Finite Group Databasebeta

← #1393473

Subgroups — #1393473

Order 512.

4786 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2409C211yesmaximal, characteristic, complemented
2C2×#2626C211yesmaximal, characteristic, complemented
3C22×#393C211yesmaximal, characteristic, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic
5#17077C211yesmaximal, characteristic, complemented
6#16814C211yesmaximal, characteristic, complemented
7#16600C211yesmaximal, characteristic, complemented
8#16556C212yesmaximal, complemented
9#16520C212yesmaximal, complemented
10#16320C212yesmaximal, complemented
11#16297C212yesmaximal, complemented
12#16265C211yesmaximal, characteristic, complemented
13#15161C211yesmaximal, characteristic, complemented
14#14873C211yesmaximal, characteristic, complemented
15#14836C211yesmaximal, characteristic, complemented
16#14748C212yesmaximal, complemented
17#14734C211yesmaximal, characteristic, complemented
18#14726C212yesmaximal, complemented
19#14717C211yesmaximal, characteristic, complemented
20#14319C211yesmaximal, characteristic, complemented
21#13975C212yesmaximal, complemented
22#13899C211yesmaximal, characteristic, complemented
23#13867C212yesmaximal
24C24×Q8C2211yescharacteristic, complemented
25C24×D4C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic, complemented
27C22×C22⋊Q8C2211yescharacteristic, complemented
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2212yes—
33#2626—28no—
34#2409—28no—
35C2×#399C2211yescharacteristic
36C2×#399C2211yescharacteristic, complemented
37C2×#399C2211yescharacteristic, complemented
38C2×#396C2212yes—
39C2×#396C2212yescomplemented
40C2×#396C2212yescomplemented
41C2×#395C2212yescomplemented
42C2×#393—28no—
43C2×#393C2211yescharacteristic
44C2×#393C2212yes—
45C2×#393C2211yescharacteristic
46C2×#393C2211yescharacteristic, complemented
47C2×#393C2212yescomplemented
48C2×#393C2211yescharacteristic, complemented
49C2×#393C2212yescomplemented
50C2×#393C2211yescharacteristic, complemented
51C2×#393C2211yescharacteristic, complemented
52C2×#393C2212yescomplemented
53D4×C22⋊C4—28no—
54C2×#391C2211yescharacteristic, complemented
55C2×#391C2211yescharacteristic, complemented
56C2×#390C2211yescharacteristic
57C2×#390C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#385C2212yescomplemented
67C2×#385C2212yescomplemented
68C2×#385C2212yescomplemented
69C2×#385C2212yescomplemented
70C2×#380C2211yescharacteristic
71C2×#380C2211yescharacteristic, complemented
72C2×#380C2211yescharacteristic, complemented
73C2×#380C2212yescomplemented
74C2×#379C2212yes—
75C2×#379C2211yescharacteristic
76C2×#379C2211yescharacteristic
77C2×#379C2212yes—
78C2×#379C2212yes—
79C2×C4×C22⋊C4C2211yescharacteristic
80C22×#95C2211yescharacteristic, complemented
81C22×#95C2212yescomplemented
82#1446C2211yescharacteristic, complemented
83#1446C2212yescomplemented
84#1446C2211yescharacteristic, complemented
85#1445C2211yescharacteristic, complemented
86#1445C2212yescomplemented
87#1444C2212yescomplemented
88#1444C2211yescharacteristic, complemented
89#1443C2212yescomplemented
90#1442C2212yescomplemented
91#1441C2212yescomplemented
92#1441C2212yescomplemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1439C2212yes—
96#1439C2212yes—
97#1439C2211yescharacteristic
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2211yescharacteristic, complemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2211yescharacteristic, complemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1438C2212yes—
114#1438C2212yes—
115#1438C2212yes—
116#1438C2212yes—
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119C4⋊#95C2211yescharacteristic, complemented
120#1434C2211yescharacteristic, complemented
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2211yescharacteristic, complemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2211yescharacteristic, complemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8—24no—
130C23×Q8—24no—
131C23×Q8—44no—
132C23×Q8—42no—
133C23×Q8—44no—
134C23×Q8C2311yescharacteristic
135C23×Q8C2312yes—
136C23×Q8C2311yescharacteristic
137C23×D4—24no—
138C23×D4—24no—
139C23×D4—44no—
140C23×D4—44no—
141C23×D4Q818yescomplemented
142C23×D4C2311yescharacteristic
143C23×D4C2311yescharacteristic
144C23×D4C2311yescharacteristic
145C23×D4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—44no—
