Finite Group Databasebeta

← C151×#24044 #50328969

Subgroups — C151×#24044 #50328969

Order 38656.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C151C211yesmaximal, characteristic
2C2×#482×C151C211yesmaximal, characteristic, complemented
3C2×#418×C151C211yesmaximal, characteristic, complemented
4#2485×C151C211yesmaximal, characteristic, complemented
5#2041×C151C211yesmaximal, characteristic, complemented
6#2041×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1895×C151C211yesmaximal, characteristic, complemented
10#1870×C151C211yesmaximal, characteristic, complemented
11#1864×C151C211yesmaximal, characteristic, complemented
12#1862×C151C211yesmaximal, characteristic, complemented
13#1786×C151C211yesmaximal, characteristic, complemented
14#1786×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C23×D4×C151—21no—
17C23×D4×C151C2211yescharacteristic
18C23×D4×C151C2211yescharacteristic
19C22×M16×C151C2211yescharacteristic, complemented
20D42×C151—24no—
21D42×C151—24no—
22C2×#127×C151C2211yescharacteristic
23C2×#121×C151—21no—
24C2×#121×C151C2211yescharacteristic
25C2×#121×C151C2211yescharacteristic
26C2×#120×C151—21no—
27C2×#120×C151—21no—
28C2×C4×D4×C151C2211yescharacteristic
29C2×C4×D4×C151C2211yescharacteristic
30C2×#117×C151C2211yescharacteristic, complemented
31#482×C151—24no—
32C2×#107×C151C2211yescharacteristic, complemented
33C2×#106×C151C2211yescharacteristic, complemented
34#418×C151—24no—
35C2×#102×C151C2211yescharacteristic
36C2×#102×C151C2211yescharacteristic
37C2×#102×C151C2211yescharacteristic
38C2×#102×C151C2211yescharacteristic
39C2×#102×C151C2211yescharacteristic, complemented
40C2×#102×C151C2211yescharacteristic, complemented
41C2×#102×C151C2211yescharacteristic, complemented
42C2×#102×C151C2211yescharacteristic, complemented
43C2×#102×C151C2211yescharacteristic, complemented
44C2×#102×C151C2211yescharacteristic, complemented
45C2×#102×C151C2211yescharacteristic, complemented
46C2×#102×C151C2211yescharacteristic, complemented
47C2×C22⋊C8×C151C2211yescharacteristic, complemented
48C2×C22⋊C8×C151C2211yescharacteristic, complemented
49C2×C22⋊C8×C151C2211yescharacteristic, complemented
50#397×C151—21no—
51#394×C151—21no—
52#389×C151C2211yescharacteristic, complemented
53#389×C151C2211yescharacteristic, complemented
54#388×C151—21no—
55#387×C151—21no—
56#380×C151C2211yescharacteristic, complemented
57#380×C151C2211yescharacteristic, complemented
58#380×C151C2211yescharacteristic, complemented
59#340×C151C2211yescharacteristic, complemented
60#340×C151C2211yescharacteristic, complemented
61#336×C151C2211yescharacteristic, complemented
62#336×C151C2211yescharacteristic, complemented
63C25×C151—21no—
64C25×C151—21no—
65C22×D4×C151—28no—
66C22×D4×C151—22no—
67C22×D4×C151—22no—
68C22×D4×C151—21no—
69C22×D4×C151—21no—
70C22×D4×C151—21no—
71C22×D4×C151—22no—
72C22×D4×C151—21no—
73C22×D4×C151—21no—
74C22×D4×C151—21no—
75C22×D4×C151—22no—
76C22×D4×C151—22no—
77C22×D4×C151—22no—
78C22×D4×C151—22no—
79C22×D4×C151—41no—
80C22×D4×C151—41no—
81C22×D4×C151—41no—
82C22×D4×C151—41no—
83C22×D4×C151—44no—
84C22×D4×C151—44no—
85C22×D4×C151D414yes—
86C22×D4×C151D411yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C22×D4×C151C2311yescharacteristic
