Finite Group Databasebeta

← #534718

Subgroups — #534718

Order 512.

4680 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#555C211yesmaximal, characteristic
2C2×#2363C211yesmaximal, characteristic, complemented
3C2×C4×#121C211yesmaximal, characteristic, complemented
4#14473C212yesmaximal, complemented
5#14363C212yesmaximal, complemented
6#14098C212yesmaximal, complemented
7#14098C212yesmaximal, complemented
8#14053C211yesmaximal, characteristic, complemented
9#14053C211yesmaximal, characteristic, complemented
10#14027C212yesmaximal, complemented
11#14023C212yesmaximal, complemented
12#13970C211yesmaximal, characteristic, complemented
13#13970C211yesmaximal, characteristic, complemented
14#13951C211yesmaximal, characteristic, complemented
15#13943C212yesmaximal, complemented
16#13939C211yesmaximal, characteristic, complemented
17#13916C211yesmaximal, characteristic, complemented
18#13871C211yesmaximal, characteristic, complemented
19D4×#95C211yesmaximal, characteristic, complemented
20#13801C211yesmaximal, characteristic, complemented
21#13799C212yesmaximal, complemented
22C4×#386C211yesmaximal, characteristic, complemented
23#13756C211yesmaximal, characteristic, complemented
24C2×#555—28no—
25C2×#555—28no—
26C2×#555C4116yescomplemented
27C22×C4⋊Q8C2211yescharacteristic
28C22×#124C2212yes—
29C22×#124C2212yes—
30C22×#121C2212yes—
31C22×#121C2211yescharacteristic
32C22×#121C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C22×C4×D4C2211yescharacteristic
35C22×C4×D4C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C22×C4×D4C2212yes—
38C22×#117C2211yescharacteristic
39C22×#117C2211yescharacteristic
40C22×#117C2212yes—
41C22×#117C2211yescharacteristic
42C23×C42C2211yescharacteristic
43#2363—28no—
44C4×#121—28no—
45C2×#391C2212yes—
46C2×#391C2212yes—
47C2×#390C2212yes—
48C2×#390C2211yescharacteristic
49C2×#390C2211yescharacteristic
50C2×#389C2211yescharacteristic
51C2×#389C2211yescharacteristic
52C2×#388C2212yes—
53C2×#388C2212yes—
54C2×#386C2211yescharacteristic
55C2×#386C2212yes—
56C2×#386C2212yes—
57C2×#386C2211yescharacteristic
58C2×#386C2212yes—
59C2×#386C2212yes—
60C2×#381C2212yes—
61C2×#380C2211yescharacteristic
62C2×#380C2211yescharacteristic
63C2×#380C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C4⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2212yes—
67C2×C4×C22⋊C4C2212yes—
68C2×C4×C22⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2211yescharacteristic
70C2×C4×C22⋊C4C2211yescharacteristic
71C22×#95C2212yes—
72#1446C2212yes—
73#1446C2212yes—
74#1441C2212yes—
75#1441C2212yes—
76#1440C2212yes—
77#1440C2212yes—
78#1440C2212yes—
79#1440C2212yes—
80#1440C2212yes—
81#1440C2212yes—
82#1440C2212yes—
83#1439C2212yes—
84#1439C2212yes—
85#1438C2212yes—
86#1438C2212yes—
87#1438C2212yes—
88#1437C2212yes—
89#1437C2211yescharacteristic
90#1437C2211yescharacteristic
91#1437C2212yes—
92#1437C2212yes—
93#1436C2212yes—
94#1436C2212yes—
95#1436C2211yescharacteristic
