Finite Group Databasebeta

← #721545

Subgroups — #721545

Order 512.

5019 conjugacy classes of subgroups.

The subgroup lattice has 1361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2559C211yesmaximal, characteristic, complemented
2C2×#2480C212yesmaximal, complemented
3C2×#2424C212yesmaximal, complemented
4C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
5#17071C211yesmaximal, characteristic, complemented
6#16810C211yesmaximal, characteristic, complemented
7#16807C211yesmaximal, characteristic, complemented
8#16807C211yesmaximal, characteristic, complemented
9#15526C212yesmaximal, complemented
10#15315C212yesmaximal, complemented
11#15283C212yesmaximal, complemented
12#15283C212yesmaximal, complemented
13#15123C211yesmaximal, characteristic, complemented
14#14977C212yesmaximal, complemented
15#14807C211yesmaximal, characteristic, complemented
16#14796C212yesmaximal, complemented
17#14715C211yesmaximal, characteristic, complemented
18#14715C211yesmaximal, characteristic, complemented
19#14321C211yesmaximal, characteristic, complemented
20#14228C211yesmaximal, characteristic, complemented
21#14189C211yesmaximal, characteristic, complemented
22C4×#392C211yesmaximal, characteristic, complemented
23#13788C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#126C2211yescharacteristic
26C22×#121C2211yescharacteristic
27C22×#121C2212yescomplemented
28C22×#120C2212yes—
29C22×#120C2212yes—
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2212yescomplemented
33C23×C22⋊C4C2212yes—
34#2559—28no—
35#2480—216no—
36#2424—216no—
37C2×#400C2211yescharacteristic, complemented
38C2×#399C2212yescomplemented
39C2×#399C2212yescomplemented
40C2×#397C2212yes—
41C2×#397C2212yes—
42C2×#397C2212yescomplemented
43C2×#396C2212yescomplemented
44C2×#396C2212yescomplemented
45C2×#394C2211yescharacteristic
46C2×#394C2211yescharacteristic
47C2×#394C2212yes—
48C2×#394C2212yes—
49C2×#394C2211yescharacteristic, complemented
50C2×#392C2211yescharacteristic
51C2×#392C2211yescharacteristic
52C2×#392C2211yescharacteristic
53C2×#392C2211yescharacteristic
54C2×#392C2212yes—
55C2×#392C2212yes—
56C2×#392C2212yescomplemented
57D4×C22⋊C4—28no—
58C2×#390C2211yescharacteristic
59C2×#390C2211yescharacteristic
60C2×#390C2211yescharacteristic, complemented
61C2×#390C2212yescomplemented
62C2×#390C2212yescomplemented
63C2×#390C2212yescomplemented
64C2×#389C2211yescharacteristic, complemented
65C2×#388C2212yes—
66C2×#388C2211yescharacteristic, complemented
67C2×#388C2211yescharacteristic, complemented
68C2×#388C2212yescomplemented
69C2×#388C2212yescomplemented
70C2×#386C2211yescharacteristic
71C2×#386C2211yescharacteristic
72C2×#386C2212yes—
73C2×#386C2212yes—
74C2×#386C2212yescomplemented
75C2×#386C2212yescomplemented
76C2×#385C2211yescharacteristic, complemented
77C2×#385C2212yescomplemented
78C2×#385C2212yescomplemented
79C2×#385C2212yescomplemented
80C2×#380C2211yescharacteristic
81C2×#380C2212yescomplemented
82C2×#379C2212yes—
83C2×#379C2212yes—
84C2×#379C2212yes—
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2211yescharacteristic, complemented
87C2×C4×C22⋊C4C2212yescomplemented
88#1445C2212yescomplemented
89#1445C2212yescomplemented
90#1444C2211yescharacteristic, complemented
91#1444C2211yescharacteristic, complemented
92#1444C2211yescharacteristic, complemented
93#1444C2211yescharacteristic, complemented
94#1439C2211yescharacteristic, complemented
95#1439C2211yescharacteristic, complemented
96#1439C2212yescomplemented
97#1439C2211yescharacteristic, complemented
98#1439C2211yescharacteristic, complemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1438C2211yescharacteristic
105#1438C2211yescharacteristic
106#1438C2212yes—
107#1438C2211yescharacteristic
108#1438C2212yes—
109#1438C2211yescharacteristic
