Finite Group Databasebeta

← #523412

Subgroups — #523412

Order 512.

4612 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2404C211yesmaximal, characteristic
2C2×#2339C211yesmaximal, characteristic, complemented
3C2×#2321C211yesmaximal, characteristic, complemented
4C2×#2311C211yesmaximal, characteristic, complemented
5C22×#388C211yesmaximal, characteristic, complemented
6#14696C211yesmaximal, characteristic, complemented
7#14522C212yesmaximal, complemented
8#14520C212yesmaximal, complemented
9#14410C212yesmaximal, complemented
10#14374C212yesmaximal, complemented
11#14263C211yesmaximal, characteristic, complemented
12#14255C211yesmaximal, characteristic, complemented
13#14232C212yesmaximal, complemented
14#14228C212yesmaximal, complemented
15#14020C211yesmaximal, characteristic, complemented
16#14016C211yesmaximal, characteristic, complemented
17#14012C212yesmaximal, complemented
18#13999C212yesmaximal, complemented
19#13995C211yesmaximal, characteristic, complemented
20#13967C211yesmaximal, characteristic, complemented
21#13868C211yesmaximal, characteristic, complemented
22#13799C211yesmaximal, characteristic, complemented
23C4×#386C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C22×#120C2211yescharacteristic
26C22×#120C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C22×C4×D4C2211yescharacteristic
29C22×#117C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C42C2211yescharacteristic
35#2404C4116yescomplemented
36C2×#393C2212yes—
37C2×#392C2212yes—
38#2339—28no—
39#2321—28no—
40#2311—28no—
41C2×#391C2211yescharacteristic, complemented
42C2×#391C2211yescharacteristic, complemented
43C2×#391C2212yescomplemented
44C2×#390C2212yes—
45C2×#390C2212yes—
46C2×#390C2212yescomplemented
47C2×#388—28no—
48C2×#388C2212yes—
49C2×#388C2212yes—
50C2×#388C2212yes—
51C2×#388C2212yes—
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#388C2212yescomplemented
55C2×#386C2212yes—
56C2×#386C2211yescharacteristic
57C2×#386C2211yescharacteristic
58C2×#386C2211yescharacteristic
59C2×#386C2211yescharacteristic
60C2×#386C2211yescharacteristic
61C2×#386C2212yes—
62C2×#386C2211yescharacteristic
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic, complemented
68C2×#386C2211yescharacteristic, complemented
69C2×#385C2211yescharacteristic
70C2×#385C2211yescharacteristic
71C2×#381C2211yescharacteristic
72C2×#381C2211yescharacteristic
73C2×#381C2211yescharacteristic, complemented
74C2×#380C2212yescomplemented
75C2×#380C2211yescharacteristic, complemented
76C2×#380C2212yescomplemented
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C2×C4×C22⋊C4C2211yescharacteristic
81C2×C4×C22⋊C4C2211yescharacteristic, complemented
82C2×C4×C22⋊C4C2212yescomplemented
83C22×#95C2211yescharacteristic
84C22×#95C2211yescharacteristic
85C22×#95C2211yescharacteristic, complemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1443C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yescomplemented
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yescomplemented
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1437C2212yes—
105#1437C2212yes—
106#1437C2212yes—
107#1437C2212yes—
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1436C2212yescomplemented
112#1436C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1434C2212yescomplemented
117#1434C2212yescomplemented
118#1434C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C4×#95C2212yescomplemented
127C4×#95C2212yescomplemented
128C26C2311yescharacteristic
129C22×#41—24no—
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—42no—
134C22×#41—42no—
135C22×#41C2×C418yes—
136C23×Q8C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C2×#120—24no—
153C2×#120—24no—
154C2×#120—42no—
155C2×#120—42no—
156C2×#120C2×C418yes—
157C2×#120C2×C418yescomplemented
158C2×C4×D4—24no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—42no—
163C2×C4×D4—42no—
164C2×#117—24no—
165C2×#117—24no—
166C2×#117—42no—
167C22×C4⋊C4—24no—
168C22×C4⋊C4—24no—
169C22×C4⋊C4—42no—
170C22×C4⋊C4C2312yes—
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—24no—
179C22×C22⋊C4—24no—
180C22×C22⋊C4—24no—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—44no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4C2×C418yescomplemented
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C42—24no—
