Finite Group Databasebeta

← #1409019

Subgroups — #1409019

Order 512.

5498 conjugacy classes of subgroups.

The subgroup lattice has 1401 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2435C211yesmaximal, characteristic, complemented
2C2×#2480C211yesmaximal, characteristic, complemented
3C2×#2662C211yesmaximal, characteristic, complemented
4C22×#392C211yesmaximal, characteristic
5#16819C211yesmaximal, characteristic, complemented
6#16680C211yesmaximal, characteristic, complemented
7#16655C211yesmaximal, characteristic, complemented
8#16552C212yesmaximal, complemented
9#16526C212yesmaximal, complemented
10#16504C211yesmaximal, characteristic, complemented
11#16290C212yesmaximal, complemented
12#16274C212yesmaximal, complemented
13#14928C211yesmaximal, characteristic, complemented
14#14815C211yesmaximal, characteristic, complemented
15#14758C211yesmaximal, characteristic, complemented
16#14726C212yesmaximal, complemented
17#14724C212yesmaximal, complemented
18#14724C211yesmaximal, characteristic, complemented
19#14717C211yesmaximal, characteristic, complemented
20#14321C211yesmaximal, characteristic, complemented
21#13902C212yesmaximal, complemented
22#13873C212yesmaximal, complemented
23#13814C211yesmaximal, characteristic, complemented
24C24×D4C2212yes—
25C24×D4C2211yescharacteristic
26C22×#126C2211yescharacteristic, complemented
27C22×#124C2211yescharacteristic, complemented
28C22×#124C2211yescharacteristic, complemented
29C22×C22⋊Q8C2211yescharacteristic
30C23×C22⋊C4C2212yes—
31C23×C22⋊C4C2211yescharacteristic
32#2662—28no—
33#2480—28no—
34#2435—28no—
35C2×#397C2211yescharacteristic, complemented
36C2×#397C2211yescharacteristic, complemented
37C2×#397C2211yescharacteristic, complemented
38C2×#396C2212yescomplemented
39C2×#396C2211yescharacteristic, complemented
40C2×#396C2212yescomplemented
41C2×#395C2211yescharacteristic, complemented
42C2×#394C2212yescomplemented
43C2×#394C2211yescharacteristic, complemented
44C2×#394C2212yescomplemented
45C2×#394C2212yescomplemented
46C2×#394C2211yescharacteristic, complemented
47C2×#394C2212yescomplemented
48C2×#394C2212yescomplemented
49C2×#394C2212yescomplemented
50C2×#394C2212yescomplemented
51C2×#393C2211yescharacteristic, complemented
52C2×#393C2211yescharacteristic, complemented
53C2×#392—28no—
54C2×#392C2211yescharacteristic
55C2×#392C2211yescharacteristic
56C2×#392C2211yescharacteristic
57C2×#392C2212yes—
58C2×#392C2212yes—
59C2×#392C2211yescharacteristic
60C2×#390C2211yescharacteristic, complemented
61C2×#390C2212yescomplemented
62C2×#390C2211yescharacteristic, complemented
63C2×#390C2212yescomplemented
64C2×#390C2212yescomplemented
65C2×#390C2212yescomplemented
66C2×#388C2212yescomplemented
67C2×#388C2211yescharacteristic, complemented
68C2×#388C2211yescharacteristic, complemented
69C2×#388C2211yescharacteristic, complemented
70C2×#388C2212yescomplemented
71C2×#385C2211yescharacteristic
72C2×#385C2211yescharacteristic
73C2×#385C2212yes—
74C2×#380C2211yescharacteristic
75C2×#380C2212yes—
76C2×#379C2212yes—
77C2×#379C2211yescharacteristic
78C2×#379C2211yescharacteristic
79C2×#379C2212yes—
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×#379C2212yes—
83C2×C4×C4⋊C4C2211yescharacteristic, complemented
84C2×C4×C22⋊C4C2212yes—
85C2×C4×C22⋊C4C2211yescharacteristic
86C22×#95C2211yescharacteristic
87#1446C2211yescharacteristic, complemented
88#1444C2212yescomplemented
89#1444C2211yescharacteristic, complemented
90#1441C2211yescharacteristic, complemented
91#1441C2212yescomplemented
92#1440C2212yescomplemented
