Finite Group Databasebeta

← #825290

Subgroups — #825290

Order 512.

4622 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2539C211yesmaximal, characteristic, complemented
2C2×#2422C211yesmaximal, characteristic, complemented
3C2×#2455C212yesmaximal, complemented
4C2×#2418C212yesmaximal, complemented
5C2×#2397C211yesmaximal, characteristic, complemented
6C2×#2358C211yesmaximal, characteristic, complemented
7#17068C211yesmaximal, characteristic, complemented
8#16508C211yesmaximal, characteristic, complemented
9#15696C212yesmaximal, complemented
10#15493C212yesmaximal, complemented
11#15384C212yesmaximal, complemented
12#15267C212yesmaximal, complemented
13#15155C211yesmaximal, characteristic, complemented
14#15135C211yesmaximal, characteristic, complemented
15#14910C211yesmaximal, characteristic, complemented
16#14839C211yesmaximal, characteristic, complemented
17#14807C211yesmaximal, characteristic, complemented
18#14796C211yesmaximal, characteristic, complemented
19#14734C211yesmaximal, characteristic, complemented
20#14228C211yesmaximal, characteristic, complemented
21#14189C212yesmaximal, complemented
22#13977C212yesmaximal, complemented
23#13816C211yesmaximal, characteristic, complemented
24C22×#123C2212yes—
25C22×#123C2212yes—
26C22×#121C2211yescharacteristic
27C22×#120C2211yescharacteristic
28C22×#120C2212yes—
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2212yes—
32C22×C4×D4C2212yescomplemented
33C22×C4×D4C2211yescharacteristic, complemented
34C23×C22⋊C4C2211yescharacteristic
35C23×C22⋊C4C2211yescharacteristic
36#2539—28no—
37#2455—216no—
38#2422—28no—
39#2418—216no—
40#2397—28no—
41C2×#399C2211yescharacteristic
42C2×#399C2211yescharacteristic
43C2×#399C2211yescharacteristic
44C2×#399C2212yes—
45C2×#399C2211yescharacteristic
46C2×#399C2212yescomplemented
47C2×#399C2212yescomplemented
48C2×#399C2211yescharacteristic, complemented
49C2×#399C2211yescharacteristic, complemented
50C2×#397C2212yes—
51C2×#397C2212yescomplemented
52C2×#394C2212yes—
53C2×#394C2212yes—
54C2×#394C2212yes—
55C2×#394C2212yes—
56C2×#394C2212yescomplemented
57C2×#392C2211yescharacteristic
58C2×#392C2212yes—
59C2×#392C2212yes—
60C2×#392C2212yes—
61C2×#392C2211yescharacteristic
62C2×#392C2211yescharacteristic, complemented
63#2358—28no—
64C2×#390C2212yes—
65C2×#390C2212yes—
66C2×#390C2211yescharacteristic
67C2×#390C2212yes—
68C2×#390C2212yes—
69C2×#390C2211yescharacteristic, complemented
70C2×#389C2212yescomplemented
71C2×#389C2212yescomplemented
72C2×#389C2211yescharacteristic, complemented
73C2×#388C2211yescharacteristic
74C2×#388C2212yes—
75C2×#388C2211yescharacteristic
76C2×#388C2212yes—
77C2×#388C2212yescomplemented
78C2×#386C2211yescharacteristic
79C2×#386C2211yescharacteristic
80C2×#386C2211yescharacteristic
81C2×#386C2212yes—
82C2×#386C2212yes—
83C2×#385C2211yescharacteristic
84C2×#385C2212yes—
85C2×#385C2211yescharacteristic
86C2×#385C2212yes—
87C2×#385C2212yescomplemented
88C2×#385C2212yescomplemented
89C2×#385C2212yescomplemented
90C2×#384C2211yescharacteristic, complemented
91C2×#384C2212yescomplemented
92C2×#380C2212yes—
93C2×#380C2211yescharacteristic
94C2×#379C2212yes—
95C2×C4×C22⋊C4C2211yescharacteristic
96C2×C4×C22⋊C4C2211yescharacteristic
97C2×C4×C22⋊C4C2211yescharacteristic
98C2×#376C2211yescharacteristic, complemented
99#1445C2212yescomplemented
100#1445C2211yescharacteristic, complemented
101#1445C2211yescharacteristic, complemented
102#1444C2212yescomplemented
103#1444C2212yescomplemented
104#1444C2211yescharacteristic, complemented
105#1439C2212yes—
106#1439C2212yes—
107#1439C2211yescharacteristic
108#1439C2212yes—
109#1439C2212yes—
110#1439C2211yescharacteristic
111#1439C2212yescomplemented
112#1439C2212yescomplemented
113#1439C2212yescomplemented
114#1439C2211yescharacteristic, complemented
115#1438C2212yes—
116#1438C2212yes—
117#1438C2212yescomplemented
