Finite Group Databasebeta

← #648406

Subgroups — #648406

Order 512.

5777 conjugacy classes of subgroups.

The subgroup lattice has 1427 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2411C211yesmaximal, characteristic, complemented
2C2×#2412C211yesmaximal, characteristic, complemented
3C2×#2410C211yesmaximal, characteristic
4C2×#2342C211yesmaximal, characteristic, complemented
5C22×#386C211yesmaximal, characteristic, complemented
6C22×#385C211yesmaximal, characteristic, complemented
7#15577C212yesmaximal, complemented
8#15419C212yesmaximal, complemented
9#15404C212yesmaximal, complemented
10#15403C212yesmaximal, complemented
11#14921C211yesmaximal, characteristic, complemented
12#14918C211yesmaximal, characteristic, complemented
13#14912C211yesmaximal, characteristic, complemented
14#14747C212yesmaximal, complemented
15#14729C212yesmaximal, complemented
16#14726C211yesmaximal, characteristic, complemented
17#14694C211yesmaximal, characteristic, complemented
18#14137C212yesmaximal, complemented
19#14044C211yesmaximal, characteristic, complemented
20#13999C212yesmaximal, complemented
21#13995C211yesmaximal, characteristic, complemented
22#13962C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×#123C2211yescharacteristic
27C22×#121C2212yes—
28C22×#120C2211yescharacteristic
29C22×#120C2211yescharacteristic
30C22×#117C2211yescharacteristic
31C23×C4⋊C4C2212yescomplemented
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36C23×C22⋊C4C2211yescharacteristic
37#2412—28no—
38#2411—28no—
39#2410—28no—
40C2×#397C2211yescharacteristic, complemented
41C2×#397C2211yescharacteristic, complemented
42C2×#396C2212yescomplemented
43C2×#396C2212yescomplemented
44C2×#394C2212yes—
45C2×#394C2211yescharacteristic, complemented
46C2×#394C2212yescomplemented
47C2×#394C2211yescharacteristic, complemented
48C2×#392C2212yes—
49#2342—28no—
50C2×#390C2212yescomplemented
51C2×#390C2212yescomplemented
52C2×#388C2212yescomplemented
53C2×#388C2212yescomplemented
54C2×#388C2212yescomplemented
55C2×#386—28no—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#386C2211yescharacteristic
61C2×#386C2211yescharacteristic
62C2×#386C2211yescharacteristic
63C2×#386C2212yes—
64C2×#386C2212yes—
65C2×#386C2212yes—
66C2×#386C2211yescharacteristic
67C2×#386C2211yescharacteristic, complemented
68C2×#386C2211yescharacteristic, complemented
69C2×#386C2212yescomplemented
70C2×#386C2212yescomplemented
71C2×#385—28no—
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic
74C2×#385C2211yescharacteristic
75C2×#385C2211yescharacteristic
76C2×#385C2211yescharacteristic
77C2×#385C2211yescharacteristic
78C2×#385C2212yescomplemented
79C2×#385C2212yescomplemented
80C2×#385C2212yescomplemented
81C2×#381C2211yescharacteristic
82C2×#381C2211yescharacteristic
83C2×#380C2211yescharacteristic
84C2×#380C2211yescharacteristic, complemented
85C2×#380C2211yescharacteristic, complemented
86C2×#379C2211yescharacteristic
87C2×#379C2211yescharacteristic
88C2×#379C2211yescharacteristic
89C2×#379C2211yescharacteristic
90C2×C4×C22⋊C4C2211yescharacteristic
91C2×C4×C22⋊C4C2212yescomplemented
92C22×#95C2211yescharacteristic
93C22×#95C2211yescharacteristic
94C22×#95C2212yescomplemented
95#1443C2212yescomplemented
96#1442C2212yescomplemented
