Finite Group Databasebeta

← #721536

Subgroups — #721536

Order 512.

5035 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2557C211yesmaximal, characteristic, complemented
2C2×#2472C212yesmaximal, complemented
3C2×#2418C212yesmaximal, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#17068C211yesmaximal, characteristic, complemented
6#16814C211yesmaximal, characteristic, complemented
7#16807C211yesmaximal, characteristic, complemented
8#16807C211yesmaximal, characteristic, complemented
9#15493C212yesmaximal, complemented
10#15480C212yesmaximal, complemented
11#15453C212yesmaximal, complemented
12#15267C212yesmaximal, complemented
13#15177C211yesmaximal, characteristic, complemented
14#14985C212yesmaximal, complemented
15#14811C211yesmaximal, characteristic, complemented
16#14811C212yesmaximal, complemented
17#14715C211yesmaximal, characteristic, complemented
18#14715C211yesmaximal, characteristic, complemented
19#14321C211yesmaximal, characteristic, complemented
20#14228C211yesmaximal, characteristic, complemented
21#14189C211yesmaximal, characteristic, complemented
22C4×#392C211yesmaximal, characteristic, complemented
23#13788C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×C22⋊Q8C2212yescomplemented
28C22×#120C2212yes—
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yescomplemented
33C23×C22⋊C4C2212yes—
34#2557—28no—
35#2472—216no—
36#2418—216no—
37C2×#399C2212yescomplemented
38C2×#397C2211yescharacteristic
39C2×#397C2212yes—
40C2×#397C2212yes—
41C2×#397C2211yescharacteristic, complemented
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2212yescomplemented
45C2×#394C2212yescomplemented
46C2×#393C2211yescharacteristic, complemented
47C2×#393C2212yescomplemented
48C2×#392C2211yescharacteristic
49C2×#392C2211yescharacteristic
50C2×#392C2211yescharacteristic
51C2×#392C2211yescharacteristic
52C2×#392C2211yescharacteristic
53C2×#392C2212yes—
54C2×#392C2212yes—
55C2×#392C2212yescomplemented
56C2×#392C2212yescomplemented
57D4×C22⋊C4—28no—
58C2×#391C2211yescharacteristic, complemented
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic
61C2×#390C2211yescharacteristic, complemented
62C2×#390C2212yescomplemented
63C2×#390C2212yescomplemented
64C2×#390C2212yescomplemented
65C2×#388C2212yes—
66C2×#388C2211yescharacteristic, complemented
67C2×#388C2212yescomplemented
68C2×#388C2212yescomplemented
69C2×#387C2211yescharacteristic, complemented
70C2×#386C2211yescharacteristic
71C2×#386C2211yescharacteristic
72C2×#386C2212yes—
73C2×#386C2212yes—
74C2×#386C2211yescharacteristic, complemented
75C2×#386C2212yescomplemented
76C2×#386C2212yescomplemented
77C2×#386C2212yescomplemented
78C2×#386C2212yescomplemented
79C2×#385C2212yescomplemented
80C2×#380C2211yescharacteristic
81C2×#380C2212yescomplemented
82C2×#379C2212yes—
83C2×#379C2212yes—
84C2×#379C2212yes—
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic, complemented
87C2×C4×C22⋊C4C2212yescomplemented
88#1445C2212yescomplemented
89#1445C2212yescomplemented
90#1444C2211yescharacteristic, complemented
91#1444C2211yescharacteristic, complemented
92#1444C2211yescharacteristic, complemented
93#1444C2211yescharacteristic, complemented
94#1439C2212yescomplemented
95#1439C2211yescharacteristic, complemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2211yescharacteristic, complemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2211yescharacteristic, complemented
107#1439C2211yescharacteristic, complemented
108#1438C2211yescharacteristic
109#1438C2211yescharacteristic
110#1438C2212yes—
111#1438C2212yes—
112#1438C2211yescharacteristic
113#1438C2211yescharacteristic
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yes—
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120C4⋊#95C2211yescharacteristic, complemented
121#1434C2212yescomplemented
122#1434C2211yescharacteristic, complemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—44no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2311yescharacteristic
143C23×D4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C2×#124—28no—
149C2×#124—24no—
150C2×#123—28no—
151C2×#123—24no—
152C2×C22⋊Q8—28no—
153C2×C22⋊Q8—44no—
154C2×C22⋊Q8—44no—
155C2×#120—28no—
156C2×#120—28no—
157C2×#120—44no—
158C2×#120—44no—
159C2×#120—44no—
160C2×#120—44no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—28no—
164C2×C4×D4—44no—
165C2×C4×D4—44no—
166C2×C4×D4—44no—
167C2×C4×D4—44no—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—28no—
180C22×C22⋊C4—28no—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2312yes—
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224#399—28no—
225#397—28no—
226#397—28no—
227#397—24no—
228#397—24no—
229#394—28no—
230#394—28no—
231#394—28no—
232#394—28no—
233#393—24no—
234#393—28no—
235#392—24no—
236#392—24no—
237#392—24no—
238#392—24no—
239#392—24no—
240#392—44no—
241#392—44no—
242#392—44no—
243#392—44no—
244#391—24no—
245#390—24no—
246#390—24no—
247#390—24no—