216C22×C42—44no—
217C22×C42C2312yes—
218C22×C42C2312yes—
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2312yes—
223C22×C42C2312yes—
224#393C2×C4116yescomplemented
225#392C2×C4116yescomplemented
226#391—28no—
227#391—24no—
228#391—24no—
229#390—28no—
230#390—28no—
231#390—44no—
232#388—28no—
233#388—28no—
234#388—28no—
235#388—28no—
236#388—28no—
237#388—28no—
238#388—44no—
239#386—24no—
240#386—24no—
241#386—24no—
242#386—24no—
243#386—24no—
244#386—28no—
245#386—24no—
246#386—24no—
247#386—44no—
248#386C2×C418yes—
249#386C2×C4116yescomplemented
250#386C2×C4116yescomplemented
251#386C2×C418yescomplemented
252#386D418yescomplemented
253#385—24no—
254#385—42no—
255#381—24no—
256#381—24no—
257#381C2×C418yescomplemented
258#380—28no—
259#380—28no—
260#380—24no—
261#379—24no—
262#379—42no—
263C4×C22⋊C4—24no—
264C4×C22⋊C4—24no—
265C4×C22⋊C4—44no—
266C4×C22⋊C4—42no—
267C2×#95—24no—
268C2×#95—24no—
269C2×#95D418yescomplemented
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2311yescharacteristic
273C2×#95C2311yescharacteristic
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C25—22no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25C22×C414yes—
319C25C2412yes—
320C25C2411yescharacteristic
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C2×#41—232no—
324C2×#41—232no—
325C2×#41—416no—
326C2×#41—416no—
327C2×#41—416no—
328C2×#41—416no—
329C2×#41—416no—
330C22×Q8—22no—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8—22no—
334C22×Q8—41no—
335C22×Q8—41no—
336C22×Q8C22×C414yes—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—22no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—22no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—41no—
354C22×D4—41no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4C22×C414yes—
366C22×D4C22×C414yes—
367C22×D4C22×C414yes—
368C22×D4C22×C418yes—
369C22×D4C22×C418yes—
370C22×D4C2×D414yes—
371C22×D4#4114yes—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—22no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—22no—
379C23×C4—22no—
380C23×C4—22no—
381C23×C4—22no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—41no—
405C23×C4—41no—
406C23×C4—41no—
407C23×C4—41no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—41no—
412C23×C4—41no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4C22×C414yes—
420C23×C4C22×C414yes—
421C23×C4C22×C414yes—
422C23×C4C22×C414yes—
423C23×C4C2×D414yes—
424C23×C4C2×D414yes—
425C23×C4C2×D414yes—
426C23×C4C2×D414yes—
427C23×C4#4114yes—
428C23×C4C2411yescharacteristic
429C23×C4C2412yes—
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2411yescharacteristic
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435C23×C4C2412yes—
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2411yescharacteristic
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447#120—232no—
448#120—416no—
449C4×D4—416no—
450C4×D4—416no—
451#117—416no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—416no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—232no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
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—41no—
527C2×C22⋊C4—41no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—416no—
534C2×C22⋊C4—416no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—42no—
547C2×C22⋊C4—42no—
548C2×C22⋊C4—42no—
549C2×C22⋊C4—42no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4C22×C418yes—
554C2×C22⋊C4C22×C418yes—
555C2×C22⋊C4C22×C414yes—
556C2×C22⋊C4C22×C418yes—
557C2×C22⋊C4C22×C414yes—
558C2×C22⋊C4C22×C418yes—
559C2×C22⋊C4C22×C418yes—
560C2×C22⋊C4C22×C418yes—
561C2×C22⋊C4C2×D414yes—
562C2×C22⋊C4C2×D418yes—
563C2×C42—24no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—22no—
567C2×C42—24no—
568C2×C42—24no—
569C2×C42—24no—
570C2×C42—22no—
571C2×C42—24no—
572C2×C42—24no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—42no—
576C2×C42—41no—
577C2×C42—41no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—416no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—24no—
589#95—24no—
590#95—22no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—24no—
600#95—24no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95C22×C418yes—
615#95C22×C418yes—
616#95C22×C418yes—
617#95C22×C418yes—
618#95C2×D414yes—
619#95C2×D414yes—
620#95C2×D414yes—