97#1442C2212yescomplemented
98#1441C2212yescomplemented
99#1441C2212yescomplemented
100#1441C2212yescomplemented
101#1441C2212yescomplemented
102#1441C2212yescomplemented
103#1440C2212yescomplemented
104#1440C2212yescomplemented
105#1440C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1439C2212yescomplemented
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120C4⋊#95C2212yescomplemented
121C4⋊#95C2212yescomplemented
122#1434C2212yescomplemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2211yescharacteristic
126C22⋊#95C2211yescharacteristic
127C22⋊#95C2212yescomplemented
128C22⋊#95C2212yescomplemented
129C26C2311yescharacteristic
130C26C2311yescharacteristic
131C23×D4—24no—
132C23×D4—28no—
133C23×D4—24no—
134C23×D4—24no—
135C23×D4—44no—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C23×D4C2312yes—
139C23×D4C2312yes—
140C23×D4C2312yes—
141C23×D4C2311yescharacteristic
142C24×C4—24no—
143C24×C4—24no—
144C24×C4—44no—
145C24×C4—42no—
146C24×C4—44no—
147C24×C4C2311yescharacteristic
148C24×C4C2311yescharacteristic
149C24×C4C2312yes—
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2311yescharacteristic
153C24×C4C2312yes—
154C24×C4C2312yes—
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157C2×#123—24no—
158C2×#123—24no—
159C2×#123—42no—
160C2×#121—28no—
161C2×#121—28no—
162C2×#121—44no—
163C2×#120—24no—
164C2×#120—24no—
165C2×#120—24no—
166C2×#120—24no—
167C2×#120—24no—
168C2×#120—24no—
169C2×#117—24no—
170C2×#117—24no—
171C2×#117—24no—
172C22×C4⋊C4—28no—
173C22×C4⋊C4—44no—
174C22×C4⋊C4—44no—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C4⋊C4C2312yes—
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C22⋊C4—24no—
187C22×C22⋊C4—24no—
188C22×C22⋊C4—24no—
189C22×C22⋊C4—24no—
190C22×C22⋊C4—24no—
191C22×C22⋊C4—24no—
192C22×C22⋊C4—24no—
193C22×C22⋊C4—24no—
194C22×C22⋊C4—24no—
195C22×C22⋊C4—44no—
196C22×C22⋊C4—42no—
197C22×C22⋊C4—42no—
198C22×C22⋊C4D418yes—
199C22×C22⋊C4D418yescomplemented
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2311yescharacteristic
236C22×C42C2312yes—
237C22×C42C2312yes—
238#397—24no—
239#397—24no—
240#396—28no—
241#396—44no—
242#394—28no—
243#394—24no—
244#394—24no—
245#394—28no—
246#392—28no—
247#390—28no—
248#390—44no—
249#388—28no—
250#388—28no—
251#388—28no—
252#386—28no—
253#386—28no—
254#386—24no—
255#386—24no—
256#386—24no—
257#386—24no—
258#386—24no—
259#386—28no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—44no—
264#386—42no—
265#386—44no—
266#386—44no—
267#385—28no—
268#385—24no—
269#385—24no—
270#385—28no—
271#385—24no—
272#385—24no—
273#385—24no—
274#385—28no—
275#385D418yescomplemented
276#381—24no—
277#381—24no—
278#380—24no—
279#380—24no—
280#380—24no—
281#379—24no—
282#379—24no—
283#379—24no—
284#379—42no—
285C4×C22⋊C4—28no—
286C4×C22⋊C4—24no—
287C2×#95—24no—
288C2×#95—24no—
289C2×#95—28no—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2311yescharacteristic
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C2×#95C2312yes—
320C2×#95C2312yes—
321C2×#95C2312yes—
322C25—22no—
323C25—22no—
324C25—24no—
325C25—22no—
326C25—24no—
327C25—22no—
328C25—22no—
329C25—24no—
330C25—22no—
331C25—22no—
332C25—22no—
333C25—22no—
334C25—22no—
335C25—22no—
336C25—42no—
337C25—42no—