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1438C2212yescomplemented
115#1438C2212yescomplemented
116#1437C2212yes—
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120C4⋊#95C2211yescharacteristic, complemented
121#1434C2212yescomplemented
122#1434C2211yescharacteristic, complemented
123C22⋊#95C2211yescharacteristic
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2211yescharacteristic, complemented
127C26C2312yes—
128C23×D4—24no—
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—44no—
132C23×D4—44no—
133C23×D4C2311yescharacteristic
134C23×D4C2312yes—
135C23×D4C2312yes—
136C23×D4C2312yes—
137C23×D4C2311yescharacteristic
138C23×D4C2311yescharacteristic
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2311yescharacteristic
143C24×C4C2312yes—
144C24×C4C2312yes—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C2×#126—28no—
148C2×#126—24no—
149C2×#121—28no—
150C2×#121—28no—
151C2×#121—24no—
152C2×#121—44no—
153C2×#121—44no—
154C2×#120—28no—
155C2×#120—28no—
156C2×#120—44no—
157C2×#120—44no—
158C2×#120—44no—
159C2×#120—44no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—28no—
163C2×C4×D4—44no—
164C2×C4×D4—44no—
165C2×C4×D4—44no—
166C2×C4×D4—44no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2312yes—
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2312yes—
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2312yes—
180C22×C22⋊C4—28no—
181C22×C22⋊C4—28no—
182C22×C22⋊C4—28no—
183C22×C22⋊C4C2311yescharacteristic
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2312yes—
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2311yescharacteristic
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2312yes—
226#400—24no—
227#399—44no—
228#399—44no—
229#397—28no—
230#397—28no—
231#397—28no—
232#396—28no—
233#396—28no—
234#394—28no—
235#394—28no—
236#394—24no—
237#394—24no—
238#394—24no—
239#392—24no—
240#392—24no—
241#392—24no—
242#392—24no—
243#392—28no—
244#392—44no—
245#392—44no—
246#390—24no—
247#390—24no—
248#390—24no—
249#390—28no—
250#390—44no—
251#390—44no—
252#389—24no—
253#388—24no—
254#388—28no—
255#388—24no—
256#388—28no—
257#388D4116yescomplemented
258#386—24no—
259#386—24no—
260#386—28no—
261#386—28no—
262#386—28no—
263#386—28no—
264#385—24no—
265#385—28no—
266#385—28no—
267#385—28no—
268#380—24no—
269#380—28no—
270#379—28no—
271#379—28no—
272#379—28no—
273C4×C22⋊C4—24no—
274C4×C22⋊C4—28no—
275C4×C22⋊C4D418yescomplemented
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C2×#95C2312yes—
303C2×#95C2312yes—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—24no—
308C25—24no—
309C25—24no—
310C25—24no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25C2411yescharacteristic
320C25C2412yes—
321C25C2411yescharacteristic
322C25C2411yescharacteristic
323C25C2412yes—
324C22×D4—24no—
325C22×D4—24no—
326C22×D4—232no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—24no—
339C22×D4—22no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—24no—
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—22no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—42no—
364C22×D4—42no—
365C22×D4—42no—
366C22×D4—42no—
367C22×D4—42no—
368C22×D4—42no—
369C22×D4—42no—
370C22×D4—42no—
371C22×D4—42no—
372C22×D4—42no—
373C22×D4—41no—
374C22×D4—42no—
375C22×D4—42no—
376C22×D4—42no—
377C22×D4—42no—
378C22×D4—41no—
379C22×D4—41no—
380C22×D4—42no—
381C22×D4—42no—
382C22×D4—42no—
383C22×D4—416no—
384C22×D4—416no—
385C22×D4—432no—
386C22×D4—432no—
387C22×D4#4114yes—
388C22×D4#4114yes—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—24no—
397C23×C4—24no—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—41no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4C2×D414yes—
413C23×C4C2411yescharacteristic
