Finite Group Databasebeta

← #647684

Subgroups — #647684

Order 512.

5196 conjugacy classes of subgroups.

The subgroup lattice has 1334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2483C211yesmaximal, characteristic, complemented
2C2×D4×C22⋊C4C211yesmaximal, characteristic
3C22×#386C211yesmaximal, characteristic
4C22×#381C211yesmaximal, characteristic, complemented
5#15954C212yesmaximal, complemented
6#15952C212yesmaximal, complemented
7#15287C212yesmaximal, complemented
8#15285C212yesmaximal, complemented
9#15019C211yesmaximal, characteristic, complemented
10#14936C211yesmaximal, characteristic, complemented
11#14918C211yesmaximal, characteristic, complemented
12#14918C211yesmaximal, characteristic, complemented
13#14737C212yesmaximal, complemented
14#14735C212yesmaximal, complemented
15#14681C211yesmaximal, characteristic, complemented
16#14127C211yesmaximal, characteristic, complemented
17#13992C211yesmaximal, characteristic, complemented
18#13992C211yesmaximal, characteristic, complemented
19#13975C212yesmaximal, complemented
20#13894C212yesmaximal, complemented
21#13877C211yesmaximal, characteristic, complemented
22#13869C211yesmaximal, characteristic, complemented
23#13867C211yesmaximal, characteristic
24C24×D4C2211yescharacteristic
25C25×C4C2211yescharacteristic
26C22×C4×D4C2211yescharacteristic
27C22×C4×D4C2211yescharacteristic
28C23×C22⋊C4C2211yescharacteristic
29C23×C22⋊C4C2211yescharacteristic
30C23×C22⋊C4C2211yescharacteristic
31C23×C22⋊C4C2211yescharacteristic
32C23×C22⋊C4C2211yescharacteristic
33C23×C22⋊C4C2211yescharacteristic
34#2483—28no—
35C2×#397C2212yescomplemented
36C2×#397C2212yescomplemented
37D4×C22⋊C4—28no—
38C2×#390C2211yescharacteristic
39C2×#390C2211yescharacteristic
40C2×#386—28no—
41C2×#386C2212yes—
42C2×#386C2211yescharacteristic
43C2×#386C2211yescharacteristic
44C2×#386C2211yescharacteristic
45C2×#386C2211yescharacteristic
46C2×#386C2212yes—
47C2×#386C2212yes—
48C2×#386C2212yes—
49C2×#386C2212yes—
50C2×#386C2212yes—
51C2×#385C2211yescharacteristic
52C2×#385C2211yescharacteristic
53C2×#385C2211yescharacteristic
54C2×#385C2211yescharacteristic
55C2×#385C2212yescomplemented
56C2×#385C2212yescomplemented
57C2×#381—28no—
58C2×#381C2211yescharacteristic
59C2×#381C2211yescharacteristic
60C2×#381C2211yescharacteristic
61C2×#381C2211yescharacteristic
62C2×#381C2211yescharacteristic
63C2×#381C2211yescharacteristic
64C2×#381C2211yescharacteristic
65C2×#381C2211yescharacteristic
66C2×#381C2212yescomplemented
67C2×#381C2212yescomplemented
68C2×#381C2212yescomplemented
69C2×#380C2211yescharacteristic
70C2×#380C2212yescomplemented
71C2×#379C2211yescharacteristic
72C2×#379C2211yescharacteristic
73C2×#379C2211yescharacteristic
74C2×#379C2211yescharacteristic
75C2×#379C2211yescharacteristic
76C2×C4×C22⋊C4C2211yescharacteristic
77C22×#95C2211yescharacteristic
78C22×#95C2211yescharacteristic
79C22×#95C2212yescomplemented
80C22×#95C2212yescomplemented
81#1445C2212yescomplemented
82#1445C2212yescomplemented
83#1445C2212yescomplemented
84#1445C2212yescomplemented
85#1444C2212yescomplemented
86#1443C2212yescomplemented
87#1443C2212yescomplemented
88#1443C2212yescomplemented
89#1443C2212yescomplemented
90#1442C2212yescomplemented
91#1442C2212yescomplemented
92#1442C2212yescomplemented
93#1440C2212yescomplemented
94#1440C2212yescomplemented
95#1440C2212yescomplemented
96#1440C2212yescomplemented
97#1440C2212yescomplemented
98#1440C2212yescomplemented
99#1439C2212yescomplemented
100#1439C2212yescomplemented
101#1439C2212yescomplemented
102#1439C2212yescomplemented
103#1439C2212yescomplemented
104#1439C2212yescomplemented
105#1439C2212yescomplemented
106#1439C2212yescomplemented
107#1438C2212yes—
108#1438C2212yes—