248#390—28no—
249#390—44no—
250#390—44no—
251#388—24no—
252#388—28no—
253#388—28no—
254#388D4116yescomplemented
255#387—24no—
256#386—24no—
257#386—24no—
258#386—28no—
259#386—28no—
260#386—24no—
261#386—28no—
262#386—28no—
263#386—28no—
264#386—28no—
265#385—28no—
266#380—24no—
267#380—28no—
268#379—28no—
269#379—28no—
270#379—28no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4—28no—
273C4×C22⋊C4D418yescomplemented
274C2×#95C2311yescharacteristic
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—24no—
309C25—24no—
310C25—24no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25C2411yescharacteristic
320C25C2412yes—
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C25C2412yes—
324C22×Q8—24no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—42no—
328C22×Q8—41no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—232no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—22no—
338C22×D4—24no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—41no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—41no—
382C22×D4—41no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—416no—
389C22×D4—416no—
390C22×D4—432no—
391C22×D4—432no—
392C22×D4#4114yes—
393C22×D4#4114yes—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—22no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—41no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4C2×D414yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2412yes—
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436#124—416no—
437#123—416no—
438C22⋊Q8—432no—
439#120—432no—
440#120—432no—
441C4×D4—416no—
442C4×D4—416no—
443C4×D4—432no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4C2×D418yescomplemented
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—41no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—432no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4C2×D418yes—
570C2×C22⋊C4C2×D418yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D418yes—
574C2×C42—22no—
575C2×C42—24no—
576C2×C42—42no—
577C2×C42—42no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42C2×D414yes—
584C2×C42C2×D414yes—
585C2×C42C2×D418yescomplemented
586#95—22no—
587#95—24no—
588#95—24no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—24no—
598#95—24no—
599#95—22no—
600#95—24no—
601#95—22no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95C2×D414yes—
613#95C2×D414yes—
614#95C2×D418yescomplemented
615#95C2×D418yescomplemented
616C24—22no—
617C24—22no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—216no—
638C24—22no—
639C24—22no—
640C24—21no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—21no—
661C24—22no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—21no—
666C24—22no—
667C24—21no—
668C24—22no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—21no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24C22×D414yes—
708C24C22×D412yes—
709C24C2×#4114yes—
710C24C2×#4114yes—
711C24H(5,𝔽2)12yes—
712C24H(5,𝔽2)14yes—
713C24H(5,𝔽2)14yes—
714C24C2511yescharacteristic
715C2×Q8—48no—
716C2×Q8—44no—
717C2×Q8—44no—
718C2×Q8—82no—
719C2×Q8—84no—
720C2×D4—28no—
721C2×D4—28no—
722C2×D4—216no—
723C2×D4—216no—
724C2×D4—216no—
725C2×D4—216no—
726C2×D4—28no—
727C2×D4—28no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—4128no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—48no—
762C2×D4—82no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—82no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—82no—
776C2×D4—84no—
777C2×D4—84no—
778C2×D4—84no—
779C2×D4—84no—
780C2×D4—84no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—28no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—48no—
879C22×C4—44no—
880C22×C4—48no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—44no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D414yes—
896C22×C4C22×D414yes—
897C22×C4C22×D414yes—
898C22×C4C22×D414yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D414yes—
903C22×C4C22×D414yes—
904C22×C4C2×#4112yes—
905C22×C4C2×#4112yes—
906C22×C4H(5,𝔽2)12yes—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—84no—
917C22⋊C4—216no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—44no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—82no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—82no—
948C22⋊C4—82no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C22⋊C4#127116yes—
955C42—44no—
956C42—44no—
957C42—48no—
958C42—44no—
959C42—84no—
960C23—22no—
961C23—24no—
962C23—22no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—22no—
976C23—24no—
977C23—24no—
978C23—22no—
979C23—22no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—432no—
1003C23—432no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—41no—
1018C23—42no—
1019C23—41no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—42no—
1032C23—41no—
1033C23—41no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—41no—
1045C23—42no—
