Finite Group Databasebeta

← C151×#18923 #50323848

Subgroups — C151×#18923 #50323848

Order 38656.

1122 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3497×C151C211yesmaximal, characteristic
2#3227×C151C211yesmaximal, characteristic, complemented
3#3206×C151C211yesmaximal, characteristic, complemented
4C2×#475×C151C211yesmaximal, characteristic, complemented
5#1651×C151C214yesmaximal, complemented
6#1642×C151C214yesmaximal, complemented
7#1540×C151C211yesmaximal, characteristic, complemented
8#1480×C151C211yesmaximal, characteristic, complemented
9#1479×C151C211yesmaximal, characteristic, complemented
10C2×2−1+4×C151—21no—
11#550×C151—21no—
12#550×C151C2212yes—
13D4×Q8×C151—21no—
14D4×Q8×C151C2212yes—
15#548×C151—22no—
16#548×C151—22no—
17#537×C151—22no—
18#537×C151—21no—
19#532×C151—22no—
20#532×C151C2211yescharacteristic
21#532×C151C2211yescharacteristic
22C2×C4⋊Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24#498×C151C2212yes—
25#492×C151—21no—
26#487×C151—21no—
27#486×C151C2212yes—
28#481×C151—22no—
29#476×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#332×C151C2212yes—
40#331×C151C2212yes—
41Q8⋊C8×C151C2214yes—
42D4⋊C8×C151C2214yes—
432−1+4×C151—44no—
442−1+4×C151—44no—
45C2×#41×C151—24no—
46C2×#41×C151—22no—
47C2×#41×C151—21no—
48C2×#41×C151—21no—
49C2×#41×C151—22no—
50C22×Q8×C151—22no—
51C22×Q8×C151—22no—
52C22×Q8×C151—21no—
53C22×Q8×C151D411yescharacteristic
54C2×SD16×C151—24no—
55C22×C8×C151—21no—
56C4⋊Q8×C151—22no—
57C4⋊Q8×C151—21no—
58C4⋊Q8×C151—21no—
59C4⋊Q8×C151—21no—
60C4⋊Q8×C151D411yescharacteristic
61C4⋊Q8×C151C2312yes—
62C4⋊Q8×C151C2311yescharacteristic
63#127×C151—22no—
64#127×C151D411yescharacteristic
65#127×C151C2311yescharacteristic
66#124×C151—24no—
67#124×C151—21no—
68#124×C151—21no—
69C22⋊Q8×C151—24no—
70C22⋊Q8×C151—22no—
71C22⋊Q8×C151—24no—
72C22⋊Q8×C151—22no—
73#121×C151—24no—
74#121×C151—22no—
75#121×C151—24no—
76#121×C151—24no—
77#121×C151—21no—
78#121×C151—21no—
79#121×C151—22no—
80#121×C151D412yes—
81#121×C151D412yes—
82C4×Q8×C151—21no—
83C4×Q8×C151—21no—
84C4×Q8×C151D412yes—
85C4×Q8×C151C2312yes—
86C4×D4×C151—24no—
87C4×D4×C151—22no—
88C4×D4×C151—22no—
89C4×D4×C151—21no—
90C4×D4×C151—21no—
91C4×D4×C151D412yes—
92C4×D4×C151C2312yes—
93C2×C4⋊C4×C151—21no—
94C2×C4⋊C4×C151—21no—
95C2×C4⋊C4×C151—21no—
96C2×C4⋊C4×C151D411yescharacteristic
97C2×C42×C151—21no—
98C2×C42×C151C2311yescharacteristic
99#106×C151—24no—
100#106×C151—24no—
101C4⋊C8×C151—21no—
102C4⋊C8×C151—21no—
103C4⋊C8×C151C2312yes—
104C4⋊C8×C151C2312yes—
105#103×C151—24no—
106#103×C151—24no—
107#102×C151—24no—
108C22⋊C8×C151—21no—
109C22⋊C8×C151—21no—
110C4×C8×C151—21no—
111C4×C8×C151C2312yes—
112#41×C151—416no—
113#41×C151—44no—
114#41×C151—48no—
115#41×C151—44no—
116#41×C151—42no—
117#41×C151—42no—
118#41×C151—42no—
119#41×C151—42no—
120C2×Q8×C151—24no—
121C2×Q8×C151—21no—
122C2×Q8×C151—21no—
123C2×Q8×C151—22no—
124C2×Q8×C151—21no—
125C2×Q8×C151—22no—
