Finite Group Databasebeta

← C151×#23888 #50328813

Subgroups — C151×#23888 #50328813

Order 38656.

1682 conjugacy classes of subgroups.

The subgroup lattice has 1026 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#577×C151C211yesmaximal, characteristic, complemented
2C2×#576×C151C211yesmaximal, characteristic, complemented
3C2×#454×C151C211yesmaximal, characteristic, complemented
4C2×#455×C151C211yesmaximal, characteristic, complemented
5#3013×C151C211yesmaximal, characteristic, complemented
6#3012×C151C211yesmaximal, characteristic, complemented
7#2019×C151C211yesmaximal, characteristic, complemented
8#2018×C151C211yesmaximal, characteristic, complemented
9#2012×C151C211yesmaximal, characteristic, complemented
10#2006×C151C211yesmaximal, characteristic, complemented
11#1908×C151C211yesmaximal, characteristic, complemented
12#1907×C151C211yesmaximal, characteristic, complemented
13#1876×C151C211yesmaximal, characteristic, complemented
14#1876×C151C211yesmaximal, characteristic, complemented
15#1792×C151C211yesmaximal, characteristic, complemented
16C2×2−1+4×C151C2211yescharacteristic, complemented
17C2×H(5,𝔽2)×C151C2211yescharacteristic
18C2×H(5,𝔽2)×C151C2211yescharacteristic
19#577×C151—24no—
20#577×C151—24no—
21#576×C151—24no—
22#576×C151—24no—
23C2×#137×C151—21no—
24C2×#137×C151C2211yescharacteristic
25C2×#137×C151C2211yescharacteristic, complemented
26C2×AGL(1,ℤ/8)×C151—21no—
27C2×AGL(1,ℤ/8)×C151—21no—
28C2×AGL(1,ℤ/8)×C151—21no—
29C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C151C2211yescharacteristic
31C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
32C2×AGL(1,ℤ/8)×C151C2211yescharacteristic, complemented
33C2×#135×C151—21no—
34C2×#135×C151—21no—
35C2×#135×C151C2211yescharacteristic
36C2×#135×C151C2211yescharacteristic
37C22×SD16×C151—21no—
38C22×SD16×C151C2211yescharacteristic, complemented
39C22×D8×C151—21no—
40C22×D8×C151C2211yescharacteristic
41C2×#131×C151C2211yescharacteristic
42C2×#131×C151C2211yescharacteristic, complemented
43#537×C151C2211yescharacteristic, complemented
44C2×#124×C151C2211yescharacteristic, complemented
45#455×C151—24no—
46#454×C151—24no—
47#452×C151—21no—
48#452×C151—21no—
49#451×C151—21no—
50#450×C151—21no—
51#449×C151—21no—
52#449×C151—21no—
53#448×C151—21no—
54#447×C151—21no—
55C2×#104×C151C2211yescharacteristic
56C2×#104×C151C2211yescharacteristic, complemented
57C2×#104×C151C2211yescharacteristic, complemented
58C2×#104×C151C2211yescharacteristic, complemented
59#417×C151C2211yescharacteristic
60#417×C151C2211yescharacteristic, complemented
61C2×#103×C151C2211yescharacteristic, complemented
62C2×#102×C151C2211yescharacteristic, complemented
63C2×#101×C151C2211yescharacteristic, complemented
64C2×#100×C151C2211yescharacteristic, complemented
65C2×#100×C151C2211yescharacteristic, complemented
66#408×C151C2211yescharacteristic, complemented
67#408×C151C2211yescharacteristic, complemented
68#390×C151C2211yescharacteristic, complemented
69#343×C151C2211yescharacteristic, complemented
70#341×C151C2211yescharacteristic, complemented
71#341×C151C2211yescharacteristic, complemented
72#336×C151C2211yescharacteristic, complemented
732−1+4×C151—22no—
742−1+4×C151—22no—
752−1+4×C151—22no—
