Finite Group Databasebeta

← C151×#24221 #50329146

Subgroups — C151×#24221 #50329146

Order 38656.

1364 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C151C211yesmaximal, characteristic
2C2×#464×C151C211yesmaximal, characteristic, complemented
3C2×#462×C151C211yesmaximal, characteristic, complemented
4C2×#452×C151C211yesmaximal, characteristic
5C2×#451×C151C211yesmaximal, characteristic, complemented
6#2323×C151C211yesmaximal, characteristic, complemented
7#2043×C151C211yesmaximal, characteristic, complemented
8#2042×C151C211yesmaximal, characteristic, complemented
9#2016×C151C211yesmaximal, characteristic, complemented
10#2015×C151C211yesmaximal, characteristic, complemented
11#1983×C151C211yesmaximal, characteristic, complemented
12#1981×C151C211yesmaximal, characteristic, complemented
13#1798×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic
15#1787×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×Q8×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C22×Q16×C151C2211yescharacteristic
20C22×Q16×C151C2211yescharacteristic
21C22×SD16×C151C2211yescharacteristic
22#536×C151—24no—
23#536×C151—24no—
24C2×C4⋊Q8×C151C2211yescharacteristic
25C2×C4⋊Q8×C151C2211yescharacteristic
26C2×#124×C151C2211yescharacteristic
27C2×#124×C151C2211yescharacteristic
28C2×#123×C151—21no—
29C2×#123×C151—21no—
30C2×C22⋊Q8×C151—21no—
31C2×C22⋊Q8×C151—21no—
32C2×C22⋊Q8×C151C2211yescharacteristic
33C2×C4×Q8×C151C2211yescharacteristic
34C2×#117×C151C2211yescharacteristic
35#464×C151—24no—
36#462×C151—24no—
37#452×C151—24no—
38#451×C151—24no—
39C2×C4⋊C8×C151C2211yescharacteristic
40C2×C4⋊C8×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#103×C151C2211yescharacteristic
47C2×#103×C151C2211yescharacteristic
48C2×#103×C151C2211yescharacteristic
49C2×#103×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic
51C2×#102×C151C2211yescharacteristic
52C2×#102×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55#391×C151C2211yescharacteristic
56#389×C151—21no—
57#389×C151C2211yescharacteristic
58#388×C151—21no—
59#388×C151—21no—
60#387×C151—21no—
61#380×C151C2211yescharacteristic
62C4×C4⋊C4×C151C2211yescharacteristic
63#336×C151C2211yescharacteristic
64#336×C151C2211yescharacteristic
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—41no—
70C2×#41×C151—41no—
71C22×Q8×C151—21no—
72C22×Q8×C151—22no—
73C22×Q8×C151—22no—
74C22×Q8×C151—22no—
75C22×Q8×C151—22no—
76C22×Q8×C151—41no—
77C22×Q8×C151—41no—
78C22×Q8×C151C2311yescharacteristic
79C22×Q8×C151C2311yescharacteristic
80C22×Q8×C151C2311yescharacteristic
81C22×Q8×C151C2311yescharacteristic
82C22×D4×C151—21no—
83C22×D4×C151C2311yescharacteristic
84C23×C4×C151—21no—
85C23×C4×C151—21no—
86C23×C4×C151C2311yescharacteristic
87C2×Q16×C151—22no—
88C2×Q16×C151—22no—
89C2×Q16×C151—22no—
90C2×Q16×C151—22no—
91C2×Q16×C151—22no—
92C2×Q16×C151—22no—
93C2×Q16×C151—41no—
94C2×Q16×C151—41no—
95C2×Q16×C151—41no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—41no—
99C22×C8×C151C2311yescharacteristic
100C22×C8×C151C2311yescharacteristic