338C25—42no—
339C25—42no—
340C25—42no—
341C25C2×D414yes—
342C25C2×D414yes—
343C25#4114yes—
344C25C2411yescharacteristic
345C25C2412yes—
346C25C2411yescharacteristic
347C25C2411yescharacteristic
348C25C2411yescharacteristic
349C22×D4—232no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—22no—
363C22×D4—24no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—24no—
370C22×D4—24no—
371C22×D4—24no—
372C22×D4—22no—
373C22×D4—22no—
374C22×D4—22no—
375C22×D4—22no—
376C22×D4—24no—
377C22×D4—24no—
378C22×D4—24no—
379C22×D4—24no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—42no—
387C22×D4—432no—
388C22×D4—432no—
389C22×D4—416no—
390C22×D4—416no—
391C22×D4#4118yes—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—24no—
408C23×C4—24no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4—22no—
414C23×C4—24no—
415C23×C4—24no—
416C23×C4—22no—
417C23×C4—22no—
418C23×C4—24no—
419C23×C4—22no—
420C23×C4—22no—
421C23×C4—22no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—22no—
425C23×C4—22no—
426C23×C4—24no—
427C23×C4—24no—
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—41no—
442C23×C4—41no—
443C23×C4—42no—
444C23×C4—42no—
445C23×C4—42no—
446C23×C4—416no—
447C23×C4—416no—
448C23×C4—432no—
449C23×C4—416no—
450C23×C4—432no—
451C23×C4C2×D414yes—
452C23×C4C2×D418yes—
453C23×C4C2×D414yes—
454C23×C4C2×D414yes—
455C23×C4C2412yes—
456C23×C4C2412yes—
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459C23×C4C2411yescharacteristic
460C23×C4C2411yescharacteristic
461C23×C4C2411yescharacteristic
462C23×C4C2411yescharacteristic
463C23×C4C2411yescharacteristic
464C23×C4C2412yes—
465C23×C4C2411yescharacteristic
466C23×C4C2411yescharacteristic
467C23×C4C2411yescharacteristic
468C23×C4C2411yescharacteristic
469C23×C4C2412yes—
470C23×C4C2412yes—
471C23×C4C2412yes—
472C23×C4C2412yes—
473#123—416no—
474#121—432no—
475#120—416no—
476#120—416no—
477#117—416no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—22no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—42no—
498C2×C4⋊C4—42no—
499C2×C4⋊C4—42no—
500C2×C4⋊C4—42no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—41no—
503C2×C4⋊C4—41no—
504C2×C4⋊C4—432no—
505C2×C4⋊C4—42no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—42no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4C2×D418yescomplemented
510C2×C22⋊C4—232no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—232no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
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—24no—
540C2×C22⋊C4—22no—
541C2×C22⋊C4—22no—
542C2×C22⋊C4—22no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
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—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—24no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—416no—
581C2×C22⋊C4—42no—
582C2×C22⋊C4—42no—
583C2×C22⋊C4—42no—
584C2×C22⋊C4—42no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—41no—
592C2×C22⋊C4—416no—
593C2×C22⋊C4—416no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4—42no—
599C2×C22⋊C4—42no—
600C2×C22⋊C4—42no—
601C2×C22⋊C4—42no—
602C2×C22⋊C4—42no—
603C2×C22⋊C4—42no—
604C2×C22⋊C4—42no—
605C2×C22⋊C4—42no—
606C2×C22⋊C4—42no—
607C2×C22⋊C4—42no—
608C2×C22⋊C4—42no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4—42no—
