Finite Group Databasebeta

← C151×#24395 #50329320

Subgroups — C151×#24395 #50329320

Order 38656.

1450 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C151C211yesmaximal, characteristic
2C2×#470×C151C211yesmaximal, characteristic, complemented
3C2×#465×C151C211yesmaximal, characteristic, complemented
4C2×#452×C151C211yesmaximal, characteristic, complemented
5C2×#408×C151C211yesmaximal, characteristic, complemented
6#2616×C151C211yesmaximal, characteristic, complemented
7#2035×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2001×C151C211yesmaximal, characteristic, complemented
10#2000×C151C211yesmaximal, characteristic, complemented
11#1895×C151C211yesmaximal, characteristic, complemented
12#1892×C151C211yesmaximal, characteristic, complemented
13#1872×C151C211yesmaximal, characteristic, complemented
14#1853×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic
19C22×SD16×C151C2211yescharacteristic
20C22×M16×C151C2211yescharacteristic
21C23×C8×C151C2211yescharacteristic
22#537×C151—24no—
23#537×C151—24no—
24C2×C22⋊Q8×C151—21no—
25C2×C22⋊Q8×C151C2211yescharacteristic
26C2×C22⋊Q8×C151C2211yescharacteristic
27C2×C22⋊Q8×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×C22⋊Q8×C151C2211yescharacteristic
30C2×#121×C151—21no—
31C2×#121×C151—21no—
32C2×#121×C151—21no—
33C2×#121×C151C2211yescharacteristic
34C2×#121×C151C2211yescharacteristic
35C22×C4⋊C4×C151C2211yescharacteristic
36#470×C151—24no—
37#465×C151—24no—
38#452×C151—24no—
39C2×#106×C151C2211yescharacteristic
40C2×#106×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#103×C151C2211yescharacteristic
45C2×#103×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49#408×C151—24no—
50C2×C22⋊C8×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic
53C2×C22⋊C8×C151C2211yescharacteristic
54#395×C151—21no—
55#394×C151—21no—
56#394×C151—21no—
57#394×C151—21no—
58#380×C151C2211yescharacteristic
59#380×C151C2211yescharacteristic
60#380×C151C2211yescharacteristic
61#340×C151C2211yescharacteristic
62#340×C151C2211yescharacteristic
63#340×C151C2211yescharacteristic
64#340×C151C2211yescharacteristic
65C2×#41×C151—22no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—22no—
71C2×#41×C151—22no—
72C2×#41×C151—22no—
73C2×#41×C151—41no—
74C2×#41×C151—41no—
75C2×#41×C151—41no—
76C2×#41×C151—41no—
77C22×Q8×C151D411yescharacteristic
78C22×Q8×C151C2311yescharacteristic
79C22×Q8×C151C2311yescharacteristic
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151D411yescharacteristic
84C22×D4×C151D411yescharacteristic
85C22×D4×C151D411yescharacteristic
86C22×D4×C151C2311yescharacteristic
87C23×C4×C151—21no—
88C23×C4×C151—21no—
89C23×C4×C151C2311yescharacteristic
90C23×C4×C151C2311yescharacteristic
91C23×C4×C151C2311yescharacteristic
92C2×Q16×C151—22no—
93C2×Q16×C151—22no—
94C2×Q16×C151—41no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—41no—
98C2×M16×C151—22no—
99C2×M16×C151—22no—
100C2×M16×C151—41no—
101C22×C8×C151—22no—
102C22×C8×C151—22no—
103C22×C8×C151—41no—
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107C22×C8×C151C2311yescharacteristic
108C22⋊Q8×C151—28no—
109C22⋊Q8×C151—22no—
110C22⋊Q8×C151—22no—
111C22⋊Q8×C151—22no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151—41no—
117C22⋊Q8×C151—41no—
118C22⋊Q8×C151D414yes—
119#121×C151—28no—
120#121×C151—28no—
121#121×C151—28no—
122#121×C151—22no—
123#121×C151—22no—
124#121×C151—22no—
125#121×C151D414yes—
126C2×C4⋊C4×C151—21no—
127C2×C4⋊C4×C151—21no—
128C2×C4⋊C4×C151—21no—
