Finite Group Databasebeta

← #531126

Subgroups — #531126

Order 512.

5094 conjugacy classes of subgroups.

The subgroup lattice has 1277 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2342C211yesmaximal, characteristic, complemented
2C2×#2308C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4#14693C211yesmaximal, characteristic, complemented
5#14427C212yesmaximal, complemented
6#14391C212yesmaximal, complemented
7#14375C212yesmaximal, complemented
8#14373C212yesmaximal, complemented
9#14335C211yesmaximal, characteristic
10#14262C211yesmaximal, characteristic, complemented
11#14068C212yesmaximal, complemented
12#14064C212yesmaximal, complemented
13#13992C211yesmaximal, characteristic, complemented
14#13992C211yesmaximal, characteristic, complemented
15#13988C212yesmaximal, complemented
16#13984C212yesmaximal, complemented
17#13972C211yesmaximal, characteristic, complemented
18#13972C211yesmaximal, characteristic, complemented
19#13877C211yesmaximal, characteristic, complemented
20#13869C211yesmaximal, characteristic, complemented
21C22⋊C42C211yesmaximal, characteristic, complemented
22#13775C211yesmaximal, characteristic, complemented
23C4×#379C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#117C2211yescharacteristic, complemented
27C23×C22⋊C4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32#2342—28no—
33#2308C4116yescomplemented
34C2×#388C2211yescharacteristic, complemented
35C2×#388C2211yescharacteristic, complemented
36C2×#388C2211yescharacteristic, complemented
37C2×#388C2211yescharacteristic, complemented
38C2×#386—28no—
39C2×#386C2212yes—
40C2×#386C2212yes—
41C2×#386C2212yes—
42C2×#386C2212yes—
43C2×#386C2212yes—
44C2×#386C2212yes—
45C2×#386C2212yes—
46C2×#386C2212yes—
47C2×#385C2211yescharacteristic
48C2×#385C2211yescharacteristic
49C2×#385C2211yescharacteristic
50C2×#385C2211yescharacteristic
51C2×#385C2212yescomplemented
52C2×#385C2212yescomplemented
53C2×#381C2211yescharacteristic
54C2×#381C2211yescharacteristic
55C2×#381C2211yescharacteristic
56C2×#381C2211yescharacteristic
57C2×#381C2211yescharacteristic, complemented
58C2×#381C2212yescomplemented
59C2×#380C2211yescharacteristic, complemented
60C2×#380C2212yescomplemented
61C2×#379C2211yescharacteristic
62C2×#379C2211yescharacteristic
63C2×#379C2211yescharacteristic
64C2×#379C2211yescharacteristic
65C2×#379C2211yescharacteristic
66C2×#379C2211yescharacteristic
67C2×C4×C22⋊C4C2211yescharacteristic
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic, complemented
72C2×C4×C22⋊C4C2212yescomplemented
73C2×C4×C22⋊C4C2212yescomplemented
74C2×C4×C22⋊C4C2212yescomplemented
75C22×#95C2211yescharacteristic
76C22×#95C2211yescharacteristic
77#1443C2212yescomplemented
78#1443C2212yescomplemented
79#1443C2212yescomplemented
80#1443C2212yescomplemented
81#1442C2212yescomplemented
82#1442C2212yescomplemented
83#1442C2212yescomplemented
84#1442C2212yescomplemented
85#1440C2212yescomplemented
86#1440C2212yescomplemented
87#1439C2212yescomplemented
88#1439C2212yescomplemented
89#1439C2212yescomplemented
90#1439C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1438C2212yes—
94#1438C2212yes—
95#1438C2212yes—
96#1438C2212yes—
97#1437C2212yescomplemented
98#1437C2212yescomplemented
99#1437C2212yescomplemented
100#1437C2212yescomplemented
101#1437C2212yescomplemented
102#1437C2212yescomplemented
103#1436C2212yescomplemented
104#1436C2212yescomplemented
105#1436C2212yescomplemented
106#1436C2212yescomplemented
107#1434C2212yescomplemented
108#1434C2212yescomplemented
109#1434C2212yescomplemented
110#1434C2212yescomplemented
111C22⋊#95C2211yescharacteristic
112C22⋊#95C2211yescharacteristic
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C26C2311yescharacteristic
127C26C2311yescharacteristic
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—42no—
134C23×D4C2×C418yes—
135C23×D4C2312yes—
136C23×D4C2312yes—
137C24×C4—24no—
138C24×C4—24no—
139C24×C4—44no—
140C24×C4—44no—
141C24×C4—42no—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2312yes—
