Finite Group Databasebeta

← C151×#24071 #50328996

Subgroups — C151×#24071 #50328996

Order 38656.

1002 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#541×C151C211yesmaximal, characteristic
2C2×#484×C151C211yesmaximal, characteristic
3C2×#483×C151C211yesmaximal, characteristic
4#2317×C151C211yesmaximal, characteristic
5#2059×C151C212yesmaximal, complemented
6#2043×C151C212yesmaximal, complemented
7#1873×C151C211yesmaximal, characteristic
8#1873×C151C211yesmaximal, characteristic
9#1865×C151C212yesmaximal, complemented
10#1863×C151C212yesmaximal, complemented
11#1818×C151C211yesmaximal, characteristic
12#541×C151—24no—
13#541×C151—24no—
14C2×C4⋊Q8×C151C2211yescharacteristic
15C2×#126×C151—21no—
16C2×#126×C151—21no—
17C2×#125×C151—21no—
18C2×#125×C151—21no—
19C2×#125×C151C2211yescharacteristic
20C2×C22⋊Q8×C151C2211yescharacteristic
21C2×C22⋊Q8×C151C2211yescharacteristic
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24C2×#117×C151C2211yescharacteristic
25C2×#117×C151C2211yescharacteristic
26C22×C4⋊C4×C151C2211yescharacteristic
27#484×C151—24no—
28#483×C151—24no—
29C2×#107×C151C2212yes—
30C2×#106×C151C2212yes—
31C2×#103×C151C2212yes—
32C2×#103×C151C2212yes—
33C2×#103×C151C2212yes—
34C2×#103×C151C2212yes—
35C2×C22⋊C8×C151C2211yescharacteristic
36C2×C22⋊C8×C151C2211yescharacteristic
37#389×C151C2212yes—
38#389×C151C2212yes—
39#385×C151—21no—
40#385×C151—21no—
41#384×C151—21no—
42#382×C151—21no—
43#340×C151C2212yes—
44#340×C151C2212yes—
45#336×C151C2212yes—
46#336×C151C2212yes—
47C22×Q8×C151C2311yescharacteristic
48C22×Q8×C151C2311yescharacteristic
49C23×C4×C151—21no—
50C23×C4×C151C2311yescharacteristic
51C22×C8×C151C2312yes—
52C22×C8×C151C2312yes—
53C4⋊Q8×C151—22no—
54C4⋊Q8×C151—22no—
55#126×C151—28no—
56#126×C151—28no—
57#125×C151—28no—
58#125×C151—28no—
59#125×C151—22no—
60#125×C151—22no—
61C22⋊Q8×C151—22no—
62C22⋊Q8×C151—22no—
63C22⋊Q8×C151D414yes—
64C22⋊Q8×C151D414yes—
65C4×Q8×C151—22no—
66C4×Q8×C151—22no—
67C4×Q8×C151—22no—
68C4×Q8×C151—22no—
69#117×C151—22no—
70#117×C151—22no—
71#117×C151—24no—
72C2×C4⋊C4×C151—21no—
73C2×C4⋊C4×C151—21no—
74C2×C4⋊C4×C151—21no—
75C2×C4⋊C4×C151—21no—
76C2×C4⋊C4×C151—21no—
77C2×C4⋊C4×C151—21no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—22no—
82C2×C4⋊C4×C151—21no—
83C2×C4⋊C4×C151—22no—
84C2×C4⋊C4×C151—22no—
85C2×C4⋊C4×C151D411yescharacteristic
86C2×C4⋊C4×C151D411yescharacteristic
87C2×C4⋊C4×C151C2312yes—
88C2×C4⋊C4×C151C2311yescharacteristic
89C2×C4⋊C4×C151C2311yescharacteristic
90C2×C4⋊C4×C151C2312yes—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—21no—
93C2×C22⋊C4×C151—21no—
94C2×C22⋊C4×C151D411yescharacteristic
95C2×C22⋊C4×C151D411yescharacteristic
96C2×C42×C151—21no—
97C2×C42×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151C2311yescharacteristic
100C2×C42×C151C2311yescharacteristic
101#107×C151—24no—
