Finite Group Databasebeta

← #527662

Subgroups — #527662

Order 512.

4326 conjugacy classes of subgroups.

The subgroup lattice has 1321 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2435C211yesmaximal, characteristic
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C2×C4×#124C211yesmaximal, characteristic, complemented
4#14700C211yesmaximal, characteristic, complemented
5#14539C212yesmaximal, complemented
6#14527C212yesmaximal, complemented
7#14365C212yesmaximal, complemented
8#14365C212yesmaximal, complemented
9#14303C212yesmaximal, complemented
10#14199C212yesmaximal, complemented
11#14153C211yesmaximal, characteristic, complemented
12#14027C211yesmaximal, characteristic, complemented
13#14026C211yesmaximal, characteristic, complemented
14#14018C211yesmaximal, characteristic, complemented
15#14002C211yesmaximal, characteristic, complemented
16#13997C211yesmaximal, characteristic, complemented
17#13991C212yesmaximal, complemented
18#13969C211yesmaximal, characteristic, complemented
19#13902C211yesmaximal, characteristic
20#13875C211yesmaximal, characteristic, complemented
21#13820C211yesmaximal, characteristic, complemented
22#13775C212yesmaximal, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic
26C22×#124C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic, complemented
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C23×C22⋊C4C2212yes—
32#2435C4116yescomplemented
33C2×#394C2212yes—
34C2×#394C2212yes—
35D4×C22⋊C4—28no—
36C4×#124—28no—
37C2×#391C2211yescharacteristic, complemented
38C2×#391C2211yescharacteristic, complemented
39C2×#391C2211yescharacteristic, complemented
40C2×#390C2211yescharacteristic
41C2×#390C2211yescharacteristic
42C2×#390C2211yescharacteristic
43C2×#390C2211yescharacteristic
44C2×#390C2211yescharacteristic
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#389C2211yescharacteristic, complemented
49C2×#388C2211yescharacteristic
50C2×#388C2211yescharacteristic
51C2×#388C2212yescomplemented
52C2×#388C2212yescomplemented
53C2×#388C2212yescomplemented
54C2×#388C2212yescomplemented
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#385C2212yescomplemented
58C2×#382C2211yescharacteristic, complemented
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#379C2212yes—
62C2×#379C2212yes—
63C2×#379C2212yes—
64C2×#379C2212yes—
65C2×#379C2212yes—
66C2×C4×C4⋊C4C2211yescharacteristic, complemented
67C2×C4×C4⋊C4C2211yescharacteristic, complemented
68C2×C4×C4⋊C4C2211yescharacteristic, complemented
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2212yescomplemented
73C2×C4×C22⋊C4C2212yescomplemented
74C2×C4×C22⋊C4C2212yescomplemented
75C2×C43C2211yescharacteristic, complemented
76#1445C2212yescomplemented
77#1443C2212yescomplemented
78#1441C2212yescomplemented
79#1440C2212yes—
80#1440C2212yescomplemented
81#1440C2212yescomplemented
82#1440C2212yescomplemented
83#1440C2212yescomplemented
84#1439C2212yes—
85#1439C2212yes—
86#1439C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1438C2212yes—
93#1438C2212yes—
94#1437C2211yescharacteristic
95#1437C2212yes—
96#1437C2212yes—
97#1437C2212yes—
98#1437C2211yescharacteristic
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1437C2212yescomplemented
104#1437C2212yescomplemented
105#1437C2212yescomplemented
106#1437C2212yescomplemented
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2211yescharacteristic, complemented
111#1436C2211yescharacteristic, complemented
112C4⋊#95C2211yescharacteristic, complemented
113C4⋊#95C2211yescharacteristic, complemented
114C4⋊#95C2211yescharacteristic, complemented
115C4⋊#95C2212yescomplemented
116C4⋊#95C2211yescharacteristic, complemented
117#1434C2212yescomplemented
118#1434C2211yescharacteristic, complemented
119#1434C2211yescharacteristic, complemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C4×#95C2211yescharacteristic, complemented
125C4×#95C2211yescharacteristic, complemented
126C26C2312yes—
127C23×Q8C2311yescharacteristic
