Finite Group Databasebeta

← C151×#24390 #50329315

Subgroups — C151×#24390 #50329315

Order 38656.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C151C211yesmaximal, characteristic, complemented
2C2×#469×C151C211yesmaximal, characteristic, complemented
3C2×#466×C151C211yesmaximal, characteristic, complemented
4C2×#447×C151C211yesmaximal, characteristic, complemented
5C2×#408×C151C211yesmaximal, characteristic, complemented
6#2615×C151C211yesmaximal, characteristic, complemented
7#2034×C151C211yesmaximal, characteristic, complemented
8#2033×C151C211yesmaximal, characteristic, complemented
9#1999×C151C211yesmaximal, characteristic, complemented
10#1999×C151C211yesmaximal, characteristic, complemented
11#1895×C151C211yesmaximal, characteristic, complemented
12#1893×C151C211yesmaximal, characteristic, complemented
13#1875×C151C211yesmaximal, characteristic, complemented
14#1854×C151C211yesmaximal, characteristic, complemented
15#1786×C151C211yesmaximal, characteristic, complemented
16C22×#41×C151C2211yescharacteristic
17C23×D4×C151C2211yescharacteristic
18C22×D8×C151C2211yescharacteristic
19C22×D8×C151C2211yescharacteristic
20C22×M16×C151C2211yescharacteristic, complemented
21C23×C8×C151C2211yescharacteristic, complemented
22#535×C151—24no—
23#535×C151—24no—
24C2×#127×C151—21no—
25C2×#124×C151—21no—
26C2×#121×C151C2211yescharacteristic
27C2×#121×C151C2211yescharacteristic
28C2×#121×C151C2211yescharacteristic
29C2×#121×C151C2211yescharacteristic
30C2×#121×C151C2211yescharacteristic
31C2×#121×C151C2211yescharacteristic, complemented
32C2×#121×C151C2211yescharacteristic, complemented
33C2×#120×C151—21no—
34C2×#120×C151—21no—
35C2×#117×C151C2211yescharacteristic
36#469×C151—24no—
37#466×C151—24no—
38#447×C151—24no—
39C2×#107×C151C2211yescharacteristic, complemented
40C2×#106×C151C2211yescharacteristic, complemented
41C2×#102×C151C2211yescharacteristic
42C2×#102×C151C2211yescharacteristic
43C2×#102×C151C2211yescharacteristic
44C2×#102×C151C2211yescharacteristic
45C2×#102×C151C2211yescharacteristic
46C2×#102×C151C2211yescharacteristic
47C2×#102×C151C2211yescharacteristic, complemented
48C2×#102×C151C2211yescharacteristic, complemented
49#408×C151—24no—
50C2×C22⋊C8×C151C2211yescharacteristic
51C2×C22⋊C8×C151C2211yescharacteristic
52C2×C22⋊C8×C151C2211yescharacteristic, complemented
53C2×C22⋊C8×C151C2211yescharacteristic, complemented
54#393×C151—21no—
55#392×C151—21no—
56#392×C151—21no—
57#392×C151—21no—
58#380×C151C2211yescharacteristic
59#380×C151C2211yescharacteristic, complemented
60#380×C151C2211yescharacteristic, complemented
61#340×C151C2211yescharacteristic, complemented
62#340×C151C2211yescharacteristic, complemented
63#340×C151C2211yescharacteristic, complemented
64#340×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×C151D411yescharacteristic
73C22×D4×C151—22no—
74C22×D4×C151—22no—
75C22×D4×C151—21no—
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—21no—
83C22×D4×C151—22no—
84C22×D4×C151—22no—
85C22×D4×C151—41no—
86C22×D4×C151—41no—
87C22×D4×C151D411yescharacteristic