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152C2×#117—24no—
153C2×#117—44no—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2311yescharacteristic
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2312yes—
160C22×C22⋊C4—24no—
161C22×C22⋊C4—24no—
162C22×C22⋊C4—24no—
163C22×C22⋊C4—24no—
164C22×C22⋊C4—24no—
165C22×C22⋊C4—44no—
166C22×C22⋊C4—44no—
167C22×C22⋊C4—42no—
168C22×C22⋊C4—42no—
169C22×C22⋊C4—42no—
170C22×C22⋊C4C2×C418yescomplemented
171C22×C22⋊C4C2×C418yescomplemented
172C22×C22⋊C4D418yes—
173C22×C22⋊C4C2311yescharacteristic
174C22×C22⋊C4C2311yescharacteristic
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2312yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2311yescharacteristic
182C22×C22⋊C4C2311yescharacteristic
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C42C2311yescharacteristic
207C22×C42C2311yescharacteristic
208C22×C42C2311yescharacteristic
209C22×C42C2312yes—
210C22×C42C2311yescharacteristic
211C22×C42C2312yes—
212#388—24no—
213#388—24no—
214#388—24no—
215#388—24no—
216#386—28no—
217#386—28no—
218#386—28no—
219#386—28no—
220#386C2×C4116yescomplemented
221#386C2×C4116yescomplemented
222#386C2×C4116yescomplemented
223#386C2×C4116yescomplemented
224#385—24no—
225#385—24no—
226#385—44no—
227#385—44no—
228#385—42no—
229#385—42no—
230#381—24no—
231#381—44no—
232#381—42no—
233#381—42no—
234#381C2×C418yescomplemented
235#381C2×C418yescomplemented
236#380—24no—
237#380—44no—
238#379—24no—
239#379—24no—
240#379—24no—
241#379—24no—
242#379C2×C418yes—
243#379C2×C418yes—
244C4×C22⋊C4—24no—
245C4×C22⋊C4—24no—
246C4×C22⋊C4—24no—
247C4×C22⋊C4—44no—
248C4×C22⋊C4—44no—
249C4×C22⋊C4—44no—
250C4×C22⋊C4—42no—
251C4×C22⋊C4—42no—
252C2×#95—24no—
253C2×#95—24no—
254C2×#95C2312yes—
255C2×#95C2312yes—
256C2×#95C2312yes—
257C2×#95C2312yes—
258C2×#95C2311yescharacteristic
259C2×#95C2311yescharacteristic
260C2×#95C2311yescharacteristic
261C2×#95C2311yescharacteristic
262C2×#95C2312yes—
263C2×#95C2311yescharacteristic
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2311yescharacteristic
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×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C25—22no—
295C25—22no—
296C25—22no—
297C25—22no—
298C25—22no—
299C25—22no—
300C25—22no—
301C25—22no—
302C25—42no—
303C25—42no—
304C25—42no—
305C25—42no—
306C25—42no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25C22×C414yes—
311C25C22×C414yes—
312C25C2×D414yes—
313C25#4114yes—
314C25#4114yes—
315C25#4114yes—
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C25C2412yes—
319C25C2411yescharacteristic
320C22×D4—232no—
321C22×D4—232no—
322C22×D4—24no—
323C22×D4—24no—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—416no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—416no—
336C22×D4—416no—
337C22×D4—416no—
338C22×D4—416no—
339C22×D4C22×C418yes—
340C22×D4C22×C418yes—
341C23×C4—22no—
342C23×C4—22no—
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—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—24no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—24no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—42no—
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—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—416no—
394C23×C4—416no—
395C23×C4—432no—
396C23×C4—416no—
397C23×C4—432no—
398C23×C4C22×C414yes—
399C23×C4C22×C414yescomplemented
400C23×C4C22×C414yescomplemented
401C23×C4C22×C418yescomplemented
402C23×C4C2×D414yes—
403C23×C4C2×D414yes—
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2412yes—
411C23×C4C2411yescharacteristic
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2412yes—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2411yescharacteristic
423#117—416no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—42no—
431C2×C4⋊C4—42no—
432C2×C4⋊C4—42no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—42no—
438C2×C22⋊C4—232no—
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—24no—
452C2×C22⋊C4—24no—
453C2×C22⋊C4—24no—
