Finite Group Databasebeta

← #657168

Subgroups — #657168

Order 512.

4743 conjugacy classes of subgroups.

The subgroup lattice has 1367 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2561C211yesmaximal, characteristic, complemented
2C2×#2472C211yesmaximal, characteristic, complemented
3C2×#2412C211yesmaximal, characteristic, complemented
4C22×#390C211yesmaximal, characteristic, complemented
5#15694C212yesmaximal, complemented
6#15651C212yesmaximal, complemented
7#15501C212yesmaximal, complemented
8#15476C212yesmaximal, complemented
9#14949C212yesmaximal, complemented
10#14928C212yesmaximal, complemented
11#14918C211yesmaximal, characteristic, complemented
12#14911C211yesmaximal, characteristic, complemented
13#14720C211yesmaximal, characteristic, complemented
14#14715C211yesmaximal, characteristic
15#14706C211yesmaximal, characteristic, complemented
16#14228C212yesmaximal, complemented
17#14019C211yesmaximal, characteristic, complemented
18#14012C212yesmaximal, complemented
19#13995C211yesmaximal, characteristic, complemented
20#13991C211yesmaximal, characteristic, complemented
21#13867C211yesmaximal, characteristic, complemented
22C22⋊C42C211yesmaximal, characteristic, complemented
23C4×#381C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#124C2211yescharacteristic, complemented
26C22×#123C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C23×C4⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C42C2211yescharacteristic
37#2561—28no—
38#2472—28no—
39#2412—28no—
40C2×#397C2212yescomplemented
41C2×#397C2211yescharacteristic, complemented
42C2×#397C2212yescomplemented
43C2×#395C2212yescomplemented
44C2×#394C2211yescharacteristic, complemented
45C2×#394C2212yescomplemented
46C2×#394C2211yescharacteristic, complemented
47C2×#393C2212yescomplemented
48C2×#393C2211yescharacteristic, complemented
49C2×#392C2212yes—
50C2×#392C2212yes—
51C2×#390—28no—
52C2×#390C2212yes—
53C2×#390C2212yes—
54C2×#390C2212yes—
55C2×#390C2212yes—
56C2×#390C2211yescharacteristic, complemented
57C2×#390C2212yescomplemented
58C2×#388C2212yescomplemented
59C2×#388C2212yescomplemented
60C2×#388C2211yescharacteristic, complemented
61C2×#388C2211yescharacteristic, complemented
62C2×#388C2212yescomplemented
63C2×#388C2212yescomplemented
64C2×#386C2212yes—
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic
68C2×#386C2211yescharacteristic
69C2×#386C2212yes—
70C2×#386C2212yescomplemented
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#381C2211yescharacteristic
74C2×#381C2211yescharacteristic
75C2×#381C2211yescharacteristic
76C2×#380C2212yescomplemented
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2211yescharacteristic
80C2×#379C2211yescharacteristic
81C2×#379C2211yescharacteristic
82C2×C4×C22⋊C4C2211yescharacteristic
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×C4×C22⋊C4C2212yescomplemented
86#1444C2212yescomplemented
87#1444C2212yescomplemented
88#1442C2212yescomplemented
89#1441C2212yescomplemented
90#1440C2212yescomplemented
91#1440C2212yescomplemented
92#1440C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yescomplemented
105#1438C2212yescomplemented
106#1438C2212yescomplemented
107#1437C2212yescomplemented
108#1437C2212yescomplemented
109#1437C2212yescomplemented
110#1437C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1436C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1434C2212yescomplemented
117#1434C2212yescomplemented
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2211yescharacteristic
122C22⋊#95C2211yescharacteristic
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2212yescomplemented
125C4×#95C2212yescomplemented
126C4×#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—28no—
132C23×D4—24no—
133C23×D4—44no—
134C23×D4—42no—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C24×C4C2311yescharacteristic
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2312yes—
146C24×C4C2311yescharacteristic
147C2×#124—24no—
148C2×#124—44no—
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—42no—
152C2×C22⋊Q8—24no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—42no—
155C2×#120—24no—
156C2×#120—24no—
157C2×#120—24no—
158C2×#120—42no—
159C2×#120—42no—
160C2×#120—42no—
161C22×C4⋊C4—24no—
162C22×C4⋊C4—44no—
163C22×C4⋊C4C2311yescharacteristic
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2312yes—
171C22×C22⋊C4—24no—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—44no—
179C22×C22⋊C4—44no—