101C22×C8×C151C2311yescharacteristic
102C22×C8×C151C2311yescharacteristic
103C4⋊Q8×C151—22no—
104C4⋊Q8×C151—22no—
105C4⋊Q8×C151—22no—
106C4⋊Q8×C151D414yes—
107#124×C151—22no—
108#124×C151—22no—
109#124×C151—22no—
110#124×C151D414yes—
111#123×C151—28no—
112#123×C151—28no—
113C22⋊Q8×C151—28no—
114C22⋊Q8×C151—28no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151D414yes—
117C4×Q8×C151—22no—
118C4×Q8×C151—22no—
119#117×C151—22no—
120#117×C151—22no—
121C2×C4⋊C4×C151—21no—
122C2×C4⋊C4×C151—21no—
123C2×C4⋊C4×C151—21no—
124C2×C4⋊C4×C151—21no—
125C2×C4⋊C4×C151—21no—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151D411yescharacteristic
129C2×C4⋊C4×C151D411yescharacteristic
130C2×C4⋊C4×C151C2311yescharacteristic
131C2×C4⋊C4×C151C2311yescharacteristic
132C2×C4⋊C4×C151C2311yescharacteristic
133C2×C22⋊C4×C151—21no—
134C2×C22⋊C4×C151—21no—
135C2×C22⋊C4×C151—21no—
136C2×C22⋊C4×C151—21no—
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
139C2×C22⋊C4×C151D411yescharacteristic
140C2×C22⋊C4×C151D411yescharacteristic
141C2×C42×C151—21no—
142C2×C42×C151—21no—
143C2×C42×C151C2311yescharacteristic
144C2×C42×C151C2311yescharacteristic
145C4⋊C8×C151—22no—
146C4⋊C8×C151—22no—
147#103×C151—22no—
148#103×C151—22no—
149#103×C151—22no—
150#103×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151—41no—
154#103×C151—41no—
155#103×C151—41no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—41no—
159C22⋊C8×C151—22no—
160C22⋊C8×C151—22no—
161#95×C151—21no—
162#95×C151—21no—
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—21no—
167C24×C151C2×D411yescharacteristic
168#41×C151—44no—
169#41×C151—44no—
170#41×C151—44no—
171#41×C151—44no—
172C2×Q8×C151—24no—
173C2×Q8×C151—21no—
174C2×Q8×C151—21no—
175C2×Q8×C151—21no—
176C2×Q8×C151—21no—
177C2×Q8×C151—21no—
178C2×Q8×C151—21no—
179C2×Q8×C151—21no—
180C2×Q8×C151—21no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151—21no—
188C2×Q8×C151—21no—
189C2×Q8×C151—21no—
190C2×Q8×C151—21no—
191C2×Q8×C151—21no—
192C2×Q8×C151—21no—
193C2×Q8×C151—44no—
194C2×Q8×C151—44no—
195C2×Q8×C151—44no—
196C2×Q8×C151—44no—
197C2×Q8×C151—42no—
198C2×Q8×C151—42no—
199C2×Q8×C151C2×D412yes—
200C2×Q8×C151C2×D412yes—
201C2×Q8×C151C2×D412yes—
202C2×Q8×C151C2×D412yes—
203C2×D4×C151—24no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—21no—
209C2×D4×C151—42no—
210C2×D4×C151—42no—
211C2×D4×C151C2×D412yes—
212C22×C4×C151—21no—
213C22×C4×C151—21no—
214C22×C4×C151—21no—
215C22×C4×C151—21no—
216C22×C4×C151—24no—
217C22×C4×C151—24no—
218C22×C4×C151—21no—
219C22×C4×C151—21no—
220C22×C4×C151—21no—
221C22×C4×C151—21no—
222C22×C4×C151—21no—
223C22×C4×C151—21no—
224C22×C4×C151—21no—
225C22×C4×C151—42no—
226C22×C4×C151—42no—
227C22×C4×C151—42no—
228C22×C4×C151—42no—
229C22×C4×C151C2×D411yescharacteristic
230C22×C4×C151C2×D411yescharacteristic
231C22×C4×C151C2×D411yescharacteristic
232C22×C4×C151C2×D411yescharacteristic
233C22×C4×C151C2×D411yescharacteristic
234C22×C4×C151C2×D412yes—
235C22×C4×C151#4112yes—
236C22×C4×C151C2411yescharacteristic
237Q16×C151—44no—
238Q16×C151—44no—