762−1+4×C151—41no—
77H(5,𝔽2)×C151—22no—
78H(5,𝔽2)×C151—22no—
79H(5,𝔽2)×C151—22no—
80H(5,𝔽2)×C151—22no—
81H(5,𝔽2)×C151—22no—
82H(5,𝔽2)×C151—41no—
83H(5,𝔽2)×C151—41no—
84H(5,𝔽2)×C151D414yescomplemented
85C2×#41×C151—21no—
86C2×#41×C151—21no—
87C2×#41×C151—21no—
88C2×#41×C151—21no—
89C2×#41×C151—21no—
90C2×#41×C151—21no—
91C2×#41×C151—41no—
92C2×#41×C151C2311yescharacteristic
93C2×#41×C151C2311yescharacteristic
94C2×#41×C151C2311yescharacteristic
95C2×#41×C151C2311yescharacteristic
96C22×Q8×C151—21no—
97C22×Q8×C151—21no—
98C22×Q8×C151C2311yescharacteristic
99C22×D4×C151—21no—
100C22×D4×C151—21no—
101C22×D4×C151—21no—
102C22×D4×C151—21no—
103C22×D4×C151—41no—
104C22×D4×C151—41no—
105C22×D4×C151C2311yescharacteristic
106C22×D4×C151C2311yescharacteristic
107#137×C151—28no—
108#137×C151—22no—
109#137×C151—22no—
110#137×C151—41no—
111#137×C151D414yescomplemented
112AGL(1,ℤ/8)×C151—28no—
113AGL(1,ℤ/8)×C151—28no—
114AGL(1,ℤ/8)×C151—28no—
115AGL(1,ℤ/8)×C151—22no—
116AGL(1,ℤ/8)×C151—22no—
117AGL(1,ℤ/8)×C151—22no—
118AGL(1,ℤ/8)×C151—22no—
119AGL(1,ℤ/8)×C151—22no—
120AGL(1,ℤ/8)×C151—22no—
121AGL(1,ℤ/8)×C151—41no—
122AGL(1,ℤ/8)×C151D414yescomplemented
123#135×C151—28no—
124#135×C151—28no—
125#135×C151—22no—
126#135×C151—22no—
127#135×C151—22no—
128#135×C151—22no—
129C2×Q16×C151—21no—
130C2×Q16×C151—21no—
131C2×Q16×C151D411yescharacteristic
132C2×Q16×C151D411yescharacteristic
133C2×SD16×C151—28no—
134C2×SD16×C151—21no—
135C2×SD16×C151—22no—
136C2×SD16×C151—21no—
137C2×SD16×C151—21no—
138C2×SD16×C151—21no—
139C2×SD16×C151—21no—
140C2×SD16×C151—22no—
141C2×SD16×C151—21no—
142C2×SD16×C151—21no—
143C2×SD16×C151—21no—
144C2×SD16×C151D411yescharacteristic
145C2×SD16×C151D411yescharacteristic
146C2×SD16×C151D411yescharacteristic
147C2×SD16×C151D411yescharacteristic
148C2×D8×C151—28no—
149C2×D8×C151—21no—
150C2×D8×C151—21no—
151C2×D8×C151—22no—
152C2×D8×C151—22no—
153C2×D8×C151—21no—
154C2×D8×C151—21no—
155C2×D8×C151—21no—
156C2×D8×C151—21no—
157C2×D8×C151D411yescharacteristic
158C2×D8×C151D411yescharacteristic
159#131×C151—22no—
160#131×C151—22no—
161#131×C151—22no—
162#131×C151—22no—
163C2×M16×C151—21no—
164C2×M16×C151—21no—
165C2×M16×C151C2311yescharacteristic
166C2×M16×C151C2311yescharacteristic
167C2×M16×C151C2311yescharacteristic
168C2×M16×C151C2311yescharacteristic
169C22×C8×C151—21no—
170C22×C8×C151—21no—
171C22×C8×C151C2311yescharacteristic
172C22×C8×C151C2311yescharacteristic
173#124×C151—22no—
174#124×C151—22no—
175C22⋊Q8×C151—21no—
176C22⋊Q8×C151—21no—
177#121×C151—21no—
178#121×C151—21no—
179#121×C151—41no—
180C2×C4⋊C4×C151C2311yescharacteristic
181C2×C22⋊C4×C151—41no—
182C2×C22⋊C4×C151—41no—
183C2×C42×C151C2311yescharacteristic
184#104×C151—22no—
185#104×C151—22no—
186#104×C151—22no—
187#104×C151—22no—
188#103×C151—21no—
189#103×C151—21no—
190#103×C151—21no—
191#103×C151—21no—
192#102×C151—21no—
193#102×C151—21no—
194#102×C151—21no—
195#102×C151—21no—
196#101×C151—22no—
197#100×C151—22no—
198#100×C151—41no—
199C22⋊C8×C151—21no—
200C22⋊C8×C151—21no—
201C22⋊C8×C151—21no—
202C22⋊C8×C151—21no—
203C24×C151—21no—
204C24×C151—21no—
205C24×C151—41no—
206C24×C151—41no—
207#41×C151—21no—
208#41×C151—21no—
209#41×C151—21no—
210#41×C151—21no—
211#41×C151—24no—