157C2×C22⋊Q8—42no—
158C2×C4×D4—24no—
159C2×C4×D4—44no—
160C2×C4×D4—44no—
161C2×C4×D4D418yes—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—28no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4—42no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219#399—24no—
220#399—24no—
221#399—42no—
222#396—28no—
223#396—28no—
224#396—44no—
225#395—28no—
226#393—24no—
227#393—24no—
228#393—24no—
229#393—28no—
230#393—28no—
231#393—24no—
232#393—28no—
233#393—44no—
234#393—42no—
235#393D418yescomplemented
236#391—24no—
237#391—24no—
238#390—24no—
239#390—24no—
240#386—28no—
241#386—28no—
242#386—24no—
243#386—24no—
244#386—24no—
245#386—24no—
246#386—44no—
247#386—44no—
248#385—28no—
249#385—28no—
250#385—44no—
251#385—44no—
252#380—24no—
253#380—24no—
254#380—24no—
255#380—44no—
256#379—24no—
257#379—24no—
258#379—28no—
259#379—44no—
260#379—44no—
261C4×C22⋊C4—24no—
262C2×#95—24no—
263C2×#95—28no—
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C25—22no—
300C25—22no—
301C25—22no—
302C25—22no—
303C25—22no—
304C25—22no—
305C25—24no—
306C25—24no—
307C25—22no—
308C25—22no—
309C25—41no—
310C25—42no—
311C25—41no—
312C25—42no—
313C25—42no—
314C25—41no—
315C25—42no—
316C25—41no—
317C25—42no—
318C25—42no—
319C25C2×Q814yes—
320C25C2×Q814yescomplemented
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C22×Q8—22no—
327C22×Q8—22no—
328C22×Q8—24no—
329C22×Q8—22no—
330C22×Q8—24no—
331C22×Q8—24no—
332C22×Q8—22no—
333C22×Q8—24no—
334C22×Q8—22no—
335C22×Q8—42no—
336C22×Q8—42no—
337C22×Q8—42no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×Q8—42no—
342C22×Q8—416no—
343C22×Q8—432no—
344C22×Q8—416no—
345C22×Q8—416no—
346C22×Q8—432no—
347C22×Q8C2×D414yescomplemented
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—232no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—432no—
364C22×D4—416no—
365C22×D4—416no—
366C22×D4—432no—
367C22×D4C2×D414yes—
368C22×D4C2×Q814yes—
369C22×D4C2×Q814yes—
370C22×D4C2×Q814yescomplemented
371C22×D4C2×Q814yescomplemented
372C22×D4#4114yes—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—42no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—41no—
400C23×C4—41no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4C2×D414yes—
410C23×C4C2×D414yes—
411C23×C4C2×Q814yescomplemented
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2412yes—
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2412yes—
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C22⋊Q8—416no—
431C22⋊Q8—416no—
432C4×D4—416no—
433C4×D4—416no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4—42no—
451C2×C4⋊C4—42no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
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⋊C4C2×D414yes—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
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—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—416no—
517C2×C22⋊C4—416no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—41no—
522C2×C22⋊C4—41no—
523C2×C22⋊C4—41no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—41no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—41no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—432no—
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—42no—
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⋊C4C2×D414yes—
561C2×C22⋊C4C2×D414yes—
562C2×C22⋊C4C2×D418yes—
563C2×C22⋊C4C2×D414yes—
564C2×C42—22no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42C2×D414yes—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—22no—
573#95—22no—
574#95—22no—
575#95—22no—
576#95—22no—
577#95—24no—
578#95—22no—
579#95—24no—
580#95—24no—
581#95—24no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—22no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95C2×D414yescomplemented
602#95C2×D418yescomplemented
603C24—21no—
604C24—21no—
605C24—22no—
606C24—21no—
607C24—21no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—22no—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—22no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—21no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—22no—
625C24—28no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—28no—
647C24—28no—
648C24—216no—
649C24—28no—
650C24—48no—
651C24—48no—
652C24—44no—
653C24—44no—
654C24—48no—