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2411yescharacteristic
422C23×C4C2412yes—
423C23×C4C2412yes—
424C23×C4C2412yes—
425C23×C4C2412yes—
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431#126—416no—
432#121—432no—
433#121—416no—
434#120—432no—
435#120—432no—
436C4×D4—432no—
437C4×D4—416no—
438C4×D4—416no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4C2×D418yescomplemented
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—22no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—24no—
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—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—24no—
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—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—22no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
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—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—432no—
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⋊C4—42no—
571C2×C22⋊C4C2×D418yes—
572C2×C22⋊C4C2×D418yes—
573C2×C22⋊C4C2×D414yes—
574C2×C22⋊C4C2×D414yes—
575C2×C22⋊C4C2×D418yes—
576C2×C42—22no—
577C2×C42—24no—
578C2×C42—42no—
579C2×C42—42no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—42no—
585C2×C42C2×D414yes—
586C2×C42C2×D414yes—
587C2×C42C2×D418yescomplemented
588#95—22no—
589#95—22no—
590#95—24no—
591#95—24no—
592#95—24no—
593#95—24no—
594#95—24no—
595#95—24no—
596#95—22no—
597#95—24no—
598#95—24no—
599#95—22no—
600#95—22no—
601#95—24no—
602#95—22no—
603#95—22no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95C2×D414yes—
613#95C2×D414yes—
614#95C2×D418yescomplemented
615#95C2×D418yescomplemented
616C24—22no—
617C24—22no—
618C24—22no—
619C24—21no—
620C24—21no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—216no—
638C24—22no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—21no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—21no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—21no—
661C24—22no—
662C24—21no—
663C24—22no—
664C24—21no—
665C24—21no—
666C24—22no—
667C24—22no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—22no—
672C24—21no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—48no—
684C24—48no—
685C24—48no—
686C24—48no—
687C24—48no—
688C24—48no—
689C24—84no—
690C24—84no—
691C24—84no—
692C24—84no—
693C24—84no—
694C24—84no—
695C24—84no—
696C24—84no—
697C24—84no—
698C24—84no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—84no—
706C24—84no—
707C24C22×D414yes—
708C24C22×D412yes—
709C24C2×#4114yes—
710C24C2×#4114yes—
711C24H(5,𝔽2)12yes—
712C24H(5,𝔽2)14yes—
713C24H(5,𝔽2)14yes—
714C24C2511yescharacteristic
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—216no—
718C2×D4—216no—
719C2×D4—216no—
720C2×D4—216no—
721C2×D4—28no—
722C2×D4—28no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—44no—
741C2×D4—48no—
742C2×D4—4128no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—82no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—82no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C2×D4—84no—
771C2×D4—82no—
772C2×D4—84no—
773C2×D4—84no—
774C2×D4—84no—
775C2×D4—84no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—21no—
805C22×C4—22no—
806C22×C4—22no—
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—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—28no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—22no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—21no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—21no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—48no—
867C22×C4—44no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—48no—
871C22×C4—48no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4—48no—
875C22×C4—48no—
876C22×C4—48no—
877C22×C4—48no—
878C22×C4—44no—
879C22×C4—82no—
880C22×C4—84no—
