Finite Group Databasebeta

← C151×#22880 #50327805

Subgroups — C151×#22880 #50327805

Order 38656.

1330 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#447×C151C211yesmaximal, characteristic
2C2×C4×D8×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4#2363×C151C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C151C211yesmaximal, characteristic, complemented
6#1972×C151C211yesmaximal, characteristic, complemented
7#1934×C151C211yesmaximal, characteristic, complemented
8#1925×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1879×C151C211yesmaximal, characteristic, complemented
11#1879×C151C211yesmaximal, characteristic, complemented
12#1864×C151C211yesmaximal, characteristic, complemented
13#1854×C151C211yesmaximal, characteristic, complemented
14#1762×C151C211yesmaximal, characteristic, complemented
15#1753×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151C2211yescharacteristic
17C22×D8×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic
20C2×#121×C151C2211yescharacteristic
21C2×C4×D4×C151C2211yescharacteristic
22C2×C4×D4×C151C2211yescharacteristic
23C2×C4×D4×C151C2211yescharacteristic, complemented
24C2×#117×C151C2211yescharacteristic
25C22×C22⋊C4×C151—21no—
26#447×C151C418yescomplemented
27C4×D8×C151—24no—
28C2×#107×C151C2211yescharacteristic, complemented
29C2×#106×C151C2211yescharacteristic, complemented
30#418×C151—24no—
31C2×#102×C151C2211yescharacteristic
32C2×#102×C151C2211yescharacteristic
33C2×#102×C151C2211yescharacteristic
34C2×#102×C151C2211yescharacteristic
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic, complemented
38C2×#102×C151C2211yescharacteristic, complemented
39C2×C22⋊C8×C151C2211yescharacteristic
40C2×#97×C151C2211yescharacteristic, complemented
41C2×C4×C8×C151C2211yescharacteristic, complemented
42#390×C151—21no—
43#390×C151C2211yescharacteristic
44#390×C151C2211yescharacteristic
45#390×C151C2211yescharacteristic, complemented
46#389×C151C2211yescharacteristic, complemented
47#388×C151—21no—
48#386×C151—21no—
49#386×C151—21no—
50#386×C151—21no—
51#380×C151C2211yescharacteristic
52#379×C151—21no—
53C4×C4⋊C4×C151C2211yescharacteristic, complemented
54C4×C22⋊C4×C151—21no—
55C4×C22⋊C4×C151C2211yescharacteristic
56#340×C151C2211yescharacteristic, complemented
57#340×C151C2211yescharacteristic, complemented
58#340×C151C2211yescharacteristic, complemented
59#340×C151C2211yescharacteristic, complemented
60#336×C151C2211yescharacteristic, complemented
61#336×C151C2211yescharacteristic, complemented
62C25×C151—21no—
63C22×D4×C151—21no—
64C22×D4×C151—22no—
65C22×D4×C151—21no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—41no—
69C22×D4×C151—41no—
70C22×D4×C151C2×C414yescomplemented
71C22×D4×C151C2311yescharacteristic
72C22×D4×C151C2311yescharacteristic
73C22×D4×C151C2311yescharacteristic
74C23×C4×C151—21no—
75C23×C4×C151—21no—
76C23×C4×C151—21no—
77C23×C4×C151C2311yescharacteristic
78C2×D8×C151—22no—
79C2×D8×C151—22no—
80C2×D8×C151—41no—
81C2×D8×C151—41no—
82C2×D8×C151C2×C414yes—
83C2×D8×C151C2×C414yescomplemented
84C2×M16×C151—22no—
85C2×M16×C151—22no—
86C2×M16×C151—41no—
87C22×C8×C151C2311yescharacteristic
88C22×C8×C151C2311yescharacteristic
89C22×C8×C151C2311yescharacteristic
90C22×C8×C151C2311yescharacteristic
91#121×C151—22no—