96#1436C2211yescharacteristic
97#1436C2212yes—
98C4⋊#95C2211yescharacteristic
99C4⋊#95C2211yescharacteristic
100C4⋊#95C2211yescharacteristic
101C4⋊#95C2211yescharacteristic
102C4⋊#95C2211yescharacteristic
103C4⋊#95C2211yescharacteristic
104C4⋊#95C2211yescharacteristic
105C4⋊#95C2212yes—
106C4⋊#95C2211yescharacteristic
107C4⋊#95C2211yescharacteristic
108C4⋊#95C2211yescharacteristic
109#1434C2212yes—
110#1434C2212yes—
111#1434C2212yes—
112#1434C2212yes—
113C22⋊#95C2212yes—
114C22⋊#95C2212yes—
115C22⋊#95C2212yes—
116C22⋊#95C2212yes—
117C22⋊#95C2212yes—
118C22⋊#95C2211yescharacteristic
119C22⋊#95C2212yes—
120C22⋊#95C2212yes—
121C22⋊#95C2212yes—
122C22⋊#95C2211yescharacteristic
123C4×#95C2212yes—
124C4×#95C2212yes—
125C4×#95C2211yescharacteristic
126C4×#95C2211yescharacteristic
127C4×#95C2212yes—
128C23×Q8C2312yes—
129C23×D4C2311yescharacteristic
130C23×D4C2311yescharacteristic
131C23×D4C2312yes—
132C23×D4C2312yes—
133C24×C4C2311yescharacteristic
134C24×C4C2311yescharacteristic
135C24×C4C2312yes—
136C24×C4C2312yes—
137C24×C4C2311yescharacteristic
138C24×C4C2311yescharacteristic
139C24×C4C2312yes—
140#555—2128no—
141C2×C4⋊Q8—24no—
142C2×C4⋊Q8—24no—
143C2×C4⋊Q8C2×C418yescomplemented
144C2×#124—28no—
145C2×#124—28no—
146C2×#124—28no—
147C2×#124—28no—
148C2×#124C2×C4116yescomplemented
149C2×#124C2×C4116yescomplemented
150C2×#121—24no—
151C2×#121—24no—
152C2×#121—28no—
153C2×#121—28no—
154C2×#121C2×C418yes—
155C2×#121C2×C418yescomplemented
156C2×#121C2×C4116yescomplemented
157C2×#121D418yes—
158C2×#121D418yes—
159C2×C4×D4—24no—
160C2×C4×D4—24no—
161C2×C4×D4—24no—
162C2×C4×D4—24no—
163C2×C4×D4—24no—
164C2×C4×D4—24no—
165C2×C4×D4—28no—
166C2×C4×D4—24no—
167C2×C4×D4—24no—
168C2×C4×D4—42no—
169C2×C4×D4—42no—
170C2×C4×D4—44no—
171C2×C4×D4—44no—
172C2×C4×D4C2×C418yescomplemented
173C2×C4×D4C2×C418yescomplemented
174C2×#117—24no—
175C2×#117—24no—
176C2×#117—24no—
177C2×#117—24no—
178C2×#117—24no—
179C2×#117—24no—
180C2×#117—28no—
181C2×#117—28no—
182C2×#117—42no—
183C2×#117C2×C418yescomplemented
184C2×#117C2×C418yescomplemented
185C2×#117C2×C4116yescomplemented
186C22×C4⋊C4C2311yescharacteristic
187C22×C4⋊C4C2311yescharacteristic
188C22×C4⋊C4C2311yescharacteristic
189C22×C4⋊C4C2312yes—
190C22×C4⋊C4C2311yescharacteristic
191C22×C4⋊C4C2311yescharacteristic
192C22×C4⋊C4C2311yescharacteristic
193C22×C4⋊C4C2312yes—
194C22×C4⋊C4C2311yescharacteristic
195C22×C4⋊C4C2312yes—
196C22×C4⋊C4C2311yescharacteristic
197C22×C22⋊C4C2311yescharacteristic
198C22×C22⋊C4C2312yes—
199C22×C22⋊C4C2312yes—
200C22×C22⋊C4C2312yes—
201C22×C22⋊C4C2312yes—
202C22×C22⋊C4C2312yes—
203C22×C22⋊C4C2312yes—
204C22×C22⋊C4C2311yescharacteristic
205C22×C22⋊C4C2311yescharacteristic
206C22×C22⋊C4C2311yescharacteristic
207C22×C22⋊C4C2311yescharacteristic
208C22×C22⋊C4C2312yes—
209C22×C22⋊C4C2312yes—
210C22×C22⋊C4C2312yes—
211C22×C22⋊C4C2311yescharacteristic
212C22×C22⋊C4C2312yes—
213C22×C22⋊C4C2311yescharacteristic
214C22×C22⋊C4C2312yes—
215C22×C22⋊C4C2312yes—
