Finite Group Databasebeta

← #530655

Subgroups — #530655

Order 512.

5136 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2342C211yesmaximal, characteristic, complemented
2C22×#386C211yesmaximal, characteristic
3C2×#2280C211yesmaximal, characteristic, complemented
4#14680C211yesmaximal, characteristic, complemented
5#14410C212yesmaximal, complemented
6#14401C212yesmaximal, complemented
7#14374C212yesmaximal, complemented
8#14373C212yesmaximal, complemented
9#14267C212yesmaximal, complemented
10#14071C212yesmaximal, complemented
11#14064C212yesmaximal, complemented
12#13908C211yesmaximal, characteristic, complemented
13#13903C211yesmaximal, characteristic, complemented
14#13903C211yesmaximal, characteristic, complemented
15#13902C211yesmaximal, characteristic
16#13878C211yesmaximal, characteristic, complemented
17#13877C211yesmaximal, characteristic, complemented
18#13874C211yesmaximal, characteristic, complemented
19#13873C211yesmaximal, characteristic, complemented
20#13868C211yesmaximal, characteristic, complemented
21#13867C211yesmaximal, characteristic
22#13802C211yesmaximal, characteristic, complemented
23#13791C212yesmaximal, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C22×#117C2212yescomplemented
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32#2342—28no—
33C2×#390C2212yes—
34C2×#390C2212yes—
35C2×#388C2212yescomplemented
36C2×#388C2212yescomplemented
37C2×#388C2212yescomplemented
38C2×#386C4116yescomplemented
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2211yescharacteristic
42C2×#386C2211yescharacteristic
43C2×#386C2211yescharacteristic
44C2×#386C2211yescharacteristic
45C2×#386C2211yescharacteristic
46C2×#386C2211yescharacteristic
47C2×#386C2211yescharacteristic
48C2×#386C2211yescharacteristic
49C2×#385C2212yescomplemented
50C2×#385C2212yescomplemented
51#2280—28no—
52C2×#381C2211yescharacteristic
53C2×#381C2211yescharacteristic
54C2×#381C2211yescharacteristic
55C2×#381C2212yescomplemented
56C2×#380C2211yescharacteristic
57C2×#380C2211yescharacteristic
58C2×#380C2211yescharacteristic
59C2×#380C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2211yescharacteristic
62C2×#380C2212yescomplemented
63C2×#380C2212yescomplemented
64C2×#380C2212yescomplemented
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic
67C2×#379C2211yescharacteristic
68C2×#379C2211yescharacteristic
69C2×#379C2211yescharacteristic
70C2×#379C2211yescharacteristic
71C2×#379C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C4×C22⋊C4C2211yescharacteristic
74C2×C4×C22⋊C4C2211yescharacteristic
75C2×C4×C22⋊C4C2211yescharacteristic
76C2×C4×C22⋊C4C2212yescomplemented
77C2×C4×C22⋊C4C2212yescomplemented
78C22×#95C2211yescharacteristic
79C22×#95C2211yescharacteristic
80#1444C2212yescomplemented
81#1444C2212yescomplemented
82#1443C2212yescomplemented
83#1442C2212yescomplemented
84#1442C2212yescomplemented
85#1442C2212yescomplemented
86#1440C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1438C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1437C2212yescomplemented
104#1437C2212yescomplemented
105#1437C2212yescomplemented
106#1437C2212yescomplemented
107#1436C2212yescomplemented
108#1436C2212yescomplemented
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1434C2212yescomplemented
115#1434C2212yescomplemented
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C4×#95C2212yescomplemented
126C26C2311yescharacteristic
127C26C2311yescharacteristic
128C23×D4—28no—
129C23×D4—42no—
130C23×D4—42no—
131C23×D4—44no—
132C23×D4C2×C418yes—
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C24×C4—24no—
138C24×C4—24no—
139C24×C4—44no—
140C24×C4—44no—
141C24×C4C2×C418yescomplemented
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C2×#117—24no—
153C2×#117—28no—
154C2×#117—42no—
155C2×#117—42no—
156C2×#117—44no—
157C2×#117—44no—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2312yes—
160C22×C4⋊C4C2312yes—
161C22×C4⋊C4C2312yes—
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2312yes—
165C22×C22⋊C4—24no—
166C22×C22⋊C4—24no—
167C22×C22⋊C4—24no—
168C22×C22⋊C4—44no—
169C22×C22⋊C4—42no—
170C22×C22⋊C4—42no—
