Finite Group Databasebeta

← C151×#24913 #50329838

Subgroups — C151×#24913 #50329838

Order 38656.

1226 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic
2C2×#442×C151C211yesmaximal, characteristic, complemented
3#2422×C151C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
5#2094×C151C211yesmaximal, characteristic, complemented
6#2077×C151C211yesmaximal, characteristic, complemented
7#2054×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#1936×C151C211yesmaximal, characteristic, complemented
10#1924×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1879×C151C211yesmaximal, characteristic, complemented
13#1864×C151C211yesmaximal, characteristic, complemented
14#1802×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C2×#123×C151—21no—
20C2×#121×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic, complemented
24C22×C22⋊C4×C151—21no—
25#447×C151—24no—
26#442×C151—24no—
27C2×#106×C151C2211yescharacteristic, complemented
28C2×#106×C151C2211yescharacteristic, complemented
29C2×C4⋊C8×C151C2211yescharacteristic, complemented
30C2×#102×C151C2211yescharacteristic
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic, complemented
37C2×#102×C151C2211yescharacteristic, complemented
38C2×C22⋊C8×C151C2211yescharacteristic
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic, complemented
41#397×C151—21no—
42#394×C151—21no—
43#390×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic, complemented
46#389×C151C2211yescharacteristic, complemented
47#386×C151—21no—
48#386×C151—21no—
49#385×C151—21no—
50#384×C151C2211yescharacteristic, complemented
51#380×C151C2211yescharacteristic
52#380×C151C2211yescharacteristic
53#379×C151—21no—
54C4×C22⋊C4×C151C2211yescharacteristic
55#340×C151C2211yescharacteristic, complemented
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#336×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61C25×C151—21no—
62C22×D4×C151—22no—
63C22×D4×C151—22no—
64C22×D4×C151—21no—
65C22×D4×C151—21no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—41no—
69C22×D4×C151—41no—
70C22×D4×C151C2311yescharacteristic
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C23×C4×C151—21no—
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151C2311yescharacteristic
77C2×D8×C151—22no—
78C2×D8×C151—22no—
79C2×D8×C151—22no—
80C2×D8×C151—22no—
81C2×D8×C151—41no—
82C2×D8×C151D414yes—
83C22×C8×C151C2311yescharacteristic
84C22×C8×C151C2311yescharacteristic
85C22×C8×C151C2311yescharacteristic
86C22×C8×C151C2311yescharacteristic
87#123×C151—44no—
88#121×C151—22no—
89#121×C151—41no—
90C4×D4×C151—22no—
91C4×D4×C151—22no—
92C4×D4×C151—22no—
93C4×D4×C151—41no—
94C4×D4×C151—41no—
95C4×D4×C151—41no—
96C2×C4⋊C4×C151—21no—
97C2×C4⋊C4×C151—21no—
98C2×C4⋊C4×C151—21no—
99C2×C4⋊C4×C151C2311yescharacteristic
100C2×C4⋊C4×C151C2311yescharacteristic
101C2×C4⋊C4×C151C2311yescharacteristic
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C22⋊C4×C151—21no—
105C2×C22⋊C4×C151—21no—
106C2×C22⋊C4×C151—21no—
107C2×C22⋊C4×C151—21no—
108C2×C22⋊C4×C151—21no—
109C2×C22⋊C4×C151—21no—