89C22×D4×C151C2311yescharacteristic
90C23×C4×C151—21no—
91C23×C4×C151C2311yescharacteristic
92C23×C4×C151C2311yescharacteristic
93C2×M16×C151—22no—
94C2×M16×C151—41no—
95C2×M16×C151—41no—
96C22×C8×C151C2311yescharacteristic
97C22×C8×C151C2311yescharacteristic
98C22×C8×C151C2311yescharacteristic
99C22×C8×C151C2311yescharacteristic
100#127×C151—22no—
101#127×C151—22no—
102#121×C151—28no—
103#121×C151—22no—
104#121×C151—22no—
105#121×C151—22no—
106#121×C151D414yes—
107#120×C151—28no—
108#120×C151—28no—
109C4×D4×C151—22no—
110C4×D4×C151—22no—
111C4×D4×C151—22no—
112C4×D4×C151—22no—
113#117×C151—22no—
114#117×C151—22no—
115C2×C4⋊C4×C151—21no—
116C2×C4⋊C4×C151—21no—
117C2×C4⋊C4×C151D411yescharacteristic
118C2×C4⋊C4×C151C2311yescharacteristic
119C2×C4⋊C4×C151C2311yescharacteristic
120C2×C4⋊C4×C151C2311yescharacteristic
121C2×C4⋊C4×C151C2311yescharacteristic
122C2×C4⋊C4×C151C2311yescharacteristic
123C2×C22⋊C4×C151—21no—
124C2×C22⋊C4×C151—21no—
125C2×C22⋊C4×C151—21no—
126C2×C22⋊C4×C151—21no—
127C2×C22⋊C4×C151—21no—
128C2×C22⋊C4×C151—21no—
129C2×C22⋊C4×C151—21no—
130C2×C22⋊C4×C151D411yescharacteristic
131C2×C22⋊C4×C151D411yescharacteristic
132C2×C42×C151—21no—
133C2×C42×C151C2311yescharacteristic
134#107×C151—22no—
135#106×C151—22no—
136#102×C151—22no—
137#102×C151—22no—
138#102×C151—22no—
139#102×C151—22no—
140#102×C151—22no—
141#102×C151—22no—
142#102×C151—22no—
143#102×C151—22no—
144#102×C151—41no—
145#102×C151—41no—
146#102×C151—41no—
147#102×C151—41no—
148C22⋊C8×C151—22no—
149C22⋊C8×C151—41no—
150C22⋊C8×C151—41no—
151#95×C151—21no—
152#95×C151—21no—
153#95×C151—21no—
154#95×C151—21no—
155#95×C151—21no—
156C24×C151—21no—
157C24×C151—24no—
158C24×C151—21no—
159C24×C151—21no—
160C24×C151—24no—
161C24×C151—42no—
162C24×C151—42no—
163C24×C151—42no—
164C24×C151—42no—
165C24×C151—42no—
166C24×C151—42no—
167C24×C151—42no—
168C24×C151—42no—
169C24×C151—81no—
170C24×C151—81no—
171C24×C151—81no—
172C24×C151—81no—
173C24×C151C2×D411yescharacteristic
174C24×C151C2×D411yescharacteristic
175C2×D4×C151—22no—
176C2×D4×C151—22no—
177C2×D4×C151—28no—
178C2×D4×C151—24no—
179C2×D4×C151—24no—
180C2×D4×C151—24no—
181C2×D4×C151—24no—
182C2×D4×C151—24no—
183C2×D4×C151—24no—
184C2×D4×C151—22no—
185C2×D4×C151—21no—
186C2×D4×C151—21no—
187C2×D4×C151—21no—
188C2×D4×C151—21no—
189C2×D4×C151—21no—
190C2×D4×C151—21no—
191C2×D4×C151—21no—
192C2×D4×C151—21no—
193C2×D4×C151—21no—
194C2×D4×C151—21no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
197C2×D4×C151—21no—
198C2×D4×C151—44no—
199C2×D4×C151—44no—
200C2×D4×C151—44no—
201C2×D4×C151—42no—
202C2×D4×C151—42no—
203C2×D4×C151—42no—
204C2×D4×C151—42no—
205C2×D4×C151—42no—
206C2×D4×C151—44no—
207C2×D4×C151—44no—
208C2×D4×C151—432no—
209C2×D4×C151—44no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—44no—
215C2×D4×C151—42no—
216C2×D4×C151—81no—
217C2×D4×C151—81no—
218C2×D4×C151C2×D412yes—
219C2×D4×C151C2×D412yes—
220C2×D4×C151C2×D412yes—
221C2×D4×C151#4112yes—
222C2×D4×C151#4112yes—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—21no—
226C22×C4×C151—21no—
227C22×C4×C151—24no—
228C22×C4×C151—21no—
229C22×C4×C151—21no—
230C22×C4×C151—21no—
231C22×C4×C151—21no—