118#1438C2211yescharacteristic, complemented
119#1437C2212yes—
120#1437C2212yescomplemented
121#1437C2212yescomplemented
122#1436C2212yescomplemented
123C4⋊#95C2211yescharacteristic, complemented
124C4⋊#95C2212yescomplemented
125#1434C2211yescharacteristic, complemented
126C22⋊#95C2211yescharacteristic
127C4×#95C2211yescharacteristic, complemented
128C4×#95C2212yescomplemented
129C26C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2312yes—
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C2×#123—28no—
145C2×#123—28no—
146C2×#123—28no—
147C2×#123—28no—
148C2×#123—28no—
149C2×#123—44no—
150C2×#121—24no—
151C2×#121—24no—
152C2×#121—42no—
153C2×#120—24no—
154C2×#120—28no—
155C2×#120—24no—
156C2×#120—28no—
157C2×#120—24no—
158C2×#120—44no—
159C2×C4×D4—28no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—28no—
164C2×C4×D4—28no—
165C2×C4×D4—24no—
166C2×C4×D4—28no—
167C2×C4×D4—24no—
168C2×C4×D4—28no—
169C2×C4×D4—42no—
170C2×C4×D4—44no—
171C2×C4×D4—44no—
172C2×C4×D4—42no—
173C22×C4⋊C4C2312yes—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2312yes—
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2312yes—
182C22×C4⋊C4C2312yes—
183C22×C4⋊C4C2311yescharacteristic
184C22×C4⋊C4C2312yes—
185C22×C4⋊C4C2312yes—
186C22×C4⋊C4C2312yes—
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C22⋊C4—24no—
191C22×C22⋊C4—24no—
192C22×C22⋊C4—28no—
193C22×C22⋊C4—24no—
194C22×C22⋊C4—42no—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2312yes—
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2311yescharacteristic
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2311yescharacteristic
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2312yes—
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2311yescharacteristic
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2311yescharacteristic
230C22×C42C2311yescharacteristic
231C22×C42C2312yes—
232C22×C42C2312yes—
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235C22×C42C2311yescharacteristic
236#399—24no—
237#399—24no—
238#399—28no—
239#399—28no—
240#399—24no—
241#399—24no—
242#399—28no—
243#399—42no—
244#399—42no—
245#397—28no—
246#397—28no—
247#394—28no—
248#394—28no—
249#394—28no—
250#394—28no—
251#394—28no—
252#392—28no—
253#392—24no—
254#392—24no—
255#392—28no—
256#392—28no—
257#392D418yescomplemented
258#390—28no—
259#390—28no—
260#390—28no—
261#390—24no—
262#390—24no—
263#390—44no—
264#389—28no—
265#389—24no—
266#389—28no—
267#388—24no—
268#388—28no—
269#388—24no—
270#388—28no—
271#388D4116yescomplemented
272#386—24no—
273#386—24no—
274#386—24no—
275#386—28no—
276#386—28no—
277#385—24no—
278#385—28no—
279#385—24no—
280#385—28no—
281#385—28no—
282#385—28no—
283#385—28no—
284#384—24no—
285#384—44no—
286#380—24no—
287#380—28no—
288#379—28no—
289C4×C22⋊C4—24no—
290C4×C22⋊C4—24no—
291C4×C22⋊C4D418yescomplemented
292#376—24no—
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C2×#95C2311yescharacteristic
309C2×#95C2312yes—
310C2×#95C2311yescharacteristic
311C2×#95C2311yescharacteristic
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2311yescharacteristic
315C2×#95C2311yescharacteristic
316C2×#95C2312yes—
317C2×#95C2311yescharacteristic
318C2×#95C2312yes—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—22no—
323C25—24no—
324C25—22no—
325C25—41no—
326C25—41no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25C2412yes—
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—22no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—22no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—24no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—22no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—41no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—41no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—42no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—42no—