239Q16×C151—44no—
240SD16×C151—44no—
241C2×C8×C151—21no—
242C2×C8×C151—21no—
243C2×C8×C151—21no—
244C2×C8×C151—21no—
245C2×C8×C151—21no—
246C2×C8×C151—21no—
247C2×C8×C151—21no—
248C2×C8×C151—21no—
249C2×C8×C151—21no—
250C2×C8×C151—21no—
251C2×C8×C151—21no—
252C2×C8×C151—21no—
253C4⋊C4×C151—24no—
254C4⋊C4×C151—24no—
255C4⋊C4×C151—24no—
256C4⋊C4×C151—24no—
257C4⋊C4×C151—22no—
258C4⋊C4×C151—22no—
259C4⋊C4×C151—24no—
260C4⋊C4×C151—21no—
261C4⋊C4×C151—21no—
262C4⋊C4×C151—21no—
263C4⋊C4×C151—21no—
264C4⋊C4×C151—21no—
265C4⋊C4×C151—42no—
266C4⋊C4×C151—81no—
267C4⋊C4×C151C2×D412yes—
268C22⋊C4×C151—24no—
269C22⋊C4×C151—24no—
270C22⋊C4×C151—24no—
271C22⋊C4×C151—24no—
272C22⋊C4×C151—24no—
273C22⋊C4×C151—22no—
274C22⋊C4×C151—22no—
275C22⋊C4×C151—81no—
276C42×C151—21no—
277C42×C151—21no—
278C42×C151—42no—
279C42×C151—81no—
280C42×C151C2×D412yes—
281C42×C151C2×D412yes—
282C23×C151—21no—
283C23×C151—21no—
284C23×C151—21no—
285C23×C151—21no—
286C23×C151—21no—
287C23×C151—21no—
288C23×C151—22no—
289C23×C151—41no—
290C23×C151—41no—
291C23×C151—41no—
292C23×C151—41no—
293C23×C151—41no—
294C23×C151—41no—
295C23×C151#12112yes—
296C23×C151C22×D411yescharacteristic
297Q8×C151—22no—
298Q8×C151—22no—
299Q8×C151—22no—
300Q8×C151—22no—
301Q8×C151—22no—
302Q8×C151—22no—
303Q8×C151—22no—
304Q8×C151—22no—
305Q8×C151—48no—
306Q8×C151—41no—
307Q8×C151—41no—
308Q8×C151—41no—
309Q8×C151—41no—
310Q8×C151—41no—
311Q8×C151—41no—
312Q8×C151—41no—
313Q8×C151—41no—
314D4×C151—22no—
315D4×C151—22no—
316D4×C151—48no—
317D4×C151—41no—
318D4×C151—41no—
319C2×C4×C151—21no—
320C2×C4×C151—21no—
321C2×C4×C151—21no—
322C2×C4×C151—21no—
323C2×C4×C151—21no—
324C2×C4×C151—21no—
325C2×C4×C151—22no—
326C2×C4×C151—22no—
327C2×C4×C151—22no—
328C2×C4×C151—22no—
329C2×C4×C151—22no—
330C2×C4×C151—22no—
331C2×C4×C151—22no—
332C2×C4×C151—21no—
333C2×C4×C151—21no—
334C2×C4×C151—22no—
335C2×C4×C151—22no—
336C2×C4×C151—21no—
337C2×C4×C151—21no—
338C2×C4×C151—21no—
339C2×C4×C151—21no—
340C2×C4×C151—48no—
341C2×C4×C151—48no—
342C2×C4×C151—41no—
343C2×C4×C151—41no—
344C2×C4×C151—41no—
345C2×C4×C151—41no—
346C2×C4×C151—41no—
347C2×C4×C151—41no—
348C2×C4×C151—41no—
349C2×C4×C151—41no—
350C2×C4×C151—41no—
351C2×C4×C151—41no—
352C2×C4×C151—41no—
353C2×C4×C151—41no—
354C2×C4×C151—41no—
355C2×C4×C151—41no—
356C2×C4×C151—41no—
357C2×C4×C151—41no—
358C2×C4×C151#12012yes—
359C2×C4×C151#12012yes—
360C2×C4×C151#12112yes—
361C2×C4×C151C22×D411yescharacteristic
362C2×C4×C151C22×D411yescharacteristic
363C2×C4×C151C22×D411yescharacteristic
364C2×C4×C151C2×#4111yescharacteristic
365C2×C4×C151H(5,𝔽2)11yescharacteristic
366C2×C4×C151H(5,𝔽2)11yescharacteristic
367C8×C151—41no—
368C8×C151—41no—
369C8×C151—41no—
370C8×C151—41no—
371C22×C151—22no—
372C22×C151—22no—
373C22×C151—22no—
374C22×C151—41no—
375C22×C151—41no—
376C22×C151—41no—
377C22×C151—41no—
378C22×C151—42no—
379C22×C151—42no—
380C22×C151—42no—
381C22×C151—81no—
382C22×C151—81no—
383C22×C151—81no—
384C22×C151—81no—
385C22×C151C2×#12011yescharacteristic
386C22×C151C2×#12111yescharacteristic