881C22×C4—84no—
882C22×C4—84no—
883C22×C4—84no—
884C22×C4—84no—
885C22×C4—84no—
886C22×C4—84no—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D414yes—
890C22×C4C22×D414yes—
891C22×C4C22×D414yes—
892C22×C4C22×D414yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D414yes—
898C22×C4C22×D414yes—
899C22×C4C2×#4112yes—
900C22×C4C2×#4112yes—
901C22×C4H(5,𝔽2)12yes—
902C4⋊C4—48no—
903C4⋊C4—44no—
904C4⋊C4—48no—
905C4⋊C4—44no—
906C4⋊C4—44no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—82no—
912C4⋊C4—84no—
913C4⋊C4—84no—
914C4⋊C4—84no—
915C22⋊C4—216no—
916C22⋊C4—44no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—44no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—48no—
942C22⋊C4—48no—
943C22⋊C4—44no—
944C22⋊C4—82no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—82no—
948C22⋊C4—82no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4#127116yes—
953C42—44no—
954C42—44no—
955C42—48no—
956C42—44no—
957C42—84no—
958C23—22no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—22no—
973C23—22no—
974C23—24no—
975C23—24no—
976C23—22no—
977C23—22no—
978C23—24no—
979C23—24no—
980C23—24no—
981C23—24no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—22no—
996C23—24no—
997C23—24no—
998C23—22no—
999C23—24no—
1000C23—432no—
1001C23—432no—
1002C23—42no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—42no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—41no—
1016C23—42no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—41no—
1029C23—42no—
1030C23—41no—
1031C23—41no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
1042C23—42no—
1043C23—41no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—41no—
1049C23—42no—
1050C23—42no—
1051C23—41no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—41no—
1060C23—42no—
1061C23—41no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—42no—
1070C23—42no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—41no—
1082C23—41no—
1083C23—42no—
1084C23—42no—
1085C23—41no—
1086C23—41no—
1087C23—42no—
1088C23—42no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—816no—
1098C23—816no—
1099C23—816no—
1100C23—816no—
1101C23—816no—
1102C23—816no—
1103C23—816no—
1104C23—816no—
1105C23—816no—
1106C23—816no—
1107C23—816no—
1108C23—816no—
1109C23—816no—
1110C23C2×#12714yes—
1111C23#53818yes—
1112C23C23×D411yescharacteristic
1113C23C23×D412yes—
1114C23C22×#4111yescharacteristic
1115C23C22×#4111yescharacteristic
1116C23C2×H(5,𝔽2)12yes—
1117C23C2×H(5,𝔽2)12yes—
1118C23C2×H(5,𝔽2)11yescharacteristic
1119C23C2×H(5,𝔽2)11yescharacteristic
1120C23#58512yes—
1121C23#58511yescharacteristic
1122C23#58511yescharacteristic
1123D4—232no—
1124D4—416no—
1125D4—432no—
1126D4—432no—
1127D4—88no—
1128D4—88no—
1129D4—816no—
1130D4—816no—
1131D4—816no—
1132D4—88no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—24no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—24no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—24no—
1149C2×C4—24no—
1150C2×C4—24no—
1151C2×C4—24no—
1152C2×C4—24no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—24no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—24no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—24no—
1165C2×C4—24no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—416no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—42no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—42no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—41no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—41no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—41no—
1233C2×C4—88no—
1234C2×C4—816no—
1235C2×C4—816no—
1236C2×C4#52514yes—
1237C2×C4C2×#12714yes—
1238C2×C4C2×#12714yes—
1239C22—24no—
1240C22—24no—
1241C22—28no—
1242C22—28no—
1243C22—24no—
1244C22—28no—
1245C22—44no—
