Finite Group Databasebeta

← C151×#19394 #50324319

Subgroups — C151×#19394 #50324319

Order 38656.

650 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3228×C151C211yesmaximal, characteristic, complemented
2#3109×C151C211yesmaximal, characteristic
3#3101×C151C211yesmaximal, characteristic, complemented
4#2972×C151C211yesmaximal, characteristic, complemented
5#1681×C151C212yesmaximal, complemented
6#1677×C151C212yesmaximal, complemented
7#1675×C151C212yesmaximal, complemented
8#1671×C151C212yesmaximal, complemented
9#1572×C151C211yesmaximal, characteristic, complemented
10#1554×C151C211yesmaximal, characteristic, complemented
11#1543×C151C211yesmaximal, characteristic, complemented
12#533×C151C2211yescharacteristic
13#532×C151C2211yescharacteristic
14C2×C4×D4×C151C2211yescharacteristic
15#500×C151C2211yescharacteristic, complemented
16#498×C151C2211yescharacteristic, complemented
17#486×C151C2211yescharacteristic, complemented
18#486×C151C2211yescharacteristic, complemented
19#483×C151—21no—
20#482×C151—22no—
21#481×C151—21no—
22#478×C151—22no—
23#476×C151C2212yes—
24#476×C151C2212yes—
25#461×C151C2212yes—
26#459×C151C2212yes—
27#450×C151—21no—
28#447×C151—21no—
29#442×C151—22no—
30C4×SD16×C151—22no—
31C8×D4×C151—22no—
32C8×D4×C151C2212yes—
33C8×D4×C151C2212yes—
34#432×C151C2211yescharacteristic
35#431×C151C2211yescharacteristic
36#431×C151C2211yescharacteristic
37#431×C151C2211yescharacteristic
38C2×C22⋊C8×C151—22no—
39#335×C151C2212yescomplemented
40#334×C151C2212yescomplemented
41#333×C151C2212yescomplemented
42#333×C151C2212yescomplemented
43#332×C151C2212yescomplemented
44#331×C151C2212yescomplemented
45C2×#41×C151—21no—
46C22×D4×C151D411yescharacteristic
47C23×C4×C151—21no—
48C2×SD16×C151—22no—
49C2×D8×C151—22no—
50C22×C8×C151—22no—
51C22×C8×C151—22no—
52C4⋊Q8×C151C2311yescharacteristic
53C4⋊Q8×C151C2311yescharacteristic
54C4⋊Q8×C151C2311yescharacteristic
55#127×C151C2311yescharacteristic
56#125×C151—21no—
57#124×C151—21no—
58C22⋊Q8×C151—21no—
59C22⋊Q8×C151—21no—
60#121×C151—21no—
61#121×C151—21no—
62C4×Q8×C151—21no—
63C4×Q8×C151—21no—
64C4×D4×C151—21no—
65C4×D4×C151—21no—
66C4×D4×C151—21no—
67C4×D4×C151—21no—
68C4×D4×C151D412yes—
69C4×D4×C151C2312yes—
70#117×C151—21no—
71C2×C4⋊C4×C151D411yescharacteristic
72C2×C22⋊C4×C151—21no—
73C2×C42×C151C2311yescharacteristic
74#107×C151—22no—
75#106×C151—22no—
76#106×C151—22no—
77#106×C151—22no—
78C4⋊C8×C151D412yes—
79C4⋊C8×C151C2312yes—
80C4⋊C8×C151C2312yes—
81C4⋊C8×C151C2312yes—
82#103×C151—22no—
83#102×C151—22no—
84#102×C151—22no—
85#102×C151—22no—
86#102×C151—22no—
87#102×C151—22no—
88C22⋊C8×C151—21no—
89C22⋊C8×C151—21no—
90C22⋊C8×C151—21no—
91C22⋊C8×C151—22no—
92C22⋊C8×C151—22no—
93C22⋊C8×C151D412yes—
94#97×C151—21no—
95C4×C8×C151—21no—
96C4×C8×C151—21no—
97C4×C8×C151C2311yescharacteristic
98C4×C8×C151C2311yescharacteristic
99C24×C151—21no—
100#41×C151—82no—
101C2×Q8×C151—21no—
102C2×Q8×C151—21no—
103C2×Q8×C151—21no—
104C2×D4×C151—24no—
105C2×D4×C151—21no—
106C2×D4×C151—21no—
107C2×D4×C151—21no—
108C2×D4×C151—21no—
109C2×D4×C151—41no—
110C2×D4×C151C2×D412yes—
111C22×C4×C151—21no—
112C22×C4×C151—22no—
113C22×C4×C151—22no—
114C22×C4×C151—41no—
115C22×C4×C151—82no—
116C22×C4×C151C2×D411yescharacteristic
117C22×C4×C151C2×D411yescharacteristic
118C22×C4×C151#4111yescharacteristic
119SD16×C151—44no—
120D8×C151—44no—
121C2×C8×C151—22no—
122C2×C8×C151—22no—
123C2×C8×C151—22no—
124C2×C8×C151—82no—
125C2×C8×C151—82no—
126C2×C8×C151C2×D412yes—
127C2×C8×C151C2×D412yes—
128C4⋊C4×C151—21no—
129C4⋊C4×C151—21no—
130C4⋊C4×C151—21no—
131C4⋊C4×C151—21no—
132C4⋊C4×C151—21no—
133C4⋊C4×C151—21no—
134C4⋊C4×C151—21no—
135C4⋊C4×C151—41no—
136C4⋊C4×C151—41no—
137C4⋊C4×C151C2×D412yes—
138C22⋊C4×C151—22no—
139C22⋊C4×C151—22no—
140C22⋊C4×C151—41no—
