Finite Group Databasebeta

← C151×#24220 #50329145

Subgroups — C151×#24220 #50329145

Order 38656.

1556 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C151C211yesmaximal, characteristic
2C2×#464×C151C211yesmaximal, characteristic, complemented
3C2×#460×C151C211yesmaximal, characteristic, complemented
4C2×#452×C151C211yesmaximal, characteristic, complemented
5C2×#450×C151C211yesmaximal, characteristic, complemented
6#2323×C151C211yesmaximal, characteristic, complemented
7#2042×C151C211yesmaximal, characteristic, complemented
8#2041×C151C211yesmaximal, characteristic, complemented
9#2015×C151C211yesmaximal, characteristic, complemented
10#2014×C151C211yesmaximal, characteristic, complemented
11#1983×C151C211yesmaximal, characteristic, complemented
12#1982×C151C211yesmaximal, characteristic, complemented
13#1798×C151C211yesmaximal, characteristic, complemented
14#1788×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×Q16×C151C2211yescharacteristic, complemented
19C22×SD16×C151C2211yescharacteristic
20C22×SD16×C151C2211yescharacteristic
21C22×SD16×C151C2211yescharacteristic, complemented
22#535×C151—24no—
23#535×C151—24no—
24C2×#127×C151C2211yescharacteristic
25C2×#127×C151C2211yescharacteristic
26C2×#124×C151C2211yescharacteristic
27C2×#124×C151C2211yescharacteristic
28C2×C22⋊Q8×C151C2211yescharacteristic
29C2×#121×C151—21no—
30C2×#121×C151—21no—
31C2×#120×C151—21no—
32C2×#120×C151—21no—
33C2×C4×Q8×C151C2211yescharacteristic, complemented
34C2×#117×C151C2211yescharacteristic
35#464×C151—24no—
36#460×C151—24no—
37#452×C151—24no—
38#450×C151—24no—
39C2×C4⋊C8×C151C2211yescharacteristic, complemented
40C2×C4⋊C8×C151C2211yescharacteristic, complemented
41C2×#103×C151C2211yescharacteristic, complemented
42C2×#103×C151C2211yescharacteristic, complemented
43C2×#103×C151C2211yescharacteristic, complemented
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic
48C2×#102×C151C2211yescharacteristic
49C2×#102×C151C2211yescharacteristic
50C2×#102×C151C2211yescharacteristic, complemented
51C2×#102×C151C2211yescharacteristic, complemented
52C2×#102×C151C2211yescharacteristic, complemented
53C2×C22⋊C8×C151C2211yescharacteristic
54C2×C22⋊C8×C151C2211yescharacteristic
55#391×C151C2211yescharacteristic, complemented
56#389×C151—21no—
57#389×C151C2211yescharacteristic, complemented
58#388×C151—21no—
59#388×C151—21no—
60#387×C151—21no—
61#380×C151C2211yescharacteristic
62C4×C4⋊C4×C151C2211yescharacteristic, complemented
63#336×C151C2211yescharacteristic, complemented
64#336×C151C2211yescharacteristic, complemented
65C25×C151—21no—
66C2×#41×C151—22no—
67C2×#41×C151—22no—
68C2×#41×C151—22no—
69C2×#41×C151—22no—
70C2×#41×C151—41no—
71C2×#41×C151—41no—
72C22×Q8×C151C2311yescharacteristic
73C22×Q8×C151C2311yescharacteristic
74C22×D4×C151—22no—
75C22×D4×C151—22no—
76C22×D4×C151—21no—
77C22×D4×C151—21no—
78C22×D4×C151—21no—
79C22×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—22no—
83C22×D4×C151—22no—
84C22×D4×C151—41no—
85C22×D4×C151—41no—
86C22×D4×C151C2311yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C22×D4×C151C2311yescharacteristic
89C23×C4×C151—21no—
90C23×C4×C151C2311yescharacteristic
91C2×Q16×C151—22no—
92C2×Q16×C151—22no—
93C2×Q16×C151—41no—
