Finite Group Databasebeta

← #764795

Subgroups — #764795

Order 512.

3812 conjugacy classes of subgroups.

The subgroup lattice has 903 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#541C211yesmaximal, characteristic, complemented
2C2×#2547C211yesmaximal, characteristic, complemented
3C2×#2566C211yesmaximal, characteristic, complemented
4C2×#2324C211yesmaximal, characteristic
5#16004C214yesmaximal, complemented
6#15996C214yesmaximal, complemented
7#15913C214yesmaximal, complemented
8#15880C214yesmaximal, complemented
9#15236C211yesmaximal, characteristic, complemented
10#15215C211yesmaximal, characteristic
11#15215C211yesmaximal, characteristic
12#15182C211yesmaximal, characteristic, complemented
13#14160C211yesmaximal, characteristic, complemented
14#14155C211yesmaximal, characteristic, complemented
15#14026C211yesmaximal, characteristic, complemented
16#14026C211yesmaximal, characteristic, complemented
17#13978C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19#13852C211yesmaximal, characteristic, complemented
20C2×#541—28no—
21C2×#541—28no—
22C2×#541—28no—
23C22×C4⋊Q8C2211yescharacteristic
24C22×#126C2212yes—
25C22×#126C2212yes—
26C22×#125C2212yes—
27C22×#125C2212yes—
28C22×#125C2211yescharacteristic
29C22×#124C2211yescharacteristic
30C22×#124C2211yescharacteristic
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×C4×Q8C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C22×C4×D4C2211yescharacteristic
37C22×#117C2211yescharacteristic
38#2566—28no—
39#2547—28no—
40C2×#397C2214yes—
41C2×#396C2214yes—
42#2324—28no—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#390C2212yes—
50C2×#390C2211yescharacteristic
51C2×#390C2211yescharacteristic
52C2×#390C2211yescharacteristic
53C2×#389C2211yescharacteristic
54C2×#388C2212yes—
55C2×#386C2212yes—
56C2×#385C2212yes—
57C2×#385C2214yes—
58C2×#384C2211yescharacteristic
59C2×#382C2211yescharacteristic
60C2×#380C2211yescharacteristic
61C2×#380C2214yes—
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C4⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67#1445C2214yes—
68#1444C2214yes—
69#1442C2214yes—
70#1442C2214yes—
71#1441C2212yes—
72#1441C2214yes—
73#1441C2212yes—
74#1441C2214yes—
75#1440C2214yes—
76#1439C2214yes—
77#1439C2214yes—
78#1439C2214yes—
79#1439C2212yes—
80#1439C2212yes—
81#1439C2214yes—
82#1439C2214yes—
83#1438C2214yes—
84#1438C2214yes—
85#1437C2214yes—
86#1437C2214yes—
87#1436C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2211yescharacteristic
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94C4⋊#95C2211yescharacteristic
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8C2311yescharacteristic
98C23×Q8C2311yescharacteristic
99C23×D4C2311yescharacteristic
100C23×D4C2312yes—
101C24×C4C2311yescharacteristic
102C24×C4C2312yes—
103#541—2128no—
104C2×C4⋊Q8—24no—
105C2×C4⋊Q8—24no—
106C2×C4⋊Q8D418yescomplemented
107C2×#126—28no—
108C2×#126—28no—
109C2×#126—28no—
110C2×#126—28no—
111C2×#126—28no—
112C2×#126—28no—
113C2×#125—28no—
114C2×#125—28no—
115C2×#125—28no—
116C2×#125—28no—
117C2×#125—28no—
118C2×#125—28no—
119C2×#125—24no—
120C2×#125—24no—
121C2×#125D418yescomplemented
122C2×#124—24no—
123C2×#124—24no—
124C2×#124—24no—
125C2×#124—24no—
126C2×#124—42no—
127C2×#124—42no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—24no—
132C2×C22⋊Q8—24no—
133C2×C22⋊Q8—24no—
134C2×#121—24no—
135C2×#121—24no—
136C2×#121—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—24no—
