Finite Group Databasebeta

← #918074

Subgroups — #918074

Order 512.

4266 conjugacy classes of subgroups.

The subgroup lattice has 1364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2543C211yesmaximal, characteristic, complemented
2C2×#2436C211yesmaximal, characteristic, complemented
3C2×#2617C211yesmaximal, characteristic, complemented
4C22×#393C211yesmaximal, characteristic, complemented
5#17105C212yesmaximal, complemented
6#17098C212yesmaximal, complemented
7#16544C212yesmaximal, complemented
8#16509C212yesmaximal, complemented
9#16378C212yesmaximal, complemented
10#16357C212yesmaximal, complemented
11#15631C212yesmaximal, complemented
12#15314C212yesmaximal, complemented
13#14921C211yesmaximal, characteristic, complemented
14#14913C211yesmaximal, characteristic, complemented
15#14913C211yesmaximal, characteristic, complemented
16#14873C211yesmaximal, characteristic, complemented
17#14716C211yesmaximal, characteristic, complemented
18#14716C211yesmaximal, characteristic, complemented
19#14255C211yesmaximal, characteristic, complemented
20#14016C211yesmaximal, characteristic, complemented
21#13995C211yesmaximal, characteristic, complemented
22#13967C211yesmaximal, characteristic, complemented
23#13883C211yesmaximal, characteristic, complemented
24C24×Q8C2211yescharacteristic
25C22×#124C2212yescomplemented
26C22×#121C2211yescharacteristic
27C22×#121C2211yescharacteristic
28C22×#121C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#120C2211yescharacteristic
31C22×#120C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2617—28no—
37#2543—28no—
38#2436—28no—
39C2×#398C2211yescharacteristic, complemented
40C2×#397C2212yes—
41C2×#397C2211yescharacteristic, complemented
42C2×#394C2212yes—
43C2×#394C2212yes—
44C2×#394C2211yescharacteristic, complemented
45C2×#393—28no—
46C2×#393C2212yes—
47C2×#393C2212yes—
48C2×#393C2212yes—
49C2×#393C2212yes—
50C2×#393C2212yescomplemented
51C2×#393C2212yescomplemented
52C2×#393C2212yescomplemented
53C2×#393C2212yescomplemented
54C2×#392C2212yes—
55C2×#392C2212yes—
56C2×#392C2212yes—
57C2×#392C2211yescharacteristic, complemented
58C2×#391C2212yescomplemented
59C2×#390C2212yes—
60C2×#388C2211yescharacteristic, complemented
61C2×#388C2211yescharacteristic, complemented
62C2×#386C2211yescharacteristic
63C2×#386C2211yescharacteristic
64C2×#386C2211yescharacteristic
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2211yescharacteristic
70C2×#386C2211yescharacteristic
71C2×#386C2211yescharacteristic
72C2×#386C2212yes—
73C2×#386C2211yescharacteristic
74C2×#386C2211yescharacteristic, complemented
75C2×#386C2211yescharacteristic, complemented
76C2×#385C2211yescharacteristic
77C2×#380C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C22×#95C2211yescharacteristic
81C22×#95C2211yescharacteristic
82C22×#95C2211yescharacteristic
83#1446C2212yescomplemented
84#1446C2212yescomplemented
85#1443C2212yescomplemented
86#1443C2212yescomplemented
87#1442C2212yescomplemented
88#1442C2212yescomplemented
89#1442C2212yescomplemented
90#1442C2212yescomplemented
91#1441C2212yescomplemented
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1439C2212yes—
99#1439C2212yes—
100#1439C2212yes—
101#1439C2212yes—
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yes—
110#1438C2212yes—
111#1438C2212yes—
112#1438C2212yes—
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1437C2212yes—
116#1437C2212yes—
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119#1434C2212yescomplemented
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C23×Q8—24no—
129C23×Q8—24no—
130C23×Q8—42no—
131C23×Q8—44no—
132C23×Q8—44no—
133C23×Q8C2312yes—
134C23×Q8C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2311yescharacteristic
143C23×D4C2312yes—
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C2×#124—28no—
152C2×#124—44no—
153C2×#124—44no—
154C2×#121—24no—
155C2×#121—24no—
156C2×#121—24no—
157C2×#121—24no—
158C2×#121—24no—
159C2×#121—42no—
160C2×#121—42no—
161C2×#121—42no—
162C2×#121—42no—
163C2×#120—24no—
164C2×#120—24no—
165C2×#120—24no—
166C2×#120—24no—
167C2×#120—24no—
168C2×#120—42no—
169C2×#120—42no—
170C2×#120—42no—
171C2×#120—42no—
172C2×C4×D4—24no—
173C2×C4×D4—42no—
