Finite Group Databasebeta

← C151×#24397 #50329322

Subgroups — C151×#24397 #50329322

Order 38656.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C151C211yesmaximal, characteristic, complemented
2C2×#469×C151C211yesmaximal, characteristic, complemented
3C2×#465×C151C211yesmaximal, characteristic, complemented
4C2×#449×C151C211yesmaximal, characteristic, complemented
5C2×#408×C151C211yesmaximal, characteristic, complemented
6#2615×C151C211yesmaximal, characteristic, complemented
7#2035×C151C211yesmaximal, characteristic, complemented
8#2034×C151C211yesmaximal, characteristic, complemented
9#2000×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1894×C151C211yesmaximal, characteristic, complemented
12#1893×C151C211yesmaximal, characteristic, complemented
13#1874×C151C211yesmaximal, characteristic, complemented
14#1853×C151C211yesmaximal, characteristic, complemented
15#1788×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C22×#41×C151C2211yescharacteristic
18C22×SD16×C151C2211yescharacteristic
19C22×D8×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×#121×C151—21no—
28C2×#121×C151—21no—
29C2×#121×C151—21no—
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic
32C2×#121×C151C2211yescharacteristic
33C2×#121×C151C2211yescharacteristic
34C2×#121×C151C2211yescharacteristic
35C22×C4⋊C4×C151C2211yescharacteristic
36#469×C151—24no—
37#465×C151—24no—
38#449×C151—24no—
39C2×#106×C151C2211yescharacteristic
40C2×#106×C151C2211yescharacteristic
41C2×#103×C151C2211yescharacteristic
42C2×#103×C151C2211yescharacteristic
43C2×#103×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×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#393×C151—21no—
55#392×C151—21no—
56#392×C151—21no—
57#392×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×D4×C151—21no—
80C22×D4×C151—21no—
81C22×D4×C151—21no—
82C22×D4×C151—21no—
83C22×D4×C151—21no—
84C22×D4×C151—21no—
85C22×D4×C151D411yescharacteristic
86C22×D4×C151D411yescharacteristic
87C22×D4×C151D411yescharacteristic
88C22×D4×C151C2311yescharacteristic
89C22×D4×C151C2311yescharacteristic
90C23×C4×C151—21no—
91C23×C4×C151—21no—
92C23×C4×C151C2311yescharacteristic
93C23×C4×C151C2311yescharacteristic
94C23×C4×C151C2311yescharacteristic
95C2×SD16×C151—22no—
96C2×SD16×C151—22no—
97C2×SD16×C151—41no—
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—41no—
101C2×M16×C151—22no—
102C2×M16×C151—22no—
103C2×M16×C151—41no—
104C22×C8×C151—22no—
105C22×C8×C151—22no—
106C22×C8×C151—41no—
107C22×C8×C151C2311yescharacteristic
108C22×C8×C151C2311yescharacteristic
109C22×C8×C151C2311yescharacteristic
110C22×C8×C151C2311yescharacteristic
111C22⋊Q8×C151—28no—
112C22⋊Q8×C151—22no—
113C22⋊Q8×C151—22no—
114C22⋊Q8×C151—22no—
115C22⋊Q8×C151D414yescomplemented
116#121×C151—28no—
117#121×C151—28no—
118#121×C151—28no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—22no—
124#121×C151—22no—
125#121×C151—22no—
126#121×C151—41no—
127#121×C151—41no—
128#121×C151D414yescomplemented
129C2×C4⋊C4×C151—21no—
130C2×C4⋊C4×C151—21no—
131C2×C4⋊C4×C151—21no—
132C2×C4⋊C4×C151—22no—
133C2×C4⋊C4×C151—22no—
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—41no—
154#102×C151—22no—
155#102×C151—22no—
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×C151—21no—
168C24×C151C2×D411yescharacteristic
169C24×C151C2×D411yescharacteristic
170C24×C151C2×D411yescharacteristic
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—
178#41×C151—44no—
179C2×Q8×C151—22no—
180C2×Q8×C151—22no—
181C2×Q8×C151—21no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—41no—
187C2×Q8×C151C2×D412yes—
188C2×D4×C151—24no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—22no—
192C2×D4×C151—22no—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—22no—
196C2×D4×C151—22no—
197C2×D4×C151—21no—
198C2×D4×C151—21no—
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—41no—
209C2×D4×C151—41no—