655C24—44no—
656C24—48no—
657C24—44no—
658C24—44no—
659C24—48no—
660C24—44no—
661C24—44no—
662C24—48no—
663C24—48no—
664C24—44no—
665C24—44no—
666C24—44no—
667C24—44no—
668C24—44no—
669C24—48no—
670C24—44no—
671C24—44no—
672C24—48no—
673C24—82no—
674C24—82no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—82no—
681C24—84no—
682C24—84no—
683C24—82no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24C22×D412yes—
692C24C22×D412yes—
693C24C22×D412yes—
694C24C22×Q812yes—
695C24C22×Q812yes—
696C24C22×Q812yes—
697C24C22×Q812yes—
698C24C22×Q812yes—
699C24C2×#4112yes—
700C24C2×#4112yes—
701C24H(5,𝔽2)14yes—
702C24H(5,𝔽2)14yes—
703C242−1+412yes—
704C24C2511yescharacteristic
705C2×Q8—28no—
706C2×Q8—28no—
707C2×Q8—48no—
708C2×Q8—48no—
709C2×Q8—48no—
710C2×Q8—48no—
711C2×Q8—48no—
712C2×Q8—48no—
713C2×Q8—44no—
714C2×Q8—44no—
715C2×Q8—44no—
716C2×Q8—48no—
717C2×Q8—48no—
718C2×Q8—48no—
719C2×Q8—48no—
720C2×Q8—4128no—
721C2×Q8—48no—
722C2×Q8—44no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—216no—
726C2×D4—216no—
727C2×D4—28no—
728C2×D4—28no—
729C2×D4—216no—
730C2×D4—28no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—48no—
736C2×D4—4128no—
737C2×D4—44no—
738C2×D4—44no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—48no—
743C2×D4C22⋊Q8116yes—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—216no—
749C22×C4—28no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
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—22no—
810C22×C4—22no—
811C22×C4—21no—
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—22no—
824C22×C4—21no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—44no—
842C22×C4—48no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—48no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—48no—
865C22×C4—84no—
866C22×C4—84no—
867C22×C4—84no—
868C22×C4—82no—
869C22×C4—82no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D414yes—
878C22×C4C22×D412yes—
879C22×C4C22×D414yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C22×Q812yes—
885C22×C4C22×Q812yes—
886C22×C4C2×#4112yes—
887C22×C4H(5,𝔽2)14yes—
888C22×C4H(5,𝔽2)12yes—
889C4⋊C4—44no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—84no—
896C4⋊C4—84no—
897C4⋊C4—84no—
898C4⋊C4—84no—
899C4⋊C4—84no—
900C4⋊C4—84no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—44no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—82no—
923C22⋊C4—82no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—82no—
927C22⋊C4—82no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C42—44no—
936C42—44no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—22no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—24no—
968C23—24no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—22no—
974C23—24no—
975C23—22no—
976C23—24no—
977C23—22no—
978C23—22no—
979C23—24no—
980C23—24no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—24no—
989C23—22no—
990C23—22no—
991C23—432no—
992C23—416no—
993C23—416no—
994C23—416no—
995C23—41no—
996C23—41no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—42no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—416no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—41no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—42no—
1035C23—42no—
1036C23—41no—
1037C23—41no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—88no—
1051C23—816no—
1052C23—816no—
1053C23—88no—
1054C23—88no—
1055C23—88no—
1056C23—88no—
1057C23—816no—
1058C23—88no—
1059C23—816no—
1060C23—816no—
1061C23—88no—
1062C23—88no—
1063C23—88no—
1064C23—816no—
1065C23—88no—
1066C23—816no—
1067C23C2×C22⋊Q814yes—
1068C23C2×C22⋊Q814yes—
1069C23#53414yes—
1070C23#53514yes—
1071C23#53818yes—
1072C23#54318yes—
1073C23D4×Q814yes—
1074C23C23×D411yescharacteristic
1075C23C23×D411yescharacteristic
1076C23C23×Q811yescharacteristic
1077C23C22×#4111yescharacteristic
1078C23C2×H(5,𝔽2)12yes—
1079C23C2×H(5,𝔽2)12yes—
1080C23C2×H(5,𝔽2)11yescharacteristic
1081C23C2×H(5,𝔽2)12yes—
1082C23C2×2−1+411yescharacteristic
1083C23#58511yescharacteristic
1084C23#58512yes—
1085Q8—416no—
1086Q8—416no—
1087Q8—432no—
1088D4—232no—
1089D4—416no—
1090D4—416no—
1091D4—416no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—24no—
1096C2×C4—24no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—24no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—22no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—416no—