216C22×C22⋊C4C2312yes—
217C22×C22⋊C4C2311yescharacteristic
218C22×C22⋊C4C2312yes—
219C22×C22⋊C4C2312yes—
220C22×C42—24no—
221C22×C42—24no—
222C22×C42—42no—
223C22×C42C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C22×C42C2311yescharacteristic
226C22×C42C2311yescharacteristic
227C22×C42C2311yescharacteristic
228C22×C42C2312yes—
229C22×C42C2312yes—
230C22×C42C2312yes—
231C22×C42C2312yes—
232C22×C42C2311yescharacteristic
233C22×C42C2311yescharacteristic
234C22×C42C2312yes—
235#391—44no—
236#391—44no—
237#390—24no—
238#390—28no—
239#390—24no—
240#389—24no—
241#389—24no—
242#388—28no—
243#388—28no—
244#386—28no—
245#386—28no—
246#386—24no—
247#386—24no—
248#386—44no—
249#386—44no—
250#381—28no—
251#380—24no—
252#380—24no—
253#380—42no—
254C4×C4⋊C4—24no—
255C4×C4⋊C4—24no—
256C4×C22⋊C4—24no—
257C4×C22⋊C4—28no—
258C4×C22⋊C4—28no—
259C4×C22⋊C4—24no—
260C4×C22⋊C4—42no—
261C2×#95—28no—
262C2×#95C2311yescharacteristic
263C2×#95C2312yes—
264C2×#95C2311yescharacteristic
265C2×#95C2312yes—
266C2×#95C2311yescharacteristic
267C2×#95C2311yescharacteristic
268C2×#95C2312yes—
269C2×#95C2312yes—
270C2×#95C2312yes—
271C2×#95C2311yescharacteristic
272C2×#95C2312yes—
273C2×#95C2312yes—
274C2×#95C2311yescharacteristic
275C2×#95C2312yes—
276C2×#95C2312yes—
277C2×#95C2311yescharacteristic
278C2×#95C2312yes—
279C2×#95C2311yescharacteristic
280C2×#95C2312yes—
281C2×#95C2312yes—
282C2×#95C2312yes—
283C2×#95C2312yes—
284C2×#95C2312yes—
285C2×#95C2311yescharacteristic
286C2×#95C2312yes—
287C2×#95C2312yes—
288C2×#95C2312yes—
289C2×#95C2311yescharacteristic
290C2×#95C2311yescharacteristic
291C2×#95C2312yes—
292C2×#95C2312yes—
293C2×#95C2312yes—
294C2×#95C2312yes—
295C2×#95C2312yes—
296C2×#95C2312yes—
297C2×#95C2311yescharacteristic
298C2×#95C2312yes—
299C2×#95C2312yes—
300C2×#95C2312yes—
301C2×#95C2311yescharacteristic
302C2×#95C2311yescharacteristic
303C25C2411yescharacteristic
304C25C2412yes—
305C25C2411yescharacteristic
306C22×Q8—24no—
307C22×Q8—24no—
308C22×Q8—42no—
309C22×Q8—42no—
310C22×Q8—42no—
311C22×Q8—42no—
312C22×Q8C22×C418yes—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—24no—
316C22×D4—24no—
317C22×D4—22no—
318C22×D4—22no—
319C22×D4—22no—
320C22×D4—22no—
321C22×D4—22no—
322C22×D4—22no—
323C22×D4—42no—
324C22×D4—42no—
325C22×D4—42no—
326C22×D4—42no—
327C22×D4—41no—
328C22×D4—41no—
329C22×D4—42no—
330C22×D4—42no—
331C22×D4—42no—
332C22×D4—42no—
333C22×D4C22×C414yes—
334C22×D4C22×C414yes—
335C22×D4C22×C418yes—
336C22×D4C22×C418yes—
337C22×D4C2×D414yes—
338C22×D4C2×D414yes—
339C22×D4C2×D418yes—
340C22×D4C2×D418yes—
341C23×C4—22no—
342C23×C4—22no—
343C23×C4—22no—
344C23×C4—22no—
345C23×C4—24no—
346C23×C4—24no—
347C23×C4—22no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—24no—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—24no—
354C23×C4—22no—
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—22no—
358C23×C4—24no—
359C23×C4—22no—
360C23×C4—24no—
361C23×C4—22no—
362C23×C4—22no—
363C23×C4—22no—