126C2×Q8×C151—44no—
127C2×Q8×C151—48no—
128C2×Q8×C151—44no—
129C2×Q8×C151—41no—
130C2×Q8×C151—82no—
131C2×Q8×C151SD1614yescomplemented
132C2×Q8×C151C2×D412yes—
133C2×D4×C151—24no—
134C2×D4×C151—22no—
135C2×D4×C151—22no—
136C2×D4×C151—24no—
137C2×D4×C151—21no—
138C2×D4×C151—21no—
139C2×D4×C151—21no—
140C2×D4×C151—21no—
141C2×D4×C151C2×D412yes—
142C2×D4×C151C2×D412yes—
143C22×C4×C151—21no—
144C22×C4×C151—24no—
145C22×C4×C151—24no—
146C22×C4×C151—21no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—41no—
150C22×C4×C151C2×D411yescharacteristic
151C22×C4×C151C2×D411yescharacteristic
152C22×C4×C151C2×D411yescharacteristic
153SD16×C151—84no—
154C2×C8×C151—22no—
155C2×C8×C151—22no—
156C2×C8×C151—22no—
157C2×C8×C151—42no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—21no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—22no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—41no—
167C4⋊C4×C151—41no—
168C4⋊C4×C151C2×D412yes—
169C4⋊C4×C151C2×D412yes—
170C4⋊C4×C151C2×D412yes—
171C22⋊C4×C151—24no—
172C22⋊C4×C151—24no—
173C22⋊C4×C151—22no—
174C22⋊C4×C151—22no—
175C22⋊C4×C151—22no—
176C22⋊C4×C151—22no—
177C42×C151—22no—
178C42×C151—22no—
179C42×C151C2×D411yescharacteristic
180C42×C151C2×D411yescharacteristic
181C42×C151C2×D411yescharacteristic
182C42×C151C2411yescharacteristic
183C23×C151—22no—
184C23×C151—22no—
185C23×C151#12011yescharacteristic
186Q8×C151—22no—
187Q8×C151—24no—
188Q8×C151—48no—
189Q8×C151—41no—
190Q8×C151—41no—
191Q8×C151—42no—
192Q8×C151—44no—
193Q8×C151—82no—
194Q8×C151C2×SD1614yes—
195D4×C151—24no—
196D4×C151—42no—
197D4×C151—48no—
198D4×C151—44no—
199D4×C151—44no—
200D4×C151—41no—
201D4×C151—41no—
202D4×C151—42no—
203D4×C151—42no—
204D4×C151—81no—
205D4×C151—84no—
206C2×C4×C151—22no—
207C2×C4×C151—24no—
208C2×C4×C151—22no—
209C2×C4×C151—22no—
210C2×C4×C151—22no—
211C2×C4×C151—22no—
212C2×C4×C151—41no—
213C2×C4×C151—48no—
214C2×C4×C151—48no—
215C2×C4×C151—42no—
216C2×C4×C151—42no—
217C2×C4×C151—44no—
218C2×C4×C151—42no—
219C2×C4×C151—81no—
220C2×C4×C151—82no—
221C2×C4×C151#12011yescharacteristic
222C2×C4×C151#12011yescharacteristic
223C2×C4×C151#12011yescharacteristic
224C2×C4×C151C2×SD1612yes—
225C2×C4×C151AGL(1,ℤ/8)12yes—
226C2×C4×C151C22×D411yescharacteristic
227C2×C4×C151C22×D411yescharacteristic
228C2×C4×C151C22×D411yescharacteristic
229C8×C151—42no—
230C8×C151—42no—
231C8×C151—42no—
232C22×C151—21no—
233C22×C151—21no—
234C22×C151—42no—
235C22×C151—42no—
236C22×C151—42no—
237C22×C151—42no—
238C22×C151—42no—
239C22×C151—42no—
240C22×C151#45012yes—
241C22×C151C2×#12011yescharacteristic
242C4×C151—24no—
243C4×C151—21no—
244C4×C151—21no—
245C4×C151—21no—
246C4×C151—42no—
247C4×C151—42no—
248C4×C151—42no—
249C4×C151—82no—
250C4×C151#45012yes—
251C4×C151C22×SD1611yescharacteristic
252C4×C151C2×AGL(1,ℤ/8)11yescharacteristic
253C4×C151#57712yes—
254C2×C151—22no—
255C2×C151—82no—
256C2×C151—82no—
257C2×C151C2×#45011yescharacteristic