88C22×D4×C151D411yescharacteristic
89C22×D4×C151D411yescharacteristic
90C22×D4×C151C2311yescharacteristic
91C22×D4×C151C2311yescharacteristic
92C22×D4×C151C2311yescharacteristic
93C23×C4×C151C2311yescharacteristic
94C23×C4×C151C2311yescharacteristic
95C23×C4×C151C2311yescharacteristic
96C2×D8×C151—22no—
97C2×D8×C151—22no—
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—41no—
101C2×D8×C151—41no—
102C2×M16×C151—22no—
103C2×M16×C151—22no—
104C2×M16×C151—41no—
105C22×C8×C151—22no—
106C22×C8×C151—22no—
107C22×C8×C151—41no—
108C22×C8×C151C2311yescharacteristic
109C22×C8×C151C2311yescharacteristic
110C22×C8×C151C2311yescharacteristic
111C22×C8×C151C2311yescharacteristic
112#127×C151—28no—
113#124×C151—28no—
114#121×C151—22no—
115#121×C151—22no—
116#121×C151—22no—
117#121×C151—22no—
118#121×C151—22no—
119#121×C151—22no—
120#121×C151—22no—
121#121×C151—22no—
122#121×C151—22no—
123#121×C151—22no—
124#121×C151—41no—
125#121×C151—41no—
126#121×C151D414yescomplemented
127#121×C151D414yescomplemented
128#120×C151—28no—
129#120×C151—28no—
130#117×C151—22no—
131#117×C151—22no—
132C2×C4⋊C4×C151C2311yescharacteristic
133C2×C4⋊C4×C151C2311yescharacteristic
134C2×C4⋊C4×C151C2311yescharacteristic
135C2×C4⋊C4×C151C2311yescharacteristic
136C2×C4⋊C4×C151C2311yescharacteristic
137C2×C22⋊C4×C151—21no—
138C2×C22⋊C4×C151—21no—
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×C42×C151—21no—
149#107×C151—22no—
150#106×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—22no—
157#102×C151—41no—
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—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
177C24×C151C2×D411yescharacteristic
178C24×C151C2×D411yescharacteristic
179#41×C151—44no—
180#41×C151—44no—
181#41×C151—44no—
182#41×C151—44no—
183C2×Q8×C151—22no—
184C2×Q8×C151—22no—
185C2×Q8×C151—41no—
186C2×D4×C151—24no—
187C2×D4×C151—22no—
188C2×D4×C151—22no—
189C2×D4×C151—22no—
190C2×D4×C151—22no—
191C2×D4×C151—24no—
192C2×D4×C151—24no—
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—21no—
209C2×D4×C151—21no—
210C2×D4×C151—21no—
211C2×D4×C151—21no—
212C2×D4×C151—21no—
213C2×D4×C151—44no—
214C2×D4×C151—44no—
215C2×D4×C151—44no—
216C2×D4×C151—44no—
217C2×D4×C151—41no—
218C2×D4×C151—41no—
219C2×D4×C151—41no—
220C2×D4×C151—42no—
221C2×D4×C151—42no—
222C2×D4×C151—42no—
223C2×D4×C151—42no—
224C2×D4×C151—42no—
225C2×D4×C151—81no—
226C2×D4×C151—81no—
227C2×D4×C151—81no—
228C2×D4×C151—81no—
229C2×D4×C151—81no—
230C2×D4×C151—81no—
231C2×D4×C151—81no—
232C2×D4×C151—81no—
233C2×D4×C151—81no—
234C2×D4×C151—81no—
235C2×D4×C151—81no—
236C2×D4×C151—81no—
237C2×D4×C151—81no—
238C2×D4×C151—81no—
239C2×D4×C151C2×D412yes—
240C2×D4×C151C2×D412yes—
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—21no—
250C22×C4×C151—21no—
251C22×C4×C151—21no—
252C22×C4×C151—21no—
253C22×C4×C151—21no—
254C22×C4×C151—21no—
255C22×C4×C151—21no—
256C22×C4×C151—21no—
257C22×C4×C151—21no—
258C22×C4×C151—21no—
259C22×C4×C151—21no—
260C22×C4×C151C2×D411yescharacteristic
261C22×C4×C151C2×D411yescharacteristic
262C22×C4×C151C2×D412yes—
263C22×C4×C151C2×D412yes—