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—42no—
131C23×D4—42no—
132C23×D4—42no—
133C23×D4—42no—
134C23×D4C2×C418yes—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2312yes—
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140C24×C4C2312yes—
141C2×#124—24no—
142C2×#124—24no—
143C2×#124—42no—
144C2×#124—42no—
145C2×#124C2×C418yes—
146C2×#124C2×C418yescomplemented
147C2×C22⋊Q8—42no—
148C2×C22⋊Q8—42no—
149C2×C22⋊Q8C2×C418yescomplemented
150C2×C4×Q8—24no—
151C2×C4×Q8—42no—
152C2×C4×Q8—42no—
153C2×C4×D4—24no—
154C2×C4×D4—42no—
155C2×C4×D4—42no—
156C2×C4×D4—42no—
157C2×C4×D4—42no—
158C2×C4×D4D418yes—
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C22⋊C4—28no—
170C22×C22⋊C4—28no—
171C22×C22⋊C4—44no—
172C22×C22⋊C4C2312yes—
173C22×C22⋊C4C2312yes—
174C22×C22⋊C4C2312yes—
175C22×C22⋊C4C2312yes—
176C22×C22⋊C4C2312yes—
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C42C2311yescharacteristic
204C22×C42C2311yescharacteristic
205C22×C42C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2311yescharacteristic
210C22×C42C2311yescharacteristic
211C22×C42C2311yescharacteristic
212C22×C42C2312yes—
213C22×C42C2311yescharacteristic
214C22×C42C2312yes—
215C22×C42C2312yes—
216#394C2×C4116yescomplemented
217#394C2×C4116yescomplemented
218#391—24no—
219#391—42no—
220#391—42no—
221#390—24no—
222#390—24no—
223#390—24no—
224#390—24no—
225#390—42no—
226#390—42no—
227#390C2×C418yes—
228#390C2×C418yescomplemented
229#389—42no—
230#388—28no—
231#388—28no—
232#388—24no—
233#388—24no—
234#388—44no—
235#388—44no—
236#386—28no—
237#386—28no—
238#385—44no—
239#382—24no—
240#380—24no—
241#380—42no—
242#379—28no—
243#379—28no—
244#379—44no—
245#379C2×C4116yescomplemented
246#379C2×C4116yescomplemented
247C4×C4⋊C4—42no—
248C4×C4⋊C4—42no—
249C4×C4⋊C4—42no—
250C4×C22⋊C4—28no—
251C4×C22⋊C4—28no—
252C4×C22⋊C4—24no—
253C4×C22⋊C4—44no—
254C4×C22⋊C4—42no—
255C4×C22⋊C4C2×C418yescomplemented
256C2×#95C2311yescharacteristic
257C2×#95C2311yescharacteristic
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2311yescharacteristic
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C43—24no—
294C25—24no—
295C25—24no—
296C25—24no—
297C25—24no—
298C25—42no—
299C25—42no—
300C25—42no—
301C25—42no—
302C25—42no—
303C25—42no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25C22×C418yes—
309C25C2412yes—
310C25C2412yes—
311C25C2411yescharacteristic
312C22×Q8—22no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—22no—
316C22×Q8—22no—
317C22×Q8—22no—
318C22×Q8C22×C414yes—
319C22×D4—24no—
320C22×D4—24no—
321C22×D4—232no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—22no—
332C22×D4—416no—
333C22×D4—416no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—416no—
339C22×D4—416no—
340C22×D4—416no—
341C22×D4—416no—
342C22×D4C22×C414yes—
343C22×D4C22×C414yes—
344C22×D4C22×C418yes—
345C22×D4C2×D414yes—
346C22×D4#4114yes—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—24no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—42no—
362C23×C4—42no—
363C23×C4—42no—
364C23×C4—42no—
365C23×C4—42no—
366C23×C4C22×C414yes—
367C23×C4C2×D418yes—
368C23×C4C2412yes—
369C23×C4C2411yescharacteristic
370C23×C4C2412yes—
371C23×C4C2411yescharacteristic
372C23×C4C2412yes—
373C23×C4C2412yes—
374C23×C4C2412yes—
375C23×C4C2411yescharacteristic
376C23×C4C2411yescharacteristic
377C23×C4C2411yescharacteristic
378C23×C4C2411yescharacteristic
379C23×C4C2411yescharacteristic
380C23×C4C2411yescharacteristic
381C23×C4C2412yes—
382C23×C4C2411yescharacteristic
383C23×C4C2411yescharacteristic
384C23×C4C2411yescharacteristic
385C23×C4C2411yescharacteristic
386C23×C4C2411yescharacteristic
387C23×C4C2411yescharacteristic
388#124—232no—
389#124—416no—
390C22⋊Q8—416no—
391C4×Q8—416no—
392C4×D4—416no—
393C4×D4—416no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—41no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4—42no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—41no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4C22×C414yes—
