Finite Group Databasebeta

← C151×#24326 #50329251

Subgroups — C151×#24326 #50329251

Order 38656.

1330 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C151C211yesmaximal, characteristic, complemented
2C2×#474×C151C211yesmaximal, characteristic, complemented
3C2×C4×D8×C151C211yesmaximal, characteristic
4#2538×C151C211yesmaximal, characteristic, complemented
5#2057×C151C212yesmaximal, complemented
6#2023×C151C212yesmaximal, complemented
7#1990×C151C211yesmaximal, characteristic, complemented
8#1984×C151C211yesmaximal, characteristic, complemented
9#1879×C151C212yesmaximal
10#1862×C151C212yesmaximal, complemented
11#1802×C151C211yesmaximal, characteristic, complemented
12C23×Q8×C151—21no—
13C22×D8×C151C2211yescharacteristic
14D4×Q8×C151—24no—
15D4×Q8×C151—24no—
16C2×C4⋊Q8×C151C2212yes—
17C2×C4⋊Q8×C151C2211yescharacteristic
18C2×C22⋊Q8×C151—21no—
19C2×C22⋊Q8×C151—21no—
20C2×C22⋊Q8×C151—22no—
21C2×C4×Q8×C151C2211yescharacteristic
22C2×C4×D4×C151C2212yes—
23C2×C4×D4×C151C2211yescharacteristic
24C2×C4×D4×C151C2211yescharacteristic
25#474×C151—24no—
26C4×D8×C151—24no—
27C2×#107×C151C2212yes—
28C2×#107×C151C2211yescharacteristic
29C2×C4⋊C8×C151C2211yescharacteristic
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2212yes—
32C2×#102×C151C2212yes—
33C2×#102×C151C2211yescharacteristic
34C2×C4×C8×C151C2211yescharacteristic
35#396×C151—22no—
36#390×C151C2212yes—
37#389×C151C2212yes—
38#384×C151C2211yescharacteristic
39#380×C151—21no—
40#340×C151C2212yes—
41#340×C151C2212yes—
42#340×C151C2212yes—
43#336×C151C2212yes—
44#336×C151C2212yes—
45C22×Q8×C151—28no—
46C22×Q8×C151—22no—
47C22×Q8×C151—21no—
48C22×Q8×C151—44no—
49C22×Q8×C151—44no—
50C22×Q8×C151D411yescharacteristic
51C22×D4×C151C2311yescharacteristic
52C22×D4×C151C2311yescharacteristic
53C23×C4×C151—22no—
54C23×C4×C151—21no—
55C23×C4×C151—21no—
56C2×D8×C151—22no—
57C2×D8×C151—22no—
58C2×D8×C151Q814yescomplemented
59C22×C8×C151C2311yescharacteristic
60C22×C8×C151C2312yes—
61C22×C8×C151C2311yescharacteristic
62C4⋊Q8×C151—24no—
63C4⋊Q8×C151—24no—
64C4⋊Q8×C151—22no—
65C4⋊Q8×C151D414yes—
66C22⋊Q8×C151—216no—
67C22⋊Q8×C151—28no—
68C22⋊Q8×C151—44no—
69C4×Q8×C151—22no—
70C4×Q8×C151—22no—
71C4×D4×C151—24no—
72C4×D4×C151—24no—
73C4×D4×C151—22no—
74C4×D4×C151—22no—
75C4×D4×C151—22no—
76C4×D4×C151D414yes—
77C2×C4⋊C4×C151—22no—
78C2×C4⋊C4×C151—21no—
79C2×C4⋊C4×C151—21no—
80C2×C4⋊C4×C151—22no—
81C2×C4⋊C4×C151—21no—
82C2×C4⋊C4×C151D411yescharacteristic
83C2×C4⋊C4×C151D412yes—
84C2×C4⋊C4×C151C2312yes—
85C2×C4⋊C4×C151C2311yescharacteristic
86C2×C4⋊C4×C151C2312yes—
87C2×C4⋊C4×C151C2311yescharacteristic
88C2×C22⋊C4×C151—22no—
89C2×C22⋊C4×C151—21no—
90C2×C22⋊C4×C151—22no—
91C2×C22⋊C4×C151—21no—
92C2×C22⋊C4×C151—22no—