264C22×C4×C151C2×D411yescharacteristic
265C22×C4×C151C2×D412yes—
266C22×C4×C151#4112yes—
267C22×C4×C151C2411yescharacteristic
268D8×C151—44no—
269D8×C151—44no—
270M16×C151—44no—
271C2×C8×C151—21no—
272C2×C8×C151—21no—
273C2×C8×C151—21no—
274C2×C8×C151—21no—
275C2×C8×C151—21no—
276C2×C8×C151—21no—
277C2×C8×C151—21no—
278C2×C8×C151—21no—
279C2×C8×C151—21no—
280C2×C8×C151—21no—
281C2×C8×C151—44no—
282C2×C8×C151C2×D412yes—
283C2×C8×C151C2×D412yes—
284C4⋊C4×C151—21no—
285C4⋊C4×C151—21no—
286C4⋊C4×C151—21no—
287C4⋊C4×C151—21no—
288C4⋊C4×C151—21no—
289C4⋊C4×C151—21no—
290C4⋊C4×C151—21no—
291C4⋊C4×C151—21no—
292C4⋊C4×C151C2×D412yes—
293C4⋊C4×C151C2×D412yes—
294C22⋊C4×C151—24no—
295C22⋊C4×C151—24no—
296C22⋊C4×C151—24no—
297C22⋊C4×C151—24no—
298C22⋊C4×C151—24no—
299C22⋊C4×C151—42no—
300C22⋊C4×C151—42no—
301C22⋊C4×C151—42no—
302C22⋊C4×C151—81no—
303C22⋊C4×C151—81no—
304C22⋊C4×C151—81no—
305C42×C151—24no—
306C23×C151—21no—
307C23×C151—21no—
308C23×C151—21no—
309C23×C151—21no—
310C23×C151—21no—
311C23×C151—21no—
312C23×C151—21no—
313C23×C151—21no—
314C23×C151—21no—
315C23×C151—21no—
316C23×C151—21no—
317C23×C151—21no—
318C23×C151—22no—
319C23×C151—22no—
320C23×C151—21no—
321C23×C151—21no—
322C23×C151—21no—
323C23×C151—21no—
324C23×C151—21no—
325C23×C151—21no—
326C23×C151—21no—
327C23×C151—48no—
328C23×C151—41no—
329C23×C151—41no—
330C23×C151—41no—
331C23×C151—41no—
332C23×C151—41no—
333C23×C151—41no—
334C23×C151—41no—
335C23×C151—41no—
336C23×C151—41no—
337C23×C151—41no—
338C23×C151—41no—
339C23×C151—41no—
340C23×C151—41no—
341C23×C151—41no—
342C23×C151—41no—
343C23×C151—41no—
344C23×C151—41no—
345C23×C151—41no—
346C23×C151—41no—
347C23×C151—84no—
348C23×C151—84no—
349C23×C151—84no—
350C23×C151—84no—
351C23×C151—84no—
352C23×C151—84no—
353C23×C151#12012yes—
354C23×C151#12112yes—
355C23×C151C22×D411yescharacteristic
356Q8×C151—44no—
357D4×C151—22no—
358D4×C151—22no—
359D4×C151—22no—
360D4×C151—22no—
361D4×C151—44no—
362D4×C151—44no—
363D4×C151—48no—
364D4×C151—44no—
365D4×C151—41no—
366D4×C151—41no—
367D4×C151—41no—
368D4×C151—41no—
369D4×C151—41no—
370D4×C151—41no—
371D4×C151—41no—
372D4×C151—41no—
373D4×C151—84no—
374D4×C151—84no—
375D4×C151—84no—
376D4×C151—84no—
377D4×C151—84no—
378D4×C151—84no—
379D4×C151—84no—
380C2×C4×C151—21no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—21no—
384C2×C4×C151—22no—
385C2×C4×C151—22no—
386C2×C4×C151—22no—
387C2×C4×C151—22no—
388C2×C4×C151—22no—
389C2×C4×C151—22no—
390C2×C4×C151—22no—
391C2×C4×C151—22no—
392C2×C4×C151—21no—
393C2×C4×C151—22no—
394C2×C4×C151—22no—
395C2×C4×C151—21no—
396C2×C4×C151—21no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—41no—
400C2×C4×C151—41no—
401C2×C4×C151—41no—
402C2×C4×C151—41no—
403C2×C4×C151—41no—
404C2×C4×C151—41no—
405C2×C4×C151—41no—
406C2×C4×C151—41no—
407C2×C4×C151—41no—
408C2×C4×C151—41no—
409C2×C4×C151—41no—
410C2×C4×C151—41no—
411C2×C4×C151—41no—
412C2×C4×C151—41no—
413C2×C4×C151—41no—
414C2×C4×C151#12012yes—
415C2×C4×C151#12112yes—
416C2×C4×C151C22×D411yescharacteristic
417C2×C4×C151C22×D411yescharacteristic