422C2×C4⋊C4C22×C418yes—
423C2×C4⋊C4C2×D414yes—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4—24no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—24no—
433C2×C22⋊C4—24no—
434C2×C22⋊C4—24no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—24no—
439C2×C22⋊C4—24no—
440C2×C22⋊C4—24no—
441C2×C22⋊C4—24no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—24no—
451C2×C22⋊C4—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—432no—
458C2×C22⋊C4—42no—
459C2×C22⋊C4—42no—
460C2×C22⋊C4—41no—
461C2×C22⋊C4—41no—
462C2×C22⋊C4—42no—
463C2×C22⋊C4—42no—
464C2×C22⋊C4—42no—
465C2×C22⋊C4—42no—
466C2×C22⋊C4—41no—
467C2×C22⋊C4—41no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—42no—
470C2×C22⋊C4—42no—
471C2×C22⋊C4—42no—
472C2×C22⋊C4—42no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—42no—
476C2×C22⋊C4—42no—
477C2×C22⋊C4—42no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—42no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—42no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—42no—
485C2×C22⋊C4—42no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4C22×C418yes—
505C2×C22⋊C4C22×C418yes—
506C2×C22⋊C4C22×C414yes—
507C2×C22⋊C4C22×C418yes—
508C2×C22⋊C4C22×C418yes—
509C2×C22⋊C4C22×C418yes—
510C2×C22⋊C4C22×C414yes—
511C2×C22⋊C4C22×C418yes—
512C2×C22⋊C4C22×C418yes—
513C2×C22⋊C4C22×C418yes—
514C2×C22⋊C4C22×C418yes—
515C2×C22⋊C4C2×D418yes—
516C2×C22⋊C4#4114yes—
517C2×C22⋊C4#4114yes—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—24no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—22no—
529C2×C42—22no—
530C2×C42—22no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—22no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—42no—
543C2×C42—42no—
544C2×C42—41no—
545C2×C42—41no—
546C2×C42—41no—
547C2×C42—41no—
548C2×C42—42no—
549C2×C42—42no—
550C2×C42—42no—
551C2×C42—42no—
552C2×C42—42no—
553C2×C42—42no—
554C2×C42C22×C414yes—
555C2×C42C22×C414yes—
556C2×C42C2×D414yes—
557#95—24no—
558#95—24no—
559#95—22no—
560#95—22no—
561#95—24no—
562#95—24no—
563#95—24no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—24no—
570#95—42no—
571#95—41no—
572#95—41no—
573#95—41no—
574#95—42no—
575#95—41no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95—42no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95—42no—
585#95—42no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95C22×C414yes—
593#95C22×C414yes—
594C24—21no—
595C24—22no—
596C24—22no—
597C24—21no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—22no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—216no—
633C24—216no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—48no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—84no—
648C24—84no—
649C24—84no—
650C24—84no—
651C24—84no—
652C24—84no—
653C24—84no—
654C24—84no—
655C24—84no—
656C24—84no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24C23×C414yes—
668C24C23×C414yes—
669C24C23×C412yes—
670C24C22×D414yes—
671C24C2×#4114yes—
672C24C2×#4112yes—
673C24C2×#4112yes—
674C24C2511yescharacteristic
675C2×Q8—28no—
676C2×Q8—28no—
677C2×Q8—28no—
678C2×Q8—44no—
679C2×Q8—44no—
680C2×Q8—44no—
681C2×Q8—44no—
682C2×D4—216no—
683C2×D4—28no—
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—28no—
690C2×D4—28no—
691C2×D4—28no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—4128no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—44no—
702C2×D4—44no—
703C2×D4C4×D4116yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—22no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—28no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—216no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—48no—
833C22×C4—84no—
834C22×C4—84no—
835C22×C4—84no—
836C22×C4—84no—
837C22×C4—84no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4C23×C412yes—
843C22×C4C23×C412yes—
844C22×C4C23×C412yes—
845C22×C4C23×C412yes—
846C22×C4C23×C412yes—
847C22×C4C23×C414yes—
848C22×C4C23×C414yes—
849C22×C4C23×C412yes—
850C22×C4C22×D414yes—
851C22×C4C22×D412yes—
