Finite Group Databasebeta

← #758012

Subgroups — #758012

Order 512.

4806 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#551C211yesmaximal, characteristic, complemented
2C2×#2636C211yesmaximal, characteristic, complemented
3C2×#2392C211yesmaximal, characteristic, complemented
4C2×#2328C211yesmaximal, characteristic, complemented
5#16265C212yesmaximal, complemented
6#16256C212yesmaximal, complemented
7#15927C211yesmaximal, characteristic, complemented
8#15909C211yesmaximal, characteristic, complemented
9#15670C211yesmaximal, characteristic, complemented
10#15464C211yesmaximal, characteristic, complemented
11#15453C211yesmaximal, characteristic, complemented
12#15283C211yesmaximal, characteristic, complemented
13#15261C211yesmaximal, characteristic, complemented
14#15258C211yesmaximal, characteristic
15#14915C212yesmaximal, complemented
16#14732C212yesmaximal, complemented
17#14725C212yesmaximal, complemented
18#14721C212yesmaximal, complemented
19#14166C211yesmaximal, characteristic, complemented
20#14064C212yesmaximal, complemented
21#13967C212yesmaximal, complemented
22#13957C211yesmaximal, characteristic, complemented
23#13905C211yesmaximal, characteristic, complemented
24C2×#551—28no—
25C2×#551—28no—
26C2×#551—28no—
27C22×#127C2211yescharacteristic
28C22×#126C2211yescharacteristic
29C22×#126C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×#123C2211yescharacteristic
32C22×#123C2211yescharacteristic
33C22×#123C2211yescharacteristic
34C22×C22⋊Q8C2211yescharacteristic
35C22×C22⋊Q8C2211yescharacteristic
36C22×#120C2211yescharacteristic
37C22×#120C2212yes—
38C22×C4×D4C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C22×C4×D4C2212yes—
41C22×C4×D4C2211yescharacteristic, complemented
42C22×#117C2211yescharacteristic
43C22×#117C2211yescharacteristic
44C23×C22⋊C4C2211yescharacteristic
45C23×C22⋊C4C2211yescharacteristic
46#2636—28no—
47C2×#400C2211yescharacteristic, complemented
48C2×#399C2211yescharacteristic
49#2392—28no—
50C2×#398C2211yescharacteristic, complemented
51C2×#397C2211yescharacteristic
52C2×#396C2212yescomplemented
53C2×#396C2212yescomplemented
54C2×#394C2212yes—
55C2×#394C2212yes—
56C2×#394C2212yes—
57C2×#394C2211yescharacteristic, complemented
58C2×#394C2211yescharacteristic, complemented
59C2×#393C2212yescomplemented
60C2×#392C2211yescharacteristic
61C2×#392C2211yescharacteristic
62C2×#392C2212yes—
63C2×#392C2212yes—
64#2328—28no—
65C2×#390C2211yescharacteristic
66C2×#390C2211yescharacteristic, complemented
67C2×#386C2212yes—
68C2×#386C2212yes—
69C2×#386C2212yes—
70C2×#386C2212yes—
71C2×#386C2212yes—
72C2×#386C2212yescomplemented
73C2×#386C2212yescomplemented
74C2×#385C2212yescomplemented
75C2×#382C2211yescharacteristic, complemented
76C2×#382C2211yescharacteristic, complemented
77C2×#380C2212yes—
78C2×#380C2212yescomplemented
79C2×#379C2212yes—
80C2×C4×C4⋊C4C2211yescharacteristic, complemented
81C2×C4×C22⋊C4C2212yescomplemented
82C2×#376C2211yescharacteristic, complemented
83#1446C2212yescomplemented
84#1445C2211yescharacteristic, complemented
85#1445C2211yescharacteristic, complemented
86#1444C2212yescomplemented
87#1442C2212yescomplemented
88#1441C2212yescomplemented
89#1441C2212yescomplemented
90#1440C2212yes—
91#1440C2212yes—
92#1440C2212yescomplemented
93#1439C2212yes—
94#1439C2212yes—
95#1439C2212yes—
96#1439C2212yes—
97#1439C2212yes—
98#1439C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1438C2212yes—
102#1438C2212yes—
103#1438C2212yes—
104#1438C2211yescharacteristic