174C2×C4×D4—42no—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C22⋊C4—24no—
182C22×C22⋊C4—24no—
183C22×C22⋊C4—24no—
184C22×C22⋊C4—24no—
185C22×C22⋊C4—44no—
186C22×C22⋊C4—44no—
187C22×C22⋊C4—42no—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2312yes—
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226#398—24no—
227#397—28no—
228#397—24no—
229#394—28no—
230#394—28no—
231#394—24no—
232#393—28no—
233#393—28no—
234#393—28no—
235#393—28no—
236#393—28no—
237#393—28no—
238#393—44no—
239#393—44no—
240#392—28no—
241#392—24no—
242#392—44no—
243#392—44no—
244#391—28no—
245#390—44no—
246#388—24no—
247#388—24no—
248#386—24no—
249#386—24no—
250#386—24no—
251#386—24no—
252#386—24no—
253#386—24no—
254#386—24no—
255#386—24no—
256#386—44no—
257#386—42no—
258#386—42no—
259#386—42no—
260#386—42no—
261#386D418yescomplemented
262#385—42no—
263#380—24no—
264#379—42no—
265C4×C22⋊C4—24no—
266C2×#95—24no—
267C2×#95—24no—
268C2×#95D418yescomplemented
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×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
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×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2312yes—
305C25—22no—
306C25—22no—
307C25—22no—
308C25—22no—
309C25—22no—
310C25—22no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25#4114yes—
316C25C2411yescharacteristic
317C25C2411yescharacteristic
318C25C2411yescharacteristic
319C25C2412yes—
320C25C2411yescharacteristic
321C22×Q8—24no—
322C22×Q8—24no—
323C22×Q8—24no—
324C22×Q8—24no—
325C22×Q8—24no—
326C22×Q8—24no—
327C22×Q8—24no—
328C22×Q8—24no—
329C22×Q8—42no—
330C22×Q8—42no—
331C22×Q8—42no—
332C22×Q8—42no—
333C22×Q8—42no—
334C22×Q8—42no—
335C22×Q8—416no—
336C22×Q8—416no—
337C22×Q8—416no—
338C22×Q8—432no—
339C22×Q8—432no—
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—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—24no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—22no—
370C22×D4—24no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—41no—
376C22×D4—41no—
377C22×D4—41no—
378C22×D4—41no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—42no—
388C22×D4—42no—
389C22×D4—42no—
390C22×D4—42no—
391C22×D4—42no—
392C22×D4—42no—
393C22×D4—42no—
394C22×D4—42no—
395C22×D4—42no—
396C22×D4C2×D414yes—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—22no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—24no—
407C23×C4—24no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—41no—
421C23×C4—41no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4C2×D414yes—
429C23×C4C2×D414yes—
430C23×C4C2×D414yes—
431C23×C4C2×D414yes—
432C23×C4C2411yescharacteristic
433C23×C4C2412yes—
434C23×C4C2412yes—
435C23×C4C2411yescharacteristic
436C23×C4C2411yescharacteristic
437C23×C4C2411yescharacteristic
438C23×C4C2412yes—
439C23×C4C2412yes—
440C23×C4C2411yescharacteristic
441C23×C4C2411yescharacteristic
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2412yes—
445C23×C4C2411yescharacteristic
446C23×C4C2411yescharacteristic
447C23×C4C2411yescharacteristic
448C23×C4C2412yes—
449C23×C4C2411yescharacteristic
450#124—432no—
451#121—416no—
452#121—416no—
453#121—416no—
454#120—416no—
455#120—416no—
456#120—416no—
457C4×D4—416no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—41no—
466C2×C4⋊C4—41no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—41no—
469C2×C4⋊C4—41no—
470C2×C4⋊C4—41no—
471C2×C4⋊C4—42no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—42no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—42no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—22no—
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—24no—
497C2×C22⋊C4—24no—
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—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
545C2×C22⋊C4—41no—
546C2×C22⋊C4—41no—
547C2×C22⋊C4—41no—
548C2×C22⋊C4—41no—
549C2×C22⋊C4—41no—
550C2×C22⋊C4—41no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—416no—
558C2×C22⋊C4—416no—
559C2×C22⋊C4—416no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4—42no—
581C2×C22⋊C4C2×D414yes—
582C2×C22⋊C4C2×D418yes—
583C2×C42—22no—
584C2×C42—24no—
585C2×C42—24no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42—42no—
589#95—24no—
590#95—24no—
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—24no—