92#121×C151C2×C414yescomplemented
93C4×D4×C151—22no—
94C4×D4×C151—22no—
95C4×D4×C151—22no—
96C4×D4×C151—41no—
97C4×D4×C151—41no—
98C4×D4×C151—41no—
99#117×C151—22no—
100#117×C151—41no—
101C2×C4⋊C4×C151—21no—
102C2×C4⋊C4×C151C2311yescharacteristic
103C2×C4⋊C4×C151C2311yescharacteristic
104C2×C4⋊C4×C151C2311yescharacteristic
105C2×C4⋊C4×C151C2311yescharacteristic
106C2×C4⋊C4×C151C2311yescharacteristic
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—21no—
117C2×C22⋊C4×C151—21no—
118C2×C22⋊C4×C151—21no—
119C2×C22⋊C4×C151—44no—
120C2×C22⋊C4×C151D411yescharacteristic
121C2×C22⋊C4×C151D411yescharacteristic
122C2×C42×C151—21no—
123C2×C42×C151—21no—
124C2×C42×C151C2311yescharacteristic
125C2×C42×C151C2311yescharacteristic
126#107×C151—22no—
127#106×C151—41no—
128#102×C151—22no—
129#102×C151—22no—
130#102×C151—22no—
131#102×C151—22no—
132#102×C151—41no—
133#102×C151C2×C414yescomplemented
134#102×C151C2×C414yescomplemented
135#102×C151D414yescomplemented
136C22⋊C8×C151C2×C414yescomplemented
137#97×C151—41no—
138C4×C8×C151—22no—
139#95×C151—21no—
140#95×C151—21no—
141#95×C151—21no—
142#95×C151D411yescharacteristic
143#95×C151D411yescharacteristic
144C24×C151—21no—
145C24×C151—21no—
146C24×C151—21no—
147C24×C151—24no—
148C24×C151—42no—
149C24×C151—42no—
150C24×C151—42no—
151C24×C151—42no—
152C24×C151—81no—
153C24×C151—81no—
154C24×C151C2×D411yescharacteristic
155C2×D4×C151—28no—
156C2×D4×C151—24no—
157C2×D4×C151—24no—
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—21no—
166C2×D4×C151—21no—
167C2×D4×C151—21no—
168C2×D4×C151—21no—
169C2×D4×C151—21no—
170C2×D4×C151—21no—
171C2×D4×C151—44no—
172C2×D4×C151—44no—
173C2×D4×C151—44no—
174C2×D4×C151—42no—
175C2×D4×C151—42no—
176C2×D4×C151—81no—
177C2×D4×C151—81no—
178C2×D4×C151C22×C412yes—
179C2×D4×C151C22×C412yes—
180C2×D4×C151C22×C412yes—
181C2×D4×C151C2×D412yes—
182C2×D4×C151#4112yes—
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—21no—
191C22×C4×C151—21no—
192C22×C4×C151—42no—
193C22×C4×C151—42no—
194C22×C4×C151—42no—
195C22×C4×C151—42no—
196C22×C4×C151—42no—
197C22×C4×C151—42no—
198C22×C4×C151—81no—
199C22×C4×C151—81no—
200C22×C4×C151—81no—
201C22×C4×C151C22×C412yes—
202C22×C4×C151C2×D411yescharacteristic
203C22×C4×C151C2×D411yescharacteristic
204C22×C4×C151C2×D411yescharacteristic
205C22×C4×C151C2×D411yescharacteristic
206C22×C4×C151C2×D411yescharacteristic
207C22×C4×C151#4112yes—
208C22×C4×C151C2411yescharacteristic
209D8×C151—28no—
210D8×C151—44no—
211M16×C151—44no—
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×C151—21no—
219C2×C8×C151—21no—
220C2×C8×C151—21no—
221C2×C8×C151C22×C412yes—
222C2×C8×C151C22×C412yes—
223C2×C8×C151C2×D412yes—
224C4⋊C4×C151—21no—
225C4⋊C4×C151—21no—
226C4⋊C4×C151—21no—
227C4⋊C4×C151—21no—
228C4⋊C4×C151—21no—
229C4⋊C4×C151—21no—
230C4⋊C4×C151—21no—
231C4⋊C4×C151—21no—
232C4⋊C4×C151—81no—
233C4⋊C4×C151C22×C412yes—
234C4⋊C4×C151C2×D412yes—
235C22⋊C4×C151—24no—
236C22⋊C4×C151—22no—
237C22⋊C4×C151—41no—
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—42no—
245C22⋊C4×C151—42no—
246C22⋊C4×C151—81no—
247C22⋊C4×C151—81no—
248C22⋊C4×C151—81no—
249C42×C151—21no—
250C42×C151—21no—
251C42×C151—21no—
252C42×C151—21no—
253C42×C151—42no—
254C42×C151—81no—
255C23×C151—22no—
256C23×C151—22no—
257C23×C151—21no—
