Finite Group Databasebeta

← #824886

Subgroups — #824886

Order 512.

4902 conjugacy classes of subgroups.

The subgroup lattice has 1326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2408C211yesmaximal, characteristic
2C2×#2418C212yesmaximal, complemented
3C2×#2392C211yesmaximal, characteristic, complemented
4C2×#2359C211yesmaximal, characteristic, complemented
5C2×D4×C22⋊C4C211yesmaximal, characteristic, complemented
6#16811C211yesmaximal, characteristic, complemented
7#16399C211yesmaximal, characteristic, complemented
8#15335C212yesmaximal, complemented
9#15297C212yesmaximal, complemented
10#15274C212yesmaximal, complemented
11#15266C212yesmaximal, complemented
12#15160C211yesmaximal, characteristic, complemented
13#15129C211yesmaximal, characteristic, complemented
14#14886C211yesmaximal, characteristic, complemented
15#14824C211yesmaximal, characteristic, complemented
16#14813C211yesmaximal, characteristic, complemented
17#14801C211yesmaximal, characteristic, complemented
18#14724C211yesmaximal, characteristic, complemented
19#14195C212yesmaximal, complemented
20#14175C211yesmaximal, characteristic, complemented
21#14023C212yesmaximal, complemented
22#13891C211yesmaximal, characteristic, complemented
23#13873C212yesmaximal, complemented
24C24×D4C2211yescharacteristic
25C22×#123C2211yescharacteristic
26C22×#121C2212yes—
27C22×#120C2212yes—
28C22×C4×D4C2211yescharacteristic
29C22×C4×D4C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2212yescomplemented
32C22×#117C2211yescharacteristic, complemented
33C23×C22⋊C4C2212yes—
34#2418—216no—
35#2408—28no—
36C2×#399C2212yescomplemented
37#2392—28no—
38C2×#398C2211yescharacteristic, complemented
39C2×#398C2211yescharacteristic, complemented
40C2×#397C2212yes—
41C2×#397C2211yescharacteristic, complemented
42C2×#396C2212yescomplemented
43C2×#394C2211yescharacteristic
44C2×#394C2211yescharacteristic
45C2×#394C2212yes—
46C2×#394C2211yescharacteristic
47C2×#394C2212yes—
48C2×#394C2211yescharacteristic
49C2×#394C2212yescomplemented
50C2×#394C2212yescomplemented
51C2×#392C2211yescharacteristic
52C2×#392C2211yescharacteristic
53#2359—28no—
54D4×C22⋊C4—28no—
55C2×#390C2211yescharacteristic
56C2×#390C2211yescharacteristic
57C2×#390C2212yes—
58C2×#389C2211yescharacteristic, complemented
59C2×#388C2211yescharacteristic
60C2×#388C2212yes—
61C2×#388C2211yescharacteristic
62C2×#388C2212yescomplemented
63C2×#387C2211yescharacteristic, complemented
64C2×#387C2211yescharacteristic, complemented
65C2×#386C2212yes—
66C2×#386C2212yes—
67C2×#386C2211yescharacteristic
68C2×#386C2212yescomplemented
69C2×#386C2212yescomplemented
70C2×#386C2212yescomplemented
71C2×#386C2212yescomplemented
72C2×#385C2211yescharacteristic
73C2×#385C2211yescharacteristic, complemented
74C2×#385C2212yescomplemented
75C2×#380C2211yescharacteristic
76C2×#380C2211yescharacteristic
77C2×#380C2212yescomplemented
78C2×#380C2212yescomplemented
79C2×#379C2212yes—
80C2×#379C2212yes—
81C2×#379C2212yes—
82C2×#379C2212yes—
83C2×C4×C4⋊C4C2211yescharacteristic, complemented
84C2×C4×C4⋊C4C2211yescharacteristic, complemented
85C2×C4×C22⋊C4C2211yescharacteristic
86C2×C4×C22⋊C4C2212yescomplemented
87C2×C4×C22⋊C4C2211yescharacteristic, complemented
88C22×#95C2211yescharacteristic, complemented
89#1445C2211yescharacteristic, complemented
90#1444C2212yescomplemented
91#1442C2211yescharacteristic, complemented
92#1441C2211yescharacteristic, complemented
93#1441C2212yescomplemented
94#1441C2212yescomplemented
95#1441C2211yescharacteristic, complemented
96#1440C2212yes—
97#1440C2212yes—
98#1440C2212yescomplemented
99#1440C2212yescomplemented
100#1440C2212yescomplemented
101#1439C2212yes—
