Finite Group Databasebeta

← #760372

Subgroups — #760372

Order 512.

6164 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic, complemented
2C2×#2564C211yesmaximal, characteristic, complemented
3C2×#2543C211yesmaximal, characteristic, complemented
4C2×C4×#120C211yesmaximal, characteristic, complemented
5#16632C211yesmaximal, characteristic, complemented
6#16606C211yesmaximal, characteristic, complemented
7#16557C211yesmaximal, characteristic, complemented
8#16508C211yesmaximal, characteristic, complemented
9#14964C212yesmaximal, complemented
10#14906C211yesmaximal, characteristic, complemented
11#14905C211yesmaximal, characteristic, complemented
12#14889C211yesmaximal, characteristic, complemented
13#14885C211yesmaximal, characteristic, complemented
14#14725C212yesmaximal, complemented
15#14721C212yesmaximal, complemented
16#14716C212yesmaximal, complemented
17#14173C212yesmaximal, complemented
18#14171C212yesmaximal, complemented
19#14159C211yesmaximal, characteristic, complemented
20#14152C211yesmaximal, characteristic, complemented
21#14023C212yesmaximal, complemented
22#13975C212yesmaximal, complemented
23C2×C22⋊#95C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C2×#525—28no—
27C2×#525—28no—
28C2×#525—28no—
29C22×#123C2212yes—
30C22×C22⋊Q8C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×#121C2212yes—
34C22×#121C2211yescharacteristic
35C22×#120C2211yescharacteristic
36C22×#120C2212yes—
37C22×C4×D4C2211yescharacteristic
38C22×C4×D4C2212yes—
39C22×C4×D4C2212yes—
40C22×C4×D4C2211yescharacteristic
41C22×C4×D4C2211yescharacteristic
42C22×#117C2211yescharacteristic
43C23×C22⋊C4C2212yes—
44#2564—28no—
45#2543—28no—
46C2×#400C2211yescharacteristic, complemented
47C2×#399C2211yescharacteristic, complemented
48C2×#398C2211yescharacteristic, complemented
49C2×#397C2211yescharacteristic, complemented
50C2×#395C2211yescharacteristic, complemented
51C2×#394C2212yes—
52C2×#394C2212yes—
53C2×#394C2211yescharacteristic, complemented
54C2×#393C2211yescharacteristic, complemented
55C2×#392C2212yes—
56C2×#392C2212yes—
57C2×#392C2211yescharacteristic, complemented
58C4×#120—28no—
59C2×#388C2212yescomplemented
60C2×#387C2212yescomplemented
61C2×#386C2212yes—
62C2×#386C2212yes—
63C2×#386C2211yescharacteristic
64C2×#386C2212yes—
65C2×#386C2211yescharacteristic
66C2×#386C2211yescharacteristic
67C2×#386C2212yes—
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#385C2211yescharacteristic
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2212yescomplemented
74C2×#385C2212yescomplemented
75C2×#380C2212yes—
76C2×#379C2211yescharacteristic
77C2×C4×C22⋊C4C2211yescharacteristic
78C2×C4×C22⋊C4C2211yescharacteristic
79C2×C4×C22⋊C4C2211yescharacteristic
80C22×#95C2211yescharacteristic
81C22×#95C2211yescharacteristic
82C22×#95C2212yes—
83#1446C2211yescharacteristic, complemented
84#1446C2211yescharacteristic, complemented
85#1445C2211yescharacteristic, complemented
86#1445C2211yescharacteristic, complemented
87#1445C2211yescharacteristic, complemented
88#1445C2211yescharacteristic, complemented
89#1444C2212yescomplemented
90#1442C2212yescomplemented
91#1441C2212yescomplemented
92#1440C2212yes—
93#1440C2212yes—
94#1440C2212yescomplemented
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yes—
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1438C2212yes—
103#1438C2212yes—
104#1438C2212yes—
105#1438C2212yes—
106#1438C2212yes—
107#1438C2212yes—
108#1438C2211yescharacteristic, complemented
109#1438C2211yescharacteristic, complemented
110#1438C2212yescomplemented
111#1437C2212yescomplemented
112#1437C2212yescomplemented
113#1437C2212yescomplemented
114#1436C2212yescomplemented
115#1436C2212yescomplemented
116#1436C2212yescomplemented
117#1436C2212yescomplemented
118#1436C2212yescomplemented
119C22⋊#95C2211yescharacteristic
120C22⋊#95C2211yescharacteristic
121C22⋊#95C2212yes—
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2212yescomplemented
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—24no—
