Finite Group Databasebeta

← #524879

Subgroups — #524879

Order 512.

5988 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#546C211yesmaximal, characteristic
2C2×#2353C211yesmaximal, characteristic, complemented
3C2×#2290C211yesmaximal, characteristic, complemented
4#14698C211yesmaximal, characteristic, complemented
5#14506C212yesmaximal, complemented
6#14448C212yesmaximal, complemented
7#14418C212yesmaximal, complemented
8#14358C212yesmaximal, complemented
9#14290C211yesmaximal, characteristic, complemented
10#14288C211yesmaximal, characteristic, complemented
11#14169C211yesmaximal, characteristic, complemented
12#14152C211yesmaximal, characteristic, complemented
13#14136C211yesmaximal, characteristic, complemented
14#13996C212yesmaximal, complemented
15#13995C212yesmaximal, complemented
16#13959C211yesmaximal, characteristic, complemented
17#13956C212yesmaximal, complemented
18#13903C211yesmaximal, characteristic, complemented
19#13868C211yesmaximal, characteristic, complemented
20#13867C212yesmaximal, complemented
21#13785C211yesmaximal, characteristic, complemented
22#13775C211yesmaximal, characteristic, complemented
23C2×#1437C211yesmaximal, characteristic, complemented
24C23×#41C2211yescharacteristic
25C24×D4C2211yescharacteristic
26C2×#546—28no—
27C2×#546—28no—
28C2×#546C4116yescomplemented
29C22×#124C2211yescharacteristic
30C22×#123C2211yescharacteristic
31C22×#123C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×#121C2211yescharacteristic
36C22×#120C2211yescharacteristic
37C22×#120C2211yescharacteristic
38C22×C4×D4C2211yescharacteristic
39C22×C4×D4C2211yescharacteristic
40C22×#117C2211yescharacteristic, complemented
41C23×C22⋊C4C2211yescharacteristic
42C23×C22⋊C4C2211yescharacteristic
43C23×C22⋊C4C2212yes—
44C23×C42C2211yescharacteristic, complemented
45#2353—28no—
46C2×#390C2212yes—
47C2×#390C2212yescomplemented
48C2×#390C2212yescomplemented
49#2290—28no—
50C2×#388C2212yescomplemented
51C2×#388C2212yescomplemented
52C2×#387C2212yescomplemented
53C2×#387C2212yescomplemented
54C2×#386C2212yes—
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2212yes—
58C2×#386C2212yescomplemented
59C2×#386C2212yescomplemented
60C2×#385C2212yescomplemented
61C2×#383C2211yescharacteristic, complemented
62C2×#381C2211yescharacteristic, complemented
63C2×#381C2212yescomplemented
64C2×#380C2211yescharacteristic, complemented
65C2×#379C2212yes—
66C2×#379C2212yes—
67C2×#379C2212yes—
68C2×C4×C4⋊C4C2211yescharacteristic, complemented
69C2×C4×C22⋊C4C2211yescharacteristic, complemented
70C2×C4×C22⋊C4C2212yescomplemented
71C2×C4×C22⋊C4C2211yescharacteristic, complemented
72C2×C4×C22⋊C4C2211yescharacteristic, complemented
73C2×#376C2211yescharacteristic, complemented
74C2×#376C2211yescharacteristic, complemented
75C22×#95C2211yescharacteristic, complemented
76C22×#95C2212yescomplemented
77#1446C2212yescomplemented
78#1446C2212yescomplemented
79#1445C2212yescomplemented
80#1445C2212yescomplemented
81#1445C2212yescomplemented
82#1439C2212yes—
83#1439C2212yes—
84#1439C2212yescomplemented
85#1439C2212yescomplemented
86#1439C2212yescomplemented
87#1439C2212yescomplemented
88#1438C2212yes—
89#1438C2212yes—
90#1438C2212yes—
91#1438C2212yes—
