Finite Group Databasebeta

← C151×#19365 #50324290

Subgroups — C151×#19365 #50324290

Order 38656.

584 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3239×C151C211yesmaximal, characteristic
2#3238×C151C211yesmaximal, characteristic
3C2×#487×C151C211yesmaximal, characteristic, complemented
4#2966×C151C211yesmaximal, characteristic
5#1704×C151C212yesmaximal, complemented
6#1703×C151C212yesmaximal, complemented
7#1684×C151C212yesmaximal, complemented
8#1683×C151C212yesmaximal, complemented
9#1568×C151C211yesmaximal, characteristic, complemented
10#1558×C151C211yesmaximal, characteristic, complemented
11#1556×C151C211yesmaximal, characteristic, complemented
12C2×C4⋊Q8×C151C2211yescharacteristic
13C2×C4⋊Q8×C151C2211yescharacteristic
14#529×C151C2211yescharacteristic
15#501×C151—21no—
16#501×C151—21no—
17#489×C151—21no—
18#489×C151—21no—
19#487×C151—21no—
20#487×C151—21no—
21#487×C151C2212yes—
22#487×C151C2212yes—
23#484×C151—21no—
24#483×C151—21no—
25#481×C151—21no—
26#480×C151—21no—
27#477×C151C2212yes—
28#476×C151C2212yes—
29#475×C151C2212yes—
30#474×C151C2212yes—
31#446×C151C2211yescharacteristic
32C8×Q8×C151C2211yescharacteristic
33#436×C151C2211yescharacteristic
34#435×C151—21no—
35C8×D4×C151—21no—
36C8×D4×C151C2211yescharacteristic
37#433×C151—21no—
38#432×C151C2211yescharacteristic
39#432×C151C2211yescharacteristic
40#432×C151C2211yescharacteristic
41C2×#103×C151—21no—
42C2×#103×C151—21no—
43#405×C151—21no—
44C2×C4×C8×C151C2211yescharacteristic
45#335×C151C2212yes—
46#334×C151C2212yes—
47#333×C151C2212yes—
48#333×C151C2212yes—
49#332×C151C2212yes—
50#332×C151C2212yes—
51C22×Q8×C151—21no—
52C22×Q8×C151—21no—
53C2×M16×C151—21no—
54C22×C8×C151—21no—
55C22×C8×C151D411yescharacteristic
56C22×C8×C151D411yescharacteristic
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151—21no—
61C4⋊Q8×C151—21no—
62C4⋊Q8×C151—21no—
63C4⋊Q8×C151C2312yes—
64C4⋊Q8×C151C2312yes—
65#126×C151—21no—
66#125×C151D411yescharacteristic
67#124×C151D411yescharacteristic
68#123×C151—21no—
69C22⋊Q8×C151D411yescharacteristic
70#121×C151D411yescharacteristic
71C4×Q8×C151C2311yescharacteristic
72C4×D4×C151—21no—
73C4×D4×C151C2311yescharacteristic
74#117×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C42×C151C2311yescharacteristic
80#107×C151—22no—
81#107×C151—22no—
82#106×C151—22no—
83#106×C151—22no—
84C4⋊C8×C151—21no—
85C4⋊C8×C151—21no—
86C4⋊C8×C151C2311yescharacteristic
87C4⋊C8×C151C2311yescharacteristic
88C4⋊C8×C151C2312yes—
89C4⋊C8×C151C2312yes—
90#103×C151—22no—
91#103×C151—22no—
92#103×C151—22no—
93#103×C151—22no—
94#103×C151—22no—
95#103×C151—22no—
96#102×C151—22no—
97#102×C151—22no—
98C22⋊C8×C151—21no—
99C22⋊C8×C151—21no—
100C22⋊C8×C151—21no—
101C22⋊C8×C151—21no—
102C22⋊C8×C151—21no—
103#97×C151—21no—
104#97×C151—21no—
105#97×C151—21no—
106#97×C151—21no—
107C4×C8×C151—21no—
108C4×C8×C151D411yescharacteristic
109C4×C8×C151D411yescharacteristic
110C4×C8×C151C2311yescharacteristic
111C4×C8×C151C2311yescharacteristic
112C2×Q8×C151—22no—
113C2×Q8×C151—22no—
114C2×Q8×C151—42no—
115C2×Q8×C151—42no—
116C2×Q8×C151—41no—
117C2×Q8×C151—41no—
118C2×Q8×C151—82no—
119C2×Q8×C151C2×D411yescharacteristic
120C2×D4×C151—21no—
121C2×D4×C151C2×D411yescharacteristic
122C22×C4×C151—21no—
123C22×C4×C151—41no—
124C22×C4×C151—41no—
125C22×C4×C151C2×D411yescharacteristic
126C22×C4×C151C2×D411yescharacteristic
127C22×C4×C151#4111yescharacteristic
128M16×C151—42no—
129C2×C8×C151—21no—
130C2×C8×C151—21no—
131C2×C8×C151—22no—
132C2×C8×C151—22no—
133C2×C8×C151—41no—
134C2×C8×C151—41no—
135C2×C8×C151—42no—
136C2×C8×C151C2×D411yescharacteristic
137C2×C8×C151C2×D411yescharacteristic
138C2×C8×C151C2×D411yescharacteristic
139C2×C8×C151C2×D411yescharacteristic
140C4⋊C4×C151—21no—