364C23×C4—22no—
365C23×C4—24no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—41no—
371C23×C4—42no—
372C23×C4—42no—
373C23×C4—41no—
374C23×C4—41no—
375C23×C4—41no—
376C23×C4—41no—
377C23×C4—41no—
378C23×C4—42no—
379C23×C4—42no—
380C23×C4—42no—
381C23×C4—42no—
382C23×C4—42no—
383C23×C4—42no—
384C23×C4—42no—
385C23×C4C22×C414yes—
386C23×C4C22×C418yes—
387C23×C4C22×C414yes—
388C23×C4C2×D414yes—
389C23×C4C2×D414yes—
390C23×C4C2412yes—
391C23×C4C2411yescharacteristic
392C23×C4C2412yes—
393C23×C4C2411yescharacteristic
394C23×C4C2412yes—
395C23×C4C2411yescharacteristic
396C23×C4C2411yescharacteristic
397C23×C4C2412yes—
398C23×C4C2412yes—
399C23×C4C2411yescharacteristic
400C23×C4C2412yes—
401C23×C4C2411yescharacteristic
402C23×C4C2411yescharacteristic
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2412yes—
407C23×C4C2411yescharacteristic
408C23×C4C2411yescharacteristic
409C23×C4C2411yescharacteristic
410C4⋊Q8—232no—
411#124—264no—
412#124—264no—
413#121—232no—
414#121—264no—
415#121C22⋊C4164yescomplemented
416C4×D4—232no—
417C4×D4—232no—
418C4×D4—416no—
419C4×D4—416no—
420C4×D4—432no—
421#117—232no—
422#117—232no—
423#117—264no—
424#117—416no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—24no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—22no—
446C2×C4⋊C4—24no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—42no—
450C2×C4⋊C4C22×C414yes—
451C2×C4⋊C4C22×C414yes—
452C2×C4⋊C4C22×C414yes—
453C2×C4⋊C4C22×C418yes—
454C2×C4⋊C4C22×C414yes—
455C2×C4⋊C4C2×D414yes—
456C2×C4⋊C4C2×D414yes—
457C2×C4⋊C4#4114yes—
458C2×C22⋊C4—24no—
459C2×C22⋊C4—24no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—22no—
469C2×C22⋊C4—22no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—24no—
475C2×C22⋊C4—22no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—22no—
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—24no—
485C2×C22⋊C4—24no—
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—22no—
495C2×C22⋊C4—24no—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—41no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—41no—
502C2×C22⋊C4—41no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4—42no—
505C2×C22⋊C4—42no—
506C2×C22⋊C4—42no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—41no—
510C2×C22⋊C4—41no—
511C2×C22⋊C4—42no—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—42no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4C22×C418yes—
519C2×C22⋊C4C22×C418yes—
520C2×C22⋊C4C22×C418yes—
521C2×C22⋊C4C22×C414yes—
522C2×C22⋊C4C22×C418yes—
523C2×C22⋊C4C22×C414yes—
524C2×C22⋊C4C22×C418yes—
525C2×C22⋊C4C2×D418yes—
526C2×C22⋊C4C2×D418yes—
527C2×C42—24no—
528C2×C42—24no—
529C2×C42—24no—
530C2×C42—24no—
531C2×C42—22no—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535C2×C42—24no—
536C2×C42—24no—
537C2×C42—22no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541C2×C42—22no—
542C2×C42—24no—
543C2×C42—22no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—22no—
547C2×C42—22no—