109#1436C2212yescomplemented
110#1436C2212yescomplemented
111#1434C2212yescomplemented
112#1434C2212yescomplemented
113C22⋊#95C2211yescharacteristic
114C22⋊#95C2211yescharacteristic
115C22⋊#95C2211yescharacteristic
116C22⋊#95C2211yescharacteristic
117C22⋊#95C2211yescharacteristic
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2212yescomplemented
120C22⋊#95C2212yescomplemented
121C22⋊#95C2212yescomplemented
122C22⋊#95C2212yescomplemented
123C22⋊#95C2212yescomplemented
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C26C2311yescharacteristic
128C26C2311yescharacteristic
129C23×D4—24no—
130C23×D4—24no—
131C23×D4—28no—
132C23×D4—44no—
133C23×D4D418yes—
134C23×D4C2311yescharacteristic
135C23×D4C2311yescharacteristic
136C23×D4C2311yescharacteristic
137C23×D4C2311yescharacteristic
138C24×C4—24no—
139C24×C4—24no—
140C24×C4—24no—
141C24×C4—24no—
142C24×C4—24no—
143C24×C4—42no—
144C24×C4—42no—
145C24×C4C2311yescharacteristic
146C24×C4C2311yescharacteristic
147C24×C4C2312yes—
148C24×C4C2312yes—
149C24×C4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2311yescharacteristic
152C24×C4C2312yes—
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157C2×C4×D4—24no—
158C2×C4×D4—24no—
159C2×C4×D4—28no—
160C2×C4×D4—44no—
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2312yes—
166C22×C4⋊C4C2312yes—
167C22×C22⋊C4—24no—
168C22×C22⋊C4—24no—
169C22×C22⋊C4—24no—
170C22×C22⋊C4—24no—
171C22×C22⋊C4—24no—
172C22×C22⋊C4—24no—
173C22×C22⋊C4—24no—
174C22×C22⋊C4—24no—
175C22×C22⋊C4—24no—
176C22×C22⋊C4—24no—
177C22×C22⋊C4—24no—
178C22×C22⋊C4—42no—
179C22×C22⋊C4—42no—
180C22×C22⋊C4—42no—
181C22×C22⋊C4—44no—
182C22×C22⋊C4—42no—
183C22×C22⋊C4—42no—
184C22×C22⋊C4C2311yescharacteristic
185C22×C22⋊C4C2311yescharacteristic
186C22×C22⋊C4C2311yescharacteristic
187C22×C22⋊C4C2312yes—
188C22×C22⋊C4C2311yescharacteristic
189C22×C22⋊C4C2311yescharacteristic
190C22×C22⋊C4C2311yescharacteristic
191C22×C22⋊C4C2311yescharacteristic
192C22×C22⋊C4C2311yescharacteristic
193C22×C22⋊C4C2311yescharacteristic
194C22×C22⋊C4C2312yes—
195C22×C22⋊C4C2312yes—
196C22×C22⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2311yescharacteristic
201C22×C22⋊C4C2311yescharacteristic
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2312yes—
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2312yes—
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2311yescharacteristic
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2312yes—
212C22×C22⋊C4C2311yescharacteristic
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2311yescharacteristic
215C22×C22⋊C4C2311yescharacteristic
216C22×C22⋊C4C2312yes—
217C22×C42C2311yescharacteristic
218C22×C42C2311yescharacteristic
219#397—28no—
220#397—28no—
221#390—24no—
222#390—24no—
223#386—24no—
224#386—24no—
225#386—24no—
226#386—24no—
227#386—28no—
228#386—28no—
229#386—28no—
230#386—28no—
231#386—28no—
232#386—44no—
233#385—24no—
234#385—24no—
235#385—28no—
236#385—42no—
237#385—42no—
238#385—44no—
239#381—24no—
240#381—24no—
241#381—24no—
242#381—24no—
243#381—24no—
244#381—28no—
245#381—28no—
246#381—28no—
247#381—42no—
248#381—42no—
249#381D418yescomplemented
250#380—24no—
251#380—44no—
252#379—24no—
253#379—24no—
254#379—24no—
255#379—24no—
256#379—42no—
257C4×C22⋊C4—24no—
258C2×#95—24no—
259C2×#95—24no—
260C2×#95—28no—
261C2×#95—28no—
262C2×#95C2312yes—
263C2×#95C2312yes—
264C2×#95C2312yes—
265C2×#95C2312yes—
266C2×#95C2312yes—
267C2×#95C2312yes—
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2312yes—
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2312yes—
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2312yes—
278C2×#95C2311yescharacteristic
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2311yescharacteristic