110C2×C22⋊C4×C151—21no—
111C2×C22⋊C4×C151—21no—
112C2×C22⋊C4×C151—21no—
113C2×C22⋊C4×C151—21no—
114C2×C22⋊C4×C151—21no—
115C2×C22⋊C4×C151—21no—
116C2×C22⋊C4×C151—44no—
117C2×C22⋊C4×C151D411yescharacteristic
118C2×C22⋊C4×C151D411yescharacteristic
119C2×C42×C151C2311yescharacteristic
120C2×C42×C151C2311yescharacteristic
121#106×C151—22no—
122#106×C151—41no—
123C4⋊C8×C151—41no—
124#102×C151—22no—
125#102×C151—22no—
126#102×C151—22no—
127#102×C151—22no—
128#102×C151—22no—
129#102×C151—22no—
130#102×C151—41no—
131#102×C151—41no—
132C22⋊C8×C151—22no—
133C22⋊C8×C151—41no—
134#97×C151—22no—
135#95×C151—21no—
136#95×C151—21no—
137#95×C151—21no—
138#95×C151D411yescharacteristic
139#95×C151D411yescharacteristic
140C24×C151—21no—
141C24×C151—24no—
142C24×C151—21no—
143C24×C151—21no—
144C24×C151—42no—
145C24×C151—42no—
146C24×C151—42no—
147C24×C151—42no—
148C24×C151—81no—
149C24×C151—81no—
150C24×C151C2×D411yescharacteristic
151C2×D4×C151—24no—
152C2×D4×C151—21no—
153C2×D4×C151—21no—
154C2×D4×C151—21no—
155C2×D4×C151—21no—
156C2×D4×C151—21no—
157C2×D4×C151—21no—
158C2×D4×C151—21no—
159C2×D4×C151—21no—
160C2×D4×C151—21no—
161C2×D4×C151—21no—
162C2×D4×C151—21no—
163C2×D4×C151—21no—
164C2×D4×C151—21no—
165C2×D4×C151—42no—
166C2×D4×C151—42no—
167C2×D4×C151—44no—
168C2×D4×C151—44no—
169C2×D4×C151—44no—
170C2×D4×C151—44no—
171C2×D4×C151—42no—
172C2×D4×C151—42no—
173C2×D4×C151—81no—
174C2×D4×C151C2×D412yes—
175C2×D4×C151C2×D412yes—
176C2×D4×C151#4112yes—
177C2×D4×C151#4112yes—
178C2×D4×C151#4112yes—
179C22×C4×C151—21no—
180C22×C4×C151—21no—
181C22×C4×C151—21no—
182C22×C4×C151—21no—
183C22×C4×C151—21no—
184C22×C4×C151—21no—
185C22×C4×C151—21no—
186C22×C4×C151—21no—
187C22×C4×C151—21no—
188C22×C4×C151—21no—
189C22×C4×C151—21no—
190C22×C4×C151—42no—
191C22×C4×C151—42no—
192C22×C4×C151—42no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—42no—
196C22×C4×C151—81no—
197C22×C4×C151—81no—
198C22×C4×C151—81no—
199C22×C4×C151C2×D411yescharacteristic
200C22×C4×C151C2×D411yescharacteristic
201C22×C4×C151C2×D411yescharacteristic
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2411yescharacteristic
205D8×C151—28no—
206D8×C151—44no—
207C2×C8×C151—21no—
208C2×C8×C151—21no—
209C2×C8×C151—21no—
210C2×C8×C151—21no—
211C2×C8×C151—21no—
212C2×C8×C151—21no—
213C2×C8×C151—21no—
214C2×C8×C151—21no—
215C2×C8×C151—21no—
216C2×C8×C151—21no—
217C2×C8×C151—21no—
218C2×C8×C151C2×D412yes—
219C4⋊C4×C151—21no—
220C4⋊C4×C151—21no—
221C4⋊C4×C151—21no—
222C4⋊C4×C151—21no—
223C4⋊C4×C151—21no—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—42no—
230C4⋊C4×C151—42no—
231C4⋊C4×C151—81no—
232C22⋊C4×C151—22no—
233C22⋊C4×C151—22no—
234C22⋊C4×C151—42no—
235C22⋊C4×C151—42no—
236C22⋊C4×C151—42no—
237C22⋊C4×C151—42no—
238C22⋊C4×C151—42no—
239C22⋊C4×C151—42no—
240C22⋊C4×C151—42no—
241C22⋊C4×C151—42no—
242C22⋊C4×C151—42no—
243C22⋊C4×C151—42no—
244C22⋊C4×C151—81no—
245C22⋊C4×C151—81no—
246C42×C151—21no—
247C42×C151—21no—
248C42×C151—21no—
249C42×C151—21no—
250C23×C151—21no—
251C23×C151—22no—
252C23×C151—22no—