139C2×C4×Q8—24no—
140C2×C4×Q8—24no—
141C2×C4×Q8—24no—
142C2×C4×Q8—24no—
143C2×C4×D4—24no—
144C2×C4×D4—24no—
145C2×C4×D4—24no—
146C2×#117—24no—
147C2×#117—24no—
148C2×#117D418yes—
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2311yescharacteristic
155C22×C4⋊C4C2312yes—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2312yes—
163C22×C4⋊C4C2312yes—
164C22×C4⋊C4C2311yescharacteristic
165C22×C4⋊C4C2314yes—
166C22×C4⋊C4C2312yes—
167C22×C4⋊C4C2312yes—
168C22×C22⋊C4C2312yes—
169C22×C22⋊C4C2312yes—
170C22×C22⋊C4C2312yes—
171C22×C22⋊C4C2312yes—
172C22×C22⋊C4C2314yes—
173C22×C22⋊C4C2314yes—
174C22×C22⋊C4C2314yes—
175C22×C22⋊C4C2311yescharacteristic
176C22×C22⋊C4C2311yescharacteristic
177C22×C22⋊C4C2314yes—
178C22×C22⋊C4C2312yes—
179C22×C22⋊C4C2312yes—
180C22×C22⋊C4C2312yes—
181C22×C22⋊C4C2312yes—
182C22×C22⋊C4C2312yes—
183C22×C42C2312yes—
184C22×C42C2312yes—
185C22×C42C2311yescharacteristic
186C22×C42C2311yescharacteristic
187C22×C42C2311yescharacteristic
188C22×C42C2311yescharacteristic
189C22×C42C2311yescharacteristic
190C22×C42C2312yes—
191C22×C42C2311yescharacteristic
192#397—216no—
193#396—216no—
194#391—24no—
195#391—24no—
196#391—24no—
197#391—24no—
198#391—42no—
199#391—42no—
200#390—24no—
201#390—24no—
202#390—28no—
203#390—24no—
204#389—24no—
205#388—28no—
206#386—28no—
207#385—216no—
208#385—28no—
209#384—24no—
210#382—24no—
211#380—24no—
212#380—216no—
213C4×C4⋊C4—24no—
214C4×C4⋊C4—24no—
215C4×C4⋊C4—24no—
216C4×C22⋊C4—42no—
217C4×C22⋊C4—42no—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2314yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2312yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2314yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2314yes—
238C2×#95C2312yes—
239C2×#95C2312yes—
240C25C2411yescharacteristic
241C25C2412yes—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8C2×D414yes—
255C22×Q8C2×D414yes—
256C22×D4—24no—
257C22×D4—24no—
258C22×D4—22no—
259C22×D4—22no—
260C22×D4—22no—
261C22×D4—22no—
262C22×D4—24no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—44no—
266C22×D4—44no—
267C22×D4#4114yes—
268C23×C4—22no—
269C23×C4—22no—
270C23×C4—22no—
271C23×C4—22no—
272C23×C4—22no—
273C23×C4—22no—
274C23×C4—24no—
275C23×C4—24no—
276C23×C4—24no—
277C23×C4—44no—
278C23×C4—44no—
279C23×C4C2×D414yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2412yes—
289C23×C4C2412yes—
290C23×C4C2411yescharacteristic
291C23×C4C2411yescharacteristic
292C23×C4C2412yes—
293C23×C4C2412yes—
294C23×C4C2411yescharacteristic
295C23×C4C2411yescharacteristic
296C23×C4C2411yescharacteristic
297C4⋊Q8—232no—
298#126—264no—
299#126—264no—
300#125—264no—
301#125—264no—
302#125—232no—
303#124—416no—
304#124—416no—
305C22⋊Q8—232no—
306C22⋊Q8—232no—
307#121—232no—
308C4×Q8—232no—
309C4×Q8—232no—
310C4×D4—416no—
311#117—232no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—22no—
317C2×C4⋊C4—22no—
318C2×C4⋊C4—22no—
319C2×C4⋊C4—22no—
320C2×C4⋊C4—24no—
321C2×C4⋊C4—24no—
322C2×C4⋊C4—24no—
323C2×C4⋊C4—24no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—24no—
331C2×C4⋊C4—24no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—22no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—44no—
357C2×C4⋊C4—44no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4C2×D414yes—
360C2×C4⋊C4C2×D414yes—
361C2×C4⋊C4C2×D414yes—
362C2×C4⋊C4C2×D414yes—
363C2×C4⋊C4C2×D418yes—
364C2×C4⋊C4C2×D418yes—
365C2×C4⋊C4C2×D418yes—
366C2×C4⋊C4C2×D418yes—
