Finite Group Databasebeta

← C151×#18909 #50323834

Subgroups — C151×#18909 #50323834

Order 38656.

882 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3507×C151C211yesmaximal, characteristic
2#3230×C151C211yesmaximal, characteristic, complemented
3#3206×C151C211yesmaximal, characteristic
4C2×#475×C151C211yesmaximal, characteristic, complemented
5#1650×C151C214yesmaximal, complemented
6#1643×C151C214yesmaximal, complemented
7#1542×C151C211yesmaximal, characteristic, complemented
8#1480×C151C211yesmaximal, characteristic
9#1479×C151C211yesmaximal, characteristic, complemented
10#559×C151—21no—
11#557×C151—21no—
12#556×C151—22no—
13#556×C151C2212yes—
14#554×C151C2212yes—
15#552×C151—22no—
16#539×C151—22no—
17#536×C151—21no—
18#533×C151C2211yescharacteristic
19#532×C151C2211yescharacteristic
20C2×C4⋊Q8×C151C2211yescharacteristic
21#529×C151—22no—
22#520×C151—21no—
23C2×C4×Q8×C151C2211yescharacteristic
24#500×C151C2212yes—
25#492×C151—21no—
26#487×C151—21no—
27#487×C151C2212yes—
28#484×C151—22no—
29#477×C151—22no—
30#475×C151—22no—
31#475×C151C2214yes—
32#461×C151C2214yes—
33#448×C151—22no—
34#431×C151C2211yescharacteristic
35#431×C151C2211yescharacteristic
36C2×#106×C151—21no—
37C2×C4⋊C8×C151C2211yescharacteristic
38C2×#103×C151—21no—
39#333×C151C2212yes—
40#332×C151C2212yes—
41Q8⋊C8×C151C2214yes—
42D4⋊C8×C151C2214yes—
43C2×#41×C151—21no—
44C22×Q8×C151—21no—
45C22×Q8×C151D411yescharacteristic
46C2×SD16×C151—24no—
47C22×C8×C151—21no—
48C4⋊Q8×C151—22no—
49C4⋊Q8×C151—21no—
50C4⋊Q8×C151—21no—
51C4⋊Q8×C151—21no—
52C4⋊Q8×C151D411yescharacteristic
53C4⋊Q8×C151C2312yes—
54C4⋊Q8×C151C2311yescharacteristic
55C4⋊Q8×C151C2311yescharacteristic
56#127×C151D411yescharacteristic
57#126×C151—24no—
58#126×C151—24no—
59#125×C151—24no—
60#125×C151—22no—
61#125×C151—21no—
62#124×C151—22no—
63#124×C151—22no—
64#124×C151—21no—
65#123×C151—24no—
66#123×C151—24no—
67C22⋊Q8×C151—21no—
68C22⋊Q8×C151—22no—
69C22⋊Q8×C151—22no—
70C22⋊Q8×C151—24no—
71C22⋊Q8×C151D412yes—
72#121×C151—21no—
73#121×C151D412yes—
74C4×Q8×C151—22no—
75C4×Q8×C151—22no—
76C4×Q8×C151—21no—
77C4×Q8×C151—21no—
78C4×Q8×C151—21no—
79C4×Q8×C151D412yes—
80C4×Q8×C151D412yes—
81C4×Q8×C151C2312yes—
82C4×D4×C151—24no—
83C4×D4×C151—22no—
84C4×D4×C151—22no—
85C4×D4×C151—21no—
86C4×D4×C151C2312yes—
87#117×C151—24no—
88#117×C151—21no—
89#117×C151—22no—
90C2×C4⋊C4×C151—21no—
91C2×C4⋊C4×C151—22no—
92C2×C4⋊C4×C151—21no—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151D411yescharacteristic
95C2×C42×C151—21no—
96C2×C42×C151C2311yescharacteristic
97#107×C151—24no—
98#106×C151—24no—
99C4⋊C8×C151—21no—
100C4⋊C8×C151—21no—
101C4⋊C8×C151C2312yes—
102C4⋊C8×C151C2312yes—
103#103×C151—24no—
104#103×C151—24no—
105#103×C151—24no—
106C22⋊C8×C151—21no—
107C22⋊C8×C151—21no—
108C4×C8×C151—21no—
109C4×C8×C151C2312yes—
110#41×C151—42no—
111#41×C151—42no—
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—21no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151—41no—
119C2×Q8×C151—82no—
120C2×Q8×C151C2×D412yes—
121C2×Q8×C151C2×D412yes—
122C2×D4×C151—22no—
123C2×D4×C151—21no—
124C2×D4×C151—21no—
125C2×D4×C151C2×D412yes—
126C22×C4×C151—21no—
127C22×C4×C151—24no—
128C22×C4×C151—21no—
129C22×C4×C151—22no—
130C22×C4×C151—41no—
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134SD16×C151—84no—
135C2×C8×C151—22no—
136C2×C8×C151—22no—
137C2×C8×C151—22no—
138C2×C8×C151—42no—
139C4⋊C4×C151—24no—
140C4⋊C4×C151—24no—
141C4⋊C4×C151—24no—
142C4⋊C4×C151—22no—
143C4⋊C4×C151—21no—
144C4⋊C4×C151—22no—
145C4⋊C4×C151—21no—
146C4⋊C4×C151—22no—
147C4⋊C4×C151—21no—
148C4⋊C4×C151—22no—
149C4⋊C4×C151—21no—
