Finite Group Databasebeta

← #559939

Subgroups — #559939

Order 512.

4676 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#386C211yesmaximal, characteristic
2#14681C211yesmaximal, characteristic, complemented
3#14680C211yesmaximal, characteristic, complemented
4#14666C212yesmaximal, complemented
5#14415C212yesmaximal, complemented
6#14407C212yesmaximal, complemented
7#14376C212yesmaximal, complemented
8#14375C212yesmaximal, complemented
9#14374C212yesmaximal, complemented
10#14373C212yesmaximal, complemented
11#13903C211yesmaximal, characteristic, complemented
12#13902C211yesmaximal, characteristic
13#13883C211yesmaximal, characteristic, complemented
14#13883C211yesmaximal, characteristic, complemented
15#13878C211yesmaximal, characteristic, complemented
16#13877C211yesmaximal, characteristic, complemented
17#13874C211yesmaximal, characteristic, complemented
18#13873C211yesmaximal, characteristic, complemented
19#13869C211yesmaximal, characteristic, complemented
20#13868C211yesmaximal, characteristic, complemented
21#13868C211yesmaximal, characteristic, complemented
22#13867C211yesmaximal, characteristic
23#13832C212yesmaximal, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#117C2211yescharacteristic
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C2×#390C2212yes—
32C2×#390C2212yes—
33C2×#388C2212yescomplemented
34C2×#386C4116yescomplemented
35C2×#386C2212yes—
36C2×#386C2212yes—
37C2×#386C2211yescharacteristic
38C2×#386C2211yescharacteristic
39C2×#386C2211yescharacteristic
40C2×#386C2211yescharacteristic
41C2×#386C2211yescharacteristic
42C2×#386C2211yescharacteristic
43C2×#386C2211yescharacteristic
44C2×#386C2211yescharacteristic
45C2×#385C2212yescomplemented
46C2×#381C2211yescharacteristic
47C2×#381C2211yescharacteristic
48C2×#381C2211yescharacteristic
49C2×#381C2212yescomplemented
50C2×#381C2212yescomplemented
51C2×#380C2211yescharacteristic
52C2×#380C2211yescharacteristic
53C2×#380C2211yescharacteristic
54C2×#380C2211yescharacteristic
55C2×#380C2212yescomplemented
56C2×#380C2212yescomplemented
57C2×#379C2211yescharacteristic
58C2×#379C2211yescharacteristic
59C2×#379C2211yescharacteristic
60C2×#379C2211yescharacteristic
61C2×#379C2211yescharacteristic
62C2×#379C2211yescharacteristic
63C2×#379C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C22×#95C2211yescharacteristic
67C22×#95C2211yescharacteristic
68#1444C2212yescomplemented
69#1443C2212yescomplemented
70#1443C2212yescomplemented
71#1443C2212yescomplemented
72#1442C2212yescomplemented
73#1442C2212yescomplemented
74#1442C2212yescomplemented
75#1442C2212yescomplemented
76#1440C2212yescomplemented
77#1440C2212yescomplemented
78#1440C2212yescomplemented
79#1439C2212yescomplemented
80#1439C2212yescomplemented
81#1439C2212yescomplemented
82#1439C2212yescomplemented
83#1439C2212yescomplemented
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1439C2212yescomplemented
87#1439C2212yescomplemented
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1438C2212yes—
92#1437C2212yescomplemented
93#1437C2212yescomplemented
94#1437C2212yescomplemented
95#1437C2212yescomplemented
96#1437C2212yescomplemented
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1436C2212yescomplemented
100#1436C2212yescomplemented
101#1436C2212yescomplemented
102#1436C2212yescomplemented
103#1436C2212yescomplemented
104#1434C2212yescomplemented
105#1434C2212yescomplemented
106#1434C2212yescomplemented
107C22⋊#95C2211yescharacteristic
108C22⋊#95C2211yescharacteristic
109C22⋊#95C2211yescharacteristic
110C22⋊#95C2211yescharacteristic
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2212yescomplemented
118C22⋊#95C2212yescomplemented
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C26C2311yescharacteristic
125C26C2311yescharacteristic
126C23×D4—28no—
127C23×D4—42no—
128C23×D4—42no—
129C23×D4—44no—
130C23×D4C2×C418yes—