141C22⋊C4×C151—41no—
142C22⋊C4×C151—41no—
143C42×C151—41no—
144C42×C151C2×D411yescharacteristic
145C42×C151C2×D411yescharacteristic
146C42×C151#4111yescharacteristic
147C42×C151C2411yescharacteristic
148C23×C151—24no—
149C23×C151—22no—
150C23×C151—41no—
151C23×C151—81no—
152C23×C151—81no—
153C23×C151#12111yescharacteristic
154Q8×C151—42no—
155Q8×C151—81no—
156Q8×C151—81no—
157D4×C151—24no—
158D4×C151—22no—
159D4×C151—42no—
160D4×C151—42no—
161D4×C151—81no—
162D4×C151—82no—
163D4×C151#13514yes—
164C2×C4×C151—22no—
165C2×C4×C151—22no—
166C2×C4×C151—22no—
167C2×C4×C151—41no—
168C2×C4×C151—42no—
169C2×C4×C151—42no—
170C2×C4×C151—41no—
171C2×C4×C151—41no—
172C2×C4×C151—41no—
173C2×C4×C151—82no—
174C2×C4×C151—82no—
175C2×C4×C151—81no—
176C2×C4×C151#12111yescharacteristic
177C2×C4×C151#12111yescharacteristic
178C2×C4×C151#12111yescharacteristic
179C2×C4×C151C22×D411yescharacteristic
180C2×C4×C151C22×D411yescharacteristic
181C2×C4×C151C2×#4111yescharacteristic
182C8×C151—22no—
183C8×C151—22no—
184C8×C151—42no—
185C8×C151—42no—
186C8×C151—42no—
187C22×C151—21no—
188C22×C151—21no—
189C22×C151—24no—
190C22×C151—21no—
191C22×C151—42no—
192C22×C151—42no—
193C22×C151—84no—
194C22×C151—81no—
195C22×C151—81no—
196C22×C151—81no—
197C22×C151C2×#12111yescharacteristic
198C4×C151—21no—
199C4×C151—21no—
200C4×C151—21no—
201C4×C151—21no—
202C4×C151—42no—
203C4×C151—81no—
204C4×C151—81no—
205C4×C151—81no—
206C4×C151C2×#13512yes—
207C4×C151#57712yes—
208C2×C151—41no—
209C2×C151—44no—
210C2×C151—161no—
211C2×C151#304211yescharacteristic
212C2×C151#305011yescharacteristic
213C2×C151#306811yescharacteristic
214#19394C15111yesmaximal, characteristic, direct product factor, Sylow
215C151#1939411yescharacteristic, direct product factor, Sylow
216#3228C2×C15111yescharacteristic, complemented
217#3109C2×C15111yescharacteristic
218#3101C2×C15111yescharacteristic, complemented
219#2972C2×C15111yescharacteristic, complemented
220#1681C2×C15112yescomplemented
221#1677C2×C15112yescomplemented
222#1675C2×C15112yescomplemented
223#1671C2×C15112yescomplemented
224#1572C2×C15111yescharacteristic, complemented
225#1554C2×C15111yescharacteristic, complemented
226#1543C2×C15111yescharacteristic, complemented
227#533C22×C15111yescharacteristic
228#532C22×C15111yescharacteristic
229C2×C4×D4C22×C15111yescharacteristic
230#500C22×C15111yescharacteristic, complemented
231#498C22×C15111yescharacteristic, complemented
232#486C22×C15111yescharacteristic, complemented
233#486C22×C15111yescharacteristic, complemented
234#483—21no—
235#482—22no—
236#481—21no—
237#478—22no—
238#476C22×C15112yes—
239#476C22×C15112yes—
240#461C22×C15112yes—
241#459C22×C15112yes—
242#450—21no—
243#447—21no—
244#442—22no—
245C4×SD16—22no—
246C8×D4—22no—
247C8×D4C22×C15112yes—
248C8×D4C22×C15112yes—
249#432C22×C15111yescharacteristic
250#431C22×C15111yescharacteristic
251#431C22×C15111yescharacteristic
252#431C22×C15111yescharacteristic
253C2×C22⋊C8—22no—
254#335C22×C15112yescomplemented
255#334C22×C15112yescomplemented
256#333C22×C15112yescomplemented
257#333C22×C15112yescomplemented
258#332C22×C15112yescomplemented
259#331C22×C15112yescomplemented
260C2×#41—21no—
261C22×D4D4×C15111yescharacteristic
262C23×C4—21no—
263C2×SD16—22no—
264C2×D8—22no—
265C22×C8—22no—
266C22×C8—22no—
267C4⋊Q8C23×C15111yescharacteristic
268C4⋊Q8C23×C15111yescharacteristic
269C4⋊Q8C23×C15111yescharacteristic
270#127C23×C15111yescharacteristic
271#125—21no—
272#124—21no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—21no—
276#121—21no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C4×D4D4×C15112yes—
284C4×D4C23×C15112yes—
285#117—21no—
286C2×C4⋊C4D4×C15111yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C23×C15111yescharacteristic
289#107—22no—
290#106—22no—