133C22×#41—44no—
134C22×#41—44no—
135C23×Q8C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2311yescharacteristic
141C23×D4C2312yes—
142C23×D4C2312yes—
143C23×D4C2311yescharacteristic
144C24×C4—24no—
145C24×C4—24no—
146C24×C4—44no—
147C24×C4—44no—
148C24×C4D418yescomplemented
149C24×C4C2311yescharacteristic
150C24×C4C2312yes—
151C24×C4C2312yes—
152C24×C4C2312yes—
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158C24×C4C2311yescharacteristic
159#525—2128no—
160C2×#123—28no—
161C2×#123—28no—
162C2×#123—28no—
163C2×C22⋊Q8—24no—
164C2×C22⋊Q8—24no—
165C2×C22⋊Q8—24no—
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—24no—
168C2×C22⋊Q8D418yescomplemented
169C2×#121—24no—
170C2×#121—24no—
171C2×#121—24no—
172C2×#121—24no—
173C2×#121—28no—
174C2×#121—28no—
175C2×#121—24no—
176C2×#121—44no—
177C2×#121D418yescomplemented
178C2×#120—28no—
179C2×#120—24no—
180C2×#120—28no—
181C2×#120—24no—
182C2×#120—28no—
183C2×#120—24no—
184C2×C4×D4—28no—
185C2×C4×D4—28no—
186C2×C4×D4—28no—
187C2×C4×D4—24no—
188C2×C4×D4—24no—
189C2×C4×D4—24no—
190C2×C4×D4—24no—
191C2×C4×D4—24no—
192C2×C4×D4—28no—
193C2×C4×D4—28no—
194C2×C4×D4—28no—
195C2×C4×D4—44no—
196C2×C4×D4—44no—
197C2×#117—24no—
198C2×#117—24no—
199C2×#117—24no—
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2312yes—
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2312yes—
204C22×C4⋊C4C2312yes—
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2311yescharacteristic
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C4⋊C4C2311yescharacteristic
210C22×C22⋊C4—28no—
211C22×C22⋊C4—44no—
212C22×C22⋊C4—44no—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2311yescharacteristic
240C22×C22⋊C4C2311yescharacteristic
241C22×C22⋊C4C2311yescharacteristic
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C42C2312yes—
245C22×C42C2311yescharacteristic
246C22×C42C2311yescharacteristic
247C22×C42C2311yescharacteristic
248#400—24no—
249#399—24no—
250#398—24no—
251#397—24no—
252#395—24no—
253#394—24no—
254#394—28no—
255#394—44no—
256#393—24no—
257#392—24no—
258#392—28no—
259#392—44no—
260#388—28no—
261#387—28no—
262#386—28no—
263#386—24no—
264#386—24no—
265#386—24no—
266#386—28no—
267#386—28no—
268#386—28no—
269#386—44no—
270#386—44no—
271#385—24no—
272#385—24no—
273#385—24no—
274#385—28no—
275#385—44no—
276#380—28no—
277#379—24no—
278C4×C22⋊C4—24no—
279C4×C22⋊C4—24no—
280C4×C22⋊C4—24no—
281C2×#95—24no—
282C2×#95—24no—
283C2×#95—44no—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2311yescharacteristic
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C25—24no—
319C25—22no—
320C25—24no—
321C25—22no—
322C25—22no—
323C25—22no—
324C25—22no—
325C25—22no—
326C25—42no—
327C25—42no—
328C25C2×D414yes—
329C25C2412yes—
330C25C2411yescharacteristic
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C2×#41—232no—
335C2×#41—432no—
336C2×#41—432no—
337C2×#41—416no—
338C2×#41—416no—
339C22×Q8—22no—
340C22×Q8—22no—
341C22×Q8—42no—
342C22×Q8—42no—
343C22×Q8C2×D414yes—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—22no—
349C22×D4—22no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—22no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—22no—
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—24no—
372C22×D4—24no—
373C22×D4—24no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—22no—
377C22×D4—22no—
378C22×D4—24no—
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×D4C2×D418yes—
392C22×D4C2×D414yes—
393C22×D4#4114yescomplemented
394C23×C4—24no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—232no—
403C23×C4—22no—
404C23×C4—22no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—22no—
410C23×C4—22no—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4—24no—
414C23×C4—24no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—24no—
418C23×C4—24no—
419C23×C4—22no—
420C23×C4—24no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—416no—
427C23×C4—416no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4—42no—