621#95C2×D414yes—
622#95C2×D418yes—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—21no—
628C24—21no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—28no—
636C24—22no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—21no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—28no—
661C24—28no—
662C24—48no—
663C24—48no—
664C24—44no—
665C24—44no—
666C24—48no—
667C24—44no—
668C24—44no—
669C24—48no—
670C24—44no—
671C24—44no—
672C24—44no—
673C24—44no—
674C24—84no—
675C24—84no—
676C24—84no—
677C24—84no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24C23×C414yes—
683C24C23×C412yes—
684C24C23×C412yes—
685C24C23×C412yes—
686C24C22×D412yes—
687C24C22×D412yes—
688C24C22×D412yes—
689C24C2×#4112yes—
690C24C2×#4112yes—
691C24C2×#4112yes—
692C24H(5,𝔽2)12yes—
693C24H(5,𝔽2)12yes—
694C24C2511yescharacteristic
695#41—4128no—
696C2×Q8—28no—
697C2×Q8—28no—
698C2×Q8—44no—
699C2×Q8—44no—
700C2×Q8—44no—
701C2×Q8—44no—
702C2×Q8—44no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—28no—
706C2×D4—28no—
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—28no—
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—44no—
716C2×D4—44no—
717C2×D4—44no—
718C2×D4—44no—
719C2×D4—44no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—84no—
730C2×D4—84no—
731C2×D4—84no—
732C2×D4—84no—
733C2×D4—84no—
734C2×D4—84no—
735C2×D4—84no—
736C2×D4—84no—
737C2×D4C4×D4116yes—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—28no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—28no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—28no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
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—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
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—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—28no—
815C22×C4—28no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—48no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—48no—
875C22×C4—44no—
876C22×C4—48no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—82no—
882C22×C4—84no—
883C22×C4—82no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4—84no—
888C22×C4—84no—
889C22×C4—84no—
890C22×C4C4×D4116yes—
891C22×C4C23×C414yes—
892C22×C4C23×C414yes—
893C22×C4C23×C414yes—
894C22×C4C23×C412yes—
895C22×C4C23×C412yes—
896C22×C4C23×C412yes—
897C22×C4C23×C412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D414yes—
901C22×C4C22×D414yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C2×#4112yes—
908C22×C4C2×#4112yes—
909C22×C4C2×#4112yes—
910C22×C4H(5,𝔽2)14yes—
911C4⋊C4—48no—
912C4⋊C4—48no—
913C4⋊C4—48no—
914C4⋊C4—44no—
915C4⋊C4—44no—
916C4⋊C4—84no—
917C4⋊C4—84no—
918C22⋊C4—28no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—216no—
922C22⋊C4—216no—
923C22⋊C4—216no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—82no—
940C22⋊C4—82no—
941C22⋊C4—84no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C42—48no—
949C42—44no—
950C42—44no—
951C42—48no—
952C42—48no—
953C42—84no—
954C42—84no—
955C23—24no—
956C23—24no—
957C23—22no—
958C23—22no—
959C23—24no—
960C23—22no—
961C23—22no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—22no—
972C23—22no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—24no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—416no—
996C23—416no—
997C23—41no—
998C23—41no—
999C23—42no—
1000C23—41no—
1001C23—41no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—416no—
1008C23—42no—
1009C23—41no—
1010C23—41no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—42no—
1020C23—42no—
1021C23—41no—
1022C23—42no—
1023C23—41no—
1024C23—42no—
1025C23—41no—
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—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—816no—
1055C23—816no—
1056C23—816no—
1057C23—88no—
1058C23—88no—
1059C23—88no—
1060C23—88no—
1061C23—816no—
1062C23C2×C4×D414yes—
1063C23C2×C4×D414yes—
1064C23C2×C4×D414yes—
1065C23#51814yes—
1066C23D4214yes—
1067C23#54614yes—
1068C23#54614yes—
1069C23#55114yes—
1070C23C24×C411yescharacteristic
1071C23C23×D411yescharacteristic
1072C23C23×D411yescharacteristic
1073C23C22×#4111yescharacteristic
1074C23C22×#4111yescharacteristic
1075C23C2×H(5,𝔽2)11yescharacteristic
1076C23C2×H(5,𝔽2)11yescharacteristic
1077C23C2×H(5,𝔽2)12yes—
1078C23#58512yes—
1079C23#58512yes—