150C4⋊C4×C151—21no—
151C4⋊C4×C151—22no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—41no—
154C4⋊C4×C151—41no—
155C4⋊C4×C151C2×D412yes—
156C4⋊C4×C151C2×D412yes—
157C4⋊C4×C151C2×D412yes—
158C22⋊C4×C151—24no—
159C22⋊C4×C151—24no—
160C22⋊C4×C151—24no—
161C22⋊C4×C151—22no—
162C22⋊C4×C151—22no—
163C22⋊C4×C151—22no—
164C42×C151—24no—
165C42×C151—22no—
166C42×C151—22no—
167C42×C151—22no—
168C42×C151C2×D411yescharacteristic
169C42×C151C2×D411yescharacteristic
170C42×C151C2×D411yescharacteristic
171C42×C151C2411yescharacteristic
172C23×C151—22no—
173C23×C151#12011yescharacteristic
174Q8×C151—22no—
175Q8×C151—22no—
176Q8×C151—42no—
177Q8×C151—42no—
178Q8×C151—42no—
179Q8×C151—42no—
180Q8×C151—44no—
181Q8×C151—82no—
182D4×C151—24no—
183D4×C151—44no—
184D4×C151—42no—
185D4×C151—81no—
186C2×C4×C151—22no—
187C2×C4×C151—22no—
188C2×C4×C151—22no—
189C2×C4×C151—22no—
190C2×C4×C151—22no—
191C2×C4×C151—22no—
192C2×C4×C151—41no—
193C2×C4×C151—42no—
194C2×C4×C151—42no—
195C2×C4×C151—42no—
196C2×C4×C151—42no—
197C2×C4×C151—81no—
198C2×C4×C151—84no—
199C2×C4×C151—82no—
200C2×C4×C151#12011yescharacteristic
201C2×C4×C151#12011yescharacteristic
202C2×C4×C151#12011yescharacteristic
203C2×C4×C151#13512yes—
204C2×C4×C151#13712yes—
205C2×C4×C151C22×D411yescharacteristic
206C2×C4×C151C22×D411yescharacteristic
207C2×C4×C151C22×D411yescharacteristic
208C8×C151—42no—
209C8×C151—42no—
210C8×C151—42no—
211C22×C151—21no—
212C22×C151—21no—
213C22×C151—42no—
214C22×C151—42no—
215C22×C151—42no—
216C22×C151#45212yes—
217C22×C151C2×#12011yescharacteristic
218C4×C151—21no—
219C4×C151—21no—
220C4×C151—21no—
221C4×C151—42no—
222C4×C151—42no—
223C4×C151—42no—
224C4×C151—42no—
225C4×C151—42no—
226C4×C151—82no—
227C4×C151#45212yes—
228C4×C151C2×#13511yescharacteristic
229C4×C151C2×#13711yescharacteristic
230C4×C151#57712yes—
231C2×C151—22no—
232C2×C151—82no—
233C2×C151C2×#45211yescharacteristic
234C2×C151#301011yescharacteristic
235C2×C151#302211yescharacteristic
236#18909C15111yesmaximal, characteristic, direct product factor, Sylow
237C151#1890911yescharacteristic, direct product factor, Sylow
238#3507C2×C15111yescharacteristic
239#3230C2×C15111yescharacteristic, complemented
240#3206C2×C15111yescharacteristic
241C2×#475C2×C15111yescharacteristic, complemented
242#1650C2×C15114yescomplemented
243#1643C2×C15114yescomplemented
244#1542C2×C15111yescharacteristic, complemented
245#1480C2×C15111yescharacteristic
246#1479C2×C15111yescharacteristic, complemented
247#559—21no—
248#557—21no—
249#556—22no—
250#556C22×C15112yes—
251#554C22×C15112yes—
252#552—22no—
253#539—22no—
254#536—21no—
255#533C22×C15111yescharacteristic
256#532C22×C15111yescharacteristic
257C2×C4⋊Q8C22×C15111yescharacteristic
258#529—22no—
259#520—21no—
260C2×C4×Q8C22×C15111yescharacteristic
261#500C22×C15112yes—
262#492—21no—
263#487—21no—
264#487C22×C15112yes—
265#484—22no—
266#477—22no—
267#475—22no—
268#475C22×C15114yes—
269#461C22×C15114yes—
270#448—22no—
271#431C22×C15111yescharacteristic
272#431C22×C15111yescharacteristic
273C2×#106—21no—
274C2×C4⋊C8C22×C15111yescharacteristic
275C2×#103—21no—
276#333C22×C15112yes—
277#332C22×C15112yes—
278Q8⋊C8C22×C15114yes—
279D4⋊C8C22×C15114yes—
280C2×#41—21no—
281C22×Q8—21no—
282C22×Q8D4×C15111yescharacteristic
283C2×SD16—24no—
284C22×C8—21no—
285C4⋊Q8—22no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8D4×C15111yescharacteristic
290C4⋊Q8C23×C15112yes—
291C4⋊Q8C23×C15111yescharacteristic
292C4⋊Q8C23×C15111yescharacteristic
293#127D4×C15111yescharacteristic
294#126—24no—
295#126—24no—
296#125—24no—
297#125—22no—
298#125—21no—
299#124—22no—