433C23×C4—42no—
434C23×C4—42no—
435C23×C4—42no—
436C23×C4—42no—
437C23×C4—42no—
438C23×C4—42no—
439C23×C4—42no—
440C23×C4—42no—
441C23×C4—42no—
442C23×C4—42no—
443C23×C4—42no—
444C23×C4—42no—
445C23×C4—432no—
446C23×C4—432no—
447C23×C4C2×D414yes—
448C23×C4C2×D414yes—
449C23×C4C2×D414yes—
450C23×C4C2×D414yes—
451C23×C4C2×D414yes—
452C23×C4C2×D414yes—
453C23×C4C2×D414yes—
454C23×C4C2×D414yes—
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2412yes—
460C23×C4C2412yes—
461C23×C4C2412yes—
462C23×C4C2412yes—
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2412yes—
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2411yescharacteristic
471C23×C4C2411yescharacteristic
472C23×C4C2411yescharacteristic
473#123—264no—
474C22⋊Q8—232no—
475C22⋊Q8—232no—
476#121—232no—
477#121—232no—
478#121—432no—
479#120—232no—
480#120—264no—
481C4×D4—264no—
482C4×D4—264no—
483C4×D4—416no—
484C4×D4—416no—
485C4×D4—416no—
486#117—232no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—24no—
502C2×C4⋊C4—24no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—24no—
505C2×C4⋊C4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—42no—
510C2×C4⋊C4—42no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4C2×D414yes—
513C2×C4⋊C4C2×D414yes—
514C2×C4⋊C4C2×D418yes—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—22no—
535C2×C22⋊C4—22no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4—22no—
538C2×C22⋊C4—22no—
539C2×C22⋊C4—22no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—24no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—24no—
569C2×C22⋊C4—24no—
570C2×C22⋊C4—24no—
571C2×C22⋊C4—24no—
572C2×C22⋊C4—24no—
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⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—42no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—432no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4—42no—
593C2×C22⋊C4—42no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4C2×D418yes—
600C2×C22⋊C4C2×D418yes—
601C2×C22⋊C4#4114yescomplemented
602C2×C22⋊C4#4118yescomplemented
603C2×C42—24no—
604C2×C42—24no—
605C2×C42—24no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—42no—
612C2×C42—42no—
613#95—24no—
614#95—24no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—24no—
633#95—24no—
634#95—24no—
635#95—24no—
636#95—24no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95—42no—
642#95—42no—
643#95—42no—
644#95—42no—
645#95—42no—
646#95—42no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—216no—
652C24—216no—
653C24—28no—
654C24—28no—
655C24—28no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—22no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—21no—
671C24—21no—
672C24—22no—
673C24—22no—
674C24—28no—
675C24—28no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—21no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—21no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—44no—
701C24—44no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—44no—
715C24—44no—
716C24C22×D414yes—
717C24C22×D412yes—
718C24C22×D412yes—
719C24C22×D412yes—
720C24C22×D412yes—
721C24C22×D412yes—
722C24C2×#4112yes—
723C24C2×#4114yes—
724C24C2×#4112yes—
725C24C2×#4112yes—
726C24H(5,𝔽2)14yes—
727C24H(5,𝔽2)12yes—
728C242−1+412yes—
729C24C2511yescharacteristic
730#41—4128no—
731C2×Q8—28no—
732C2×Q8—48no—
733C2×Q8—44no—
734C2×Q8—44no—
735C2×Q8—48no—
736C2×D4—216no—
737C2×D4—216no—
738C2×D4—28no—
739C2×D4—28no—
740C2×D4—216no—
741C2×D4—28no—
742C2×D4—28no—
743C2×D4—216no—
744C2×D4—216no—
745C2×D4—28no—
746C2×D4—28no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—44no—
766C2×D4—44no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—44no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—44no—
781C2×D4—48no—
782C2×D4—84no—
783C2×D4—84no—
784C2×D4—84no—
785C2×D4—84no—
786C22×C4—216no—
787C22×C4—216no—
788C22×C4—28no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—28no—
797C22×C4—28no—
798C22×C4—216no—
799C22×C4—28no—