141C4⋊C4×C151—21no—
142C4⋊C4×C151—21no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—22no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—22no—
148C4⋊C4×C151—41no—
149C4⋊C4×C151—41no—
150C4⋊C4×C151—41no—
151C4⋊C4×C151—41no—
152C4⋊C4×C151C2×D411yescharacteristic
153C4⋊C4×C151C2×D411yescharacteristic
154C22⋊C4×C151—21no—
155C22⋊C4×C151—21no—
156C22⋊C4×C151—21no—
157C22⋊C4×C151—21no—
158C22⋊C4×C151—21no—
159C42×C151—21no—
160C42×C151C2×D411yescharacteristic
161C42×C151C2×D411yescharacteristic
162C42×C151#4111yescharacteristic
163C42×C151C2411yescharacteristic
164C23×C151—21no—
165C23×C151#12111yescharacteristic
166Q8×C151—22no—
167Q8×C151—42no—
168Q8×C151—42no—
169Q8×C151—82no—
170Q8×C151—82no—
171Q8×C151—82no—
172D4×C151—22no—
173D4×C151—42no—
174C2×C4×C151—22no—
175C2×C4×C151—21no—
176C2×C4×C151—21no—
177C2×C4×C151—22no—
178C2×C4×C151—21no—
179C2×C4×C151—21no—
180C2×C4×C151—21no—
181C2×C4×C151—41no—
182C2×C4×C151—41no—
183C2×C4×C151—42no—
184C2×C4×C151—42no—
185C2×C4×C151—82no—
186C2×C4×C151—82no—
187C2×C4×C151#12111yescharacteristic
188C2×C4×C151#12111yescharacteristic
189C2×C4×C151#12111yescharacteristic
190C2×C4×C151C22×D411yescharacteristic
191C2×C4×C151C22×D411yescharacteristic
192C2×C4×C151C2×#4111yescharacteristic
193C8×C151—21no—
194C8×C151—21no—
195C8×C151—21no—
196C8×C151—21no—
197C8×C151—41no—
198C8×C151—41no—
199C8×C151—42no—
200C8×C151—42no—
201C22×C151—21no—
202C22×C151—21no—
203C22×C151—41no—
204C22×C151—41no—
205C22×C151—41no—
206C22×C151#47112yes—
207C22×C151C2×#12111yescharacteristic
208C4×C151—21no—
209C4×C151—21no—
210C4×C151—21no—
211C4×C151—21no—
212C4×C151—41no—
213C4×C151—41no—
214C4×C151—41no—
215C4×C151—82no—
216C4×C151—82no—
217C4×C151#57511yescharacteristic
218C4×C151#57511yescharacteristic
219C4×C151#57812yes—
220C2×C151—22no—
221C2×C151—81no—
222C2×C151#304011yescharacteristic
223C2×C151#305911yescharacteristic
224C2×C151C2×#47111yescharacteristic
225#19365C15111yesmaximal, characteristic, direct product factor, Sylow
226C151#1936511yescharacteristic, direct product factor, Sylow
227#3239C2×C15111yescharacteristic
228#3238C2×C15111yescharacteristic
229C2×#487C2×C15111yescharacteristic, complemented
230#2966C2×C15111yescharacteristic
231#1704C2×C15112yescomplemented
232#1703C2×C15112yescomplemented
233#1684C2×C15112yescomplemented
234#1683C2×C15112yescomplemented
235#1568C2×C15111yescharacteristic, complemented
236#1558C2×C15111yescharacteristic, complemented
237#1556C2×C15111yescharacteristic, complemented
238C2×C4⋊Q8C22×C15111yescharacteristic
239C2×C4⋊Q8C22×C15111yescharacteristic
240#529C22×C15111yescharacteristic
241#501—21no—
242#501—21no—
243#489—21no—
244#489—21no—
245#487—21no—
246#487—21no—
247#487C22×C15112yes—
248#487C22×C15112yes—
249#484—21no—
250#483—21no—
251#481—21no—
252#480—21no—
253#477C22×C15112yes—
254#476C22×C15112yes—
255#475C22×C15112yes—
256#474C22×C15112yes—
257#446C22×C15111yescharacteristic
258C8×Q8C22×C15111yescharacteristic
259#436C22×C15111yescharacteristic
260#435—21no—
261C8×D4—21no—
262C8×D4C22×C15111yescharacteristic
263#433—21no—
264#432C22×C15111yescharacteristic
265#432C22×C15111yescharacteristic
266#432C22×C15111yescharacteristic
267C2×#103—21no—
268C2×#103—21no—
269#405—21no—
270C2×C4×C8C22×C15111yescharacteristic
271#335C22×C15112yes—
272#334C22×C15112yes—
273#333C22×C15112yes—
274#333C22×C15112yes—
275#332C22×C15112yes—
276#332C22×C15112yes—
277C22×Q8—21no—
278C22×Q8—21no—
279C2×M16—21no—
280C22×C8—21no—
281C22×C8D4×C15111yescharacteristic
282C22×C8D4×C15111yescharacteristic
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8C23×C15112yes—
290C4⋊Q8C23×C15112yes—
291#126—21no—
292#125D4×C15111yescharacteristic
293#124D4×C15111yescharacteristic
294#123—21no—