105#1438C2211yescharacteristic
106#1438C2212yes—
107#1438C2212yes—
108#1438C2212yes—
109#1438C2212yescomplemented
110#1438C2212yescomplemented
111#1437C2211yescharacteristic
112#1437C2211yescharacteristic
113#1437C2211yescharacteristic
114#1437C2212yes—
115#1437C2212yes—
116#1437C2211yescharacteristic
117#1437C2212yescomplemented
118#1437C2212yescomplemented
119#1436C2211yescharacteristic, complemented
120#1436C2211yescharacteristic, complemented
121#1436C2211yescharacteristic, complemented
122#1436C2212yescomplemented
123#1436C2211yescharacteristic, complemented
124#1436C2212yescomplemented
125#1434C2212yescomplemented
126C22⋊#95C2212yes—
127C22⋊#95C2212yes—
128C22⋊#95C2212yes—
129C26C2311yescharacteristic
130C23×Q8C2311yescharacteristic
131C23×D4C2311yescharacteristic
132C23×D4C2312yes—
133C23×D4C2311yescharacteristic
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2312yes—
137C23×D4C2312yes—
138C23×D4C2312yes—
139C24×C4C2311yescharacteristic
140C24×C4C2311yescharacteristic
141C24×C4C2311yescharacteristic
142C24×C4C2312yes—
143C24×C4C2311yescharacteristic
144C24×C4C2311yescharacteristic
145#551—2128no—
146C2×#127—24no—
147C2×#127—28no—
148C2×#126—24no—
149C2×#126—24no—
150C2×#126—24no—
151C2×#126—24no—
152C2×#126—24no—
153C2×#126D418yescomplemented
154C2×#124—24no—
155C2×#124—24no—
156C2×#124—24no—
157C2×#123—24no—
158C2×#123—24no—
159C2×#123—24no—
160C2×#123—24no—
161C2×#123—24no—
162C2×#123—24no—
163C2×#123—24no—
164C2×#123—24no—
165C2×#123—24no—
166C2×C22⋊Q8—24no—
167C2×C22⋊Q8—24no—
168C2×C22⋊Q8—24no—
169C2×C22⋊Q8—24no—
170C2×C22⋊Q8—24no—
171C2×C22⋊Q8—24no—
172C2×#120—24no—
173C2×#120—28no—
174C2×#120—24no—
175C2×#120—24no—
176C2×#120—44no—
177C2×#120—44no—
178C2×C4×D4—24no—
179C2×C4×D4—28no—
180C2×C4×D4—24no—
181C2×C4×D4—24no—
182C2×C4×D4—24no—
183C2×C4×D4—24no—
184C2×C4×D4—24no—
185C2×C4×D4—24no—
186C2×C4×D4—24no—
187C2×C4×D4—44no—
188C2×C4×D4—44no—
189C2×C4×D4D418yescomplemented
190C2×#117—24no—
191C2×#117—24no—
192C2×#117—24no—
193C2×#117—24no—
194C2×#117—24no—
195C2×#117D418yescomplemented
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2311yescharacteristic
201C22×C4⋊C4C2311yescharacteristic
202C22×C4⋊C4C2311yescharacteristic
203C22×C4⋊C4C2311yescharacteristic
204C22×C4⋊C4C2311yescharacteristic
205C22×C4⋊C4C2311yescharacteristic
206C22×C4⋊C4C2312yes—
207C22×C4⋊C4C2312yes—
208C22×C4⋊C4C2312yes—
209C22×C22⋊C4—24no—
210C22×C22⋊C4—24no—
211C22×C22⋊C4—24no—
212C22×C22⋊C4—24no—
213C22×C22⋊C4—24no—
214C22×C22⋊C4—24no—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2312yes—
225C22×C22⋊C4C2312yes—
226C22×C22⋊C4C2312yes—
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2311yescharacteristic
231C22×C22⋊C4C2311yescharacteristic
232C22×C22⋊C4C2311yescharacteristic
233C22×C22⋊C4C2311yescharacteristic
234C22×C22⋊C4C2311yescharacteristic
235C22×C22⋊C4C2311yescharacteristic
236C22×C22⋊C4C2311yescharacteristic
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2312yes—
243C22×C22⋊C4C2312yes—
244C22×C22⋊C4C2312yes—
245C22×C22⋊C4C2312yes—
246C22×C22⋊C4C2312yes—
247C22×C22⋊C4C2312yes—
248C22×C22⋊C4C2312yes—
249C22×C22⋊C4C2312yes—
250C22×C42C2311yescharacteristic
251C22×C42C2311yescharacteristic
252C22×C42C2311yescharacteristic
253C22×C42C2312yes—
254C22×C42C2311yescharacteristic
255C22×C42C2311yescharacteristic
256#400—24no—
257#399—24no—
258#398—24no—
259#397—24no—
260#396—28no—
261#396—28no—
262#394—24no—
263#394—24no—
264#394—28no—
265#394—28no—
266#394—44no—
267#393—44no—
268#392—24no—
269#392—24no—
270#392—44no—