602#95—24no—
603#95—24no—
604#95—24no—
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#95—42no—
615#95—42no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95C2×D414yes—
621#95C2×D414yes—
622#95C2×D414yes—
623#95C2×D414yes—
624#95C2×D418yes—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—28no—
630C24—22no—
631C24—22no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—28no—
655C24—28no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—48no—
679C24—48no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—48no—
685C24—48no—
686C24—44no—
687C24—44no—
688C24—44no—
689C24—44no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24C22×D412yes—
699C24C22×D412yes—
700C24C22×D412yes—
701C24C2×#4114yes—
702C24C2×#4112yes—
703C24H(5,𝔽2)12yes—
704C24H(5,𝔽2)12yes—
705C24H(5,𝔽2)12yes—
706C242−1+412yes—
707C24C2511yescharacteristic
708C2×Q8—216no—
709C2×Q8—48no—
710C2×Q8—48no—
711C2×Q8—48no—
712C2×Q8—48no—
713C2×Q8—48no—
714C2×Q8—48no—
715C2×Q8—48no—
716C2×Q8—48no—
717C2×Q8—48no—
718C2×Q8—48no—
719C2×Q8—48no—
720C2×Q8—4128no—
721C2×Q8—48no—
722C2×Q8—48no—
723C2×D4—28no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—48no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—44no—
735C2×D4—44no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—82no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—82no—
759C2×D4—82no—
760C2×D4—82no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C2×D4—84no—
777C2×D4—84no—
778C2×D4—84no—
779C2×D4—84no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—28no—
784C22×C4—28no—
785C22×C4—28no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
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—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—28no—
831C22×C4—28no—
832C22×C4—28no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—22no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—22no—
884C22×C4—22no—
885C22×C4—44no—
886C22×C4—48no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—82no—
905C22×C4—82no—
906C22×C4—84no—
907C22×C4—84no—
908C22×C4—84no—
909C22×C4—84no—
910C22×C4—84no—
911C22×C4—84no—
912C22×C4—84no—
913C22×C4—84no—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D414yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C22×D414yes—
921C22×C4C22×D412yes—
922C22×C4C22×D412yes—
923C22×C4H(5,𝔽2)14yes—
924C22×C4H(5,𝔽2)14yes—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—84no—
930C4⋊C4—84no—
931C22⋊C4—28no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—44no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—48no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—44no—
957C22⋊C4—48no—
958C22⋊C4—82no—
959C22⋊C4—84no—
960C22⋊C4—82no—
961C22⋊C4—84no—
962C22⋊C4—84no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C42—48no—
968C42—44no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—24no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—24no—
989C23—22no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—416no—
998C23—416no—
999C23—416no—
1000C23—42no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—42no—
1005C23—41no—
1006C23—42no—
1007C23—41no—
1008C23—42no—
1009C23—41no—
1010C23—42no—
1011C23—41no—
1012C23—42no—
1013C23—42no—
1014C23—41no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
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—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—42no—
1063C23—41no—
1064C23—42no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—41no—
1075C23—41no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—42no—
1083C23—42no—
1084C23—42no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—816no—
1093C23—816no—
1094C23—88no—
1095C23—816no—
1096C23—816no—
1097C23—88no—
1098C23—88no—
1099C23—88no—
1100C23#53514yes—
1101C23#53714yes—
1102C23#53814yes—
1103C23D4214yes—
1104C23#54614yes—
1105C23#54814yes—
1106C23#56214yes—
1107C23C23×D411yescharacteristic
1108C23C23×D411yescharacteristic
1109C23C22×#4111yescharacteristic
1110C23C2×H(5,𝔽2)11yescharacteristic
1111C23C2×H(5,𝔽2)11yescharacteristic
1112C23C2×H(5,𝔽2)12yes—
1113C23C2×H(5,𝔽2)11yescharacteristic
1114C23C2×H(5,𝔽2)12yes—
1115C23C2×2−1+411yescharacteristic
1116C23#58512yes—
1117C23#58512yes—
