Finite Group Databasebeta

← C151×#24218 #50329143

Subgroups — C151×#24218 #50329143

Order 38656.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C151C211yesmaximal, characteristic, complemented
2C2×#463×C151C211yesmaximal, characteristic, complemented
3C2×#459×C151C211yesmaximal, characteristic, complemented
4C2×#449×C151C211yesmaximal, characteristic, complemented
5C2×#447×C151C211yesmaximal, characteristic, complemented
6#2324×C151C211yesmaximal, characteristic, complemented
7#2042×C151C211yesmaximal, characteristic, complemented
8#2041×C151C211yesmaximal, characteristic, complemented
9#2012×C151C211yesmaximal, characteristic, complemented
10#2011×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×SD16×C151C2211yescharacteristic, complemented
19C22×D8×C151C2211yescharacteristic
20C22×D8×C151C2211yescharacteristic
21C22×D8×C151C2211yescharacteristic, complemented
22#535×C151—24no—
23#535×C151—24no—
24C2×#127×C151C2211yescharacteristic
25C2×#127×C151C2211yescharacteristic
26C2×#124×C151C2211yescharacteristic
27C2×#124×C151C2211yescharacteristic
28C2×#121×C151—21no—
29C2×#121×C151—21no—
30C2×#121×C151C2211yescharacteristic
31C2×#120×C151—21no—
32C2×#120×C151—21no—
33C2×C4×D4×C151C2211yescharacteristic, complemented
34C2×#117×C151C2211yescharacteristic
35#463×C151—24no—
36#459×C151—24no—
37#449×C151—24no—
38#447×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#390×C151—21no—
56#390×C151C2211yescharacteristic, complemented
57#389×C151C2211yescharacteristic, complemented
58#388×C151—21no—
59#386×C151—21no—
60#385×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×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—22no—
83C22×D4×C151—22no—
84C22×D4×C151—41no—
85C22×D4×C151—41no—
86C22×D4×C151C2311yescharacteristic
87C22×D4×C151C2311yescharacteristic
88C22×D4×C151C2311yescharacteristic
89C22×D4×C151C2311yescharacteristic
90C23×C4×C151—21no—
91C23×C4×C151—21no—
92C23×C4×C151C2311yescharacteristic
93C2×SD16×C151—22no—
94C2×SD16×C151—22no—
95C2×SD16×C151—41no—
96C2×D8×C151—22no—
97C2×D8×C151—22no—
98C2×D8×C151—22no—
99C2×D8×C151—22no—
100C2×D8×C151—22no—
101C2×D8×C151—22no—
102C2×D8×C151—41no—
103C2×D8×C151—41no—
104C2×D8×C151—41no—
105C22×C8×C151C2311yescharacteristic
106C22×C8×C151C2311yescharacteristic
107C22×C8×C151C2311yescharacteristic
108C22×C8×C151C2311yescharacteristic
109#127×C151—22no—
110#127×C151—22no—
111#127×C151—22no—
112#127×C151D414yescomplemented
113#124×C151—22no—
114#124×C151—22no—
115#124×C151—22no—
116#124×C151D414yescomplemented
117#121×C151—28no—
118#121×C151—28no—
119#121×C151—22no—
120#121×C151D414yescomplemented
121#120×C151—28no—
122#120×C151—28no—
123C4×D4×C151—22no—
124C4×D4×C151—22no—
125#117×C151—22no—
126#117×C151—22no—
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×C151—21no—
140C2×C22⋊C4×C151—21no—
141C2×C22⋊C4×C151—21no—
142C2×C22⋊C4×C151D411yescharacteristic
143C2×C22⋊C4×C151D411yescharacteristic
144C2×C42×C151—21no—
145C2×C42×C151C2311yescharacteristic
146C2×C42×C151C2311yescharacteristic
147C4⋊C8×C151—22no—
148C4⋊C8×C151—22no—
149#103×C151—22no—
150#103×C151—22no—
151#103×C151—41no—
152#102×C151—22no—
153#102×C151—22no—
154#102×C151—22no—
155#102×C151—22no—
156#102×C151—22no—
157#102×C151—22no—
158#102×C151—41no—
159#102×C151—41no—
160#102×C151—41no—
161C22⋊C8×C151—22no—
162C22⋊C8×C151—22no—
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—21no—