611C2×C22⋊C4C2×D414yes—
612C2×C22⋊C4C2×D414yes—
613C2×C22⋊C4C2×D418yes—
614C2×C22⋊C4C2×D414yes—
615C2×C22⋊C4C2×D414yes—
616C2×C22⋊C4C2×D414yes—
617C2×C22⋊C4C2×D414yes—
618C2×C22⋊C4C2×D414yes—
619C2×C22⋊C4C2×D414yes—
620C2×C22⋊C4#4114yes—
621C2×C42—24no—
622C2×C42—24no—
623C2×C42—24no—
624C2×C42—24no—
625C2×C42—42no—
626C2×C42—42no—
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—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—24no—
642#95—22no—
643#95—22no—
644#95—24no—
645#95—22no—
646#95—22no—
647#95—24no—
648#95—24no—
649#95—24no—
650#95—24no—
651#95—24no—
652#95—42no—
653#95—42no—
654#95—42no—
655#95—42no—
656#95—42no—
657#95—42no—
658#95C2×D418yescomplemented
659C24—21no—
660C24—21no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—21no—
665C24—22no—
666C24—21no—
667C24—22no—
668C24—22no—
669C24—28no—
670C24—28no—
671C24—28no—
672C24—28no—
673C24—28no—
674C24—216no—
675C24—28no—
676C24—28no—
677C24—216no—
678C24—28no—
679C24—21no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—22no—
684C24—22no—
685C24—21no—
686C24—22no—
687C24—28no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—22no—
702C24—21no—
703C24—21no—
704C24—21no—
705C24—22no—
706C24—21no—
707C24—21no—
708C24—22no—
709C24—21no—
710C24—22no—
711C24—21no—
712C24—22no—
713C24—44no—
714C24—44no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—48no—
730C24—48no—
731C24—44no—
732C24—44no—
733C24—44no—
734C24—44no—
735C24—44no—
736C24—44no—
737C24—44no—
738C24—44no—
739C24—44no—
740C24—44no—
741C24—84no—
742C24—84no—
743C24—84no—
744C24—84no—
745C24—84no—
746C24—84no—
747C24#121116yes—
748C24C22×D412yes—
749C24C22×D412yes—
750C24C22×D412yes—
751C24C22×D412yes—
752C24C22×D412yes—
753C24C22×D412yes—
754C24C22×D412yes—
755C24C2×#4114yes—
756C24C2×#4112yes—
757C24C2×#4112yes—
758C24C2×#4112yes—
759C24C2×#4112yes—
760C24C2×#4114yes—
761C24H(5,𝔽2)14yes—
762C24H(5,𝔽2)12yes—
763C242−1+412yes—
764C24C2511yescharacteristic
765C2×D4—216no—
766C2×D4—216no—
767C2×D4—216no—
768C2×D4—216no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—4128no—
777C2×D4—48no—
778C2×D4—48no—
779C2×D4—48no—
780C2×D4—48no—
781C2×D4—48no—
782C2×D4—48no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—44no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—48no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—48no—
796C2×D4—44no—
797C2×D4—48no—
798C2×D4—84no—
799C2×D4—84no—
800C2×D4—84no—
801C2×D4—82no—
802C2×D4—82no—
803C2×D4—84no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—28no—
809C22×C4—216no—
810C22×C4—28no—
811C22×C4—28no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—216no—
815C22×C4—28no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—22no—
835C22×C4—21no—
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—21no—
849C22×C4—21no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—28no—
869C22×C4—216no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—22no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
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—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—22no—
893C22×C4—22no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—22no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—22no—