92#1438C2212yes—
93#1438C2212yescomplemented
94#1438C2212yescomplemented
95#1438C2212yescomplemented
96#1438C2212yescomplemented
97#1437C2212yes—
98#1437C2211yescharacteristic
99#1437C2211yescharacteristic
100#1437C2211yescharacteristic
101#1437C2212yes—
102#1437C2211yescharacteristic
103#1437C2212yescomplemented
104#1437C2211yescharacteristic, complemented
105#1437C2211yescharacteristic, complemented
106#1437C2211yescharacteristic, complemented
107#1437C2211yescharacteristic, complemented
108#1437C2211yescharacteristic, complemented
109#1437C2211yescharacteristic, complemented
110#1437C2211yescharacteristic, complemented
111#1437C2211yescharacteristic, complemented
112#1437C2211yescharacteristic, complemented
113#1437C2212yescomplemented
114#1437C2212yescomplemented
115#1437C2212yescomplemented
116#1437C2211yescharacteristic, complemented
117#1437C2211yescharacteristic, complemented
118#1437C2211yescharacteristic, complemented
119C4⋊#95C2212yescomplemented
120C4⋊#95C2212yescomplemented
121C4⋊#95C2212yescomplemented
122C22⋊#95C2212yes—
123C22⋊#95C2212yes—
124C22⋊#95C2212yescomplemented
125C22⋊#95C2212yescomplemented
126C22⋊#95C2212yescomplemented
127C22⋊#95C2212yescomplemented
128C26C2311yescharacteristic
129C26C2311yescharacteristic
130C22×#41—24no—
131C22×#41—24no—
132C22×#41—44no—
133C22×#41—44no—
134C22×#41C2×C418yes—
135C23×Q8C2311yescharacteristic
136C23×D4—24no—
137C23×D4—24no—
138C23×D4—44no—
139C23×D4—44no—
140C23×D4C2×C418yes—
141C23×D4C2311yescharacteristic
142C23×D4C2311yescharacteristic
143C23×D4C2311yescharacteristic
144C23×D4C2311yescharacteristic
145C23×D4C2311yescharacteristic
146C23×D4C2311yescharacteristic
147C23×D4C2311yescharacteristic
148C23×D4C2311yescharacteristic
149C23×D4C2311yescharacteristic
150C24×C4C2311yescharacteristic
151C24×C4C2312yes—
152C24×C4C2312yes—
153C24×C4C2311yescharacteristic
154C24×C4C2311yescharacteristic
155C24×C4C2311yescharacteristic
156C24×C4C2311yescharacteristic
157C24×C4C2311yescharacteristic
158#546—2128no—
159C2×#124—24no—
160C2×#124—24no—
161C2×#124C2×C418yescomplemented
162C2×#123—24no—
163C2×#123—24no—
164C2×#123—24no—
165C2×#123—24no—
166C2×#123C2×C418yes—
167C2×#123C2×C418yescomplemented
168C2×C22⋊Q8—24no—
169C2×C22⋊Q8—24no—
170C2×C22⋊Q8C2×C418yescomplemented
171C2×#121—24no—
172C2×#121—24no—
173C2×#121—24no—
174C2×#121—24no—
175C2×#121—24no—
176C2×#121—24no—
177C2×#121C2×C418yes—
178C2×#121C2×C418yescomplemented
179C2×#121C2×C418yescomplemented
180C2×#120—24no—
181C2×#120—24no—
182C2×#120—24no—
183C2×#120—24no—
184C2×#120C2×C418yes—
185C2×#120C2×C418yescomplemented
186C2×C4×D4—24no—
187C2×C4×D4—24no—
188C2×C4×D4C2×C418yes—
189C2×C4×D4C2×C418yescomplemented
190C2×C4×D4D418yes—
191C2×C4×D4D418yes—
192C2×#117—24no—
193C2×#117—44no—
194C22×C4⋊C4C2312yes—
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C4⋊C4C2311yescharacteristic
198C22×C4⋊C4C2311yescharacteristic
199C22×C4⋊C4C2312yes—
200C22×C4⋊C4C2311yescharacteristic
201C22×C22⋊C4—24no—
202C22×C22⋊C4—24no—
203C22×C22⋊C4—24no—
204C22×C22⋊C4—24no—
205C22×C22⋊C4—28no—
206C22×C22⋊C4—44no—
207C22×C22⋊C4—44no—
208C22×C22⋊C4C2×C418yes—
209C22×C22⋊C4C2×C418yescomplemented
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×C22⋊C4C2311yescharacteristic