283C2×#95C2311yescharacteristic
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2312yes—
290C2×#95C2312yes—
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2312yes—
302C25—22no—
303C25—22no—
304C25—24no—
305C25—22no—
306C25—22no—
307C25—24no—
308C25—24no—
309C25—22no—
310C25—22no—
311C25—22no—
312C25—22no—
313C25—22no—
314C25—22no—
315C25—42no—
316C25—42no—
317C25—42no—
318C25—42no—
319C25—42no—
320C25C2×D414yes—
321C25C2×D414yes—
322C25#4114yes—
323C25#4114yes—
324C25C2411yescharacteristic
325C25C2411yescharacteristic
326C25C2411yescharacteristic
327C25C2411yescharacteristic
328C25C2411yescharacteristic
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—232no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—24no—
340C22×D4—22no—
341C22×D4—24no—
342C22×D4—232no—
343C22×D4—24no—
344C22×D4—42no—
345C22×D4—42no—
346C22×D4—416no—
347C22×D4—432no—
348C22×D4—432no—
349C22×D4C2×D414yes—
350C22×D4C2×D414yes—
351C22×D4C2×D414yes—
352C22×D4C2×D414yes—
353C22×D4#4118yes—
354C23×C4—232no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—22no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—22no—
367C23×C4—22no—
368C23×C4—22no—
369C23×C4—22no—
370C23×C4—22no—
371C23×C4—24no—
372C23×C4—24no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—22no—
377C23×C4—22no—
378C23×C4—24no—
379C23×C4—24no—
380C23×C4—24no—
381C23×C4—24no—
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—22no—
385C23×C4—22no—
386C23×C4—24no—
387C23×C4—24no—
388C23×C4—24no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—24no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—22no—
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—24no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—42no—
402C23×C4—42no—
403C23×C4—42no—
404C23×C4—42no—
405C23×C4—42no—
406C23×C4—42no—
407C23×C4—41no—
408C23×C4—41no—
409C23×C4—41no—
410C23×C4—41no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4—42no—
415C23×C4—42no—
416C23×C4—42no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—416no—
423C23×C4—416no—
424C23×C4—416no—
425C23×C4—416no—
426C23×C4—416no—
427C23×C4—416no—
428C23×C4C2×D414yes—
429C23×C4C2×D414yes—
430C23×C4#4114yes—
431C23×C4C2411yescharacteristic
432C23×C4C2412yes—
433C23×C4C2412yes—
434C23×C4C2411yescharacteristic
435C23×C4C2411yescharacteristic
436C23×C4C2412yes—
437C23×C4C2411yescharacteristic
438C23×C4C2411yescharacteristic
439C23×C4C2411yescharacteristic
440C23×C4C2412yes—
441C23×C4C2412yes—
442C23×C4C2412yes—
443C23×C4C2411yescharacteristic
444C23×C4C2411yescharacteristic
445C23×C4C2412yes—
446C23×C4C2411yescharacteristic
447C23×C4C2412yes—
448C23×C4C2411yescharacteristic
449C4×D4—416no—
450C4×D4—416no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—42no—
459C2×C4⋊C4—42no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—42no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—42no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—42no—
467C2×C22⋊C4—22no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—22no—
471C2×C22⋊C4—22no—
472C2×C22⋊C4—22no—
473C2×C22⋊C4—22no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—22no—
483C2×C22⋊C4—22no—
484C2×C22⋊C4—22no—
485C2×C22⋊C4—22no—
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—24no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
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—416no—
531C2×C22⋊C4—416no—
532C2×C22⋊C4—416no—
533C2×C22⋊C4—42no—
534C2×C22⋊C4—41no—
535C2×C22⋊C4—41no—
536C2×C22⋊C4—41no—
537C2×C22⋊C4—41no—
538C2×C22⋊C4—42no—
539C2×C22⋊C4—42no—
540C2×C22⋊C4—42no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—42no—
544C2×C22⋊C4—42no—
545C2×C22⋊C4—42no—
546C2×C22⋊C4—416no—
547C2×C22⋊C4—416no—
548C2×C22⋊C4—416no—