800C22×C4—28no—
801C22×C4—21no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—21no—
840C22×C4—22no—
841C22×C4—22no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—28no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—28no—
853C22×C4—28no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
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—22no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—22no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—44no—
892C22×C4—44no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—48no—
898C22×C4—48no—
899C22×C4—48no—
900C22×C4—48no—
901C22×C4—48no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—4128no—
908C22×C4—48no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—48no—
912C22×C4—48no—
913C22×C4—48no—
914C22×C4—48no—
915C22×C4—48no—
916C22×C4—48no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—44no—
923C22×C4—84no—
924C22×C4—84no—
925C22×C4—84no—
926C22×C4—84no—
927C22×C4—84no—
928C22×C4—84no—
929C22×C4—84no—
930C22×C4—84no—
931C22×C4#120116yes—
932C22×C4C22×D414yes—
933C22×C4C22×D414yes—
934C22×C4C22×D412yes—
935C22×C4C22×D414yes—
936C22×C4C22×D412yes—
937C22×C4C22×D412yes—
938C22×C4C22×D412yes—
939C22×C4C22×D412yes—
940C22×C4C22×D412yes—
941C22×C4C22×D412yes—
942C22×C4C22×D412yes—
943C22×C4C2×#4112yes—
944C22×C4C2×#4112yes—
945C22×C4C2×#4114yes—
946C22×C4C2×#4114yes—
947C22×C4C2×#4112yes—
948C22×C4H(5,𝔽2)14yes—
949C4⋊C4—216no—
950C4⋊C4—28no—
951C4⋊C4—28no—
952C4⋊C4—216no—
953C4⋊C4—48no—
954C4⋊C4—48no—
955C4⋊C4—44no—
956C4⋊C4—44no—
957C4⋊C4—44no—
958C4⋊C4—84no—
959C22⋊C4—216no—
960C22⋊C4—216no—
961C22⋊C4—216no—
962C22⋊C4—28no—
963C22⋊C4—28no—
964C22⋊C4—216no—
965C22⋊C4—28no—
966C22⋊C4—216no—
967C22⋊C4—48no—
968C22⋊C4—48no—
969C22⋊C4—48no—
970C22⋊C4—48no—
971C22⋊C4—48no—
972C22⋊C4—48no—
973C22⋊C4—48no—
974C22⋊C4—48no—
975C22⋊C4—44no—
976C22⋊C4—44no—
977C22⋊C4—48no—
978C22⋊C4—44no—
979C22⋊C4—44no—
980C22⋊C4—44no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—44no—
984C22⋊C4—44no—
985C22⋊C4—84no—
986C22⋊C4—84no—
987C22⋊C4—84no—
988C22⋊C4—84no—
989C22⋊C4—84no—
990C42—216no—
991C42—44no—
992C42—44no—
993C42—44no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—232no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—24no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—24no—
1034C23—24no—
1035C23—24no—
1036C23—22no—
1037C23—22no—
1038C23—24no—
1039C23—24no—
1040C23—22no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—416no—
1048C23—416no—
1049C23—416no—
1050C23—416no—
1051C23—416no—
1052C23—432no—
1053C23—432no—
1054C23—432no—
1055C23—432no—
1056C23—416no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—41no—
1078C23—42no—
1079C23—41no—
1080C23—42no—
1081C23—41no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—41no—
1086C23—42no—
1087C23—42no—
1088C23—41no—
1089C23—41no—
1090C23—42no—
1091C23—41no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—42no—
1118C23—42no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23C2×#12014yes—
1124C23#52514yes—
1125C23#53214yes—
1126C23#53414yes—
1127C23#53714yes—
1128C23#54614yes—
1129C23#54714yes—
1130C23#54814yes—
1131C23#55014yes—
1132C23C23×D411yescharacteristic
1133C23C23×D411yescharacteristic
1134C23C23×D411yescharacteristic
1135C23C22×#4111yescharacteristic
1136C23C22×#4111yescharacteristic
1137C23C22×#4112yes—
1138C23C2×H(5,𝔽2)12yes—
1139C23C2×H(5,𝔽2)12yes—
1140C23C2×H(5,𝔽2)11yescharacteristic
1141C23C2×2−1+411yescharacteristic
1142C23#58512yes—
1143Q8—416no—
1144D4—416no—
1145D4—416no—
1146D4—432no—
1147D4—416no—
1148D4—432no—
1149D4—432no—
1150D4—416no—
1151D4—816no—
1152C2×C4—232no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—24no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—24no—
1167C2×C4—22no—
1168C2×C4—24no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—416no—
1191C2×C4—416no—
1192C2×C4—416no—
1193C2×C4—416no—
1194C2×C4—416no—
1195C2×C4—432no—