102#1439C2211yescharacteristic, complemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1439C2212yescomplemented
108#1439C2212yescomplemented
109#1439C2212yescomplemented
110#1439C2212yescomplemented
111#1438C2211yescharacteristic
112#1438C2211yescharacteristic
113#1438C2212yes—
114#1438C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2212yescomplemented
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2212yescomplemented
120#1436C2212yescomplemented
121C4⋊#95C2211yescharacteristic, complemented
122#1434C2211yescharacteristic, complemented
123#1434C2211yescharacteristic, complemented
124C22⋊#95C2211yescharacteristic
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C22⋊#95C2212yescomplemented
128C26C2312yes—
129C23×D4—28no—
130C23×D4—24no—
131C23×D4—24no—
132C23×D4—42no—
133C23×D4—44no—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2311yescharacteristic
139C23×D4C2312yes—
140C24×C4C2312yes—
141C24×C4C2312yes—
142C24×C4C2311yescharacteristic
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145C24×C4C2311yescharacteristic
146C2×#123—24no—
147C2×#123—24no—
148C2×#123D418yescomplemented
149C2×#121—28no—
150C2×#121—28no—
151C2×#121—44no—
152C2×#120—28no—
153C2×#120—28no—
154C2×#120—44no—
155C2×C4×D4—24no—
156C2×C4×D4—28no—
157C2×C4×D4—24no—
158C2×C4×D4—28no—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—42no—
163C2×C4×D4—42no—
164C2×C4×D4—44no—
165C2×C4×D4—44no—
166C2×#117—24no—
167C2×#117—24no—
168C2×#117—42no—
169C22×C4⋊C4C2311yescharacteristic
170C22×C4⋊C4C2311yescharacteristic
171C22×C4⋊C4C2311yescharacteristic
172C22×C4⋊C4C2311yescharacteristic
173C22×C4⋊C4C2311yescharacteristic
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C4⋊C4C2312yes—
179C22×C4⋊C4C2312yes—
180C22×C4⋊C4C2312yes—
181C22×C4⋊C4C2311yescharacteristic
182C22×C4⋊C4C2311yescharacteristic
183C22×C22⋊C4—28no—
184C22×C22⋊C4—28no—
185C22×C22⋊C4—28no—
186C22×C22⋊C4C2312yes—
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2312yes—
189C22×C22⋊C4C2312yes—
190C22×C22⋊C4C2312yes—
191C22×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
203C22×C22⋊C4C2311yescharacteristic
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2312yes—
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2312yes—
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C42C2311yescharacteristic
220C22×C42C2311yescharacteristic
221C22×C42C2312yes—
222C22×C42C2311yescharacteristic
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225#399—28no—
226#398—24no—
227#398—42no—
228#397—28no—
229#397—24no—
230#396—28no—
231#394—24no—
232#394—24no—
233#394—28no—
234#394—28no—
235#394—28no—
236#394—28no—
237#394—24no—
238#394—42no—
239#392—24no—
240#392D418yes—
241#390—28no—
242#390—24no—
243#390—24no—
244#389—24no—
245#388—28no—
246#388—24no—
247#388—24no—
248#388—28no—
249#387—24no—
250#387—24no—
251#386—28no—
252#386—24no—
253#386—28no—
254#386—28no—
255#386—28no—
256#386—44no—
257#386—44no—
258#385—24no—
259#385—28no—
260#385—24no—
261#380—24no—
262#380—28no—
263#380—24no—
264#380—44no—
265#379—28no—
266#379—28no—
267#379—28no—
268#379—44no—
269C4×C4⋊C4—24no—
270C4×C4⋊C4—24no—
271C4×C22⋊C4—28no—
272C4×C22⋊C4—24no—
273C4×C22⋊C4D418yescomplemented
274C2×#95—24no—
275C2×#95C2311yescharacteristic
276C2×#95C2311yescharacteristic
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2312yes—
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2311yescharacteristic
287C2×#95C2311yescharacteristic
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2311yescharacteristic
293C2×#95C2311yescharacteristic
294C2×#95C2311yescharacteristic
295C2×#95C2311yescharacteristic
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2311yescharacteristic