219C22×C22⋊C4C2311yescharacteristic
220C22×C22⋊C4C2311yescharacteristic
221C22×C22⋊C4C2311yescharacteristic
222C22×C22⋊C4C2311yescharacteristic
223C22×C22⋊C4C2311yescharacteristic
224C22×C22⋊C4C2311yescharacteristic
225C22×C22⋊C4C2311yescharacteristic
226C22×C22⋊C4C2311yescharacteristic
227C22×C22⋊C4C2312yes—
228C22×C22⋊C4C2312yes—
229C22×C22⋊C4C2312yes—
230C22×C22⋊C4C2312yes—
231C22×C22⋊C4C2312yes—
232C22×C22⋊C4C2312yes—
233C22×C22⋊C4C2312yes—
234C22×C22⋊C4C2312yes—
235C22×C22⋊C4C2312yes—
236C22×C22⋊C4C2312yes—
237C22×C22⋊C4C2312yes—
238C22×C22⋊C4C2312yes—
239C22×C22⋊C4C2312yes—
240C22×C22⋊C4C2312yes—
241C22×C22⋊C4C2312yes—
242C22×C22⋊C4C2311yescharacteristic
243C22×C22⋊C4C2311yescharacteristic
244C22×C42—24no—
245C22×C42—44no—
246C22×C42C2311yescharacteristic
247C22×C42C2312yes—
248C22×C42C2312yes—
249C22×C42C2311yescharacteristic
250C22×C42C2311yescharacteristic
251C22×C42C2312yes—
252C22×C42C2311yescharacteristic
253C22×C42C2311yescharacteristic
254#390—28no—
255#390—44no—
256#390—44no—
257#388—28no—
258#388—28no—
259#387—28no—
260#387—28no—
261#386—28no—
262#386—28no—
263#386—44no—
264#386—44no—
265#386—44no—
266#386—44no—
267#385—28no—
268#383—24no—
269#381—24no—
270#381—44no—
271#380—24no—
272#379—28no—
273#379—44no—
274#379—44no—
275C4×C4⋊C4—24no—
276C4×C22⋊C4—24no—
277C4×C22⋊C4—24no—
278C4×C22⋊C4—24no—
279C4×C22⋊C4—28no—
280#376—24no—
281#376—24no—
282C2×#95—24no—
283C2×#95—44no—
284C2×#95C2312yes—
285C2×#95C2312yes—
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2311yescharacteristic
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2311yescharacteristic
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2312yes—
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—
314C25—24no—
315C25—22no—
316C25—22no—
317C25—22no—
318C25—22no—
319C25—24no—
320C25—24no—
321C25—24no—
322C25—42no—
323C25—42no—
324C25—42no—
325C25—42no—
326C25—42no—
327C25—42no—
328C25—42no—
329C25—42no—
330C25C22×C414yes—
331C25C22×C414yes—
332C25C2411yescharacteristic
333C25C2411yescharacteristic
334C25C2411yescharacteristic
335C25C2411yescharacteristic
336C25C2411yescharacteristic
337C25C2411yescharacteristic
338C2×#41—232no—
339C2×#41—432no—
340C2×#41—416no—
341C2×#41—432no—
342C2×#41—416no—
343C22×Q8—22no—
344C22×Q8—22no—
345C22×Q8—42no—
346C22×Q8—42no—
347C22×Q8C22×C414yes—
348C22×D4—24no—
349C22×D4—24no—
350C22×D4—22no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—24no—
362C22×D4—24no—
363C22×D4—232no—
364C22×D4—22no—
365C22×D4—22no—
366C22×D4—22no—
367C22×D4—22no—
368C22×D4—22no—
369C22×D4—22no—
370C22×D4—22no—
371C22×D4—22no—
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—432no—
384C22×D4—416no—
385C22×D4—432no—
386C22×D4—416no—
387C22×D4C22×C414yes—
388C22×D4C22×C414yes—
389C22×D4C22×C414yes—
390C22×D4C22×C414yes—
391C22×D4C22×C414yes—
392C22×D4C22×C414yes—
393C22×D4C22×C414yes—
394C22×D4C22×C414yes—
395C22×D4C22×C414yes—
396C22×D4C2×D414yes—
397C22×D4C2×D414yes—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4—22no—
402C23×C4—24no—
403C23×C4—24no—
404C23×C4—24no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—24no—
410C23×C4—24no—
411C23×C4—24no—
412C23×C4—24no—
413C23×C4—24no—
