—42no—
304C2×D4—42no—
305C2×D4—82no—
306C2×D4—82no—
307C22×C4—41no—
308C22×C4C2×D4×C15111yescharacteristic
309C22×C4C2×D4×C15111yescharacteristic
310C22×C4#41×C15111yescharacteristic
311Q16—84no—
312SD16—84no—
313M16—42no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—22no—
319C2×C8C2×D4×C15111yescharacteristic
320C2×C8C2×D4×C15111yescharacteristic
321C2×C8C2×D4×C15111yescharacteristic
322C2×C8C2×D4×C15111yescharacteristic
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—22no—
327C4⋊C4—22no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4C2×D4×C15112yes—
333C22⋊C4—22no—
334C42—22no—
335C42C2×D4×C15111yescharacteristic
336C42C2×D4×C15111yescharacteristic
337C42#41×C15111yescharacteristic
338C42C24×C15111yescharacteristic
339C23—42no—
340C23—82no—
341C23—82no—
342C23—82no—
343C23#121×C15111yescharacteristic
344Q8—24no—
345Q8—42no—
346Q8—44no—
347Q8—82no—
348D4—42no—
349D4—42no—
350D4—44no—
351D4—82no—
352D4—82no—
353D4—82no—
354D4—82no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—42no—
360C2×C4—82no—
361C2×C4#121×C15111yescharacteristic
362C2×C4#121×C15111yescharacteristic
363C2×C4#121×C15111yescharacteristic
364C2×C4#135×C15112yes—
365C2×C4#137×C15112yes—
366C2×C4C22×D4×C15111yescharacteristic
367C2×C4C22×D4×C15111yescharacteristic
368C2×C4C2×#41×C15111yescharacteristic
369C8—21no—
370C8—21no—
371C8—21no—
372C8—21no—
373C8—42no—
374C8—42no—
375C8—42no—
376C22—21no—
377C22—21no—
378C22—82no—
379C22—82no—
380C22—82no—
381C22—164no—
382C22#464×C15112yes—
383C22C2×#121×C15111yescharacteristic
384C4—21no—
385C4—21no—
386C4—42no—
387C4—42no—
388C4—82no—
389C4#464×C15112yes—
390C4#471×C15112yes—
391C4C2×#135×C15111yescharacteristic
392C4C2×#137×C15111yescharacteristic
393C4#576×C15112yes—
394C2—22no—
395C2—162no—
396C2C2×#464×C15111yescharacteristic
397C2#3058×C15111yescharacteristic
398C2C2×#471×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#127×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3209×C151C2semidirect
4. #2960×C151C2semidirect
5. #1702×C151C2semidirect
6. #1682×C151C2semidirect
7. #1564×C151C2semidirect
8. #1549×C151C2semidirect
21. #462×C151C22semidirect
26. #446×C151C22semidirect
28. C8×Q8×C151C22semidirect
37. #335×C151C22semidirect
38. #334×C151C22semidirect
39. #332×C151C22semidirect
199. #19214C151direct (N × H)
200. C151#19214direct (N × H)
201. #3209C2×C151semidirect
204. #2960C2×C151semidirect
205. #1702C2×C151semidirect
206. #1682C2×C151semidirect
207. #1564C2×C151semidirect
208. #1549C2×C151semidirect
221. #462C22×C151semidirect
226. #446C22×C151semidirect
228. C8×Q8C22×C151semidirect
237. #335C22×C151semidirect
238. #334C22×C151semidirect
239. #332C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3209×C1512
#3208×C1512
C2×#486×C1512
#2960×C1512
#1702×C1512
#1682×C1512
#1564×C1512
#1549×C1512
#1545×C1512
#19214151