306C2×#95C2311yescharacteristic
307C2×#95C2311yescharacteristic
308C25—24no—
309C25—24no—
310C25—24no—
311C25—24no—
312C25—24no—
313C25—24no—
314C25—24no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25—42no—
321C25—42no—
322C25—42no—
323C25C2412yes—
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C25C2412yes—
327C22×D4—24no—
328C22×D4—24no—
329C22×D4—232no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—22no—
333C22×D4—24no—
334C22×D4—24no—
335C22×D4—22no—
336C22×D4—24no—
337C22×D4—24no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—24no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—22no—
348C22×D4—22no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—416no—
353C22×D4—41no—
354C22×D4—42no—
355C22×D4—42no—
356C22×D4—42no—
357C22×D4—42no—
358C22×D4—42no—
359C22×D4—41no—
360C22×D4—42no—
361C22×D4—42no—
362C22×D4—42no—
363C22×D4—432no—
364C22×D4—416no—
365C22×D4—432no—
366C22×D4C2×D414yes—
367C22×D4C2×D418yes—
368C22×D4C2×D414yes—
369C22×D4#4118yes—
370C23×C4—22no—
371C23×C4—22no—
372C23×C4—22no—
373C23×C4—22no—
374C23×C4—22no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—24no—
378C23×C4—22no—
379C23×C4—24no—
380C23×C4—22no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—24no—
384C23×C4—24no—
385C23×C4—22no—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—41no—
391C23×C4—41no—
392C23×C4—42no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4—42no—
396C23×C4—41no—
397C23×C4—42no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4—42no—
401C23×C4—42no—
402C23×C4—41no—
403C23×C4—42no—
404C23×C4C2×D414yes—
405C23×C4C2×D414yescomplemented
406C23×C4C2411yescharacteristic
407C23×C4C2412yes—
408C23×C4C2412yes—
409C23×C4C2412yes—
410C23×C4C2411yescharacteristic
411C23×C4C2412yes—
412C23×C4C2411yescharacteristic
413C23×C4C2412yes—
414C23×C4C2411yescharacteristic
415C23×C4C2411yescharacteristic
416C23×C4C2411yescharacteristic
417C23×C4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2411yescharacteristic
420C23×C4C2412yes—
421C23×C4C2411yescharacteristic
422C23×C4C2411yescharacteristic
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425#123—232no—
426#121—432no—
427#120—432no—
428C4×D4—416no—
429C4×D4—416no—
430C4×D4—432no—
431C4×D4—416no—
432#117—416no—
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—22no—
445C2×C4⋊C4—24no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—24no—
448C2×C4⋊C4—24no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—41no—
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×D414yescomplemented
471C2×C4⋊C4C2×D414yescomplemented
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—22no—
477C2×C22⋊C4—22no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—22no—
481C2×C22⋊C4—22no—
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—24no—
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—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—24no—
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—22no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—42no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4—42no—
530C2×C22⋊C4—42no—
531C2×C22⋊C4—42no—
532C2×C22⋊C4—41no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—42no—
537C2×C22⋊C4—42no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—432no—
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⋊C4C2×D414yes—
563C2×C22⋊C4C2×D414yes—
564C2×C22⋊C4C2×D418yes—
565C2×C22⋊C4C2×D414yes—
566C2×C22⋊C4C2×D414yes—
567C2×C22⋊C4C2×D414yes—
568C2×C22⋊C4C2×D414yescomplemented
569C2×C22⋊C4#4114yes—
570C2×C42—22no—
571C2×C42—22no—
572C2×C42—22no—
573C2×C42—22no—
574C2×C42—24no—
575C2×C42—22no—
