Finite Group Databasebeta

← C151×#22480 #50327405

Subgroups — C151×#22480 #50327405

Order 38656.

1068 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#552×C151C211yesmaximal, characteristic
2D4×M16×C151C212yesmaximal
3#1998×C151C212yesmaximal, complemented
4#1901×C151C212yesmaximal, complemented
5#1901×C151C212yesmaximal, complemented
6#1822×C151C211yesmaximal, characteristic, complemented
7#1821×C151C211yesmaximal, characteristic, complemented
8#1801×C151C211yesmaximal, characteristic, complemented
9C4×#101×C151C211yesmaximal, characteristic, complemented
10#1742×C151C211yesmaximal, characteristic, complemented
11C2×#343×C151C211yesmaximal, characteristic, complemented
12C22×M16×C151C2212yes—
13C22×M16×C151C2212yes—
14#552×C151—22no—
15#552×C151—22no—
16#552×C151—22no—
17#552×C151—22no—
18C2×#126×C151C412yes—
19C2×#125×C151C412yes—
20C2×#125×C151C2211yescharacteristic
21C2×#123×C151C412yes—
22C2×C22⋊Q8×C151C2211yescharacteristic
23C2×C22⋊Q8×C151C2211yescharacteristic
24C2×C4×Q8×C151C2211yescharacteristic
25C2×C4×D4×C151C2211yescharacteristic
26C2×#117×C151C412yes—
27C2×#117×C151C2211yescharacteristic
28C22×C4⋊C4×C151C2211yescharacteristic
29#436×C151—22no—
30#435×C151—22no—
31#435×C151—22no—
32C8×D4×C151—22no—
33#423×C151C2212yes—
34C2×#101×C151C2212yes—
35C2×#101×C151C2212yes—
36#407×C151C2212yes—
37#407×C151C2212yes—
38C4×M16×C151C2212yes—
39#343×C151C2211yescharacteristic
40#343×C151C2212yes—
41#343×C151C2211yescharacteristic
42#343×C151C2212yes—
43#343×C151C2211yescharacteristic
44#343×C151C2212yes—
45#343×C151C2212yes—
46#343×C151C2211yescharacteristic
47C22×Q8×C151C2311yescharacteristic
48C22×D4×C151C2×C411yescharacteristic
49C23×C4×C151C2×C412yes—
50C23×C4×C151C2311yescharacteristic
51C23×C4×C151C2311yescharacteristic
52C2×M16×C151—22no—
53C2×M16×C151—22no—
54C2×M16×C151—24no—
55C2×M16×C151—24no—
56C2×M16×C151—42no—
57C2×M16×C151—42no—
58C2×M16×C151C2312yes—
59C2×M16×C151C2312yes—
60C2×M16×C151C2312yes—
61C2×M16×C151C2312yes—
62C22×C8×C151—22no—
63C22×C8×C151—22no—
64#126×C151—24no—
65#126×C151—24no—
66#125×C151—24no—
67#125×C151—24no—
68#125×C151—22no—
69#125×C151—22no—
70#123×C151—24no—
71#123×C151—24no—
72C22⋊Q8×C151—22no—
73C22⋊Q8×C151—22no—
74C22⋊Q8×C151—22no—
75C22⋊Q8×C151—22no—
76C4×Q8×C151—22no—
77C4×Q8×C151—22no—
78C4×D4×C151D412yes—
79C4×D4×C151D412yes—
80C4×D4×C151D412yes—
81C4×D4×C151D412yes—
82#117×C151—22no—
83#117×C151—22no—
84#117×C151—22no—
85#117×C151—22no—
86#117×C151—22no—
87#117×C151—22no—
88C2×C4⋊C4×C151—22no—
89C2×C4⋊C4×C151—22no—
90C2×C4⋊C4×C151C2×C412yes—
91C2×C4⋊C4×C151C2×C412yes—
92C2×C4⋊C4×C151C2×C412yes—
93C2×C4⋊C4×C151C2×C412yes—
94C2×C4⋊C4×C151C2×C412yes—
95C2×C4⋊C4×C151C2×C412yes—
96C2×C4⋊C4×C151C2×C411yescharacteristic
97C2×C4⋊C4×C151C2311yescharacteristic