258C2×C151#301011yescharacteristic
259C2×C151#302211yescharacteristic
260#18923C15111yesmaximal, characteristic, direct product factor, Sylow
261C151#1892311yescharacteristic, direct product factor, Sylow
262#3497C2×C15111yescharacteristic
263#3227C2×C15111yescharacteristic, complemented
264#3206C2×C15111yescharacteristic, complemented
265C2×#475C2×C15111yescharacteristic, complemented
266#1651C2×C15114yescomplemented
267#1642C2×C15114yescomplemented
268#1540C2×C15111yescharacteristic, complemented
269#1480C2×C15111yescharacteristic, complemented
270#1479C2×C15111yescharacteristic, complemented
271C2×2−1+4—21no—
272#550—21no—
273#550C22×C15112yes—
274D4×Q8—21no—
275D4×Q8C22×C15112yes—
276#548—22no—
277#548—22no—
278#537—22no—
279#537—21no—
280#532—22no—
281#532C22×C15111yescharacteristic
282#532C22×C15111yescharacteristic
283C2×C4⋊Q8C22×C15111yescharacteristic
284C2×C4×Q8C22×C15111yescharacteristic
285#498C22×C15112yes—
286#492—21no—
287#487—21no—
288#486C22×C15112yes—
289#481—22no—
290#476—22no—
291#475—22no—
292#475C22×C15114yes—
293#461C22×C15114yes—
294#448—22no—
295#431C22×C15111yescharacteristic
296#431C22×C15111yescharacteristic
297C2×#106—21no—
298C2×C4⋊C8C22×C15111yescharacteristic
299C2×#103—21no—
300#332C22×C15112yes—
301#331C22×C15112yes—
302Q8⋊C8C22×C15114yes—
303D4⋊C8C22×C15114yes—
3042−1+4—44no—
3052−1+4—44no—
306C2×#41—24no—
307C2×#41—22no—
308C2×#41—22no—
309C2×#41—21no—
310C2×#41—21no—
311C22×Q8—22no—
312C22×Q8—22no—
313C22×Q8—21no—
314C22×Q8D4×C15111yescharacteristic
315C2×SD16—24no—
316C22×C8—21no—
317C4⋊Q8—22no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8D4×C15111yescharacteristic
322C4⋊Q8C23×C15112yes—
323C4⋊Q8C23×C15111yescharacteristic
324#127—22no—
325#127D4×C15111yescharacteristic
326#127C23×C15111yescharacteristic
327#124—24no—
328#124—21no—
329#124—21no—
330C22⋊Q8—22no—
331C22⋊Q8—24no—
332C22⋊Q8—22no—
333C22⋊Q8—24no—
334#121—24no—
335#121—22no—
336#121—24no—
337#121—24no—
338#121—21no—
339#121—21no—
340#121—22no—
341#121D4×C15112yes—
342#121D4×C15112yes—
343C4×Q8—21no—
344C4×Q8—21no—
345C4×Q8D4×C15112yes—
346C4×Q8C23×C15112yes—
347C4×D4—24no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—21no—
351C4×D4—21no—
352C4×D4D4×C15112yes—
353C4×D4C23×C15112yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4D4×C15111yescharacteristic
358C2×C42—21no—
359C2×C42C23×C15111yescharacteristic
360#106—24no—
361#106—24no—
362C4⋊C8—21no—
363C4⋊C8—21no—
364C4⋊C8C23×C15112yes—
365C4⋊C8C23×C15112yes—
366#103—24no—
367#103—24no—
368#102—24no—
369C22⋊C8—21no—
370C22⋊C8—21no—
371C4×C8—21no—
372C4×C8C23×C15112yes—
373#41—416no—
374#41—48no—
375#41—44no—
376#41—44no—
377#41—42no—
378#41—42no—
379#41—42no—
380#41—42no—
381C2×Q8—24no—
382C2×Q8—21no—
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—48no—
388C2×Q8—44no—
389C2×Q8—44no—
390C2×Q8—41no—
391C2×Q8—82no—
392C2×Q8SD16×C15114yescomplemented
393C2×Q8C2×D4×C15112yes—
394C2×D4—24no—