232C22×C4×C151—21no—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—42no—
240C22×C4×C151—42no—
241C22×C4×C151C2×D411yescharacteristic
242C22×C4×C151C2×D411yescharacteristic
243C22×C4×C151C2×D411yescharacteristic
244C22×C4×C151C2×D412yes—
245C22×C4×C151C2×D412yes—
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151C2411yescharacteristic
248M16×C151—44no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C2×C8×C151—21no—
254C2×C8×C151—21no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C4⋊C4×C151—22no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—21no—
266C4⋊C4×C151—21no—
267C4⋊C4×C151—21no—
268C4⋊C4×C151—21no—
269C4⋊C4×C151—21no—
270C4⋊C4×C151—21no—
271C4⋊C4×C151—42no—
272C4⋊C4×C151—81no—
273C4⋊C4×C151C2×D412yes—
274C22⋊C4×C151—24no—
275C22⋊C4×C151—24no—
276C22⋊C4×C151—22no—
277C22⋊C4×C151—24no—
278C22⋊C4×C151—22no—
279C22⋊C4×C151—42no—
280C22⋊C4×C151—42no—
281C22⋊C4×C151—81no—
282C22⋊C4×C151—81no—
283C42×C151—21no—
284C42×C151—21no—
285C42×C151—42no—
286C23×C151—22no—
287C23×C151—21no—
288C23×C151—22no—
289C23×C151—22no—
290C23×C151—21no—
291C23×C151—21no—
292C23×C151—21no—
293C23×C151—21no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—22no—
302C23×C151—22no—
303C23×C151—48no—
304C23×C151—48no—
305C23×C151—48no—
306C23×C151—48no—
307C23×C151—41no—
308C23×C151—41no—
309C23×C151—41no—
310C23×C151—41no—
311C23×C151—41no—
312C23×C151—41no—
313C23×C151—41no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151—41no—
321C23×C151—41no—
322C23×C151—41no—
323C23×C151—84no—
324C23×C151—84no—
325C23×C151—84no—
326C23×C151—84no—
327C23×C151—84no—
328C23×C151—84no—
329C23×C151—84no—
330C23×C151—84no—
331C23×C151—84no—
332C23×C151—84no—
333C23×C151#12012yes—
334C23×C151AGL(1,ℤ/8)12yes—
335C23×C151C22×D411yescharacteristic
336D4×C151—28no—
337D4×C151—22no—
338D4×C151—22no—
339D4×C151—22no—
340D4×C151—22no—
341D4×C151—22no—
342D4×C151—22no—
343D4×C151—22no—
344D4×C151—48no—
345D4×C151—48no—
346D4×C151—48no—
347D4×C151—48no—
348D4×C151—48no—
349D4×C151—41no—
350D4×C151—41no—
351D4×C151—41no—
352D4×C151—41no—
353D4×C151—84no—
354D4×C151#12314yes—
355C2×C4×C151—21no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—22no—
360C2×C4×C151—22no—
361C2×C4×C151—22no—
362C2×C4×C151—22no—
363C2×C4×C151—21no—
364C2×C4×C151—21no—
365C2×C4×C151—22no—
366C2×C4×C151—21no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—21no—
370C2×C4×C151—48no—
371C2×C4×C151—41no—
372C2×C4×C151—41no—
373C2×C4×C151—41no—
374C2×C4×C151—41no—
375C2×C4×C151—41no—
376C2×C4×C151—41no—
377C2×C4×C151—41no—
378C2×C4×C151—41no—
379C2×C4×C151—41no—
380C2×C4×C151—41no—
381C2×C4×C151—41no—
382C2×C4×C151—41no—
383C2×C4×C151—41no—
384C2×C4×C151—41no—
385C2×C4×C151—41no—
386C2×C4×C151—41no—
387C2×C4×C151—41no—
388C2×C4×C151—41no—
389C2×C4×C151#12012yes—
390C2×C4×C151AGL(1,ℤ/8)12yes—
391C2×C4×C151C22×D411yescharacteristic
392C2×C4×C151C22×D411yescharacteristic
393C2×C4×C151C2×#4111yescharacteristic
394C2×C4×C151C2×#4111yescharacteristic
395C2×C4×C151H(5,𝔽2)11yescharacteristic
396C2×C4×C151H(5,𝔽2)11yescharacteristic
397C8×C151—41no—
398C8×C151—41no—
399C8×C151—41no—
400C8×C151—41no—
401C22×C151—22no—
402C22×C151—24no—
403C22×C151—22no—
404C22×C151—22no—