212#41×C151—24no—
213#41×C151—24no—
214#41×C151—24no—
215#41×C151—21no—
216#41×C151—21no—
217#41×C151—21no—
218#41×C151—21no—
219#41×C151—21no—
220#41×C151—21no—
221#41×C151—21no—
222#41×C151—21no—
223#41×C151—42no—
224#41×C151—44no—
225#41×C151—42no—
226#41×C151—42no—
227#41×C151—42no—
228#41×C151—42no—
229#41×C151—42no—
230#41×C151—44no—
231#41×C151—42no—
232#41×C151—42no—
233#41×C151C2×D412yes—
234#41×C151C2×D412yes—
235#41×C151C2×D412yes—
236#41×C151C2×D412yes—
237C2×Q8×C151—21no—
238C2×Q8×C151—24no—
239C2×Q8×C151—21no—
240C2×Q8×C151—21no—
241C2×Q8×C151—21no—
242C2×Q8×C151—21no—
243C2×Q8×C151—41no—
244C2×Q8×C151—42no—
245C2×Q8×C151—42no—
246C2×Q8×C151—42no—
247C2×Q8×C151C2×D411yescharacteristic
248C2×Q8×C151C2×D411yescharacteristic
249C2×Q8×C151C2×D412yes—
250C2×Q8×C151C2×D411yescharacteristic
251C2×Q8×C151C2×D411yescharacteristic
252C2×D4×C151—21no—
253C2×D4×C151—21no—
254C2×D4×C151—24no—
255C2×D4×C151—24no—
256C2×D4×C151—24no—
257C2×D4×C151—21no—
258C2×D4×C151—21no—
259C2×D4×C151—21no—
260C2×D4×C151—21no—
261C2×D4×C151—21no—
262C2×D4×C151—21no—
263C2×D4×C151—21no—
264C2×D4×C151—21no—
265C2×D4×C151—21no—
266C2×D4×C151—21no—
267C2×D4×C151—21no—
268C2×D4×C151—21no—
269C2×D4×C151—42no—
270C2×D4×C151—42no—
271C2×D4×C151—42no—
272C2×D4×C151—41no—
273C2×D4×C151—41no—
274C2×D4×C151—41no—
275C2×D4×C151—41no—
276C2×D4×C151—44no—
277C2×D4×C151—42no—
278C2×D4×C151—44no—
279C2×D4×C151—44no—
280C2×D4×C151—44no—
281C2×D4×C151—41no—
282C2×D4×C151—42no—
283C2×D4×C151—41no—
284C2×D4×C151C2×D411yescharacteristic
285C2×D4×C151C2×D411yescharacteristic
286C2×D4×C151C2×D412yes—
287C2×D4×C151C2×D412yes—
288C2×D4×C151C2×D411yescharacteristic
289C2×D4×C151C2×D411yescharacteristic
290C22×C4×C151—21no—
291C22×C4×C151—21no—
292C22×C4×C151—21no—
293C22×C4×C151—21no—
294C22×C4×C151—21no—
295C22×C4×C151—21no—
296C22×C4×C151—21no—
297C22×C4×C151—41no—
298C22×C4×C151—41no—
299C22×C4×C151—41no—
300C22×C4×C151—41no—
301C22×C4×C151C2411yescharacteristic
302Q16×C151—24no—
303Q16×C151—22no—
304Q16×C151—22no—
305Q16×C151—42no—
306SD16×C151—24no—
307SD16×C151—24no—
308SD16×C151—24no—
309SD16×C151—24no—
310SD16×C151—24no—
311SD16×C151—22no—
312SD16×C151—22no—
313SD16×C151—22no—
314SD16×C151—24no—
315SD16×C151—22no—
316SD16×C151—42no—
317SD16×C151—42no—
318D8×C151—24no—
319D8×C151—24no—
320D8×C151—24no—
321D8×C151—24no—
322D8×C151—22no—
323D8×C151—24no—
324D8×C151—22no—
325D8×C151—42no—
326M16×C151—24no—
327M16×C151—24no—
328M16×C151—21no—
329M16×C151—21no—
330M16×C151—21no—
331M16×C151—21no—
332M16×C151—21no—
333M16×C151—21no—
334M16×C151C2×D412yes—
335M16×C151C2×D412yes—
336C2×C8×C151—24no—
337C2×C8×C151—24no—
338C2×C8×C151—21no—
339C2×C8×C151—21no—
340C2×C8×C151—21no—
341C2×C8×C151—21no—
342C2×C8×C151—21no—
343C2×C8×C151—21no—
344C2×C8×C151—21no—
345C2×C8×C151—21no—
346C2×C8×C151C2×D411yescharacteristic
347C2×C8×C151C2×D411yescharacteristic
348C2×C8×C151C2×D411yescharacteristic
349C2×C8×C151C2×D411yescharacteristic
350C4⋊C4×C151—21no—
351C4⋊C4×C151—21no—
352C4⋊C4×C151—41no—
353C22⋊C4×C151—44no—
354C22⋊C4×C151—41no—
355C22⋊C4×C151—41no—
356C22⋊C4×C151—82no—
357C42×C151—21no—
358C42×C151—21no—
359C23×C151—21no—
360C23×C151—21no—
361C23×C151—21no—
362C23×C151—21no—
363C23×C151—22no—