379C22×D4—42no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4C2×D418yes—
383C22×D4C2×D414yes—
384C22×D4#4114yes—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—22no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—41no—
404C23×C4—41no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—41no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—41no—
415C23×C4—42no—
416C23×C4C2×D414yes—
417C23×C4C2412yes—
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2412yes—
427C23×C4C2412yes—
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435#123—432no—
436#123—432no—
437#121—416no—
438#120—232no—
439#120—432no—
440C4×D4—416no—
441C4×D4—432no—
442C4×D4—432no—
443C4×D4—416no—
444C4×D4—416no—
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—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—24no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—24no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—42no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—42no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—42no—
489C2×C4⋊C4—42no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—42no—
492C2×C4⋊C4C2×D418yes—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—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—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—22no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
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—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—24no—
563C2×C22⋊C4—416no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
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—416no—
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⋊C4C2×D414yes—
587C2×C22⋊C4C2×D418yes—
588C2×C22⋊C4C2×D418yes—
589C2×C22⋊C4C2×D414yes—
590C2×C22⋊C4C2×D418yes—
591C2×C22⋊C4C2×D414yes—
592C2×C22⋊C4C2×D418yes—
593C2×C22⋊C4#4114yes—
594C2×C42—22no—
595C2×C42—24no—
596C2×C42—22no—
597C2×C42—24no—
598C2×C42—22no—
599C2×C42—24no—
600C2×C42—24no—
601C2×C42—24no—
602C2×C42—24no—
603C2×C42—42no—
604C2×C42—42no—
605C2×C42—42no—
606C2×C42—42no—
607C2×C42C2×D414yes—
608C2×C42C2×D418yes—
609C2×C42C2×D414yes—
610#95—22no—
611#95—24no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—22no—
620#95—22no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—24no—
626#95—24no—
627#95—24no—
628#95—22no—
629#95—42no—
630#95—42no—
631#95C2×D414yes—
632#95C2×D414yes—
633#95C2×D414yes—
634#95C2×D418yes—
635#95C2×D418yes—
636C24—21no—
637C24—22no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—21no—
652C24—22no—
653C24—28no—
654C24—21no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—21no—
663C24—22no—
664C24—22no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—21no—
676C24—21no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—22no—
686C24—21no—
687C24—22no—
688C24—44no—
689C24—48no—
690C24—48no—
691C24—44no—
692C24—44no—
693C24—44no—
694C24—48no—
695C24—48no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—44no—
700C24—84no—
701C24—82no—
702C24—84no—
703C24—84no—
704C24—82no—
705C24—84no—
706C24—84no—
707C24—84no—
708C24—84no—
709C24—84no—
710C24C22×D414yes—
711C24C22×D414yes—
712C24C22×D412yes—
713C24C22×D412yes—
714C24C2×#4112yes—
715C24C2×#4112yes—
716C24C2×#4112yes—
717C242−1+412yes—
718C24C2511yescharacteristic
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—28no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4—48no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
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—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—21no—
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—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—28no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—22no—
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—21no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4—44no—