1123C2×C4—416no—
1124C2×C4—432no—
1125C2×C4—41no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—42no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
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—42no—
1198C2×C4—42no—
1199C2×C4—88no—
1200C2×C4—88no—
1201C2×C4—816no—
1202C2×C4—88no—
1203C2×C4C2×C22⋊Q814yes—
1204C2×C4D4214yes—
1205C22—24no—
1206C22—24no—
1207C22—28no—
1208C22—24no—
1209C22—28no—
1210C22—24no—
1211C22—24no—
1212C22—28no—
1213C22—28no—
1214C22—24no—
1215C22—28no—
1216C22—24no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22—44no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—42no—
1237C22—44no—
1238C22—44no—
1239C22—42no—
1240C22—42no—
1241C22—44no—
1242C22—44no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—832no—
1248C22—832no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—82no—
1256C22—82no—
1257C22—81no—
1258C22—81no—
1259C22—82no—
1260C22—82no—
1261C22#262618yescomplemented
1262C22C22×C22⋊Q811yescharacteristic
1263C22C2×#53411yescharacteristic
1264C22C2×#53511yescharacteristic
1265C22C2×#53812yes—
1266C22C2×#54312yes—
1267C22C2×D4211yescharacteristic
1268C22C2×D4×Q811yescharacteristic
1269C22D4×#4111yescharacteristic
1270C22#348412yes—
1271C22#348411yescharacteristic
1272C22#348812yes—
1273C22#348911yescharacteristic
1274C22#350011yescharacteristic
1275C22#350112yes—
1276C22#350111yescharacteristic
1277C22#351412yes—
1278C22#352011yescharacteristic
1279C22#353212yes—
1280C22#353512yes—
1281C22#353612yes—
1282C22#354512yes—
1283C22#355812yes—
1284C22#355812yes—
1285C4—24no—
1286C4—24no—
1287C4—42no—
1288C4—44no—
1289C4—44no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—44no—
1294C4—42no—
1295C4—82no—
1296C4—81no—
1297C4—81no—
1298C4—82no—
1299C4—82no—
1300C4—81no—
1301C4—82no—
1302C4—82no—
1303C2—28no—
1304C2—44no—
1305C2—44no—
1306C2—82no—
1307C2—82no—
1308C2C2×#262611yescharacteristic
1309C2#3570211yescharacteristic
1310C2D4×C22⋊Q811yescharacteristic
1311C2#3764411yescharacteristic
1312C2#3767711yescharacteristic
1313C2#3768412yes—
1314C2#3771612yes—
1315C2#4059311yescharacteristic
1316C2#4060812yes—
1317C2#4089312yes—
1318C2#4229411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2409C2semidirect
2. C2×#2626C2semidirect
3. C22×#393C2semidirect
5. #17077C2semidirect
6. #16814C2semidirect
7. #16600C2semidirect
8. #16556C2semidirect
9. #16520C2semidirect
10. #16320C2semidirect
11. #16297C2semidirect
12. #16265C2semidirect
13. #15161C2semidirect
14. #14873C2semidirect
15. #14836C2semidirect
16. #14748C2semidirect
17. #14734C2semidirect
18. #14726C2semidirect
19. #14717C2semidirect
20. #14319C2semidirect
21. #13975C2semidirect
22. #13899C2semidirect
24. C24×Q8C22semidirect
26. C22×C22⋊Q8C22semidirect
27. C22×C22⋊Q8C22semidirect
36. C2×#399C22semidirect
37. C2×#399C22semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
41. C2×#395C22semidirect
46. C2×#393C22semidirect
47. C2×#393C22semidirect
48. C2×#393C22semidirect
49. C2×#393C22semidirect
50. C2×#393C22semidirect
51. C2×#393C22semidirect
52. C2×#393C22semidirect
54. C2×#391C22semidirect
55. C2×#391C22semidirect
66. C2×#385C22semidirect
67. C2×#385C22semidirect
68. C2×#385C22semidirect
69. C2×#385C22semidirect
71. C2×#380C22semidirect
72. C2×#380C22semidirect
73. C2×#380C22semidirect
80. C22×#95C22semidirect
81. C22×#95C22semidirect
82. #1446C22semidirect
83. #1446C22semidirect
84. #1446C22semidirect
85. #1445C22semidirect
86. #1445C22semidirect
87. #1444C22semidirect
88. #1444C22semidirect
89. #1443C22semidirect
90. #1442C22semidirect
91. #1441C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. C4⋊#95C22semidirect
120. #1434C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
141. C23×D4Q8semidirect
235. #393D4semidirect
320. C25C2×Q8semidirect
347. C22×Q8C2×D4semidirect
370. C22×D4C2×Q8semidirect
371. C22×D4C2×Q8semidirect
411. C23×C4C2×Q8semidirect
601. #95C2×D4semidirect
602. #95C2×D4semidirect
1261. C22#2626semidirect

Maximal subgroups

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

subgroupindex
C2×#24092
C2×#26262
C22×#3932
C2×D4×C22⋊C42
#170772
#168142
#166002
#165562
#165202
#163202
#162972
#162652
#151612
#148732
#148362
#147482
#147342
#147262
#147172
#143192
#139752
#138992
#138672