Finite Group Databasebeta

← #526112

Subgroups — #526112

Order 512.

4350 conjugacy classes of subgroups.

The subgroup lattice has 1325 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2428C211yesmaximal, characteristic
2C2×#2361C211yesmaximal, characteristic, complemented
3C2×#2325C212yesmaximal, complemented
4C2×C4×#127C211yesmaximal, characteristic, complemented
5#14699C211yesmaximal, characteristic, complemented
6#14573C212yesmaximal, complemented
7#14519C212yesmaximal, complemented
8#14397C212yesmaximal, complemented
9#14361C212yesmaximal, complemented
10#14300C212yesmaximal, complemented
11#14171C212yesmaximal, complemented
12#14137C211yesmaximal, characteristic, complemented
13#14025C211yesmaximal, characteristic, complemented
14#14022C211yesmaximal, characteristic, complemented
15#13981C211yesmaximal, characteristic, complemented
16#13977C211yesmaximal, characteristic, complemented
17#13975C212yesmaximal, complemented
18#13970C211yesmaximal, characteristic, complemented
19#13970C211yesmaximal, characteristic, complemented
20#13906C211yesmaximal, characteristic, complemented
21#13880C211yesmaximal, characteristic, complemented
22D4×#95C211yesmaximal, characteristic, complemented
23C4×#388C211yesmaximal, characteristic, complemented
24C22×#127C2211yescharacteristic
25C22×#121C2212yes—
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×C4×D4C2212yes—
29C22×C4×D4C2212yes—
30C22×C4×D4C2212yes—
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C23×C4⋊C4C2211yescharacteristic
36#2428C4116yescomplemented
37C2×#394C2212yes—
38C2×#392C2212yes—
39#2361—28no—
40#2325—216no—
41C4×#127—28no—
42C2×#390C2212yes—
43C2×#390C2211yescharacteristic
44C2×#390C2212yes—
45C2×#390C2211yescharacteristic
46C2×#390C2211yescharacteristic
47C2×#390C2211yescharacteristic
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388C2212yes—
53C2×#388C2211yescharacteristic
54C2×#388C2212yes—
55C2×#388C2211yescharacteristic
56C2×#387C2212yes—
57C2×#387C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2212yes—
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#385C2212yes—
67C2×#385C2212yes—
68C2×#385C2212yes—
69C2×#385C2212yes—
70C2×#385C2212yes—
71C2×#384C2211yescharacteristic
72C2×#384C2211yescharacteristic
73C2×#380C2212yes—
74C2×#380C2212yes—
75C2×#380C2211yescharacteristic
76C2×C4×C4⋊C4C2211yescharacteristic
77C2×C4×C4⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C22×#95C2212yes—
82C2×C43C2211yescharacteristic
83#1444C2212yes—
84#1444C2212yes—
85#1442C2212yes—
86#1441C2212yes—
87#1440C2212yes—
88#1440C2212yes—
89#1440C2212yes—
90#1439C2212yes—
91#1439C2212yes—
92#1439C2212yes—
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1438C2212yes—
98#1438C2212yes—
99#1438C2212yes—
100#1438C2212yes—
101#1437C2211yescharacteristic
102#1437C2212yes—
103#1437C2211yescharacteristic
104#1436C2212yes—
105#1436C2211yescharacteristic
106#1436C2212yes—
107#1436C2212yes—
108#1436C2211yescharacteristic
109C4⋊#95C2211yescharacteristic
110C4⋊#95C2211yescharacteristic
111C4⋊#95C2211yescharacteristic
112C4⋊#95C2211yescharacteristic
113C4⋊#95C2211yescharacteristic
114C4⋊#95C2211yescharacteristic
115C4⋊#95C2211yescharacteristic
116C4⋊#95C2211yescharacteristic
117#1434C2212yes—
118#1434C2211yescharacteristic
119#1434C2211yescharacteristic
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C23×D4C2311yescharacteristic
128C23×D4C2312yes—
129C23×D4C2312yes—
130C23×D4C2312yes—
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2312yes—
135C24×C4C2312yes—
136C24×C4C2312yes—
137C24×C4C2312yes—
138C24×C4C2312yes—
139C2×#127—24no—