93#1440C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2211yescharacteristic, complemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2211yescharacteristic, complemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1438C2212yescomplemented
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2211yescharacteristic, complemented
111#1438C2212yescomplemented
112#1438C2212yescomplemented
113#1438C2212yescomplemented
114#1438C2211yescharacteristic, complemented
115#1438C2212yescomplemented
116#1438C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121C4⋊#95C2211yescharacteristic, complemented
122#1434C2211yescharacteristic, complemented
123C22⋊#95C2212yes—
124C22⋊#95C2212yes—
125C22⋊#95C2211yescharacteristic
126C4×#95C2211yescharacteristic, complemented
127C26C2311yescharacteristic
128C26C2312yes—
129C23×Q8C2311yescharacteristic
130C23×D4—24no—
131C23×D4—28no—
132C23×D4—24no—
133C23×D4—28no—
134C23×D4—42no—
135C23×D4—44no—
136C23×D4—44no—
137C23×D4—44no—
138C23×D4—44no—
139C23×D4—44no—
140C23×D4—44no—
141C23×D4—44no—
142C23×D4C2311yescharacteristic
143C23×D4C2312yes—
144C23×D4C2312yes—
145C23×D4C2312yes—
146C23×D4C2312yes—
147C23×D4C2311yescharacteristic
148C23×D4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152C2×#126—24no—
153C2×#126—24no—
154C2×#126—42no—
155C2×#124—24no—
156C2×#124—24no—
157C2×#124—24no—
158C2×#124—42no—
159C2×#124—44no—
160C2×C22⋊Q8—24no—
161C2×C22⋊Q8—44no—
162C22×C4⋊C4C2311yescharacteristic
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2311yescharacteristic
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2312yes—
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2312yes—
173C22×C4⋊C4C2311yescharacteristic
174C22×C22⋊C4—24no—
175C22×C22⋊C4—28no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—28no—
178C22×C22⋊C4—42no—
179C22×C22⋊C4—44no—
180C22×C22⋊C4C2311yescharacteristic
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2312yes—
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2311yescharacteristic
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2311yescharacteristic
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2312yes—
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C22⋊C4C2312yes—
221C22×C22⋊C4C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2312yes—
224C22×C42C2312yes—
225C22×C42C2311yescharacteristic
226#397—24no—
227#397—24no—
228#397—24no—
229#396—28no—
230#396—24no—
231#396—44no—
232#395—24no—
233#394—24no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—44no—
238#394—42no—
239#394—44no—
240#394—44no—
241#394—44no—
242#393—24no—
243#393—42no—
244#392—24no—
245#392—28no—
246#392—24no—
247#392—28no—
248#392—24no—
249#392D418yes—
250#390—28no—
251#390—24no—
252#390—24no—
253#390—44no—
254#390—44no—
255#390—44no—
256#388—28no—
257#388—24no—
258#388—24no—
259#388—24no—
260#388—44no—
261#385—24no—
262#385—28no—
263#385—24no—
264#380—24no—
265#380—44no—
266#379—28no—
267#379—28no—
268#379—24no—
269#379—24no—
270#379—44no—
271#379—44no—
272#379—44no—
273C4×C4⋊C4—24no—
274C4×C22⋊C4—44no—
275C4×C22⋊C4D418yescomplemented
276C2×#95—24no—
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2311yescharacteristic
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2311yescharacteristic
285C2×#95C2311yescharacteristic
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2311yescharacteristic
303C2×#95C2311yescharacteristic
304C2×#95C2311yescharacteristic
305C25—22no—
306C25—24no—
307C25—24no—
308C25—22no—
309C25—24no—
310C25—22no—
311C25—22no—
312C25—24no—
313C25—24no—
314C25—24no—
315C25—24no—
316C25—24no—
317C25—24no—
318C25—24no—
319C25—22no—
320C25—24no—
321C25—41no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—41no—
330C25—42no—
331C25C2411yescharacteristic