131C23×D4C2311yescharacteristic
132C23×D4C2311yescharacteristic
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C24×C4—44no—
136C24×C4—42no—
137C24×C4—42no—
138C24×C4—44no—
139C24×C4C2×C418yescomplemented
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C2×#117—42no—
151C2×#117—42no—
152C2×#117—42no—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C22⋊C4—44no—
159C22×C22⋊C4—42no—
160C22×C22⋊C4—42no—
161C22×C22⋊C4—42no—
162C22×C22⋊C4—42no—
163C22×C22⋊C4—42no—
164C22×C22⋊C4—42no—
165C22×C22⋊C4—42no—
166C22×C22⋊C4C2×C418yes—
167C22×C22⋊C4C2×C418yes—
168C22×C22⋊C4C2×C418yescomplemented
169C22×C22⋊C4C2311yescharacteristic
170C22×C22⋊C4C2311yescharacteristic
171C22×C22⋊C4C2311yescharacteristic
172C22×C22⋊C4C2311yescharacteristic
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2311yescharacteristic
178C22×C22⋊C4C2311yescharacteristic
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C42C2312yes—
205C22×C42C2312yes—
206C22×C42C2312yes—
207#390—28no—
208#390—44no—
209#388—44no—
210#386—28no—
211#386—44no—
212#386C2×C418yes—
213#386C2×C418yes—
214#386C2×C418yes—
215#386C2×C418yes—
216#386C2×C418yescomplemented
217#386C2×C418yescomplemented
218#386C2×C418yescomplemented
219#386C2×C418yescomplemented
220#385—44no—
221#381—44no—
222#381—42no—
223#381—42no—
224#381—42no—
225#381—44no—
226#380—42no—
227#380—42no—
228#380—42no—
229#380—42no—
230#380—44no—
231#380—44no—
232#379—42no—
233#379—42no—
234#379—42no—
235#379—42no—
236#379—42no—
237#379—42no—
238#379—42no—
239C4×C22⋊C4—42no—
240C4×C22⋊C4—42no—
241C2×#95C2×C418yescomplemented
242C2×#95C2×C418yescomplemented
243C2×#95C2312yes—
244C2×#95C2312yes—
245C2×#95C2312yes—
246C2×#95C2312yes—
247C2×#95C2312yes—
248C2×#95C2312yes—
249C2×#95C2312yes—
250C2×#95C2312yes—
251C2×#95C2312yes—
252C2×#95C2312yes—
253C2×#95C2312yes—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2312yes—
259C2×#95C2312yes—
260C2×#95C2312yes—
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×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C25—24no—
284C25—22no—
285C25—22no—
286C25—24no—
287C25—24no—
288C25—22no—
289C25—22no—
290C25—22no—
291C25—22no—
292C25—22no—
293C25—22no—
294C25—22no—
295C25—22no—
296C25—22no—
297C25—22no—
298C25—42no—
299C25—42no—
300C25—42no—
301C25—42no—
302C25—42no—
303C25C22×C414yes—
304C25C22×C414yes—
305C25C2411yescharacteristic
306C25C2411yescharacteristic
307C25C2411yescharacteristic
308C25C2411yescharacteristic
309C25C2411yescharacteristic
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—232no—
315C22×D4—24no—
316C22×D4—416no—
317C22×D4—41no—
318C22×D4—41no—
319C22×D4—42no—
320C22×D4—41no—
321C22×D4—41no—
322C22×D4—41no—
323C22×D4—41no—
324C22×D4—41no—
325C22×D4—41no—
326C22×D4—42no—
327C22×D4—416no—
328C22×D4—432no—
329C22×D4—432no—
330C22×D4C22×C414yes—
331C22×D4C22×C414yes—
332C22×D4C22×C414yes—
333C22×D4C22×C414yes—
334C22×D4#4118yes—
335C23×C4—22no—
336C23×C4—22no—
337C23×C4—22no—
338C23×C4—22no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—22no—
342C23×C4—24no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—22no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—24no—
352C23×C4—24no—
353C23×C4—24no—
354C23×C4—24no—
355C23×C4—24no—
356C23×C4—416no—
357C23×C4—416no—
358C23×C4—416no—
359C23×C4—42no—
360C23×C4—42no—
361C23×C4—41no—
362C23×C4—41no—
363C23×C4—41no—
364C23×C4—41no—
365C23×C4—42no—
366C23×C4—42no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—41no—
370C23×C4—41no—
371C23×C4—42no—
372C23×C4—41no—
373C23×C4—41no—
374C23×C4—42no—
375C23×C4—42no—
376C23×C4—42no—
377C23×C4—42no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—432no—
384C23×C4—432no—
385C23×C4C22×C414yes—
386C23×C4C22×C414yes—
387C23×C4C22×C414yes—
388C23×C4C22×C414yes—
389C23×C4C22×C414yes—
390C23×C4C22×C414yes—
391C23×C4C22×C414yes—
392C23×C4C22×C414yes—
393C23×C4C22×C414yes—