414C23×C4—24no—
415C23×C4—24no—
416C23×C4—24no—
417C23×C4—42no—
418C23×C4—42no—
419C23×C4—42no—
420C23×C4—42no—
421C23×C4—42no—
422C23×C4—42no—
423C23×C4—42no—
424C23×C4—42no—
425C23×C4—42no—
426C23×C4—42no—
427C23×C4—42no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4—42no—
431C23×C4—42no—
432C23×C4C22×C414yes—
433C23×C4C22×C414yes—
434C23×C4C22×C414yes—
435C23×C4C22×C414yes—
436C23×C4C22×C414yes—
437C23×C4C22×C414yes—
438C23×C4C2×D414yes—
439C23×C4C2×D414yes—
440C23×C4C2×D414yes—
441C23×C4C2×D414yes—
442C23×C4C2412yes—
443C23×C4C2412yes—
444C23×C4C2412yes—
445C23×C4C2412yes—
446C23×C4C2412yes—
447C23×C4C2411yescharacteristic
448C23×C4C2411yescharacteristic
449C23×C4C2411yescharacteristic
450C23×C4C2411yescharacteristic
451C23×C4C2412yes—
452C23×C4C2412yes—
453C23×C4C2412yes—
454C23×C4C2411yescharacteristic
455C23×C4C2411yescharacteristic
456C23×C4C2411yescharacteristic
457C23×C4C2411yescharacteristic
458C23×C4C2411yescharacteristic
459#124—232no—
460#123—232no—
461#123—232no—
462C22⋊Q8—232no—
463#121—232no—
464#121—232no—
465#121—232no—
466#120—232no—
467#120—232no—
468C4×D4—232no—
469C4×D4C22⋊C4164yescomplemented
470#117—416no—
471C2×C4⋊C4—22no—
472C2×C4⋊C4—22no—
473C2×C4⋊C4—22no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4C22×C414yes—
487C2×C4⋊C4C22×C414yes—
488C2×C4⋊C4C22×C414yes—
489C2×C4⋊C4C22×C414yes—
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—24no—
515C2×C22⋊C4—24no—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—24no—
522C2×C22⋊C4—24no—
523C2×C22⋊C4—24no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—24no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
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—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—432no—
550C2×C22⋊C4—42no—
551C2×C22⋊C4—42no—
552C2×C22⋊C4—42no—
553C2×C22⋊C4—42no—
554C2×C22⋊C4—42no—
555C2×C22⋊C4—42no—
556C2×C22⋊C4—42no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4—42no—
559C2×C22⋊C4—42no—
560C2×C22⋊C4—42no—
561C2×C22⋊C4—42no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4—42no—
566C2×C22⋊C4—42no—
567C2×C22⋊C4—42no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4—42no—
573C2×C22⋊C4—42no—
574C2×C22⋊C4—42no—
575C2×C22⋊C4—42no—
576C2×C22⋊C4—42no—
577C2×C22⋊C4—42no—
578C2×C22⋊C4—42no—
579C2×C22⋊C4—42no—
580C2×C22⋊C4C22×C414yes—
581C2×C22⋊C4C22×C414yes—
582C2×C22⋊C4C22×C414yes—
583C2×C22⋊C4C22×C414yes—
584C2×C22⋊C4C22×C414yes—
585C2×C22⋊C4C22×C414yes—
586C2×C22⋊C4C22×C414yes—
587C2×C22⋊C4C22×C414yes—
588C2×C22⋊C4C22×C414yes—
589C2×C22⋊C4C22×C414yes—
590C2×C22⋊C4C22×C414yes—
591C2×C22⋊C4C22×C414yes—
592C2×C22⋊C4C2×D414yes—
593C2×C22⋊C4C2×D414yes—
594C2×C22⋊C4C2×D414yes—
595C2×C22⋊C4C2×D414yes—
596C2×C22⋊C4#4118yescomplemented
597C2×C42—22no—
598C2×C42—24no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—24no—
602C2×C42—22no—
603C2×C42—24no—
604C2×C42—24no—
605C2×C42—24no—
606C2×C42—24no—
607C2×C42—416no—
608C2×C42—42no—
609C2×C42—42no—
610C2×C42—42no—
611C2×C42—42no—
612C2×C42—42no—
613C2×C42—42no—
614C2×C42—42no—
615C2×C42C22×C414yes—
616C2×C42C2×D414yes—
617C2×C42C2×D414yes—
618#95—22no—
619#95—22no—
620#95—24no—
621#95—22no—
622#95—24no—
623#95—24no—
624#95—24no—
625#95—22no—
