Finite Group Databasebeta

← #1293651

Subgroups — #1293651

Order 512.

4440 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2556C211yesmaximal, characteristic, complemented
2C2×#2435C211yesmaximal, characteristic, complemented
3C2×#2433C211yesmaximal, characteristic
4C2×#2641C211yesmaximal, characteristic, complemented
5#17069C211yesmaximal, characteristic, complemented
6#16633C211yesmaximal, characteristic, complemented
7#16503C211yesmaximal, characteristic, complemented
8#16253C211yesmaximal, characteristic, complemented
9#15617C212yesmaximal, complemented
10#15317C212yesmaximal, complemented
11#15283C212yesmaximal, complemented
12#15268C212yesmaximal, complemented
13#15140C211yesmaximal, characteristic, complemented
14#15127C211yesmaximal, characteristic, complemented
15#15007C212yesmaximal, complemented
16#14928C212yesmaximal, complemented
17#14898C211yesmaximal, characteristic, complemented
18#14764C211yesmaximal, characteristic, complemented
19#14724C211yesmaximal, characteristic, complemented
20#14358C212yesmaximal, complemented
21#14358C212yesmaximal, complemented
22#14227C211yesmaximal, characteristic, complemented
23#13816C211yesmaximal, characteristic, complemented
24C24×D4C2211yescharacteristic
25C22×#127C2211yescharacteristic
26C22×#127C2211yescharacteristic
27C22×#125C2211yescharacteristic, complemented
28C22×#124C2212yes—
29C22×C22⋊Q8C2211yescharacteristic
30C22×#121C2211yescharacteristic
31C22×#120C2212yes—
32C22×#120C2212yes—
33#2641—28no—
34#2556—28no—
35#2435—28no—
36#2433—28no—
37C2×#399C2211yescharacteristic
38C2×#398C2211yescharacteristic, complemented
39C2×#397C2212yescomplemented
40C2×#396C2211yescharacteristic
41C2×#395C2211yescharacteristic, complemented
42C2×#394C2211yescharacteristic
43C2×#394C2211yescharacteristic
44C2×#394C2211yescharacteristic
45C2×#394C2211yescharacteristic
46C2×#394C2212yes—
47C2×#394C2211yescharacteristic
48C2×#394C2211yescharacteristic
49C2×#394C2212yescomplemented
50C2×#394C2211yescharacteristic, complemented
51C2×#394C2211yescharacteristic, complemented
52C2×#394C2212yescomplemented
53C2×#394C2212yescomplemented
54C2×#394C2212yescomplemented
55C2×#394C2211yescharacteristic, complemented
56C2×#393C2212yescomplemented
57C2×#392C2212yes—
58C2×#392C2212yes—
59C2×#391C2211yescharacteristic, complemented
60C2×#390C2212yes—
61C2×#390C2211yescharacteristic
62C2×#390C2211yescharacteristic
63C2×#390C2212yescomplemented
64C2×#390C2212yescomplemented
65C2×#390C2212yescomplemented
66C2×#390C2212yescomplemented
67C2×#390C2212yescomplemented
68C2×#390C2212yescomplemented
69C2×#389C2211yescharacteristic, complemented
70C2×#389C2211yescharacteristic, complemented
71C2×#388C2211yescharacteristic
72C2×#388C2211yescharacteristic
73C2×#388C2212yes—
74C2×#388C2212yescomplemented
75C2×#388C2212yescomplemented
76C2×#387C2211yescharacteristic, complemented
77C2×#385C2211yescharacteristic
78C2×#379C2212yes—
79C2×#379C2212yes—
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×C4×C4⋊C4C2211yescharacteristic, complemented
83C2×C4×C22⋊C4C2211yescharacteristic
84C2×C4×C22⋊C4C2211yescharacteristic
85C2×#376C2211yescharacteristic, complemented
86#1442C2211yescharacteristic, complemented
87#1441C2211yescharacteristic, complemented
88#1441C2211yescharacteristic, complemented
89#1441C2211yescharacteristic, complemented
90#1440C2212yescomplemented
91#1439C2212yescomplemented
92#1439C2212yescomplemented
93#1439C2212yescomplemented
94#1439C2212yescomplemented
95#1439C2212yescomplemented
96#1439C2212yescomplemented
97#1439C2212yescomplemented
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1438C2212yes—
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2211yescharacteristic
105#1438C2211yescharacteristic
106#1438C2212yes—
107#1438C2212yescomplemented
108#1438C2212yescomplemented
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1438C2212yescomplemented
112#1438C2211yescharacteristic, complemented