271#392—44no—
272#390—24no—
273#390—24no—
274#386—28no—
275#386—28no—
276#386—28no—
277#386—28no—
278#386—28no—
279#386—28no—
280#386—44no—
281#385—28no—
282#382—24no—
283#382—24no—
284#380—44no—
285#380—44no—
286#379—44no—
287C4×C4⋊C4—24no—
288C4×C22⋊C4—28no—
289#376—24no—
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2311yescharacteristic
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C2×#95C2312yes—
303C2×#95C2312yes—
304C2×#95C2312yes—
305C2×#95C2312yes—
306C2×#95C2312yes—
307C2×#95C2312yes—
308C2×#95C2312yes—
309C2×#95C2312yes—
310C2×#95C2312yes—
311C2×#95C2312yes—
312C2×#95C2312yes—
313C2×#95C2312yes—
314C2×#95C2312yes—
315C2×#95C2312yes—
316C2×#95C2312yes—
317C2×#95C2312yes—
318C2×#95C2312yes—
319C25—22no—
320C25—22no—
321C25—22no—
322C25—24no—
323C25—24no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25C2411yescharacteristic
329C25C2411yescharacteristic
330C25C2412yes—
331C25C2411yescharacteristic
332C25C2411yescharacteristic
333C22×Q8—22no—
334C22×Q8—22no—
335C22×Q8—22no—
336C22×Q8—42no—
337C22×Q8—42no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—24no—
341C22×D4—24no—
342C22×D4—24no—
343C22×D4—24no—
344C22×D4—22no—
345C22×D4—22no—
346C22×D4—24no—
347C22×D4—24no—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—24no—
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—22no—
360C22×D4—22no—
361C22×D4—22no—
362C22×D4—24no—
363C22×D4—24no—
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×D4C2×D414yes—
385C22×D4#4118yes—
386C23×C4—22no—
387C23×C4—24no—
388C23×C4—22no—
389C23×C4—22no—
390C23×C4—22no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—24no—
400C23×C4—24no—
401C23×C4—24no—
402C23×C4—24no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—42no—
408C23×C4—42no—
409C23×C4—42no—
410C23×C4—42no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4C2×D414yes—
416C23×C4C2×D414yes—
417C23×C4C2×D414yes—
418C23×C4C2412yes—
419C23×C4C2412yes—
420C23×C4C2412yes—
421C23×C4C2412yes—
422C23×C4C2412yes—
423C23×C4C2411yescharacteristic
424C23×C4C2411yescharacteristic
425C23×C4C2411yescharacteristic
426C23×C4C2411yescharacteristic
427C23×C4C2411yescharacteristic
428C23×C4C2411yescharacteristic
429C23×C4C2411yescharacteristic
430C23×C4C2411yescharacteristic
431C23×C4C2412yes—
432C23×C4C2412yes—
433C23×C4C2411yescharacteristic
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436#127—232no—
437#126—232no—
438#126—232no—
439#124—232no—
440#123—232no—
441#123—232no—
442#123—232no—
443C22⋊Q8—232no—
444C22⋊Q8—232no—
445#120—232no—
446#120—432no—
447C4×D4—232no—
448C4×D4—232no—
449C4×D4—432no—
450C4×D4—416no—
451#117—232no—
452#117—232no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—22no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—22no—
468C2×C4⋊C4—22no—
469C2×C4⋊C4—22no—
470C2×C4⋊C4—22no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—24no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—42no—
480C2×C4⋊C4—42no—
481C2×C4⋊C4—42no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4C2×D414yes—
487C2×C4⋊C4C2×D414yes—
488C2×C4⋊C4C2×D414yes—
489C2×C4⋊C4C2×D414yes—
490C2×C4⋊C4C2×D414yes—
491C2×C4⋊C4C2×D414yes—
492C2×C22⋊C4—232no—
493C2×C22⋊C4—232no—
494C2×C22⋊C4—22no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—22no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
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—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—24no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—24no—
538C2×C22⋊C4—24no—