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×C42—22no—
565C2×C42—22no—
566C2×C42—24no—
567C2×C42—42no—
568#95—24no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—24no—
575#95—24no—
576#95—24no—
577#95—24no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—24no—
587#95—24no—
588#95—24no—
589#95—24no—
590#95—42no—
591#95—42no—
592#95—42no—
593#95—42no—
594#95—42no—
595#95—42no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95—42no—
604#95—42no—
605#95—42no—
606#95C2×D418yescomplemented
607#95C2×D418yescomplemented
608C24—21no—
609C24—21no—
610C24—22no—
611C24—21no—
612C24—21no—
613C24—22no—
614C24—22no—
615C24—22no—
616C24—22no—
617C24—22no—
618C24—28no—
619C24—28no—
620C24—28no—
621C24—28no—
622C24—28no—
623C24—28no—
624C24—28no—
625C24—28no—
626C24—216no—
627C24—216no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—28no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—22no—
651C24—21no—
652C24—21no—
653C24—22no—
654C24—22no—
655C24—22no—
656C24—28no—
657C24—28no—
658C24—28no—
659C24—44no—
660C24—44no—
661C24—48no—
662C24—48no—
663C24—44no—
664C24—44no—
665C24—44no—
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—48no—
679C24—48no—
680C24—44no—
681C24—44no—
682C24—44no—
683C24—44no—
684C24—84no—
685C24—84no—
686C24—84no—
687C24—84no—
688C24—84no—
689C24—84no—
690C24#123116yes—
691C24C22×D412yes—
692C24C22×D412yes—
693C24C22×D412yes—
694C24C22×D412yes—
695C24C22×D412yes—
696C24C22×D412yes—
697C24C2×#4114yes—
698C24C2×#4112yes—
699C24C2×#4112yes—
700C24C2×#4112yes—
701C24C2×#4112yes—
702C24C2×#4112yes—
703C24C2×#4114yes—
704C24C2×#4112yes—
705C24C2×#4112yes—
706C24H(5,𝔽2)14yes—
707C24H(5,𝔽2)12yes—
708C24H(5,𝔽2)12yes—
709C24C2511yescharacteristic
710C2×D4—28no—
711C2×D4—28no—
712C2×D4—216no—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—28no—
716C2×D4—28no—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—4128no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—48no—
729C2×D4—48no—
730C2×D4#123116yes—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—216no—
735C22×C4—216no—
736C22×C4—28no—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—28no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—22no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—21no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—22no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—22no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
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—21no—
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—22no—
833C22×C4—22no—
834C22×C4—22no—
835C22×C4—22no—
836C22×C4—22no—
837C22×C4—22no—
838C22×C4—22no—
839C22×C4—44no—
840C22×C4—48no—
841C22×C4—48no—
842C22×C4—48no—
843C22×C4—48no—
844C22×C4—48no—
845C22×C4—48no—
846C22×C4—48no—
847C22×C4—48no—
848C22×C4—48no—
849C22×C4—48no—
850C22×C4—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—48no—
855C22×C4—48no—
856C22×C4—48no—
857C22×C4—48no—
858C22×C4—48no—
859C22×C4—48no—
860C22×C4—4128no—
861C22×C4—48no—
862C22×C4—48no—
863C22×C4—48no—
864C22×C4—48no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4—44no—
872C22×C4—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—48no—
884C22×C4—84no—
885C22×C4—82no—
886C22×C4—82no—
887C22×C4—82no—
888C22×C4—82no—
889C22×C4—84no—
890C22×C4—84no—
891C22×C4—84no—
892C22×C4—84no—
893C22×C4—84no—
894C22×C4—84no—
895C22×C4—84no—
896C22×C4—84no—
897C22×C4—84no—
898C22×C4—84no—
899C22×C4—84no—
900C22×C4C22×D412yes—
901C22×C4C22×D412yes—
902C22×C4C22×D414yes—
903C22×C4C22×D414yes—
904C22×C4C22×D412yes—
905C22×C4C22×D412yes—
906C22×C4C2×#4114yes—
907C22×C4C2×#4114yes—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—84no—
911C4⋊C4—84no—