405C22×C151—22no—
406C22×C151—22no—
407C22×C151—22no—
408C22×C151—41no—
409C22×C151—42no—
410C22×C151—41no—
411C22×C151—42no—
412C22×C151—41no—
413C22×C151—42no—
414C22×C151—41no—
415C22×C151—42no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—42no—
419C22×C151—41no—
420C22×C151—41no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—42no—
424C22×C151—42no—
425C22×C151—42no—
426C22×C151—42no—
427C22×C151—42no—
428C22×C151—816no—
429C22×C151—816no—
430C22×C151—81no—
431C22×C151—81no—
432C22×C151—81no—
433C22×C151—81no—
434C22×C151—81no—
435C22×C151—81no—
436C22×C151—81no—
437C22×C151—81no—
438C22×C151C2×#12011yescharacteristic
439C22×C151#54611yescharacteristic
440C22×C151#54611yescharacteristic
441C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C151C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C151#57611yescharacteristic
444C22×C151#57711yescharacteristic
445C4×C151—22no—
446C4×C151—22no—
447C4×C151—41no—
448C4×C151—42no—
449C4×C151—41no—
450C4×C151—81no—
451C4×C151—81no—
452C4×C151—81no—
453C4×C151—81no—
454C4×C151C2×#12311yescharacteristic
455C4×C151#53411yescharacteristic
456C4×C151#54611yescharacteristic
457C4×C151#54611yescharacteristic
458C2×C151—42no—
459C2×C151—42no—
460C2×C151—44no—
461C2×C151—82no—
462C2×C151—82no—
463C2×C151#240511yescharacteristic
464C2×C151#300311yescharacteristic
465C2×C151#301211yescharacteristic
466C2×C151#331011yescharacteristic
467C2×C151#331811yescharacteristic
468C2×C151#332411yescharacteristic
469C2×C151#332511yescharacteristic
470#24044C15111yesmaximal, characteristic, direct product factor, Sylow
471C151#2404411yescharacteristic, direct product factor, Sylow
472C2×D42C2×C15111yescharacteristic
473C2×#482C2×C15111yescharacteristic, complemented
474C2×#418C2×C15111yescharacteristic, complemented
475#2485C2×C15111yescharacteristic, complemented
476#2041C2×C15111yescharacteristic, complemented
477#2041C2×C15111yescharacteristic, complemented
478#2034C2×C15111yescharacteristic, complemented
479#2033C2×C15111yescharacteristic, complemented
480#1895C2×C15111yescharacteristic, complemented
481#1870C2×C15111yescharacteristic, complemented
482#1864C2×C15111yescharacteristic, complemented
483#1862C2×C15111yescharacteristic, complemented
484#1786C2×C15111yescharacteristic, complemented
485#1786C2×C15111yescharacteristic, complemented
486#1786C2×C15111yescharacteristic, complemented
487C23×D4—21no—
488C23×D4C22×C15111yescharacteristic
489C23×D4C22×C15111yescharacteristic
490C22×M16C22×C15111yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C15111yescharacteristic
494C2×#121—21no—
495C2×#121C22×C15111yescharacteristic
496C2×#121C22×C15111yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C15111yescharacteristic
500C2×C4×D4C22×C15111yescharacteristic
501C2×#117C22×C15111yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C15111yescharacteristic, complemented
504C2×#106C22×C15111yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C15111yescharacteristic
507C2×#102C22×C15111yescharacteristic
508C2×#102C22×C15111yescharacteristic
509C2×#102C22×C15111yescharacteristic
510C2×#102C22×C15111yescharacteristic, complemented
511C2×#102C22×C15111yescharacteristic, complemented