539C2×C22⋊C4—24no—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—24no—
544C2×C22⋊C4—24no—
545C2×C22⋊C4—24no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—24no—
548C2×C22⋊C4—24no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—24no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
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⋊C4—42no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—42no—
591C2×C22⋊C4—42no—
592C2×C22⋊C4C2×D414yes—
593C2×C22⋊C4C2×D414yes—
594C2×C22⋊C4C2×D414yes—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4C2×D414yes—
597C2×C22⋊C4C2×D414yes—
598C2×C22⋊C4C2×D414yes—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—22no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42—42no—
611C2×C42C2×D414yes—
612C2×C42C2×D414yes—
613C2×C42C2×D414yes—
614C2×C42C2×D414yes—
615#95—24no—
616#95—24no—
617#95—24no—
618#95—24no—
619#95—22no—
620#95—22no—
621#95—24no—
622#95—24no—
623#95—24no—
624#95—22no—
625#95—22no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—24no—
633#95—42no—
634#95—42no—
635#95—42no—
636#95—42no—
637#95—42no—
638#95—42no—
639#95—42no—
640#95—42no—
641#95—42no—
642#95—42no—
643#95—42no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—28no—
659C24—21no—
660C24—21no—
661C24—22no—
662C24—22no—
663C24—21no—
664C24—21no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—22no—
685C24—22no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—44no—
696C24—44no—
697C24—44no—
698C24—44no—
699C24—84no—
700C24—84no—
701C24—84no—
702C24—84no—
703C24—84no—
704C24—84no—
705C24—82no—
706C24—82no—
707C24—84no—
708C24—84no—
709C24C22×D412yes—
710C24C22×D412yes—
711C24C22×D412yes—
712C24C22×D412yes—
713C24C2×#4114yes—
714C24C2×#4114yes—
715C24H(5,𝔽2)14yes—
716C24C2511yescharacteristic
717C2×Q8—28no—
718C2×Q8—84no—
719C2×Q8—84no—
720C2×Q8—82no—
721C2×Q8—82no—
722C2×D4—28no—
723C2×D4—216no—
724C2×D4—28no—
725C2×D4—28no—
726C2×D4—28no—
727C2×D4—216no—
728C2×D4—216no—
729C2×D4—28no—
730C2×D4—44no—
731C2×D4—48no—
732C2×D4—48no—
733C2×D4—48no—
734C2×D4—48no—
735C2×D4—48no—
736C2×D4—48no—
737C2×D4—48no—
738C2×D4—44no—
739C2×D4—48no—
740C2×D4—48no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—44no—
745C2×D4—48no—
746C2×D4—48no—
747C2×D4—44no—
748C2×D4—48no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—84no—
752C2×D4—84no—
753C2×D4—84no—
754C2×D4—84no—
755C2×D4—84no—
756C2×D4—84no—
757C2×D4—84no—
758C2×D4—84no—
759C2×D4—82no—
760C2×D4—82no—
761C2×D4—84no—
762C2×D4—84no—
763C2×D4—84no—
764C2×D4—84no—
765C2×D4—84no—
766C2×D4—84no—
767C2×D4—84no—
768C2×D4—84no—
769C2×D4—84no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—28no—
777C22×C4—28no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
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—22no—
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—22no—
820C22×C4—22no—
821C22×C4—22no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—28no—
825C22×C4—28no—
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—22no—
841C22×C4—22no—
842C22×C4—22no—
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—22no—
853C22×C4—22no—
854C22×C4—22no—
855C22×C4—22no—
856C22×C4—22no—
857C22×C4—22no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—22no—
861C22×C4—44no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—48no—
866C22×C4—48no—
867C22×C4—48no—
868C22×C4—48no—
869C22×C4—48no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—48no—
873C22×C4—84no—
874C22×C4—84no—
875C22×C4—84no—