332C25C2412yes—
333C25C2411yescharacteristic
334C25C2412yes—
335C25C2411yescharacteristic
336C22×Q8—22no—
337C22×Q8—22no—
338C22×Q8—22no—
339C22×Q8—42no—
340C22×Q8—42no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—24no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4—24no—
358C22×D4—24no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—22no—
362C22×D4—24no—
363C22×D4—416no—
364C22×D4—432no—
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—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×D4—42no—
383C22×D4—42no—
384C22×D4—42no—
385C22×D4—42no—
386C22×D4—416no—
387C22×D4—432no—
388C22×D4—416no—
389C22×D4—432no—
390C22×D4—432no—
391C22×D4—432no—
392C22×D4—432no—
393C22×D4—432no—
394C22×D4—432no—
395C22×D4—432no—
396C22×D4C2×D414yes—
397C22×D4C2×D418yes—
398C23×C4—24no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—22no—
404C23×C4—24no—
405C23×C4—22no—
406C23×C4—24no—
407C23×C4—22no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—41no—
413C23×C4C2×D414yes—
414C23×C4#4118yes—
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2412yes—
418C23×C4C2412yes—
419C23×C4C2411yescharacteristic
420C23×C4C2411yescharacteristic
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2412yes—
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433#126—416no—
434#124—416no—
435#124—416no—
436C22⋊Q8—416no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—41no—
459C2×C4⋊C4—41no—
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×C22⋊C4—24no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—22no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—24no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—416no—
532C2×C22⋊C4—432no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—41no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—41no—
544C2×C22⋊C4—41no—
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—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊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—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⋊C4C2×D414yes—
588C2×C22⋊C4C2×D418yes—
589C2×C22⋊C4C2×D414yes—
590C2×C22⋊C4C2×D414yes—
591C2×C42—22no—
592C2×C42—22no—
593C2×C42—24no—
594C2×C42—24no—
595C2×C42—42no—
596C2×C42—42no—
597C2×C42—42no—
598C2×C42—42no—
599C2×C42—42no—
600C2×C42C2×D414yescomplemented
601C2×C42C2×D414yescomplemented
602#95—22no—
603#95—24no—
604#95—22no—
605#95—22no—
606#95—22no—
607#95—22no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—24no—
612#95—24no—
613#95—24no—
614#95—24no—
615#95—24no—
616#95—22no—
617#95—42no—
618#95—42no—
619#95—42no—
620#95—42no—
621#95—42no—
622#95—42no—
623#95—42no—
624#95—42no—
625#95—42no—
626#95—42no—
627#95C2×D414yes—
628#95C2×D414yescomplemented
629#95C2×D414yescomplemented
630C24—21no—
631C24—21no—
632C24—22no—
633C24—22no—
634C24—21no—
635C24—21no—
636C24—216no—
637C24—28no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—21no—
651C24—22no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—21no—
674C24—22no—
675C24—21no—
676C24—22no—
677C24—21no—
678C24—21no—
679C24—22no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—22no—
684C24—21no—
685C24—22no—
686C24—44no—
687C24—48no—
688C24—48no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—48no—
700C24—44no—
701C24—44no—
702C24—48no—
703C24—48no—
704C24—44no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—44no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—44no—
717C24—48no—
718C24—44no—
719C24—48no—
720C24—48no—
721C24—48no—
722C24—48no—
723C24—82no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24—84no—
728C24—82no—
729C24—84no—
730C24—84no—
731C24—84no—