548C2×C42—22no—
549C2×C42—24no—
550C2×C42—22no—
551C2×C42—22no—
552C2×C42—24no—
553C2×C42—416no—
554C2×C42—42no—
555C2×C42—42no—
556C2×C42—41no—
557C2×C42—41no—
558C2×C42—42no—
559C2×C42—42no—
560C2×C42C22×C418yes—
561C2×C42C22×C418yes—
562C2×C42C22×C414yes—
563C2×C42#4114yes—
564#95—22no—
565#95—24no—
566#95—24no—
567#95—24no—
568#95—22no—
569#95—24no—
570#95—24no—
571#95—24no—
572#95—24no—
573#95—24no—
574#95—22no—
575#95—22no—
576#95—24no—
577#95—24no—
578#95—24no—
579#95—24no—
580#95—22no—
581#95—22no—
582#95—24no—
583#95—24no—
584#95—22no—
585#95—22no—
586#95—42no—
587#95—42no—
588#95—42no—
589#95—42no—
590#95—42no—
591#95—42no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—42no—
597#95—42no—
598#95—42no—
599#95—42no—
600#95—42no—
601#95—42no—
602#95—42no—
603#95#4114yes—
604#95#4114yes—
605C24—21no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—21no—
610C24—21no—
611C24—21no—
612C24—22no—
613C24—22no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—22no—
618C24—22no—
619C24—21no—
620C24—22no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—21no—
625C24—22no—
626C24—21no—
627C24—21no—
628C24—22no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C23×C412yes—
644C24C23×C412yes—
645C24C23×C414yes—
646C24C22×D412yes—
647C24C22×D414yes—
648C24C22×D414yes—
649C24C22×D412yes—
650C24C2511yescharacteristic
651C2×Q8—216no—
652C2×Q8—48no—
653C2×Q8—48no—
654C2×Q8—84no—
655C2×Q8—84no—
656C2×Q8—84no—
657C2×Q8—84no—
658C2×D4—28no—
659C2×D4—216no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—48no—
668C2×D4—44no—
669C2×D4—48no—
670C2×D4—48no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—44no—
675C2×D4—44no—
676C2×D4—44no—
677C2×D4—44no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—84no—
681C2×D4—84no—
682C2×D4—84no—
683C2×D4—84no—
684C2×D4C2×C22⋊C4116yes—
685C2×D4C2×C22⋊C4132yes—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—28no—
703C22×C4—28no—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—28no—
708C22×C4—28no—
709C22×C4—216no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—22no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—22no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—22no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—28no—
771C22×C4—216no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—22no—
786C22×C4—21no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—21no—
793C22×C4—22no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—21no—
800C22×C4—22no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—22no—
804C22×C4—22no—
805C22×C4—21no—
806C22×C4—22no—
807C22×C4—22no—
808C22×C4—21no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—48no—
814C22×C4—44no—
815C22×C4—44no—
816C22×C4—44no—
817C22×C4—48no—
818C22×C4—48no—
819C22×C4—48no—
820C22×C4—48no—
821C22×C4—44no—
822C22×C4—44no—
823C22×C4—44no—
824C22×C4—44no—
825C22×C4—48no—
826C22×C4—48no—
827C22×C4—48no—
828C22×C4—48no—
829C22×C4—48no—
830C22×C4—44no—