876C22×C4—84no—
877C22×C4—84no—
878C22×C4—84no—
879C22×C4—82no—
880C22×C4—82no—
881C22×C4—82no—
882C22×C4—82no—
883C22×C4—84no—
884C22×C4—82no—
885C22×C4—82no—
886C22×C4—84no—
887C22×C4C22×D412yes—
888C22×C4C22×D412yes—
889C22×C4C22×D412yes—
890C22×C4C22×D412yes—
891C22×C4C22×D412yes—
892C22×C4C22×D412yes—
893C22×C4C22×D412yes—
894C22×C4C22×D412yes—
895C22×C4C22×D412yes—
896C22×C4C22×D412yes—
897C22×C4C22×D412yes—
898C22×C4C22×D412yes—
899C22×C4C22×D412yes—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D412yes—
903C22×C4C22×D412yes—
904C22×C4C2×#4114yes—
905C22×C4H(5,𝔽2)14yes—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—28no—
910C4⋊C4—28no—
911C4⋊C4—28no—
912C4⋊C4—28no—
913C4⋊C4—28no—
914C4⋊C4—48no—
915C4⋊C4—48no—
916C4⋊C4—44no—
917C4⋊C4—84no—
918C4⋊C4—84no—
919C22⋊C4—28no—
920C22⋊C4—28no—
921C22⋊C4—28no—
922C22⋊C4—28no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—28no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—28no—
933C22⋊C4—48no—
934C22⋊C4—48no—
935C22⋊C4—48no—
936C22⋊C4—48no—
937C22⋊C4—48no—
938C22⋊C4—48no—
939C22⋊C4—48no—
940C22⋊C4—48no—
941C22⋊C4—48no—
942C22⋊C4—84no—
943C22⋊C4—84no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C22⋊C4—84no—
948C22⋊C4—84no—
949C22⋊C4—84no—
950C22⋊C4—84no—
951C22⋊C4—84no—
952C22⋊C4—84no—
953C22⋊C4—84no—
954C42—28no—
955C42—28no—
956C42—28no—
957C42—44no—
958C42—48no—
959C42#120116yescomplemented
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
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—24no—
977C23—24no—
978C23—24no—
979C23—24no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—24no—
984C23—22no—
985C23—24no—
986C23—24no—
987C23—24no—
988C23—24no—
989C23—24no—
990C23—24no—
991C23—24no—
992C23—24no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—24no—
997C23—416no—
998C23—416no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—42no—
1004C23—42no—
1005C23—42no—
1006C23—42no—
1007C23—42no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—42no—
1013C23—42no—
1014C23—42no—
1015C23—42no—
1016C23—42no—
1017C23—42no—
1018C23—42no—
1019C23—42no—
1020C23—41no—
1021C23—42no—
1022C23—41no—
1023C23—41no—
1024C23—42no—
1025C23—42no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
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—41no—
1055C23—41no—
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—42no—
1079C23—816no—
1080C23—816no—
1081C23—88no—
1082C23—816no—
1083C23—816no—
1084C23—816no—
1085C23—816no—
1086C23#52514yes—
1087C23#53514yes—
1088C23C23×D411yescharacteristic
1089C23C23×D411yescharacteristic
1090C23C23×D411yescharacteristic
1091C23C22×#4112yes—
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)12yes—
1094C23#58512yes—
1095C23#58512yes—
1096C23#58512yes—
1097Q8—88no—
1098D4—416no—
1099D4—416no—
1100D4—416no—
1101D4—432no—
1102D4—816no—
1103D4—816no—
1104D4—88no—
1105D4—816no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—24no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—416no—
1143C2×C4—416no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—42no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—42no—
1171C2×C4—42no—
1172C2×C4—42no—
1173C2×C4—42no—
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—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—42no—
1208C2×C4—42no—
1209C2×C4—88no—
1210C2×C4—88no—
1211C2×C4—816no—
1212C2×C4—88no—
1213C2×C4C2×#12014yes—
1214C2×C4C2×#12014yes—
1215C2×C4C2×#12014yes—
1216C22—24no—
1217C22—24no—
1218C22—28no—
1219C22—28no—
1220C22—44no—
1221C22—44no—