905C22×C4—22no—
906C22×C4—21no—
907C22×C4—22no—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—22no—
911C22×C4—48no—
912C22×C4—48no—
913C22×C4—48no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—48no—
917C22×C4—48no—
918C22×C4—48no—
919C22×C4—48no—
920C22×C4—48no—
921C22×C4—48no—
922C22×C4—48no—
923C22×C4—48no—
924C22×C4—48no—
925C22×C4—48no—
926C22×C4—48no—
927C22×C4—48no—
928C22×C4—48no—
929C22×C4—48no—
930C22×C4—48no—
931C22×C4—48no—
932C22×C4—44no—
933C22×C4—44no—
934C22×C4—48no—
935C22×C4—48no—
936C22×C4—44no—
937C22×C4—44no—
938C22×C4—44no—
939C22×C4—48no—
940C22×C4—48no—
941C22×C4—48no—
942C22×C4—44no—
943C22×C4—4128no—
944C22×C4—48no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—48no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—44no—
952C22×C4—44no—
953C22×C4—44no—
954C22×C4—82no—
955C22×C4—82no—
956C22×C4—84no—
957C22×C4—84no—
958C22×C4—84no—
959C22×C4—84no—
960C22×C4C22×D412yes—
961C22×C4C22×D412yes—
962C22×C4C22×D414yes—
963C22×C4C22×D412yes—
964C22×C4C22×D412yes—
965C22×C4C22×D412yes—
966C22×C4C22×D414yes—
967C22×C4C22×D412yes—
968C22×C4C22×D414yes—
969C22×C4C22×D414yes—
970C22×C4C2×#4114yes—
971C22×C4C2×#4114yes—
972C22×C4H(5,𝔽2)14yes—
973C4⋊C4—48no—
974C4⋊C4—48no—
975C4⋊C4—48no—
976C4⋊C4—48no—
977C4⋊C4—44no—
978C4⋊C4—44no—
979C4⋊C4—48no—
980C4⋊C4—48no—
981C4⋊C4—82no—
982C4⋊C4—82no—
983C4⋊C4—84no—
984C22⋊C4—28no—
985C22⋊C4—28no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—216no—
991C22⋊C4—48no—
992C22⋊C4—48no—
993C22⋊C4—48no—
994C22⋊C4—48no—
995C22⋊C4—48no—
996C22⋊C4—44no—
997C22⋊C4—44no—
998C22⋊C4—48no—
999C22⋊C4—44no—
1000C22⋊C4—44no—
1001C22⋊C4—48no—
1002C22⋊C4—44no—
1003C22⋊C4—44no—
1004C22⋊C4—44no—
1005C22⋊C4—44no—
1006C22⋊C4—44no—
1007C22⋊C4—44no—
1008C22⋊C4—48no—
1009C22⋊C4—48no—
1010C22⋊C4—82no—
1011C22⋊C4—84no—
1012C22⋊C4—84no—
1013C22⋊C4—82no—
1014C22⋊C4—84no—
1015C22⋊C4—84no—
1016C22⋊C4—84no—
1017C22⋊C4—84no—
1018C22⋊C4—84no—
1019C22⋊C4#121116yes—
1020C42—48no—
1021C42—84no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—24no—
1028C23—22no—
1029C23—22no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—22no—
1034C23—24no—
1035C23—24no—
1036C23—24no—
1037C23—22no—
1038C23—22no—
1039C23—24no—
1040C23—22no—
1041C23—22no—
1042C23—24no—
1043C23—24no—
1044C23—24no—
1045C23—24no—
1046C23—24no—
1047C23—24no—
1048C23—24no—
1049C23—24no—
1050C23—24no—
1051C23—24no—
1052C23—24no—
1053C23—24no—
1054C23—24no—
1055C23—24no—
1056C23—22no—
1057C23—232no—
1058C23—22no—
1059C23—232no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—24no—
1064C23—22no—
1065C23—22no—
1066C23—24no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—24no—
1071C23—24no—
1072C23—24no—
1073C23—24no—
1074C23—24no—
1075C23—24no—
1076C23—24no—
1077C23—24no—
1078C23—24no—
1079C23—416no—
1080C23—416no—
1081C23—416no—
1082C23—432no—
1083C23—416no—
1084C23—432no—
1085C23—432no—
1086C23—416no—
1087C23—432no—
1088C23—416no—
1089C23—416no—
1090C23—416no—
1091C23—42no—
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—
1123C23—42no—
1124C23—42no—
1125C23—42no—
1126C23—42no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—42no—
1134C23—41no—
1135C23—41no—
1136C23—42no—
1137C23—42no—
1138C23—41no—
1139C23—42no—
1140C23—41no—