171C24×C151—42no—
172C24×C151—42no—
173C24×C151—81no—
174C24×C151—81no—
175C24×C151—81no—
176C24×C151—81no—
177C24×C151C2×D411yescharacteristic
178#41×C151—44no—
179#41×C151—44no—
180#41×C151—44no—
181#41×C151—44no—
182C2×Q8×C151—21no—
183C2×Q8×C151—21no—
184C2×Q8×C151—21no—
185C2×Q8×C151—21no—
186C2×Q8×C151—21no—
187C2×Q8×C151C2×D412yes—
188C2×D4×C151—24no—
189C2×D4×C151—24no—
190C2×D4×C151—24no—
191C2×D4×C151—24no—
192C2×D4×C151—24no—
193C2×D4×C151—24no—
194C2×D4×C151—24no—
195C2×D4×C151—21no—
196C2×D4×C151—21no—
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—21no—
214C2×D4×C151—21no—
215C2×D4×C151—44no—
216C2×D4×C151—44no—
217C2×D4×C151—44no—
218C2×D4×C151—44no—
219C2×D4×C151—42no—
220C2×D4×C151—42no—
221C2×D4×C151—42no—
222C2×D4×C151—42no—
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×C151—81no—
231C2×D4×C151—81no—
232C2×D4×C151—81no—
233C2×D4×C151C2×D412yes—
234C2×D4×C151C2×D412yes—
235C2×D4×C151C2×D412yes—
236C2×D4×C151C2×D412yes—
237C22×C4×C151—21no—
238C22×C4×C151—21no—
239C22×C4×C151—21no—
240C22×C4×C151—21no—
241C22×C4×C151—24no—
242C22×C4×C151—21no—
243C22×C4×C151—21no—
244C22×C4×C151—21no—
245C22×C4×C151—21no—
246C22×C4×C151—42no—
247C22×C4×C151—42no—
248C22×C4×C151—42no—
249C22×C4×C151—81no—
250C22×C4×C151—81no—
251C22×C4×C151C2×D411yescharacteristic
252C22×C4×C151C2×D411yescharacteristic
253C22×C4×C151C2×D411yescharacteristic
254C22×C4×C151C2×D411yescharacteristic
255C22×C4×C151C2×D411yescharacteristic
256C22×C4×C151C2×D412yes—
257C22×C4×C151#4112yes—
258C22×C4×C151C2411yescharacteristic
259SD16×C151—44no—
260D8×C151—44no—
261D8×C151—44no—
262D8×C151—44no—
263C2×C8×C151—21no—
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—21no—
275C4⋊C4×C151—22no—
276C4⋊C4×C151—22no—
277C4⋊C4×C151—21no—
278C4⋊C4×C151—21no—
279C4⋊C4×C151—21no—
280C4⋊C4×C151—21no—
281C4⋊C4×C151—21no—
282C4⋊C4×C151—81no—
283C4⋊C4×C151C2×D412yes—
284C22⋊C4×C151—24no—
285C22⋊C4×C151—24no—
286C22⋊C4×C151—24no—
287C22⋊C4×C151—24no—
288C22⋊C4×C151—22no—
289C22⋊C4×C151—22no—
290C22⋊C4×C151—24no—
291C22⋊C4×C151—42no—
292C22⋊C4×C151—81no—
293C22⋊C4×C151—81no—
294C22⋊C4×C151—81no—
295C42×C151—21no—
296C42×C151—21no—
297C42×C151—81no—
298C42×C151C2×D412yes—
299C42×C151C2×D412yes—
300C23×C151—21no—
301C23×C151—21no—
302C23×C151—21no—
303C23×C151—21no—
304C23×C151—21no—
305C23×C151—21no—
306C23×C151—22no—
307C23×C151—22no—
308C23×C151—22no—
309C23×C151—22no—
310C23×C151—48no—
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—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—41no—
334C23×C151—41no—
335C23×C151—84no—
336C23×C151—84no—
337C23×C151—84no—
338C23×C151—84no—
339C23×C151—84no—
340C23×C151—84no—
341C23×C151#12112yes—
342C23×C151C22×D411yescharacteristic
343Q8×C151—22no—
344Q8×C151—22no—
345Q8×C151—41no—
346Q8×C151—41no—
347D4×C151—22no—
348D4×C151—22no—
349D4×C151—22no—
350D4×C151—22no—
351D4×C151—22no—
352D4×C151—22no—
353D4×C151—22no—
354D4×C151—22no—
355D4×C151—48no—
356D4×C151—48no—
357D4×C151—41no—
358D4×C151—41no—
359D4×C151—41no—
360D4×C151—41no—
361D4×C151—41no—
362D4×C151—41no—
363D4×C151—41no—
364D4×C151—41no—
365D4×C151—84no—
366D4×C151—84no—
367D4×C151—84no—
368D4×C151—84no—
369D4×C151—84no—
370C2×C4×C151—21no—
371C2×C4×C151—21no—
372C2×C4×C151—21no—
373C2×C4×C151—21no—
374C2×C4×C151—21no—
375C2×C4×C151—21no—
376C2×C4×C151—22no—
377C2×C4×C151—22no—
378C2×C4×C151—22no—