912C4⋊C4—84no—
913C4⋊C4—84no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—48no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—48no—
922C22⋊C4—48no—
923C22⋊C4—48no—
924C22⋊C4—48no—
925C22⋊C4—48no—
926C22⋊C4—48no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—48no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—48no—
939C22⋊C4—84no—
940C22⋊C4—82no—
941C22⋊C4—82no—
942C22⋊C4—82no—
943C22⋊C4—82no—
944C22⋊C4—84no—
945C22⋊C4—84no—
946C22⋊C4—84no—
947C42—44no—
948C42—44no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—24no—
957C23—24no—
958C23—22no—
959C23—24no—
960C23—24no—
961C23—24no—
962C23—24no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
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—24no—
981C23—24no—
982C23—24no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—232no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—24no—
996C23—22no—
997C23—24no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—22no—
1003C23—22no—
1004C23—22no—
1005C23—22no—
1006C23—24no—
1007C23—24no—
1008C23—232no—
1009C23—24no—
1010C23—24no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—22no—
1018C23—416no—
1019C23—416no—
1020C23—416no—
1021C23—432no—
1022C23—432no—
1023C23—432no—
1024C23—432no—
1025C23—416no—
1026C23—416no—
1027C23—416no—
1028C23—416no—
1029C23—416no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—42no—
1034C23—41no—
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—41no—
1049C23—416no—
1050C23—41no—
1051C23—41no—
1052C23—42no—
1053C23—42no—
1054C23—42no—
1055C23—41no—
1056C23—42no—
1057C23—42no—
1058C23—42no—
1059C23—42no—
1060C23—42no—
1061C23—42no—
1062C23—42no—
1063C23—42no—
1064C23—42no—
1065C23—88no—
1066C23—88no—
1067C23—88no—
1068C23—816no—
1069C23—816no—
1070C23—816no—
1071C23—816no—
1072C23C2×#12314yes—
1073C23C2×#12314yes—
1074C23C2×#12314yes—
1075C23C2×#12314yes—
1076C23C2×#12314yes—
1077C23#52514yes—
1078C23#53414yes—
1079C23#53814yes—
1080C23D4214yes—
1081C23#54614yes—
1082C23#54614yes—
1083C23#55114yes—
1084C23#55118yes—
1085C23#55118yes—
1086C23C23×D411yescharacteristic
1087C23C23×D411yescharacteristic
1088C23C22×#4111yescharacteristic
1089C23C22×#4111yescharacteristic
1090C23C22×#4112yes—
1091C23C22×#4111yescharacteristic
1092C23C2×H(5,𝔽2)12yes—
1093C23C2×H(5,𝔽2)11yescharacteristic
1094C23C2×H(5,𝔽2)11yescharacteristic
1095C23#58512yes—
1096C23#58512yes—
1097D4—232no—
1098D4—416no—
1099D4—416no—
1100D4—416no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—24no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—22no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—24no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—24no—
1118C2×C4—24no—
1119C2×C4—24no—
1120C2×C4—24no—
1121C2×C4—416no—
1122C2×C4—432no—
1123C2×C4—432no—
1124C2×C4—41no—
1125C2×C4—42no—
1126C2×C4—42no—
1127C2×C4—416no—
1128C2×C4—416no—
1129C2×C4—41no—
1130C2×C4—42no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—42no—
1142C2×C4—42no—
1143C2×C4—42no—
1144C2×C4—42no—
1145C2×C4—42no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—42no—
1156C2×C4—42no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—42no—
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—41no—
1175C2×C4—41no—
1176C2×C4—41no—
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—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—42no—
1210C2×C4—42no—
1211C2×C4—88no—
1212C2×C4—816no—
1213C2×C4—88no—
1214C2×C4—88no—
1215C2×C4—88no—
1216C2×C4—88no—
1217C2×C4—88no—
1218C2×C4C2×#12314yes—
1219C22—24no—
1220C22—24no—
1221C22—24no—
1222C22—24no—
1223C22—28no—
1224C22—28no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—28no—
1229C22—28no—
1230C22—28no—
1231C22—28no—
1232C22—28no—
1233C22—28no—