454C2×C22⋊C4—24no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
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—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—416no—
484C2×C22⋊C4—416no—
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⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—416no—
510C2×C22⋊C4—416no—
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⋊C4C22×C414yes—
520C2×C22⋊C4C22×C414yes—
521C2×C22⋊C4C22×C414yes—
522C2×C22⋊C4C22×C414yes—
523C2×C22⋊C4C22×C418yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C22×C418yes—
526C2×C22⋊C4C22×C418yes—
527C2×C22⋊C4C22×C414yescomplemented
528C2×C22⋊C4C22×C414yescomplemented
529C2×C22⋊C4C22×C418yescomplemented
530C2×C22⋊C4C2×D414yes—
531C2×C22⋊C4C2×D414yes—
532C2×C22⋊C4C2×D414yes—
533C2×C22⋊C4C2×D414yes—
534C2×C42—22no—
535C2×C42—22no—
536C2×C42—24no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—24no—
540C2×C42—42no—
541C2×C42—42no—
542C2×C42—42no—
543C2×C42—42no—
544C2×C42—42no—
545C2×C42—42no—
546C2×C42—42no—
547C2×C42—42no—
548#95—24no—
549#95—24no—
550#95—24no—
551#95—24no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—24no—
561#95—24no—
562#95—24no—
563#95—24no—
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#95—42no—
575#95—42no—
576#95—42no—
577#95—42no—
578#95—42no—
579#95—42no—
580#95—42no—
581#95—42no—
582#95—42no—
583#95—42no—
584#95C22×C418yescomplemented
585#95C22×C418yescomplemented
586#95C22×C418yescomplemented
587#95C22×C418yescomplemented
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—28no—
593C24—28no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—28no—
598C24—22no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—21no—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—22no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—28no—
627C24—28no—
628C24—28no—
629C24—28no—
630C24—28no—
631C24—28no—
632C24—48no—
633C24—48no—
634C24—48no—
635C24—48no—
636C24—48no—
637C24—48no—
638C24—44no—
639C24—44no—
640C24—48no—
641C24—48no—
642C24—44no—
643C24—44no—
644C24—48no—
645C24—48no—
646C24—44no—
647C24—44no—
648C24—48no—
649C24—44no—
650C24—48no—
651C24—44no—
652C24—48no—
653C24—48no—
654C24—48no—
655C24—48no—
656C24—84no—
657C24—84no—
658C24—84no—
659C24—84no—
660C24—84no—
661C24—84no—
662C24—84no—
663C24—84no—
664C24#117116yescomplemented
665C24C4×D4116yes—
666C24C23×C414yes—
667C24C23×C412yes—
668C24C23×C412yes—
669C24C23×C412yes—
670C24C22×D412yes—
671C24C22×D412yes—
672C24C22×D412yes—
673C24C2×#4114yes—
674C24C2×#4114yes—
675C24C2×#4112yes—
676C24C2×#4112yes—
677C24C2×#4112yes—
678C24C2×#4112yes—
679C24C2×#4112yes—
680C24H(5,𝔽2)12yes—
681C24H(5,𝔽2)12yes—
682C24C2511yescharacteristic
683C2×D4—216no—
684C2×D4—216no—
685C2×D4—216no—
686C2×D4—216no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—4128no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—48no—
693C2×D4—48no—
694C2×D4—48no—
695C2×D4—48no—
696C2×D4—48no—
697C2×D4—48no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—28no—
702C22×C4—216no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—22no—
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—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—22no—
732C22×C4—22no—
733C22×C4—22no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—22no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
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—44no—
805C22×C4—48no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—48no—
812C22×C4—48no—
813C22×C4—48no—
814C22×C4—44no—
815C22×C4—48no—
816C22×C4—48no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—48no—
822C22×C4—48no—
823C22×C4—48no—
824C22×C4—48no—
825C22×C4—48no—
826C22×C4—44no—
827C22×C4—44no—
828C22×C4—48no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—4128no—
832C22×C4—48no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—44no—
838C22×C4—48no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—82no—
843C22×C4—82no—
844C22×C4—84no—
845C22×C4—84no—
846C22×C4—84no—
847C22×C4—84no—
848C22×C4—84no—
849C22×C4—84no—
850C22×C4—84no—