210C2×D4×C151—41no—
211C2×D4×C151—42no—
212C2×D4×C151—42no—
213C2×D4×C151—42no—
214C2×D4×C151—42no—
215C2×D4×C151—42no—
216C2×D4×C151—81no—
217C2×D4×C151—81no—
218C2×D4×C151—81no—
219C2×D4×C151—81no—
220C2×D4×C151—81no—
221C2×D4×C151—81no—
222C2×D4×C151—81no—
223C2×D4×C151—81no—
224C2×D4×C151—81no—
225C2×D4×C151—81no—
226C2×D4×C151C2×D412yes—
227C22×C4×C151—21no—
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—24no—
236C22×C4×C151—21no—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—24no—
240C22×C4×C151—21no—
241C22×C4×C151—21no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—21no—
247C22×C4×C151—21no—
248C22×C4×C151—21no—
249C22×C4×C151—42no—
250C22×C4×C151—42no—
251C22×C4×C151—81no—
252C22×C4×C151—81no—
253C22×C4×C151C2×D411yescharacteristic
254C22×C4×C151C2×D411yescharacteristic
255C22×C4×C151C2×D412yes—
256C22×C4×C151C2×D412yes—
257C22×C4×C151C2×D411yescharacteristic
258C22×C4×C151C2×D412yes—
259C22×C4×C151#4112yes—
260C22×C4×C151C2411yescharacteristic
261SD16×C151—44no—
262D8×C151—44no—
263M16×C151—44no—
264C2×C8×C151—21no—
265C2×C8×C151—21no—
266C2×C8×C151—21no—
267C2×C8×C151—21no—
268C2×C8×C151—21no—
269C2×C8×C151—21no—
270C2×C8×C151—21no—
271C2×C8×C151—21no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151—44no—
275C2×C8×C151C2×D412yes—
276C2×C8×C151C2×D412yes—
277C4⋊C4×C151—24no—
278C4⋊C4×C151—24no—
279C4⋊C4×C151—24no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—21no—
283C4⋊C4×C151—21no—
284C4⋊C4×C151—21no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—21no—
288C4⋊C4×C151C2×D412yes—
289C4⋊C4×C151C2×D412yes—
290C22⋊C4×C151—24no—
291C22⋊C4×C151—24no—
292C22⋊C4×C151—24no—
293C22⋊C4×C151—24no—
294C22⋊C4×C151—42no—
295C22⋊C4×C151—42no—
296C22⋊C4×C151—42no—
297C22⋊C4×C151—81no—
298C22⋊C4×C151—81no—
299C22⋊C4×C151—81no—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—22no—
313C23×C151—21no—
314C23×C151—21no—
315C23×C151—21no—
316C23×C151—21no—
317C23×C151—21no—
318C23×C151—21no—
319C23×C151—21no—
320C23×C151—41no—
321C23×C151—41no—
322C23×C151—41no—
323C23×C151—41no—
324C23×C151—41no—
325C23×C151—41no—
326C23×C151—41no—
327C23×C151—41no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—41no—
331C23×C151—41no—
332C23×C151—41no—
333C23×C151#12012yes—
334C23×C151#12112yes—
335C23×C151C22×D411yescharacteristic
336Q8×C151—22no—
337Q8×C151—22no—
338Q8×C151—44no—
339Q8×C151—41no—
340Q8×C151—41no—
341D4×C151—22no—
342D4×C151—22no—
343D4×C151—44no—
344D4×C151—44no—
345D4×C151—44no—
346D4×C151—48no—
347D4×C151—41no—
348D4×C151—41no—
349D4×C151—41no—
350D4×C151—41no—
351D4×C151—41no—
352D4×C151—41no—
353D4×C151—84no—
354D4×C151—84no—
355D4×C151—84no—
356D4×C151—84no—
357D4×C151—84no—
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—22no—
368C2×C4×C151—22no—
369C2×C4×C151—22no—
370C2×C4×C151—21no—
371C2×C4×C151—22no—
372C2×C4×C151—22no—
373C2×C4×C151—22no—
374C2×C4×C151—21no—
375C2×C4×C151—21no—
376C2×C4×C151—48no—
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—41no—
390C2×C4×C151—41no—
391C2×C4×C151—41no—
392C2×C4×C151—41no—
393C2×C4×C151—41no—
394C2×C4×C151—41no—
395C2×C4×C151—41no—
396C2×C4×C151—84no—
397C2×C4×C151#12012yes—
398C2×C4×C151#12112yes—
399C2×C4×C151C22×D411yescharacteristic
400C2×C4×C151C22×D411yescharacteristic
401C2×C4×C151C22×D411yescharacteristic
402C2×C4×C151C2×#4111yescharacteristic
403C2×C4×C151H(5,𝔽2)11yescharacteristic
404C2×C4×C151H(5,𝔽2)11yescharacteristic
405C8×C151—22no—
406C8×C151—22no—
407C8×C151—41no—
408C8×C151—41no—
409C22×C151—22no—
410C22×C151—22no—
411C22×C151—22no—
412C22×C151—22no—
413C22×C151—22no—
414C22×C151—22no—
415C22×C151—41no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—41no—
419C22×C151—41no—
420C22×C151—41no—
421C22×C151—41no—
422C22×C151—41no—
423C22×C151—42no—
424C22×C151—41no—
425C22×C151—41no—
426C22×C151—41no—
427C22×C151—41no—
428C22×C151—42no—
429C22×C151—41no—
430C22×C151—42no—
431C22×C151—41no—