1141C23—42no—
1142C23—41no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—42no—
1150C23—816no—
1151C23—816no—
1152C23—816no—
1153C23—816no—
1154C23—88no—
1155C23—88no—
1156C23—88no—
1157C23—88no—
1158C23C2×#12114yes—
1159C23C2×#12114yes—
1160C23C2×#12114yes—
1161C23C2×#12114yes—
1162C23#52514yes—
1163C23#53514yes—
1164C23#53714yes—
1165C23D4214yes—
1166C23#54618yes—
1167C23#54714yes—
1168C23#54814yes—
1169C23#55118yes—
1170C23#55314yes—
1171C23C23×D411yescharacteristic
1172C23C23×D411yescharacteristic
1173C23C23×D411yescharacteristic
1174C23C22×#4111yescharacteristic
1175C23C22×#4111yescharacteristic
1176C23C22×#4112yes—
1177C23C2×H(5,𝔽2)12yes—
1178C23C2×H(5,𝔽2)11yescharacteristic
1179C23C2×H(5,𝔽2)12yes—
1180C23C2×2−1+411yescharacteristic
1181C23#58512yes—
1182D4—432no—
1183D4—432no—
1184D4—816no—
1185D4—88no—
1186D4—88no—
1187D4—88no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—24no—
1192C2×C4—24no—
1193C2×C4—24no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—24no—
1199C2×C4—24no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—22no—
1203C2×C4—22no—
1204C2×C4—24no—
1205C2×C4—24no—
1206C2×C4—24no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—24no—
1210C2×C4—24no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—24no—
1214C2×C4—24no—
1215C2×C4—24no—
1216C2×C4—24no—
1217C2×C4—24no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—24no—
1221C2×C4—24no—
1222C2×C4—432no—
1223C2×C4—432no—
1224C2×C4—416no—
1225C2×C4—416no—
1226C2×C4—416no—
1227C2×C4—432no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—416no—
1233C2×C4—41no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—41no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—41no—
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—42no—
1263C2×C4—42no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—42no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—42no—
1278C2×C4—42no—
1279C2×C4—42no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—41no—
1286C2×C4—42no—
1287C2×C4—42no—
1288C2×C4—41no—
1289C2×C4—42no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—42no—
1296C2×C4—42no—
1297C2×C4—42no—
1298C2×C4—42no—
1299C2×C4—42no—
1300C2×C4—42no—
1301C2×C4—42no—
1302C2×C4—42no—
1303C2×C4—42no—
1304C2×C4—88no—
1305C2×C4—88no—
1306C2×C4—88no—
1307C2×C4C2×#12118yes—
1308C22—24no—
1309C22—24no—
1310C22—24no—
1311C22—24no—
1312C22—24no—
1313C22—24no—
1314C22—24no—
1315C22—28no—
1316C22—28no—
1317C22—24no—
1318C22—24no—
1319C22—24no—
1320C22—28no—
1321C22—28no—
1322C22—28no—
1323C22—28no—
1324C22—24no—
1325C22—24no—
1326C22—28no—
1327C22—28no—
1328C22—24no—
1329C22—24no—
1330C22—24no—
1331C22—464no—
1332C22—42no—
1333C22—42no—
1334C22—44no—
1335C22—42no—
1336C22—44no—
1337C22—44no—
1338C22—42no—
1339C22—44no—
1340C22—44no—
1341C22—44no—
1342C22—44no—
1343C22—44no—
1344C22—44no—
1345C22—44no—
1346C22—44no—
1347C22—832no—
1348C22—82no—
1349C22—82no—
1350C22—82no—
1351C22—82no—
1352C22—82no—
1353C22—82no—
1354C22—82no—
1355C22—82no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—82no—
1361C22—81no—
1362C22—81no—
1363C22—82no—
1364C22—82no—
1365C22—81no—
1366C22—82no—
1367C22#241118yescomplemented
1368C22#241618yes—
1369C22C22×#12111yescharacteristic
1370C22C22×#12111yescharacteristic