94C2×SD16×C151—22no—
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—22no—
98C2×SD16×C151—22no—
99C2×SD16×C151—22no—
100C2×SD16×C151—41no—
101C2×SD16×C151—41no—
102C2×SD16×C151—41no—
103C22×C8×C151C2311yescharacteristic
104C22×C8×C151C2311yescharacteristic
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107#127×C151—22no—
108#127×C151—22no—
109#127×C151—22no—
110#127×C151D414yes—
111#124×C151—22no—
112#124×C151—22no—
113#124×C151—22no—
114#124×C151D414yes—
115C22⋊Q8×C151—22no—
116C22⋊Q8×C151D414yescomplemented
117#121×C151—28no—
118#121×C151—28no—
119#120×C151—28no—
120#120×C151—28no—
121C4×Q8×C151—22no—
122C4×Q8×C151—22no—
123#117×C151—22no—
124#117×C151—22no—
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—41no—
150#102×C151—22no—
151#102×C151—22no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—41no—
157#102×C151—41no—
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—24no—
167C24×C151—21no—
168C24×C151—21no—
169C24×C151—21no—
170C24×C151—42no—
171C24×C151—42no—
172C24×C151—81no—
173C24×C151—81no—
174C24×C151—81no—
175C24×C151—81no—
176C24×C151C2×D411yescharacteristic
177#41×C151—44no—
178#41×C151—44no—
179#41×C151—44no—
180#41×C151—44no—
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×C151C2×D412yes—
192C2×Q8×C151C2×D412yes—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—24no—
196C2×D4×C151—24no—
197C2×D4×C151—24no—
198C2×D4×C151—24no—
199C2×D4×C151—21no—
200C2×D4×C151—21no—
201C2×D4×C151—21no—
202C2×D4×C151—21no—
203C2×D4×C151—21no—
204C2×D4×C151—21no—
205C2×D4×C151—21no—
206C2×D4×C151—21no—
207C2×D4×C151—21no—
208C2×D4×C151—21no—
209C2×D4×C151—21no—
210C2×D4×C151—21no—
211C2×D4×C151—21no—
212C2×D4×C151—21no—
213C2×D4×C151—21no—
214C2×D4×C151—44no—
215C2×D4×C151—44no—
216C2×D4×C151—44no—
217C2×D4×C151—44no—
218C2×D4×C151—42no—
219C2×D4×C151—42no—
220C2×D4×C151—42no—
221C2×D4×C151—42no—
222C2×D4×C151—81no—
223C2×D4×C151—81no—
224C2×D4×C151—81no—
225C2×D4×C151—81no—
226C2×D4×C151—81no—
227C2×D4×C151—81no—
228C2×D4×C151—81no—
229C2×D4×C151—81no—
230C2×D4×C151C2×D412yes—
231C2×D4×C151C2×D412yes—
232C2×D4×C151C2×D412yes—
233C22×C4×C151—21no—
234C22×C4×C151—21no—
235C22×C4×C151—21no—
236C22×C4×C151—21no—
237C22×C4×C151—24no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—42no—
244C22×C4×C151—42no—
245C22×C4×C151C2×D411yescharacteristic
246C22×C4×C151C2×D411yescharacteristic
247C22×C4×C151C2×D411yescharacteristic
248C22×C4×C151C2×D411yescharacteristic
249C22×C4×C151C2×D411yescharacteristic
250C22×C4×C151C2×D412yes—
251C22×C4×C151#4112yes—
252C22×C4×C151C2411yescharacteristic
253Q16×C151—44no—
254SD16×C151—44no—
255SD16×C151—44no—
256SD16×C151—44no—
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—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C4⋊C4×C151—22no—
270C4⋊C4×C151—22no—
271C4⋊C4×C151—24no—
272C4⋊C4×C151—21no—
273C4⋊C4×C151—21no—
274C4⋊C4×C151—21no—
275C4⋊C4×C151—21no—
276C4⋊C4×C151—21no—
277C4⋊C4×C151—42no—
278C4⋊C4×C151—81no—
279C4⋊C4×C151C2×D412yes—
280C22⋊C4×C151—24no—
281C22⋊C4×C151—24no—
282C22⋊C4×C151—24no—
283C22⋊C4×C151—24no—
284C22⋊C4×C151—24no—
285C22⋊C4×C151—22no—
286C22⋊C4×C151—22no—
287C22⋊C4×C151—81no—
288C42×C151—21no—
289C42×C151—21no—
290C42×C151—42no—