576C2×C42—24no—
577C2×C42—22no—
578C2×C42—22no—
579C2×C42—41no—
580C2×C42—42no—
581C2×C42—42no—
582C2×C42—41no—
583C2×C42—42no—
584C2×C42C2×D414yes—
585C2×C42C2×D414yes—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—24no—
592#95—24no—
593#95—22no—
594#95—22no—
595#95—24no—
596#95—24no—
597#95—24no—
598#95—22no—
599#95—24no—
600#95—22no—
601#95—24no—
602#95—22no—
603#95—24no—
604#95—24no—
605#95—24no—
606#95—22no—
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#95—42no—
616#95C2×D414yes—
617#95C2×D414yes—
618#95C2×D414yes—
619C24—21no—
620C24—22no—
621C24—21no—
622C24—22no—
623C24—21no—
624C24—22no—
625C24—22no—
626C24—22no—
627C24—22no—
628C24—21no—
629C24—22no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—22no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—21no—
644C24—22no—
645C24—22no—
646C24—21no—
647C24—216no—
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—48no—
663C24—48no—
664C24—48no—
665C24—48no—
666C24—48no—
667C24—48no—
668C24—48no—
669C24—48no—
670C24—48no—
671C24—48no—
672C24—48no—
673C24—48no—
674C24—48no—
675C24—48no—
676C24—48no—
677C24—48no—
678C24—84no—
679C24—84no—
680C24—84no—
681C24—84no—
682C24—84no—
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—
696C24C22×D412yes—
697C24C22×D412yes—
698C24C22×D412yes—
699C24C22×D412yes—
700C24C22×D414yes—
701C24C2×#4114yes—
702C24C2×#4112yes—
703C24C2×#4114yes—
704C24H(5,𝔽2)12yes—
705C24H(5,𝔽2)14yes—
706C24C2511yescharacteristic
707C2×D4—28no—
708C2×D4—28no—
709C2×D4—216no—
710C2×D4—216no—
711C2×D4—28no—
712C2×D4—28no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—216no—
716C2×D4—216no—
717C2×D4—216no—
718C2×D4—28no—
719C2×D4—48no—
720C2×D4—48no—
721C2×D4—44no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—4128no—
730C2×D4—44no—
731C2×D4—48no—
732C2×D4—44no—
733C2×D4—48no—
734C2×D4—44no—
735C2×D4—48no—
736C2×D4—44no—
737C2×D4—48no—
738C2×D4—48no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—44no—
743C2×D4—84no—
744C2×D4—84no—
745C2×D4—84no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—28no—
758C22×C4—21no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—28no—
793C22×C4—28no—
794C22×C4—28no—
795C22×C4—21no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—21no—
799C22×C4—22no—
800C22×C4—21no—
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—21no—
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—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—22no—
830C22×C4—22no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—22no—
840C22×C4—22no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—22no—
845C22×C4—44no—
846C22×C4—44no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—44no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—48no—
854C22×C4—48no—
855C22×C4—44no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—48no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—82no—
867C22×C4—84no—
868C22×C4—84no—
869C22×C4—84no—
870C22×C4—84no—
871C22×C4—84no—
872C22×C4—84no—
873C22×C4—84no—
874C22×C4—82no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4C22×D412yes—
878C22×C4C22×D412yes—
879C22×C4C22×D412yes—
880C22×C4C22×D412yes—
881C22×C4C22×D412yes—
882C22×C4C22×D412yes—
883C22×C4C22×D414yes—
884C22×C4C22×D412yes—
885C22×C4C22×D412yes—
886C22×C4C22×D412yes—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C2×#4112yes—
892C22×C4C2×#4112yes—
893C22×C4C2×#4114yes—
894C22×C4H(5,𝔽2)12yes—
895C4⋊C4—28no—
896C4⋊C4—28no—
897C4⋊C4—44no—
898C4⋊C4—48no—
899C4⋊C4—48no—
900C4⋊C4—48no—
901C4⋊C4—44no—
902C4⋊C4—44no—
903C4⋊C4—44no—
904C4⋊C4—44no—
905C4⋊C4—44no—
906C4⋊C4—82no—
907C4⋊C4—84no—
908C4⋊C4—84no—
909C22⋊C4—28no—
910C22⋊C4—28no—