180C22×C22⋊C4—42no—
181C22×C22⋊C4—42no—
182C22×C22⋊C4—42no—
183C22×C22⋊C4D418yescomplemented
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2312yes—
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2311yescharacteristic
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2312yes—
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C42—24no—
225C22×C42—24no—
226C22×C42—42no—
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229C22×C42C2312yes—
230C22×C42C2312yes—
231C22×C42C2311yescharacteristic
232C22×C42C2312yes—
233#397—24no—
234#397—28no—
235#397—28no—
236#395—44no—
237#394—24no—
238#394—24no—
239#394—28no—
240#393—24no—
241#393—28no—
242#392—28no—
243#392—44no—
244#390—24no—
245#390—28no—
246#390—28no—
247#390—28no—
248#390—28no—
249#390—44no—
250#388—24no—
251#388—24no—
252#388—28no—
253#388—28no—
254#388—44no—
255#388—44no—
256#386—28no—
257#386—24no—
258#386—24no—
259#386—24no—
260#386—24no—
261#386—28no—
262#386—44no—
263#385—24no—
264#385—42no—
265#381—24no—
266#381—24no—
267#381D418yescomplemented
268#380—28no—
269#379—24no—
270#379—24no—
271#379—24no—
272#379—24no—
273#379—24no—
274C4×C22⋊C4—24no—
275C4×C22⋊C4—24no—
276C4×C22⋊C4—44no—
277C4×C22⋊C4—42no—
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2311yescharacteristic
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C25—22no—
309C25—24no—
310C25—24no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25C2×D414yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2412yes—
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C22×Q8—22no—
336C22×Q8—22no—
337C22×Q8—41no—
338C22×Q8—42no—
339C22×Q8—42no—
340C22×D4—232no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
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—24no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—24no—
364C22×D4—432no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—416no—
370C22×D4—416no—
371C22×D4—432no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—41no—
375C22×D4—41no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4#4118yes—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—24no—
386C23×C4—24no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4C2×D414yes—
414C23×C4C2×D414yes—
415C23×C4C2×D414yes—
416C23×C4#4114yes—
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2412yes—
435#124—416no—
436#123—416no—
437C22⋊Q8—416no—
438#120—416no—
439#120—416no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—416no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
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—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—22no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
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—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—416no—
532C2×C22⋊C4—416no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
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—41no—
545C2×C22⋊C4—41no—
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⋊C4—416no—
554C2×C22⋊C4—416no—
555C2×C22⋊C4—416no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
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⋊C4C2×D414yes—
571C2×C22⋊C4C2×D414yes—
572C2×C22⋊C4C2×D414yes—
573C2×C22⋊C4C2×D414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D414yes—
576C2×C22⋊C4#4114yes—
577C2×C22⋊C4#4114yes—
578C2×C42—22no—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—24no—
582C2×C42—24no—
583C2×C42—24no—
584C2×C42—24no—
585C2×C42—22no—
586C2×C42—24no—
587C2×C42—42no—
588C2×C42—42no—
589C2×C42—416no—
590C2×C42—42no—
591C2×C42—42no—
592C2×C42—42no—
593C2×C42—42no—
594C2×C42—42no—
595#95—22no—
596#95—24no—
597#95—22no—
598#95—24no—
599#95—24no—
600#95—24no—
601#95—24no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—24no—
607#95—24no—
608#95—24no—
609#95—24no—
610#95—24no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—42no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95C2×D418yescomplemented
624#95C2×D418yescomplemented
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—21no—
635C24—22no—
636C24—21no—
637C24—22no—
638C24—28no—
639C24—28no—
640C24—22no—
641C24—21no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—21no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—21no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—28no—
665C24—28no—
666C24—28no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—21no—
673C24—22no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—44no—