140C2×#127—24no—
141C2×#127C2×C418yescomplemented
142C2×#121—24no—
143C2×#121—24no—
144C2×#121—28no—
145C2×#121—28no—
146C2×#121—42no—
147C2×#121—42no—
148C2×#121C2×C4116yescomplemented
149C2×#121C2×C418yescomplemented
150C2×#121C2×C418yescomplemented
151C2×C4×D4—24no—
152C2×C4×D4—28no—
153C2×C4×D4—28no—
154C2×C4×D4—28no—
155C2×C4×D4—28no—
156C2×C4×D4—24no—
157C2×C4×D4—28no—
158C2×C4×D4—44no—
159C2×C4×D4—42no—
160C2×C4×D4—42no—
161C2×C4×D4—42no—
162C2×C4×D4—42no—
163C2×C4×D4—44no—
164C2×C4×D4—42no—
165C2×C4×D4—42no—
166C2×C4×D4—42no—
167C2×C4×D4—42no—
168C2×C4×D4—44no—
169C2×C4×D4—44no—
170C2×C4×D4C2×C418yescomplemented
171C2×C4×D4D418yescomplemented
172C22×C4⋊C4—24no—
173C22×C4⋊C4—42no—
174C22×C4⋊C4—42no—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2311yescharacteristic
185C22×C4⋊C4C2311yescharacteristic
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2312yes—
188C22×C4⋊C4C2312yes—
189C22×C4⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2311yescharacteristic
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C42C2311yescharacteristic
216C22×C42C2311yescharacteristic
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#394C2×C4116yescomplemented
227#392C2×C4116yescomplemented
228#390—24no—
229#390—24no—
230#390—24no—
231#390—28no—
232#390—28no—
233#390—42no—
234#390—42no—
235#390C2×C418yescomplemented
236#389—24no—
237#389C2×C418yescomplemented
238#388—28no—
239#388—28no—
240#388—24no—
241#388D418yescomplemented
242#387—28no—
243#387—28no—
244#386—28no—
245#386—28no—
246#386—28no—
247#386—28no—
248#386—28no—
249#386—44no—
250#386—44no—
251#386C2×C4116yescomplemented
252#385—28no—
253#385—28no—
254#385—28no—
255#385—44no—
256#385—44no—
257#384—24no—
258#384—42no—
259#380—28no—
260#380—44no—
261#380—42no—
262C4×C4⋊C4—24no—
263C4×C4⋊C4—42no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4—42no—
266C4×C22⋊C4C2×C418yescomplemented
267C2×#95—28no—
268C2×#95C2311yescharacteristic
269C2×#95C2311yescharacteristic
270C2×#95C2311yescharacteristic
271C2×#95C2311yescharacteristic
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2311yescharacteristic
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C43—24no—
305C25C2412yes—
306C25C2411yescharacteristic
307C25C2412yes—
308C22×D4—24no—
309C22×D4—24no—
310C22×D4—24no—
311C22×D4—24no—
312C22×D4—24no—
313C22×D4—24no—
314C22×D4—24no—
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—24no—
318C22×D4—24no—
319C22×D4—22no—
320C22×D4—24no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—22no—
324C22×D4—22no—
325C22×D4—22no—
326C22×D4—24no—
327C22×D4—22no—
328C22×D4—22no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—22no—
332C22×D4—42no—
333C22×D4—42no—
334C22×D4—42no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—42no—
339C22×D4—42no—
340C22×D4—42no—
341C22×D4—42no—
342C22×D4C22×C414yes—
343C22×D4C22×C418yes—
344C22×D4C22×C418yes—
345C22×D4C22×C418yes—
346C22×D4C22×C414yes—
347C22×D4C22×C418yes—
348C22×D4C2×D414yes—
349C22×D4#4114yes—
350C23×C4—22no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—24no—
357C23×C4—24no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—24no—
364C23×C4—24no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—42no—
368C23×C4—42no—
369C23×C4—42no—
370C23×C4—42no—
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×C4C22×C414yes—
390C23×C4C22×C418yes—
391C23×C4C2×D418yes—
392C23×C4C2411yescharacteristic
393C23×C4C2411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2412yes—
396C23×C4C2412yes—
397C23×C4C2411yescharacteristic
398C23×C4C2411yescharacteristic