831C22×C4—44no—
832C22×C4—44no—
833C22×C4—44no—
834C22×C4—44no—
835C22×C4—44no—
836C22×C4—44no—
837C22×C4—48no—
838C22×C4—84no—
839C22×C4—84no—
840C22×C4—84no—
841C22×C4—84no—
842C22×C4—84no—
843C22×C4—84no—
844C22×C4—84no—
845C22×C4C2×C22⋊C4116yes—
846C22×C4C23×C412yes—
847C22×C4C23×C414yes—
848C22×C4C23×C412yes—
849C22×C4C23×C414yes—
850C22×C4C23×C412yes—
851C22×C4C23×C414yes—
852C22×C4C23×C412yes—
853C22×C4C23×C412yes—
854C22×C4C22×D412yes—
855C22×C4C22×D412yes—
856C22×C4C22×D414yes—
857C22×C4C22×D414yes—
858C22×C4C22×D412yes—
859C22×C4C22×D412yes—
860C22×C4C2×#4112yes—
861C22×C4C2×#4112yes—
862C22×C4C2×#4112yes—
863C22×C4C2×#4112yes—
864C22×C4C2×#4114yes—
865C22×C4C2×#4112yes—
866C22×C4C2×#4112yes—
867C22×C4C2×#4112yes—
868C22×C4C2×#4112yes—
869C22×C4C2×#4112yes—
870C22×C4C2×#4112yes—
871C22×C4H(5,𝔽2)12yes—
872C22×C4H(5,𝔽2)12yes—
873C22×C4H(5,𝔽2)12yes—
874C22×C42−1+412yes—
875C4⋊C4—28no—
876C4⋊C4—28no—
877C4⋊C4—216no—
878C4⋊C4—28no—
879C4⋊C4—28no—
880C4⋊C4—48no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C4⋊C4—84no—
885C4⋊C4C2×C22⋊C4116yes—
886C22⋊C4—216no—
887C22⋊C4—216no—
888C22⋊C4—28no—
889C22⋊C4—216no—
890C22⋊C4—216no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—48no—
895C22⋊C4—44no—
896C22⋊C4—48no—
897C22⋊C4—44no—
898C22⋊C4—48no—
899C22⋊C4—48no—
900C22⋊C4—48no—
901C22⋊C4—48no—
902C22⋊C4—44no—
903C22⋊C4—48no—
904C22⋊C4—44no—
905C22⋊C4—84no—
906C22⋊C4—84no—
907C22⋊C4—84no—
908C22⋊C4C2×C22⋊C4132yes—
909C42—216no—
910C42—216no—
911C42—28no—
912C42—28no—
913C42—44no—
914C42—44no—
915C42—48no—
916C42—48no—
917C42—44no—
918C42—44no—
919C42—44no—
920C42—84no—
921C23—22no—
922C23—24no—
923C23—24no—
924C23—22no—
925C23—22no—
926C23—24no—
927C23—24no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—24no—
932C23—24no—
933C23—22no—
934C23—24no—
935C23—24no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—24no—
940C23—24no—
941C23—24no—
942C23—24no—
943C23—22no—
944C23—22no—
945C23—24no—
946C23—24no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—24no—
951C23—22no—
952C23—24no—
953C23—24no—
954C23—24no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—41no—
965C23—42no—
966C23—41no—
967C23—42no—
968C23—42no—
969C23—41no—
970C23—41no—
971C23—42no—
972C23—41no—
973C23—42no—
974C23—41no—
975C23—42no—
976C23—41no—
977C23—42no—
978C23—42no—
979C23—41no—
980C23—42no—
981C23—41no—
982C23—41no—
983C23—42no—
984C23—41no—
985C23—42no—
986C23—41no—
987C23—42no—
988C23—41no—
989C23—42no—
990C23—41no—
991C23—42no—
992C23—41no—
993C23—42no—
994C23—41no—
995C23—42no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23C22×C22⋊C414yes—
1025C23C22×C22⋊C418yes—
1026C23C24×C411yescharacteristic
1027C23C23×D411yescharacteristic
1028C23C23×D411yescharacteristic
1029C23C22×#4111yescharacteristic
1030C23C22×#4111yescharacteristic
1031C23C22×#4111yescharacteristic
1032C23C22×#4111yescharacteristic
1033C23C2×H(5,𝔽2)11yescharacteristic
1034C23C2×H(5,𝔽2)11yescharacteristic
1035C23C2×H(5,𝔽2)11yescharacteristic
