Finite Group Databasebeta

← C151×#24255 #50329180

Subgroups — C151×#24255 #50329180

Order 38656.

1392 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C151C211yesmaximal, characteristic
2C2×#462×C151C211yesmaximal, characteristic, complemented
3C2×#451×C151C212yesmaximal, complemented
4C2×#441×C151C211yesmaximal, characteristic, complemented
5#2536×C151C211yesmaximal, characteristic
6#2035×C151C212yesmaximal, complemented
7#2001×C151C212yesmaximal, complemented
8#1960×C151C211yesmaximal, characteristic, complemented
9#1955×C151C211yesmaximal, characteristic
10#1805×C151C211yesmaximal, characteristic, complemented
11#1787×C151C212yesmaximal, complemented
12C23×Q8×C151C2212yes—
13C22×Q16×C151C2212yes—
14C22×Q16×C151C2211yescharacteristic
15D4×Q8×C151—24no—
16D4×Q8×C151—24no—
17C2×C4⋊Q8×C151—21no—
18C2×C4⋊Q8×C151C2211yescharacteristic
19C2×C22⋊Q8×C151—22no—
20C2×C22⋊Q8×C151C2212yes—
21C2×C22⋊Q8×C151C2212yes—
22C2×C4×Q8×C151C2211yescharacteristic
23C2×C4×Q8×C151C2211yescharacteristic
24C2×C4×D4×C151—21no—
25C2×C4×D4×C151C2211yescharacteristic
26#462×C151—24no—
27#451×C151—28no—
28#441×C151—24no—
29C2×#106×C151C2211yescharacteristic
30C2×C4⋊C8×C151C2211yescharacteristic
31C2×#103×C151C2211yescharacteristic
32C2×#103×C151C2211yescharacteristic
33C2×#103×C151C2212yes—
34C2×#103×C151C2212yes—
35C2×#103×C151C2212yes—
36C2×#103×C151C2212yes—
37C2×C22⋊C8×C151C2212yes—
38C2×C22⋊C8×C151C2212yes—
39C2×#97×C151C2211yescharacteristic
40#398×C151—21no—
41#394×C151—21no—
42#388×C151—22no—
43#382×C151C2211yescharacteristic
44#380×C151C2212yes—
45#340×C151C2212yes—
46C22×Q8×C151—22no—
47C22×Q8×C151—24no—
48C22×Q8×C151—24no—
49C22×Q8×C151—24no—
50C22×Q8×C151—24no—
51C22×Q8×C151—42no—
52C22×Q8×C151—42no—
53C22×Q8×C151C2312yes—
54C22×Q8×C151C2311yescharacteristic
55C22×Q8×C151C2311yescharacteristic
56C22×D4×C151D411yescharacteristic
57C23×C4×C151—22no—
58C23×C4×C151C2312yes—
59C2×Q16×C151—22no—
60C2×Q16×C151—24no—
61C2×Q16×C151—24no—
62C2×Q16×C151—22no—
63C2×Q16×C151—42no—
64C2×Q16×C151D414yescomplemented
65C22×C8×C151C2312yes—
66C22×C8×C151C2311yescharacteristic
67C22×C8×C151C2311yescharacteristic
68C4⋊Q8×C151—28no—
69C4⋊Q8×C151—22no—
70C4⋊Q8×C151D414yes—
71C22⋊Q8×C151—216no—
72C22⋊Q8×C151—24no—
73C22⋊Q8×C151—24no—
74C22⋊Q8×C151—24no—
75C22⋊Q8×C151—42no—
76C4×Q8×C151—22no—
77C4×Q8×C151—22no—
78C4×Q8×C151—22no—
79C4×Q8×C151D414yes—
80C4×D4×C151—28no—
81C4×D4×C151—22no—
82C4×D4×C151—22no—
83C2×C4⋊C4×C151—21no—
84C2×C4⋊C4×C151—21no—
85C2×C4⋊C4×C151—21no—
86C2×C4⋊C4×C151—22no—
87C2×C4⋊C4×C151—22no—
88C2×C4⋊C4×C151—21no—
89C2×C4⋊C4×C151D411yescharacteristic
90C2×C4⋊C4×C151C2312yes—
91C2×C4⋊C4×C151C2311yescharacteristic
92C2×C4⋊C4×C151C2311yescharacteristic
93C2×C22⋊C4×C151—22no—
94C2×C22⋊C4×C151—22no—
95C2×C22⋊C4×C151—22no—
96C2×C22⋊C4×C151D412yes—
97C2×C42×C151—21no—
98C2×C42×C151—21no—
99C2×C42×C151C2311yescharacteristic
100#106×C151—22no—
101C4⋊C8×C151—22no—
102#103×C151—24no—
103#103×C151—22no—
104#103×C151—22no—
105#103×C151—24no—
106#103×C151—24no—
107#103×C151—42no—
108C22⋊C8×C151—24no—
109C22⋊C8×C151—42no—
110#97×C151—22no—
111#95×C151—22no—
112#95×C151—21no—
113#95×C151—21no—
114C24×C151C2×D412yes—
115C2×Q8×C151—28no—