432C22×C151—41no—
433C22×C151—81no—
434C22×C151—81no—
435C22×C151—81no—
436C22×C151—81no—
437C22×C151—81no—
438C22×C151—81no—
439C22×C151—81no—
440C22×C151—81no—
441C22×C151—81no—
442C22×C151—81no—
443C22×C151—81no—
444C22×C151C2×#12011yescharacteristic
445C22×C151C2×#12111yescharacteristic
446C22×C151#53411yescharacteristic
447C22×C151#57611yescharacteristic
448C22×C151#57711yescharacteristic
449C22×C151#57711yescharacteristic
450C22×C151#57711yescharacteristic
451C4×C151—22no—
452C4×C151—22no—
453C4×C151—41no—
454C4×C151—42no—
455C4×C151—42no—
456C4×C151—42no—
457C4×C151—81no—
458C4×C151—81no—
459C4×C151—81no—
460C4×C151D4211yescharacteristic
461C4×C151D4211yescharacteristic
462C4×C151#54611yescharacteristic
463C4×C151#54611yescharacteristic
464C2×C151—42no—
465C2×C151—42no—
466C2×C151—81no—
467C2×C151—82no—
468C2×C151—161no—
469C2×C151#241011yescharacteristic
470C2×C151#301011yescharacteristic
471C2×C151#301211yescharacteristic
472C2×C151#306011yescharacteristic
473C2×C151#306211yescharacteristic
474C2×C151#319811yescharacteristic
475C2×C151#320411yescharacteristic
476#24397C15111yesmaximal, characteristic, direct product factor, Sylow
477C151#2439711yescharacteristic, direct product factor, Sylow
478C2×#537C2×C15111yescharacteristic, complemented
479C2×#469C2×C15111yescharacteristic, complemented
480C2×#465C2×C15111yescharacteristic, complemented
481C2×#449C2×C15111yescharacteristic, complemented
482C2×#408C2×C15111yescharacteristic, complemented
483#2615C2×C15111yescharacteristic, complemented
484#2035C2×C15111yescharacteristic, complemented
485#2034C2×C15111yescharacteristic, complemented
486#2000C2×C15111yescharacteristic, complemented
487#1999C2×C15111yescharacteristic, complemented
488#1894C2×C15111yescharacteristic, complemented
489#1893C2×C15111yescharacteristic, complemented
490#1874C2×C15111yescharacteristic, complemented
491#1853C2×C15111yescharacteristic, complemented
492#1788C2×C15111yescharacteristic, complemented
493C22×#41C22×C15111yescharacteristic
494C22×#41C22×C15111yescharacteristic
495C22×SD16C22×C15111yescharacteristic
496C22×D8C22×C15111yescharacteristic
497C22×M16C22×C15111yescharacteristic
498C23×C8C22×C15111yescharacteristic
499#537—24no—
500#537—24no—
501C2×C22⋊Q8—21no—
502C2×C22⋊Q8C22×C15111yescharacteristic
503C2×C22⋊Q8C22×C15111yescharacteristic
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—21no—
507C2×#121C22×C15111yescharacteristic
508C2×#121C22×C15111yescharacteristic
509C2×#121C22×C15111yescharacteristic
510C2×#121C22×C15111yescharacteristic
511C2×#121C22×C15111yescharacteristic
512C22×C4⋊C4C22×C15111yescharacteristic
513#469—24no—
514#465—24no—
515#449—24no—
516C2×#106C22×C15111yescharacteristic
517C2×#106C22×C15111yescharacteristic
518C2×#103C22×C15111yescharacteristic
519C2×#103C22×C15111yescharacteristic
520C2×#103C22×C15111yescharacteristic
521C2×#102C22×C15111yescharacteristic
522C2×#102C22×C15111yescharacteristic
523C2×#102C22×C15111yescharacteristic
524C2×#102C22×C15111yescharacteristic
525C2×#102C22×C15111yescharacteristic
526#408—24no—
527C2×C22⋊C8C22×C15111yescharacteristic
528C2×C22⋊C8C22×C15111yescharacteristic
529C2×C22⋊C8C22×C15111yescharacteristic
530C2×C22⋊C8C22×C15111yescharacteristic
531#393—21no—
532#392—21no—
533#392—21no—
534#392—21no—
535#380C22×C15111yescharacteristic
536#380C22×C15111yescharacteristic
537#380C22×C15111yescharacteristic
538#340C22×C15111yescharacteristic
539#340C22×C15111yescharacteristic
540#340C22×C15111yescharacteristic
541#340C22×C15111yescharacteristic
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C15111yescharacteristic
555C22×Q8C23×C15111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C15111yescharacteristic
563C22×D4D4×C15111yescharacteristic
564C22×D4D4×C15111yescharacteristic
565C22×D4C23×C15111yescharacteristic
566C22×D4C23×C15111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C15111yescharacteristic