367C2×C4⋊C4#4114yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—28no—
382C2×C22⋊C4—28no—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—28no—
387C2×C22⋊C4—28no—
388C2×C22⋊C4—28no—
389C2×C22⋊C4—28no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—44no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—42no—
399C2×C22⋊C4—44no—
400C2×C22⋊C4—44no—
401C2×C22⋊C4—42no—
402C2×C22⋊C4—42no—
403C2×C22⋊C4—44no—
404C2×C22⋊C4—44no—
405C2×C22⋊C4—44no—
406C2×C22⋊C4—44no—
407C2×C22⋊C4—44no—
408C2×C22⋊C4C2×D414yes—
409C2×C22⋊C4C2×D414yes—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—24no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—22no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—22no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—44no—
432C2×C42C2×D414yes—
433C2×C42C2×D414yes—
434C2×C42C2×D414yes—
435C2×C42C2×D414yes—
436#95—24no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—28no—
441#95—28no—
442#95—28no—
443#95—24no—
444#95—28no—
445#95—28no—
446#95—24no—
447#95—44no—
448#95—44no—
449#95—42no—
450#95—42no—
451#95—44no—
452#95—44no—
453#95—42no—
454#95—42no—
455#95—42no—
456#95—44no—
457#95—44no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—22no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—24no—
470C24—21no—
471C24—22no—
472C24—22no—
473C24—24no—
474C24—24no—
475C24—24no—
476C24—22no—
477C24—22no—
478C24C22×D412yes—
479C24C2×#4114yes—
480C24C2511yescharacteristic
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—28no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×D4—216no—
496C2×D4—28no—
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—88no—
504C2×D4—84no—
505C2×D4—84no—
506C2×D4—88no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—24no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—24no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—28no—
556C22×C4—28no—
557C22×C4—28no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—24no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—24no—
588C22×C4—24no—
589C22×C4—416no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—84no—
596C22×C4—88no—
597C22×C4—84no—
598C22×C4C22×D412yes—
599C22×C4C22×D414yes—
600C22×C4C22×D414yes—
601C22×C4C22×D414yes—
602C22×C4C22×D412yes—
603C22×C4C22×D412yes—
604C22×C4C22×D414yes—
605C22×C4C22×D412yes—
606C22×C4C22×D412yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D412yes—
610C22×C4C22×D412yes—
611C22×C4C22×D412yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C2×#4114yes—
615C22×C4C2×#4112yes—
616C22×C4C2×#4112yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C42−1+414yes—
619C22×C42−1+412yes—
620C4⋊C4—216no—
621C4⋊C4—216no—
622C4⋊C4—216no—
623C4⋊C4—216no—
624C4⋊C4—28no—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—216no—
629C4⋊C4—216no—
630C4⋊C4—216no—
631C4⋊C4—216no—
632C4⋊C4—28no—
633C4⋊C4—48no—
634C4⋊C4—48no—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—88no—
638C4⋊C4—84no—
639C22⋊C4—216no—
640C22⋊C4—216no—
641C22⋊C4—216no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—416no—
645C22⋊C4—416no—
646C22⋊C4—416no—
647C22⋊C4—48no—
648C22⋊C4—48no—
649C22⋊C4—48no—
650C22⋊C4—84no—
651C22⋊C4—84no—
652C22⋊C4—88no—
653C22⋊C4—84no—
654C42—216no—
655C42—216no—
656C42—28no—
657C42—44no—
658C42—44no—
659C42—44no—
660C42—44no—
661C42—84no—
662C42#120116yes—
663C23—22no—
664C23—24no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—28no—
674C23—28no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—41no—