258C23×C151—22no—
259C23×C151—21no—
260C23×C151—21no—
261C23×C151—21no—
262C23×C151—21no—
263C23×C151—21no—
264C23×C151—22no—
265C23×C151—22no—
266C23×C151—48no—
267C23×C151—48no—
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—41no—
280C23×C151—41no—
281C23×C151—41no—
282C23×C151—41no—
283C23×C151—41no—
284C23×C151—84no—
285C23×C151—84no—
286C23×C151—84no—
287C23×C151—84no—
288C23×C151—84no—
289C23×C151C4×D412yes—
290C23×C151C22×D411yescharacteristic
291D4×C151—22no—
292D4×C151—22no—
293D4×C151—22no—
294D4×C151—22no—
295D4×C151—22no—
296D4×C151—22no—
297D4×C151—22no—
298D4×C151—48no—
299D4×C151—41no—
300D4×C151—41no—
301D4×C151—41no—
302D4×C151—41no—
303D4×C151—84no—
304D4×C151C4×D414yes—
305C2×C4×C151—21no—
306C2×C4×C151—21no—
307C2×C4×C151—21no—
308C2×C4×C151—21no—
309C2×C4×C151—22no—
310C2×C4×C151—22no—
311C2×C4×C151—22no—
312C2×C4×C151—22no—
313C2×C4×C151—22no—
314C2×C4×C151—21no—
315C2×C4×C151—22no—
316C2×C4×C151—21no—
317C2×C4×C151—21no—
318C2×C4×C151—21no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
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—41no—
334C2×C4×C151—41no—
335C2×C4×C151—41no—
336C2×C4×C151—41no—
337C2×C4×C151—84no—
338C2×C4×C151—84no—
339C2×C4×C151—84no—
340C2×C4×C151C4×D412yes—
341C2×C4×C151AGL(1,ℤ/8)12yes—
342C2×C4×C151C23×C411yescharacteristic
343C2×C4×C151C22×D411yescharacteristic
344C2×C4×C151C2×#4111yescharacteristic
345C2×C4×C151C2×#4111yescharacteristic
346C2×C4×C151H(5,𝔽2)11yescharacteristic
347C2×C4×C151H(5,𝔽2)11yescharacteristic
348C8×C151—22no—
349C8×C151—22no—
350C8×C151—22no—
351C8×C151—41no—
352C22×C151—22no—
353C22×C151—24no—
354C22×C151—22no—
355C22×C151—22no—
356C22×C151—42no—
357C22×C151—42no—
358C22×C151—42no—
359C22×C151—41no—
360C22×C151—41no—
361C22×C151—42no—
362C22×C151—41no—
363C22×C151—42no—
364C22×C151—42no—
365C22×C151—41no—
366C22×C151—42no—
367C22×C151—42no—
368C22×C151—42no—
369C22×C151—42no—
370C22×C151—42no—
371C22×C151—42no—
372C22×C151—816no—
373C22×C151—81no—
374C22×C151—81no—
375C22×C151—81no—
376C22×C151—81no—
377C22×C151—81no—
378C22×C151—81no—
379C22×C151—81no—
380C22×C151—81no—
381C22×C151C2×C4×D411yescharacteristic
382C22×C151D4211yescharacteristic
383C22×C151#54611yescharacteristic
384C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
385C22×C151#57511yescharacteristic
386C22×C151#57611yescharacteristic
387C22×C151#57611yescharacteristic
388C4×C151—22no—
389C4×C151—22no—
390C4×C151—42no—
391C4×C151—42no—
392C4×C151—41no—
393C4×C151—41no—
394C4×C151—41no—
395C4×C151—81no—
396C4×C151—81no—
397C4×C151—81no—
398C4×C151C2×C4×D411yescharacteristic
399C4×C151#51811yescharacteristic
400C4×C151#54611yescharacteristic
401C4×C151#55111yescharacteristic
402C2×C151—42no—
403C2×C151—44no—
404C2×C151—82no—
405C2×C151—82no—
406C2×C151#235811yescharacteristic
407C2×C151C4×AGL(1,ℤ/8)11yescharacteristic
408C2×C151#294811yescharacteristic
409C2×C151#326411yescharacteristic
410C2×C151#326811yescharacteristic
411C2×C151#332211yescharacteristic
412C2×C151#332511yescharacteristic
413#22880C15111yesmaximal, characteristic, direct product factor, Sylow
414C151#2288011yescharacteristic, direct product factor, Sylow
415C2×#447C2×C15111yescharacteristic
416C2×C4×D8C2×C15111yescharacteristic, complemented