859C22×C4—48no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—48no—
874C22×C4—82no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—82no—
879C22×C4—84no—
880C22×C4—82no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—84no—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D414yes—
890C22×C4C22×D414yes—
891C22×C4C22×D414yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D414yes—
896C22×C4C22×D412yes—
897C22×C4C22×D414yes—
898C22×C4C22×D412yes—
899C22×C4C22×D414yes—
900C22×C4C22×D414yes—
901C22×C4C22×D412yes—
902C22×C4C2×#4112yes—
903C22×C4C2×#4112yes—
904C22×C4C2×#4112yes—
905C22×C4H(5,𝔽2)12yes—
906C22×C4H(5,𝔽2)14yes—
907C4⋊C4—48no—
908C4⋊C4—48no—
909C4⋊C4—44no—
910C4⋊C4—48no—
911C4⋊C4—48no—
912C4⋊C4—44no—
913C4⋊C4—44no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—48no—
917C4⋊C4—44no—
918C4⋊C4—44no—
919C4⋊C4—48no—
920C4⋊C4—82no—
921C4⋊C4—84no—
922C4⋊C4—84no—
923C4⋊C4—84no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—216no—
929C22⋊C4—216no—
930C22⋊C4—48no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—44no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—48no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—44no—
949C22⋊C4—48no—
950C22⋊C4—44no—
951C22⋊C4—48no—
952C22⋊C4—44no—
953C22⋊C4—48no—
954C22⋊C4—84no—
955C22⋊C4—82no—
956C22⋊C4—84no—
957C22⋊C4—84no—
958C22⋊C4#127116yes—
959C42—216no—
960C42—28no—
961C42—44no—
962C42—48no—
963C42—44no—
964C42—84no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—22no—
972C23—24no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—24no—
977C23—22no—
978C23—24no—
979C23—22no—
980C23—24no—
981C23—22no—
982C23—24no—
983C23—22no—
984C23—24no—
985C23—22no—
986C23—24no—
987C23—22no—
988C23—24no—
989C23—22no—
990C23—22no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—22no—
998C23—22no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—416no—
1007C23—416no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—42no—
1013C23—41no—
1014C23—42no—
1015C23—42no—
1016C23—41no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—42no—
1022C23—41no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—41no—
1030C23—42no—
1031C23—41no—
1032C23—42no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—42no—
1038C23—42no—
1039C23—41no—
1040C23—41no—
1041C23—42no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—41no—
1054C23—42no—
1055C23—42no—
1056C23—41no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—41no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—41no—
1070C23—42no—
1071C23—42no—
1072C23—41no—
1073C23—42no—
1074C23—41no—
1075C23—42no—
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—88no—
1093C23—816no—
1094C23—88no—
1095C23—88no—
1096C23—816no—
1097C23—816no—
1098C23—88no—
1099C23—88no—
1100C23—816no—
1101C23C2×#12714yes—
1102C23#54714yes—
1103C23C23×D411yescharacteristic
1104C23C23×D412yes—
1105C23C23×D411yescharacteristic
1106C23C22×#4111yescharacteristic
1107C23C22×#4111yescharacteristic
1108C23C2×H(5,𝔽2)12yes—
1109C23C2×H(5,𝔽2)11yescharacteristic
1110C23C2×2−1+411yescharacteristic
1111C23#58512yes—
1112C23#58511yescharacteristic
1113C23#58512yes—
1114D4—432no—
1115D4—416no—
1116D4—416no—
1117D4—416no—
1118D4—432no—
1119D4—88no—
1120D4—816no—
1121D4—816no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—22no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—22no—
1151C2×C4—24no—
1152C2×C4—22no—
1153C2×C4—24no—
1154C2×C4—24no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—22no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—41no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—41no—
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—41no—
1191C2×C4—42no—
1192C2×C4—41no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—42no—
1203C2×C4—42no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—41no—
1210C2×C4—42no—
1211C2×C4—41no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—88no—