102#106×C151—24no—
103#103×C151—24no—
104#103×C151—24no—
105#103×C151—24no—
106#103×C151—24no—
107C22⋊C8×C151—22no—
108C22⋊C8×C151—22no—
109#95×C151—22no—
110#95×C151—22no—
111C24×C151C2×D411yescharacteristic
112C2×Q8×C151—21no—
113C2×Q8×C151—21no—
114C2×Q8×C151—22no—
115C2×Q8×C151—22no—
116C2×Q8×C151—22no—
117C2×Q8×C151—22no—
118C2×Q8×C151C2×D412yes—
119C2×Q8×C151C2×D412yes—
120C22×C4×C151—22no—
121C22×C4×C151—22no—
122C22×C4×C151—22no—
123C22×C4×C151—21no—
124C22×C4×C151—21no—
125C22×C4×C151—21no—
126C22×C4×C151—21no—
127C22×C4×C151—22no—
128C22×C4×C151—42no—
129C22×C4×C151—82no—
130C22×C4×C151C2×D411yescharacteristic
131C22×C4×C151C2×D411yescharacteristic
132C22×C4×C151C2×D411yescharacteristic
133C22×C4×C151C2×D411yescharacteristic
134C22×C4×C151C2×D411yescharacteristic
135C22×C4×C151C2×D412yes—
136C22×C4×C151C2×D412yes—
137C22×C4×C151C2411yescharacteristic
138C2×C8×C151—22no—
139C2×C8×C151—22no—
140C2×C8×C151—22no—
141C2×C8×C151—22no—
142C2×C8×C151—22no—
143C2×C8×C151—22no—
144C4⋊C4×C151—24no—
145C4⋊C4×C151—24no—
146C4⋊C4×C151—24no—
147C4⋊C4×C151—24no—
148C4⋊C4×C151—24no—
149C4⋊C4×C151—24no—
150C4⋊C4×C151—24no—
151C4⋊C4×C151—24no—
152C4⋊C4×C151—22no—
153C4⋊C4×C151—22no—
154C4⋊C4×C151—21no—
155C4⋊C4×C151—21no—
156C4⋊C4×C151—22no—
157C4⋊C4×C151—22no—
158C4⋊C4×C151—22no—
159C4⋊C4×C151—42no—
160C4⋊C4×C151—82no—
161C4⋊C4×C151—82no—
162C4⋊C4×C151C2×D412yes—
163C4⋊C4×C151C2×D412yes—
164C4⋊C4×C151#4114yes—
165C22⋊C4×C151—24no—
166C22⋊C4×C151—24no—
167C22⋊C4×C151—24no—
168C22⋊C4×C151—22no—
169C22⋊C4×C151—22no—
170C42×C151—24no—
171C42×C151—24no—
172C42×C151—24no—
173C42×C151—21no—
174C42×C151—21no—
175C42×C151—21no—
176C42×C151—21no—
177C23×C151—21no—
178C23×C151—21no—
179C23×C151—22no—
180C23×C151—22no—
181C23×C151#12012yes—
182C23×C151C22×D411yescharacteristic
183Q8×C151—24no—
184Q8×C151—24no—
185Q8×C151—42no—
186Q8×C151—42no—
187C2×C4×C151—21no—
188C2×C4×C151—21no—
189C2×C4×C151—24no—
190C2×C4×C151—24no—
191C2×C4×C151—22no—
192C2×C4×C151—22no—
193C2×C4×C151—21no—
194C2×C4×C151—21no—
195C2×C4×C151—21no—
196C2×C4×C151—21no—
197C2×C4×C151—22no—
198C2×C4×C151—22no—
199C2×C4×C151—24no—
200C2×C4×C151—22no—
201C2×C4×C151—22no—
202C2×C4×C151—22no—
203C2×C4×C151—22no—
204C2×C4×C151—41no—
205C2×C4×C151—41no—
206C2×C4×C151—41no—
207C2×C4×C151—41no—
208C2×C4×C151—42no—
209C2×C4×C151—42no—
210C2×C4×C151—42no—
211C2×C4×C151—42no—
212C2×C4×C151—42no—
213C2×C4×C151—42no—
214C2×C4×C151—42no—
215C2×C4×C151—84no—
216C2×C4×C151#12012yes—
217C2×C4×C151C22×D411yescharacteristic
218C2×C4×C151C22×D411yescharacteristic
219C2×C4×C151C2×#4112yes—
220C2×C4×C1512−1+412yes—
221C8×C151—42no—
222C8×C151—42no—
223C22×C151—22no—
224C22×C151—22no—
225C22×C151—22no—
226C22×C151—42no—
227C22×C151—42no—
228C22×C151C2×#12011yescharacteristic
229C22×C151#52511yescharacteristic
230C22×C151#53611yescharacteristic
231C22×C151#57712yes—