732C24—84no—
733C24—84no—
734C24—84no—
735C24—84no—
736C24—84no—
737C24—84no—
738C24—84no—
739C24—84no—
740C24—84no—
741C24—84no—
742C24C22×D412yes—
743C24C22×D414yes—
744C24C22×D412yes—
745C24C2×#4114yes—
746C24H(5,𝔽2)14yes—
747C24H(5,𝔽2)12yes—
748C24H(5,𝔽2)14yes—
749C24H(5,𝔽2)12yes—
750C242−1+412yes—
751C24C2511yescharacteristic
752C2×Q8—44no—
753C2×Q8—44no—
754C2×Q8—44no—
755C2×Q8—84no—
756C2×Q8—84no—
757C2×D4—28no—
758C2×D4—216no—
759C2×D4—28no—
760C2×D4—216no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—48no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—48no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—48no—
773C2×D4—48no—
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—48no—
783C2×D4—48no—
784C2×D4—48no—
785C2×D4—48no—
786C2×D4—48no—
787C2×D4—48no—
788C2×D4—48no—
789C2×D4—48no—
790C2×D4—48no—
791C2×D4—48no—
792C2×D4—48no—
793C2×D4—48no—
794C2×D4—48no—
795C2×D4—48no—
796C2×D4—48no—
797C2×D4—4128no—
798C2×D4—4256no—
799C2×D4—48no—
800C2×D4—48no—
801C2×D4—48no—
802C2×D4—44no—
803C2×D4—48no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—28no—
811C22×C4—216no—
812C22×C4—21no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—22no—
837C22×C4—21no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—28no—
845C22×C4—216no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—22no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
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—22no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—22no—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—21no—
890C22×C4—22no—
891C22×C4—22no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—22no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—22no—
900C22×C4—22no—
901C22×C4—44no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—48no—
908C22×C4—48no—
909C22×C4—44no—
910C22×C4—48no—
911C22×C4—44no—
912C22×C4—82no—
913C22×C4—84no—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D412yes—
919C22×C4C22×D412yes—
920C22×C4C22×D412yes—
921C22×C4C22×D412yes—
922C22×C4C22×D414yes—
923C22×C4C2×#4114yes—
924C22×C4C2×#4114yes—
925C22×C4H(5,𝔽2)12yes—
926C22×C4H(5,𝔽2)14yes—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C4⋊C4—44no—
930C4⋊C4—48no—
931C4⋊C4—44no—
932C4⋊C4—48no—
933C4⋊C4—84no—
934C4⋊C4—84no—
935C4⋊C4—82no—
936C4⋊C4—84no—
937C4⋊C4—82no—
938C4⋊C4—82no—
939C22⋊C4—28no—
940C22⋊C4—28no—
941C22⋊C4—28no—
942C22⋊C4—216no—
943C22⋊C4—44no—
944C22⋊C4—48no—
945C22⋊C4—44no—
946C22⋊C4—44no—
947C22⋊C4—44no—
948C22⋊C4—48no—
949C22⋊C4—48no—
950C22⋊C4—48no—
951C22⋊C4—48no—
952C22⋊C4—48no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C22⋊C4—44no—
956C22⋊C4—48no—
957C22⋊C4—44no—
958C22⋊C4—48no—
959C22⋊C4—44no—
960C22⋊C4—48no—
961C22⋊C4—82no—
962C22⋊C4—82no—
963C22⋊C4—84no—
964C22⋊C4—84no—
965C22⋊C4—84no—
966C22⋊C4—84no—
967C22⋊C4—82no—
968C22⋊C4—82no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C22⋊C4—84no—
973C22⋊C4—84no—
974C22⋊C4—84no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C42—28no—
982C42—44no—
983C42—84no—
984C42—84no—
985C23—22no—
986C23—24no—
987C23—24no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—24no—
993C23—24no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—22no—
1000C23—24no—
1001C23—22no—
1002C23—24no—
1003C23—22no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—24no—
1011C23—24no—
1012C23—24no—
1013C23—22no—
1014C23—24no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—24no—
1023C23—24no—
1024C23—24no—
1025C23—22no—
1026C23—24no—
1027C23—432no—
1028C23—432no—
1029C23—432no—
1030C23—416no—
1031C23—432no—
1032C23—41no—
1033C23—42no—
1034C23—41no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—42no—