295C22⋊Q8D4×C15111yescharacteristic
296#121D4×C15111yescharacteristic
297C4×Q8C23×C15111yescharacteristic
298C4×D4—21no—
299C4×D4C23×C15111yescharacteristic
300#117—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C42C23×C15111yescharacteristic
306#107—22no—
307#107—22no—
308#106—22no—
309#106—22no—
310C4⋊C8—21no—
311C4⋊C8—21no—
312C4⋊C8C23×C15111yescharacteristic
313C4⋊C8C23×C15111yescharacteristic
314C4⋊C8C23×C15112yes—
315C4⋊C8C23×C15112yes—
316#103—22no—
317#103—22no—
318#103—22no—
319#103—22no—
320#103—22no—
321#103—22no—
322#102—22no—
323#102—22no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329#97—21no—
330#97—21no—
331#97—21no—
332#97—21no—
333C4×C8—21no—
334C4×C8D4×C15111yescharacteristic
335C4×C8D4×C15111yescharacteristic
336C4×C8C23×C15111yescharacteristic
337C4×C8C23×C15111yescharacteristic
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—42no—
341C2×Q8—42no—
342C2×Q8—41no—
343C2×Q8—41no—
344C2×Q8—82no—
345C2×Q8C2×D4×C15111yescharacteristic
346C2×D4—21no—
347C2×D4C2×D4×C15111yescharacteristic
348C22×C4—21no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4C2×D4×C15111yescharacteristic
352C22×C4C2×D4×C15111yescharacteristic
353C22×C4#41×C15111yescharacteristic
354M16—42no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—22no—
358C2×C8—22no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—42no—
362C2×C8C2×D4×C15111yescharacteristic
363C2×C8C2×D4×C15111yescharacteristic
364C2×C8C2×D4×C15111yescharacteristic
365C2×C8C2×D4×C15111yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4C2×D4×C15111yescharacteristic
379C4⋊C4C2×D4×C15111yescharacteristic
380C22⋊C4—21no—
381C22⋊C4—21no—
382C22⋊C4—21no—
383C22⋊C4—21no—
384C22⋊C4—21no—
385C42—21no—
386C42C2×D4×C15111yescharacteristic
387C42C2×D4×C15111yescharacteristic
388C42#41×C15111yescharacteristic
389C42C24×C15111yescharacteristic
390C23—21no—
391C23#121×C15111yescharacteristic
392Q8—22no—
393Q8—42no—
394Q8—42no—
395Q8—82no—
396Q8—82no—
397Q8—82no—
398D4—22no—
399D4—42no—
400C2×C4—22no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—82no—
412C2×C4—82no—
413C2×C4#121×C15111yescharacteristic
414C2×C4#121×C15111yescharacteristic
415C2×C4#121×C15111yescharacteristic
416C2×C4C22×D4×C15111yescharacteristic
417C2×C4C22×D4×C15111yescharacteristic
418C2×C4C2×#41×C15111yescharacteristic
419C8—21no—
420C8—21no—
421C8—21no—
422C8—21no—
423C8—41no—
424C8—41no—
425C8—42no—
426C8—42no—
427C22—21no—
428C22—21no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22#471×C15112yes—
433C22C2×#121×C15111yescharacteristic
434C4—21no—
435C4—21no—
436C4—21no—
437C4—21no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—82no—
442C4—82no—
443C4#575×C15111yescharacteristic
444C4#575×C15111yescharacteristic
445C4#578×C15112yes—
446C2—22no—
447C2—81no—
448C2#3040×C15111yescharacteristic
449C2#3059×C15111yescharacteristic
450C2C2×#471×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#121
commutator, Frattini, cosocleC42C24×C151
prime radical#121×C151D4
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
3. C2×#487×C151C2semidirect
5. #1704×C151C2semidirect
6. #1703×C151C2semidirect
7. #1684×C151C2semidirect
8. #1683×C151C2semidirect
9. #1568×C151C2semidirect
10. #1558×C151C2semidirect
11. #1556×C151C2semidirect
225. #19365C151direct (N × H)
226. C151#19365direct (N × H)
229. C2×#487C2×C151semidirect
231. #1704C2×C151semidirect
232. #1703C2×C151semidirect
233. #1684C2×C151semidirect
234. #1683C2×C151semidirect
235. #1568C2×C151semidirect
236. #1558C2×C151semidirect
237. #1556C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3239×C1512
#3238×C1512
C2×#487×C1512
#2966×C1512
#1704×C1512
#1703×C1512
#1684×C1512
#1683×C1512
#1568×C1512
#1558×C1512
#1556×C1512
#19365151