911C22⋊C4—28no—
912C22⋊C4—44no—
913C22⋊C4—48no—
914C22⋊C4—48no—
915C22⋊C4—48no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—48no—
919C22⋊C4—44no—
920C22⋊C4—48no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—48no—
928C22⋊C4—48no—
929C22⋊C4—48no—
930C22⋊C4—48no—
931C22⋊C4—84no—
932C22⋊C4—84no—
933C22⋊C4—84no—
934C22⋊C4—84no—
935C22⋊C4—82no—
936C22⋊C4—84no—
937C22⋊C4—84no—
938C22⋊C4—84no—
939C22⋊C4—84no—
940C22⋊C4—84no—
941C22⋊C4#121116yescomplemented
942C42—28no—
943C42—44no—
944C42—44no—
945C42—48no—
946C42—44no—
947C42—44no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—22no—
952C23—22no—
953C23—24no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—24no—
959C23—24no—
960C23—22no—
961C23—24no—
962C23—24no—
963C23—22no—
964C23—24no—
965C23—24no—
966C23—24no—
967C23—24no—
968C23—22no—
969C23—24no—
970C23—24no—
971C23—24no—
972C23—24no—
973C23—24no—
974C23—22no—
975C23—24no—
976C23—22no—
977C23—24no—
978C23—24no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—24no—
983C23—24no—
984C23—24no—
985C23—24no—
986C23—22no—
987C23—22no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—24no—
997C23—24no—
998C23—24no—
999C23—432no—
1000C23—432no—
1001C23—42no—
1002C23—41no—
1003C23—41no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—42no—
1009C23—41no—
1010C23—42no—
1011C23—42no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—41no—
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—816no—
1064C23—816no—
1065C23—816no—
1066C23—816no—
1067C23—816no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23—816no—
1073C23—816no—
1074C23—816no—
1075C23—816no—
1076C23C2×#12114yes—
1077C23D4214yes—
1078C23#54618yes—
1079C23C23×D411yescharacteristic
1080C23C23×D411yescharacteristic
1081C23C23×D411yescharacteristic
1082C23C22×#4111yescharacteristic
1083C23C22×#4112yes—
1084C23C2×H(5,𝔽2)11yescharacteristic
1085C23C2×H(5,𝔽2)11yescharacteristic
1086C23C2×H(5,𝔽2)12yes—
1087C23#58512yes—
1088C23#58511yescharacteristic
1089C23#58512yes—
1090D4—232no—
1091D4—432no—
1092D4—416no—
1093D4—432no—
1094D4—416no—
1095D4—816no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—24no—
1101C2×C4—24no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—24no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—22no—
1115C2×C4—22no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—24no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—24no—
1125C2×C4—24no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—416no—
1134C2×C4—416no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—41no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—42no—
1165C2×C4—41no—
1166C2×C4—42no—
1167C2×C4—42no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—42no—
1185C2×C4—42no—
1186C2×C4—42no—
1187C2×C4—41no—
1188C2×C4—42no—
1189C2×C4—42no—
1190C2×C4—42no—
1191C2×C4—42no—
1192C2×C4—42no—
1193C2×C4—42no—
1194C2×C4—42no—
1195C2×C4—42no—
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—88no—
1208C2×C4—816no—
1209C2×C4—816no—
1210C2×C4—88no—
1211C2×C4C2×#12114yes—
1212C2×C4C2×#12114yes—
1213C2×C4#52514yes—
1214C2×C4D4214yes—
1215C22—28no—
1216C22—28no—
1217C22—28no—
1218C22—24no—
1219C22—24no—
1220C22—28no—
1221C22—24no—
1222C22—24no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—44no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—42no—
1233C22—44no—
1234C22—42no—
1235C22—44no—
1236C22—44no—
1237C22—42no—
1238C22—44no—
1239C22—42no—
1240C22—44no—
1241C22—42no—
1242C22—44no—
1243C22—42no—
1244C22—44no—
1245C22—44no—
1246C22—44no—
1247C22—44no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—44no—
1252C22—44no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—864no—