1043C23—42no—
1044C23—42no—
1045C23—42no—
1046C23—42no—
1047C23—42no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—42no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—42no—
1056C23—41no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—41no—
1062C23—41no—
1063C23—42no—
1064C23—42no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—42no—
1069C23—41no—
1070C23—41no—
1071C23—42no—
1072C23—42no—
1073C23—42no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—41no—
1082C23—42no—
1083C23—42no—
1084C23—41no—
1085C23—42no—
1086C23—42no—
1087C23—42no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
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—41no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—42no—
1116C23—42no—
1117C23—41no—
1118C23—41no—
1119C23—42no—
1120C23—42no—
1121C23—42no—
1122C23—42no—
1123C23—42no—
1124C23—88no—
1125C23—816no—
1126C23—88no—
1127C23—816no—
1128C23—816no—
1129C23—816no—
1130C23—816no—
1131C23—816no—
1132C23—816no—
1133C23—88no—
1134C23—816no—
1135C23—816no—
1136C23—88no—
1137C23—816no—
1138C23—88no—
1139C23—816no—
1140C23—816no—
1141C23—816no—
1142C23—816no—
1143C23—816no—
1144C23—88no—
1145C23#53214yes—
1146C23#53514yes—
1147C23#53714yes—
1148C23#53818yes—
1149C23#54218yes—
1150C23C23×D411yescharacteristic
1151C23C23×D411yescharacteristic
1152C23C22×#4112yes—
1153C23C2×H(5,𝔽2)12yes—
1154C23C2×H(5,𝔽2)11yescharacteristic
1155C23C2×H(5,𝔽2)11yescharacteristic
1156C23C2×H(5,𝔽2)12yes—
1157C23C2×H(5,𝔽2)12yes—
1158C23C2×H(5,𝔽2)11yescharacteristic
1159C23C2×2−1+411yescharacteristic
1160C23#58511yescharacteristic
1161Q8—88no—
1162D4—416no—
1163D4—416no—
1164D4—432no—
1165D4—432no—
1166D4—432no—
1167D4—432no—
1168D4—432no—
1169C2×C4—22no—
1170C2×C4—24no—
1171C2×C4—22no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—24no—
1177C2×C4—24no—
1178C2×C4—24no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—24no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—24no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—416no—
1200C2×C4—432no—
1201C2×C4—41no—
1202C2×C4—42no—
1203C2×C4—41no—
1204C2×C4—42no—
1205C2×C4—42no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—42no—
1209C2×C4—42no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—41no—
1218C2×C4—42no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—41no—
1230C2×C4—42no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—41no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—42no—
1247C2×C4—41no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
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—42no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—41no—
1268C2×C4—42no—
1269C2×C4—41no—
1270C2×C4—42no—
1271C2×C4—42no—
1272C2×C4—42no—
1273C2×C4—42no—
1274C2×C4—42no—
1275C2×C4—88no—
1276C2×C4D4214yes—
1277C2×C4#54618yes—
1278C22—24no—
1279C22—24no—
1280C22—24no—
1281C22—28no—
1282C22—28no—
1283C22—24no—
1284C22—24no—
1285C22—28no—
1286C22—24no—
1287C22—28no—
1288C22—44no—
1289C22—44no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—44no—
1294C22—42no—
1295C22—44no—
1296C22—44no—
1297C22—44no—
1298C22—44no—
1299C22—44no—
1300C22—44no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—44no—
1305C22—44no—
1306C22—44no—
1307C22—42no—
1308C22—44no—
1309C22—44no—
1310C22—42no—
1311C22—44no—
1312C22—864no—
1313C22—832no—
1314C22—81no—
1315C22—82no—
1316C22—81no—
1317C22—82no—
1318C22—82no—
1319C22—82no—
1320C22—81no—
1321C22—81no—
1322C22—82no—
1323C22—82no—
1324C22—82no—
1325C22—81no—
1326C22—81no—
1327C22—82no—
1328C22—81no—
1329C22—82no—
1330C22—82no—
1331C22—82no—
1332C22—82no—
1333C22—82no—