1036C23C2×2−1+411yescharacteristic
1037C23#58511yescharacteristic
1038C23#58511yescharacteristic
1039C23#58511yescharacteristic
1040C23#58511yescharacteristic
1041Q8—816no—
1042D4—232no—
1043D4—432no—
1044D4—416no—
1045D4—816no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—24no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—22no—
1066C2×C4—24no—
1067C2×C4—24no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—232no—
1071C2×C4—22no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—24no—
1075C2×C4—22no—
1076C2×C4—24no—
1077C2×C4—22no—
1078C2×C4—24no—
1079C2×C4—24no—
1080C2×C4—24no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—24no—
1085C2×C4—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—22no—
1092C2×C4—24no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—24no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—432no—
1102C2×C4—416no—
1103C2×C4—416no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—42no—
1119C2×C4—41no—
1120C2×C4—42no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—42no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—42no—
1130C2×C4—41no—
1131C2×C4—42no—
1132C2×C4—42no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—42no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—416no—
1145C2×C4—41no—
1146C2×C4—42no—
1147C2×C4—42no—
1148C2×C4—41no—
1149C2×C4—42no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—41no—
1153C2×C4—42no—
1154C2×C4—42no—
1155C2×C4—41no—
1156C2×C4—42no—
1157C2×C4—42no—
1158C2×C4—41no—
1159C2×C4—42no—
1160C2×C4—42no—
1161C2×C4—42no—
1162C2×C4—41no—
1163C2×C4—42no—
1164C2×C4—41no—
1165C2×C4—42no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—42no—
1169C2×C4—42no—
1170C2×C4—42no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—41no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—42no—
1180C2×C4—816no—
1181C2×C4—816no—
1182C2×C4C22×C22⋊C414yes—
1183C2×C4C22×C22⋊C418yes—
1184C2×C4C22×C22⋊C414yes—
1185C2×C4C4×#4114yes—
1186C2×C4C4×#4114yes—
1187C2×C4#52014yes—
1188C2×C4#54614yes—
1189C2×C4#54614yes—
1190C2×C4#54714yes—
1191C2×C4#54714yes—
1192C2×C4#55514yescomplemented
1193C22—24no—
1194C22—28no—
1195C22—28no—
1196C22—24no—
1197C22—24no—
1198C22—28no—
1199C22—42no—
1200C22—44no—
1201C22—44no—
1202C22—42no—
1203C22—42no—
1204C22—44no—
1205C22—42no—
1206C22—44no—
1207C22—42no—
1208C22—44no—
1209C22—42no—
1210C22—44no—
1211C22—42no—
1212C22—44no—
1213C22—42no—
1214C22—44no—
1215C22—44no—
1216C22—42no—
1217C22—42no—
1218C22—44no—
1219C22—42no—
1220C22—44no—
1221C22—42no—
1222C22—44no—
1223C22—42no—
1224C22—42no—
1225C22—42no—
1226C22—42no—
1227C22—42no—
1228C22—42no—
1229C22—42no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22C23×C22⋊C411yescharacteristic
1239C22C2×C4×#4111yescharacteristic
1240C22C2×C4×#4111yescharacteristic
1241C22C2×#52011yescharacteristic
1242C22#342811yescharacteristic
1243C22C4×H(5,𝔽2)11yescharacteristic
1244C22C4×H(5,𝔽2)11yescharacteristic