570C23×C4C23×C15111yescharacteristic
571C23×C4C23×C15111yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C15111yescharacteristic
585C22×C8C23×C15111yescharacteristic
586C22×C8C23×C15111yescharacteristic
587C22×C8C23×C15111yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C15114yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C15114yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C15111yescharacteristic
612C2×C4⋊C4C23×C15111yescharacteristic
613C2×C4⋊C4C23×C15111yescharacteristic
614C2×C4⋊C4C23×C15111yescharacteristic
615C2×C4⋊C4C23×C15111yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C15114yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C15111yescharacteristic
646C24C2×D4×C15111yescharacteristic
647C24C2×D4×C15111yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C15112yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C15112yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C15111yescharacteristic
731C22×C4C2×D4×C15111yescharacteristic
732C22×C4C2×D4×C15112yes—
733C22×C4C2×D4×C15112yes—
734C22×C4C2×D4×C15111yescharacteristic
735C22×C4C2×D4×C15112yes—
736C22×C4#41×C15112yes—
737C22×C4C24×C15111yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C15112yes—
753C2×C8C2×D4×C15112yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C15112yes—
766C4⋊C4C2×D4×C15112yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23#120×C15112yes—
811C23#121×C15112yes—
812C23C22×D4×C15111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4#120×C15112yes—
875C2×C4#121×C15112yes—
876C2×C4C22×D4×C15111yescharacteristic
877C2×C4C22×D4×C15111yescharacteristic
878C2×C4C22×D4×C15111yescharacteristic
879C2×C4C2×#41×C15111yescharacteristic
880C2×C4H(5,𝔽2)×C15111yescharacteristic
881C2×C4H(5,𝔽2)×C15111yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C15111yescharacteristic
922C22C2×#121×C15111yescharacteristic
923C22#534×C15111yescharacteristic
924C22#576×C15111yescharacteristic
925C22#577×C15111yescharacteristic
926C22#577×C15111yescharacteristic
927C22#577×C15111yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C15111yescharacteristic
938C4D42×C15111yescharacteristic
939C4#546×C15111yescharacteristic
940C4#546×C15111yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2#2410×C15111yescharacteristic
947C2#3010×C15111yescharacteristic
948C2#3012×C15111yescharacteristic
949C2#3060×C15111yescharacteristic
950C2#3062×C15111yescharacteristic
951C2#3198×C15111yescharacteristic
952C2#3204×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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
1. C2×#537×C151C2semidirect
2. C2×#469×C151C2semidirect
3. C2×#465×C151C2semidirect
4. C2×#449×C151C2semidirect
5. C2×#408×C151C2semidirect
6. #2615×C151C2semidirect
7. #2035×C151C2semidirect
8. #2034×C151C2semidirect
9. #2000×C151C2semidirect
10. #1999×C151C2semidirect
11. #1894×C151C2semidirect
12. #1893×C151C2semidirect
13. #1874×C151C2semidirect
14. #1853×C151C2semidirect
15. #1788×C151C2semidirect
115. C22⋊Q8×C151D4semidirect
128. #121×C151D4semidirect
162. C22⋊C8×C151D4semidirect
476. #24397C151direct (N × H)
477. C151#24397direct (N × H)
478. C2×#537C2×C151semidirect
479. C2×#469C2×C151semidirect
480. C2×#465C2×C151semidirect
481. C2×#449C2×C151semidirect
482. C2×#408C2×C151semidirect
483. #2615C2×C151semidirect
484. #2035C2×C151semidirect
485. #2034C2×C151semidirect
486. #2000C2×C151semidirect
487. #1999C2×C151semidirect
488. #1894C2×C151semidirect
489. #1893C2×C151semidirect
490. #1874C2×C151semidirect
491. #1853C2×C151semidirect
492. #1788C2×C151semidirect
592. C22⋊Q8D4×C151semidirect
605. #121D4×C151semidirect
639. 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×#469×C1512
C2×#465×C1512
C2×#449×C1512
C2×#408×C1512
#2615×C1512
#2035×C1512
#2034×C1512
#2000×C1512
#1999×C1512
#1894×C1512
#1893×C1512
#1874×C1512
#1853×C1512
#1788×C1512
#24397151