418C2×C4×C151C22×D411yescharacteristic
419C2×C4×C151C2×#4111yescharacteristic
420C2×C4×C151H(5,𝔽2)11yescharacteristic
421C2×C4×C151H(5,𝔽2)11yescharacteristic
422C8×C151—22no—
423C8×C151—22no—
424C8×C151—41no—
425C8×C151—41no—
426C22×C151—22no—
427C22×C151—22no—
428C22×C151—22no—
429C22×C151—22no—
430C22×C151—22no—
431C22×C151—22no—
432C22×C151—41no—
433C22×C151—41no—
434C22×C151—41no—
435C22×C151—41no—
436C22×C151—41no—
437C22×C151—41no—
438C22×C151—41no—
439C22×C151—41no—
440C22×C151—41no—
441C22×C151—42no—
442C22×C151—42no—
443C22×C151—41no—
444C22×C151—41no—
445C22×C151—41no—
446C22×C151—42no—
447C22×C151—42no—
448C22×C151—41no—
449C22×C151—42no—
450C22×C151—42no—
451C22×C151—41no—
452C22×C151—41no—
453C22×C151—816no—
454C22×C151—81no—
455C22×C151—81no—
456C22×C151—81no—
457C22×C151—81no—
458C22×C151—81no—
459C22×C151—81no—
460C22×C151—81no—
461C22×C151—81no—
462C22×C151—81no—
463C22×C151—81no—
464C22×C151—81no—
465C22×C151—81no—
466C22×C151—81no—
467C22×C151—81no—
468C22×C151—81no—
469C22×C151C2×#12011yescharacteristic
470C22×C151C2×#12111yescharacteristic
471C22×C151#53411yescharacteristic
472C22×C151#57611yescharacteristic
473C22×C151#57611yescharacteristic
474C22×C151#57611yescharacteristic
475C22×C151#57711yescharacteristic
476C4×C151—22no—
477C4×C151—22no—
478C4×C151—41no—
479C4×C151—42no—
480C4×C151—42no—
481C4×C151—81no—
482C4×C151—81no—
483C4×C151—81no—
484C4×C151D4211yescharacteristic
485C4×C151D4211yescharacteristic
486C4×C151#54611yescharacteristic
487C4×C151#54611yescharacteristic
488C2×C151—42no—
489C2×C151—42no—
490C2×C151—81no—
491C2×C151—82no—
492C2×C151—82no—
493C2×C151—161no—
494C2×C151#241011yescharacteristic
495C2×C151#300811yescharacteristic
496C2×C151#301211yescharacteristic
497C2×C151#305811yescharacteristic
498C2×C151#306211yescharacteristic
499C2×C151#319811yescharacteristic
500C2×C151#319911yescharacteristic
501#24390C15111yesmaximal, characteristic, direct product factor, Sylow
502C151#2439011yescharacteristic, direct product factor, Sylow
503C2×#535C2×C15111yescharacteristic, complemented
504C2×#469C2×C15111yescharacteristic, complemented
505C2×#466C2×C15111yescharacteristic, complemented
506C2×#447C2×C15111yescharacteristic, complemented
507C2×#408C2×C15111yescharacteristic, complemented
508#2615C2×C15111yescharacteristic, complemented
509#2034C2×C15111yescharacteristic, complemented
510#2033C2×C15111yescharacteristic, complemented
511#1999C2×C15111yescharacteristic, complemented
512#1999C2×C15111yescharacteristic, complemented
513#1895C2×C15111yescharacteristic, complemented
514#1893C2×C15111yescharacteristic, complemented
515#1875C2×C15111yescharacteristic, complemented
516#1854C2×C15111yescharacteristic, complemented
517#1786C2×C15111yescharacteristic, complemented
518C22×#41C22×C15111yescharacteristic
519C23×D4C22×C15111yescharacteristic
520C22×D8C22×C15111yescharacteristic
521C22×D8C22×C15111yescharacteristic
522C22×M16C22×C15111yescharacteristic, complemented
523C23×C8C22×C15111yescharacteristic, complemented
524#535—24no—
525#535—24no—
526C2×#127—21no—
527C2×#124—21no—