129C2×C4⋊C4×C151—22no—
130C2×C4⋊C4×C151—22no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151—21no—
133C2×C4⋊C4×C151—21no—
134C2×C4⋊C4×C151C2311yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C4⋊C4×C151C2311yescharacteristic
138C2×C4⋊C4×C151C2311yescharacteristic
139C2×C22⋊C4×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—21no—
142C2×C22⋊C4×C151—21no—
143C2×C22⋊C4×C151—21no—
144C2×C22⋊C4×C151—21no—
145C2×C22⋊C4×C151—21no—
146C2×C22⋊C4×C151—21no—
147C2×C22⋊C4×C151—21no—
148C2×C22⋊C4×C151—21no—
149#106×C151—22no—
150#106×C151—22no—
151#103×C151—22no—
152#103×C151—22no—
153#103×C151—22no—
154#103×C151—22no—
155#103×C151—41no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—41no—
159C22⋊C8×C151—22no—
160C22⋊C8×C151—22no—
161C22⋊C8×C151—22no—
162C22⋊C8×C151D414yescomplemented
163#95×C151—21no—
164#95×C151—21no—
165#95×C151—21no—
166C24×C151—21no—
167C24×C151C2×D411yescharacteristic
168C24×C151C2×D411yescharacteristic
169C24×C151C2×D411yescharacteristic
170#41×C151—44no—
171#41×C151—44no—
172#41×C151—44no—
173#41×C151—44no—
174#41×C151—44no—
175#41×C151—44no—
176#41×C151—44no—
177#41×C151—44no—
178C2×Q8×C151—22no—
179C2×Q8×C151—22no—
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—41no—
192C2×Q8×C151C2×D412yes—
193C2×D4×C151—24no—
194C2×D4×C151—22no—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
197C2×D4×C151—22no—
198C2×D4×C151—24no—
199C2×D4×C151—24no—
200C2×D4×C151—22no—
201C2×D4×C151—22no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—41no—
208C2×D4×C151—41no—
209C2×D4×C151—41no—
210C2×D4×C151—42no—
211C2×D4×C151—42no—
212C2×D4×C151—81no—
213C2×D4×C151—81no—
214C2×D4×C151—81no—
215C2×D4×C151—81no—
216C2×D4×C151C2×D412yes—
217C22×C4×C151—21no—
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—24no—
226C22×C4×C151—21no—
227C22×C4×C151—21no—
228C22×C4×C151—21no—
229C22×C4×C151—24no—
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—21no—
240C22×C4×C151—42no—
241C22×C4×C151—42no—
242C22×C4×C151—81no—
243C22×C4×C151—81no—
244C22×C4×C151C2×D411yescharacteristic
245C22×C4×C151C2×D411yescharacteristic
246C22×C4×C151C2×D412yes—
247C22×C4×C151C2×D412yes—
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D412yes—
250C22×C4×C151#4112yes—
251C22×C4×C151C2411yescharacteristic
252Q16×C151—44no—
253SD16×C151—44no—
254M16×C151—44no—
255C2×C8×C151—21no—
256C2×C8×C151—21no—
257C2×C8×C151—21no—
258C2×C8×C151—21no—
259C2×C8×C151—21no—
260C2×C8×C151—21no—
261C2×C8×C151—21no—
262C2×C8×C151—21no—
263C2×C8×C151—21no—
264C2×C8×C151—21no—
265C2×C8×C151—44no—
266C2×C8×C151C2×D412yes—
267C2×C8×C151C2×D412yes—
268C4⋊C4×C151—24no—
269C4⋊C4×C151—24no—
270C4⋊C4×C151—24no—
271C4⋊C4×C151—21no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—42no—
280C4⋊C4×C151—42no—
281C4⋊C4×C151—42no—
282C4⋊C4×C151C2×D412yes—
283C4⋊C4×C151C2×D412yes—
284C22⋊C4×C151—24no—
285C22⋊C4×C151—24no—
286C22⋊C4×C151—24no—
287C22⋊C4×C151—24no—
288C22⋊C4×C151—42no—
289C22⋊C4×C151—42no—
290C22⋊C4×C151—42no—
291C22⋊C4×C151—81no—
292C22⋊C4×C151—81no—
293C22⋊C4×C151—81no—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—22no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—21no—
313C23×C151—21no—
314C23×C151—41no—
315C23×C151—41no—
316C23×C151—41no—
317C23×C151—41no—
318C23×C151—41no—
319C23×C151—41no—
320C23×C151#12012yes—
321C23×C151#12112yes—
322C23×C151C22×D411yescharacteristic
323Q8×C151—22no—
324Q8×C151—22no—
325Q8×C151—44no—
326Q8×C151—41no—
327Q8×C151—41no—
328Q8×C151—41no—