379C2×C4×C151—22no—
380C2×C4×C151—22no—
381C2×C4×C151—21no—
382C2×C4×C151—21no—
383C2×C4×C151—22no—
384C2×C4×C151—21no—
385C2×C4×C151—21no—
386C2×C4×C151—21no—
387C2×C4×C151—21no—
388C2×C4×C151—48no—
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—41no—
397C2×C4×C151—41no—
398C2×C4×C151—41no—
399C2×C4×C151—84no—
400C2×C4×C151#12012yes—
401C2×C4×C151#12012yes—
402C2×C4×C151#12112yes—
403C2×C4×C151C22×D411yescharacteristic
404C2×C4×C151C22×D411yescharacteristic
405C2×C4×C151C22×D411yescharacteristic
406C2×C4×C151C2×#4111yescharacteristic
407C2×C4×C151H(5,𝔽2)11yescharacteristic
408C2×C4×C151H(5,𝔽2)11yescharacteristic
409C8×C151—41no—
410C8×C151—41no—
411C8×C151—41no—
412C8×C151—41no—
413C22×C151—22no—
414C22×C151—22no—
415C22×C151—22no—
416C22×C151—41no—
417C22×C151—41no—
418C22×C151—41no—
419C22×C151—41no—
420C22×C151—42no—
421C22×C151—42no—
422C22×C151—42no—
423C22×C151—42no—
424C22×C151—42no—
425C22×C151—42no—
426C22×C151—42no—
427C22×C151—42no—
428C22×C151—42no—
429C22×C151—42no—
430C22×C151—42no—
431C22×C151—42no—
432C22×C151—816no—
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×C151—81no—
445C22×C151—81no—
446C22×C151—81no—
447C22×C151—81no—
448C22×C151—81no—
449C22×C151C2×#12011yescharacteristic
450C22×C151C2×#12111yescharacteristic
451C22×C151#53511yescharacteristic
452C22×C151#57611yescharacteristic
453C22×C151#57611yescharacteristic
454C22×C151#57611yescharacteristic
455C22×C151#57711yescharacteristic
456C4×C151—22no—
457C4×C151—22no—
458C4×C151—22no—
459C4×C151—42no—
460C4×C151—41no—
461C4×C151—41no—
462C4×C151—42no—
463C4×C151—81no—
464C4×C151—81no—
465C4×C151D4211yescharacteristic
466C4×C151D4211yescharacteristic
467C4×C151#54611yescharacteristic
468C4×C151#54611yescharacteristic
469C2×C151—42no—
470C2×C151—82no—
471C2×C151—82no—
472C2×C151—82no—
473C2×C151—82no—
474C2×C151#240811yescharacteristic
475C2×C151#300811yescharacteristic
476C2×C151#301211yescharacteristic
477C2×C151#304111yescharacteristic
478C2×C151#304511yescharacteristic
479C2×C151#322011yescharacteristic
480C2×C151#322411yescharacteristic
481#24218C15111yesmaximal, characteristic, direct product factor, Sylow
482C151#2421811yescharacteristic, direct product factor, Sylow
483C2×#535C2×C15111yescharacteristic, complemented
484C2×#463C2×C15111yescharacteristic, complemented
485C2×#459C2×C15111yescharacteristic, complemented
486C2×#449C2×C15111yescharacteristic, complemented
487C2×#447C2×C15111yescharacteristic, complemented
488#2324C2×C15111yescharacteristic, complemented
489#2042C2×C15111yescharacteristic, complemented
490#2041C2×C15111yescharacteristic, complemented
491#2012C2×C15111yescharacteristic, complemented
492#2011C2×C15111yescharacteristic, complemented
493#1983C2×C15111yescharacteristic, complemented
494#1982C2×C15111yescharacteristic, complemented
495#1798C2×C15111yescharacteristic, complemented
496#1788C2×C15111yescharacteristic, complemented
497#1786C2×C15111yescharacteristic, complemented
498C22×#41C22×C15111yescharacteristic
499C23×D4C22×C15111yescharacteristic
500C22×SD16C22×C15111yescharacteristic, complemented
501C22×D8C22×C15111yescharacteristic
502C22×D8C22×C15111yescharacteristic
503C22×D8C22×C15111yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127C22×C15111yescharacteristic
507C2×#127C22×C15111yescharacteristic
508C2×#124C22×C15111yescharacteristic