512C2×#102C22×C15111yescharacteristic, complemented
513C2×#102C22×C15111yescharacteristic, complemented
514C2×#102C22×C15111yescharacteristic, complemented
515C2×#102C22×C15111yescharacteristic, complemented
516C2×#102C22×C15111yescharacteristic, complemented
517C2×#102C22×C15111yescharacteristic, complemented
518C2×C22⋊C8C22×C15111yescharacteristic, complemented
519C2×C22⋊C8C22×C15111yescharacteristic, complemented
520C2×C22⋊C8C22×C15111yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C15111yescharacteristic, complemented
524#389C22×C15111yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C15111yescharacteristic, complemented
528#380C22×C15111yescharacteristic, complemented
529#380C22×C15111yescharacteristic, complemented
530#340C22×C15111yescharacteristic, complemented
531#340C22×C15111yescharacteristic, complemented
532#336C22×C15111yescharacteristic, complemented
533#336C22×C15111yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C15111yescharacteristic
557C22×D4D4×C15114yes—
558C22×D4C23×C15111yescharacteristic
559C22×D4C23×C15111yescharacteristic
560C22×D4C23×C15111yescharacteristic
561C23×C4—21no—
562C23×C4C23×C15111yescharacteristic
563C23×C4C23×C15111yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C15111yescharacteristic
568C22×C8C23×C15111yescharacteristic
569C22×C8C23×C15111yescharacteristic
570C22×C8C23×C15111yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C15114yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C15111yescharacteristic
589C2×C4⋊C4C23×C15111yescharacteristic
590C2×C4⋊C4C23×C15111yescharacteristic
591C2×C4⋊C4C23×C15111yescharacteristic
592C2×C4⋊C4C23×C15111yescharacteristic
593C2×C4⋊C4C23×C15111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C15111yescharacteristic
602C2×C22⋊C4D4×C15111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C15111yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C15111yescharacteristic
645C24C2×D4×C15111yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C15112yes—
690C2×D4C2×D4×C15112yes—
691C2×D4C2×D4×C15112yes—
692C2×D4#41×C15112yes—
693C2×D4#41×C15112yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C15111yescharacteristic
713C22×C4C2×D4×C15111yescharacteristic
714C22×C4C2×D4×C15111yescharacteristic
715C22×C4C2×D4×C15112yes—
716C22×C4C2×D4×C15112yes—
717C22×C4C2×D4×C15111yescharacteristic
718C22×C4C24×C15111yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C15112yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C15112yes—
805C23AGL(1,ℤ/8)×C15112yes—
806C23C22×D4×C15111yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C15114yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C15112yes—
861C2×C4AGL(1,ℤ/8)×C15112yes—
862C2×C4C22×D4×C15111yescharacteristic
863C2×C4C22×D4×C15111yescharacteristic
864C2×C4C2×#41×C15111yescharacteristic
865C2×C4C2×#41×C15111yescharacteristic
866C2×C4H(5,𝔽2)×C15111yescharacteristic
867C2×C4H(5,𝔽2)×C15111yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—24no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—42no—
885C22—41no—
886C22—42no—
887C22—41no—
888C22—41no—
889C22—42no—
890C22—41no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C15111yescharacteristic