93C2×C42×C151C2312yes—
94C2×C42×C151C2311yescharacteristic
95#107×C151—22no—
96#107×C151—24no—
97C4⋊C8×C151—22no—
98#102×C151—22no—
99#102×C151—24no—
100#102×C151—22no—
101#102×C151—24no—
102C4×C8×C151—22no—
103#95×C151—22no—
104C24×C151—21no—
105C24×C151—21no—
106C2×Q8×C151—28no—
107C2×Q8×C151—22no—
108C2×Q8×C151—24no—
109C2×Q8×C151—22no—
110C2×Q8×C151—44no—
111C2×Q8×C151—432no—
112C2×Q8×C151—44no—
113C2×Q8×C151—42no—
114C2×Q8×C151—42no—
115C2×Q8×C151D814yescomplemented
116C2×D4×C151—21no—
117C2×D4×C151—21no—
118C2×D4×C151—21no—
119C2×D4×C151—21no—
120C2×D4×C151—21no—
121C2×D4×C151—21no—
122C2×D4×C151—21no—
123C2×D4×C151—21no—
124C2×D4×C151C2×D412yes—
125C2×D4×C151C2×Q812yes—
126C2×D4×C151C2×Q812yescomplemented
127C2×D4×C151#4112yes—
128C22×C4×C151—28no—
129C22×C4×C151—21no—
130C22×C4×C151—22no—
131C22×C4×C151—24no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—44no—
135C22×C4×C151—44no—
136C22×C4×C151—42no—
137C22×C4×C151—42no—
138C22×C4×C151—42no—
139C22×C4×C151—42no—
140C22×C4×C151—42no—
141C22×C4×C151C2×D412yes—
142C22×C4×C151C2×D411yescharacteristic
143C22×C4×C151C2×D412yes—
144C22×C4×C151C2×D411yescharacteristic
145C22×C4×C151C2411yescharacteristic
146D8×C151—28no—
147C2×C8×C151—21no—
148C2×C8×C151—21no—
149C2×C8×C151—21no—
150C2×C8×C151—22no—
151C2×C8×C151—22no—
152C2×C8×C151—21no—
153C2×C8×C151—21no—
154C2×C8×C151—22no—
155C2×C8×C151C2×Q812yescomplemented
156C4⋊C4×C151—28no—
157C4⋊C4×C151—24no—
158C4⋊C4×C151—24no—
159C4⋊C4×C151—22no—
160C4⋊C4×C151—22no—
161C4⋊C4×C151—21no—
162C4⋊C4×C151—21no—
163C4⋊C4×C151—21no—
164C4⋊C4×C151—22no—
165C4⋊C4×C151—22no—
166C4⋊C4×C151—42no—
167C4⋊C4×C151—44no—
168C4⋊C4×C151—81no—
169C4⋊C4×C151C2×D414yes—
170C4⋊C4×C151C2×D412yes—
171C22⋊C4×C151—28no—
172C22⋊C4×C151—24no—
173C22⋊C4×C151—42no—
174C22⋊C4×C151—44no—
175C22⋊C4×C151—82no—
176C42×C151—22no—
177C42×C151—22no—
178C42×C151C2×D412yes—
179C42×C151C2×D412yes—
180C23×C151—22no—
181C23×C151—22no—
182C23×C151—22no—
183C23×C151—22no—
184C23×C151—41no—
185C23×C151—41no—
186C23×C151—41no—
187C23×C151—41no—
188C23×C151—41no—
189C23×C151—41no—
190C23×C151—41no—
191C23×C151—41no—
192C23×C151—41no—
193C23×C151—41no—
194C23×C151C22×D411yescharacteristic
195Q8×C151—28no—
196Q8×C151—416no—
197Q8×C151—48no—
198D4×C151—22no—
199D4×C151—22no—
200D4×C151—22no—
201D4×C151—22no—
202D4×C151—22no—
203D4×C151—41no—
204D4×C151—41no—
205D4×C151C22⋊Q814yescomplemented
206C2×C4×C151—22no—
207C2×C4×C151—22no—
208C2×C4×C151—21no—
209C2×C4×C151—21no—
210C2×C4×C151—22no—
211C2×C4×C151—24no—
212C2×C4×C151—22no—
213C2×C4×C151—22no—
214C2×C4×C151—22no—
215C2×C4×C151—416no—
216C2×C4×C151—42no—
217C2×C4×C151—41no—
218C2×C4×C151—41no—
219C2×C4×C151—42no—
220C2×C4×C151—48no—