1224C2×C4—88no—
1225C2×C4—88no—
1226C2×C4—816no—
1227C2×C4—88no—
1228C2×C4—88no—
1229C2×C4#52514yes—
1230C2×C4C2×#12714yes—
1231C2×C4C2×#12714yes—
1232C2×C4D4218yes—
1233C2×C4D4214yes—
1234C22—24no—
1235C22—24no—
1236C22—28no—
1237C22—24no—
1238C22—24no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—44no—
1255C22—44no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—44no—
1260C22—42no—
1261C22—44no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—42no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—44no—
1271C22—44no—
1272C22—44no—
1273C22—832no—
1274C22—82no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—81no—
1285C22—82no—
1286C22—81no—
1287C22—81no—
1288C22—82no—
1289C22—81no—
1290C22—82no—
1291C22—82no—
1292C22—82no—
1293C22—82no—
1294C22C2×#52511yescharacteristic
1295C22C22×#12711yescharacteristic
1296C22#344911yescharacteristic
1297C22C2×D4211yescharacteristic
1298C22C2×D4212yes—
1299C22C2×#54711yescharacteristic
1300C22D4×#4111yescharacteristic
1301C22D4×#4112yes—
1302C22D4×#4112yes—
1303C22#348511yescharacteristic
1304C22#348512yes—
1305C22#348512yes—
1306C22#348911yescharacteristic
1307C22#348912yes—
1308C22#349811yescharacteristic
1309C22#349812yes—
1310C22#350512yes—
1311C22#350611yescharacteristic
1312C22#351312yes—
1313C22#352011yescharacteristic
1314C22#353312yes—
1315C22#353512yes—
1316C22#354012yes—
1317C4—24no—
1318C4—24no—
1319C4—24no—
1320C4—28no—
1321C4—24no—
1322C4—42no—
1323C4—42no—
1324C4—42no—
1325C4—42no—
1326C4—44no—
1327C4—44no—
1328C4—44no—
1329C4—81no—
1330C4—81no—
1331C4—82no—
1332C4—82no—
1333C4—82no—
1334C4—81no—
1335C2—44no—
1336C2—44no—
1337C2—82no—
1338C2—84no—
1339C2—82no—
1340C2#3493611yescharacteristic
1341C2#3584011yescharacteristic
1342C2#3606011yescharacteristic
1343C2#3610011yescharacteristic
1344C2D4×#12711yescharacteristic
1345C2#3765411yescharacteristic
1346C2#4196011yescharacteristic
1347C2#4416212yes—
1348C2#4427212yes—
1349C2#5899512yes—
1350C2#5900012yes—
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×#2539C2semidirect
2. C2×#2422C2semidirect
3. C2×#2455C2semidirect
4. C2×#2418C2semidirect
5. C2×#2397C2semidirect
6. C2×#2358C2semidirect
7. #17068C2semidirect
8. #16508C2semidirect
9. #15696C2semidirect
10. #15493C2semidirect
11. #15384C2semidirect
12. #15267C2semidirect
13. #15155C2semidirect
14. #15135C2semidirect
15. #14910C2semidirect
16. #14839C2semidirect
17. #14807C2semidirect
18. #14796C2semidirect
19. #14734C2semidirect
20. #14228C2semidirect
21. #14189C2semidirect
22. #13977C2semidirect
23. #13816C2semidirect
32. C22×C4×D4C22semidirect
33. C22×C4×D4C22semidirect
46. C2×#399C22semidirect
47. C2×#399C22semidirect
48. C2×#399C22semidirect
49. C2×#399C22semidirect
51. C2×#397C22semidirect
56. C2×#394C22semidirect
62. C2×#392C22semidirect
69. C2×#390C22semidirect
70. C2×#389C22semidirect
71. C2×#389C22semidirect
72. C2×#389C22semidirect
77. C2×#388C22semidirect
87. C2×#385C22semidirect
88. C2×#385C22semidirect
89. C2×#385C22semidirect
90. C2×#384C22semidirect
91. C2×#384C22semidirect
98. C2×#376C22semidirect
99. #1445C22semidirect
100. #1445C22semidirect
101. #1445C22semidirect
102. #1444C22semidirect
103. #1444C22semidirect
104. #1444C22semidirect
111. #1439C22semidirect
112. #1439C22semidirect
113. #1439C22semidirect
114. #1439C22semidirect
117. #1438C22semidirect
118. #1438C22semidirect
120. #1437C22semidirect
121. #1437C22semidirect
122. #1436C22semidirect
123. C4⋊#95C22semidirect
124. C4⋊#95C22semidirect
125. #1434C22semidirect
127. C4×#95C22semidirect
128. C4×#95C22semidirect
257. #392D4semidirect
271. #388D4semidirect
291. C4×C22⋊C4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25392
C2×#24222
C2×#24552
C2×#24182
C2×#23972
C2×#23582
#170682
#165082
#156962
#154932
#153842
#152672
#151552
#151352
#149102
#148392
#148072
#147962
#147342
#142282
#141892
#139772
#138162