98C2×C4⋊C4×C151C2311yescharacteristic
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C22⋊C4×C151C2×C412yes—
101C2×C22⋊C4×C151C2×C412yes—
102C2×C22⋊C4×C151C2×C412yes—
103C2×C22⋊C4×C151C2×C411yescharacteristic
104C2×C22⋊C4×C151C2×C411yescharacteristic
105C2×C42×C151C2×C412yes—
106C2×C42×C151C2×C412yes—
107C2×C42×C151C2311yescharacteristic
108C4⋊C8×C151—22no—
109C4⋊C8×C151—22no—
110#101×C151—24no—
111#101×C151—42no—
112C22⋊C8×C151—22no—
113C22⋊C8×C151—22no—
114C22⋊C8×C151—22no—
115C22⋊C8×C151—22no—
116#97×C151—22no—
117C4×C8×C151—22no—
118C24×C151C22×C411yescharacteristic
119C24×C151C22×C411yescharacteristic
120C2×Q8×C151—22no—
121C2×Q8×C151—22no—
122C2×Q8×C151—21no—
123C2×Q8×C151—21no—
124C2×D4×C151—42no—
125C2×D4×C151C22⋊C412yes—
126C2×D4×C151C22⋊C412yes—
127C22×C4×C151—22no—
128C22×C4×C151—22no—
129C22×C4×C151—21no—
130C22×C4×C151—21no—
131C22×C4×C151—21no—
132C22×C4×C151—21no—
133C22×C4×C151—22no—
134C22×C4×C151—22no—
135C22×C4×C151—44no—
136C22×C4×C151C22×C412yes—
137C22×C4×C151C22×C411yescharacteristic
138C22×C4×C151C22×C411yescharacteristic
139C22×C4×C151C22×C412yes—
140C22×C4×C151C22×C412yes—
141C22×C4×C151C22×C412yes—
142C22×C4×C151C22×C411yescharacteristic
143C22×C4×C151C22×C411yescharacteristic
144C22×C4×C151C2×D412yes—
145C22×C4×C151C2×D412yes—
146C22×C4×C151C2×D412yes—
147C22×C4×C151C2×D412yes—
148C22×C4×C151C2411yescharacteristic
149M16×C151—22no—
150M16×C151—22no—
151M16×C151—22no—
152M16×C151—22no—
153M16×C151—22no—
154M16×C151—22no—
155M16×C151—22no—
156M16×C151—44no—
157M16×C151—44no—
158M16×C151#4114yes—
159C2×C8×C151—22no—
160C2×C8×C151—22no—
161C2×C8×C151—22no—
162C2×C8×C151—22no—
163C2×C8×C151—44no—
164C2×C8×C151—44no—
165C4⋊C4×C151—24no—
166C4⋊C4×C151—22no—
167C4⋊C4×C151—22no—
168C4⋊C4×C151—22no—
169C4⋊C4×C151—22no—
170C4⋊C4×C151—24no—
171C4⋊C4×C151—24no—
172C4⋊C4×C151—24no—
173C4⋊C4×C151—22no—
174C4⋊C4×C151—22no—
175C4⋊C4×C151—22no—
176C4⋊C4×C151C22⋊C412yes—
177C4⋊C4×C151C22⋊C412yes—
178C22⋊C4×C151—22no—
179C22⋊C4×C151—22no—
180C22⋊C4×C151—24no—
181C22⋊C4×C151—24no—
182C22⋊C4×C151C22⋊C411yescharacteristic
183C22⋊C4×C151C22⋊C411yescharacteristic
184C22⋊C4×C151C22⋊C411yescharacteristic
185C22⋊C4×C151C22⋊C411yescharacteristic
186C22⋊C4×C151C22⋊C412yes—
187C22⋊C4×C151C22⋊C412yes—
188C42×C151—22no—
189C42×C151—22no—
190C42×C151—22no—
191C42×C151—22no—
192C42×C151C2×D412yes—
193C42×C151C2×D412yes—
194C23×C151—21no—
195C23×C151—21no—
196C23×C151—22no—
197C23×C151—21no—
198C23×C151—21no—
199C23×C151—41no—
200C23×C151—41no—
201C23×C151—41no—
202C23×C151C2×C22⋊C412yes—
203C23×C151C2×C22⋊C411yescharacteristic
204C23×C151C2×C22⋊C411yescharacteristic
205C23×C151C23×C411yescharacteristic
206Q8×C151—42no—
207Q8×C151—42no—
208D4×C151—24no—
209D4×C151—42no—
210C2×C4×C151—21no—
211C2×C4×C151—21no—
212C2×C4×C151—21no—
213C2×C4×C151—21no—