113#1438C2212yescomplemented
114#1437C2212yes—
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1437C2212yescomplemented
120#1437C2212yescomplemented
121#1436C2212yescomplemented
122C4⋊#95C2211yescharacteristic, complemented
123#1434C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic
125C4×#95C2211yescharacteristic, complemented
126C4×#95C2212yescomplemented
127C26C2312yes—
128C23×Q8C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—44no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4C2312yes—
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C23×D4C2311yescharacteristic
140C23×D4C2312yes—
141C23×D4C2312yes—
142C23×D4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C2×#127—24no—
145C2×#127—24no—
146C2×#127—24no—
147C2×#127—42no—
148C2×#127—44no—
149C2×#125—24no—
150C2×#125—24no—
151C2×#125—42no—
152C2×#124—28no—
153C2×#124—44no—
154C2×#124—44no—
155C2×C22⋊Q8—24no—
156C2×C22⋊Q8—24no—
157C2×C22⋊Q8—42no—
158C2×#121—24no—
159C2×#121—44no—
160C2×#120—28no—
161C2×#120—28no—
162C2×#120—28no—
163C2×#120—28no—
164C2×#120—44no—
165C2×#120—44no—
166C22×C4⋊C4C2311yescharacteristic
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2311yescharacteristic
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2311yescharacteristic
175C22×C4⋊C4C2311yescharacteristic
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C22⋊C4C2312yes—
184C22×C22⋊C4C2312yes—
185C22×C22⋊C4C2312yes—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2311yescharacteristic
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
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⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2312yes—
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⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C42C2312yes—
219C22×C42C2312yes—
220C22×C42C2311yescharacteristic
221C22×C42C2311yescharacteristic
222C22×C42C2312yes—
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#399—24no—
226#398—24no—
227#397—44no—
228#396—24no—
229#395—24no—
230#394—24no—
231#394—24no—
232#394—24no—
233#394—24no—
234#394—28no—
235#394—28no—
236#394—24no—
237#394—24no—
238#394—44no—
239#394—42no—
240#394—42no—
241#394—44no—
242#394—44no—
243#394D418yescomplemented
244#393—44no—
245#392—28no—
246#392—28no—
247#391—24no—
248#390—28no—
249#390—28no—
250#390—28no—
251#390—24no—
252#390—24no—
253#390—44no—
254#390—44no—
255#390—44no—
256#390—44no—
257#389—24no—
258#389—24no—
259#388—24no—
260#388—24no—
261#388—28no—
262#388—44no—
263#388—44no—
264#387—24no—
265#385—24no—
266#379—28no—
267#379—28no—
268#379—44no—
269#379—44no—
270C4×C4⋊C4—24no—
271C4×C22⋊C4—24no—
272C4×C22⋊C4D418yes—
273#376—24no—
274C2×#95C2312yes—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2311yescharacteristic
281C2×#95C2311yescharacteristic
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2311yescharacteristic
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2311yescharacteristic
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2311yescharacteristic
300C2×#95C2311yescharacteristic
301C2×#95C2311yescharacteristic
302C25—24no—
303C25—24no—
304C25—24no—
305C25—24no—
306C25—24no—
307C25—42no—
308C25—42no—
309C25—42no—
310C25—42no—
311C25—42no—
312C25—42no—
313C25—42no—
314C25—42no—
315C25—42no—
316C25—42no—
317C25C2412yes—
318C25C2412yes—
319C25C2412yes—
320C25C2411yescharacteristic
321C22×Q8—22no—
322C22×Q8—22no—
323C22×Q8—24no—
324C22×Q8—41no—
325C22×Q8—42no—
326C22×D4—24no—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—24no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—24no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
351C22×D4—22no—
352C22×D4—24no—
353C22×D4—22no—
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—22no—
357C22×D4—416no—
358C22×D4—42no—
359C22×D4—42no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—416no—
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—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—416no—