387C22×C151#53511yescharacteristic
388C22×C151#57711yescharacteristic
389C22×C151#57811yescharacteristic
390C22×C151#57811yescharacteristic
391C22×C151#57811yescharacteristic
392C4×C151—22no—
393C4×C151—22no—
394C4×C151—22no—
395C4×C151—42no—
396C4×C151—42no—
397C4×C151—42no—
398C4×C151—42no—
399C4×C151—41no—
400C4×C151—41no—
401C4×C151—42no—
402C4×C151—81no—
403C4×C151—81no—
404C4×C151D4211yescharacteristic
405C4×C151D4211yescharacteristic
406C4×C151#54611yescharacteristic
407C4×C151#54611yescharacteristic
408C2×C151—42no—
409C2×C151—82no—
410C2×C151#240811yescharacteristic
411C2×C151#301111yescharacteristic
412C2×C151#301311yescharacteristic
413C2×C151#304411yescharacteristic
414C2×C151#304611yescharacteristic
415C2×C151#322311yescharacteristic
416C2×C151#322511yescharacteristic
417#24221C15111yesmaximal, characteristic, direct product factor, Sylow
418C151#2422111yescharacteristic, direct product factor, Sylow
419C2×#536C2×C15111yescharacteristic
420C2×#464C2×C15111yescharacteristic, complemented
421C2×#462C2×C15111yescharacteristic, complemented
422C2×#452C2×C15111yescharacteristic
423C2×#451C2×C15111yescharacteristic, complemented
424#2323C2×C15111yescharacteristic, complemented
425#2043C2×C15111yescharacteristic, complemented
426#2042C2×C15111yescharacteristic, complemented
427#2016C2×C15111yescharacteristic, complemented
428#2015C2×C15111yescharacteristic, complemented
429#1983C2×C15111yescharacteristic, complemented
430#1981C2×C15111yescharacteristic, complemented
431#1798C2×C15111yescharacteristic, complemented
432#1788C2×C15111yescharacteristic
433#1787C2×C15111yescharacteristic, complemented
434C22×#41C22×C15111yescharacteristic
435C23×Q8C22×C15111yescharacteristic
436C22×Q16C22×C15111yescharacteristic
437C22×Q16C22×C15111yescharacteristic
438C22×Q16C22×C15111yescharacteristic
439C22×SD16C22×C15111yescharacteristic
440#536—24no—
441#536—24no—
442C2×C4⋊Q8C22×C15111yescharacteristic
443C2×C4⋊Q8C22×C15111yescharacteristic
444C2×#124C22×C15111yescharacteristic
445C2×#124C22×C15111yescharacteristic
446C2×#123—21no—
447C2×#123—21no—
448C2×C22⋊Q8—21no—
449C2×C22⋊Q8—21no—
450C2×C22⋊Q8C22×C15111yescharacteristic
451C2×C4×Q8C22×C15111yescharacteristic
452C2×#117C22×C15111yescharacteristic
453#464—24no—
454#462—24no—
455#452—24no—
456#451—24no—
457C2×C4⋊C8C22×C15111yescharacteristic
458C2×C4⋊C8C22×C15111yescharacteristic
459C2×#103C22×C15111yescharacteristic
460C2×#103C22×C15111yescharacteristic
461C2×#103C22×C15111yescharacteristic
462C2×#103C22×C15111yescharacteristic
463C2×#103C22×C15111yescharacteristic
464C2×#103C22×C15111yescharacteristic
465C2×#103C22×C15111yescharacteristic
466C2×#103C22×C15111yescharacteristic
467C2×#103C22×C15111yescharacteristic
468C2×#102C22×C15111yescharacteristic
469C2×#102C22×C15111yescharacteristic
470C2×#102C22×C15111yescharacteristic
471C2×C22⋊C8C22×C15111yescharacteristic
472C2×C22⋊C8C22×C15111yescharacteristic
473#391C22×C15111yescharacteristic
474#389—21no—
475#389C22×C15111yescharacteristic
476#388—21no—
477#388—21no—
478#387—21no—