329Q8×C151—41no—
330Q8×C151—41no—
331Q8×C151—41no—
332D4×C151—22no—
333D4×C151—22no—
334D4×C151—44no—
335D4×C151—44no—
336D4×C151—44no—
337D4×C151—48no—
338D4×C151—41no—
339D4×C151—41no—
340D4×C151—84no—
341D4×C151—84no—
342C2×C4×C151—21no—
343C2×C4×C151—21no—
344C2×C4×C151—21no—
345C2×C4×C151—21no—
346C2×C4×C151—22no—
347C2×C4×C151—22no—
348C2×C4×C151—22no—
349C2×C4×C151—22no—
350C2×C4×C151—22no—
351C2×C4×C151—22no—
352C2×C4×C151—22no—
353C2×C4×C151—22no—
354C2×C4×C151—21no—
355C2×C4×C151—22no—
356C2×C4×C151—22no—
357C2×C4×C151—22no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—48no—
361C2×C4×C151—41no—
362C2×C4×C151—41no—
363C2×C4×C151—41no—
364C2×C4×C151—41no—
365C2×C4×C151—41no—
366C2×C4×C151—41no—
367C2×C4×C151—41no—
368C2×C4×C151—41no—
369C2×C4×C151—41no—
370C2×C4×C151—41no—
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—84no—
384C2×C4×C151#12012yes—
385C2×C4×C151#12112yes—
386C2×C4×C151C22×D411yescharacteristic
387C2×C4×C151C22×D411yescharacteristic
388C2×C4×C151C22×D411yescharacteristic
389C2×C4×C151C2×#4111yescharacteristic
390C2×C4×C151H(5,𝔽2)11yescharacteristic
391C2×C4×C151H(5,𝔽2)11yescharacteristic
392C8×C151—22no—
393C8×C151—22no—
394C8×C151—41no—
395C8×C151—41no—
396C22×C151—22no—
397C22×C151—22no—
398C22×C151—22no—
399C22×C151—22no—
400C22×C151—22no—
401C22×C151—22no—
402C22×C151—41no—
403C22×C151—41no—
404C22×C151—41no—
405C22×C151—41no—
406C22×C151—41no—
407C22×C151—41no—
408C22×C151—41no—
409C22×C151—41no—
410C22×C151—42no—
411C22×C151—41no—
412C22×C151—41no—
413C22×C151—41no—
414C22×C151—41no—
415C22×C151—42no—
416C22×C151—41no—
417C22×C151—42no—
418C22×C151—41no—
419C22×C151—41no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151—81no—
423C22×C151—81no—
424C22×C151C2×#12011yescharacteristic
425C22×C151C2×#12111yescharacteristic
426C22×C151#53411yescharacteristic
427C22×C151#57711yescharacteristic
428C22×C151#57711yescharacteristic
429C22×C151#57711yescharacteristic
430C22×C151#57811yescharacteristic
431C4×C151—22no—
432C4×C151—22no—
433C4×C151—41no—
434C4×C151—42no—
435C4×C151—42no—
436C4×C151—42no—
437C4×C151—81no—
438C4×C151—81no—
439C4×C151—81no—
440C4×C151—81no—
441C4×C151D4211yescharacteristic
442C4×C151D4211yescharacteristic
443C4×C151#54611yescharacteristic
444C4×C151#54611yescharacteristic
445C2×C151—42no—
446C2×C151—42no—
447C2×C151—81no—
448C2×C151—82no—
449C2×C151#241011yescharacteristic
450C2×C151#300911yescharacteristic
451C2×C151#301311yescharacteristic
452C2×C151#306011yescharacteristic
453C2×C151#306311yescharacteristic
454C2×C151#320111yescharacteristic
455C2×C151#320411yescharacteristic
456#24395C15111yesmaximal, characteristic, direct product factor, Sylow
457C151#2439511yescharacteristic, direct product factor, Sylow
458C2×#537C2×C15111yescharacteristic
459C2×#470C2×C15111yescharacteristic, complemented
460C2×#465C2×C15111yescharacteristic, complemented
461C2×#452C2×C15111yescharacteristic, complemented
462C2×#408C2×C15111yescharacteristic, complemented
463#2616C2×C15111yescharacteristic, complemented
464#2035C2×C15111yescharacteristic, complemented
465#2034C2×C15111yescharacteristic, complemented
466#2001C2×C15111yescharacteristic, complemented
467#2000C2×C15111yescharacteristic, complemented
468#1895C2×C15111yescharacteristic, complemented
469#1892C2×C15111yescharacteristic, complemented
470#1872C2×C15111yescharacteristic, complemented
471#1853C2×C15111yescharacteristic, complemented
472#1788C2×C15111yescharacteristic, complemented