626#95—24no—
627#95—24no—
628#95—24no—
629#95—24no—
630#95—24no—
631#95—24no—
632#95—42no—
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—
644#95—42no—
645#95—42no—
646#95—42no—
647#95—42no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—21no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—22no—
662C24—22no—
663C24—22no—
664C24—22no—
665C24—28no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
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—22no—
690C24—28no—
691C24—28no—
692C24—216no—
693C24—28no—
694C24—48no—
695C24—44no—
696C24—48no—
697C24—44no—
698C24—48no—
699C24—48no—
700C24—48no—
701C24—48no—
702C24—48no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—44no—
708C24—44no—
709C24—48no—
710C24—44no—
711C24—48no—
712C24—44no—
713C24—82no—
714C24—82no—
715C24—84no—
716C24—84no—
717C24—84no—
718C24—84no—
719C24—84no—
720C24—82no—
721C24—82no—
722C24—84no—
723C24—84no—
724C24—84no—
725C24—84no—
726C24—84no—
727C24—84no—
728C24—84no—
729C24—84no—
730C24—84no—
731C24C23×C412yes—
732C24C23×C412yes—
733C24C23×C412yes—
734C24C23×C412yes—
735C24C23×C412yes—
736C24C23×C412yes—
737C24C22×D412yes—
738C24C22×D412yes—
739C24C22×D412yes—
740C24C22×D412yes—
741C24C2×#4114yes—
742C24H(5,𝔽2)14yes—
743C24H(5,𝔽2)14yes—
744C24C2511yescharacteristic
745#41—4128no—
746C2×Q8—28no—
747C2×Q8—48no—
748C2×Q8—44no—
749C2×Q8—44no—
750C2×Q8—48no—
751C2×D4—216no—
752C2×D4—28no—
753C2×D4—216no—
754C2×D4—28no—
755C2×D4—28no—
756C2×D4—28no—
757C2×D4—28no—
758C2×D4—28no—
759C2×D4—28no—
760C2×D4—216no—
761C2×D4—216no—
762C2×D4—28no—
763C2×D4—28no—
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—48no—
767C2×D4—48no—
768C2×D4—44no—
769C2×D4—48no—
770C2×D4—48no—
771C2×D4—48no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—48no—
775C2×D4—48no—
776C2×D4—48no—
777C2×D4—4128no—
778C2×D4—44no—
779C2×D4—44no—
780C2×D4—48no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—48no—
784C2×D4—44no—
785C2×D4—48no—
786C2×D4—44no—
787C2×D4—44no—
788C2×D4—48no—
789C2×D4—44no—
790C2×D4—82no—
791C2×D4—82no—
792C2×D4—82no—
793C2×D4—82no—
794C2×D4—84no—
795C2×D4—84no—
796C2×D4C2×C22⋊C4116yes—
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—216no—
808C22×C4—28no—
809C22×C4—28no—
810C22×C4—216no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—22no—
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—22no—
828C22×C4—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—28no—
846C22×C4—28no—
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—22no—
862C22×C4—22no—
863C22×C4—22no—
864C22×C4—22no—
865C22×C4—22no—
866C22×C4—22no—
867C22×C4—22no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—22no—
871C22×C4—22no—
872C22×C4—22no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—22no—
880C22×C4—22no—
881C22×C4—22no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—48no—
885C22×C4—48no—
886C22×C4—48no—
887C22×C4—48no—
888C22×C4—48no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4—48no—
892C22×C4—48no—
893C22×C4—48no—
894C22×C4—48no—
895C22×C4—48no—
896C22×C4—48no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—48no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—48no—
903C22×C4—48no—
904C22×C4—48no—