291#106—22no—
292#106—22no—
293C4⋊C8D4×C15112yes—
294C4⋊C8C23×C15112yes—
295C4⋊C8C23×C15112yes—
296C4⋊C8C23×C15112yes—
297#103—22no—
298#102—22no—
299#102—22no—
300#102—22no—
301#102—22no—
302#102—22no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—22no—
307C22⋊C8—22no—
308C22⋊C8D4×C15112yes—
309#97—21no—
310C4×C8—21no—
311C4×C8—21no—
312C4×C8C23×C15111yescharacteristic
313C4×C8C23×C15111yescharacteristic
314C24—21no—
315#41—82no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×D4—24no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—41no—
325C2×D4C2×D4×C15112yes—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—41no—
330C22×C4—82no—
331C22×C4C2×D4×C15111yescharacteristic
332C22×C4C2×D4×C15111yescharacteristic
333C22×C4#41×C15111yescharacteristic
334SD16—44no—
335D8—44no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—82no—
340C2×C8—82no—
341C2×C8C2×D4×C15112yes—
342C2×C8C2×D4×C15112yes—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—21no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4C2×D4×C15112yes—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C42—41no—
359C42C2×D4×C15111yescharacteristic
360C42C2×D4×C15111yescharacteristic
361C42#41×C15111yescharacteristic
362C42C24×C15111yescharacteristic
363C23—24no—
364C23—22no—
365C23—41no—
366C23—81no—
367C23—81no—
368C23#121×C15111yescharacteristic
369Q8—42no—
370Q8—81no—
371Q8—81no—
372D4—24no—
373D4—22no—
374D4—42no—
375D4—42no—
376D4—81no—
377D4—82no—
378D4#135×C15114yes—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—82no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4#121×C15111yescharacteristic
392C2×C4#121×C15111yescharacteristic
393C2×C4#121×C15111yescharacteristic
394C2×C4C22×D4×C15111yescharacteristic
395C2×C4C22×D4×C15111yescharacteristic
396C2×C4C2×#41×C15111yescharacteristic
397C8—22no—
398C8—22no—
399C8—42no—
400C8—42no—
401C8—42no—
402C22—21no—
403C22—21no—
404C22—24no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—84no—
409C22—81no—
410C22—81no—
411C22—81no—
412C22C2×#121×C15111yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—42no—
418C4—81no—
419C4—81no—
420C4—81no—
421C4C2×#135×C15112yes—
422C4#577×C15112yes—
423C2—41no—
424C2—44no—
425C2—161no—
426C2#3042×C15111yescharacteristic
427C2#3050×C15111yescharacteristic
428C2#3068×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#3109×C151C2
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. #3228×C151C2semidirect
3. #3101×C151C2semidirect
4. #2972×C151C2semidirect
5. #1681×C151C2semidirect
6. #1677×C151C2semidirect
7. #1675×C151C2semidirect
8. #1671×C151C2semidirect
9. #1572×C151C2semidirect
10. #1554×C151C2semidirect
11. #1543×C151C2semidirect
15. #500×C151C22semidirect
16. #498×C151C22semidirect
17. #486×C151C22semidirect
18. #486×C151C22semidirect
39. #335×C151C22semidirect
40. #334×C151C22semidirect
41. #333×C151C22semidirect
42. #333×C151C22semidirect
43. #332×C151C22semidirect
44. #331×C151C22semidirect
214. #19394C151direct (N × H)
215. C151#19394direct (N × H)
216. #3228C2×C151semidirect
218. #3101C2×C151semidirect
219. #2972C2×C151semidirect
220. #1681C2×C151semidirect
221. #1677C2×C151semidirect
222. #1675C2×C151semidirect
223. #1671C2×C151semidirect
224. #1572C2×C151semidirect
225. #1554C2×C151semidirect
226. #1543C2×C151semidirect
230. #500C22×C151semidirect
231. #498C22×C151semidirect
232. #486C22×C151semidirect
233. #486C22×C151semidirect
254. #335C22×C151semidirect
255. #334C22×C151semidirect
256. #333C22×C151semidirect
257. #333C22×C151semidirect
258. #332C22×C151semidirect
259. #331C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3228×C1512
#3109×C1512
#3101×C1512
#2972×C1512
#1681×C1512
#1677×C1512
#1675×C1512
#1671×C1512
#1572×C1512
#1554×C1512
#1543×C1512
#19394151