291C42×C151—81no—
292C42×C151C2×D412yes—
293C42×C151C2×D412yes—
294C23×C151—21no—
295C23×C151—21no—
296C23×C151—21no—
297C23×C151—21no—
298C23×C151—21no—
299C23×C151—21no—
300C23×C151—22no—
301C23×C151—22no—
302C23×C151—22no—
303C23×C151—48no—
304C23×C151—41no—
305C23×C151—41no—
306C23×C151—41no—
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—84no—
323C23×C151—84no—
324C23×C151—84no—
325C23×C151—84no—
326C23×C151—84no—
327C23×C151—84no—
328C23×C151#12112yes—
329C23×C151C22×D411yescharacteristic
330Q8×C151—22no—
331Q8×C151—22no—
332Q8×C151—22no—
333Q8×C151—22no—
334Q8×C151—41no—
335Q8×C151—41no—
336Q8×C151—41no—
337Q8×C151—41no—
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—41no—
347D4×C151—41no—
348D4×C151—41no—
349D4×C151—41no—
350D4×C151—41no—
351D4×C151—41no—
352D4×C151—84no—
353D4×C151—84no—
354D4×C151—84no—
355D4×C151—84no—
356C2×C4×C151—21no—
357C2×C4×C151—21no—
358C2×C4×C151—21no—
359C2×C4×C151—21no—
360C2×C4×C151—21no—
361C2×C4×C151—21no—
362C2×C4×C151—22no—
363C2×C4×C151—22no—
364C2×C4×C151—22no—
365C2×C4×C151—22no—
366C2×C4×C151—22no—
367C2×C4×C151—21no—
368C2×C4×C151—21no—
369C2×C4×C151—22no—
370C2×C4×C151—22no—
371C2×C4×C151—21no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—21no—
375C2×C4×C151—48no—
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#12012yes—
389C2×C4×C151#12012yes—
390C2×C4×C151#12112yes—
391C2×C4×C151C22×D411yescharacteristic
392C2×C4×C151C22×D411yescharacteristic
393C2×C4×C151C22×D411yescharacteristic
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—22no—
403C22×C151—22no—
404C22×C151—41no—
405C22×C151—41no—
406C22×C151—41no—
407C22×C151—41no—
408C22×C151—42no—
409C22×C151—42no—
410C22×C151—42no—
411C22×C151—42no—
412C22×C151—42no—
413C22×C151—42no—
414C22×C151—42no—
415C22×C151—42no—
416C22×C151—42no—
417C22×C151—816no—
418C22×C151—81no—
419C22×C151—81no—
420C22×C151—81no—
421C22×C151—81no—
422C22×C151—81no—
423C22×C151—81no—
424C22×C151—81no—
425C22×C151—81no—
426C22×C151—81no—
427C22×C151—81no—
428C22×C151—81no—
429C22×C151—81no—
430C22×C151C2×#12011yescharacteristic
431C22×C151C2×#12111yescharacteristic
432C22×C151#53511yescharacteristic
433C22×C151#57611yescharacteristic
434C22×C151#57711yescharacteristic
435C22×C151#57711yescharacteristic
436C22×C151#57711yescharacteristic
437C4×C151—22no—
438C4×C151—22no—
439C4×C151—22no—
440C4×C151—42no—
441C4×C151—42no—
442C4×C151—41no—
443C4×C151—41no—
444C4×C151—42no—
445C4×C151—81no—
446C4×C151—81no—
447C4×C151D4211yescharacteristic
448C4×C151D4211yescharacteristic
449C4×C151#54611yescharacteristic
450C4×C151#54611yescharacteristic
451C2×C151—42no—
452C2×C151—82no—
453C2×C151—82no—
454C2×C151—82no—
455C2×C151#240811yescharacteristic
456C2×C151#300911yescharacteristic
457C2×C151#301211yescharacteristic
458C2×C151#304311yescharacteristic
459C2×C151#304511yescharacteristic
460C2×C151#322211yescharacteristic
461C2×C151#322411yescharacteristic
462#24220C15111yesmaximal, characteristic, direct product factor, Sylow
463C151#2422011yescharacteristic, direct product factor, Sylow
464C2×#535C2×C15111yescharacteristic
465C2×#464C2×C15111yescharacteristic, complemented
466C2×#460C2×C15111yescharacteristic, complemented
467C2×#452C2×C15111yescharacteristic, complemented