679C24—44no—
680C24—44no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—44no—
694C24—44no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—44no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24—44no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24—84no—
711C24—84no—
712C24—84no—
713C24—84no—
714C24—84no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24—84no—
719C24C22×D412yes—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C22×D412yes—
723C24C2×#4114yes—
724C24C2×#4114yes—
725C24C2×#4112yes—
726C24C2×#4112yes—
727C24C2×#4112yes—
728C24H(5,𝔽2)12yes—
729C24H(5,𝔽2)12yes—
730C24C2511yescharacteristic
731C2×Q8—44no—
732C2×Q8—44no—
733C2×Q8—82no—
734C2×Q8—84no—
735C2×Q8—84no—
736C2×D4—216no—
737C2×D4—216no—
738C2×D4—216no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—4128no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—44no—
756C2×D4—44no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—48no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—82no—
768C2×D4—82no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—84no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C22×C4—28no—
776C22×C4—28no—
777C22×C4—216no—
778C22×C4—28no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—216no—
787C22×C4—28no—
788C22×C4—28no—
789C22×C4—28no—
790C22×C4—28no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—28no—
836C22×C4—28no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—22no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—22no—
852C22×C4—22no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—22no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—48no—
882C22×C4—48no—
883C22×C4—48no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4—84no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4—84no—
901C22×C4C22×D412yes—
902C22×C4C22×D414yes—
903C22×C4C22×D414yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C22×D412yes—
907C22×C4C22×D412yes—
908C22×C4C22×D412yes—
909C22×C4C2×#4114yes—
910C22×C4C2×#4114yes—
911C22×C4C2×#4114yes—
912C22×C4C2×#4114yes—
913C22×C4H(5,𝔽2)14yes—
914C22×C4H(5,𝔽2)14yes—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—44no—
920C4⋊C4—48no—
921C4⋊C4—84no—
922C4⋊C4—84no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—48no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—48no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—44no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—82no—
955C22⋊C4—82no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4—84no—
959C22⋊C4—84no—
960C22⋊C4—84no—
961C22⋊C4—82no—
962C22⋊C4—82no—
963C42—48no—
964C42—48no—
965C42—44no—
966C42—82no—
967C42—84no—
968C42—84no—
969C23—22no—
970C23—22no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—22no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—24no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—24no—
1010C23—24no—
1011C23—416no—
1012C23—416no—
1013C23—416no—
1014C23—416no—
1015C23—416no—
1016C23—416no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—41no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—41no—
1033C23—42no—
1034C23—41no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—41no—
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—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—416no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—42no—
1081C23—42no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—41no—
1086C23—41no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—88no—
1096C23—88no—
1097C23—88no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—88no—
1107C23—88no—
1108C23—88no—
1109C23—88no—
1110C23#52514yes—
1111C23#53214yes—
1112C23#53214yes—
1113C23#53814yes—
1114C23D4214yes—
1115C23#54614yes—
1116C23#54614yes—
1117C23#55514yes—
1118C23C23×D411yescharacteristic
1119C23C23×D411yescharacteristic
1120C23C22×#4112yes—
1121C23C22×#4111yescharacteristic
1122C23C22×#4111yescharacteristic
1123C23C22×#4111yescharacteristic
1124C23C2×H(5,𝔽2)12yes—
1125C23C2×H(5,𝔽2)11yescharacteristic
1126C23C2×H(5,𝔽2)11yescharacteristic
1127C23C2×H(5,𝔽2)12yes—
1128C23#58512yes—
1129Q8—88no—
1130D4—432no—
1131D4—432no—
1132D4—88no—
1133D4—88no—
1134D4—816no—
1135D4—88no—
1136C2×C4—232no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—24no—
1145C2×C4—24no—
1146C2×C4—24no—
1147C2×C4—24no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—24no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—24no—