1046C23—41no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—41no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—41no—
1063C23—42no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—41no—
1086C23—42no—
1087C23—41no—
1088C23—41no—
1089C23—42no—
1090C23—42no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—816no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23—816no—
1109C23—816no—
1110C23—816no—
1111C23—816no—
1112C23C2×#12714yes—
1113C23#53818yes—
1114C23C23×D411yescharacteristic
1115C23C23×D412yes—
1116C23C22×#4111yescharacteristic
1117C23C22×#4111yescharacteristic
1118C23C2×H(5,𝔽2)12yes—
1119C23C2×H(5,𝔽2)12yes—
1120C23C2×H(5,𝔽2)11yescharacteristic
1121C23C2×H(5,𝔽2)11yescharacteristic
1122C23#58512yes—
1123C23#58511yescharacteristic
1124C23#58511yescharacteristic
1125Q8—88no—
1126D4—232no—
1127D4—416no—
1128D4—432no—
1129D4—432no—
1130D4—88no—
1131D4—816no—
1132D4—816no—
1133D4—88no—
1134D4—816no—
1135D4—88no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—22no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—24no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—416no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—816no—
1237C2×C4—88no—
1238C2×C4—816no—
1239C2×C4#52514yes—
1240C2×C4C2×#12714yes—
1241C2×C4C2×#12714yes—
1242C22—24no—
1243C22—24no—
1244C22—28no—
1245C22—28no—
1246C22—24no—
1247C22—28no—
1248C22—44no—
1249C22—42no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—44no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—42no—
1265C22—42no—
1266C22—44no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—44no—
1278C22—42no—
1279C22—44no—
1280C22—864no—
1281C22—82no—
1282C22—81no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—81no—
1292C22—81no—
1293C22—82no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—82no—
1299C22—82no—
1300C22—82no—
1301C22—82no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22C2×#52511yescharacteristic
1307C22C22×#12711yescharacteristic
1308C22#344911yescharacteristic
1309C22C2×#53812yes—
1310C22D4×#4112yes—
1311C22D4×#4112yes—
1312C22#348411yescharacteristic
1313C22#348412yes—
1314C22#348412yes—
1315C22#348411yescharacteristic
1316C22#348811yescharacteristic
1317C22#348812yes—
1318C22#348812yes—
1319C22#348811yescharacteristic
1320C22#349012yes—
1321C22#351311yescharacteristic
1322C22#351411yescharacteristic
1323C22#351911yescharacteristic
1324C22#352111yescharacteristic
1325C22#353312yes—
1326C22#353412yes—
1327C22#354512yes—
1328C22#355812yes—
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—44no—
1335C4—44no—
1336C4—44no—
1337C4—44no—
1338C4—42no—
1339C4—42no—
1340C4—82no—
1341C4—82no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C2—48no—
1348C2—44no—
1349C2—82no—
1350C2—84no—
1351C2—161no—
1352C2#3493611yescharacteristic
1353C2#3498811yescharacteristic
1354C2#3552211yescharacteristic
1355C2#3592111yescharacteristic
1356C2#3592111yescharacteristic
1357C2#3771312yes—
1358C2#3771612yes—
1359C2#4060211yescharacteristic
1360C2#4198911yescharacteristic
1361C2#4311812yes—
1362C2#4414312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2557C2semidirect
2. C2×#2472C2semidirect
3. C2×#2418C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #17068C2semidirect
6. #16814C2semidirect
7. #16807C2semidirect
8. #16807C2semidirect
9. #15493C2semidirect
10. #15480C2semidirect
11. #15453C2semidirect
12. #15267C2semidirect
13. #15177C2semidirect
14. #14985C2semidirect
15. #14811C2semidirect
16. #14811C2semidirect
17. #14715C2semidirect
18. #14715C2semidirect
19. #14321C2semidirect
20. #14228C2semidirect
21. #14189C2semidirect
22. C4×#392C2semidirect
23. #13788C2semidirect
27. C22×C22⋊Q8C22semidirect
32. C22×C4×D4C22semidirect
37. C2×#399C22semidirect
41. C2×#397C22semidirect
44. C2×#394C22semidirect
45. C2×#394C22semidirect
46. C2×#393C22semidirect
47. C2×#393C22semidirect
55. C2×#392C22semidirect
56. C2×#392C22semidirect
58. C2×#391C22semidirect
61. C2×#390C22semidirect
62. C2×#390C22semidirect
63. C2×#390C22semidirect
64. C2×#390C22semidirect
66. C2×#388C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
69. C2×#387C22semidirect
74. C2×#386C22semidirect
75. C2×#386C22semidirect
76. C2×#386C22semidirect
77. C2×#386C22semidirect
78. C2×#386C22semidirect
79. C2×#385C22semidirect
81. C2×#380C22semidirect
86. C2×C4×C22⋊C4C22semidirect
87. C2×C4×C22⋊C4C22semidirect
88. #1445C22semidirect
89. #1445C22semidirect
90. #1444C22semidirect
91. #1444C22semidirect
92. #1444C22semidirect
93. #1444C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. C4⋊#95C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
254. #388D4semidirect
273. C4×C22⋊C4D4semidirect
468. C2×C4⋊C4C2×D4semidirect
585. C2×C42C2×D4semidirect
614. #95C2×D4semidirect
615. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25572
C2×#24722
C2×#24182
C2×D4×C22⋊C42
#170682
#168142
#168072
#154932
#154802
#154532
#152672
#151772
#149852
#148112
#147152
#143212
#142282
#141892
C4×#3922
#137882