171C22×C22⋊C4—42no—
172C22×C22⋊C4—42no—
173C22×C22⋊C4C2×C418yes—
174C22×C22⋊C4C2×C418yes—
175C22×C22⋊C4C2×C418yescomplemented
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2311yescharacteristic
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C42C2312yes—
212C22×C42C2312yes—
213C22×C42C2312yes—
214C22×C42C2312yes—
215C22×C42C2312yes—
216#390—28no—
217#390—44no—
218#388—28no—
219#388—28no—
220#388—44no—
221#386—28no—
222#386—44no—
223#386C2×C418yes—
224#386C2×C418yes—
225#386C2×C418yes—
226#386C2×C418yes—
227#386C2×C418yescomplemented
228#386C2×C418yescomplemented
229#386C2×C418yescomplemented
230#386C2×C418yescomplemented
231#385—28no—
232#385—44no—
233#381—24no—
234#381—28no—
235#381—42no—
236#381—42no—
237#380—24no—
238#380—24no—
239#380—24no—
240#380—24no—
241#380—28no—
242#380—44no—
243#380—42no—
244#380—42no—
245#380—44no—
246#379—24no—
247#379—24no—
248#379—24no—
249#379—42no—
250#379—42no—
251#379—42no—
252#379—42no—
253C4×C22⋊C4—24no—
254C4×C22⋊C4—28no—
255C4×C22⋊C4—28no—
256C4×C22⋊C4—42no—
257C4×C22⋊C4—42no—
258C4×C22⋊C4D418yescomplemented
259C2×#95C2×C418yescomplemented
260C2×#95C2×C418yescomplemented
261C2×#95C2312yes—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C25—24no—
298C25—22no—
299C25—22no—
300C25—24no—
301C25—22no—
302C25—22no—
303C25—24no—
304C25—22no—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25C22×C414yes—
318C25C22×C414yes—
319C25C2411yescharacteristic
320C25C2411yescharacteristic
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C25C2411yescharacteristic
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—232no—
329C22×D4—24no—
330C22×D4—416no—
331C22×D4—41no—
332C22×D4—41no—
333C22×D4—42no—
334C22×D4—41no—
335C22×D4—41no—
336C22×D4—41no—
337C22×D4—41no—
338C22×D4—41no—
339C22×D4—41no—
340C22×D4—42no—
341C22×D4—416no—
342C22×D4—432no—
343C22×D4—432no—
344C22×D4C22×C414yes—
345C22×D4C22×C414yes—
346C22×D4C22×C414yes—
347C22×D4C22×C414yes—
348C22×D4#4118yes—
349C23×C4—24no—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—24no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—22no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—232no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—24no—
378C23×C4—416no—
379C23×C4—416no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4—42no—
386C23×C4—42no—
387C23×C4—42no—
388C23×C4—42no—
389C23×C4—42no—
390C23×C4—42no—
391C23×C4—42no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—432no—
396C23×C4—432no—
397C23×C4C22×C414yes—
398C23×C4C22×C414yes—
399C23×C4C22×C414yes—
400C23×C4C22×C414yes—
401C23×C4C22×C414yes—
402C23×C4C22×C414yes—
403C23×C4C22×C414yes—
404C23×C4C22×C414yes—
405C23×C4C22×C414yes—
406C23×C4C2×D414yes—
407C23×C4#4114yes—
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2412yes—
412C23×C4C2412yes—
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426#117—416no—
427#117—432no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—24no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—42no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—232no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
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—416no—
501C2×C22⋊C4—416no—
502C2×C22⋊C4—416no—
503C2×C22⋊C4—41no—
504C2×C22⋊C4—41no—
505C2×C22⋊C4—41no—
506C2×C22⋊C4—41no—
507C2×C22⋊C4—41no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—41no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
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⋊C4C22×C414yes—
541C2×C22⋊C4C22×C414yes—
542C2×C22⋊C4C22×C414yes—
543C2×C22⋊C4C22×C414yes—
544C2×C22⋊C4C22×C414yes—
545C2×C22⋊C4C22×C414yes—
546C2×C22⋊C4C22×C414yes—
547C2×C22⋊C4C22×C414yes—
548C2×C22⋊C4C22×C414yes—
549C2×C22⋊C4C22×C414yes—
550C2×C22⋊C4C22×C414yes—
551C2×C22⋊C4C22×C414yes—
552C2×C22⋊C4C2×D414yes—
553C2×C22⋊C4C2×D414yes—
554C2×C42—24no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—42no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42—42no—
561C2×C42—42no—
562C2×C42—42no—
563C2×C42—42no—
564C2×C42—42no—
565C2×C42—42no—
566C2×C42—42no—
567C2×C42—42no—
568C2×C42C2×D418yescomplemented