852C22×C4C22×D412yes—
853C22×C4C22×D412yes—
854C22×C4C2×#4112yes—
855C22×C4C2×#4112yes—
856C22×C4C2×#4112yes—
857C22×C4C2×#4112yes—
858C22×C4C2×#4112yes—
859C22×C4H(5,𝔽2)12yes—
860C22×C4H(5,𝔽2)12yes—
861C22×C4H(5,𝔽2)12yes—
862C22×C4H(5,𝔽2)12yes—
863C22×C4H(5,𝔽2)12yes—
864C22×C4H(5,𝔽2)12yes—
865C4⋊C4—28no—
866C4⋊C4—28no—
867C4⋊C4—48no—
868C4⋊C4—44no—
869C4⋊C4—44no—
870C4⋊C4—48no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C4⋊C4—84no—
875C22⋊C4—216no—
876C22⋊C4—216no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—44no—
880C22⋊C4—48no—
881C22⋊C4—48no—
882C22⋊C4—48no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—44no—
895C22⋊C4—48no—
896C22⋊C4—48no—
897C22⋊C4—48no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C42—28no—
907C42—28no—
908C42—28no—
909C42—44no—
910C42—44no—
911C42—44no—
912C42—48no—
913C42—44no—
914C42—44no—
915C42—44no—
916C42—44no—
917C42—84no—
918C42—84no—
919C23—22no—
920C23—24no—
921C23—22no—
922C23—22no—
923C23—24no—
924C23—24no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—22no—
930C23—22no—
931C23—24no—
932C23—24no—
933C23—24no—
934C23—24no—
935C23—22no—
936C23—24no—
937C23—22no—
938C23—24no—
939C23—22no—
940C23—24no—
941C23—24no—
942C23—22no—
943C23—24no—
944C23—24no—
945C23—22no—
946C23—22no—
947C23—24no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—432no—
963C23—432no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—42no—
971C23—42no—
972C23—42no—
973C23—42no—
974C23—42no—
975C23—42no—
976C23—42no—
977C23—41no—
978C23—42no—
979C23—41no—
980C23—42no—
981C23—41no—
982C23—42no—
983C23—42no—
984C23—41no—
985C23—41no—
986C23—42no—
987C23—41no—
988C23—42no—
989C23—42no—
990C23—41no—
991C23—41no—
992C23—42no—
993C23—42no—
994C23—41no—
995C23—41no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
1002C23—42no—
1003C23—42no—
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—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—816no—
1025C23—816no—
1026C23—816no—
1027C23—816no—
1028C23—816no—
1029C23—816no—
1030C23—816no—
1031C23—816no—
1032C23—816no—
1033C23—816no—
1034C23—816no—
1035C23—816no—
1036C23—816no—
1037C23C2×C4×D418yes—
1038C23C4×#4114yes—
1039C23C24×C411yescharacteristic
1040C23C23×D411yescharacteristic
1041C23C22×#4111yescharacteristic
1042C23C22×#4111yescharacteristic
1043C23C22×#4111yescharacteristic
1044C23C2×H(5,𝔽2)11yescharacteristic
1045C23C2×H(5,𝔽2)11yescharacteristic
1046C23C2×H(5,𝔽2)11yescharacteristic
1047C23C2×H(5,𝔽2)11yescharacteristic
1048C23C2×H(5,𝔽2)11yescharacteristic
1049C23C2×H(5,𝔽2)11yescharacteristic
1050C23#58511yescharacteristic
1051C23#58511yescharacteristic
1052C23#58511yescharacteristic
1053C23#58511yescharacteristic
1054Q8—416no—
1055D4—232no—
1056D4—432no—
1057D4—416no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—24no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—24no—
1087C2×C4—22no—
1088C2×C4—24no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—42no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—42no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—42no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—416no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—41no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—816no—
1192C2×C4—816no—
1193C2×C4C2×C4×D414yes—
1194C2×C4#51814yes—
1195C2×C4#51814yes—
1196C2×C4#53414yes—
1197C2×C4#53514yes—
1198C2×C4#53814yes—
1199C2×C4#53814yes—
1200C2×C4#54614yes—
1201C22—28no—
1202C22—24no—
1203C22—24no—
1204C22—28no—
1205C22—24no—
1206C22—28no—
1207C22—42no—
1208C22—44no—
1209C22—44no—
1210C22—42no—
1211C22—44no—
1212C22—42no—
1213C22—44no—
1214C22—42no—
1215C22—44no—
1216C22—42no—
1217C22—44no—
1218C22—42no—
1219C22—44no—
1220C22—42no—
1221C22—44no—
1222C22—44no—
1223C22—42no—
1224C22—44no—
1225C22—42no—
1226C22—42no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—42no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—864no—
1239C22—82no—
1240C22—82no—
1241C22—82no—