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412#117—416no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—42no—
417C2×C4⋊C4—42no—
418C2×C4⋊C4—42no—
419C2×C4⋊C4—42no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4—42no—
424C2×C4⋊C4—42no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4—42no—
428C2×C22⋊C4—24no—
429C2×C22⋊C4—24no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—22no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—22no—
441C2×C22⋊C4—22no—
442C2×C22⋊C4—22no—
443C2×C22⋊C4—22no—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—22no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—24no—
456C2×C22⋊C4—24no—
457C2×C22⋊C4—24no—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—416no—
466C2×C22⋊C4—416no—
467C2×C22⋊C4—416no—
468C2×C22⋊C4—41no—
469C2×C22⋊C4—41no—
470C2×C22⋊C4—41no—
471C2×C22⋊C4—41no—
472C2×C22⋊C4—41no—
473C2×C22⋊C4—41no—
474C2×C22⋊C4—41no—
475C2×C22⋊C4—41no—
476C2×C22⋊C4—41no—
477C2×C22⋊C4—41no—
478C2×C22⋊C4—42no—
479C2×C22⋊C4—42no—
480C2×C22⋊C4—41no—
481C2×C22⋊C4—41no—
482C2×C22⋊C4—41no—
483C2×C22⋊C4—41no—
484C2×C22⋊C4—41no—
485C2×C22⋊C4—41no—
486C2×C22⋊C4—42no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—416no—
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⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
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⋊C4C22×C414yes—
522C2×C22⋊C4C22×C414yes—
523C2×C22⋊C4C22×C414yes—
524C2×C22⋊C4C22×C414yes—
525C2×C22⋊C4C22×C414yes—
526C2×C22⋊C4C22×C414yes—
527C2×C22⋊C4C22×C414yes—
528C2×C22⋊C4C22×C414yes—
529C2×C22⋊C4C22×C414yes—
530C2×C22⋊C4C22×C414yes—
531C2×C22⋊C4C22×C414yes—
532C2×C22⋊C4C22×C414yes—
533C2×C42—24no—
534C2×C42—42no—
535C2×C42—42no—
536C2×C42—42no—
537C2×C42—42no—
538C2×C42—42no—
539C2×C42—42no—
540C2×C42—42no—
541C2×C42—42no—
542#95—24no—
543#95—24no—
544#95—24no—
545#95—24no—
546#95—42no—
547#95—42no—
548#95—42no—
549#95—42no—
550#95—42no—
551#95—42no—
552#95—42no—
553#95—42no—
554#95—42no—
555#95—42no—
556#95—42no—
557#95—42no—
558#95—42no—
559#95—42no—
560#95—42no—
561#95—42no—
562#95—42no—
563#95—42no—
564#95—42no—
565#95—42no—
566#95—42no—
567#95—42no—
568#95—42no—
569#95—42no—
570#95—42no—
571#95—42no—
572#95—42no—
573#95—42no—
574#95C22×C414yes—
575#95C22×C414yes—
576#95C22×C414yes—
577#95C22×C414yes—
578#95C22×C414yes—
579#95C22×C414yes—
580#95C22×C414yes—
581#95C22×C414yes—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—216no—
587C24—216no—
588C24—28no—
589C24—28no—
590C24—28no—
591C24—22no—
592C24—22no—
593C24—21no—
594C24—21no—
595C24—21no—
596C24—22no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—22no—
610C24—22no—
611C24—21no—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—28no—
619C24—28no—
620C24—28no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—22no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—28no—
632C24—28no—
633C24—28no—
634C24—44no—
635C24—44no—
636C24—44no—
637C24—44no—
638C24—44no—
639C24—48no—
640C24—48no—
641C24—48no—
642C24—48no—
643C24—48no—
644C24—48no—
645C24—48no—
646C24—48no—
647C24—48no—
648C24—48no—
649C24—48no—
650C24—48no—
651C24—48no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—44no—
656C24—44no—
657C24—44no—
658C24—44no—
659C24—44no—
660C24—44no—
661C24—44no—
662C24—44no—
663C24—84no—
664C24—84no—
665C24—84no—
666C24—84no—
667C24—84no—
668C24—84no—
669C24C23×C412yes—
670C24C23×C412yes—
671C24C23×C412yes—
672C24C23×C412yes—
673C24C23×C412yes—
674C24C2×#4114yes—
675C24C2×#4114yes—
676C24H(5,𝔽2)14yes—
677C24H(5,𝔽2)12yes—
678C24H(5,𝔽2)12yes—
679C24H(5,𝔽2)12yes—
680C24H(5,𝔽2)12yes—
681C24H(5,𝔽2)12yes—
682C242−1+412yes—
683C24C2511yescharacteristic
684C2×D4—28no—
685C2×D4—28no—
686C2×D4—28no—
687C2×D4—28no—
688C2×D4—28no—
689C2×D4—44no—
690C2×D4—44no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C2×D4—48no—
699C2×D4—48no—
700C2×D4—48no—
701C2×D4—4128no—