1245C22C2×#54611yescharacteristic
1246C22C2×#54611yescharacteristic
1247C22C2×#54711yescharacteristic
1248C22C2×#54711yescharacteristic
1249C22D4×#4111yescharacteristic
1250C22D4×#4111yescharacteristic
1251C22D4×#4111yescharacteristic
1252C22D4×#4111yescharacteristic
1253C22C2×#55511yescharacteristic
1254C22#347511yescharacteristic
1255C22#347511yescharacteristic
1256C22#348311yescharacteristic
1257C22#348411yescharacteristic
1258C22#348511yescharacteristic
1259C22#349311yescharacteristic
1260C22#349411yescharacteristic
1261C22#349611yescharacteristic
1262C22#349611yescharacteristic
1263C22#350611yescharacteristic
1264C22#351111yescharacteristic
1265C22#351411yescharacteristic
1266C22#351811yescharacteristic
1267C22#351911yescharacteristic
1268C22#352411yescharacteristic
1269C22#354011yescharacteristic
1270C22#354211yescharacteristic
1271C22#354711yescharacteristic
1272C22#356511yescharacteristic
1273C4—24no—
1274C4—24no—
1275C4—24no—
1276C4—28no—
1277C4—42no—
1278C4—44no—
1279C4—42no—
1280C4—42no—
1281C4—42no—
1282C4—44no—
1283C4—42no—
1284C4—42no—
1285C4—44no—
1286C4—42no—
1287C4—81no—
1288C4—82no—
1289C4—81no—
1290C4—82no—
1291C4—82no—
1292C4#233918yes—
1293C2—44no—
1294C2—48no—
1295C2—82no—
1296C2C2×#233911yescharacteristic
1297C2C22⋊C4×#4111yescharacteristic
1298C2C4×#55511yescharacteristic
1299C2#3425611yescharacteristic
1300C2#3430611yescharacteristic
1301C2#3432111yescharacteristic
1302C2#3446711yescharacteristic
1303C2#5901811yescharacteristic
1304C2#5902611yescharacteristic
1305C2#5911511yescharacteristic
1306C2#5911911yescharacteristic
1307C2#5922911yescharacteristic
1308C2#5931511yescharacteristic
1309C2#5956811yescharacteristic
1310C2#5981011yescharacteristic
subgroupG/H
center, Frattini, socle, cosocleC24C25
commutatorC23C24×C4
prime radicalC22×#555C2
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×#2363C2semidirect
3. C2×C4×#121C2semidirect
4. #14473C2semidirect
5. #14363C2semidirect
6. #14098C2semidirect
7. #14098C2semidirect
8. #14053C2semidirect
9. #14053C2semidirect
10. #14027C2semidirect
11. #14023C2semidirect
12. #13970C2semidirect
13. #13970C2semidirect
14. #13951C2semidirect
15. #13943C2semidirect
16. #13939C2semidirect
17. #13916C2semidirect
18. #13871C2semidirect
19. D4×#95C2semidirect
20. #13801C2semidirect
21. #13799C2semidirect
22. C4×#386C2semidirect
23. #13756C2semidirect
26. C2×#555C4semidirect
143. C2×C4⋊Q8C2×C4semidirect
148. C2×#124C2×C4semidirect
149. C2×#124C2×C4semidirect
155. C2×#121C2×C4semidirect
156. C2×#121C2×C4semidirect
172. C2×C4×D4C2×C4semidirect
173. C2×C4×D4C2×C4semidirect
183. C2×#117C2×C4semidirect
184. C2×#117C2×C4semidirect
185. C2×#117C2×C4semidirect
415. #121C22⋊C4semidirect
1192. C2×C4#555semidirect

Maximal subgroups

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

subgroupindex
C22×#5552
C2×#23632
C2×C4×#1212
#144732
#143632
#140982
#140532
#140272
#140232
#139702
#139512
#139432
#139392
#139162
#138712
D4×#952
#138012
#137992
C4×#3862
#137562