528C2×#121C22×C15111yescharacteristic
529C2×#121C22×C15111yescharacteristic
530C2×#121C22×C15111yescharacteristic
531C2×#121C22×C15111yescharacteristic
532C2×#121C22×C15111yescharacteristic
533C2×#121C22×C15111yescharacteristic, complemented
534C2×#121C22×C15111yescharacteristic, complemented
535C2×#120—21no—
536C2×#120—21no—
537C2×#117C22×C15111yescharacteristic
538#469—24no—
539#466—24no—
540#447—24no—
541C2×#107C22×C15111yescharacteristic, complemented
542C2×#106C22×C15111yescharacteristic, complemented
543C2×#102C22×C15111yescharacteristic
544C2×#102C22×C15111yescharacteristic
545C2×#102C22×C15111yescharacteristic
546C2×#102C22×C15111yescharacteristic
547C2×#102C22×C15111yescharacteristic
548C2×#102C22×C15111yescharacteristic
549C2×#102C22×C15111yescharacteristic, complemented
550C2×#102C22×C15111yescharacteristic, complemented
551#408—24no—
552C2×C22⋊C8C22×C15111yescharacteristic
553C2×C22⋊C8C22×C15111yescharacteristic
554C2×C22⋊C8C22×C15111yescharacteristic, complemented
555C2×C22⋊C8C22×C15111yescharacteristic, complemented
556#393—21no—
557#392—21no—
558#392—21no—
559#392—21no—
560#380C22×C15111yescharacteristic
561#380C22×C15111yescharacteristic, complemented
562#380C22×C15111yescharacteristic, complemented
563#340C22×C15111yescharacteristic, complemented
564#340C22×C15111yescharacteristic, complemented
565#340C22×C15111yescharacteristic, complemented
566#340C22×C15111yescharacteristic, complemented
567C25—21no—
568C2×#41—22no—
569C2×#41—22no—
570C2×#41—22no—
571C2×#41—22no—
572C2×#41—41no—
573C2×#41—41no—
574C22×Q8D4×C15111yescharacteristic
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—21no—
579C22×D4—22no—
580C22×D4—22no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—22no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—41no—
588C22×D4—41no—
589C22×D4D4×C15111yescharacteristic
590C22×D4D4×C15111yescharacteristic
591C22×D4D4×C15111yescharacteristic
592C22×D4C23×C15111yescharacteristic
593C22×D4C23×C15111yescharacteristic
594C22×D4C23×C15111yescharacteristic
595C23×C4C23×C15111yescharacteristic
596C23×C4C23×C15111yescharacteristic
597C23×C4C23×C15111yescharacteristic
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×M16—22no—
605C2×M16—22no—
606C2×M16—41no—
607C22×C8—22no—
608C22×C8—22no—
609C22×C8—41no—
610C22×C8C23×C15111yescharacteristic
611C22×C8C23×C15111yescharacteristic
612C22×C8C23×C15111yescharacteristic
613C22×C8C23×C15111yescharacteristic
614#127—28no—
615#124—28no—
616#121—22no—
617#121—22no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—41no—
627#121—41no—
628#121D4×C15114yescomplemented
629#121D4×C15114yescomplemented
630#120—28no—
631#120—28no—
632#117—22no—
633#117—22no—
634C2×C4⋊C4C23×C15111yescharacteristic
635C2×C4⋊C4C23×C15111yescharacteristic
636C2×C4⋊C4C23×C15111yescharacteristic
637C2×C4⋊C4C23×C15111yescharacteristic
638C2×C4⋊C4C23×C15111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C42—21no—
651#107—22no—
652#106—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—41no—
660#102—41no—
661C22⋊C8—22no—
662C22⋊C8—22no—
663C22⋊C8—22no—