1371C22C2×#52511yescharacteristic
1372C22C2×#53511yescharacteristic
1373C22C2×#53711yescharacteristic
1374C22C2×D4211yescharacteristic
1375C22C2×#54612yes—
1376C22C2×#54711yescharacteristic
1377C22C2×#54811yescharacteristic
1378C22D4×#4112yes—
1379C22C2×#55112yes—
1380C22C2×#55311yescharacteristic
1381C22#348112yes—
1382C22#348411yescharacteristic
1383C22#348412yes—
1384C22#348511yescharacteristic
1385C22#349612yes—
1386C22#350512yes—
1387C22#351312yes—
1388C22#351312yes—
1389C22#352012yes—
1390C22#353212yes—
1391C22#353512yes—
1392C4—28no—
1393C4—42no—
1394C4—44no—
1395C4—44no—
1396C4—42no—
1397C4—42no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—44no—
1402C4—44no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—82no—
1408C4—81no—
1409C4—82no—
1410C2—28no—
1411C2—28no—
1412C2—44no—
1413C2—84no—
1414C2—161no—
1415C2C2×#241611yescharacteristic
1416C2C2×#241111yescharacteristic
1417C2#3535811yescharacteristic
1418C2#3609911yescharacteristic
1419C2#3621412yes—
1420C2#3631711yescharacteristic
1421C2#3764511yescharacteristic
1422C2#3803911yescharacteristic
1423C2#3807712yes—
1424C2#5913312yes—
1425C2#5985012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2410C2
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×#2411C2semidirect
2. C2×#2412C2semidirect
4. C2×#2342C2semidirect
5. C22×#386C2semidirect
6. C22×#385C2semidirect
7. #15577C2semidirect
8. #15419C2semidirect
9. #15404C2semidirect
10. #15403C2semidirect
11. #14921C2semidirect
12. #14918C2semidirect
13. #14912C2semidirect
14. #14747C2semidirect
15. #14729C2semidirect
16. #14726C2semidirect
17. #14694C2semidirect
18. #14137C2semidirect
19. #14044C2semidirect
20. #13999C2semidirect
21. #13995C2semidirect
22. #13962C2semidirect
23. #13867C2semidirect
31. C23×C4⋊C4C22semidirect
40. C2×#397C22semidirect
41. C2×#397C22semidirect
42. C2×#396C22semidirect
43. C2×#396C22semidirect
45. C2×#394C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
50. C2×#390C22semidirect
51. C2×#390C22semidirect
52. C2×#388C22semidirect
53. C2×#388C22semidirect
54. C2×#388C22semidirect
67. C2×#386C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
70. C2×#386C22semidirect
78. C2×#385C22semidirect
79. C2×#385C22semidirect
80. C2×#385C22semidirect
84. C2×#380C22semidirect
85. C2×#380C22semidirect
91. C2×C4×C22⋊C4C22semidirect
94. C22×#95C22semidirect
95. #1443C22semidirect
96. #1442C22semidirect
97. #1442C22semidirect
98. #1441C22semidirect
99. #1441C22semidirect
100. #1441C22semidirect
101. #1441C22semidirect
102. #1441C22semidirect
103. #1440C22semidirect
104. #1440C22semidirect
105. #1440C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1439C22semidirect
117. #1438C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
122. #1434C22semidirect
127. C22⋊#95C22semidirect
128. C22⋊#95C22semidirect
199. C22×C22⋊C4D4semidirect
275. #385D4semidirect
509. C2×C4⋊C4C2×D4semidirect
658. #95C2×D4semidirect
1367. C22#2411semidirect

Maximal subgroups

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

subgroupindex
C2×#24112
C2×#24122
C2×#24102
C2×#23422
C22×#3862
C22×#3852
#155772
#154192
#154042
#154032
#149212
#149182
#149122
#147472
#147292
#147262
#146942
#141372
#140442
#139992
#139952
#139622
#138672