116C2×Q8×C151—21no—
117C2×Q8×C151—22no—
118C2×Q8×C151—21no—
119C2×Q8×C151—21no—
120C2×Q8×C151—21no—
121C2×Q8×C151—21no—
122C2×Q8×C151—22no—
123C2×Q8×C151—21no—
124C2×Q8×C151—21no—
125C2×Q8×C151—22no—
126C2×Q8×C151—22no—
127C2×Q8×C151—21no—
128C2×Q8×C151—22no—
129C2×Q8×C151—44no—
130C2×Q8×C151—44no—
131C2×Q8×C151—48no—
132C2×Q8×C151—48no—
133C2×Q8×C151—48no—
134C2×Q8×C151—48no—
135C2×Q8×C151C2×D414yes—
136C2×Q8×C151C2×D412yes—
137C2×Q8×C151C2×D412yes—
138C2×Q8×C151C2×D412yes—
139C2×Q8×C151#4112yes—
140C2×D4×C151—24no—
141C2×D4×C151—22no—
142C22×C4×C151—21no—
143C22×C4×C151—28no—
144C22×C4×C151—21no—
145C22×C4×C151—21no—
146C22×C4×C151—22no—
147C22×C4×C151—22no—
148C22×C4×C151—22no—
149C22×C4×C151—22no—
150C22×C4×C151—22no—
151C22×C4×C151—22no—
152C22×C4×C151—22no—
153C22×C4×C151—22no—
154C22×C4×C151—21no—
155C22×C4×C151—44no—
156C22×C4×C151—44no—
157C22×C4×C151C2×D412yes—
158C22×C4×C151C2×D411yescharacteristic
159C22×C4×C151C2×D411yescharacteristic
160C22×C4×C151C2411yescharacteristic
161Q16×C151—28no—
162Q16×C151—48no—
163C2×C8×C151—21no—
164C2×C8×C151—21no—
165C2×C8×C151—21no—
166C2×C8×C151—22no—
167C2×C8×C151—22no—
168C2×C8×C151—21no—
169C2×C8×C151—22no—
170C2×C8×C151—21no—
171C2×C8×C151C2×D412yes—
172C4⋊C4×C151—28no—
173C4⋊C4×C151—24no—
174C4⋊C4×C151—24no—
175C4⋊C4×C151—24no—
176C4⋊C4×C151—22no—
177C4⋊C4×C151—21no—
178C4⋊C4×C151—21no—
179C4⋊C4×C151—22no—
180C4⋊C4×C151—21no—
181C4⋊C4×C151—22no—
182C4⋊C4×C151—44no—
183C4⋊C4×C151—42no—
184C4⋊C4×C151C2×D412yes—
185C22⋊C4×C151—28no—
186C22⋊C4×C151—24no—
187C22⋊C4×C151—44no—
188C22⋊C4×C151—44no—
189C42×C151—24no—
190C42×C151—42no—
191C42×C151C2×D412yes—
192C42×C151C2×D412yes—
193C23×C151—22no—
194C23×C151—22no—
195C23×C151—22no—
196C23×C151—22no—
197C23×C151—22no—
198C23×C151—22no—
199C23×C151#13714yes—
200C23×C151C22×D411yescharacteristic
201Q8×C151—22no—
202Q8×C151—22no—
203Q8×C151—22no—
204Q8×C151—22no—
205Q8×C151—24no—
206Q8×C151—22no—
207Q8×C151—24no—
208Q8×C151—416no—
209Q8×C151—42no—
210Q8×C151—41no—
211Q8×C151—42no—
212Q8×C151—41no—
213Q8×C151#12114yes—
214D4×C151—28no—
215C2×C4×C151—22no—
216C2×C4×C151—22no—
217C2×C4×C151—22no—
218C2×C4×C151—22no—
219C2×C4×C151—22no—
220C2×C4×C151—22no—
221C2×C4×C151—24no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—416no—
227C2×C4×C151—41no—
228C2×C4×C151—42no—
229C2×C4×C151—42no—
230C2×C4×C151—41no—
231C2×C4×C151—42no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151—42no—
236C2×C4×C151—41no—
237C2×C4×C151—42no—
238C2×C4×C151—42no—
239C2×C4×C151—42no—
240C2×C4×C151—42no—
241C2×C4×C151#12012yes—
242C2×C4×C151#12012yes—
243C2×C4×C151C22×D411yescharacteristic
244C2×C4×C151C22×D411yescharacteristic
245C2×C4×C151C22×D411yescharacteristic
246C2×C4×C151C2×#4111yescharacteristic
247C2×C4×C151H(5,𝔽2)11yescharacteristic
248C2×C4×C151H(5,𝔽2)11yescharacteristic
249C8×C151—22no—
250C8×C151—41no—
251C8×C151—42no—
252C22×C151—24no—
253C22×C151—24no—
254C22×C151—24no—
255C22×C151—42no—
256C22×C151—42no—
257C22×C151—42no—
258C22×C151—42no—
259C22×C151C2×#12011yescharacteristic
260C22×C151D4211yescharacteristic
261C22×C151#54611yescharacteristic
262C22×C151C2×#13712yes—
263C22×C151#57812yes—
264C4×C151—24no—
265C4×C151—22no—