1242C22—82no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22C22×C4×D411yescharacteristic
1248C22C2×C4×#4111yescharacteristic
1249C22C2×#51811yescharacteristic
1250C22C2×#51811yescharacteristic
1251C22#342811yescharacteristic
1252C22C4×H(5,𝔽2)11yescharacteristic
1253C22C4×H(5,𝔽2)11yescharacteristic
1254C22C2×#53411yescharacteristic
1255C22C2×#53511yescharacteristic
1256C22C2×#53811yescharacteristic
1257C22C2×#53811yescharacteristic
1258C22C2×#54611yescharacteristic
1259C22D4×#4111yescharacteristic
1260C22#347511yescharacteristic
1261C22#348111yescharacteristic
1262C22#348511yescharacteristic
1263C22#348811yescharacteristic
1264C22#350511yescharacteristic
1265C22#350811yescharacteristic
1266C22#351411yescharacteristic
1267C22#351411yescharacteristic
1268C22#351411yescharacteristic
1269C22#351411yescharacteristic
1270C22#351411yescharacteristic
1271C22#351411yescharacteristic
1272C22#351911yescharacteristic
1273C22#352111yescharacteristic
1274C22#354311yescharacteristic
1275C22#354611yescharacteristic
1276C22#354611yescharacteristic
1277C22#355111yescharacteristic
1278C22#355811yescharacteristic
1279C22#355811yescharacteristic
1280C22#356211yescharacteristic
1281C22#356211yescharacteristic
1282C4—24no—
1283C4—42no—
1284C4—44no—
1285C4—42no—
1286C4—42no—
1287C4—42no—
1288C4—44no—
1289C4—42no—
1290C4—42no—
1291C4—42no—
1292C4—42no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—81no—
1297C4—82no—
1298C4—81no—
1299C4—82no—
1300C4—82no—
1301C4#232118yes—
1302C2—48no—
1303C2—44no—
1304C2—84no—
1305C2C2×#232111yescharacteristic
1306C2C4×#54611yescharacteristic
1307C2#3424011yescharacteristic
1308C2#3429211yescharacteristic
1309C2#3432011yescharacteristic
1310C2#3443811yescharacteristic
1311C2#3449511yescharacteristic
1312C2#3890611yescharacteristic
1313C2#3891011yescharacteristic
1314C2#3902411yescharacteristic
1315C2#3903411yescharacteristic
1316C2#3988111yescharacteristic
1317C2#3988811yescharacteristic
1318C2#4004911yescharacteristic
1319C2#4005611yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC24×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
3. C2×C4×#124C2semidirect
4. #14700C2semidirect
5. #14539C2semidirect
6. #14527C2semidirect
7. #14365C2semidirect
8. #14365C2semidirect
9. #14303C2semidirect
10. #14199C2semidirect
11. #14153C2semidirect
12. #14027C2semidirect
13. #14026C2semidirect
14. #14018C2semidirect
15. #14002C2semidirect
16. #13997C2semidirect
17. #13991C2semidirect
18. #13969C2semidirect
20. #13875C2semidirect
21. #13820C2semidirect
22. #13775C2semidirect
23. C4×#388C2semidirect
28. C22×C4×Q8C22semidirect
32. #2435C4semidirect
37. C2×#391C22semidirect
38. C2×#391C22semidirect
39. C2×#391C22semidirect
48. C2×#389C22semidirect
51. C2×#388C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
57. C2×#385C22semidirect
58. C2×#382C22semidirect
66. C2×C4×C4⋊C4C22semidirect
67. C2×C4×C4⋊C4C22semidirect
68. C2×C4×C4⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C2×C4×C22⋊C4C22semidirect
75. C2×C43C22semidirect
76. #1445C22semidirect
77. #1443C22semidirect
78. #1441C22semidirect
80. #1440C22semidirect
81. #1440C22semidirect
82. #1440C22semidirect
83. #1440C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1437C22semidirect
104. #1437C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. C4⋊#95C22semidirect
113. C4⋊#95C22semidirect
114. C4⋊#95C22semidirect
115. C4⋊#95C22semidirect
116. C4⋊#95C22semidirect
117. #1434C22semidirect
118. #1434C22semidirect
119. #1434C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C4×#95C22semidirect
125. C4×#95C22semidirect
146. C2×#124C2×C4semidirect
149. C2×C22⋊Q8C2×C4semidirect
216. #394C2×C4semidirect
217. #394C2×C4semidirect
228. #390C2×C4semidirect
245. #379C2×C4semidirect
246. #379C2×C4semidirect
255. C4×C22⋊C4C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#24352
C2×D4×C22⋊C42
C2×C4×#1242
#147002
#145392
#145272
#143652
#143032
#141992
#141532
#140272
#140262
#140182
#140022
#139972
#139912
#139692
#139022
#138752
#138202
#137752
C4×#3882