910C22#546×C15111yescharacteristic
911C22#546×C15111yescharacteristic
912C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
913C22C2×AGL(1,ℤ/8)×C15111yescharacteristic
914C22#576×C15111yescharacteristic
915C22#577×C15111yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C15111yescharacteristic
926C4#534×C15111yescharacteristic
927C4#546×C15111yescharacteristic
928C4#546×C15111yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2#2405×C15111yescharacteristic
935C2#3003×C15111yescharacteristic
936C2#3012×C15111yescharacteristic
937C2#3310×C15111yescharacteristic
938C2#3318×C15111yescharacteristic
939C2#3324×C15111yescharacteristic
940C2#3325×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×D42×C151C2
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×#482×C151C2semidirect
3. C2×#418×C151C2semidirect
4. #2485×C151C2semidirect
5. #2041×C151C2semidirect
6. #2041×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1895×C151C2semidirect
10. #1870×C151C2semidirect
11. #1864×C151C2semidirect
12. #1862×C151C2semidirect
13. #1786×C151C2semidirect
14. #1786×C151C2semidirect
15. #1786×C151C2semidirect
19. C22×M16×C151C22semidirect
30. C2×#117×C151C22semidirect
32. C2×#107×C151C22semidirect
33. C2×#106×C151C22semidirect
39. C2×#102×C151C22semidirect
40. C2×#102×C151C22semidirect
41. C2×#102×C151C22semidirect
42. C2×#102×C151C22semidirect
43. C2×#102×C151C22semidirect
44. C2×#102×C151C22semidirect
45. C2×#102×C151C22semidirect
46. C2×#102×C151C22semidirect
47. C2×C22⋊C8×C151C22semidirect
48. C2×C22⋊C8×C151C22semidirect
49. C2×C22⋊C8×C151C22semidirect
52. #389×C151C22semidirect
53. #389×C151C22semidirect
56. #380×C151C22semidirect
57. #380×C151C22semidirect
58. #380×C151C22semidirect
59. #340×C151C22semidirect
60. #340×C151C22semidirect
61. #336×C151C22semidirect
62. #336×C151C22semidirect
470. #24044C151direct (N × H)
471. C151#24044direct (N × H)
473. C2×#482C2×C151semidirect
474. C2×#418C2×C151semidirect
475. #2485C2×C151semidirect
476. #2041C2×C151semidirect
477. #2041C2×C151semidirect
478. #2034C2×C151semidirect
479. #2033C2×C151semidirect
480. #1895C2×C151semidirect
481. #1870C2×C151semidirect
482. #1864C2×C151semidirect
483. #1862C2×C151semidirect
484. #1786C2×C151semidirect
485. #1786C2×C151semidirect
486. #1786C2×C151semidirect
490. C22×M16C22×C151semidirect
501. C2×#117C22×C151semidirect
503. C2×#107C22×C151semidirect
504. C2×#106C22×C151semidirect
510. C2×#102C22×C151semidirect
511. C2×#102C22×C151semidirect
512. C2×#102C22×C151semidirect
513. C2×#102C22×C151semidirect
514. C2×#102C22×C151semidirect
515. C2×#102C22×C151semidirect
516. C2×#102C22×C151semidirect
517. C2×#102C22×C151semidirect
518. C2×C22⋊C8C22×C151semidirect
519. C2×C22⋊C8C22×C151semidirect
520. C2×C22⋊C8C22×C151semidirect
523. #389C22×C151semidirect
524. #389C22×C151semidirect
527. #380C22×C151semidirect
528. #380C22×C151semidirect
529. #380C22×C151semidirect
530. #340C22×C151semidirect
531. #340C22×C151semidirect
532. #336C22×C151semidirect
533. #336C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1512
C2×#482×C1512
C2×#418×C1512
#2485×C1512
#2041×C1512
#2034×C1512
#2033×C1512
#1895×C1512
#1870×C1512
#1864×C1512
#1862×C1512
#1786×C1512
#24044151