473C22×#41C22×C15111yescharacteristic
474C22×#41C22×C15111yescharacteristic
475C22×Q16C22×C15111yescharacteristic
476C22×SD16C22×C15111yescharacteristic
477C22×M16C22×C15111yescharacteristic
478C23×C8C22×C15111yescharacteristic
479#537—24no—
480#537—24no—
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C15111yescharacteristic
483C2×C22⋊Q8C22×C15111yescharacteristic
484C2×C22⋊Q8C22×C15111yescharacteristic
485C2×C22⋊Q8C22×C15111yescharacteristic
486C2×C22⋊Q8C22×C15111yescharacteristic
487C2×#121—21no—
488C2×#121—21no—
489C2×#121—21no—
490C2×#121C22×C15111yescharacteristic
491C2×#121C22×C15111yescharacteristic
492C22×C4⋊C4C22×C15111yescharacteristic
493#470—24no—
494#465—24no—
495#452—24no—
496C2×#106C22×C15111yescharacteristic
497C2×#106C22×C15111yescharacteristic
498C2×#103C22×C15111yescharacteristic
499C2×#103C22×C15111yescharacteristic
500C2×#103C22×C15111yescharacteristic
501C2×#103C22×C15111yescharacteristic
502C2×#103C22×C15111yescharacteristic
503C2×#102C22×C15111yescharacteristic
504C2×#102C22×C15111yescharacteristic
505C2×#102C22×C15111yescharacteristic
506#408—24no—
507C2×C22⋊C8C22×C15111yescharacteristic
508C2×C22⋊C8C22×C15111yescharacteristic
509C2×C22⋊C8C22×C15111yescharacteristic
510C2×C22⋊C8C22×C15111yescharacteristic
511#395—21no—
512#394—21no—
513#394—21no—
514#394—21no—
515#380C22×C15111yescharacteristic
516#380C22×C15111yescharacteristic
517#380C22×C15111yescharacteristic
518#340C22×C15111yescharacteristic
519#340C22×C15111yescharacteristic
520#340C22×C15111yescharacteristic
521#340C22×C15111yescharacteristic
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41—41no—
534C22×Q8D4×C15111yescharacteristic
535C22×Q8C23×C15111yescharacteristic
536C22×Q8C23×C15111yescharacteristic
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4D4×C15111yescharacteristic
541C22×D4D4×C15111yescharacteristic
542C22×D4D4×C15111yescharacteristic
543C22×D4C23×C15111yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C15111yescharacteristic
547C23×C4C23×C15111yescharacteristic
548C23×C4C23×C15111yescharacteristic
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C15111yescharacteristic
562C22×C8C23×C15111yescharacteristic
563C22×C8C23×C15111yescharacteristic
564C22×C8C23×C15111yescharacteristic
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8D4×C15114yes—
576#121—28no—
577#121—28no—
578#121—28no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121D4×C15114yes—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4C23×C15111yescharacteristic
592C2×C4⋊C4C23×C15111yescharacteristic
593C2×C4⋊C4C23×C15111yescharacteristic
594C2×C4⋊C4C23×C15111yescharacteristic
595C2×C4⋊C4C23×C15111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606#106—22no—
607#106—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C15114yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C15111yescharacteristic
625C24C2×D4×C15111yescharacteristic
626C24C2×D4×C15111yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634#41—44no—
635C2×Q8—22no—
636C2×Q8—22no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—41no—
649C2×Q8C2×D4×C15112yes—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—24no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—41no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—81no—
670C2×D4—81no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4C2×D4×C15112yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—24no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—42no—