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412#127—232no—
413#121—232no—
414#121—264no—
415#121—416no—
416C4×D4—416no—
417C4×D4—416no—
418C4×D4—432no—
419C4×D4—432no—
420C4×D4—416no—
421C4×D4—432no—
422C4×D4—416no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—24no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—24no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—416no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4C22×C414yes—
465C2×C4⋊C4C22×C414yes—
466C2×C4⋊C4C22×C418yes—
467C2×C4⋊C4C2×D414yes—
468C2×C4⋊C4C2×D414yes—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—41no—
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—41no—
516C2×C22⋊C4—41no—
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⋊C4C22×C418yes—
533C2×C22⋊C4C22×C418yes—
534C2×C22⋊C4C22×C414yes—
535C2×C22⋊C4C22×C418yes—
536C2×C22⋊C4C22×C418yes—
537C2×C22⋊C4C22×C418yes—
538C2×C22⋊C4C22×C414yes—
539C2×C22⋊C4C2×D414yes—
540C2×C22⋊C4C2×D418yes—
541C2×C22⋊C4C2×D414yes—
542C2×C22⋊C4C2×D414yes—
543C2×C22⋊C4#4114yes—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—22no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—22no—
553C2×C42—22no—
554C2×C42—22no—
555C2×C42—24no—
556C2×C42—24no—
557C2×C42—22no—
558C2×C42—22no—
559C2×C42—22no—
560C2×C42—22no—
561C2×C42—22no—
562C2×C42—22no—
563C2×C42—22no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—22no—
568C2×C42—22no—
569C2×C42—22no—
570C2×C42—42no—
571C2×C42—41no—
572C2×C42—41no—
573C2×C42C22×C414yes—
574C2×C42C22×C414yes—
575C2×C42C2×D414yes—
576C2×C42C2×D414yes—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—22no—
590#95—22no—
591#95—24no—
592#95—22no—
593#95—24no—
594#95—22no—
595#95—22no—
596#95—42no—
597#95—42no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95C22×C414yes—
609#95C22×C414yes—
610#95C22×C418yes—
611#95C2×D414yes—
612#95C2×D414yes—
613C24—21no—
614C24—22no—
615C24—21no—
616C24—22no—
617C24—21no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—22no—
632C24—22no—
633C24—21no—
634C24—21no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24C23×C414yes—
652C24C23×C414yes—
653C24C23×C412yes—
654C24C22×D414yes—
655C24C22×D412yes—
656C24C2×#4112yes—
657C24C2×#4114yes—
658C24C2511yescharacteristic
659C2×D4—216no—
660C2×D4—216no—
661C2×D4—216no—
662C2×D4—216no—
663C2×D4—216no—
664C2×D4—216no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—28no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—48no—
687C2×D4—48no—
688C2×D4—48no—
689C2×D4—48no—
690C2×D4—48no—
691C2×D4—48no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—84no—
697C2×D4—84no—
698C2×D4—84no—
699C2×D4—84no—
700C2×D4C4×D4116yes—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—22no—
730C22×C4—22no—
731C22×C4—22no—
732C22×C4—22no—
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—21no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
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—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—28no—
778C22×C4—28no—
779C22×C4—28no—
780C22×C4—216no—
781C22×C4—216no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—22no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
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—44no—
829C22×C4—44no—
830C22×C4—48no—
831C22×C4—48no—
832C22×C4—84no—
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×C4—84no—
843C22×C4—84no—
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×C4—84no—
854C22×C4C23×C412yes—
855C22×C4C23×C412yes—
856C22×C4C23×C414yes—
857C22×C4C23×C414yes—
858C22×C4C23×C412yes—
859C22×C4C23×C412yes—
860C22×C4C23×C412yes—
861C22×C4C23×C412yes—