1246C22—42no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—42no—
1259C22—42no—
1260C22—44no—
1261C22—42no—
1262C22—44no—
1263C22—44no—
1264C22—44no—
1265C22—42no—
1266C22—44no—
1267C22—44no—
1268C22—44no—
1269C22—44no—
1270C22—42no—
1271C22—44no—
1272C22—42no—
1273C22—44no—
1274C22—44no—
1275C22—44no—
1276C22—44no—
1277C22—864no—
1278C22—81no—
1279C22—82no—
1280C22—81no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22—82no—
1286C22—82no—
1287C22—82no—
1288C22—82no—
1289C22—81no—
1290C22—82no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—82no—
1303C22C2×#52511yescharacteristic
1304C22C22×#12711yescharacteristic
1305C22#344911yescharacteristic
1306C22C2×#53812yes—
1307C22D4×#4112yes—
1308C22D4×#4112yes—
1309C22#348411yescharacteristic
1310C22#348412yes—
1311C22#348412yes—
1312C22#348411yescharacteristic
1313C22#348811yescharacteristic
1314C22#348812yes—
1315C22#348812yes—
1316C22#348811yescharacteristic
1317C22#349012yes—
1318C22#351311yescharacteristic
1319C22#351411yescharacteristic
1320C22#351911yescharacteristic
1321C22#352111yescharacteristic
1322C22#353412yes—
1323C22#354212yes—
1324C22#356012yes—
1325C22#356012yes—
1326C4—24no—
1327C4—24no—
1328C4—24no—
1329C4—42no—
1330C4—42no—
1331C4—44no—
1332C4—44no—
1333C4—44no—
1334C4—42no—
1335C4—42no—
1336C4—44no—
1337C4—81no—
1338C4—81no—
1339C4—82no—
1340C4—82no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C2—48no—
1345C2—44no—
1346C2—82no—
1347C2—84no—
1348C2—161no—
1349C2#3493611yescharacteristic
1350C2#3498811yescharacteristic
1351C2#3552211yescharacteristic
1352C2#3592111yescharacteristic
1353C2#3592111yescharacteristic
1354C2#3772012yes—
1355C2#3772512yes—
1356C2#4060611yescharacteristic
1357C2#4198611yescharacteristic
1358C2#4310912yes—
1359C2#4423112yes—
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×#2559C2semidirect
2. C2×#2480C2semidirect
3. C2×#2424C2semidirect
4. C2×D4×C22⋊C4C2semidirect
5. #17071C2semidirect
6. #16810C2semidirect
7. #16807C2semidirect
8. #16807C2semidirect
9. #15526C2semidirect
10. #15315C2semidirect
11. #15283C2semidirect
12. #15283C2semidirect
13. #15123C2semidirect
14. #14977C2semidirect
15. #14807C2semidirect
16. #14796C2semidirect
17. #14715C2semidirect
18. #14715C2semidirect
19. #14321C2semidirect
20. #14228C2semidirect
21. #14189C2semidirect
22. C4×#392C2semidirect
23. #13788C2semidirect
27. C22×#121C22semidirect
32. C22×C4×D4C22semidirect
37. C2×#400C22semidirect
38. C2×#399C22semidirect
39. C2×#399C22semidirect
42. C2×#397C22semidirect
43. C2×#396C22semidirect
44. C2×#396C22semidirect
49. C2×#394C22semidirect
56. C2×#392C22semidirect
60. C2×#390C22semidirect
61. C2×#390C22semidirect
62. C2×#390C22semidirect
63. C2×#390C22semidirect
64. C2×#389C22semidirect
66. C2×#388C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
69. C2×#388C22semidirect
74. C2×#386C22semidirect
75. C2×#386C22semidirect
76. C2×#385C22semidirect
77. C2×#385C22semidirect
78. C2×#385C22semidirect
79. C2×#385C22semidirect
81. C2×#380C22semidirect
86. C2×C4×C22⋊C4C22semidirect
87. C2×C4×C22⋊C4C22semidirect
88. #1445C22semidirect
89. #1445C22semidirect
90. #1444C22semidirect
91. #1444C22semidirect
92. #1444C22semidirect
93. #1444C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. C4⋊#95C22semidirect
121. #1434C22semidirect
122. #1434C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
257. #388D4semidirect
275. C4×C22⋊C4D4semidirect
470. C2×C4⋊C4C2×D4semidirect
587. C2×C42C2×D4semidirect
614. #95C2×D4semidirect
615. #95C2×D4semidirect

Maximal subgroups

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

subgroupindex
C2×#25592
C2×#24802
C2×#24242
C2×D4×C22⋊C42
#170712
#168102
#168072
#155262
#153152
#152832
#151232
#149772
#148072
#147962
#147152
#143212
#142282
#141892
C4×#3922
#137882