698C22×C4—42no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C2×D4×C15111yescharacteristic
702C22×C4C2×D4×C15111yescharacteristic
703C22×C4C2×D4×C15112yes—
704C22×C4C2×D4×C15112yes—
705C22×C4C2×D4×C15111yescharacteristic
706C22×C4C2×D4×C15112yes—
707C22×C4#41×C15112yes—
708C22×C4C24×C15111yescharacteristic
709Q16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C15112yes—
724C2×C8C2×D4×C15112yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—42no—
738C4⋊C4—42no—
739C4⋊C4C2×D4×C15112yes—
740C4⋊C4C2×D4×C15112yes—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C22⋊C4—81no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C15112yes—
778C23#121×C15112yes—
779C23C22×D4×C15111yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—44no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789D4—22no—
790D4—22no—
791D4—44no—
792D4—44no—
793D4—44no—
794D4—48no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—48no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4#120×C15112yes—
842C2×C4#121×C15112yes—
843C2×C4C22×D4×C15111yescharacteristic
844C2×C4C22×D4×C15111yescharacteristic
845C2×C4C22×D4×C15111yescharacteristic
846C2×C4C2×#41×C15111yescharacteristic
847C2×C4H(5,𝔽2)×C15111yescharacteristic
848C2×C4H(5,𝔽2)×C15111yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—41no—
876C22—41no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C15111yescharacteristic
882C22C2×#121×C15111yescharacteristic
883C22#534×C15111yescharacteristic
884C22#577×C15111yescharacteristic
885C22#577×C15111yescharacteristic
886C22#577×C15111yescharacteristic
887C22#578×C15111yescharacteristic
888C4—22no—
889C4—22no—
890C4—41no—
891C4—42no—
892C4—42no—
893C4—42no—
894C4—81no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C15111yescharacteristic
899C4D42×C15111yescharacteristic
900C4#546×C15111yescharacteristic
901C4#546×C15111yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—82no—
906C2#2410×C15111yescharacteristic
907C2#3009×C15111yescharacteristic
908C2#3013×C15111yescharacteristic
909C2#3060×C15111yescharacteristic
910C2#3063×C15111yescharacteristic
911C2#3201×C15111yescharacteristic
912C2#3204×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#537×C151C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×#41×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#470×C151C2semidirect
3. C2×#465×C151C2semidirect
4. C2×#452×C151C2semidirect
5. C2×#408×C151C2semidirect
6. #2616×C151C2semidirect
7. #2035×C151C2semidirect
8. #2034×C151C2semidirect
9. #2001×C151C2semidirect
10. #2000×C151C2semidirect
11. #1895×C151C2semidirect
12. #1892×C151C2semidirect
13. #1872×C151C2semidirect
14. #1853×C151C2semidirect
15. #1788×C151C2semidirect
162. C22⋊C8×C151D4semidirect
456. #24395C151direct (N × H)
457. C151#24395direct (N × H)
459. C2×#470C2×C151semidirect
460. C2×#465C2×C151semidirect
461. C2×#452C2×C151semidirect
462. C2×#408C2×C151semidirect
463. #2616C2×C151semidirect
464. #2035C2×C151semidirect
465. #2034C2×C151semidirect
466. #2001C2×C151semidirect
467. #2000C2×C151semidirect
468. #1895C2×C151semidirect
469. #1892C2×C151semidirect
470. #1872C2×C151semidirect
471. #1853C2×C151semidirect
472. #1788C2×C151semidirect
619. C22⋊C8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1512
C2×#470×C1512
C2×#465×C1512
C2×#452×C1512
C2×#408×C1512
#2616×C1512
#2035×C1512
#2034×C1512
#2001×C1512
#2000×C1512
#1895×C1512
#1892×C1512
#1872×C1512
#1853×C1512
#1788×C1512
#24395151