300#124—22no—
301#124—21no—
302#123—24no—
303#123—24no—
304C22⋊Q8—22no—
305C22⋊Q8—22no—
306C22⋊Q8—24no—
307C22⋊Q8—21no—
308C22⋊Q8D4×C15112yes—
309#121—21no—
310#121D4×C15112yes—
311C4×Q8—22no—
312C4×Q8—22no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8D4×C15112yes—
317C4×Q8D4×C15112yes—
318C4×Q8C23×C15112yes—
319C4×D4—24no—
320C4×D4—22no—
321C4×D4—22no—
322C4×D4—21no—
323C4×D4C23×C15112yes—
324#117—24no—
325#117—21no—
326#117—22no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—22no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4D4×C15111yescharacteristic
332C2×C42—21no—
333C2×C42C23×C15111yescharacteristic
334#107—24no—
335#106—24no—
336C4⋊C8—21no—
337C4⋊C8—21no—
338C4⋊C8C23×C15112yes—
339C4⋊C8C23×C15112yes—
340#103—24no—
341#103—24no—
342#103—24no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C4×C8—21no—
346C4×C8C23×C15112yes—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8—22no—
353C2×Q8—22no—
354C2×Q8—22no—
355C2×Q8—41no—
356C2×Q8—82no—
357C2×Q8C2×D4×C15112yes—
358C2×Q8C2×D4×C15112yes—
359C2×D4—22no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4C2×D4×C15112yes—
363C22×C4—21no—
364C22×C4—24no—
365C22×C4—21no—
366C22×C4—22no—
367C22×C4—41no—
368C22×C4C2×D4×C15111yescharacteristic
369C22×C4C2×D4×C15111yescharacteristic
370C22×C4C2×D4×C15111yescharacteristic
371SD16—84no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—42no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—22no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4C2×D4×C15112yes—
393C4⋊C4C2×D4×C15112yes—
394C4⋊C4C2×D4×C15112yes—
395C22⋊C4—24no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—22no—
399C22⋊C4—22no—
400C22⋊C4—22no—
401C42—24no—
402C42—22no—
403C42—22no—
404C42—22no—
405C42C2×D4×C15111yescharacteristic
406C42C2×D4×C15111yescharacteristic
407C42C2×D4×C15111yescharacteristic
408C42C24×C15111yescharacteristic
409C23—22no—
410C23#120×C15111yescharacteristic
411Q8—22no—
412Q8—22no—
413Q8—42no—
414Q8—42no—
415Q8—42no—
416Q8—42no—
417Q8—44no—
418Q8—82no—
419D4—24no—
420D4—44no—
421D4—42no—
422D4—81no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—81no—
435C2×C4—84no—
436C2×C4—82no—
437C2×C4#120×C15111yescharacteristic
438C2×C4#120×C15111yescharacteristic
439C2×C4#120×C15111yescharacteristic
440C2×C4#135×C15112yes—
441C2×C4#137×C15112yes—
442C2×C4C22×D4×C15111yescharacteristic
443C2×C4C22×D4×C15111yescharacteristic
444C2×C4C22×D4×C15111yescharacteristic
445C8—42no—
446C8—42no—
447C8—42no—
448C22—21no—
449C22—21no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22#452×C15112yes—
454C22C2×#120×C15111yescharacteristic
455C4—21no—
456C4—21no—
457C4—21no—
458C4—42no—
459C4—42no—
460C4—42no—
461C4—42no—
462C4—42no—
463C4—82no—
464C4#452×C15112yes—
465C4C2×#135×C15111yescharacteristic
466C4C2×#137×C15111yescharacteristic
467C4#577×C15112yes—
468C2—22no—
469C2—82no—
470C2C2×#452×C15111yescharacteristic
471C2#3010×C15111yescharacteristic
472C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#532×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
2. #3230×C151C2semidirect
4. C2×#475×C151C2semidirect
5. #1650×C151C2semidirect
6. #1643×C151C2semidirect
7. #1542×C151C2semidirect
9. #1479×C151C2semidirect
236. #18909C151direct (N × H)
237. C151#18909direct (N × H)
239. #3230C2×C151semidirect
241. C2×#475C2×C151semidirect
242. #1650C2×C151semidirect
243. #1643C2×C151semidirect
244. #1542C2×C151semidirect
246. #1479C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3507×C1512
#3230×C1512
#3206×C1512
C2×#475×C1512
#1650×C1512
#1643×C1512
#1542×C1512
#1480×C1512
#1479×C1512
#18909151