702C2×D4—48no—
703C2×D4—48no—
704C2×D4#117116yescomplemented
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—28no—
712C22×C4—28no—
713C22×C4—28no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—28no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—22no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—22no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—28no—
758C22×C4—28no—
759C22×C4—28no—
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—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
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—44no—
817C22×C4—44no—
818C22×C4—44no—
819C22×C4—44no—
820C22×C4—44no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—44no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—48no—
833C22×C4—48no—
834C22×C4—48no—
835C22×C4—48no—
836C22×C4—48no—
837C22×C4—48no—
838C22×C4—48no—
839C22×C4—48no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—4128no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—44no—
848C22×C4—44no—
849C22×C4—48no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4—84no—
854C22×C4—84no—
855C22×C4—84no—
856C22×C4—84no—
857C22×C4—84no—
858C22×C4C23×C412yes—
859C22×C4C23×C412yes—
860C22×C4C23×C412yes—
861C22×C4C23×C412yes—
862C22×C4C23×C412yes—
863C22×C4C23×C412yes—
864C22×C4C23×C412yes—
865C22×C4C23×C412yes—
866C22×C4C23×C412yes—
867C22×C4C23×C412yes—
868C22×C4C2×#4114yes—
869C22×C4H(5,𝔽2)14yes—
870C4⋊C4—48no—
871C4⋊C4—84no—
872C4⋊C4—84no—
873C4⋊C4—84no—
874C4⋊C4—84no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—48no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—84no—
897C22⋊C4—84no—
898C22⋊C4—84no—
899C22⋊C4—84no—
900C22⋊C4—84no—
901C22⋊C4—84no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4—84no—
909C22⋊C4—84no—
910C42—48no—
911C42—84no—
912C42—84no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—24no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—24no—
928C23—24no—
929C23—232no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—24no—
949C23—24no—
950C23—24no—
951C23—24no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—24no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—416no—
974C23—416no—
975C23—416no—
976C23—416no—
977C23—416no—
978C23—416no—
979C23—416no—
980C23—416no—
981C23—432no—
982C23—432no—
983C23—432no—
984C23—432no—
985C23—416no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
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—42no—
1014C23—42no—
1015C23—42no—
1016C23—416no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—88no—
1034C23—88no—
1035C23—88no—
1036C23—816no—
1037C23—816no—
1038C23—816no—
1039C23—816no—
1040C23C2×#11714yes—
1041C23C2×#11714yes—
1042C23#51814yes—
1043C23#51814yes—
1044C23#51814yes—
1045C23#52014yes—
1046C23#56014yes—
1047C23#56014yes—
1048C23#56214yes—
1049C23#56214yes—
1050C23C24×C411yescharacteristic
1051C23C22×#4112yes—
1052C23C2×H(5,𝔽2)11yescharacteristic
1053C23C2×H(5,𝔽2)11yescharacteristic
1054C23C2×H(5,𝔽2)12yes—
1055C23C2×H(5,𝔽2)11yescharacteristic
1056C23C2×H(5,𝔽2)11yescharacteristic
1057C23C2×H(5,𝔽2)12yes—
1058C23C2×H(5,𝔽2)11yescharacteristic
1059C23C2×2−1+411yescharacteristic
1060C23#58512yes—
1061D4—416no—
1062D4—416no—
1063D4—416no—
1064D4—416no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—24no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—416no—
1098C2×C4—416no—
1099C2×C4—416no—
1100C2×C4—416no—
1101C2×C4—416no—
1102C2×C4—416no—
1103C2×C4—416no—
1104C2×C4—416no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—42no—
1116C2×C4—42no—
1117C2×C4—42no—
1118C2×C4—42no—
1119C2×C4—42no—
1120C2×C4—42no—
1121C2×C4—42no—
1122C2×C4—42no—
1123C2×C4—42no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
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—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—88no—
1182C2×C4—816no—
1183C2×C4C2×#11714yes—