509C2×#124C22×C15111yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C15111yescharacteristic
513C2×#120—21no—
514C2×#120—21no—
515C2×C4×D4C22×C15111yescharacteristic, complemented
516C2×#117C22×C15111yescharacteristic
517#463—24no—
518#459—24no—
519#449—24no—
520#447—24no—
521C2×C4⋊C8C22×C15111yescharacteristic, complemented
522C2×C4⋊C8C22×C15111yescharacteristic, complemented
523C2×#103C22×C15111yescharacteristic, complemented
524C2×#103C22×C15111yescharacteristic, complemented
525C2×#103C22×C15111yescharacteristic, complemented
526C2×#102C22×C15111yescharacteristic
527C2×#102C22×C15111yescharacteristic
528C2×#102C22×C15111yescharacteristic
529C2×#102C22×C15111yescharacteristic
530C2×#102C22×C15111yescharacteristic
531C2×#102C22×C15111yescharacteristic
532C2×#102C22×C15111yescharacteristic, complemented
533C2×#102C22×C15111yescharacteristic, complemented
534C2×#102C22×C15111yescharacteristic, complemented
535C2×C22⋊C8C22×C15111yescharacteristic
536C2×C22⋊C8C22×C15111yescharacteristic
537#390—21no—
538#390C22×C15111yescharacteristic, complemented
539#389C22×C15111yescharacteristic, complemented
540#388—21no—
541#386—21no—
542#385—21no—
543#380C22×C15111yescharacteristic
544C4×C4⋊C4C22×C15111yescharacteristic, complemented
545#336C22×C15111yescharacteristic, complemented
546#336C22×C15111yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C15111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C15111yescharacteristic
569C22×D4C23×C15111yescharacteristic
570C22×D4C23×C15111yescharacteristic
571C22×D4C23×C15111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C15111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C15111yescharacteristic
588C22×C8C23×C15111yescharacteristic
589C22×C8C23×C15111yescharacteristic
590C22×C8C23×C15111yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C15114yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C15114yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C15114yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C15111yescharacteristic
611C2×C4⋊C4D4×C15111yescharacteristic
612C2×C4⋊C4C23×C15111yescharacteristic
613C2×C4⋊C4C23×C15111yescharacteristic
614C2×C4⋊C4C23×C15111yescharacteristic
615C2×C22⋊C4—21no—
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⋊C4D4×C15111yescharacteristic
625C2×C22⋊C4D4×C15111yescharacteristic
626C2×C42—21no—
627C2×C42C23×C15111yescharacteristic
628C2×C42C23×C15111yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C15111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C15112yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
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—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C15112yes—
716C2×D4C2×D4×C15112yes—
717C2×D4C2×D4×C15112yes—
718C2×D4C2×D4×C15112yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C15111yescharacteristic
734C22×C4C2×D4×C15111yescharacteristic
735C22×C4C2×D4×C15111yescharacteristic
736C22×C4C2×D4×C15111yescharacteristic
737C22×C4C2×D4×C15111yescharacteristic
738C22×C4C2×D4×C15112yes—
739C22×C4#41×C15112yes—
740C22×C4C24×C15111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C15112yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C15112yes—
781C42C2×D4×C15112yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
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—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C15112yes—