681C23—41no—
682C23—42no—
683C23—44no—
684C23—42no—
685C23—44no—
686C23—42no—
687C23—42no—
688C23—44no—
689C23—42no—
690C23—42no—
691C23—44no—
692C23—42no—
693C23—42no—
694C23—42no—
695C23—42no—
696C23—44no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—44no—
701C23—42no—
702C23—44no—
703C23—42no—
704C23—44no—
705C23—42no—
706C23—44no—
707C23—42no—
708C23—44no—
709C23C23×D411yescharacteristic
710C23C23×D411yescharacteristic
711C23C23×D411yescharacteristic
712C23C22×#4111yescharacteristic
713C23C22×#4111yescharacteristic
714C23C2×H(5,𝔽2)11yescharacteristic
715C23C2×2−1+411yescharacteristic
716C23C2×2−1+412yes—
717C23#58512yes—
718C23#58512yes—
719C23#58512yes—
720Q8—416no—
721Q8—416no—
722D4—416no—
723D4—816no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—24no—
747C2×C4—28no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—28no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—24no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—44no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—416no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—44no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—44no—
817C2×C4—816no—
818C2×C4C2×#12014yes—
819C2×C4C2×#12014yes—
820C2×C4C2×#12014yes—
821C2×C4#52514yes—
822C2×C4#53714yes—
823C2×C4#54614yes—
824C2×C4#54714yes—
825C2×C4#54814yes—
826C2×C4#55014yes—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—44no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—48no—
836C22—42no—
837C22—44no—
838C22—48no—
839C22—82no—
840C22—82no—
841C22—82no—
842C22—82no—
843C22—82no—
844C22—82no—
845C22—84no—
846C22—82no—
847C22—84no—
848C22—82no—
849C22C22×#12011yescharacteristic
850C22C2×#52511yescharacteristic
851C22C2×#53711yescharacteristic
852C22C2×#54611yescharacteristic
853C22C2×#54711yescharacteristic
854C22C2×#54811yescharacteristic
855C22C2×#55011yescharacteristic
856C22#348712yes—
857C22#348912yes—
858C22#349712yes—
859C22#349911yescharacteristic
860C22#350011yescharacteristic
861C22#350011yescharacteristic
862C22#350011yescharacteristic
863C22#350012yes—
864C22#351512yes—
865C22#351612yes—
866C22#352112yes—
867C22#352112yes—
868C22#353912yes—
869C22#354112yes—
870C22#355512yes—
871C22#355712yes—
872C4—24no—
873C4—24no—
874C4—44no—
875C4—42no—
876C4—44no—
877C4—42no—
878C4—44no—
879C4—44no—
880C4—42no—
881C4—44no—
882C4—44no—
883C4—82no—
884C4—82no—
885C4—82no—
886C4—82no—
887C4—82no—
888C4#240718yes—
889C2—82no—
890C2—84no—
891C2C2×#240711yescharacteristic
892C2#3562211yescharacteristic
893C2#3562411yescharacteristic
894C2#3566011yescharacteristic
895C2#3567611yescharacteristic
896C2#3738911yescharacteristic
897C2#3742011yescharacteristic
898C2#4519512yes—
899C2#4519612yes—
900C2#4524212yes—
901C2#4524312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC22×#121C22
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×#541C2semidirect
2. C2×#2547C2semidirect
3. C2×#2566C2semidirect
5. #16004C2semidirect
6. #15996C2semidirect
7. #15913C2semidirect
8. #15880C2semidirect
9. #15236C2semidirect
12. #15182C2semidirect
13. #14160C2semidirect
14. #14155C2semidirect
15. #14026C2semidirect
16. #14026C2semidirect
17. #13978C2semidirect
18. #13976C2semidirect
19. #13852C2semidirect
106. C2×C4⋊Q8D4semidirect
121. C2×#125D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5412
C2×#25472
C2×#25662
C2×#23242
#160042
#159962
#159132
#158802
#152362
#152152
#151822
#141602
#141552
#140262
#139782
#139762
#138522