266C4×C151—22no—
267C4×C151—42no—
268C4×C151—44no—
269C4×C151—42no—
270C4×C151—42no—
271C4×C151—81no—
272C4×C151—82no—
273C4×C151C2×#12111yescharacteristic
274C4×C151#53511yescharacteristic
275C4×C151D4211yescharacteristic
276C4×C151#54611yescharacteristic
277C2×C151—44no—
278C2×C151#240811yescharacteristic
279C2×C151#300411yescharacteristic
280C2×C151#301111yescharacteristic
281C2×C151#327012yes—
282C2×C151#331212yes—
283#24255C15111yesmaximal, characteristic, direct product factor, Sylow
284C151#2425511yescharacteristic, direct product factor, Sylow
285C2×D4×Q8C2×C15111yescharacteristic
286C2×#462C2×C15111yescharacteristic, complemented
287C2×#451C2×C15112yescomplemented
288C2×#441C2×C15111yescharacteristic, complemented
289#2536C2×C15111yescharacteristic
290#2035C2×C15112yescomplemented
291#2001C2×C15112yescomplemented
292#1960C2×C15111yescharacteristic, complemented
293#1955C2×C15111yescharacteristic
294#1805C2×C15111yescharacteristic, complemented
295#1787C2×C15112yescomplemented
296C23×Q8C22×C15112yes—
297C22×Q16C22×C15112yes—
298C22×Q16C22×C15111yescharacteristic
299D4×Q8—24no—
300D4×Q8—24no—
301C2×C4⋊Q8—21no—
302C2×C4⋊Q8C22×C15111yescharacteristic
303C2×C22⋊Q8—22no—
304C2×C22⋊Q8C22×C15112yes—
305C2×C22⋊Q8C22×C15112yes—
306C2×C4×Q8C22×C15111yescharacteristic
307C2×C4×Q8C22×C15111yescharacteristic
308C2×C4×D4—21no—
309C2×C4×D4C22×C15111yescharacteristic
310#462—24no—
311#451—28no—
312#441—24no—
313C2×#106C22×C15111yescharacteristic
314C2×C4⋊C8C22×C15111yescharacteristic
315C2×#103C22×C15112yes—
316C2×#103C22×C15111yescharacteristic
317C2×#103C22×C15111yescharacteristic
318C2×#103C22×C15112yes—
319C2×#103C22×C15112yes—
320C2×#103C22×C15112yes—
321C2×C22⋊C8C22×C15112yes—
322C2×C22⋊C8C22×C15112yes—
323C2×#97C22×C15111yescharacteristic
324#398—21no—
325#394—21no—
326#388—22no—
327#382C22×C15111yescharacteristic
328#380C22×C15112yes—
329#340C22×C15112yes—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8—22no—
333C22×Q8—24no—
334C22×Q8—24no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×Q8C23×C15111yescharacteristic
338C22×Q8C23×C15112yes—
339C22×Q8C23×C15111yescharacteristic
340C22×D4D4×C15111yescharacteristic
341C23×C4—22no—
342C23×C4C23×C15112yes—
343C2×Q16—22no—
344C2×Q16—22no—
345C2×Q16—24no—
346C2×Q16—24no—
347C2×Q16—42no—
348C2×Q16D4×C15114yescomplemented
349C22×C8C23×C15112yes—
350C22×C8C23×C15111yescharacteristic
351C22×C8C23×C15111yescharacteristic
352C4⋊Q8—28no—
353C4⋊Q8—22no—
354C4⋊Q8D4×C15114yes—
355C22⋊Q8—216no—
356C22⋊Q8—24no—
357C22⋊Q8—24no—
358C22⋊Q8—24no—
359C22⋊Q8—42no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8D4×C15114yes—
364C4×D4—28no—
365C4×D4—22no—
366C4×D4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4D4×C15111yescharacteristic
374C2×C4⋊C4C23×C15111yescharacteristic
375C2×C4⋊C4C23×C15112yes—
376C2×C4⋊C4C23×C15111yescharacteristic
377C2×C22⋊C4—22no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4D4×C15112yes—
381C2×C42—21no—
382C2×C42—21no—
383C2×C42C23×C15111yescharacteristic
384#106—22no—
385C4⋊C8—22no—
386#103—22no—
387#103—24no—
388#103—24no—
389#103—24no—
390#103—22no—
391#103—42no—
392C22⋊C8—24no—
393C22⋊C8—42no—
394#97—22no—
395#95—22no—
396#95—21no—