664C22⋊C8D4×C15114yescomplemented
665#95—21no—
666#95—21no—
667#95—21no—
668C24—24no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—42no—
673C24—42no—
674C24—81no—
675C24—81no—
676C24—81no—
677C24—81no—
678C24C2×D4×C15111yescharacteristic
679C24C2×D4×C15111yescharacteristic
680C24C2×D4×C15111yescharacteristic
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685C2×Q8—22no—
686C2×Q8—22no—
687C2×Q8—41no—
688C2×D4—24no—
689C2×D4—22no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—22no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—42no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4—81no—
734C2×D4—81no—
735C2×D4—81no—
736C2×D4—81no—
737C2×D4—81no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4C2×D4×C15112yes—
742C2×D4C2×D4×C15112yes—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4C2×D4×C15111yescharacteristic
763C22×C4C2×D4×C15111yescharacteristic
764C22×C4C2×D4×C15112yes—
765C22×C4C2×D4×C15112yes—
766C22×C4C2×D4×C15111yescharacteristic
767C22×C4C2×D4×C15112yes—
768C22×C4#41×C15112yes—
769C22×C4C24×C15111yescharacteristic
770D8—44no—
771D8—44no—
772M16—44no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—21no—
782C2×C8—21no—
783C2×C8—44no—
784C2×C8C2×D4×C15112yes—
785C2×C8C2×D4×C15112yes—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4C2×D4×C15112yes—
795C4⋊C4C2×D4×C15112yes—
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—24no—
799C22⋊C4—24no—
800C22⋊C4—24no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—42no—
804C22⋊C4—81no—
805C22⋊C4—81no—
806C22⋊C4—81no—
807C42—24no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—22no—
821C23—22no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—48no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—84no—
850C23—84no—
851C23—84no—
852C23—84no—
853C23—84no—
854C23—84no—
855C23#120×C15112yes—
856C23#121×C15112yes—
857C23C22×D4×C15111yescharacteristic
858Q8—44no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—44no—
864D4—44no—
865D4—48no—
866D4—44no—
867D4—41no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—84no—
876D4—84no—
877D4—84no—
878D4—84no—
879D4—84no—
880D4—84no—
881D4—84no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—21no—
885C2×C4—21no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4#120×C15112yes—
917C2×C4#121×C15112yes—
918C2×C4C22×D4×C15111yescharacteristic
919C2×C4C22×D4×C15111yescharacteristic
920C2×C4C22×D4×C15111yescharacteristic
921C2×C4C2×#41×C15111yescharacteristic
922C2×C4H(5,𝔽2)×C15111yescharacteristic
923C2×C4H(5,𝔽2)×C15111yescharacteristic
924C8—22no—
925C8—22no—
926C8—41no—
927C8—41no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—41no—
935C22—41no—
936C22—41no—
937C22—41no—
938C22—41no—
939C22—41no—
940C22—41no—
941C22—41no—
942C22—41no—
943C22—42no—
944C22—42no—
945C22—41no—
946C22—41no—
947C22—41no—
948C22—42no—
949C22—42no—
950C22—41no—
951C22—42no—
952C22—42no—
953C22—41no—
954C22—41no—
955C22—816no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22—81no—
963C22—81no—
964C22—81no—
965C22—81no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22C2×#120×C15111yescharacteristic