253C23×C151—21no—
254C23×C151—22no—
255C23×C151—21no—
256C23×C151—21no—
257C23×C151—21no—
258C23×C151—21no—
259C23×C151—22no—
260C23×C151—22no—
261C23×C151—48no—
262C23×C151—48no—
263C23×C151—41no—
264C23×C151—41no—
265C23×C151—41no—
266C23×C151—41no—
267C23×C151—41no—
268C23×C151—41no—
269C23×C151—41no—
270C23×C151—41no—
271C23×C151—41no—
272C23×C151—41no—
273C23×C151—41no—
274C23×C151—41no—
275C23×C151—41no—
276C23×C151—41no—
277C23×C151—41no—
278C23×C151—41no—
279C23×C151—84no—
280C23×C151—84no—
281C23×C151—84no—
282C23×C151—84no—
283C23×C151—84no—
284C23×C151AGL(1,ℤ/8)12yes—
285C23×C151C22×D411yescharacteristic
286D4×C151—22no—
287D4×C151—22no—
288D4×C151—22no—
289D4×C151—22no—
290D4×C151—22no—
291D4×C151—22no—
292D4×C151—22no—
293D4×C151—48no—
294D4×C151—41no—
295D4×C151—41no—
296D4×C151—41no—
297D4×C151—41no—
298D4×C151—84no—
299D4×C151#12314yescomplemented
300C2×C4×C151—21no—
301C2×C4×C151—21no—
302C2×C4×C151—21no—
303C2×C4×C151—21no—
304C2×C4×C151—21no—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—21no—
310C2×C4×C151—21no—
311C2×C4×C151—21no—
312C2×C4×C151—21no—
313C2×C4×C151—21no—
314C2×C4×C151—41no—
315C2×C4×C151—41no—
316C2×C4×C151—41no—
317C2×C4×C151—41no—
318C2×C4×C151—41no—
319C2×C4×C151—41no—
320C2×C4×C151—41no—
321C2×C4×C151—41no—
322C2×C4×C151—41no—
323C2×C4×C151—41no—
324C2×C4×C151—41no—
325C2×C4×C151—41no—
326C2×C4×C151—41no—
327C2×C4×C151—41no—
328C2×C4×C151—41no—
329C2×C4×C151—41no—
330C2×C4×C151—41no—
331C2×C4×C151—41no—
332C2×C4×C151—41no—
333C2×C4×C151—84no—
334C2×C4×C151—84no—
335C2×C4×C151—84no—
336C2×C4×C151AGL(1,ℤ/8)12yes—
337C2×C4×C151C22×D411yescharacteristic
338C2×C4×C151C2×#4111yescharacteristic
339C2×C4×C151C2×#4111yescharacteristic
340C2×C4×C151C2×#4111yescharacteristic
341C2×C4×C151H(5,𝔽2)11yescharacteristic
342C2×C4×C151H(5,𝔽2)11yescharacteristic
343C8×C151—22no—
344C8×C151—41no—
345C8×C151—41no—
346C8×C151—41no—
347C22×C151—22no—
348C22×C151—24no—
349C22×C151—22no—
350C22×C151—22no—
351C22×C151—42no—
352C22×C151—41no—
353C22×C151—42no—
354C22×C151—41no—
355C22×C151—42no—
356C22×C151—42no—
357C22×C151—41no—
358C22×C151—42no—
359C22×C151—42no—
360C22×C151—41no—
361C22×C151—42no—
362C22×C151—42no—
363C22×C151—42no—
364C22×C151—42no—
365C22×C151—42no—
366C22×C151—42no—
367C22×C151—816no—
368C22×C151—81no—
369C22×C151—81no—
370C22×C151—81no—
371C22×C151—81no—
372C22×C151—81no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151#52511yescharacteristic
377C22×C151D4211yescharacteristic
378C22×C151#54611yescharacteristic
379C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
381C22×C151#57611yescharacteristic
382C22×C151#57711yescharacteristic
383C4×C151—22no—
384C4×C151—41no—
385C4×C151—41no—
386C4×C151—41no—
387C4×C151—41no—
388C4×C151—81no—
389C4×C151—81no—
390C4×C151—81no—
391C4×C151—81no—
392C4×C151—81no—
393C4×C151C2×#12311yescharacteristic
394C4×C151#53811yescharacteristic
395C4×C151#54611yescharacteristic
396C4×C151#55111yescharacteristic
397C2×C151—42no—
398C2×C151—44no—
399C2×C151—82no—
400C2×C151—82no—
401C2×C151#241811yescharacteristic