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
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#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95C22×C414yes—
597#95C22×C414yes—
598#95C22×C414yes—
599#95C22×C414yes—
600#95C22×C414yes—
601#95C22×C414yes—
602#95C22×C414yes—
603#95C22×C414yes—
604#95C2×D418yescomplemented
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—216no—
610C24—216no—
611C24—28no—
612C24—28no—
613C24—28no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—21no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—28no—
642C24—28no—
643C24—28no—
644C24—21no—
645C24—21no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—28no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—44no—
685C24—44no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24C23×C412yes—
693C24C23×C412yes—
694C24C23×C412yes—
695C24C23×C412yes—
696C24C23×C412yes—
697C24C22×D412yes—
698C24C2×#4114yes—
699C24C2×#4114yes—
700C24C2×#4112yes—
701C24H(5,𝔽2)14yes—
702C24H(5,𝔽2)12yes—
703C24H(5,𝔽2)12yes—
704C24H(5,𝔽2)12yes—
705C242−1+412yes—
706C24C2511yescharacteristic
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—4128no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4#117116yescomplemented
728C22×C4—216no—
729C22×C4—216no—
730C22×C4—28no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—28no—
745C22×C4—28no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—28no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—28no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
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—22no—
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—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
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—22no—
837C22×C4—22no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—44no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—48no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—4128no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4C4×D4116yes—
875C22×C4C23×C412yes—
876C22×C4C23×C412yes—
877C22×C4C23×C412yes—
878C22×C4C23×C412yes—
879C22×C4C23×C412yes—
880C22×C4C23×C412yes—
881C22×C4C23×C412yes—
882C22×C4C23×C412yes—
883C22×C4C23×C412yes—
884C22×C4C23×C412yes—
885C22×C4C22×D414yes—
886C22×C4C22×D414yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C2×#4114yes—
890C22×C4C2×#4112yes—
891C22×C4C2×#4112yes—
892C22×C4H(5,𝔽2)14yes—
893C4⋊C4—48no—
894C4⋊C4—48no—
895C4⋊C4—48no—
896C4⋊C4—84no—
897C4⋊C4—84no—
898C4⋊C4—84no—
899C4⋊C4—84no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—28no—
904C22⋊C4—28no—
905C22⋊C4—28no—
906C22⋊C4—28no—
907C22⋊C4—28no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—44no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C22⋊C4—44no—
924C22⋊C4—44no—
925C22⋊C4—44no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—84no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C42—48no—
936C42—48no—
937C42—48no—
938C42—84no—
939C42—84no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—24no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—232no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
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—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—416no—
1001C23—416no—
1002C23—416no—
1003C23—416no—
1004C23—416no—
1005C23—416no—
1006C23—416no—
1007C23—416no—
1008C23—432no—
1009C23—432no—
1010C23—432no—
1011C23—432no—
1012C23—416no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—416no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—88no—
1061C23—88no—
1062C23—88no—
1063C23—816no—
1064C23—816no—
1065C23—816no—
1066C23—816no—
1067C23C2×#11714yes—
1068C23C2×#11714yes—
1069C23C2×C4×D414yes—
1070C23#51814yes—
1071C23#51814yes—
1072C23#52014yes—
1073C23#53514yes—
1074C23#53714yes—
1075C23#54014yes—
1076C23#54214yes—
1077C23C24×C411yescharacteristic
1078C23C23×D411yescharacteristic
1079C23C22×#4112yes—
1080C23C22×#4111yescharacteristic
1081C23C2×H(5,𝔽2)11yescharacteristic
1082C23C2×H(5,𝔽2)11yescharacteristic
1083C23C2×H(5,𝔽2)12yes—
1084C23C2×H(5,𝔽2)12yes—
1085C23C2×H(5,𝔽2)11yescharacteristic
1086C23C2×2−1+411yescharacteristic