214C2×C4×C151—22no—
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—22no—
222C2×C4×C151—22no—
223C2×C4×C151—22no—
224C2×C4×C151—22no—
225C2×C4×C151—22no—
226C2×C4×C151—22no—
227C2×C4×C151—22no—
228C2×C4×C151—41no—
229C2×C4×C151—41no—
230C2×C4×C151—44no—
231C2×C4×C151—44no—
232C2×C4×C151—42no—
233C2×C4×C151—42no—
234C2×C4×C151—42no—
235C2×C4×C151C2×C22⋊C411yescharacteristic
236C2×C4×C151C2×C22⋊C411yescharacteristic
237C2×C4×C151C2×C22⋊C411yescharacteristic
238C2×C4×C151C2×C22⋊C411yescharacteristic
239C2×C4×C151C2×C22⋊C412yes—
240C2×C4×C151C2×C22⋊C412yes—
241C2×C4×C151C22×D412yes—
242C2×C4×C151C2×#4112yes—
243C2×C4×C151H(5,𝔽2)11yescharacteristic
244C2×C4×C1512−1+411yescharacteristic
245C8×C151—24no—
246C8×C151—42no—
247C8×C151—42no—
248C8×C151—42no—
249C22×C151—21no—
250C22×C151—21no—
251C22×C151—21no—
252C22×C151—21no—
253C22×C151—21no—
254C22×C151—22no—
255C22×C151—21no—
256C22×C151—22no—
257C22×C151—21no—
258C22×C151—22no—
259C22×C151—42no—
260C22×C151—42no—
261C22×C151—81no—
262C22×C151—81no—
263C22×C151#41312yes—
264C22×C151C22×C22⋊C411yescharacteristic
265C22×C151C4×#4111yescharacteristic
266C22×C151#52011yescharacteristic
267C4×C151—21no—
268C4×C151—22no—
269C4×C151—21no—
270C4×C151—22no—
271C4×C151—21no—
272C4×C151—21no—
273C4×C151—42no—
274C4×C151—42no—
275C4×C151—42no—
276C4×C151—42no—
277C4×C151#54612yes—
278C4×C151#54712yes—
279C2×C151—21no—
280C2×C151—21no—
281C2×C151—22no—
282C2×C151—41no—
283C2×C151—42no—
284C2×C151#233911yescharacteristic
285C2×C151C2×#41311yescharacteristic
286C2×C151#288911yescharacteristic
287#22480C15111yesmaximal, characteristic, direct product factor, Sylow
288C151#2248011yescharacteristic, direct product factor, Sylow
289C2×#552C2×C15111yescharacteristic
290D4×M16C2×C15112yes—
291#1998C2×C15112yescomplemented
292#1901C2×C15112yescomplemented
293#1901C2×C15112yescomplemented
294#1822C2×C15111yescharacteristic, complemented
295#1821C2×C15111yescharacteristic, complemented
296#1801C2×C15111yescharacteristic, complemented
297C4×#101C2×C15111yescharacteristic, complemented
298#1742C2×C15111yescharacteristic, complemented
299C2×#343C2×C15111yescharacteristic, complemented
300C22×M16C22×C15112yes—
301C22×M16C22×C15112yes—
302#552—22no—
303#552—22no—
304#552—22no—
305#552—22no—
306C2×#126C4×C15112yes—
307C2×#125C4×C15112yes—
308C2×#125C22×C15111yescharacteristic
309C2×#123C4×C15112yes—
310C2×C22⋊Q8C22×C15111yescharacteristic
311C2×C22⋊Q8C22×C15111yescharacteristic
312C2×C4×Q8C22×C15111yescharacteristic
313C2×C4×D4C22×C15111yescharacteristic
314C2×#117C4×C15112yes—
315C2×#117C22×C15111yescharacteristic
316C22×C4⋊C4C22×C15111yescharacteristic
317#436—22no—
318#435—22no—
319#435—22no—
320C8×D4—22no—
321#423C22×C15112yes—
322C2×#101C22×C15112yes—
323C2×#101C22×C15112yes—
324#407C22×C15112yes—