402C2×C151#310911yescharacteristic
403C2×C151#311811yescharacteristic
404C2×C151#326411yescharacteristic
405C2×C151#327211yescharacteristic
406C2×C151#330611yescharacteristic
407C2×C151#331811yescharacteristic
408#24913C15111yesmaximal, characteristic, direct product factor, Sylow
409C151#2491311yescharacteristic, direct product factor, Sylow
410C2×#447C2×C15111yescharacteristic
411C2×#442C2×C15111yescharacteristic, complemented
412#2422C2×C15111yescharacteristic, complemented
413D4×C22⋊C4C2×C15111yescharacteristic, complemented
414#2094C2×C15111yescharacteristic, complemented
415#2077C2×C15111yescharacteristic, complemented
416#2054C2×C15111yescharacteristic, complemented
417#2034C2×C15111yescharacteristic, complemented
418#1936C2×C15111yescharacteristic, complemented
419#1924C2×C15111yescharacteristic, complemented
420#1879C2×C15111yescharacteristic, complemented
421#1879C2×C15111yescharacteristic, complemented
422#1864C2×C15111yescharacteristic, complemented
423#1802C2×C15111yescharacteristic, complemented
424#1786C2×C15111yescharacteristic, complemented
425C23×D4C22×C15111yescharacteristic
426C22×D8C22×C15111yescharacteristic
427C22×D8C22×C15111yescharacteristic
428C2×#123—21no—
429C2×#121C22×C15111yescharacteristic
430C2×C4×D4C22×C15111yescharacteristic
431C2×C4×D4C22×C15111yescharacteristic
432C2×C4×D4C22×C15111yescharacteristic, complemented
433C22×C22⋊C4—21no—
434#447—24no—
435#442—24no—
436C2×#106C22×C15111yescharacteristic, complemented
437C2×#106C22×C15111yescharacteristic, complemented
438C2×C4⋊C8C22×C15111yescharacteristic, complemented
439C2×#102C22×C15111yescharacteristic
440C2×#102C22×C15111yescharacteristic
441C2×#102C22×C15111yescharacteristic
442C2×#102C22×C15111yescharacteristic
443C2×#102C22×C15111yescharacteristic
444C2×#102C22×C15111yescharacteristic
445C2×#102C22×C15111yescharacteristic, complemented
446C2×#102C22×C15111yescharacteristic, complemented
447C2×C22⋊C8C22×C15111yescharacteristic
448C2×C22⋊C8C22×C15111yescharacteristic
449C2×#97C22×C15111yescharacteristic, complemented
450#397—21no—
451#394—21no—
452#390C22×C15111yescharacteristic
453#390C22×C15111yescharacteristic
454#390C22×C15111yescharacteristic, complemented
455#389C22×C15111yescharacteristic, complemented
456#386—21no—
457#386—21no—
458#385—21no—
459#384C22×C15111yescharacteristic, complemented
460#380C22×C15111yescharacteristic
461#380C22×C15111yescharacteristic
462#379—21no—
463C4×C22⋊C4C22×C15111yescharacteristic
464#340C22×C15111yescharacteristic, complemented
465#340C22×C15111yescharacteristic, complemented
466#340C22×C15111yescharacteristic, complemented
467#340C22×C15111yescharacteristic, complemented
468#336C22×C15111yescharacteristic, complemented
469#336C22×C15111yescharacteristic, complemented
470C25—21no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—41no—
478C22×D4—41no—
479C22×D4C23×C15111yescharacteristic
480C22×D4C23×C15111yescharacteristic
481C22×D4C23×C15111yescharacteristic
482C23×C4—21no—
483C23×C4—21no—
484C23×C4—21no—
485C23×C4C23×C15111yescharacteristic