905C22×C4—48no—
906C22×C4—48no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—48no—
910C22×C4—48no—
911C22×C4—44no—
912C22×C4—48no—
913C22×C4—44no—
914C22×C4—48no—
915C22×C4—84no—
916C22×C4—84no—
917C22×C4—84no—
918C22×C4C2×C22⋊C4116yes—
919C22×C4C2×C22⋊C4116yescomplemented
920C22×C4C23×C412yes—
921C22×C4C23×C412yes—
922C22×C4C23×C412yes—
923C22×C4C23×C412yes—
924C22×C4C23×C412yes—
925C22×C4C23×C412yes—
926C22×C4C23×C412yes—
927C22×C4C23×C412yes—
928C22×C4C23×C412yes—
929C22×C4C22×D412yes—
930C22×C4C22×D412yes—
931C22×C4C22×D412yes—
932C22×C4C22×D412yes—
933C22×C4C22×D412yes—
934C22×C4C22×D412yes—
935C22×C4C22×D412yes—
936C22×C4C22×D412yes—
937C22×C4C22×D412yes—
938C22×C4C22×D412yes—
939C22×C4C2×#4114yes—
940C22×C4C2×#4114yes—
941C22×C4H(5,𝔽2)14yes—
942C4⋊C4—28no—
943C4⋊C4—28no—
944C4⋊C4—28no—
945C4⋊C4—48no—
946C4⋊C4—48no—
947C4⋊C4—84no—
948C4⋊C4C2×C22⋊C4116yescomplemented
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—28no—
952C22⋊C4—28no—
953C22⋊C4—28no—
954C22⋊C4—28no—
955C22⋊C4—28no—
956C22⋊C4—28no—
957C22⋊C4—28no—
958C22⋊C4—28no—
959C22⋊C4—48no—
960C22⋊C4—48no—
961C22⋊C4—48no—
962C22⋊C4—48no—
963C22⋊C4—48no—
964C22⋊C4—48no—
965C22⋊C4—48no—
966C22⋊C4—48no—
967C22⋊C4—48no—
968C22⋊C4—84no—
969C22⋊C4—84no—
970C22⋊C4—84no—
971C22⋊C4—84no—
972C22⋊C4—84no—
973C22⋊C4—84no—
974C22⋊C4—84no—
975C22⋊C4—84no—
976C22⋊C4—84no—
977C22⋊C4—84no—
978C22⋊C4—84no—
979C22⋊C4—84no—
980C22⋊C4—84no—
981C22⋊C4C2×C22⋊C4116yes—
982C22⋊C4C2×C22⋊C4116yescomplemented
983C42—28no—
984C42—48no—
985C42—48no—
986C42—44no—
987C42—44no—
988C42—44no—
989C42—84no—
990C42C2×C22⋊C4116yescomplemented
991C23—22no—
992C23—22no—
993C23—24no—
994C23—24no—
995C23—24no—
996C23—22no—
997C23—22no—
998C23—24no—
999C23—24no—
1000C23—24no—
1001C23—24no—
1002C23—24no—
1003C23—24no—
1004C23—24no—
1005C23—24no—
1006C23—24no—
1007C23—22no—
1008C23—22no—
1009C23—24no—
1010C23—24no—
1011C23—22no—
1012C23—22no—
1013C23—24no—
1014C23—24no—
1015C23—22no—
1016C23—22no—
1017C23—24no—
1018C23—24no—
1019C23—24no—
1020C23—24no—
1021C23—24no—
1022C23—22no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—24no—
1036C23—24no—
1037C23—24no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—24no—
1042C23—24no—
1043C23—24no—
1044C23—416no—
1045C23—432no—
1046C23—416no—
1047C23—416no—
1048C23—41no—
1049C23—41no—
1050C23—42no—
1051C23—41no—
1052C23—41no—
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—416no—
1067C23—41no—
1068C23—41no—
1069C23—42no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—42no—
1075C23—42no—
1076C23—42no—
1077C23—42no—
1078C23—42no—
1079C23—42no—
1080C23—42no—
1081C23—42no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—42no—
1089C23—42no—
1090C23—42no—
1091C23—42no—
1092C23—42no—
1093C23—42no—
1094C23—42no—
1095C23—42no—
1096C23—42no—
1097C23—42no—
1098C23—42no—
1099C23—42no—
1100C23—42no—
1101C23—42no—
1102C23—42no—
1103C23—42no—
1104C23—42no—
1105C23—42no—
1106C23—42no—
1107C23—42no—
1108C23—42no—
1109C23—42no—
1110C23—42no—
1111C23—42no—
1112C23—42no—
1113C23—42no—
1114C23—42no—
1115C23—816no—
1116C23—88no—
1117C23—88no—
1118C23—816no—
1119C23—816no—
1120C23—816no—
1121C23—816no—
1122C23—816no—
1123C23—816no—
1124C23—816no—
1125C23—816no—