417C2×#418C2×C15111yescharacteristic, complemented
418#2363C2×C15111yescharacteristic, complemented
419D4×C22⋊C4C2×C15111yescharacteristic, complemented
420#1972C2×C15111yescharacteristic, complemented
421#1934C2×C15111yescharacteristic, complemented
422#1925C2×C15111yescharacteristic, complemented
423#1895C2×C15111yescharacteristic, complemented
424#1879C2×C15111yescharacteristic, complemented
425#1879C2×C15111yescharacteristic, complemented
426#1864C2×C15111yescharacteristic, complemented
427#1854C2×C15111yescharacteristic, complemented
428#1762C2×C15111yescharacteristic, complemented
429#1753C2×C15111yescharacteristic, complemented
430C23×D4C22×C15111yescharacteristic
431C22×D8C22×C15111yescharacteristic
432C22×D8C22×C15111yescharacteristic
433C22×M16C22×C15111yescharacteristic
434C2×#121C22×C15111yescharacteristic
435C2×C4×D4C22×C15111yescharacteristic
436C2×C4×D4C22×C15111yescharacteristic
437C2×C4×D4C22×C15111yescharacteristic, complemented
438C2×#117C22×C15111yescharacteristic
439C22×C22⋊C4—21no—
440#447C4×C15118yescomplemented
441C4×D8—24no—
442C2×#107C22×C15111yescharacteristic, complemented
443C2×#106C22×C15111yescharacteristic, complemented
444#418—24no—
445C2×#102C22×C15111yescharacteristic
446C2×#102C22×C15111yescharacteristic
447C2×#102C22×C15111yescharacteristic
448C2×#102C22×C15111yescharacteristic
449C2×#102C22×C15111yescharacteristic
450C2×#102C22×C15111yescharacteristic
451C2×#102C22×C15111yescharacteristic, complemented
452C2×#102C22×C15111yescharacteristic, complemented
453C2×C22⋊C8C22×C15111yescharacteristic
454C2×#97C22×C15111yescharacteristic, complemented
455C2×C4×C8C22×C15111yescharacteristic, complemented
456#390—21no—
457#390C22×C15111yescharacteristic
458#390C22×C15111yescharacteristic
459#390C22×C15111yescharacteristic, complemented
460#389C22×C15111yescharacteristic, complemented
461#388—21no—
462#386—21no—
463#386—21no—
464#386—21no—
465#380C22×C15111yescharacteristic
466#379—21no—
467C4×C4⋊C4C22×C15111yescharacteristic, complemented
468C4×C22⋊C4—21no—
469C4×C22⋊C4C22×C15111yescharacteristic
470#340C22×C15111yescharacteristic, complemented
471#340C22×C15111yescharacteristic, complemented
472#340C22×C15111yescharacteristic, complemented
473#340C22×C15111yescharacteristic, complemented
474#336C22×C15111yescharacteristic, complemented
475#336C22×C15111yescharacteristic, complemented
476C25—21no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—21no—
480C22×D4—22no—
481C22×D4—21no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C2×C4×C15114yescomplemented
485C22×D4C23×C15111yescharacteristic
486C22×D4C23×C15111yescharacteristic
487C22×D4C23×C15111yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4—21no—
491C23×C4C23×C15111yescharacteristic
492C2×D8—22no—
493C2×D8—22no—
494C2×D8—41no—
495C2×D8—41no—
496C2×D8C2×C4×C15114yes—
497C2×D8C2×C4×C15114yescomplemented
498C2×M16—22no—
499C2×M16—22no—
500C2×M16—41no—
501C22×C8C23×C15111yescharacteristic
502C22×C8C23×C15111yescharacteristic
503C22×C8C23×C15111yescharacteristic
504C22×C8C23×C15111yescharacteristic
505#121—22no—
506#121C2×C4×C15114yescomplemented
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513#117—22no—
514#117—41no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4C23×C15111yescharacteristic