221C2×C4×C151—41no—
222C2×C4×C151—42no—
223C2×C4×C151—42no—
224C2×C4×C151—41no—
225C2×C4×C151—41no—
226C2×C4×C151—42no—
227C2×C4×C151—84no—
228C2×C4×C151#12012yes—
229C2×C4×C151#12012yes—
230C2×C4×C151C2×D814yes—
231C2×C4×C151C2×D812yes—
232C2×C4×C151AGL(1,ℤ/8)12yes—
233C2×C4×C151C22×D411yescharacteristic
234C2×C4×C151C22×D411yescharacteristic
235C2×C4×C151C22×Q811yescharacteristic
236C2×C4×C151C2×#4111yescharacteristic
237C2×C4×C1512−1+411yescharacteristic
238C2×C4×C1512−1+411yescharacteristic
239C8×C151—22no—
240C8×C151—41no—
241C8×C151—42no—
242C22×C151—24no—
243C22×C151—42no—
244C22×C151—42no—
245C22×C151—42no—
246C22×C151—42no—
247C22×C151—42no—
248C22×C151—42no—
249C22×C151—42no—
250C22×C151—42no—
251C22×C151—42no—
252C22×C151—81no—
253C22×C151—81no—
254C22×C151—81no—
255C22×C151—81no—
256C22×C151C2×#12011yescharacteristic
257C22×C151#54811yescharacteristic
258C22×C151D4×Q811yescharacteristic
259C22×C151C22×D811yescharacteristic
260C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C151#57711yescharacteristic
262C22×C151#57811yescharacteristic
263C4×C151—24no—
264C4×C151—22no—
265C4×C151—44no—
266C4×C151—42no—
267C4×C151—42no—
268C4×C151—82no—
269C4×C151—81no—
270C4×C151#44714yes—
271C4×C151C2×C22⋊Q811yescharacteristic
272C4×C151#53611yescharacteristic
273C4×C151#54811yescharacteristic
274C4×C151D4×Q811yescharacteristic
275C2×C151—44no—
276C2×C151—82no—
277C2×C151#240911yescharacteristic
278C2×C151C2×#44711yescharacteristic
279C2×C151#301311yescharacteristic
280C2×C151#335811yescharacteristic
281C2×C151#336711yescharacteristic
282C2×C151Q8×D811yescharacteristic
283C2×C151#338411yescharacteristic
284#24326C15111yesmaximal, characteristic, direct product factor, Sylow
285C151#2432611yescharacteristic, direct product factor, Sylow
286C2×D4×Q8C2×C15111yescharacteristic, complemented
287C2×#474C2×C15111yescharacteristic, complemented
288C2×C4×D8C2×C15111yescharacteristic
289#2538C2×C15111yescharacteristic, complemented
290#2057C2×C15112yescomplemented
291#2023C2×C15112yescomplemented
292#1990C2×C15111yescharacteristic, complemented
293#1984C2×C15111yescharacteristic, complemented
294#1879C2×C15112yes—
295#1862C2×C15112yescomplemented
296#1802C2×C15111yescharacteristic, complemented
297C23×Q8—21no—
298C22×D8C22×C15111yescharacteristic
299D4×Q8—24no—
300D4×Q8—24no—
301C2×C4⋊Q8C22×C15112yes—
302C2×C4⋊Q8C22×C15111yescharacteristic
303C2×C22⋊Q8—21no—
304C2×C22⋊Q8—21no—
305C2×C22⋊Q8—22no—
306C2×C4×Q8C22×C15111yescharacteristic
307C2×C4×D4C22×C15112yes—
308C2×C4×D4C22×C15111yescharacteristic
309C2×C4×D4C22×C15111yescharacteristic
310#474—24no—
311C4×D8—24no—
312C2×#107C22×C15111yescharacteristic
313C2×#107C22×C15112yes—
314C2×C4⋊C8C22×C15111yescharacteristic