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—41no—
491C2×D8D4×C15114yes—
492C22×C8C23×C15111yescharacteristic
493C22×C8C23×C15111yescharacteristic
494C22×C8C23×C15111yescharacteristic
495C22×C8C23×C15111yescharacteristic
496#123—44no—
497#121—22no—
498#121—41no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—41no—
503C4×D4—41no—
504C4×D4—41no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4C23×C15111yescharacteristic
509C2×C4⋊C4C23×C15111yescharacteristic
510C2×C4⋊C4C23×C15111yescharacteristic
511C2×C4⋊C4C23×C15111yescharacteristic
512C2×C4⋊C4C23×C15111yescharacteristic
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—44no—
526C2×C22⋊C4D4×C15111yescharacteristic
527C2×C22⋊C4D4×C15111yescharacteristic
528C2×C42C23×C15111yescharacteristic
529C2×C42C23×C15111yescharacteristic
530#106—22no—
531#106—41no—
532C4⋊C8—41no—
533#102—22no—
534#102—22no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102—22no—
539#102—41no—
540#102—41no—
541C22⋊C8—22no—
542C22⋊C8—41no—
543#97—22no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95D4×C15111yescharacteristic
548#95D4×C15111yescharacteristic
549C24—21no—
550C24—24no—
551C24—21no—
552C24—21no—
553C24—42no—
554C24—42no—
555C24—42no—
556C24—42no—
557C24—81no—
558C24—81no—
559C24C2×D4×C15111yescharacteristic
560C2×D4—24no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—42no—
576C2×D4—44no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—44no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—81no—
583C2×D4C2×D4×C15112yes—
584C2×D4C2×D4×C15112yes—
585C2×D4#41×C15112yes—
586C2×D4#41×C15112yes—
587C2×D4#41×C15112yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—81no—
606C22×C4—81no—
607C22×C4—81no—
608C22×C4C2×D4×C15111yescharacteristic
609C22×C4C2×D4×C15111yescharacteristic
610C22×C4C2×D4×C15111yescharacteristic
611C22×C4C2×D4×C15111yescharacteristic
612C22×C4C2×D4×C15111yescharacteristic
613C22×C4C24×C15111yescharacteristic
614D8—28no—
615D8—44no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8C2×D4×C15112yes—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4—81no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—81no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—21no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—22no—
670C23—48no—
671C23—48no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—84no—
689C23—84no—
690C23—84no—
691C23—84no—
692C23—84no—
693C23AGL(1,ℤ/8)×C15112yes—
694C23C22×D4×C15111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—48no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4#123×C15114yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—84no—
743C2×C4—84no—
744C2×C4—84no—
745C2×C4AGL(1,ℤ/8)×C15112yes—
746C2×C4C22×D4×C15111yescharacteristic
747C2×C4C2×#41×C15111yescharacteristic
748C2×C4C2×#41×C15111yescharacteristic
749C2×C4C2×#41×C15111yescharacteristic
750C2×C4H(5,𝔽2)×C15111yescharacteristic
751C2×C4H(5,𝔽2)×C15111yescharacteristic
752C8—22no—
753C8—41no—
754C8—41no—