479#380C22×C15111yescharacteristic
480C4×C4⋊C4C22×C15111yescharacteristic
481#336C22×C15111yescharacteristic
482#336C22×C15111yescharacteristic
483C2×#41—22no—
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C22×Q8—22no—
490C22×Q8—22no—
491C22×Q8—21no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8C23×C15111yescharacteristic
497C22×Q8C23×C15111yescharacteristic
498C22×Q8C23×C15111yescharacteristic
499C22×Q8C23×C15111yescharacteristic
500C22×D4—21no—
501C22×D4C23×C15111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C23×C15111yescharacteristic
505C2×Q16—22no—
506C2×Q16—22no—
507C2×Q16—22no—
508C2×Q16—22no—
509C2×Q16—22no—
510C2×Q16—22no—
511C2×Q16—41no—
512C2×Q16—41no—
513C2×Q16—41no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C22×C8C23×C15111yescharacteristic
518C22×C8C23×C15111yescharacteristic
519C22×C8C23×C15111yescharacteristic
520C22×C8C23×C15111yescharacteristic
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8D4×C15114yes—
525#124—22no—
526#124—22no—
527#124—22no—
528#124D4×C15114yes—
529#123—28no—
530#123—28no—
531C22⋊Q8—28no—
532C22⋊Q8—28no—
533C22⋊Q8—22no—
534C22⋊Q8D4×C15114yes—
535C4×Q8—22no—
536C4×Q8—22no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4D4×C15111yescharacteristic
547C2×C4⋊C4D4×C15111yescharacteristic
548C2×C4⋊C4C23×C15111yescharacteristic
549C2×C4⋊C4C23×C15111yescharacteristic
550C2×C4⋊C4C23×C15111yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4D4×C15111yescharacteristic
558C2×C22⋊C4D4×C15111yescharacteristic
559C2×C42—21no—
560C2×C42—21no—
561C2×C42C23×C15111yescharacteristic
562C2×C42C23×C15111yescharacteristic
563C4⋊C8—22no—
564C4⋊C8—22no—
565#103—22no—
566#103—22no—
567#103—22no—
568#103—22no—
569#103—22no—
570#103—22no—
571#103—41no—
572#103—41no—
573#103—41no—
574#102—22no—
575#102—22no—
576#102—41no—
577C22⋊C8—22no—
578C22⋊C8—22no—
579#95—21no—
580#95—21no—
581#95—21no—
582#95—21no—
583#95—21no—
584C24—21no—
585C24C2×D4×C15111yescharacteristic
586#41—44no—
587#41—44no—
588#41—44no—
589#41—44no—
590C2×Q8—24no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8—44no—
612C2×Q8—44no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—42no—
616C2×Q8—42no—
617C2×Q8C2×D4×C15112yes—
618C2×Q8C2×D4×C15112yes—
619C2×Q8C2×D4×C15112yes—
620C2×Q8C2×D4×C15112yes—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—42no—
628C2×D4—42no—
629C2×D4C2×D4×C15112yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—24no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4—42no—
647C22×C4C2×D4×C15111yescharacteristic
648C22×C4C2×D4×C15111yescharacteristic
649C22×C4C2×D4×C15111yescharacteristic
650C22×C4C2×D4×C15111yescharacteristic
651C22×C4C2×D4×C15111yescharacteristic
652C22×C4C2×D4×C15112yes—
653C22×C4#41×C15112yes—
654C22×C4C24×C15111yescharacteristic
655Q16—44no—
656Q16—44no—
657Q16—44no—
658SD16—44no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C4⋊C4—24no—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—24no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—42no—
684C4⋊C4—81no—