824C23C22×D4×C15111yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—84no—
882C2×C4#120×C15112yes—
883C2×C4#120×C15112yes—
884C2×C4#121×C15112yes—
885C2×C4C22×D4×C15111yescharacteristic
886C2×C4C22×D4×C15111yescharacteristic
887C2×C4C22×D4×C15111yescharacteristic
888C2×C4C2×#41×C15111yescharacteristic
889C2×C4H(5,𝔽2)×C15111yescharacteristic
890C2×C4H(5,𝔽2)×C15111yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C15111yescharacteristic
932C22C2×#121×C15111yescharacteristic
933C22#535×C15111yescharacteristic
934C22#576×C15111yescharacteristic
935C22#576×C15111yescharacteristic
936C22#576×C15111yescharacteristic
937C22#577×C15111yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—42no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—81no—
946C4—81no—
947C4D42×C15111yescharacteristic
948C4D42×C15111yescharacteristic
949C4#546×C15111yescharacteristic
950C4#546×C15111yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2#2408×C15111yescharacteristic
957C2#3008×C15111yescharacteristic
958C2#3012×C15111yescharacteristic
959C2#3041×C15111yescharacteristic
960C2#3045×C15111yescharacteristic
961C2#3220×C15111yescharacteristic
962C2#3224×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C22×D4
commutator, Frattini, cosocleC22×C4C24×C151
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
1. C2×#535×C151C2semidirect
2. C2×#463×C151C2semidirect
3. C2×#459×C151C2semidirect
4. C2×#449×C151C2semidirect
5. C2×#447×C151C2semidirect
6. #2324×C151C2semidirect
7. #2042×C151C2semidirect
8. #2041×C151C2semidirect
9. #2012×C151C2semidirect
10. #2011×C151C2semidirect
11. #1983×C151C2semidirect
12. #1982×C151C2semidirect
13. #1798×C151C2semidirect
14. #1788×C151C2semidirect
15. #1786×C151C2semidirect
18. C22×SD16×C151C22semidirect
21. C22×D8×C151C22semidirect
33. C2×C4×D4×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
56. #390×C151C22semidirect
57. #389×C151C22semidirect
62. C4×C4⋊C4×C151C22semidirect
63. #336×C151C22semidirect
64. #336×C151C22semidirect
112. #127×C151D4semidirect
116. #124×C151D4semidirect
120. #121×C151D4semidirect
481. #24218C151direct (N × H)
482. C151#24218direct (N × H)
483. C2×#535C2×C151semidirect
484. C2×#463C2×C151semidirect
485. C2×#459C2×C151semidirect
486. C2×#449C2×C151semidirect
487. C2×#447C2×C151semidirect
488. #2324C2×C151semidirect
489. #2042C2×C151semidirect
490. #2041C2×C151semidirect
491. #2012C2×C151semidirect
492. #2011C2×C151semidirect
493. #1983C2×C151semidirect
494. #1982C2×C151semidirect
495. #1798C2×C151semidirect
496. #1788C2×C151semidirect
497. #1786C2×C151semidirect
500. C22×SD16C22×C151semidirect
503. C22×D8C22×C151semidirect
515. C2×C4×D4C22×C151semidirect
521. C2×C4⋊C8C22×C151semidirect
522. C2×C4⋊C8C22×C151semidirect
523. C2×#103C22×C151semidirect
524. C2×#103C22×C151semidirect
525. C2×#103C22×C151semidirect
532. C2×#102C22×C151semidirect
533. C2×#102C22×C151semidirect
534. C2×#102C22×C151semidirect
538. #390C22×C151semidirect
539. #389C22×C151semidirect
544. C4×C4⋊C4C22×C151semidirect
545. #336C22×C151semidirect
546. #336C22×C151semidirect
594. #127D4×C151semidirect
598. #124D4×C151semidirect
602. #121D4×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×#463×C1512
C2×#459×C1512
C2×#449×C1512
C2×#447×C1512
#2324×C1512
#2042×C1512
#2041×C1512
#2012×C1512
#2011×C1512
#1983×C1512
#1982×C1512
#1798×C1512
#1788×C1512
#1786×C1512
#24218151