468C2×#450C2×C15111yescharacteristic, complemented
469#2323C2×C15111yescharacteristic, complemented
470#2042C2×C15111yescharacteristic, complemented
471#2041C2×C15111yescharacteristic, complemented
472#2015C2×C15111yescharacteristic, complemented
473#2014C2×C15111yescharacteristic, complemented
474#1983C2×C15111yescharacteristic, complemented
475#1982C2×C15111yescharacteristic, complemented
476#1798C2×C15111yescharacteristic, complemented
477#1788C2×C15111yescharacteristic, complemented
478#1786C2×C15111yescharacteristic, complemented
479C22×#41C22×C15111yescharacteristic
480C23×D4C22×C15111yescharacteristic
481C22×Q16C22×C15111yescharacteristic, complemented
482C22×SD16C22×C15111yescharacteristic
483C22×SD16C22×C15111yescharacteristic
484C22×SD16C22×C15111yescharacteristic, complemented
485#535—24no—
486#535—24no—
487C2×#127C22×C15111yescharacteristic
488C2×#127C22×C15111yescharacteristic
489C2×#124C22×C15111yescharacteristic
490C2×#124C22×C15111yescharacteristic
491C2×C22⋊Q8C22×C15111yescharacteristic
492C2×#121—21no—
493C2×#121—21no—
494C2×#120—21no—
495C2×#120—21no—
496C2×C4×Q8C22×C15111yescharacteristic, complemented
497C2×#117C22×C15111yescharacteristic
498#464—24no—
499#460—24no—
500#452—24no—
501#450—24no—
502C2×C4⋊C8C22×C15111yescharacteristic, complemented
503C2×C4⋊C8C22×C15111yescharacteristic, complemented
504C2×#103C22×C15111yescharacteristic, complemented
505C2×#103C22×C15111yescharacteristic, complemented
506C2×#103C22×C15111yescharacteristic, complemented
507C2×#102C22×C15111yescharacteristic
508C2×#102C22×C15111yescharacteristic
509C2×#102C22×C15111yescharacteristic
510C2×#102C22×C15111yescharacteristic
511C2×#102C22×C15111yescharacteristic
512C2×#102C22×C15111yescharacteristic
513C2×#102C22×C15111yescharacteristic, complemented
514C2×#102C22×C15111yescharacteristic, complemented
515C2×#102C22×C15111yescharacteristic, complemented
516C2×C22⋊C8C22×C15111yescharacteristic
517C2×C22⋊C8C22×C15111yescharacteristic
518#391C22×C15111yescharacteristic, complemented
519#389—21no—
520#389C22×C15111yescharacteristic, complemented
521#388—21no—
522#388—21no—
523#387—21no—
524#380C22×C15111yescharacteristic
525C4×C4⋊C4C22×C15111yescharacteristic, complemented
526#336C22×C15111yescharacteristic, complemented
527#336C22×C15111yescharacteristic, complemented
528C25—21no—
529C2×#41—22no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—41no—
534C2×#41—41no—
535C22×Q8C23×C15111yescharacteristic
536C22×Q8C23×C15111yescharacteristic
537C22×D4—21no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—21no—
544C22×D4—21no—
545C22×D4—21no—
546C22×D4—22no—
547C22×D4—41no—
548C22×D4—41no—
549C22×D4C23×C15111yescharacteristic
550C22×D4C23×C15111yescharacteristic
551C22×D4C23×C15111yescharacteristic
552C23×C4—21no—
553C23×C4C23×C15111yescharacteristic
554C2×Q16—22no—
555C2×Q16—22no—
556C2×Q16—41no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C22×C8C23×C15111yescharacteristic
567C22×C8C23×C15111yescharacteristic
568C22×C8C23×C15111yescharacteristic
569C22×C8C23×C15111yescharacteristic
570#127—22no—
571#127—22no—
572#127—22no—
573#127D4×C15114yes—
574#124—22no—
575#124—22no—
576#124—22no—
577#124D4×C15114yes—
578C22⋊Q8—22no—