517C2×C4⋊C4C23×C15111yescharacteristic
518C2×C4⋊C4C23×C15111yescharacteristic
519C2×C4⋊C4C23×C15111yescharacteristic
520C2×C4⋊C4C23×C15111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—44no—
534C2×C22⋊C4D4×C15111yescharacteristic
535C2×C22⋊C4D4×C15111yescharacteristic
536C2×C42—21no—
537C2×C42—21no—
538C2×C42C23×C15111yescharacteristic
539C2×C42C23×C15111yescharacteristic
540#107—22no—
541#106—41no—
542#102—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—41no—
547#102C2×C4×C15114yescomplemented
548#102C2×C4×C15114yescomplemented
549#102D4×C15114yescomplemented
550C22⋊C8C2×C4×C15114yescomplemented
551#97—41no—
552C4×C8—22no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95D4×C15111yescharacteristic
557#95D4×C15111yescharacteristic
558C24—21no—
559C24—21no—
560C24—21no—
561C24—24no—
562C24—42no—
563C24—42no—
564C24—42no—
565C24—42no—
566C24—81no—
567C24—81no—
568C24C2×D4×C15111yescharacteristic
569C2×D4—28no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—44no—
586C2×D4—44no—
587C2×D4—44no—
588C2×D4—42no—
589C2×D4—42no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C22×C4×C15112yes—
593C2×D4C22×C4×C15112yes—
594C2×D4C22×C4×C15112yes—
595C2×D4C2×D4×C15112yes—
596C2×D4#41×C15112yes—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C22×C4×C15112yes—
616C22×C4C2×D4×C15111yescharacteristic
617C22×C4C2×D4×C15111yescharacteristic
618C22×C4C2×D4×C15111yescharacteristic
619C22×C4C2×D4×C15111yescharacteristic
620C22×C4C2×D4×C15111yescharacteristic
621C22×C4#41×C15112yes—
622C22×C4C24×C15111yescharacteristic
623D8—28no—
624D8—44no—
625M16—44no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8C22×C4×C15112yes—
636C2×C8C22×C4×C15112yes—
637C2×C8C2×D4×C15112yes—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C22×C4×C15112yes—
648C4⋊C4C2×D4×C15112yes—
649C22⋊C4—24no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—42no—
655C22⋊C4—42no—
656C22⋊C4—42no—
657C22⋊C4—42no—
658C22⋊C4—42no—
659C22⋊C4—42no—
660C22⋊C4—81no—
661C22⋊C4—81no—
662C22⋊C4—81no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—42no—
668C42—81no—
669C23—22no—
670C23—21no—
671C23—22no—
672C23—22no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—48no—
681C23—48no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23—84no—
702C23—84no—
703C23C4×D4×C15112yes—
704C23C22×D4×C15111yescharacteristic
705D4—22no—
706D4—22no—
707D4—22no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—41no—
714D4—41no—
715D4—41no—
716D4—41no—
717D4—84no—
718D4C4×D4×C15114yes—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—22no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C15112yes—
755C2×C4AGL(1,ℤ/8)×C15112yes—
756C2×C4C23×C4×C15111yescharacteristic
757C2×C4C22×D4×C15111yescharacteristic
758C2×C4C2×#41×C15111yescharacteristic
759C2×C4C2×#41×C15111yescharacteristic
760C2×C4H(5,𝔽2)×C15111yescharacteristic
761C2×C4H(5,𝔽2)×C15111yescharacteristic
762C8—22no—
763C8—22no—
764C8—22no—
765C8—41no—
766C22—22no—
767C22—24no—
768C22—22no—
769C22—22no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22C2×C4×D4×C15111yescharacteristic
796C22D42×C15111yescharacteristic
797C22#546×C15111yescharacteristic
798C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
799C22#575×C15111yescharacteristic
800C22#576×C15111yescharacteristic