1126C23—816no—
1127C23—816no—
1128C23C22×C22⋊C414yes—
1129C23C22×C22⋊C414yes—
1130C23C4×#4114yes—
1131C23#51818yes—
1132C23#53514yes—
1133C23#53518yes—
1134C23#53514yes—
1135C23C24×C411yescharacteristic
1136C23C23×D411yescharacteristic
1137C23C23×D411yescharacteristic
1138C23C22×#4112yes—
1139C23C2×H(5,𝔽2)12yes—
1140C23C2×H(5,𝔽2)12yes—
1141C23C2×H(5,𝔽2)12yes—
1142C23#58512yes—
1143C23#58512yes—
1144Q8—416no—
1145D4—232no—
1146D4—416no—
1147D4—416no—
1148D4—416no—
1149D4—416no—
1150D4—416no—
1151D4—416no—
1152D4—88no—
1153D4—88no—
1154C2×C4—22no—
1155C2×C4—24no—
1156C2×C4—22no—
1157C2×C4—24no—
1158C2×C4—24no—
1159C2×C4—24no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—24no—
1163C2×C4—24no—
1164C2×C4—24no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—24no—
1172C2×C4—24no—
1173C2×C4—24no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—24no—
1179C2×C4—24no—
1180C2×C4—24no—
1181C2×C4—24no—
1182C2×C4—24no—
1183C2×C4—24no—
1184C2×C4—24no—
1185C2×C4—24no—
1186C2×C4—24no—
1187C2×C4—24no—
1188C2×C4—24no—
1189C2×C4—24no—
1190C2×C4—24no—
1191C2×C4—416no—
1192C2×C4—416no—
1193C2×C4—416no—
1194C2×C4—416no—
1195C2×C4—432no—
1196C2×C4—416no—
1197C2×C4—416no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—42no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—42no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—42no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—42no—
1212C2×C4—42no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—42no—
1216C2×C4—42no—
1217C2×C4—42no—
1218C2×C4—42no—
1219C2×C4—42no—
1220C2×C4—42no—
1221C2×C4—42no—
1222C2×C4—42no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—42no—
1239C2×C4—42no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—816no—
1258C2×C4C22×C22⋊C414yes—
1259C2×C4C22×C22⋊C414yes—
1260C2×C4C22×C22⋊C414yes—
1261C2×C4C22×C22⋊C414yes—
1262C2×C4C22×C22⋊C414yes—
1263C22—28no—
1264C22—28no—
1265C22—24no—
1266C22—28no—
1267C22—24no—
1268C22—28no—
1269C22—28no—
1270C22—28no—
1271C22—24no—
1272C22—24no—
1273C22—24no—
1274C22—24no—
1275C22—28no—
1276C22—44no—
1277C22—44no—
1278C22—44no—
1279C22—44no—
1280C22—44no—
1281C22—44no—
1282C22—42no—
1283C22—44no—
1284C22—44no—
1285C22—44no—
1286C22—44no—
1287C22—42no—
1288C22—44no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—44no—
1293C22—44no—
1294C22—44no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—44no—
1302C22—44no—
1303C22—44no—
1304C22—832no—
1305C22—832no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—82no—
1312C22—82no—
1313C22—82no—
1314C22—82no—
1315C22—82no—
1316C22—82no—
1317C22—82no—
1318C22#230918yes—
1319C22C23×C22⋊C411yescharacteristic
1320C22C2×C4×#4111yescharacteristic
1321C22C2×#51812yes—
1322C22#342811yescharacteristic
1323C22C4×H(5,𝔽2)12yes—
1324C22C2×#53511yescharacteristic
1325C22C2×#53511yescharacteristic
1326C22C2×#53512yes—
1327C22D4×#4112yes—
1328C22D4×#4112yes—
1329C22#348411yescharacteristic
1330C22#348511yescharacteristic
1331C22#349012yes—
1332C22#349412yes—
1333C22#349612yes—
1334C22#351312yes—
1335C22#351912yes—
1336C22#353412yes—
1337C22#354212yes—
1338C22#354512yes—
1339C22#356012yes—
1340C4—24no—
1341C4—24no—
1342C4—24no—
1343C4—24no—
1344C4—24no—
1345C4—44no—