385C22×D4—432no—
386C22×D4—432no—
387C22×D4C2×D414yes—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—22no—
391C23×C4—42no—
392C23×C4C2×D414yes—
393C23×C4C2411yescharacteristic
394C23×C4C2411yescharacteristic
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2411yescharacteristic
398C23×C4C2412yes—
399C23×C4C2412yes—
400C23×C4C2412yes—
401C23×C4C2412yes—
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2412yes—
405C23×C4C2411yescharacteristic
406C23×C4C2411yescharacteristic
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C23×C4C2411yescharacteristic
411C23×C4C2411yescharacteristic
412#127—416no—
413#127—416no—
414#125—416no—
415#124—432no—
416C22⋊Q8—416no—
417#121—416no—
418#120—432no—
419#120—432no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—41no—
454C2×C4⋊C4—41no—
455C2×C4⋊C4—41no—
456C2×C4⋊C4—41no—
457C2×C4⋊C4—41no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4C2×D414yes—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—24no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
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—22no—
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—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—41no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—42no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—41no—
513C2×C22⋊C4—41no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4—42no—
521C2×C22⋊C4—42no—
522C2×C22⋊C4—42no—
523C2×C22⋊C4—42no—
524C2×C22⋊C4—42no—
525C2×C22⋊C4—42no—
526C2×C22⋊C4—42no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—42no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—42no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
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—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⋊C4C2×D414yes—
567C2×C22⋊C4C2×D418yes—
568C2×C22⋊C4C2×D418yes—
569C2×C22⋊C4C2×D414yes—
570C2×C22⋊C4#4118yes—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—24no—
574C2×C42—24no—
575C2×C42—22no—
576C2×C42—24no—
577C2×C42—24no—
578C2×C42—22no—
579C2×C42—22no—
580C2×C42—24no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42—42no—
584C2×C42—41no—
585C2×C42—42no—
586C2×C42—42no—
587C2×C42—42no—
588C2×C42C2×D414yes—
589C2×C42C2×D414yes—
590#95—24no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—22no—
600#95—22no—
601#95—24no—
602#95—24no—
603#95—24no—
604#95—22no—
605#95—24no—
606#95—42no—
607#95—42no—
608#95—42no—
609#95—42no—
610#95—42no—
611#95—42no—
612#95—42no—
613#95—42no—
614#95—42no—
615#95C2×D414yes—
616#95C2×D414yes—
617#95C2×D414yes—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—22no—
624C24—22no—
625C24—22no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
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—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—48no—
679C24—48no—
680C24—48no—
681C24—48no—
682C24—48no—
683C24—84no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
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—
705C24C22×D414yes—
706C24C22×D412yes—
707C24C2×#4114yes—
708C24H(5,𝔽2)14yes—
709C24C2511yescharacteristic
710C2×Q8—44no—
711C2×Q8—48no—
712C2×Q8—44no—
713C2×Q8—82no—
714C2×Q8—84no—
715C2×D4—216no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—48no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—48no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—44no—
726C2×D4—44no—
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—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—4128no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—48no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—48no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—84no—
760C2×D4—84no—
761C2×D4—84no—
762C2×D4—84no—
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—84no—
772C2×D4—84no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—21no—
812C22×C4—28no—
813C22×C4—28no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—22no—