1087C23#58512yes—
1088D4—416no—
1089D4—416no—
1090D4—416no—
1091D4—416no—
1092C2×C4—232no—
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—24no—
1102C2×C4—24no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—24no—
1106C2×C4—24no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—416no—
1134C2×C4—416no—
1135C2×C4—416no—
1136C2×C4—416no—
1137C2×C4—416no—
1138C2×C4—416no—
1139C2×C4—416no—
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—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
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—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—88no—
1207C2×C4—816no—
1208C2×C4C2×#11714yes—
1209C2×C4C2×C4×D414yes—
1210C2×C4C2×C4×D414yes—
1211C2×C4#51814yes—
1212C22—24no—
1213C22—24no—
1214C22—24no—
1215C22—24no—
1216C22—24no—
1217C22—24no—
1218C22—28no—
1219C22—28no—
1220C22—28no—
1221C22—28no—
1222C22—24no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—464no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—832no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22#232418yes—
1269C22C22×#11711yescharacteristic
1270C22C22×C4×D411yescharacteristic
1271C22C2×#51811yescharacteristic
1272C22C2×#51811yescharacteristic
1273C22C2×#51811yescharacteristic
1274C22C2×#52011yescharacteristic
1275C22#342811yescharacteristic
1276C22C2×#53511yescharacteristic
1277C22C2×#53711yescharacteristic
1278C22C2×#54011yescharacteristic
1279C22C2×#54211yescharacteristic
1280C22D4×#4112yes—
1281C22#347512yes—
1282C22#348412yes—
1283C22#349012yes—
1284C22#349012yes—
1285C22#349012yes—
1286C22#351912yes—
1287C22#352012yes—
1288C22#353412yes—
1289C22#353512yes—
1290C22#354212yes—
1291C22#354212yes—
1292C4—24no—
1293C4—24no—
1294C4—24no—
1295C4—24no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—44no—
1303C4—44no—
1304C4—82no—
1305C4—82no—
1306C4—82no—
1307C4—82no—
1308C4—82no—
1309C4—82no—
1310C2—28no—
1311C2—44no—
1312C2—44no—
1313C2—44no—
1314C2—82no—
1315C2C2×#232411yescharacteristic
1316C2D4×#11711yescharacteristic
1317C2#3417611yescharacteristic
1318C2#3419411yescharacteristic
1319C2#3419811yescharacteristic
1320C2#3436311yescharacteristic
1321C2#3437611yescharacteristic
1322C2#3835612yes—
1323C2#3835812yes—
1324C2#3838812yes—
1325C2#3839012yes—
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
1. C2×#2342C2semidirect
3. C2×#2280C2semidirect
4. #14680C2semidirect
5. #14410C2semidirect
6. #14401C2semidirect
7. #14374C2semidirect
8. #14373C2semidirect
9. #14267C2semidirect
10. #14071C2semidirect
11. #14064C2semidirect
12. #13908C2semidirect
13. #13903C2semidirect
14. #13903C2semidirect
16. #13878C2semidirect
17. #13877C2semidirect
18. #13874C2semidirect
19. #13873C2semidirect
20. #13868C2semidirect
22. #13802C2semidirect
23. #13791C2semidirect
27. C22×#117C22semidirect
35. C2×#388C22semidirect
36. C2×#388C22semidirect
37. C2×#388C22semidirect
38. C2×#386C4semidirect
49. C2×#385C22semidirect
50. C2×#385C22semidirect
55. C2×#381C22semidirect
62. C2×#380C22semidirect
63. C2×#380C22semidirect
64. C2×#380C22semidirect
76. C2×C4×C22⋊C4C22semidirect
77. C2×C4×C22⋊C4C22semidirect
80. #1444C22semidirect
81. #1444C22semidirect
82. #1443C22semidirect
83. #1442C22semidirect
84. #1442C22semidirect
85. #1442C22semidirect
86. #1440C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1437C22semidirect
104. #1437C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1436C22semidirect
108. #1436C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1434C22semidirect
115. #1434C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C4×#95C22semidirect
141. C24×C4C2×C4semidirect
175. C22×C22⋊C4C2×C4semidirect
227. #386C2×C4semidirect
228. #386C2×C4semidirect
229. #386C2×C4semidirect
230. #386C2×C4semidirect
258. C4×C22⋊C4D4semidirect
259. C2×#95C2×C4semidirect
260. C2×#95C2×C4semidirect
568. C2×C42C2×D4semidirect
604. #95C2×D4semidirect
727. C2×D4#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23422
C22×#3862
C2×#22802
#146802
#144102
#144012
#143742
#143732
#142672
#140712
#140642
#139082
#139032
#139022
#138782
#138772
#138742
#138732
#138682
#138672
#138022
#137912