1234C22—24no—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—24no—
1245C22—464no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—44no—
1250C22—44no—
1251C22—42no—
1252C22—42no—
1253C22—44no—
1254C22—44no—
1255C22—44no—
1256C22—44no—
1257C22—44no—
1258C22—44no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—832no—
1270C22—82no—
1271C22—82no—
1272C22—82no—
1273C22—82no—
1274C22#241818yes—
1275C22#248318yescomplemented
1276C22C22×#12311yescharacteristic
1277C22C22×#12311yescharacteristic
1278C22C2×#52511yescharacteristic
1279C22C2×#53411yescharacteristic
1280C22C2×#53811yescharacteristic
1281C22C2×D4211yescharacteristic
1282C22C2×#54611yescharacteristic
1283C22C2×#54611yescharacteristic
1284C22D4×#4112yes—
1285C22C2×#55111yescharacteristic
1286C22C2×#55112yes—
1287C22C2×#55112yes—
1288C22#347512yes—
1289C22#348511yescharacteristic
1290C22#348511yescharacteristic
1291C22#348812yes—
1292C22#349112yes—
1293C22#349112yes—
1294C22#349412yes—
1295C22#351312yes—
1296C22#351312yes—
1297C22#353412yes—
1298C22#353412yes—
1299C4—24no—
1300C4—42no—
1301C4—44no—
1302C4—44no—
1303C4—44no—
1304C4—42no—
1305C4—42no—
1306C4—82no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—82no—
1311C4—82no—
1312C4—82no—
1313C4—81no—
1314C4—82no—
1315C4—81no—
1316C4—81no—
1317C2—28no—
1318C2—28no—
1319C2—44no—
1320C2—44no—
1321C2—82no—
1322C2C2×#241811yescharacteristic
1323C2C2×#248311yescharacteristic
1324C2#3544811yescharacteristic
1325C2D4×#12311yescharacteristic
1326C2#3615511yescharacteristic
1327C2#3622212yes—
1328C2#3764611yescharacteristic
1329C2#3783411yescharacteristic
1330C2#3805312yes—
1331C2#5901112yes—
1332C2#5919512yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC24×D4C22
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×#2483C2semidirect
4. C22×#381C2semidirect
5. #15954C2semidirect
6. #15952C2semidirect
7. #15287C2semidirect
8. #15285C2semidirect
9. #15019C2semidirect
10. #14936C2semidirect
11. #14918C2semidirect
12. #14918C2semidirect
13. #14737C2semidirect
14. #14735C2semidirect
15. #14681C2semidirect
16. #14127C2semidirect
17. #13992C2semidirect
18. #13992C2semidirect
19. #13975C2semidirect
20. #13894C2semidirect
21. #13877C2semidirect
22. #13869C2semidirect
35. C2×#397C22semidirect
36. C2×#397C22semidirect
55. C2×#385C22semidirect
56. C2×#385C22semidirect
66. C2×#381C22semidirect
67. C2×#381C22semidirect
68. C2×#381C22semidirect
70. C2×#380C22semidirect
79. C22×#95C22semidirect
80. C22×#95C22semidirect
81. #1445C22semidirect
82. #1445C22semidirect
83. #1445C22semidirect
84. #1445C22semidirect
85. #1444C22semidirect
86. #1443C22semidirect
87. #1443C22semidirect
88. #1443C22semidirect
89. #1443C22semidirect
90. #1442C22semidirect
91. #1442C22semidirect
92. #1442C22semidirect
93. #1440C22semidirect
94. #1440C22semidirect
95. #1440C22semidirect
96. #1440C22semidirect
97. #1440C22semidirect
98. #1440C22semidirect
99. #1439C22semidirect
100. #1439C22semidirect
101. #1439C22semidirect
102. #1439C22semidirect
103. #1439C22semidirect
104. #1439C22semidirect
105. #1439C22semidirect
106. #1439C22semidirect
109. #1436C22semidirect
110. #1436C22semidirect
111. #1434C22semidirect
112. #1434C22semidirect
119. C22⋊#95C22semidirect
120. C22⋊#95C22semidirect
121. C22⋊#95C22semidirect
122. C22⋊#95C22semidirect
123. C22⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
249. #381D4semidirect
606. #95C2×D4semidirect
607. #95C2×D4semidirect
1275. C22#2483semidirect

Maximal subgroups

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

subgroupindex
C2×#24832
C2×D4×C22⋊C42
C22×#3862
C22×#3812
#159542
#159522
#152872
#152852
#150192
#149362
#149182
#147372
#147352
#146812
#141272
#139922
#139752
#138942
#138772
#138692
#138672