755C8—41no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—41no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—816no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22#525×C15111yescharacteristic
786C22D42×C15111yescharacteristic
787C22#546×C15111yescharacteristic
788C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
789C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
790C22#576×C15111yescharacteristic
791C22#577×C15111yescharacteristic
792C4—22no—
793C4—41no—
794C4—41no—
795C4—41no—
796C4—41no—
797C4—81no—
798C4—81no—
799C4—81no—
800C4—81no—
801C4—81no—
802C4C2×#123×C15111yescharacteristic
803C4#538×C15111yescharacteristic
804C4#546×C15111yescharacteristic
805C4#551×C15111yescharacteristic
806C2—42no—
807C2—44no—
808C2—82no—
809C2—82no—
810C2#2418×C15111yescharacteristic
811C2#3109×C15111yescharacteristic
812C2#3118×C15111yescharacteristic
813C2#3264×C15111yescharacteristic
814C2#3272×C15111yescharacteristic
815C2#3306×C15111yescharacteristic
816C2#3318×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C4×C22⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#442×C151C2semidirect
3. #2422×C151C2semidirect
4. D4×C22⋊C4×C151C2semidirect
5. #2094×C151C2semidirect
6. #2077×C151C2semidirect
7. #2054×C151C2semidirect
8. #2034×C151C2semidirect
9. #1936×C151C2semidirect
10. #1924×C151C2semidirect
11. #1879×C151C2semidirect
12. #1879×C151C2semidirect
13. #1864×C151C2semidirect
14. #1802×C151C2semidirect
15. #1786×C151C2semidirect
23. C2×C4×D4×C151C22semidirect
27. C2×#106×C151C22semidirect
28. C2×#106×C151C22semidirect
29. C2×C4⋊C8×C151C22semidirect
36. C2×#102×C151C22semidirect
37. C2×#102×C151C22semidirect
40. C2×#97×C151C22semidirect
45. #390×C151C22semidirect
46. #389×C151C22semidirect
50. #384×C151C22semidirect
55. #340×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #336×C151C22semidirect
60. #336×C151C22semidirect
299. D4×C151#123semidirect
408. #24913C151direct (N × H)
409. C151#24913direct (N × H)
411. C2×#442C2×C151semidirect
412. #2422C2×C151semidirect
413. D4×C22⋊C4C2×C151semidirect
414. #2094C2×C151semidirect
415. #2077C2×C151semidirect
416. #2054C2×C151semidirect
417. #2034C2×C151semidirect
418. #1936C2×C151semidirect
419. #1924C2×C151semidirect
420. #1879C2×C151semidirect
421. #1879C2×C151semidirect
422. #1864C2×C151semidirect
423. #1802C2×C151semidirect
424. #1786C2×C151semidirect
432. C2×C4×D4C22×C151semidirect
436. C2×#106C22×C151semidirect
437. C2×#106C22×C151semidirect
438. C2×C4⋊C8C22×C151semidirect
445. C2×#102C22×C151semidirect
446. C2×#102C22×C151semidirect
449. C2×#97C22×C151semidirect
454. #390C22×C151semidirect
455. #389C22×C151semidirect
459. #384C22×C151semidirect
464. #340C22×C151semidirect
465. #340C22×C151semidirect
466. #340C22×C151semidirect
467. #340C22×C151semidirect
468. #336C22×C151semidirect
469. #336C22×C151semidirect
708. D4#123×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#447×C1512
C2×#442×C1512
#2422×C1512
D4×C22⋊C4×C1512
#2094×C1512
#2077×C1512
#2054×C1512
#2034×C1512
#1936×C1512
#1924×C1512
#1879×C1512
#1864×C1512
#1802×C1512
#1786×C1512
#24913151