325#407C22×C15112yes—
326C4×M16C22×C15112yes—
327#343C22×C15111yescharacteristic
328#343C22×C15111yescharacteristic
329#343C22×C15111yescharacteristic
330#343C22×C15112yes—
331#343C22×C15112yes—
332#343C22×C15112yes—
333#343C22×C15112yes—
334#343C22×C15111yescharacteristic
335C22×Q8C23×C15111yescharacteristic
336C22×D4C2×C4×C15111yescharacteristic
337C23×C4C2×C4×C15112yes—
338C23×C4C23×C15111yescharacteristic
339C23×C4C23×C15111yescharacteristic
340C2×M16—22no—
341C2×M16—22no—
342C2×M16—24no—
343C2×M16—24no—
344C2×M16—42no—
345C2×M16—42no—
346C2×M16C23×C15112yes—
347C2×M16C23×C15112yes—
348C2×M16C23×C15112yes—
349C2×M16C23×C15112yes—
350C22×C8—22no—
351C22×C8—22no—
352#126—24no—
353#126—24no—
354#125—24no—
355#125—24no—
356#125—22no—
357#125—22no—
358#123—24no—
359#123—24no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8—22no—
364C4×Q8—22no—
365C4×Q8—22no—
366C4×D4D4×C15112yes—
367C4×D4D4×C15112yes—
368C4×D4D4×C15112yes—
369C4×D4D4×C15112yes—
370#117—22no—
371#117—22no—
372#117—22no—
373#117—22no—
374#117—22no—
375#117—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4C2×C4×C15112yes—
379C2×C4⋊C4C2×C4×C15112yes—
380C2×C4⋊C4C2×C4×C15112yes—
381C2×C4⋊C4C2×C4×C15112yes—
382C2×C4⋊C4C2×C4×C15112yes—
383C2×C4⋊C4C2×C4×C15112yes—
384C2×C4⋊C4C2×C4×C15111yescharacteristic
385C2×C4⋊C4C23×C15111yescharacteristic
386C2×C4⋊C4C23×C15111yescharacteristic
387C2×C4⋊C4C23×C15111yescharacteristic
388C2×C22⋊C4C2×C4×C15112yes—
389C2×C22⋊C4C2×C4×C15112yes—
390C2×C22⋊C4C2×C4×C15112yes—
391C2×C22⋊C4C2×C4×C15111yescharacteristic
392C2×C22⋊C4C2×C4×C15111yescharacteristic
393C2×C42C2×C4×C15112yes—
394C2×C42C2×C4×C15112yes—
395C2×C42C23×C15111yescharacteristic
396C4⋊C8—22no—
397C4⋊C8—22no—
398#101—24no—
399#101—42no—
400C22⋊C8—22no—
401C22⋊C8—22no—
402C22⋊C8—22no—
403C22⋊C8—22no—
404#97—22no—
405C4×C8—22no—
406C24C22×C4×C15111yescharacteristic
407C24C22×C4×C15111yescharacteristic
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×D4—42no—
413C2×D4C22⋊C4×C15112yes—
414C2×D4C22⋊C4×C15112yes—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—44no—
424C22×C4C22×C4×C15112yes—
425C22×C4C22×C4×C15111yescharacteristic
426C22×C4C22×C4×C15111yescharacteristic
427C22×C4C22×C4×C15112yes—
428C22×C4C22×C4×C15112yes—
429C22×C4C22×C4×C15112yes—
430C22×C4C22×C4×C15111yescharacteristic
431C22×C4C22×C4×C15111yescharacteristic
432C22×C4C2×D4×C15112yes—
433C22×C4C2×D4×C15112yes—
434C22×C4C2×D4×C15112yes—
435C22×C4C2×D4×C15112yes—
436C22×C4C24×C15111yescharacteristic
437M16—22no—
438M16—22no—
439M16—22no—
440M16—22no—
441M16—22no—
442M16—22no—
443M16—22no—
444M16—44no—
445M16—44no—
446M16#41×C15114yes—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—44no—
452C2×C8—44no—
453C4⋊C4—24no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4C22⋊C4×C15112yes—