232C22×C151#57812yes—
233C4×C151—22no—
234C4×C151—44no—
235C4×C151—42no—
236C4×C151—42no—
237C4×C151—41no—
238C4×C151—41no—
239C4×C151—42no—
240C4×C151—41no—
241C4×C151—41no—
242C4×C151—42no—
243C4×C151—82no—
244C4×C151#54712yes—
245C4×C151#54712yes—
246C2×C151—42no—
247C2×C151#240611yescharacteristic
248C2×C151#301011yescharacteristic
249C2×C151#301111yescharacteristic
250C2×C151#312012yes—
251C2×C151#324212yes—
252#24071C15111yesmaximal, characteristic, direct product factor, Sylow
253C151#2407111yescharacteristic, direct product factor, Sylow
254C2×#541C2×C15111yescharacteristic
255C2×#484C2×C15111yescharacteristic
256C2×#483C2×C15111yescharacteristic
257#2317C2×C15111yescharacteristic
258#2059C2×C15112yescomplemented
259#2043C2×C15112yescomplemented
260#1873C2×C15111yescharacteristic
261#1873C2×C15111yescharacteristic
262#1865C2×C15112yescomplemented
263#1863C2×C15112yescomplemented
264#1818C2×C15111yescharacteristic
265#541—24no—
266#541—24no—
267C2×C4⋊Q8C22×C15111yescharacteristic
268C2×#126—21no—
269C2×#126—21no—
270C2×#125—21no—
271C2×#125—21no—
272C2×#125C22×C15111yescharacteristic
273C2×C22⋊Q8C22×C15111yescharacteristic
274C2×C22⋊Q8C22×C15111yescharacteristic
275C2×C4×Q8C22×C15111yescharacteristic
276C2×C4×Q8C22×C15111yescharacteristic
277C2×#117C22×C15111yescharacteristic
278C2×#117C22×C15111yescharacteristic
279C22×C4⋊C4C22×C15111yescharacteristic
280#484—24no—
281#483—24no—
282C2×#107C22×C15112yes—
283C2×#106C22×C15112yes—
284C2×#103C22×C15112yes—
285C2×#103C22×C15112yes—
286C2×#103C22×C15112yes—
287C2×#103C22×C15112yes—
288C2×C22⋊C8C22×C15111yescharacteristic
289C2×C22⋊C8C22×C15111yescharacteristic
290#389C22×C15112yes—
291#389C22×C15112yes—
292#385—21no—
293#385—21no—
294#384—21no—
295#382—21no—
296#340C22×C15112yes—
297#340C22×C15112yes—
298#336C22×C15112yes—
299#336C22×C15112yes—
300C22×Q8C23×C15111yescharacteristic
301C22×Q8C23×C15111yescharacteristic
302C23×C4—21no—
303C23×C4C23×C15111yescharacteristic
304C22×C8C23×C15112yes—
305C22×C8C23×C15112yes—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308#126—28no—
309#126—28no—
310#125—28no—
311#125—28no—
312#125—22no—
313#125—22no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8D4×C15114yes—
317C22⋊Q8D4×C15114yes—
318C4×Q8—22no—
319C4×Q8—22no—
320C4×Q8—22no—
321C4×Q8—22no—
322#117—22no—
323#117—22no—
324#117—24no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—22no—
334C2×C4⋊C4—22no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4D4×C15111yescharacteristic
339C2×C4⋊C4D4×C15111yescharacteristic
340C2×C4⋊C4C23×C15112yes—
341C2×C4⋊C4C23×C15112yes—
342C2×C4⋊C4C23×C15111yescharacteristic
343C2×C4⋊C4C23×C15111yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4D4×C15111yescharacteristic
348C2×C22⋊C4D4×C15111yescharacteristic
349C2×C42—21no—
350C2×C42—21no—
351C2×C42—21no—
352C2×C42C23×C15111yescharacteristic