1196C2×C4—41no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—41no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—88no—
1263C2×C4—816no—
1264C2×C4—816no—
1265C2×C4C2×#12014yes—
1266C2×C4C2×#12014yes—
1267C2×C4#53414yes—
1268C22—24no—
1269C22—24no—
1270C22—28no—
1271C22—24no—
1272C22—28no—
1273C22—24no—
1274C22—28no—
1275C22—28no—
1276C22—24no—
1277C22—24no—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—24no—
1282C22—24no—
1283C22—24no—
1284C22—464no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—44no—
1291C22—44no—
1292C22—42no—
1293C22—44no—
1294C22—44no—
1295C22—42no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—42no—
1301C22—42no—
1302C22—44no—
1303C22—42no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—44no—
1308C22—44no—
1309C22—44no—
1310C22—44no—
1311C22—44no—
1312C22—42no—
1313C22—81no—
1314C22—82no—
1315C22—82no—
1316C22—81no—
1317C22—82no—
1318C22—82no—
1319C22—82no—
1320C22—81no—
1321C22—82no—
1322C22—82no—
1323C22—82no—
1324C22—81no—
1325C22—82no—
1326C22—82no—
1327C22#240718yes—
1328C22C22×#12011yescharacteristic
1329C22C2×#52511yescharacteristic
1330C22C2×#53211yescharacteristic
1331C22C2×#53411yescharacteristic
1332C22C2×#53411yescharacteristic
1333C22C2×#53711yescharacteristic
1334C22#344911yescharacteristic
1335C22C2×#54611yescharacteristic
1336C22C2×#54711yescharacteristic
1337C22C2×#54811yescharacteristic
1338C22C2×#55011yescharacteristic
1339C22D4×#4112yes—
1340C22D4×#4112yes—
1341C22#348112yes—
1342C22#348112yes—
1343C22#348412yes—
1344C22#348412yes—
1345C22#349012yes—
1346C22#349212yes—
1347C22#351312yes—
1348C22#351312yes—
1349C22#354112yes—
1350C22#354212yes—
1351C4—24no—
1352C4—24no—
1353C4—24no—
1354C4—42no—
1355C4—44no—
1356C4—42no—
1357C4—44no—
1358C4—42no—
1359C4—44no—
1360C4—44no—
1361C4—44no—
1362C4—42no—
1363C4—81no—
1364C4—82no—
1365C4—81no—
1366C4—82no—
1367C4—81no—
1368C4—81no—
1369C2—28no—
1370C2—44no—
1371C2—44no—
1372C2—82no—
1373C2—84no—
1374C2C2×#240711yescharacteristic
1375C2#3473811yescharacteristic
1376C2#3495711yescharacteristic
1377C2#3498011yescharacteristic
1378C2#3505111yescharacteristic
1379C2#3506311yescharacteristic
1380C2#3744411yescharacteristic
1381C2#5902912yes—
1382C2#5904512yes—
1383C2#5906012yes—
1384C2#5907412yes—
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. C22×#525C2semidirect
2. C2×#2564C2semidirect
3. C2×#2543C2semidirect
4. C2×C4×#120C2semidirect
5. #16632C2semidirect
6. #16606C2semidirect
7. #16557C2semidirect
8. #16508C2semidirect
9. #14964C2semidirect
10. #14906C2semidirect
11. #14905C2semidirect
12. #14889C2semidirect
13. #14885C2semidirect
14. #14725C2semidirect
15. #14721C2semidirect
16. #14716C2semidirect
17. #14173C2semidirect
18. #14171C2semidirect
19. #14159C2semidirect
20. #14152C2semidirect
21. #14023C2semidirect
22. #13975C2semidirect
23. C2×C22⋊#95C2semidirect
46. C2×#400C22semidirect
47. C2×#399C22semidirect
48. C2×#398C22semidirect
49. C2×#397C22semidirect
50. C2×#395C22semidirect
53. C2×#394C22semidirect
54. C2×#393C22semidirect
57. C2×#392C22semidirect
59. C2×#388C22semidirect
60. C2×#387C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
73. C2×#385C22semidirect
74. C2×#385C22semidirect
83. #1446C22semidirect
84. #1446C22semidirect
85. #1445C22semidirect
86. #1445C22semidirect
87. #1445C22semidirect
88. #1445C22semidirect
89. #1444C22semidirect
90. #1442C22semidirect
91. #1441C22semidirect
94. #1440C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1436C22semidirect
115. #1436C22semidirect
116. #1436C22semidirect
117. #1436C22semidirect
118. #1436C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect
148. C24×C4D4semidirect
168. C2×C22⋊Q8D4semidirect
177. C2×#121D4semidirect
393. C22×D4#41semidirect
601. C2×C22⋊C4#41semidirect
602. C2×C22⋊C4#41semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#25642
C2×#25432
C2×C4×#1202
#166322
#166062
#165572
#165082
#149642
#149062
#149052
#148892
#148852
#147252
#147212
#147162
#141732
#141712
#141592
#141522
#140232
#139752
C2×C22⋊#952