1184C2×C4#51814yes—
1185C22—24no—
1186C22—24no—
1187C22—24no—
1188C22—24no—
1189C22—24no—
1190C22—24no—
1191C22—28no—
1192C22—28no—
1193C22—28no—
1194C22—28no—
1195C22—24no—
1196C22—24no—
1197C22—24no—
1198C22—24no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—464no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—44no—
1218C22—44no—
1219C22—44no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—44no—
1225C22—44no—
1226C22—44no—
1227C22—44no—
1228C22—44no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—832no—
1237C22—82no—
1238C22—82no—
1239C22—82no—
1240C22—82no—
1241C22#237718yes—
1242C22C22×#11711yescharacteristic
1243C22C2×#51811yescharacteristic
1244C22C2×#51811yescharacteristic
1245C22C2×#51811yescharacteristic
1246C22C2×#51811yescharacteristic
1247C22C2×#52011yescharacteristic
1248C22#342811yescharacteristic
1249C22#349012yes—
1250C22#349012yes—
1251C22#351312yes—
1252C22#351312yes—
1253C22#351912yes—
1254C22#352012yes—
1255C22C2×#56011yescharacteristic
1256C22C2×#56011yescharacteristic
1257C22C2×#56211yescharacteristic
1258C22C2×#56211yescharacteristic
1259C22#353212yes—
1260C22#353212yes—
1261C22#353412yes—
1262C22#353512yes—
1263C22#354212yes—
1264C22#354212yes—
1265C4—24no—
1266C4—24no—
1267C4—42no—
1268C4—42no—
1269C4—42no—
1270C4—42no—
1271C4—42no—
1272C4—42no—
1273C4—42no—
1274C4—42no—
1275C4—82no—
1276C4—82no—
1277C4—82no—
1278C4—82no—
1279C4—82no—
1280C4—82no—
1281C4—82no—
1282C4—82no—
1283C2—28no—
1284C2—44no—
1285C2—44no—
1286C2—44no—
1287C2—82no—
1288C2#3417611yescharacteristic
1289C2#3419011yescharacteristic
1290C2#3419411yescharacteristic
1291C2C2×#237711yescharacteristic
1292C2#3435611yescharacteristic
1293C2#3436311yescharacteristic
1294C2#3437611yescharacteristic
1295C2#4552812yes—
1296C2#4552912yes—
1297C2#4556212yes—
1298C2#4556312yes—
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
2. #14681C2semidirect
3. #14680C2semidirect
4. #14666C2semidirect
5. #14415C2semidirect
6. #14407C2semidirect
7. #14376C2semidirect
8. #14375C2semidirect
9. #14374C2semidirect
10. #14373C2semidirect
11. #13903C2semidirect
13. #13883C2semidirect
14. #13883C2semidirect
15. #13878C2semidirect
16. #13877C2semidirect
17. #13874C2semidirect
18. #13873C2semidirect
19. #13869C2semidirect
20. #13868C2semidirect
21. #13868C2semidirect
23. #13832C2semidirect
33. C2×#388C22semidirect
34. C2×#386C4semidirect
45. C2×#385C22semidirect
49. C2×#381C22semidirect
50. C2×#381C22semidirect
55. C2×#380C22semidirect
56. C2×#380C22semidirect
68. #1444C22semidirect
69. #1443C22semidirect
70. #1443C22semidirect
71. #1443C22semidirect
72. #1442C22semidirect
73. #1442C22semidirect
74. #1442C22semidirect
75. #1442C22semidirect
76. #1440C22semidirect
77. #1440C22semidirect
78. #1440C22semidirect
79. #1439C22semidirect
80. #1439C22semidirect
81. #1439C22semidirect
82. #1439C22semidirect
83. #1439C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
92. #1437C22semidirect
93. #1437C22semidirect
94. #1437C22semidirect
95. #1437C22semidirect
96. #1437C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1436C22semidirect
100. #1436C22semidirect
101. #1436C22semidirect
102. #1436C22semidirect
103. #1436C22semidirect
104. #1434C22semidirect
105. #1434C22semidirect
106. #1434C22semidirect
117. C22⋊#95C22semidirect
118. C22⋊#95C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
139. C24×C4C2×C4semidirect
168. C22×C22⋊C4C2×C4semidirect
216. #386C2×C4semidirect
217. #386C2×C4semidirect
218. #386C2×C4semidirect
219. #386C2×C4semidirect
241. C2×#95C2×C4semidirect
242. C2×#95C2×C4semidirect
704. C2×D4#117semidirect

Maximal subgroups

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

subgroupindex
C22×#3862
#146812
#146802
#146662
#144152
#144072
#143762
#143752
#143742
#143732
#139032
#139022
#138832
#138782
#138772
#138742
#138732
#138692
#138682
#138672
#138322