852C22×C4—21no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—21no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—48no—
874C22×C4C22×D414yes—
875C22×C4C22×D412yes—
876C22×C4C22×D412yes—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D412yes—
884C22×C4C2×#4114yes—
885C22×C4C2×#4114yes—
886C22×C4H(5,𝔽2)12yes—
887C22×C4H(5,𝔽2)12yes—
888C22×C4H(5,𝔽2)14yes—
889C22×C4H(5,𝔽2)12yes—
890C22×C4H(5,𝔽2)12yes—
891C4⋊C4—28no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊C4—44no—
895C4⋊C4—44no—
896C4⋊C4—44no—
897C4⋊C4—44no—
898C4⋊C4—44no—
899C4⋊C4—44no—
900C4⋊C4—44no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—82no—
905C4⋊C4—84no—
906C22⋊C4—28no—
907C22⋊C4—48no—
908C22⋊C4—48no—
909C22⋊C4—48no—
910C22⋊C4—44no—
911C22⋊C4—44no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—48no—
918C22⋊C4—48no—
919C22⋊C4—48no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—84no—
923C22⋊C4—84no—
924C22⋊C4—84no—
925C22⋊C4—84no—
926C22⋊C4—84no—
927C22⋊C4—84no—
928C22⋊C4—84no—
929C22⋊C4—84no—
930C22⋊C4—82no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—84no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4—84no—
942C22⋊C4#124116yescomplemented
943C42—28no—
944C42—44no—
945C42—48no—
946C42—44no—
947C42—48no—
948C42—82no—
949C42—84no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—24no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—24no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—24no—
975C23—24no—
976C23—42no—
977C23—41no—
978C23—41no—
979C23—42no—
980C23—42no—
981C23—42no—
982C23—42no—
983C23—41no—
984C23—41no—
985C23—42no—
986C23—432no—
987C23—42no—
988C23—42no—
989C23—42no—
990C23—42no—
991C23—42no—
992C23—42no—
993C23—42no—
994C23—42no—
995C23—42no—
996C23—42no—
997C23—42no—
998C23—42no—
999C23—42no—
1000C23—42no—
1001C23—42no—
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—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—42no—
1021C23—42no—
1022C23—42no—
1023C23—42no—
1024C23—42no—
1025C23—42no—
1026C23—42no—
1027C23—42no—
1028C23—42no—
1029C23—42no—
1030C23—42no—
1031C23—42no—
1032C23—42no—
1033C23—42no—
1034C23—42no—
1035C23—42no—
1036C23—42no—
1037C23—42no—
1038C23—42no—
1039C23—42no—
1040C23—42no—
1041C23—42no—
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—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
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—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—816no—
1079C23—816no—
1080C23—816no—
1081C23—816no—
1082C23—816no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23—816no—
1087C23—816no—
1088C23—816no—
1089C23—816no—
1090C23—816no—
1091C23—816no—
1092C23C2×#12414yes—
1093C23C23×D411yescharacteristic
1094C23C23×D411yescharacteristic
1095C23C22×#4112yes—
1096C23C2×H(5,𝔽2)12yes—
1097C23C2×H(5,𝔽2)11yescharacteristic
1098C23C2×H(5,𝔽2)11yescharacteristic
1099C23C2×H(5,𝔽2)11yescharacteristic
1100C23C2×H(5,𝔽2)12yes—
1101C23C2×H(5,𝔽2)11yescharacteristic
1102C23#58512yes—
1103C23#58511yescharacteristic
1104Q8—88no—
1105D4—432no—
1106D4—416no—
1107D4—416no—
1108D4—816no—
1109D4—816no—
1110D4—816no—
1111D4—88no—
1112D4—816no—
1113D4—816no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—24no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—24no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—24no—
1145C2×C4—22no—
1146C2×C4—24no—
1147C2×C4—416no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—42no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—42no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—42no—
1197C2×C4—42no—
1198C2×C4—42no—
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—42no—
1210C2×C4—42no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—42no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4C2×#12414yes—
1224C2×C4C2×#12414yes—
1225C2×C4#53514yes—
1226C2×C4#53514yes—
1227C2×C4D4214yes—
1228C22—24no—
1229C22—24no—
1230C22—24no—
1231C22—42no—