315C2×#102C22×C15112yes—
316C2×#102C22×C15111yescharacteristic
317C2×#102C22×C15112yes—
318C2×#102C22×C15111yescharacteristic
319C2×C4×C8C22×C15111yescharacteristic
320#396—22no—
321#390C22×C15112yes—
322#389C22×C15112yes—
323#384C22×C15111yescharacteristic
324#380—21no—
325#340C22×C15112yes—
326#340C22×C15112yes—
327#340C22×C15112yes—
328#336C22×C15112yes—
329#336C22×C15112yes—
330C22×Q8—28no—
331C22×Q8—22no—
332C22×Q8—21no—
333C22×Q8—44no—
334C22×Q8—44no—
335C22×Q8D4×C15111yescharacteristic
336C22×D4C23×C15111yescharacteristic
337C22×D4C23×C15111yescharacteristic
338C23×C4—22no—
339C23×C4—21no—
340C23×C4—21no—
341C2×D8—22no—
342C2×D8—22no—
343C2×D8Q8×C15114yescomplemented
344C22×C8C23×C15111yescharacteristic
345C22×C8C23×C15112yes—
346C22×C8C23×C15111yescharacteristic
347C4⋊Q8—24no—
348C4⋊Q8—24no—
349C4⋊Q8—22no—
350C4⋊Q8D4×C15114yes—
351C22⋊Q8—28no—
352C22⋊Q8—216no—
353C22⋊Q8—44no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—24no—
357C4×D4—24no—
358C4×D4—22no—
359C4×D4—22no—
360C4×D4—22no—
361C4×D4D4×C15114yes—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4D4×C15111yescharacteristic
368C2×C4⋊C4D4×C15112yes—
369C2×C4⋊C4C23×C15111yescharacteristic
370C2×C4⋊C4C23×C15112yes—
371C2×C4⋊C4C23×C15112yes—
372C2×C4⋊C4C23×C15111yescharacteristic
373C2×C22⋊C4—22no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
378C2×C42C23×C15112yes—
379C2×C42C23×C15111yescharacteristic
380#107—22no—
381#107—24no—
382C4⋊C8—22no—
383#102—24no—
384#102—22no—
385#102—22no—
386#102—24no—
387C4×C8—22no—
388#95—22no—
389C24—21no—
390C24—21no—
391C2×Q8—28no—
392C2×Q8—22no—
393C2×Q8—24no—
394C2×Q8—22no—
395C2×Q8—44no—
396C2×Q8—432no—
397C2×Q8—44no—
398C2×Q8—42no—
399C2×Q8—42no—
400C2×Q8D8×C15114yescomplemented
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4C2×D4×C15112yes—
410C2×D4C2×Q8×C15112yes—
411C2×D4C2×Q8×C15112yescomplemented
412C2×D4#41×C15112yes—
413C22×C4—28no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—44no—
420C22×C4—44no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4C2×D4×C15112yes—
427C22×C4C2×D4×C15111yescharacteristic
428C22×C4C2×D4×C15112yes—
429C22×C4C2×D4×C15111yescharacteristic
430C22×C4C24×C15111yescharacteristic
431D8—28no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—22no—
440C2×C8C2×Q8×C15112yescomplemented
441C4⋊C4—28no—
442C4⋊C4—24no—
443C4⋊C4—24no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4—44no—
453C4⋊C4—81no—
454C4⋊C4C2×D4×C15114yes—
455C4⋊C4C2×D4×C15112yes—
456C22⋊C4—28no—
457C22⋊C4—24no—
458C22⋊C4—42no—
459C22⋊C4—44no—
460C22⋊C4—82no—
461C42—22no—
462C42—22no—
463C42C2×D4×C15112yes—
464C42C2×D4×C15112yes—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23C22×D4×C15111yescharacteristic