364C23×C151—22no—
365C23×C151—44no—
366C23×C151—44no—
367C23×C151—41no—
368C23×C151—41no—
369C23×C151—41no—
370C23×C151—41no—
371C23×C151—81no—
372C23×C151—81no—
373C23×C151—81no—
374C23×C151—81no—
375C23×C151—161no—
376C23×C151—161no—
377C23×C151—161no—
378C23×C151—161no—
379C23×C151H(5,𝔽2)11yescharacteristic
380Q8×C151—21no—
381Q8×C151—21no—
382Q8×C151—21no—
383Q8×C151—22no—
384Q8×C151—21no—
385Q8×C151—22no—
386Q8×C151—21no—
387Q8×C151—21no—
388Q8×C151—44no—
389Q8×C151—41no—
390Q8×C151—41no—
391Q8×C151#12012yes—
392Q8×C151#12012yes—
393D4×C151—22no—
394D4×C151—22no—
395D4×C151—22no—
396D4×C151—22no—
397D4×C151—21no—
398D4×C151—22no—
399D4×C151—22no—
400D4×C151—21no—
401D4×C151—22no—
402D4×C151—21no—
403D4×C151—21no—
404D4×C151—21no—
405D4×C151—21no—
406D4×C151—22no—
407D4×C151—44no—
408D4×C151—44no—
409D4×C151—44no—
410D4×C151—44no—
411D4×C151—44no—
412D4×C151—41no—
413D4×C151—41no—
414D4×C151—41no—
415D4×C151—41no—
416D4×C151—41no—
417D4×C151—41no—
418D4×C151—41no—
419D4×C151—41no—
420D4×C151—161no—
421D4×C151#12012yes—
422D4×C151#12012yes—
423C2×C4×C151—21no—
424C2×C4×C151—21no—
425C2×C4×C151—22no—
426C2×C4×C151—22no—
427C2×C4×C151—22no—
428C2×C4×C151—22no—
429C2×C4×C151—22no—
430C2×C4×C151—21no—
431C2×C4×C151—21no—
432C2×C4×C151—44no—
433C2×C4×C151—44no—
434C2×C4×C151—44no—
435C2×C4×C151—44no—
436C2×C4×C151—41no—
437C2×C4×C151—41no—
438C2×C4×C151—41no—
439C2×C4×C151—41no—
440C2×C4×C151—41no—
441C2×C4×C151—41no—
442C2×C4×C151—41no—
443C2×C4×C151—41no—
444C2×C4×C151—41no—
445C2×C4×C151—41no—
446C2×C4×C151—81no—
447C2×C4×C151C22×D411yescharacteristic
448C2×C4×C151C22×D411yescharacteristic
449C2×C4×C151C22×D411yescharacteristic
450C2×C4×C151C22×D411yescharacteristic
451C2×C4×C151C22×D411yescharacteristic
452C2×C4×C151H(5,𝔽2)11yescharacteristic
453C8×C151—21no—
454C8×C151—21no—
455C8×C151—22no—
456C8×C151—22no—
457C8×C151—21no—
458C8×C151—21no—
459C8×C151—41no—
460C8×C151—41no—
461C22×C151—21no—
462C22×C151—21no—
463C22×C151—22no—
464C22×C151—22no—
465C22×C151—41no—
466C22×C151—41no—
467C22×C151—41no—
468C22×C151—41no—
469C22×C151—41no—
470C22×C151—41no—
471C22×C151—42no—
472C22×C151—42no—
473C22×C151—41no—
474C22×C151—41no—
475C22×C151—41no—
476C22×C151—41no—
477C22×C151—82no—
478C22×C151—82no—
479C22×C151—81no—
480C22×C151—81no—
481C22×C151—81no—
482C22×C151—81no—
483C22×C151—161no—
484C22×C151—161no—
485C22×C151—164no—
486C22×C151—164no—
487C22×C151#53411yescharacteristic
488C22×C151D4211yescharacteristic
489C22×C151D4211yescharacteristic
490C4×C151—22no—
491C4×C151—22no—
492C4×C151—41no—
493C4×C151—42no—
494C4×C151—41no—
495C4×C151—81no—
496C4×C151—81no—
497C4×C151C2×#12011yescharacteristic
498C4×C151C2×#12011yescharacteristic
499C4×C151D4211yescharacteristic
500C4×C151D4211yescharacteristic
501C2×C151—21no—
502C2×C151—21no—
503C2×C151—42no—
504C2×C151—42no—
505C2×C151—81no—
506C2×C151—81no—
507C2×C151—82no—
508C2×C151—82no—
509C2×C151#240311yescharacteristic
510C2×C151#328811yescharacteristic
511C2×C151#329011yescharacteristic
512#23888C15111yesmaximal, characteristic, direct product factor, Sylow
513C151#2388811yescharacteristic, direct product factor, Sylow
514C2×#577C2×C15111yescharacteristic, complemented
515C2×#576C2×C15111yescharacteristic, complemented