1118Q8—432no—
1119Q8—432no—
1120D4—416no—
1121D4—88no—
1122D4—88no—
1123D4—816no—
1124D4—88no—
1125D4—816no—
1126D4—816no—
1127D4—88no—
1128D4—88no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—22no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—416no—
1161C2×C4—416no—
1162C2×C4—416no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—42no—
1168C2×C4—41no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—41no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—41no—
1190C2×C4—42no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—42no—
1196C2×C4—42no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—42no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—41no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—88no—
1242C2×C4—88no—
1243C2×C4—88no—
1244C2×C4—88no—
1245C2×C4#53514yes—
1246C22—24no—
1247C22—24no—
1248C22—28no—
1249C22—24no—
1250C22—28no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—28no—
1255C22—28no—
1256C22—42no—
1257C22—44no—
1258C22—44no—
1259C22—44no—
1260C22—42no—
1261C22—44no—
1262C22—42no—
1263C22—44no—
1264C22—44no—
1265C22—44no—
1266C22—44no—
1267C22—44no—
1268C22—832no—
1269C22—82no—
1270C22—81no—
1271C22—82no—
1272C22—82no—
1273C22—81no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—81no—
1278C22—82no—
1279C22—81no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—82no—
1288C22—82no—
1289C22—81no—
1290C22—81no—
1291C22—82no—
1292C22—82no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—82no—
1302C22—82no—
1303C22—82no—
1304C22—82no—
1305C22#267618yes—
1306C22C2×#53511yescharacteristic
1307C22C2×#53511yescharacteristic
1308C22C2×#53711yescharacteristic
1309C22#344911yescharacteristic
1310C22C2×#53811yescharacteristic
1311C22C2×D4211yescharacteristic
1312C22C2×#54611yescharacteristic
1313C22C2×#54811yescharacteristic
1314C22#348411yescharacteristic
1315C22#348412yes—
1316C22#348511yescharacteristic
1317C22#350012yes—
1318C22#350512yes—
1319C22#350512yes—
1320C22C2×#56211yescharacteristic
1321C22#353212yes—
1322C22#354112yes—
1323C22#354112yes—
1324C22#354512yes—
1325C22#355812yes—
1326C22#355812yes—
1327C22#355812yes—
1328C22#355812yes—
1329C4—24no—
1330C4—42no—
1331C4—44no—
1332C4—44no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—44no—
1339C4—82no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—82no—
1345C4—82no—
1346C4—82no—
1347C2—28no—
1348C2—82no—
1349C2—84no—
1350C2—161no—
1351C2—161no—
1352C2#3696711yescharacteristic
1353C2#3753611yescharacteristic
1354C2#3764511yescharacteristic
1355C2#3933311yescharacteristic
1356C2#3971611yescharacteristic
1357C2#3972211yescharacteristic
1358C2#4048912yes—
1359C2#4066012yes—
1360C2#4300012yes—
1361C2C2×#267611yescharacteristic
1362C2#5231712yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#2543C2semidirect
2. C2×#2436C2semidirect
3. C2×#2617C2semidirect
4. C22×#393C2semidirect
5. #17105C2semidirect
6. #17098C2semidirect
7. #16544C2semidirect
8. #16509C2semidirect
9. #16378C2semidirect
10. #16357C2semidirect
11. #15631C2semidirect
12. #15314C2semidirect
13. #14921C2semidirect
14. #14913C2semidirect
15. #14913C2semidirect
16. #14873C2semidirect
17. #14716C2semidirect
18. #14716C2semidirect
19. #14255C2semidirect
20. #14016C2semidirect
21. #13995C2semidirect
22. #13967C2semidirect
23. #13883C2semidirect
25. C22×#124C22semidirect
39. C2×#398C22semidirect
41. C2×#397C22semidirect
44. C2×#394C22semidirect
50. C2×#393C22semidirect
51. C2×#393C22semidirect
52. C2×#393C22semidirect
53. C2×#393C22semidirect
57. C2×#392C22semidirect
58. C2×#391C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
74. C2×#386C22semidirect
75. C2×#386C22semidirect
83. #1446C22semidirect
84. #1446C22semidirect
85. #1443C22semidirect
86. #1443C22semidirect
87. #1442C22semidirect
88. #1442C22semidirect
89. #1442C22semidirect
90. #1442C22semidirect
91. #1441C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
119. #1434C22semidirect
126. C22⋊#95C22semidirect
261. #386D4semidirect
268. C2×#95D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25432
C2×#24362
C2×#26172
C22×#3932
#171052
#170982
#165442
#165092
#163782
#163572
#156312
#153142
#149212
#149132
#148732
#147162
#142552
#140162
#139952
#139672
#138832