480Q8—28no—
481Q8—416no—
482Q8—48no—
483D4—22no—
484D4—22no—
485D4—22no—
486D4—22no—
487D4—22no—
488D4—41no—
489D4—41no—
490D4C22⋊Q8×C15114yescomplemented
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—416no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—48no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—84no—
513C2×C4#120×C15112yes—
514C2×C4#120×C15112yes—
515C2×C4C2×D8×C15114yes—
516C2×C4C2×D8×C15112yes—
517C2×C4AGL(1,ℤ/8)×C15112yes—
518C2×C4C22×D4×C15111yescharacteristic
519C2×C4C22×D4×C15111yescharacteristic
520C2×C4C22×Q8×C15111yescharacteristic
521C2×C4C2×#41×C15111yescharacteristic
522C2×C42−1+4×C15111yescharacteristic
523C2×C42−1+4×C15111yescharacteristic
524C8—22no—
525C8—41no—
526C8—42no—
527C22—24no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22—81no—
541C22C2×#120×C15111yescharacteristic
542C22#548×C15111yescharacteristic
543C22D4×Q8×C15111yescharacteristic
544C22C22×D8×C15111yescharacteristic
545C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
546C22#577×C15111yescharacteristic
547C22#578×C15111yescharacteristic
548C4—24no—
549C4—22no—
550C4—44no—
551C4—42no—
552C4—42no—
553C4—82no—
554C4—81no—
555C4#447×C15114yes—
556C4C2×C22⋊Q8×C15111yescharacteristic
557C4#536×C15111yescharacteristic
558C4#548×C15111yescharacteristic
559C4D4×Q8×C15111yescharacteristic
560C2—44no—
561C2—82no—
562C2#2409×C15111yescharacteristic
563C2C2×#447×C15111yescharacteristic
564C2#3013×C15111yescharacteristic
565C2#3358×C15111yescharacteristic
566C2#3367×C15111yescharacteristic
567C2Q8×D8×C15111yescharacteristic
568C2#3384×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D8×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D4×Q8×C151C2semidirect
2. C2×#474×C151C2semidirect
4. #2538×C151C2semidirect
5. #2057×C151C2semidirect
6. #2023×C151C2semidirect
7. #1990×C151C2semidirect
8. #1984×C151C2semidirect
10. #1862×C151C2semidirect
11. #1802×C151C2semidirect
58. C2×D8×C151Q8semidirect
115. C2×Q8×C151D8semidirect
126. C2×D4×C151C2×Q8semidirect
155. C2×C8×C151C2×Q8semidirect
205. D4×C151C22⋊Q8semidirect
284. #24326C151direct (N × H)
285. C151#24326direct (N × H)
286. C2×D4×Q8C2×C151semidirect
287. C2×#474C2×C151semidirect
289. #2538C2×C151semidirect
290. #2057C2×C151semidirect
291. #2023C2×C151semidirect
292. #1990C2×C151semidirect
293. #1984C2×C151semidirect
295. #1862C2×C151semidirect
296. #1802C2×C151semidirect
343. C2×D8Q8×C151semidirect
400. C2×Q8D8×C151semidirect
411. C2×D4C2×Q8×C151semidirect
440. C2×C8C2×Q8×C151semidirect
490. D4C22⋊Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1512
C2×#474×C1512
C2×C4×D8×C1512
#2538×C1512
#2057×C1512
#2023×C1512
#1990×C1512
#1984×C1512
#1879×C1512
#1862×C1512
#1802×C1512
#24326151