465C4⋊C4C22⋊C4×C15112yes—
466C22⋊C4—22no—
467C22⋊C4—22no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4C22⋊C4×C15111yescharacteristic
471C22⋊C4C22⋊C4×C15111yescharacteristic
472C22⋊C4C22⋊C4×C15111yescharacteristic
473C22⋊C4C22⋊C4×C15111yescharacteristic
474C22⋊C4C22⋊C4×C15112yes—
475C22⋊C4C22⋊C4×C15112yes—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42C2×D4×C15112yes—
481C42C2×D4×C15112yes—
482C23—22no—
483C23—21no—
484C23—21no—
485C23—21no—
486C23—21no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C2×C22⋊C4×C15112yes—
491C23C2×C22⋊C4×C15111yescharacteristic
492C23C2×C22⋊C4×C15111yescharacteristic
493C23C23×C4×C15111yescharacteristic
494Q8—42no—
495Q8—42no—
496D4—24no—
497D4—42no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—44no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4C2×C22⋊C4×C15111yescharacteristic
524C2×C4C2×C22⋊C4×C15111yescharacteristic
525C2×C4C2×C22⋊C4×C15111yescharacteristic
526C2×C4C2×C22⋊C4×C15111yescharacteristic
527C2×C4C2×C22⋊C4×C15112yes—
528C2×C4C2×C22⋊C4×C15112yes—
529C2×C4C22×D4×C15112yes—
530C2×C4C2×#41×C15112yes—
531C2×C4H(5,𝔽2)×C15111yescharacteristic
532C2×C42−1+4×C15111yescharacteristic
533C8—24no—
534C8—42no—
535C8—42no—
536C8—42no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—22no—
545C22—21no—
546C22—22no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22#413×C15112yes—
552C22C22×C22⋊C4×C15111yescharacteristic
553C22C4×#41×C15111yescharacteristic
554C22#520×C15111yescharacteristic
555C4—21no—
556C4—22no—
557C4—21no—
558C4—22no—
559C4—21no—
560C4—21no—
561C4—42no—
562C4—42no—
563C4—42no—
564C4—42no—
565C4#546×C15112yes—
566C4#547×C15112yes—
567C2—21no—
568C2—21no—
569C2—22no—
570C2—41no—
571C2—42no—
572C2#2339×C15111yescharacteristic
573C2C2×#413×C15111yescharacteristic
574C2#2889×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C22×C22⋊C4
commutatorC23C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC22×D4×C151C2×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C4×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1998×C151C2semidirect
4. #1901×C151C2semidirect
5. #1901×C151C2semidirect
6. #1822×C151C2semidirect
7. #1821×C151C2semidirect
8. #1801×C151C2semidirect
9. C4×#101×C151C2semidirect
10. #1742×C151C2semidirect
11. C2×#343×C151C2semidirect
287. #22480C151direct (N × H)
288. C151#22480direct (N × H)
291. #1998C2×C151semidirect
292. #1901C2×C151semidirect
293. #1901C2×C151semidirect
294. #1822C2×C151semidirect
295. #1821C2×C151semidirect
296. #1801C2×C151semidirect
297. C4×#101C2×C151semidirect
298. #1742C2×C151semidirect
299. C2×#343C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#552×C1512
D4×M16×C1512
#1998×C1512
#1901×C1512
#1822×C1512
#1821×C1512
#1801×C1512
C4×#101×C1512
#1742×C1512
C2×#343×C1512
#22480151