862C22×C4C22×D412yes—
863C22×C4C22×D412yes—
864C22×C4C22×D412yes—
865C22×C4C22×D412yes—
866C22×C4C22×D414yes—
867C22×C4C22×D412yes—
868C22×C4C22×D412yes—
869C22×C4C22×D412yes—
870C22×C4C22×D412yes—
871C22×C4C22×D412yes—
872C22×C4C2×#4112yes—
873C22×C4C2×#4112yes—
874C22×C4C2×#4112yes—
875C22×C4H(5,𝔽2)12yes—
876C22×C4H(5,𝔽2)12yes—
877C22×C4H(5,𝔽2)12yes—
878C22×C4H(5,𝔽2)12yes—
879C22×C4H(5,𝔽2)12yes—
880C22×C4H(5,𝔽2)12yes—
881C22×C42−1+412yes—
882C22×C42−1+412yes—
883C4⋊C4—28no—
884C4⋊C4—216no—
885C4⋊C4—28no—
886C4⋊C4—28no—
887C4⋊C4—44no—
888C4⋊C4—44no—
889C4⋊C4—48no—
890C4⋊C4—48no—
891C4⋊C4—48no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—48no—
896C4⋊C4—84no—
897C4⋊C4—84no—
898C22⋊C4—216no—
899C22⋊C4—216no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—48no—
903C22⋊C4—48no—
904C22⋊C4—48no—
905C22⋊C4—44no—
906C22⋊C4—48no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C22⋊C4—48no—
912C22⋊C4—48no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—84no—
917C22⋊C4—84no—
918C22⋊C4—84no—
919C22⋊C4—84no—
920C22⋊C4—84no—
921C22⋊C4—84no—
922C22⋊C4C4×D4116yescomplemented
923C42—28no—
924C42—28no—
925C42—28no—
926C42—28no—
927C42—28no—
928C42—44no—
929C42—44no—
930C42—48no—
931C42—44no—
932C42—44no—
933C42—44no—
934C23—24no—
935C23—22no—
936C23—24no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—24no—
948C23—24no—
949C23—24no—
950C23—22no—
951C23—24no—
952C23—22no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—24no—
957C23—22no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—24no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—42no—
984C23—42no—
985C23—42no—
986C23—42no—
987C23—42no—
988C23—42no—
989C23—41no—
990C23—42no—
991C23—42no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—41no—
999C23—41no—
1000C23—42no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—41no—
1005C23—42no—
1006C23—41no—
1007C23—42no—
1008C23—41no—
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—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23C2×C4×D418yes—
1038C23C2×C4×D414yes—
1039C23C24×C411yescharacteristic
1040C23C23×D411yescharacteristic
1041C23C23×D411yescharacteristic
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
1050C23C2×2−1+411yescharacteristic
1051C23C2×2−1+411yescharacteristic
1052C23#58511yescharacteristic
1053C23#58511yescharacteristic
1054D4—232no—
1055D4—432no—
1056D4—432no—
1057D4—432no—
1058D4—416no—
1059D4—816no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
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—24no—
1086C2×C4—24no—
1087C2×C4—24no—
1088C2×C4—22no—
1089C2×C4—24no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—24no—
1095C2×C4—24no—
1096C2×C4—22no—
1097C2×C4—24no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—42no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—416no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—42no—
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—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—42no—
1190C2×C4—816no—
1191C2×C4—816no—
1192C2×C4—816no—
1193C2×C4—816no—
1194C2×C4—816no—
1195C2×C4C2×C4×D414yes—
1196C2×C4C2×C4×D414yes—
1197C2×C4C2×C4×D414yes—
1198C2×C4#51814yes—
1199C2×C4#52014yes—
1200C2×C4#52014yes—
1201C2×C4#53414yes—
1202C2×C4#53714yes—
1203C2×C4#53814yes—
1204C2×C4#53914yes—
1205C2×C4D4214yes—
1206C22—24no—
1207C22—28no—
1208C22—28no—
1209C22—24no—
1210C22—24no—
1211C22—28no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—44no—
1216C22—44no—
1217C22—42no—
1218C22—44no—
1219C22—44no—
1220C22—42no—
1221C22—44no—
1222C22—42no—
1223C22—44no—
1224C22—42no—