395C2×D4—22no—
396C2×D4—22no—
397C2×D4—24no—
398C2×D4—21no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4C2×D4×C15112yes—
403C2×D4C2×D4×C15112yes—
404C22×C4—21no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—41no—
411C22×C4C2×D4×C15111yescharacteristic
412C22×C4C2×D4×C15111yescharacteristic
413C22×C4C2×D4×C15111yescharacteristic
414SD16—84no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—42no—
419C4⋊C4—24no—
420C4⋊C4—22no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4C2×D4×C15112yes—
430C4⋊C4C2×D4×C15112yes—
431C4⋊C4C2×D4×C15112yes—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C42—22no—
439C42—22no—
440C42C2×D4×C15111yescharacteristic
441C42C2×D4×C15111yescharacteristic
442C42C2×D4×C15111yescharacteristic
443C42C24×C15111yescharacteristic
444C23—22no—
445C23—22no—
446C23#120×C15111yescharacteristic
447Q8—24no—
448Q8—22no—
449Q8—48no—
450Q8—42no—
451Q8—41no—
452Q8—41no—
453Q8—44no—
454Q8—82no—
455Q8C2×SD16×C15114yes—
456D4—24no—
457D4—42no—
458D4—48no—
459D4—44no—
460D4—44no—
461D4—42no—
462D4—41no—
463D4—41no—
464D4—42no—
465D4—81no—
466D4—84no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—41no—
474C2×C4—48no—
475C2×C4—48no—
476C2×C4—44no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—81no—
481C2×C4—82no—
482C2×C4#120×C15111yescharacteristic
483C2×C4#120×C15111yescharacteristic
484C2×C4#120×C15111yescharacteristic
485C2×C4C2×SD16×C15112yes—
486C2×C4AGL(1,ℤ/8)×C15112yes—
487C2×C4C22×D4×C15111yescharacteristic
488C2×C4C22×D4×C15111yescharacteristic
489C2×C4C22×D4×C15111yescharacteristic
490C8—42no—
491C8—42no—
492C8—42no—
493C22—21no—
494C22—21no—
495C22—42no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22#450×C15112yes—
502C22C2×#120×C15111yescharacteristic
503C4—24no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—42no—
508C4—42no—
509C4—42no—
510C4—82no—
511C4#450×C15112yes—
512C4C22×SD16×C15111yescharacteristic
513C4C2×AGL(1,ℤ/8)×C15111yescharacteristic
514C4#577×C15112yes—
515C2—22no—
516C2—82no—
517C2—82no—
518C2C2×#450×C15111yescharacteristic
519C2#3010×C15111yescharacteristic
520C2#3022×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radical#3497×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
2. #3227×C151C2semidirect
3. #3206×C151C2semidirect
4. C2×#475×C151C2semidirect
5. #1651×C151C2semidirect
6. #1642×C151C2semidirect
7. #1540×C151C2semidirect
8. #1480×C151C2semidirect
9. #1479×C151C2semidirect
131. C2×Q8×C151SD16semidirect
260. #18923C151direct (N × H)
261. C151#18923direct (N × H)
263. #3227C2×C151semidirect
264. #3206C2×C151semidirect
265. C2×#475C2×C151semidirect
266. #1651C2×C151semidirect
267. #1642C2×C151semidirect
268. #1540C2×C151semidirect
269. #1480C2×C151semidirect
270. #1479C2×C151semidirect
392. C2×Q8SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#3497×C1512
#3227×C1512
#3206×C1512
C2×#475×C1512
#1651×C1512
#1642×C1512
#1540×C1512
#1480×C1512
#1479×C1512
#18923151