579C22⋊Q8D4×C15114yescomplemented
580#121—28no—
581#121—28no—
582#120—28no—
583#120—28no—
584C4×Q8—22no—
585C4×Q8—22no—
586#117—22no—
587#117—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4D4×C15111yescharacteristic
592C2×C4⋊C4D4×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⋊C4D4×C15111yescharacteristic
603C2×C22⋊C4D4×C15111yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42C23×C15111yescharacteristic
607C2×C42C23×C15111yescharacteristic
608C4⋊C8—22no—
609C4⋊C8—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#102—22no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—22no—
618#102—22no—
619#102—41no—
620#102—41no—
621#102—41no—
622C22⋊C8—22no—
623C22⋊C8—22no—
624#95—21no—
625#95—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629C24—24no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—42no—
634C24—42no—
635C24—81no—
636C24—81no—
637C24—81no—
638C24—81no—
639C24C2×D4×C15111yescharacteristic
640#41—44no—
641#41—44no—
642#41—44no—
643#41—44no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8C2×D4×C15112yes—
655C2×Q8C2×D4×C15112yes—
656C2×D4—24no—
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—24no—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—81no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4—81no—
690C2×D4—81no—
691C2×D4—81no—
692C2×D4—81no—
693C2×D4C2×D4×C15112yes—
694C2×D4C2×D4×C15112yes—
695C2×D4C2×D4×C15112yes—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—24no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—42no—
707C22×C4—42no—
708C22×C4C2×D4×C15111yescharacteristic
709C22×C4C2×D4×C15111yescharacteristic
710C22×C4C2×D4×C15111yescharacteristic
711C22×C4C2×D4×C15111yescharacteristic
712C22×C4C2×D4×C15111yescharacteristic
713C22×C4C2×D4×C15112yes—
714C22×C4#41×C15112yes—
715C22×C4C24×C15111yescharacteristic
716Q16—44no—
717SD16—44no—
718SD16—44no—
719SD16—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—22no—
734C4⋊C4—24no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—42no—
741C4⋊C4—81no—
742C4⋊C4C2×D4×C15112yes—
743C22⋊C4—24no—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—24no—
748C22⋊C4—22no—
749C22⋊C4—22no—
750C22⋊C4—81no—
751C42—21no—
752C42—21no—
753C42—42no—
754C42—81no—
755C42C2×D4×C15112yes—
756C42C2×D4×C15112yes—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—48no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—84no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#121×C15112yes—
792C23C22×D4×C15111yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801D4—22no—
802D4—22no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—48no—
808D4—48no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4—41no—
815D4—84no—
816D4—84no—
817D4—84no—
818D4—84no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—48no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
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#120×C15112yes—
852C2×C4#120×C15112yes—
853C2×C4#121×C15112yes—
854C2×C4C22×D4×C15111yescharacteristic
855C2×C4C22×D4×C15111yescharacteristic
856C2×C4C22×D4×C15111yescharacteristic
857C2×C4C2×#41×C15111yescharacteristic
858C2×C4H(5,𝔽2)×C15111yescharacteristic