397#95—21no—
398C24C2×D4×C15112yes—
399C2×Q8—28no—
400C2×Q8—21no—
401C2×Q8—22no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—44no—
414C2×Q8—44no—
415C2×Q8—48no—
416C2×Q8—48no—
417C2×Q8—48no—
418C2×Q8—48no—
419C2×Q8C2×D4×C15114yes—
420C2×Q8C2×D4×C15112yes—
421C2×Q8C2×D4×C15112yes—
422C2×Q8C2×D4×C15112yes—
423C2×Q8#41×C15112yes—
424C2×D4—24no—
425C2×D4—22no—
426C22×C4—21no—
427C22×C4—28no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—44no—
440C22×C4—44no—
441C22×C4C2×D4×C15112yes—
442C22×C4C2×D4×C15111yescharacteristic
443C22×C4C2×D4×C15111yescharacteristic
444C22×C4C24×C15111yescharacteristic
445Q16—28no—
446Q16—48no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—21no—
453C2×C8—22no—
454C2×C8—21no—
455C2×C8C2×D4×C15112yes—
456C4⋊C4—28no—
457C4⋊C4—24no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—44no—
467C4⋊C4—42no—
468C4⋊C4C2×D4×C15112yes—
469C22⋊C4—28no—
470C22⋊C4—24no—
471C22⋊C4—44no—
472C22⋊C4—44no—
473C42—24no—
474C42—42no—
475C42C2×D4×C15112yes—
476C42C2×D4×C15112yes—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23#137×C15114yes—
484C23C22×D4×C15111yescharacteristic
485Q8—22no—
486Q8—22no—
487Q8—22no—
488Q8—22no—
489Q8—22no—
490Q8—24no—
491Q8—24no—
492Q8—416no—
493Q8—42no—
494Q8—42no—
495Q8—41no—
496Q8—41no—
497Q8#121×C15114yes—
498D4—28no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—416no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4#120×C15112yes—
526C2×C4#120×C15112yes—
527C2×C4C22×D4×C15111yescharacteristic
528C2×C4C22×D4×C15111yescharacteristic
529C2×C4C22×D4×C15111yescharacteristic
530C2×C4C2×#41×C15111yescharacteristic
531C2×C4H(5,𝔽2)×C15111yescharacteristic
532C2×C4H(5,𝔽2)×C15111yescharacteristic
533C8—22no—
534C8—41no—
535C8—42no—
536C22—24no—
537C22—24no—
538C22—24no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—42no—
543C22C2×#120×C15111yescharacteristic
544C22D42×C15111yescharacteristic
545C22#546×C15111yescharacteristic
546C22C2×#137×C15112yes—
547C22#578×C15112yes—
548C4—24no—
549C4—22no—
550C4—22no—
551C4—42no—
552C4—44no—
553C4—42no—
554C4—42no—
555C4—81no—
556C4—82no—
557C4C2×#121×C15111yescharacteristic
558C4#535×C15111yescharacteristic
559C4D42×C15111yescharacteristic
560C4#546×C15111yescharacteristic
561C2—44no—
562C2#2408×C15111yescharacteristic
563C2#3004×C15111yescharacteristic
564C2#3011×C15111yescharacteristic
565C2#3270×C15112yes—
566C2#3312×C15112yes—
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#462×C151C2semidirect
3. C2×#451×C151C2semidirect
4. C2×#441×C151C2semidirect
6. #2035×C151C2semidirect
7. #2001×C151C2semidirect
8. #1960×C151C2semidirect
10. #1805×C151C2semidirect
11. #1787×C151C2semidirect
64. C2×Q16×C151D4semidirect
283. #24255C151direct (N × H)
284. C151#24255direct (N × H)
286. C2×#462C2×C151semidirect
287. C2×#451C2×C151semidirect
288. C2×#441C2×C151semidirect
290. #2035C2×C151semidirect
291. #2001C2×C151semidirect
292. #1960C2×C151semidirect
294. #1805C2×C151semidirect
295. #1787C2×C151semidirect
348. C2×Q16D4×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×#462×C1512
C2×#451×C1512
C2×#441×C1512
#2536×C1512
#2035×C1512
#2001×C1512
#1960×C1512
#1955×C1512
#1805×C1512
#1787×C1512
#24255151