1346C4—44no—
1347C4—44no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—82no—
1353C4—82no—
1354C4—82no—
1355C4—82no—
1356C4—82no—
1357C2—28no—
1358C2—44no—
1359C2—44no—
1360C2—82no—
1361C2—82no—
1362C2—82no—
1363C2C2×#230911yescharacteristic
1364C2C22⋊C4×#4111yescharacteristic
1365C2#3425611yescharacteristic
1366C2#3430212yes—
1367C2#3449212yes—
1368C2#3835812yes—
1369C2#3836212yes—
1370C2#3842012yes—
1371C2#3842312yes—
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#546C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#2353C2semidirect
3. C2×#2290C2semidirect
4. #14698C2semidirect
5. #14506C2semidirect
6. #14448C2semidirect
7. #14418C2semidirect
8. #14358C2semidirect
9. #14290C2semidirect
10. #14288C2semidirect
11. #14169C2semidirect
12. #14152C2semidirect
13. #14136C2semidirect
14. #13996C2semidirect
15. #13995C2semidirect
16. #13959C2semidirect
17. #13956C2semidirect
18. #13903C2semidirect
19. #13868C2semidirect
20. #13867C2semidirect
21. #13785C2semidirect
22. #13775C2semidirect
23. C2×#1437C2semidirect
28. C2×#546C4semidirect
40. C22×#117C22semidirect
44. C23×C42C22semidirect
47. C2×#390C22semidirect
48. C2×#390C22semidirect
50. C2×#388C22semidirect
51. C2×#388C22semidirect
52. C2×#387C22semidirect
53. C2×#387C22semidirect
58. C2×#386C22semidirect
59. C2×#386C22semidirect
60. C2×#385C22semidirect
61. C2×#383C22semidirect
62. C2×#381C22semidirect
63. C2×#381C22semidirect
64. C2×#380C22semidirect
68. C2×C4×C4⋊C4C22semidirect
69. C2×C4×C22⋊C4C22semidirect
70. C2×C4×C22⋊C4C22semidirect
71. C2×C4×C22⋊C4C22semidirect
72. C2×C4×C22⋊C4C22semidirect
73. C2×#376C22semidirect
74. C2×#376C22semidirect
75. C22×#95C22semidirect
76. C22×#95C22semidirect
77. #1446C22semidirect
78. #1446C22semidirect
79. #1445C22semidirect
80. #1445C22semidirect
81. #1445C22semidirect
84. #1439C22semidirect
85. #1439C22semidirect
86. #1439C22semidirect
87. #1439C22semidirect
93. #1438C22semidirect
94. #1438C22semidirect
95. #1438C22semidirect
96. #1438C22semidirect
103. #1437C22semidirect
104. #1437C22semidirect
105. #1437C22semidirect
106. #1437C22semidirect
107. #1437C22semidirect
108. #1437C22semidirect
109. #1437C22semidirect
110. #1437C22semidirect
111. #1437C22semidirect
112. #1437C22semidirect
113. #1437C22semidirect
114. #1437C22semidirect
115. #1437C22semidirect
116. #1437C22semidirect
117. #1437C22semidirect
118. #1437C22semidirect
119. C4⋊#95C22semidirect
120. C4⋊#95C22semidirect
121. C4⋊#95C22semidirect
124. C22⋊#95C22semidirect
125. C22⋊#95C22semidirect
126. C22⋊#95C22semidirect
127. C22⋊#95C22semidirect
161. C2×#124C2×C4semidirect
167. C2×#123C2×C4semidirect
170. C2×C22⋊Q8C2×C4semidirect
178. C2×#121C2×C4semidirect
179. C2×#121C2×C4semidirect
185. C2×#120C2×C4semidirect
189. C2×C4×D4C2×C4semidirect
209. C22×C22⋊C4C2×C4semidirect
469. C4×D4C22⋊C4semidirect
596. C2×C22⋊C4#41semidirect
919. C22×C4C2×C22⋊C4semidirect
948. C4⋊C4C2×C22⋊C4semidirect
982. C22⋊C4C2×C22⋊C4semidirect
990. C42C2×C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×#5462
C2×#23532
C2×#22902
#146982
#145062
#144482
#144182
#143582
#142902
#142882
#141692
#141522
#141362
#139962
#139952
#139592
#139562
#139032
#138682
#138672
#137852
#137752
C2×#14372