859C2×C4H(5,𝔽2)×C15111yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—22no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—816no—
881C22—81no—
882C22—81no—
883C22—81no—
884C22—81no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22—81no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22C2×#120×C15111yescharacteristic
894C22C2×#121×C15111yescharacteristic
895C22#535×C15111yescharacteristic
896C22#576×C15111yescharacteristic
897C22#577×C15111yescharacteristic
898C22#577×C15111yescharacteristic
899C22#577×C15111yescharacteristic
900C4—22no—
901C4—22no—
902C4—22no—
903C4—42no—
904C4—42no—
905C4—41no—
906C4—41no—
907C4—42no—
908C4—81no—
909C4—81no—
910C4D42×C15111yescharacteristic
911C4D42×C15111yescharacteristic
912C4#546×C15111yescharacteristic
913C4#546×C15111yescharacteristic
914C2—42no—
915C2—82no—
916C2—82no—
917C2—82no—
918C2#2408×C15111yescharacteristic
919C2#3009×C15111yescharacteristic
920C2#3012×C15111yescharacteristic
921C2#3043×C15111yescharacteristic
922C2#3045×C15111yescharacteristic
923C2#3222×C15111yescharacteristic
924C2#3224×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
prime radicalC2×#535×C151C2
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×#460×C151C2semidirect
4. C2×#452×C151C2semidirect
5. C2×#450×C151C2semidirect
6. #2323×C151C2semidirect
7. #2042×C151C2semidirect
8. #2041×C151C2semidirect
9. #2015×C151C2semidirect
10. #2014×C151C2semidirect
11. #1983×C151C2semidirect
12. #1982×C151C2semidirect
13. #1798×C151C2semidirect
14. #1788×C151C2semidirect
15. #1786×C151C2semidirect
18. C22×Q16×C151C22semidirect
21. C22×SD16×C151C22semidirect
33. C2×C4×Q8×C151C22semidirect
39. C2×C4⋊C8×C151C22semidirect
40. C2×C4⋊C8×C151C22semidirect
41. C2×#103×C151C22semidirect
42. C2×#103×C151C22semidirect
43. C2×#103×C151C22semidirect
50. C2×#102×C151C22semidirect
51. C2×#102×C151C22semidirect
52. C2×#102×C151C22semidirect
55. #391×C151C22semidirect
57. #389×C151C22semidirect
62. C4×C4⋊C4×C151C22semidirect
63. #336×C151C22semidirect
64. #336×C151C22semidirect
116. C22⋊Q8×C151D4semidirect
462. #24220C151direct (N × H)
463. C151#24220direct (N × H)
465. C2×#464C2×C151semidirect
466. C2×#460C2×C151semidirect
467. C2×#452C2×C151semidirect
468. C2×#450C2×C151semidirect
469. #2323C2×C151semidirect
470. #2042C2×C151semidirect
471. #2041C2×C151semidirect
472. #2015C2×C151semidirect
473. #2014C2×C151semidirect
474. #1983C2×C151semidirect
475. #1982C2×C151semidirect
476. #1798C2×C151semidirect
477. #1788C2×C151semidirect
478. #1786C2×C151semidirect
481. C22×Q16C22×C151semidirect
484. C22×SD16C22×C151semidirect
496. C2×C4×Q8C22×C151semidirect
502. C2×C4⋊C8C22×C151semidirect
503. C2×C4⋊C8C22×C151semidirect
504. C2×#103C22×C151semidirect
505. C2×#103C22×C151semidirect
506. C2×#103C22×C151semidirect
513. C2×#102C22×C151semidirect
514. C2×#102C22×C151semidirect
515. C2×#102C22×C151semidirect
518. #391C22×C151semidirect
520. #389C22×C151semidirect
525. C4×C4⋊C4C22×C151semidirect
526. #336C22×C151semidirect
527. #336C22×C151semidirect
579. C22⋊Q8D4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1512
C2×#464×C1512
C2×#460×C1512
C2×#452×C1512
C2×#450×C1512
#2323×C1512
#2042×C1512
#2041×C1512
#2015×C1512
#2014×C1512
#1983×C1512
#1982×C1512
#1798×C1512
#1788×C1512
#1786×C1512
#24220151