516C2×#454C2×C15111yescharacteristic, complemented
517C2×#455C2×C15111yescharacteristic, complemented
518#3013C2×C15111yescharacteristic, complemented
519#3012C2×C15111yescharacteristic, complemented
520#2019C2×C15111yescharacteristic, complemented
521#2018C2×C15111yescharacteristic, complemented
522#2012C2×C15111yescharacteristic, complemented
523#2006C2×C15111yescharacteristic, complemented
524#1908C2×C15111yescharacteristic, complemented
525#1907C2×C15111yescharacteristic, complemented
526#1876C2×C15111yescharacteristic, complemented
527#1876C2×C15111yescharacteristic, complemented
528#1792C2×C15111yescharacteristic, complemented
529C2×2−1+4C22×C15111yescharacteristic, complemented
530C2×H(5,𝔽2)C22×C15111yescharacteristic
531C2×H(5,𝔽2)C22×C15111yescharacteristic
532#577—24no—
533#577—24no—
534#576—24no—
535#576—24no—
536C2×#137—21no—
537C2×#137C22×C15111yescharacteristic
538C2×#137C22×C15111yescharacteristic, complemented
539C2×AGL(1,ℤ/8)—21no—
540C2×AGL(1,ℤ/8)—21no—
541C2×AGL(1,ℤ/8)—21no—
542C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
543C2×AGL(1,ℤ/8)C22×C15111yescharacteristic
544C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
545C2×AGL(1,ℤ/8)C22×C15111yescharacteristic, complemented
546C2×#135—21no—
547C2×#135—21no—
548C2×#135C22×C15111yescharacteristic
549C2×#135C22×C15111yescharacteristic
550C22×SD16—21no—
551C22×SD16C22×C15111yescharacteristic, complemented
552C22×D8—21no—
553C22×D8C22×C15111yescharacteristic
554C2×#131C22×C15111yescharacteristic
555C2×#131C22×C15111yescharacteristic, complemented
556#537C22×C15111yescharacteristic, complemented
557C2×#124C22×C15111yescharacteristic, complemented
558#455—24no—
559#454—24no—
560#452—21no—
561#452—21no—
562#451—21no—
563#450—21no—
564#449—21no—
565#449—21no—
566#448—21no—
567#447—21no—
568C2×#104C22×C15111yescharacteristic
569C2×#104C22×C15111yescharacteristic, complemented
570C2×#104C22×C15111yescharacteristic, complemented
571C2×#104C22×C15111yescharacteristic, complemented
572#417C22×C15111yescharacteristic
573#417C22×C15111yescharacteristic, complemented
574C2×#103C22×C15111yescharacteristic, complemented
575C2×#102C22×C15111yescharacteristic, complemented
576C2×#101C22×C15111yescharacteristic, complemented
577C2×#100C22×C15111yescharacteristic, complemented
578C2×#100C22×C15111yescharacteristic, complemented
579#408C22×C15111yescharacteristic, complemented
580#408C22×C15111yescharacteristic, complemented
581#390C22×C15111yescharacteristic, complemented
582#343C22×C15111yescharacteristic, complemented
583#341C22×C15111yescharacteristic, complemented
584#341C22×C15111yescharacteristic, complemented
585#336C22×C15111yescharacteristic, complemented
5862−1+4—22no—
5872−1+4—22no—
5882−1+4—22no—
5892−1+4—41no—
590H(5,𝔽2)—22no—
591H(5,𝔽2)—22no—
592H(5,𝔽2)—22no—
593H(5,𝔽2)—22no—
594H(5,𝔽2)—22no—
595H(5,𝔽2)—41no—
596H(5,𝔽2)—41no—
597H(5,𝔽2)D4×C15114yescomplemented
598C2×#41—21no—
599C2×#41—21no—
600C2×#41—21no—
601C2×#41—21no—
602C2×#41—21no—
603C2×#41—21no—
604C2×#41—41no—
605C2×#41C23×C15111yescharacteristic
606C2×#41C23×C15111yescharacteristic
607C2×#41C23×C15111yescharacteristic
608C2×#41C23×C15111yescharacteristic
609C22×Q8—21no—
610C22×Q8—21no—