801C22#576×C15111yescharacteristic
802C4—22no—
803C4—22no—
804C4—42no—
805C4—42no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—81no—
810C4—81no—
811C4—81no—
812C4C2×C4×D4×C15111yescharacteristic
813C4#518×C15111yescharacteristic
814C4#546×C15111yescharacteristic
815C4#551×C15111yescharacteristic
816C2—42no—
817C2—44no—
818C2—82no—
819C2—82no—
820C2#2358×C15111yescharacteristic
821C2C4×AGL(1,ℤ/8)×C15111yescharacteristic
822C2#2948×C15111yescharacteristic
823C2#3264×C15111yescharacteristic
824C2#3268×C15111yescharacteristic
825C2#3322×C15111yescharacteristic
826C2#3325×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutatorC2×C4C23×C4×C151
Frattini, cosocleC22×C4C24×C151
prime radicalC2×#447×C151C2
LCSG ▷ C2×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×C4×D8×C151C2semidirect
3. C2×#418×C151C2semidirect
4. #2363×C151C2semidirect
5. D4×C22⋊C4×C151C2semidirect
6. #1972×C151C2semidirect
7. #1934×C151C2semidirect
8. #1925×C151C2semidirect
9. #1895×C151C2semidirect
10. #1879×C151C2semidirect
11. #1879×C151C2semidirect
12. #1864×C151C2semidirect
13. #1854×C151C2semidirect
14. #1762×C151C2semidirect
15. #1753×C151C2semidirect
23. C2×C4×D4×C151C22semidirect
26. #447×C151C4semidirect
28. C2×#107×C151C22semidirect
29. C2×#106×C151C22semidirect
37. C2×#102×C151C22semidirect
38. C2×#102×C151C22semidirect
40. C2×#97×C151C22semidirect
41. C2×C4×C8×C151C22semidirect
45. #390×C151C22semidirect
46. #389×C151C22semidirect
53. C4×C4⋊C4×C151C22semidirect
56. #340×C151C22semidirect
57. #340×C151C22semidirect
58. #340×C151C22semidirect
59. #340×C151C22semidirect
60. #336×C151C22semidirect
61. #336×C151C22semidirect
70. C22×D4×C151C2×C4semidirect
83. C2×D8×C151C2×C4semidirect
92. #121×C151C2×C4semidirect
133. #102×C151C2×C4semidirect
134. #102×C151C2×C4semidirect
135. #102×C151D4semidirect
136. C22⋊C8×C151C2×C4semidirect
413. #22880C151direct (N × H)
414. C151#22880direct (N × H)
416. C2×C4×D8C2×C151semidirect
417. C2×#418C2×C151semidirect
418. #2363C2×C151semidirect
419. D4×C22⋊C4C2×C151semidirect
420. #1972C2×C151semidirect
421. #1934C2×C151semidirect
422. #1925C2×C151semidirect
423. #1895C2×C151semidirect
424. #1879C2×C151semidirect
425. #1879C2×C151semidirect
426. #1864C2×C151semidirect
427. #1854C2×C151semidirect
428. #1762C2×C151semidirect
429. #1753C2×C151semidirect
437. C2×C4×D4C22×C151semidirect
440. #447C4×C151semidirect
442. C2×#107C22×C151semidirect
443. C2×#106C22×C151semidirect
451. C2×#102C22×C151semidirect
452. C2×#102C22×C151semidirect
454. C2×#97C22×C151semidirect
455. C2×C4×C8C22×C151semidirect
459. #390C22×C151semidirect
460. #389C22×C151semidirect
467. C4×C4⋊C4C22×C151semidirect
470. #340C22×C151semidirect
471. #340C22×C151semidirect
472. #340C22×C151semidirect
473. #340C22×C151semidirect
474. #336C22×C151semidirect
475. #336C22×C151semidirect
484. C22×D4C2×C4×C151semidirect
497. C2×D8C2×C4×C151semidirect
506. #121C2×C4×C151semidirect
547. #102C2×C4×C151semidirect
548. #102C2×C4×C151semidirect
549. #102D4×C151semidirect
550. C22⋊C8C2×C4×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×C4×D8×C1512
C2×#418×C1512
#2363×C1512
D4×C22⋊C4×C1512
#1972×C1512
#1934×C1512
#1925×C1512
#1895×C1512
#1879×C1512
#1864×C1512
#1854×C1512
#1762×C1512
#1753×C1512
#22880151