353C2×C42C23×C15111yescharacteristic
354#107—24no—
355#106—24no—
356#103—24no—
357#103—24no—
358#103—24no—
359#103—24no—
360C22⋊C8—22no—
361C22⋊C8—22no—
362#95—22no—
363#95—22no—
364C24C2×D4×C15111yescharacteristic
365C2×Q8—21no—
366C2×Q8—21no—
367C2×Q8—22no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—22no—
371C2×Q8C2×D4×C15112yes—
372C2×Q8C2×D4×C15112yes—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—42no—
382C22×C4—82no—
383C22×C4C2×D4×C15111yescharacteristic
384C22×C4C2×D4×C15111yescharacteristic
385C22×C4C2×D4×C15111yescharacteristic
386C22×C4C2×D4×C15111yescharacteristic
387C22×C4C2×D4×C15111yescharacteristic
388C22×C4C2×D4×C15112yes—
389C22×C4C2×D4×C15112yes—
390C22×C4C24×C15111yescharacteristic
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C4⋊C4—24no—
398C4⋊C4—24no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—24no—
404C4⋊C4—24no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—42no—
413C4⋊C4—82no—
414C4⋊C4—82no—
415C4⋊C4C2×D4×C15112yes—
416C4⋊C4C2×D4×C15112yes—
417C4⋊C4#41×C15114yes—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—24no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C42—24no—
424C42—24no—
425C42—24no—
426C42—21no—
427C42—21no—
428C42—21no—
429C42—21no—
430C23—21no—
431C23—21no—
432C23—22no—
433C23—22no—
434C23#120×C15112yes—
435C23C22×D4×C15111yescharacteristic
436Q8—24no—
437Q8—24no—
438Q8—42no—
439Q8—42no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—24no—
443C2×C4—24no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—84no—
469C2×C4#120×C15112yes—
470C2×C4C22×D4×C15111yescharacteristic
471C2×C4C22×D4×C15111yescharacteristic
472C2×C4C2×#41×C15112yes—
473C2×C42−1+4×C15112yes—
474C8—42no—
475C8—42no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—42no—
480C22—42no—
481C22C2×#120×C15111yescharacteristic
482C22#525×C15111yescharacteristic
483C22#536×C15111yescharacteristic
484C22#577×C15112yes—
485C22#578×C15112yes—
486C4—22no—
487C4—44no—
488C4—42no—
489C4—42no—
490C4—41no—
491C4—41no—
492C4—42no—
493C4—41no—
494C4—41no—
495C4—42no—
496C4—82no—
497C4#547×C15112yes—
498C4#547×C15112yes—
499C2—42no—
500C2#2406×C15111yescharacteristic
501C2#3010×C15111yescharacteristic
502C2#3011×C15111yescharacteristic
503C2#3120×C15112yes—
504C2#3242×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC24×C151C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
5. #2059×C151C2semidirect
6. #2043×C151C2semidirect
9. #1865×C151C2semidirect
10. #1863×C151C2semidirect
252. #24071C151direct (N × H)
253. C151#24071direct (N × H)
258. #2059C2×C151semidirect
259. #2043C2×C151semidirect
262. #1865C2×C151semidirect
263. #1863C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#541×C1512
C2×#484×C1512
C2×#483×C1512
#2317×C1512
#2059×C1512
#2043×C1512
#1873×C1512
#1865×C1512
#1863×C1512
#1818×C1512
#24071151