611C22×Q8C23×C15111yescharacteristic
612C22×D4—21no—
613C22×D4—21no—
614C22×D4—21no—
615C22×D4—21no—
616C22×D4—41no—
617C22×D4—41no—
618C22×D4C23×C15111yescharacteristic
619C22×D4C23×C15111yescharacteristic
620#137—28no—
621#137—22no—
622#137—22no—
623#137—41no—
624#137D4×C15114yescomplemented
625AGL(1,ℤ/8)—28no—
626AGL(1,ℤ/8)—28no—
627AGL(1,ℤ/8)—28no—
628AGL(1,ℤ/8)—22no—
629AGL(1,ℤ/8)—22no—
630AGL(1,ℤ/8)—22no—
631AGL(1,ℤ/8)—22no—
632AGL(1,ℤ/8)—22no—
633AGL(1,ℤ/8)—22no—
634AGL(1,ℤ/8)—41no—
635AGL(1,ℤ/8)D4×C15114yescomplemented
636#135—28no—
637#135—28no—
638#135—22no—
639#135—22no—
640#135—22no—
641#135—22no—
642C2×Q16—21no—
643C2×Q16—21no—
644C2×Q16D4×C15111yescharacteristic
645C2×Q16D4×C15111yescharacteristic
646C2×SD16—28no—
647C2×SD16—21no—
648C2×SD16—22no—
649C2×SD16—21no—
650C2×SD16—21no—
651C2×SD16—21no—
652C2×SD16—22no—
653C2×SD16—21no—
654C2×SD16—21no—
655C2×SD16—21no—
656C2×SD16—21no—
657C2×SD16D4×C15111yescharacteristic
658C2×SD16D4×C15111yescharacteristic
659C2×SD16D4×C15111yescharacteristic
660C2×SD16D4×C15111yescharacteristic
661C2×D8—28no—
662C2×D8—21no—
663C2×D8—21no—
664C2×D8—22no—
665C2×D8—22no—
666C2×D8—21no—
667C2×D8—21no—
668C2×D8—21no—
669C2×D8—21no—
670C2×D8D4×C15111yescharacteristic
671C2×D8D4×C15111yescharacteristic
672#131—22no—
673#131—22no—
674#131—22no—
675#131—22no—
676C2×M16—21no—
677C2×M16—21no—
678C2×M16C23×C15111yescharacteristic
679C2×M16C23×C15111yescharacteristic
680C2×M16C23×C15111yescharacteristic
681C2×M16C23×C15111yescharacteristic
682C22×C8—21no—
683C22×C8—21no—
684C22×C8C23×C15111yescharacteristic
685C22×C8C23×C15111yescharacteristic
686#124—22no—
687#124—22no—
688C22⋊Q8—21no—
689C22⋊Q8—21no—
690#121—21no—
691#121—21no—
692#121—41no—
693C2×C4⋊C4C23×C15111yescharacteristic
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C42C23×C15111yescharacteristic
697#104—22no—
698#104—22no—
699#104—22no—
700#104—22no—
701#103—21no—
702#103—21no—
703#103—21no—
704#103—21no—
705#102—21no—
706#102—21no—
707#102—21no—
708#102—21no—
709#101—22no—
710#100—22no—
711#100—41no—
712C22⋊C8—21no—
713C22⋊C8—21no—
714C22⋊C8—21no—
715C22⋊C8—21no—
716C24—21no—
717C24—21no—
718C24—41no—
719C24—41no—
720#41—21no—
721#41—21no—
722#41—21no—
723#41—21no—
724#41—24no—
725#41—24no—
726#41—24no—
727#41—24no—
728#41—21no—
729#41—21no—
730#41—21no—
731#41—21no—
732#41—21no—
733#41—21no—
734#41—21no—
735#41—21no—
736#41—42no—
737#41—44no—
738#41—42no—
739#41—42no—
740#41—42no—
741#41—42no—
742#41—42no—
743#41—44no—
744#41—42no—
745#41—42no—
746#41C2×D4×C15112yes—
747#41C2×D4×C15112yes—
748#41C2×D4×C15112yes—
749#41C2×D4×C15112yes—
750C2×Q8—21no—
751C2×Q8—24no—
752C2×Q8—21no—
753C2×Q8—21no—
754C2×Q8—21no—
755C2×Q8—21no—
756C2×Q8—41no—
757C2×Q8—42no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8C2×D4×C15111yescharacteristic
761C2×Q8C2×D4×C15111yescharacteristic
762C2×Q8C2×D4×C15112yes—
763C2×Q8C2×D4×C15111yescharacteristic
764C2×Q8C2×D4×C15111yescharacteristic
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—24no—
768C2×D4—24no—
769C2×D4—24no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—41no—
786C2×D4—41no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—44no—
790C2×D4—42no—
791C2×D4—44no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—41no—