1232C22—42no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—42no—
1239C22—44no—
1240C22—44no—
1241C22—44no—
1242C22—44no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—864no—
1254C22—82no—
1255C22—82no—
1256C22—82no—
1257C22—82no—
1258C22—82no—
1259C22—82no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22—82no—
1269C22—82no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22—82no—
1275C22—82no—
1276C22—82no—
1277C22—82no—
1278C22—82no—
1279C22—82no—
1280C22—82no—
1281C22—82no—
1282C22—82no—
1283C22—82no—
1284C22—82no—
1285C22C22×#12411yescharacteristic
1286C22C2×#53511yescharacteristic
1287C22C2×#53511yescharacteristic
1288C22C2×D4211yescharacteristic
1289C22D4×#4112yes—
1290C22#348411yescharacteristic
1291C22#348412yes—
1292C22#348811yescharacteristic
1293C22#349611yescharacteristic
1294C22#349811yescharacteristic
1295C22#350011yescharacteristic
1296C22#350812yes—
1297C22#350812yes—
1298C22#351312yes—
1299C22#351412yes—
1300C22#351912yes—
1301C22#353212yes—
1302C22#353412yes—
1303C22#353412yes—
1304C22#354212yes—
1305C22#354611yescharacteristic
1306C22#354911yescharacteristic
1307C22#355112yes—
1308C4—24no—
1309C4—24no—
1310C4—24no—
1311C4—24no—
1312C4—24no—
1313C4—42no—
1314C4—44no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—82no—
1322C4—82no—
1323C4—82no—
1324C4—81no—
1325C4—81no—
1326C4—82no—
1327C2—44no—
1328C2—84no—
1329C2—84no—
1330C2—162no—
1331C2#3528511yescharacteristic
1332C2#3590311yescharacteristic
1333C2D4×#12411yescharacteristic
1334C2#3764511yescharacteristic
1335C2#3934211yescharacteristic
1336C2#4049411yescharacteristic
1337C2#4296211yescharacteristic
1338C2#4389612yes—
1339C2#4392612yes—
1340C2#4924712yes—
1341C2#4926412yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2433C2
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×#2556C2semidirect
2. C2×#2435C2semidirect
4. C2×#2641C2semidirect
5. #17069C2semidirect
6. #16633C2semidirect
7. #16503C2semidirect
8. #16253C2semidirect
9. #15617C2semidirect
10. #15317C2semidirect
11. #15283C2semidirect
12. #15268C2semidirect
13. #15140C2semidirect
14. #15127C2semidirect
15. #15007C2semidirect
16. #14928C2semidirect
17. #14898C2semidirect
18. #14764C2semidirect
19. #14724C2semidirect
20. #14358C2semidirect
21. #14358C2semidirect
22. #14227C2semidirect
23. #13816C2semidirect
27. C22×#125C22semidirect
38. C2×#398C22semidirect
39. C2×#397C22semidirect
41. C2×#395C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
51. C2×#394C22semidirect
52. C2×#394C22semidirect
53. C2×#394C22semidirect
54. C2×#394C22semidirect
55. C2×#394C22semidirect
56. C2×#393C22semidirect
59. C2×#391C22semidirect
63. C2×#390C22semidirect
64. C2×#390C22semidirect
65. C2×#390C22semidirect
66. C2×#390C22semidirect
67. C2×#390C22semidirect
68. C2×#390C22semidirect
69. C2×#389C22semidirect
70. C2×#389C22semidirect
74. C2×#388C22semidirect
75. C2×#388C22semidirect
76. C2×#387C22semidirect
82. C2×C4×C4⋊C4C22semidirect
85. C2×#376C22semidirect
86. #1442C22semidirect
87. #1441C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
90. #1440C22semidirect
91. #1439C22semidirect
92. #1439C22semidirect
93. #1439C22semidirect
94. #1439C22semidirect
95. #1439C22semidirect
96. #1439C22semidirect
97. #1439C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
107. #1438C22semidirect
108. #1438C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
111. #1438C22semidirect
112. #1438C22semidirect
113. #1438C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1437C22semidirect
120. #1437C22semidirect
121. #1436C22semidirect
122. C4⋊#95C22semidirect
123. #1434C22semidirect
125. C4×#95C22semidirect
126. C4×#95C22semidirect
243. #394D4semidirect
942. C22⋊C4#124semidirect

Maximal subgroups

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

subgroupindex
C2×#25562
C2×#24352
C2×#24332
C2×#26412
#170692
#166332
#165032
#162532
#156172
#153172
#152832
#152682
#151402
#151272
#150072
#149282
#148982
#147642
#147242
#143582
#142272
#138162