1170C2×C4—24no—
1171C2×C4—24no—
1172C2×C4—416no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—41no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
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—416no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—41no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—42no—
1229C2×C4—41no—
1230C2×C4—41no—
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—42no—
1242C2×C4—42no—
1243C2×C4—88no—
1244C2×C4—816no—
1245C2×C4—88no—
1246C2×C4#53414yes—
1247C2×C4#55118yes—
1248C22—24no—
1249C22—24no—
1250C22—28no—
1251C22—24no—
1252C22—24no—
1253C22—28no—
1254C22—28no—
1255C22—24no—
1256C22—28no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—42no—
1262C22—44no—
1263C22—42no—
1264C22—44no—
1265C22—44no—
1266C22—42no—
1267C22—44no—
1268C22—42no—
1269C22—42no—
1270C22—44no—
1271C22—42no—
1272C22—44no—
1273C22—42no—
1274C22—44no—
1275C22—42no—
1276C22—42no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—42no—
1281C22—44no—
1282C22—42no—
1283C22—832no—
1284C22—832no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—82no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—82no—
1301C22—81no—
1302C22—81no—
1303C22—82no—
1304C22—82no—
1305C22—81no—
1306C22—82no—
1307C22—81no—
1308C22#255518yes—
1309C22C2×#52511yescharacteristic
1310C22C2×#53211yescharacteristic
1311C22C2×#53211yescharacteristic
1312C22C2×#53411yescharacteristic
1313C22C2×#53811yescharacteristic
1314C22C2×D4211yescharacteristic
1315C22C2×#54611yescharacteristic
1316C22C2×#54611yescharacteristic
1317C22D4×#4112yes—
1318C22C2×#55112yes—
1319C22C2×#55511yescharacteristic
1320C22#348112yes—
1321C22#348112yes—
1322C22#348411yescharacteristic
1323C22#348511yescharacteristic
1324C22#349012yes—
1325C22#349412yes—
1326C22#349812yes—
1327C22#351312yes—
1328C22#351412yes—
1329C22#351412yes—
1330C22#353412yes—
1331C22#354312yes—
1332C4—28no—
1333C4—24no—
1334C4—42no—
1335C4—44no—
1336C4—44no—
1337C4—44no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—44no—
1342C4—42no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—82no—
1348C4—82no—
1349C4—81no—
1350C2—28no—
1351C2—44no—
1352C2—82no—
1353C2—84no—
1354C2—161no—
1355C2C2×#255511yescharacteristic
1356C2#3495711yescharacteristic
1357C2#3546611yescharacteristic
1358C2#3609911yescharacteristic
1359C2#3615811yescharacteristic
1360C2#3626412yes—
1361C2#3783411yescharacteristic
1362C2#3857212yes—
1363C2#3933611yescharacteristic
1364C2#5922412yes—
1365C2#5980012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#14715C2
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×#2561C2semidirect
2. C2×#2472C2semidirect
3. C2×#2412C2semidirect
4. C22×#390C2semidirect
5. #15694C2semidirect
6. #15651C2semidirect
7. #15501C2semidirect
8. #15476C2semidirect
9. #14949C2semidirect
10. #14928C2semidirect
11. #14918C2semidirect
12. #14911C2semidirect
13. #14720C2semidirect
15. #14706C2semidirect
16. #14228C2semidirect
17. #14019C2semidirect
18. #14012C2semidirect
19. #13995C2semidirect
20. #13991C2semidirect
21. #13867C2semidirect
22. C22⋊C42C2semidirect
23. C4×#381C2semidirect
25. C22×#124C22semidirect
40. C2×#397C22semidirect
41. C2×#397C22semidirect
42. C2×#397C22semidirect
43. C2×#395C22semidirect
44. C2×#394C22semidirect
45. C2×#394C22semidirect
46. C2×#394C22semidirect
47. C2×#393C22semidirect
48. C2×#393C22semidirect
56. C2×#390C22semidirect
57. C2×#390C22semidirect
58. C2×#388C22semidirect
59. C2×#388C22semidirect
60. C2×#388C22semidirect
61. C2×#388C22semidirect
62. C2×#388C22semidirect
63. C2×#388C22semidirect
70. C2×#386C22semidirect
76. C2×#380C22semidirect
85. C2×C4×C22⋊C4C22semidirect
86. #1444C22semidirect
87. #1444C22semidirect
88. #1442C22semidirect
89. #1441C22semidirect
90. #1440C22semidirect
91. #1440C22semidirect
92. #1440C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
104. #1438C22semidirect
105. #1438C22semidirect
106. #1438C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1436C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1434C22semidirect
117. #1434C22semidirect
124. C22⋊#95C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
183. C22×C22⋊C4D4semidirect
267. #381D4semidirect
623. #95C2×D4semidirect
624. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25612
C2×#24722
C2×#24122
C22×#3902
#156942
#156512
#155012
#154762
#149492
#149282
#149182
#149112
#147202
#147152
#147062
#142282
#140192
#140122
#139952
#139912
#138672
C22⋊C422
C4×#3812