795C2×D4—42no—
796C2×D4—41no—
797C2×D4C2×D4×C15111yescharacteristic
798C2×D4C2×D4×C15111yescharacteristic
799C2×D4C2×D4×C15112yes—
800C2×D4C2×D4×C15112yes—
801C2×D4C2×D4×C15111yescharacteristic
802C2×D4C2×D4×C15111yescharacteristic
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—41no—
811C22×C4—41no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4C24×C15111yescharacteristic
815Q16—24no—
816Q16—22no—
817Q16—22no—
818Q16—42no—
819SD16—24no—
820SD16—24no—
821SD16—24no—
822SD16—24no—
823SD16—24no—
824SD16—22no—
825SD16—22no—
826SD16—22no—
827SD16—24no—
828SD16—22no—
829SD16—42no—
830SD16—42no—
831D8—24no—
832D8—24no—
833D8—24no—
834D8—24no—
835D8—22no—
836D8—24no—
837D8—22no—
838D8—42no—
839M16—24no—
840M16—24no—
841M16—21no—
842M16—21no—
843M16—21no—
844M16—21no—
845M16—21no—
846M16—21no—
847M16C2×D4×C15112yes—
848M16C2×D4×C15112yes—
849C2×C8—24no—
850C2×C8—24no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8C2×D4×C15111yescharacteristic
860C2×C8C2×D4×C15111yescharacteristic
861C2×C8C2×D4×C15111yescharacteristic
862C2×C8C2×D4×C15111yescharacteristic
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—41no—
866C22⋊C4—44no—
867C22⋊C4—41no—
868C22⋊C4—41no—
869C22⋊C4—82no—
870C42—21no—
871C42—21no—
872C23—21no—
873C23—21no—
874C23—21no—
875C23—21no—
876C23—22no—
877C23—22no—
878C23—44no—
879C23—44no—
880C23—41no—
881C23—41no—
882C23—41no—
883C23—41no—
884C23—81no—
885C23—81no—
886C23—81no—
887C23—81no—
888C23—161no—
889C23—161no—
890C23—161no—
891C23—161no—
892C23H(5,𝔽2)×C15111yescharacteristic
893Q8—21no—
894Q8—21no—
895Q8—22no—
896Q8—21no—
897Q8—21no—
898Q8—21no—
899Q8—22no—
900Q8—21no—
901Q8—44no—
902Q8—41no—
903Q8—41no—
904Q8#120×C15112yes—
905Q8#120×C15112yes—
906D4—22no—
907D4—22no—
908D4—22no—
909D4—22no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—22no—
915D4—21no—
916D4—21no—
917D4—21no—
918D4—22no—
919D4—21no—
920D4—44no—
921D4—44no—
922D4—44no—
923D4—44no—
924D4—44no—
925D4—41no—
926D4—41no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—41no—
933D4—161no—
934D4#120×C15112yes—
935D4#120×C15112yes—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—22no—
939C2×C4—22no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—44no—
946C2×C4—44no—
947C2×C4—44no—
948C2×C4—44no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—81no—
960C2×C4C22×D4×C15111yescharacteristic
961C2×C4C22×D4×C15111yescharacteristic
962C2×C4C22×D4×C15111yescharacteristic
963C2×C4C22×D4×C15111yescharacteristic
964C2×C4C22×D4×C15111yescharacteristic
965C2×C4H(5,𝔽2)×C15111yescharacteristic
966C8—21no—
967C8—21no—
968C8—22no—
969C8—22no—
970C8—21no—
971C8—21no—
972C8—41no—
973C8—41no—
974C22—21no—
975C22—21no—
976C22—22no—
977C22—22no—
978C22—41no—
979C22—41no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—42no—
985C22—42no—
986C22—41no—
987C22—41no—
988C22—41no—
989C22—41no—
990C22—82no—
991C22—82no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—161no—
997C22—161no—
998C22—164no—
999C22—164no—
1000C22#534×C15111yescharacteristic
1001C22D42×C15111yescharacteristic
1002C22D42×C15111yescharacteristic
1003C4—22no—
1004C4—22no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—81no—
1009C4—81no—