1225C22—44no—
1226C22—42no—
1227C22—44no—
1228C22—42no—
1229C22—44no—
1230C22—42no—
1231C22—44no—
1232C22—42no—
1233C22—44no—
1234C22—42no—
1235C22—42no—
1236C22—44no—
1237C22—44no—
1238C22—44no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—82no—
1244C22—82no—
1245C22—82no—
1246C22—82no—
1247C22—82no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22C22×C4×D411yescharacteristic
1252C22C22×C4×D411yescharacteristic
1253C22C2×#51811yescharacteristic
1254C22C2×#52011yescharacteristic
1255C22C2×#52011yescharacteristic
1256C22C4×H(5,𝔽2)11yescharacteristic
1257C22C4×H(5,𝔽2)11yescharacteristic
1258C22C2×#53411yescharacteristic
1259C22C2×#53711yescharacteristic
1260C22C2×#53811yescharacteristic
1261C22C2×#53911yescharacteristic
1262C22C2×D4211yescharacteristic
1263C22D4×#4111yescharacteristic
1264C22D4×#4111yescharacteristic
1265C22#348111yescharacteristic
1266C22#348411yescharacteristic
1267C22#348911yescharacteristic
1268C22#349611yescharacteristic
1269C22#349811yescharacteristic
1270C22#349811yescharacteristic
1271C22#349911yescharacteristic
1272C22#351111yescharacteristic
1273C22#351111yescharacteristic
1274C22#351311yescharacteristic
1275C22#351411yescharacteristic
1276C22#351911yescharacteristic
1277C22#352011yescharacteristic
1278C22#354311yescharacteristic
1279C22#354311yescharacteristic
1280C22#354611yescharacteristic
1281C22#354711yescharacteristic
1282C22#354811yescharacteristic
1283C22#355411yescharacteristic
1284C22#355911yescharacteristic
1285C22#356211yescharacteristic
1286C4—24no—
1287C4—24no—
1288C4—24no—
1289C4—24no—
1290C4—44no—
1291C4—42no—
1292C4—44no—
1293C4—44no—
1294C4—42no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—82no—
1301C4—82no—
1302C4—81no—
1303C4—81no—
1304C4—82no—
1305C4#232518yescomplemented
1306C2—44no—
1307C2—48no—
1308C2—84no—
1309C2C2×#232511yescharacteristic
1310C2C4×D4211yescharacteristic
1311C2#3420711yescharacteristic
1312C2#3428811yescharacteristic
1313C2#3431011yescharacteristic
1314C2#3443111yescharacteristic
1315C2#3449411yescharacteristic
1316C2#3933611yescharacteristic
1317C2#3934011yescharacteristic
1318C2#3939611yescharacteristic
1319C2#3940411yescharacteristic
1320C2#3985211yescharacteristic
1321C2#3986411yescharacteristic
1322C2#4014011yescharacteristic
1323C2#4015211yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2428C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2361C2semidirect
3. C2×#2325C2semidirect
4. C2×C4×#127C2semidirect
5. #14699C2semidirect
6. #14573C2semidirect
7. #14519C2semidirect
8. #14397C2semidirect
9. #14361C2semidirect
10. #14300C2semidirect
11. #14171C2semidirect
12. #14137C2semidirect
13. #14025C2semidirect
14. #14022C2semidirect
15. #13981C2semidirect
16. #13977C2semidirect
17. #13975C2semidirect
18. #13970C2semidirect
19. #13970C2semidirect
20. #13906C2semidirect
21. #13880C2semidirect
22. D4×#95C2semidirect
23. C4×#388C2semidirect
36. #2428C4semidirect
141. C2×#127C2×C4semidirect
148. C2×#121C2×C4semidirect
149. C2×#121C2×C4semidirect
150. C2×#121C2×C4semidirect
170. C2×C4×D4C2×C4semidirect
171. C2×C4×D4D4semidirect
226. #394C2×C4semidirect
227. #392C2×C4semidirect
235. #390C2×C4semidirect
237. #389C2×C4semidirect
241. #388D4semidirect
251. #386C2×C4semidirect
266. C4×C22⋊C4C2×C4semidirect
922. C22⋊C4C4×D4semidirect
1305. C4#2325semidirect

Maximal subgroups

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

subgroupindex
C2×#24282
C2×#23612
C2×#23252
C2×C4×#1272
#146992
#145732
#145192
#143972
#143612
#143002
#141712
#141372
#140252
#140222
#139812
#139772
#139752
#139702
#139062
#138802
D4×#952
C4×#3882