1080C23#58512yes—
1081Q8—416no—
1082D4—232no—
1083D4—416no—
1084D4—416no—
1085D4—816no—
1086D4—816no—
1087C2×C4—232no—
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—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—22no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—416no—
1138C2×C4—416no—
1139C2×C4—416no—
1140C2×C4—416no—
1141C2×C4—416no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
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—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
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—88no—
1208C2×C4—88no—
1209C2×C4—88no—
1210C2×C4C2×C4×D414yes—
1211C2×C4C2×C4×D414yes—
1212C2×C4C2×C4×D414yes—
1213C2×C4#53514yes—
1214C22—28no—
1215C22—24no—
1216C22—28no—
1217C22—24no—
1218C22—24no—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—28no—
1223C22—28no—
1224C22—28no—
1225C22—24no—
1226C22—42no—
1227C22—44no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—44no—
1242C22—42no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—832no—
1248C22—82no—
1249C22—82no—
1250C22—82no—
1251C22—81no—
1252C22—82no—
1253C22—81no—
1254C22—82no—
1255C22—81no—
1256C22—82no—
1257C22—81no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22#235818yes—
1263C22C22×C4×D411yescharacteristic
1264C22C22×C4×D411yescharacteristic
1265C22C2×#51811yescharacteristic
1266C22#342812yes—
1267C22C4×H(5,𝔽2)12yes—
1268C22C2×#53511yescharacteristic
1269C22#344911yescharacteristic
1270C22#346012yes—
1271C22C2×D4211yescharacteristic
1272C22C2×#54611yescharacteristic
1273C22C2×#54611yescharacteristic
1274C22C2×#55111yescharacteristic
1275C22#348511yescharacteristic
1276C22#348711yescharacteristic
1277C22#349312yes—
1278C22#349612yes—
1279C22#350012yes—
1280C22#351312yes—
1281C22#352112yes—
1282C22#353412yes—
1283C22#354212yes—
1284C22#354512yes—
1285C22#356012yes—
1286C4—24no—
1287C4—24no—
1288C4—24no—
1289C4—24no—
1290C4—44no—
1291C4—44no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—44no—
1297C4—44no—
1298C4—44no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—82no—
1304C4—82no—
1305C2—28no—
1306C2—44no—
1307C2—82no—
1308C2—84no—
1309C2C4×#53511yescharacteristic
1310C2C2×#235811yescharacteristic
1311C2#3420111yescharacteristic
1312C2#3430912yes—
1313C2#3449212yes—
1314C2#3802311yescharacteristic
1315C2#3803111yescharacteristic
1316C2#3819912yes—
1317C2#3933311yescharacteristic
1318C2#3933911yescharacteristic
1319C2#3941512yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC2×#2404C2
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×#2339C2semidirect
3. C2×#2321C2semidirect
4. C2×#2311C2semidirect
5. C22×#388C2semidirect
6. #14696C2semidirect
7. #14522C2semidirect
8. #14520C2semidirect
9. #14410C2semidirect
10. #14374C2semidirect
11. #14263C2semidirect
12. #14255C2semidirect
13. #14232C2semidirect
14. #14228C2semidirect
15. #14020C2semidirect
16. #14016C2semidirect
17. #14012C2semidirect
18. #13999C2semidirect
19. #13995C2semidirect
20. #13967C2semidirect
21. #13868C2semidirect
22. #13799C2semidirect
23. C4×#386C2semidirect
35. #2404C4semidirect
41. C2×#391C22semidirect
42. C2×#391C22semidirect
43. C2×#391C22semidirect
46. C2×#390C22semidirect
54. C2×#388C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
73. C2×#381C22semidirect
74. C2×#380C22semidirect
75. C2×#380C22semidirect
76. C2×#380C22semidirect
81. C2×C4×C22⋊C4C22semidirect
82. C2×C4×C22⋊C4C22semidirect
85. C22×#95C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1443C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
94. #1440C22semidirect
99. #1439C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1436C22semidirect
112. #1436C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
118. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C4×#95C22semidirect
127. C4×#95C22semidirect
157. C2×#120C2×C4semidirect
184. C22×C22⋊C4C2×C4semidirect
224. #393C2×C4semidirect
225. #392C2×C4semidirect
249. #386C2×C4semidirect
250. #386C2×C4semidirect
251. #386C2×C4semidirect
252. #386D4semidirect
257. #381C2×C4semidirect
269. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#24042
C2×#23392
C2×#23212
C2×#23112
C22×#3882
#146962
#145222
#145202
#144102
#143742
#142632
#142552
#142322
#142282
#140202
#140162
#140122
#139992
#139952
#139672
#138682
#137992
C4×#3862