851C22×C4—84no—
852C22×C4—84no—
853C22×C4C23×C414yes—
854C22×C4C23×C412yes—
855C22×C4C23×C412yes—
856C22×C4C23×C412yes—
857C22×C4C23×C412yes—
858C22×C4C23×C414yes—
859C22×C4C23×C414yes—
860C22×C4C22×D412yes—
861C22×C4C22×D412yes—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4H(5,𝔽2)14yes—
865C22×C4H(5,𝔽2)14yes—
866C4⋊C4—44no—
867C4⋊C4—44no—
868C4⋊C4—82no—
869C4⋊C4—82no—
870C4⋊C4—84no—
871C4⋊C4—84no—
872C22⋊C4—28no—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—48no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—48no—
884C22⋊C4—48no—
885C22⋊C4—48no—
886C22⋊C4—48no—
887C22⋊C4—48no—
888C22⋊C4—48no—
889C22⋊C4—48no—
890C22⋊C4—48no—
891C22⋊C4—44no—
892C22⋊C4—48no—
893C22⋊C4—48no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C22⋊C4—44no—
899C22⋊C4—44no—
900C22⋊C4—82no—
901C22⋊C4—82no—
902C22⋊C4—84no—
903C22⋊C4—84no—
904C22⋊C4—84no—
905C42—44no—
906C42—44no—
907C42—82no—
908C42—84no—
909C42—82no—
910C42—84no—
911C23—24no—
912C23—24no—
913C23—22no—
914C23—22no—
915C23—24no—
916C23—22no—
917C23—22no—
918C23—24no—
919C23—24no—
920C23—24no—
921C23—24no—
922C23—24no—
923C23—24no—
924C23—24no—
925C23—24no—
926C23—24no—
927C23—232no—
928C23—22no—
929C23—22no—
930C23—24no—
931C23—22no—
932C23—22no—
933C23—24no—
934C23—24no—
935C23—24no—
936C23—24no—
937C23—24no—
938C23—24no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—24no—
955C23—24no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—232no—
975C23—432no—
976C23—416no—
977C23—416no—
978C23—416no—
979C23—416no—
980C23—416no—
981C23—416no—
982C23—432no—
983C23—432no—
984C23—432no—
985C23—416no—
986C23—416no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
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—88no—
1020C23—88no—
1021C23—816no—
1022C23—816no—
1023C23—816no—
1024C23—88no—
1025C23—816no—
1026C23—88no—
1027C23C2×#11718yes—
1028C23C2×#11714yes—
1029C23C2×C4×D414yes—
1030C23C2×C4×D414yes—
1031C23C2×C4×D414yes—
1032C23#51814yes—
1033C23#54614yes—
1034C23#54614yes—
1035C23#55114yes—
1036C23#55114yes—
1037C23C24×C411yescharacteristic
1038C23C23×D411yescharacteristic
1039C23C22×#4111yescharacteristic
1040C23C22×#4111yescharacteristic
1041C23C22×#4111yescharacteristic
1042C23C2×H(5,𝔽2)11yescharacteristic
1043C23C2×H(5,𝔽2)11yescharacteristic
1044C23C2×H(5,𝔽2)12yes—
1045C23C2×H(5,𝔽2)12yes—
1046C23#58512yes—
1047C23#58512yes—
1048D4—432no—
1049D4—432no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—24no—
1053C2×C4—24no—
1054C2×C4—24no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—24no—
1060C2×C4—24no—
1061C2×C4—24no—
1062C2×C4—24no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—24no—
1069C2×C4—24no—
1070C2×C4—24no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—24no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—24no—
1082C2×C4—24no—
1083C2×C4—416no—
1084C2×C4—432no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—432no—
1088C2×C4—416no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—42no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—42no—
1095C2×C4—42no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—42no—
1100C2×C4—42no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—42no—
1106C2×C4—42no—
1107C2×C4—42no—
1108C2×C4—42no—
1109C2×C4—42no—
1110C2×C4—42no—
1111C2×C4—42no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
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—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—42no—
1128C2×C4—42no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—41no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
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—88no—
1165C2×C4—88no—
1166C2×C4—816no—
1167C2×C4—88no—
1168C2×C4#53414yes—
1169C22—24no—
1170C22—24no—
1171C22—24no—
1172C22—28no—
1173C22—28no—
1174C22—28no—
1175C22—24no—
1176C22—28no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—24no—
1181C22—28no—
1182C22—24no—
1183C22—24no—
1184C22—28no—
1185C22—28no—
1186C22—24no—
1187C22—24no—
1188C22—464no—
1189C22—44no—
1190C22—42no—