972C22C2×#121×C15111yescharacteristic
973C22#534×C15111yescharacteristic
974C22#576×C15111yescharacteristic
975C22#576×C15111yescharacteristic
976C22#576×C15111yescharacteristic
977C22#577×C15111yescharacteristic
978C4—22no—
979C4—22no—
980C4—41no—
981C4—42no—
982C4—42no—
983C4—81no—
984C4—81no—
985C4—81no—
986C4D42×C15111yescharacteristic
987C4D42×C15111yescharacteristic
988C4#546×C15111yescharacteristic
989C4#546×C15111yescharacteristic
990C2—42no—
991C2—42no—
992C2—81no—
993C2—82no—
994C2—82no—
995C2—161no—
996C2#2410×C15111yescharacteristic
997C2#3008×C15111yescharacteristic
998C2#3012×C15111yescharacteristic
999C2#3058×C15111yescharacteristic
1000C2#3062×C15111yescharacteristic
1001C2#3198×C15111yescharacteristic
1002C2#3199×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×#535×C151C2semidirect
2. C2×#469×C151C2semidirect
3. C2×#466×C151C2semidirect
4. C2×#447×C151C2semidirect
5. C2×#408×C151C2semidirect
6. #2615×C151C2semidirect
7. #2034×C151C2semidirect
8. #2033×C151C2semidirect
9. #1999×C151C2semidirect
10. #1999×C151C2semidirect
11. #1895×C151C2semidirect
12. #1893×C151C2semidirect
13. #1875×C151C2semidirect
14. #1854×C151C2semidirect
15. #1786×C151C2semidirect
20. C22×M16×C151C22semidirect
21. C23×C8×C151C22semidirect
31. C2×#121×C151C22semidirect
32. C2×#121×C151C22semidirect
39. C2×#107×C151C22semidirect
40. C2×#106×C151C22semidirect
47. C2×#102×C151C22semidirect
48. C2×#102×C151C22semidirect
52. C2×C22⋊C8×C151C22semidirect
53. C2×C22⋊C8×C151C22semidirect
59. #380×C151C22semidirect
60. #380×C151C22semidirect
61. #340×C151C22semidirect
62. #340×C151C22semidirect
63. #340×C151C22semidirect
64. #340×C151C22semidirect
126. #121×C151D4semidirect
127. #121×C151D4semidirect
162. C22⋊C8×C151D4semidirect
501. #24390C151direct (N × H)
502. C151#24390direct (N × H)
503. C2×#535C2×C151semidirect
504. C2×#469C2×C151semidirect
505. C2×#466C2×C151semidirect
506. C2×#447C2×C151semidirect
507. C2×#408C2×C151semidirect
508. #2615C2×C151semidirect
509. #2034C2×C151semidirect
510. #2033C2×C151semidirect
511. #1999C2×C151semidirect
512. #1999C2×C151semidirect
513. #1895C2×C151semidirect
514. #1893C2×C151semidirect
515. #1875C2×C151semidirect
516. #1854C2×C151semidirect
517. #1786C2×C151semidirect
522. C22×M16C22×C151semidirect
523. C23×C8C22×C151semidirect
533. C2×#121C22×C151semidirect
534. C2×#121C22×C151semidirect
541. C2×#107C22×C151semidirect
542. C2×#106C22×C151semidirect
549. C2×#102C22×C151semidirect
550. C2×#102C22×C151semidirect
554. C2×C22⋊C8C22×C151semidirect
555. C2×C22⋊C8C22×C151semidirect
561. #380C22×C151semidirect
562. #380C22×C151semidirect
563. #340C22×C151semidirect
564. #340C22×C151semidirect
565. #340C22×C151semidirect
566. #340C22×C151semidirect
628. #121D4×C151semidirect
629. #121D4×C151semidirect
664. C22⋊C8D4×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×#469×C1512
C2×#466×C1512
C2×#447×C1512
C2×#408×C1512
#2615×C1512
#2034×C1512
#2033×C1512
#1999×C1512
#1895×C1512
#1893×C1512
#1875×C1512
#1854×C1512
#1786×C1512
#24390151