685C4⋊C4C2×D4×C15112yes—
686C22⋊C4—24no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—22no—
692C22⋊C4—22no—
693C22⋊C4—81no—
694C42—21no—
695C42—21no—
696C42—42no—
697C42—81no—
698C42C2×D4×C15112yes—
699C42C2×D4×C15112yes—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—22no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23#121×C15112yes—
714C23C22×D4×C15111yescharacteristic
715Q8—22no—
716Q8—22no—
717Q8—22no—
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8—41no—
727Q8—41no—
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—48no—
735D4—41no—
736D4—41no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—48no—
759C2×C4—48no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4#120×C15112yes—
777C2×C4#120×C15112yes—
778C2×C4#121×C15112yes—
779C2×C4C22×D4×C15111yescharacteristic
780C2×C4C22×D4×C15111yescharacteristic
781C2×C4C22×D4×C15111yescharacteristic
782C2×C4C2×#41×C15111yescharacteristic
783C2×C4H(5,𝔽2)×C15111yescharacteristic
784C2×C4H(5,𝔽2)×C15111yescharacteristic
785C8—41no—
786C8—41no—
787C8—41no—
788C8—41no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—81no—
800C22—81no—
801C22—81no—
802C22—81no—
803C22C2×#120×C15111yescharacteristic
804C22C2×#121×C15111yescharacteristic
805C22#535×C15111yescharacteristic
806C22#577×C15111yescharacteristic
807C22#578×C15111yescharacteristic
808C22#578×C15111yescharacteristic
809C22#578×C15111yescharacteristic
810C4—22no—
811C4—22no—
812C4—22no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4—42no—
820C4—81no—
821C4—81no—
822C4D42×C15111yescharacteristic
823C4D42×C15111yescharacteristic
824C4#546×C15111yescharacteristic
825C4#546×C15111yescharacteristic
826C2—42no—
827C2—82no—
828C2#2408×C15111yescharacteristic
829C2#3011×C15111yescharacteristic
830C2#3013×C15111yescharacteristic
831C2#3044×C15111yescharacteristic
832C2#3046×C15111yescharacteristic
833C2#3223×C15111yescharacteristic
834C2#3225×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC22×#41×C151C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×#117×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#464×C151C2semidirect
3. C2×#462×C151C2semidirect
5. C2×#451×C151C2semidirect
6. #2323×C151C2semidirect
7. #2043×C151C2semidirect
8. #2042×C151C2semidirect
9. #2016×C151C2semidirect
10. #2015×C151C2semidirect
11. #1983×C151C2semidirect
12. #1981×C151C2semidirect
13. #1798×C151C2semidirect
15. #1787×C151C2semidirect
417. #24221C151direct (N × H)
418. C151#24221direct (N × H)
420. C2×#464C2×C151semidirect
421. C2×#462C2×C151semidirect
423. C2×#451C2×C151semidirect
424. #2323C2×C151semidirect
425. #2043C2×C151semidirect
426. #2042C2×C151semidirect
427. #2016C2×C151semidirect
428. #2015C2×C151semidirect
429. #1983C2×C151semidirect
430. #1981C2×C151semidirect
431. #1798C2×C151semidirect
433. #1787C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C1512
C2×#464×C1512
C2×#462×C1512
C2×#452×C1512
C2×#451×C1512
#2323×C1512
#2043×C1512
#2042×C1512
#2016×C1512
#2015×C1512
#1983×C1512
#1981×C1512
#1798×C1512
#1788×C1512
#1787×C1512
#24221151