1010C4C2×#120×C15111yescharacteristic
1011C4C2×#120×C15111yescharacteristic
1012C4D42×C15111yescharacteristic
1013C4D42×C15111yescharacteristic
1014C2—21no—
1015C2—21no—
1016C2—42no—
1017C2—42no—
1018C2—81no—
1019C2—81no—
1020C2—82no—
1021C2—82no—
1022C2#2403×C15111yescharacteristic
1023C2#3288×C15111yescharacteristic
1024C2#3290×C15111yescharacteristic
subgroupG/H
center, socleC22×C151D42
commutator, Frattini, cosocleC22×C4C24×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#577×C151C2semidirect
2. C2×#576×C151C2semidirect
3. C2×#454×C151C2semidirect
4. C2×#455×C151C2semidirect
5. #3013×C151C2semidirect
6. #3012×C151C2semidirect
7. #2019×C151C2semidirect
8. #2018×C151C2semidirect
9. #2012×C151C2semidirect
10. #2006×C151C2semidirect
11. #1908×C151C2semidirect
12. #1907×C151C2semidirect
13. #1876×C151C2semidirect
14. #1876×C151C2semidirect
15. #1792×C151C2semidirect
16. C2×2−1+4×C151C22semidirect
25. C2×#137×C151C22semidirect
31. C2×AGL(1,ℤ/8)×C151C22semidirect
32. C2×AGL(1,ℤ/8)×C151C22semidirect
38. C22×SD16×C151C22semidirect
42. C2×#131×C151C22semidirect
43. #537×C151C22semidirect
44. C2×#124×C151C22semidirect
56. C2×#104×C151C22semidirect
57. C2×#104×C151C22semidirect
58. C2×#104×C151C22semidirect
60. #417×C151C22semidirect
61. C2×#103×C151C22semidirect
62. C2×#102×C151C22semidirect
63. C2×#101×C151C22semidirect
64. C2×#100×C151C22semidirect
65. C2×#100×C151C22semidirect
66. #408×C151C22semidirect
67. #408×C151C22semidirect
68. #390×C151C22semidirect
69. #343×C151C22semidirect
70. #341×C151C22semidirect
71. #341×C151C22semidirect
72. #336×C151C22semidirect
84. H(5,𝔽2)×C151D4semidirect
111. #137×C151D4semidirect
122. AGL(1,ℤ/8)×C151D4semidirect
512. #23888C151direct (N × H)
513. C151#23888direct (N × H)
514. C2×#577C2×C151semidirect
515. C2×#576C2×C151semidirect
516. C2×#454C2×C151semidirect
517. C2×#455C2×C151semidirect
518. #3013C2×C151semidirect
519. #3012C2×C151semidirect
520. #2019C2×C151semidirect
521. #2018C2×C151semidirect
522. #2012C2×C151semidirect
523. #2006C2×C151semidirect
524. #1908C2×C151semidirect
525. #1907C2×C151semidirect
526. #1876C2×C151semidirect
527. #1876C2×C151semidirect
528. #1792C2×C151semidirect
529. C2×2−1+4C22×C151semidirect
538. C2×#137C22×C151semidirect
544. C2×AGL(1,ℤ/8)C22×C151semidirect
545. C2×AGL(1,ℤ/8)C22×C151semidirect
551. C22×SD16C22×C151semidirect
555. C2×#131C22×C151semidirect
556. #537C22×C151semidirect
557. C2×#124C22×C151semidirect
569. C2×#104C22×C151semidirect
570. C2×#104C22×C151semidirect
571. C2×#104C22×C151semidirect
573. #417C22×C151semidirect
574. C2×#103C22×C151semidirect
575. C2×#102C22×C151semidirect
576. C2×#101C22×C151semidirect
577. C2×#100C22×C151semidirect
578. C2×#100C22×C151semidirect
579. #408C22×C151semidirect
580. #408C22×C151semidirect
581. #390C22×C151semidirect
582. #343C22×C151semidirect
583. #341C22×C151semidirect
584. #341C22×C151semidirect
585. #336C22×C151semidirect
597. H(5,𝔽2)D4×C151semidirect
624. #137D4×C151semidirect
635. AGL(1,ℤ/8)D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#577×C1512
C2×#576×C1512
C2×#454×C1512
C2×#455×C1512
#3013×C1512
#3012×C1512
#2019×C1512
#2018×C1512
#2012×C1512
#2006×C1512
#1908×C1512
#1907×C1512
#1876×C1512
#1792×C1512
#23888151