1191C22—42no—
1192C22—44no—
1193C22—44no—
1194C22—42no—
1195C22—42no—
1196C22—44no—
1197C22—44no—
1198C22—44no—
1199C22—44no—
1200C22—44no—
1201C22—44no—
1202C22—44no—
1203C22—44no—
1204C22—44no—
1205C22—44no—
1206C22—44no—
1207C22—44no—
1208C22—44no—
1209C22—42no—
1210C22—42no—
1211C22—44no—
1212C22—44no—
1213C22—44no—
1214C22—42no—
1215C22—42no—
1216C22—44no—
1217C22—832no—
1218C22#234218yes—
1219C22C22×#11711yescharacteristic
1220C22C22×C4×D411yescharacteristic
1221C22C2×#51811yescharacteristic
1222C22C4×H(5,𝔽2)12yes—
1223C22C4×H(5,𝔽2)12yes—
1224C22C2×#53411yescharacteristic
1225C22#344911yescharacteristic
1226C22#345912yes—
1227C22C2×#54611yescharacteristic
1228C22C2×#54611yescharacteristic
1229C22C2×#55111yescharacteristic
1230C22C2×#55111yescharacteristic
1231C22#348411yescharacteristic
1232C22#348511yescharacteristic
1233C22#349012yes—
1234C22#349112yes—
1235C22#350512yes—
1236C22#350512yes—
1237C22#350512yes—
1238C22#353212yes—
1239C22#353312yes—
1240C22#354212yes—
1241C22#354212yes—
1242C4—24no—
1243C4—42no—
1244C4—42no—
1245C4—42no—
1246C4—42no—
1247C4—44no—
1248C4—44no—
1249C4—44no—
1250C4—42no—
1251C4—44no—
1252C4—42no—
1253C4—42no—
1254C4—81no—
1255C4—82no—
1256C4—81no—
1257C4—82no—
1258C4—82no—
1259C4—81no—
1260C4—81no—
1261C2—28no—
1262C2—48no—
1263C2—44no—
1264C2—44no—
1265C2C4×#53411yescharacteristic
1266C2C2×#234211yescharacteristic
1267C2#3425112yes—
1268C2#3426411yescharacteristic
1269C2#3440712yes—
1270C2#3783211yescharacteristic
1271C2#3784211yescharacteristic
1272C2#3796412yes—
1273C2#3946011yescharacteristic
1274C2#3946611yescharacteristic
1275C2#3955612yes—
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
4. #14693C2semidirect
5. #14427C2semidirect
6. #14391C2semidirect
7. #14375C2semidirect
8. #14373C2semidirect
10. #14262C2semidirect
11. #14068C2semidirect
12. #14064C2semidirect
13. #13992C2semidirect
14. #13992C2semidirect
15. #13988C2semidirect
16. #13984C2semidirect
17. #13972C2semidirect
18. #13972C2semidirect
19. #13877C2semidirect
20. #13869C2semidirect
21. C22⋊C42C2semidirect
22. #13775C2semidirect
23. C4×#379C2semidirect
26. C22×#117C22semidirect
33. #2308C4semidirect
34. C2×#388C22semidirect
35. C2×#388C22semidirect
36. C2×#388C22semidirect
37. C2×#388C22semidirect
51. C2×#385C22semidirect
52. C2×#385C22semidirect
57. C2×#381C22semidirect
58. C2×#381C22semidirect
59. C2×#380C22semidirect
60. C2×#380C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×C4×C22⋊C4C22semidirect
74. C2×C4×C22⋊C4C22semidirect
77. #1443C22semidirect
78. #1443C22semidirect
79. #1443C22semidirect
80. #1443C22semidirect
81. #1442C22semidirect
82. #1442C22semidirect
83. #1442C22semidirect
84. #1442C22semidirect
85. #1440C22semidirect
86. #1440C22semidirect
87. #1439C22semidirect
88. #1439C22semidirect
89. #1439C22semidirect
90. #1439C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
97. #1437C22semidirect
98. #1437C22semidirect
99. #1437C22semidirect
100. #1437C22semidirect
101. #1437C22semidirect
102. #1437C22semidirect
103. #1436C22semidirect
104. #1436C22semidirect
105. #1436C22semidirect
106. #1436C22semidirect
107. #1434C22semidirect
108. #1434C22semidirect
109. #1434C22semidirect
110. #1434C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
170. C22×C22⋊C4C2×C4semidirect
171. C22×C22⋊C4C2×C4semidirect
220. #386C2×C4semidirect
221. #386C2×C4semidirect
222. #386C2×C4semidirect
223. #386C2×C4semidirect
234. #381C2×C4semidirect
235. #381C2×C4semidirect
399. C23×C4C22×C4semidirect
400. C23×C4C22×C4semidirect
401. C23×C4C22×C4semidirect
527. C2×C22⋊C4C22×C4semidirect
528. C2×C22⋊C4C22×C4semidirect
529. C2×C22⋊C4C22×C4semidirect
584. #95C22×C4semidirect
585. #95C22×C4semidirect
586. #95C22×C4semidirect
587. #95C22×C4semidirect
664. C24#117semidirect

Maximal subgroups

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

subgroupindex
C2×#23422
C2×#23082
C22×#3862
#146932
#144272
#143912
#143752
#143732
#143352
#142622
#140682
#140642
#139922
#139882
#139842
#139722
#138772
#138692
C22⋊C422
#137752
C4×#3792