1334C22—82no—
1335C22—82no—
1336C22—81no—
1337C22—82no—
1338C22—82no—
1339C22—82no—
1340C22—82no—
1341C22—82no—
1342C22#266218yescomplemented
1343C22C2×#53211yescharacteristic
1344C22C2×#53511yescharacteristic
1345C22C2×#53711yescharacteristic
1346C22C2×#53812yes—
1347C22C2×#54212yes—
1348C22C2×D4211yescharacteristic
1349C22C2×#54612yes—
1350C22#348412yes—
1351C22#348411yescharacteristic
1352C22#348411yescharacteristic
1353C22#348811yescharacteristic
1354C22#348911yescharacteristic
1355C22#349012yes—
1356C22#349412yes—
1357C22#349811yescharacteristic
1358C22#350812yes—
1359C22#353212yes—
1360C22#353212yes—
1361C22#353212yes—
1362C22#353611yescharacteristic
1363C22#353612yes—
1364C22#354211yescharacteristic
1365C22#354212yes—
1366C4—24no—
1367C4—28no—
1368C4—42no—
1369C4—42no—
1370C4—42no—
1371C4—42no—
1372C4—44no—
1373C4—42no—
1374C4—42no—
1375C4—81no—
1376C4—82no—
1377C4—81no—
1378C4—81no—
1379C4—82no—
1380C4—81no—
1381C4—82no—
1382C4—81no—
1383C4—82no—
1384C2—28no—
1385C2—84no—
1386C2—84no—
1387C2—82no—
1388C2—82no—
1389C2C2×#266211yescharacteristic
1390C2#3592211yescharacteristic
1391C2#3612111yescharacteristic
1392C2#3764511yescharacteristic
1393C2#3764811yescharacteristic
1394C2#3766012yes—
1395C2#3766412yes—
1396C2#4048811yescharacteristic
1397C2#4054212yes—
1398C2#4193411yescharacteristic
1399C2#4196212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#392C2
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×#2435C2semidirect
2. C2×#2480C2semidirect
3. C2×#2662C2semidirect
5. #16819C2semidirect
6. #16680C2semidirect
7. #16655C2semidirect
8. #16552C2semidirect
9. #16526C2semidirect
10. #16504C2semidirect
11. #16290C2semidirect
12. #16274C2semidirect
13. #14928C2semidirect
14. #14815C2semidirect
15. #14758C2semidirect
16. #14726C2semidirect
17. #14724C2semidirect
18. #14724C2semidirect
19. #14717C2semidirect
20. #14321C2semidirect
21. #13902C2semidirect
22. #13873C2semidirect
23. #13814C2semidirect
26. C22×#126C22semidirect
27. C22×#124C22semidirect
28. C22×#124C22semidirect
35. C2×#397C22semidirect
36. C2×#397C22semidirect
37. C2×#397C22semidirect
38. C2×#396C22semidirect
39. C2×#396C22semidirect
40. C2×#396C22semidirect
41. C2×#395C22semidirect
42. C2×#394C22semidirect
43. C2×#394C22semidirect
44. C2×#394C22semidirect
45. C2×#394C22semidirect
46. C2×#394C22semidirect
47. C2×#394C22semidirect
48. C2×#394C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
51. C2×#393C22semidirect
52. C2×#393C22semidirect
60. C2×#390C22semidirect
61. C2×#390C22semidirect
62. C2×#390C22semidirect
63. C2×#390C22semidirect
64. C2×#390C22semidirect
65. C2×#390C22semidirect
66. C2×#388C22semidirect
67. C2×#388C22semidirect
68. C2×#388C22semidirect
69. C2×#388C22semidirect
70. C2×#388C22semidirect
83. C2×C4×C4⋊C4C22semidirect
87. #1446C22semidirect
88. #1444C22semidirect
89. #1444C22semidirect
90. #1441C22semidirect
91. #1441C22semidirect
92. #1440C22semidirect
93. #1440C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1438C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
114. #1438C22semidirect
115. #1438C22semidirect
116. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. C4⋊#95C22semidirect
122. #1434C22semidirect
126. C4×#95C22semidirect
275. C4×C22⋊C4D4semidirect
600. C2×C42C2×D4semidirect
601. C2×C42C2×D4semidirect
628. #95C2×D4semidirect
629. #95C2×D4semidirect
1342. C22#2662semidirect

Maximal subgroups

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

subgroupindex
C2×#24352
C2×#24802
C2×#26622
C22×#3922
#168192
#166802
#166552
#165522
#165262
#165042
#162902
#162742
#149282
#148152
#147582
#147262
#147242
#147172
#143212
#139022
#138732
#138142