1222C22—44no—
1223C22—44no—
1224C22—42no—
1225C22—42no—
1226C22—44no—
1227C22—42no—
1228C22—42no—
1229C22—44no—
1230C22—44no—
1231C22—44no—
1232C22—44no—
1233C22—44no—
1234C22—44no—
1235C22—44no—
1236C22—44no—
1237C22—44no—
1238C22—42no—
1239C22—44no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—44no—
1244C22—44no—
1245C22—44no—
1246C22—42no—
1247C22—42no—
1248C22—44no—
1249C22—44no—
1250C22—44no—
1251C22—832no—
1252C22—82no—
1253C22—82no—
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—
1268C22C22×#12011yescharacteristic
1269C22C2×#52511yescharacteristic
1270C22C2×#53511yescharacteristic
1271C22#344911yescharacteristic
1272C22#344911yescharacteristic
1273C22D4×#4112yes—
1274C22D4×#4112yes—
1275C22#348812yes—
1276C22#348812yes—
1277C22#348812yes—
1278C22#349012yes—
1279C22#349112yes—
1280C22#349612yes—
1281C22#349811yescharacteristic
1282C22#350011yescharacteristic
1283C22#351312yes—
1284C22#351412yes—
1285C22#353312yes—
1286C22#353412yes—
1287C22#355112yes—
1288C22#356612yes—
1289C4—24no—
1290C4—24no—
1291C4—24no—
1292C4—42no—
1293C4—42no—
1294C4—42no—
1295C4—42no—
1296C4—44no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—42no—
1301C4—44no—
1302C4—82no—
1303C4—82no—
1304C4—82no—
1305C4—82no—
1306C4—82no—
1307C2—44no—
1308C2—44no—
1309C2—84no—
1310C2—82no—
1311C2—82no—
1312C2#3473611yescharacteristic
1313C2#3525011yescharacteristic
1314C2#3551311yescharacteristic
1315C2#3576212yes—
1316C2#3836612yes—
1317C2#3838612yes—
1318C2#4194012yes—
1319C2#4413812yes—
1320C2#4433012yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radical#15258C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#551C2semidirect
2. C2×#2636C2semidirect
3. C2×#2392C2semidirect
4. C2×#2328C2semidirect
5. #16265C2semidirect
6. #16256C2semidirect
7. #15927C2semidirect
8. #15909C2semidirect
9. #15670C2semidirect
10. #15464C2semidirect
11. #15453C2semidirect
12. #15283C2semidirect
13. #15261C2semidirect
15. #14915C2semidirect
16. #14732C2semidirect
17. #14725C2semidirect
18. #14721C2semidirect
19. #14166C2semidirect
20. #14064C2semidirect
21. #13967C2semidirect
22. #13957C2semidirect
23. #13905C2semidirect
41. C22×C4×D4C22semidirect
47. C2×#400C22semidirect
50. C2×#398C22semidirect
52. C2×#396C22semidirect
53. C2×#396C22semidirect
57. C2×#394C22semidirect
58. C2×#394C22semidirect
59. C2×#393C22semidirect
66. C2×#390C22semidirect
72. C2×#386C22semidirect
73. C2×#386C22semidirect
74. C2×#385C22semidirect
75. C2×#382C22semidirect
76. C2×#382C22semidirect
78. C2×#380C22semidirect
80. C2×C4×C4⋊C4C22semidirect
81. C2×C4×C22⋊C4C22semidirect
82. C2×#376C22semidirect
83. #1446C22semidirect
84. #1445C22semidirect
85. #1445C22semidirect
86. #1444C22semidirect
87. #1442C22semidirect
88. #1441C22semidirect
89. #1441C22semidirect
92. #1440C22semidirect
98. #1439C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
109. #1438C22semidirect
110. #1438C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. #1436C22semidirect
120. #1436C22semidirect
121. #1436C22semidirect
122. #1436C22semidirect
123. #1436C22semidirect
124. #1436C22semidirect
125. #1434C22semidirect
153. C2×#126D4semidirect
189. C2×C4×D4D4semidirect
195. C2×#117D4semidirect
959. C42#120semidirect

Maximal subgroups

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

subgroupindex
C22×#5512
C2×#26362
C2×#23922
C2×#23282
#162652
#162562
#159272
#159092
#156702
#154642
#154532
#152832
#152612
#152582
#149152
#147322
#147252
#147212
#141662
#140642
#139672
#139572
#139052