1260C22—82no—
1261C22—82no—
1262C22—82no—
1263C22—82no—
1264C22—82no—
1265C22—82no—
1266C22—82no—
1267C22—82no—
1268C22C22×#12111yescharacteristic
1269C22C2×#52511yescharacteristic
1270C22#344911yescharacteristic
1271C22C2×D4211yescharacteristic
1272C22C2×D4211yescharacteristic
1273C22C2×#54612yes—
1274C22D4×#4112yes—
1275C22D4×#4111yescharacteristic
1276C22#347512yes—
1277C22#348411yescharacteristic
1278C22#348512yes—
1279C22#348811yescharacteristic
1280C22#348812yes—
1281C22#349012yes—
1282C22#349611yescharacteristic
1283C22#350011yescharacteristic
1284C22#351312yes—
1285C22#351312yes—
1286C22#351911yescharacteristic
1287C22#352112yes—
1288C22#353412yes—
1289C22#354512yes—
1290C22#356212yes—
1291C4—24no—
1292C4—24no—
1293C4—24no—
1294C4—24no—
1295C4—42no—
1296C4—42no—
1297C4—42no—
1298C4—44no—
1299C4—42no—
1300C4—42no—
1301C4—42no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—82no—
1306C4—82no—
1307C4—82no—
1308C4—82no—
1309C4—82no—
1310C2—44no—
1311C2—48no—
1312C2—44no—
1313C2—84no—
1314C2#3493511yescharacteristic
1315C2#3572811yescharacteristic
1316C2#3598211yescharacteristic
1317C2D4×#12111yescharacteristic
1318C2#3609811yescharacteristic
1319C2#3768211yescharacteristic
1320C2#4198911yescharacteristic
1321C2#4303412yes—
1322C2#4321712yes—
1323C2#5899412yes—
1324C2#5903212yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2408C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2418C2semidirect
3. C2×#2392C2semidirect
4. C2×#2359C2semidirect
5. C2×D4×C22⋊C4C2semidirect
6. #16811C2semidirect
7. #16399C2semidirect
8. #15335C2semidirect
9. #15297C2semidirect
10. #15274C2semidirect
11. #15266C2semidirect
12. #15160C2semidirect
13. #15129C2semidirect
14. #14886C2semidirect
15. #14824C2semidirect
16. #14813C2semidirect
17. #14801C2semidirect
18. #14724C2semidirect
19. #14195C2semidirect
20. #14175C2semidirect
21. #14023C2semidirect
22. #13891C2semidirect
23. #13873C2semidirect
31. C22×C4×D4C22semidirect
32. C22×#117C22semidirect
36. C2×#399C22semidirect
38. C2×#398C22semidirect
39. C2×#398C22semidirect
41. C2×#397C22semidirect
42. C2×#396C22semidirect
49. C2×#394C22semidirect
50. C2×#394C22semidirect
58. C2×#389C22semidirect
62. C2×#388C22semidirect
63. C2×#387C22semidirect
64. C2×#387C22semidirect
68. C2×#386C22semidirect
69. C2×#386C22semidirect
70. C2×#386C22semidirect
71. C2×#386C22semidirect
73. C2×#385C22semidirect
74. C2×#385C22semidirect
77. C2×#380C22semidirect
78. C2×#380C22semidirect
83. C2×C4×C4⋊C4C22semidirect
84. C2×C4×C4⋊C4C22semidirect
86. C2×C4×C22⋊C4C22semidirect
87. C2×C4×C22⋊C4C22semidirect
88. C22×#95C22semidirect
89. #1445C22semidirect
90. #1444C22semidirect
91. #1442C22semidirect
92. #1441C22semidirect
93. #1441C22semidirect
94. #1441C22semidirect
95. #1441C22semidirect
98. #1440C22semidirect
99. #1440C22semidirect
100. #1440C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
107. #1439C22semidirect
108. #1439C22semidirect
109. #1439C22semidirect
110. #1439C22semidirect
114. #1438C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. C4⋊#95C22semidirect
122. #1434C22semidirect
123. #1434C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
127. C22⋊#95C22semidirect
148. C2×#123D4semidirect
273. C4×C22⋊C4D4semidirect
405. C23×C4C2×D4semidirect
470. C2×C4⋊C4C2×D4semidirect
471. C2×C4⋊C4C2×D4semidirect
568. C2×C22⋊C4C2×D4semidirect
941. C22⋊C4#121semidirect

Maximal subgroups

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

subgroupindex
C2×#24082
C2×#24182
C2×#23922
C2×#23592
C2×D4×C22⋊C42
#168112
#163992
#153352
#152972
#152742
#152662
#151602
#151292
#148862
#148242
#148132
#148012
#147242
#141952
#141752
#140232
#138912
#138732