Finite Group Databasebeta

← #734808

Subgroups — #734808

Order 512.

4258 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#554C211yesmaximal, characteristic, complemented
2C2×#2537C211yesmaximal, characteristic
3C2×#2562C211yesmaximal, characteristic, complemented
4C2×#2398C211yesmaximal, characteristic, complemented
5#16366C212yesmaximal, complemented
6#16253C212yesmaximal, complemented
7#15613C214yesmaximal, complemented
8#15275C214yesmaximal, complemented
9#15216C212yesmaximal, complemented
10#15125C212yesmaximal, complemented
11#14822C212yesmaximal, complemented
12#14719C212yesmaximal, complemented
13#14283C211yesmaximal, characteristic, complemented
14#13970C212yesmaximal, complemented
15#13970C212yesmaximal, complemented
16#13926C211yesmaximal, characteristic, complemented
17#13785C211yesmaximal, characteristic, complemented
18C2×#554—28no—
19C2×#554—28no—
20C2×#554—28no—
21C22×C4⋊Q8C2211yescharacteristic
22C22×#125C2211yescharacteristic
23C22×#125C2211yescharacteristic
24C22×C22⋊Q8C2212yes—
25C22×C22⋊Q8C2212yes—
26C22×C22⋊Q8C2212yes—
27C22×#121C2212yes—
28C22×#121C2212yes—
29C22×C4×Q8C2211yescharacteristic
30C22×C4×D4C2211yescharacteristic
31C22×C4×D4C2211yescharacteristic
32C22×C4×D4C2211yescharacteristic
33C22×C4×D4C2211yescharacteristic
34C23×C4⋊C4C2212yes—
35#2562—28no—
36#2537—28no—
37#2398—28no—
38C2×#400C2212yes—
39C2×#400C2211yescharacteristic
40C2×#400C2211yescharacteristic
41C2×#397C2212yes—
42C2×#394C2212yes—
43C2×#394C2214yes—
44C2×#394C2211yescharacteristic
45C2×#394C2211yescharacteristic
46C2×#393C2212yes—
47C2×#393C2214yes—
48C2×#391C2212yes—
49C2×#390C2212yes—
50C2×#388C2214yes—
51C2×#386C2214yes—
52C2×#386C2214yes—
53C2×#384C2211yescharacteristic
54C2×#380C2212yes—
55C2×#380C2212yes—
56C2×#380C2212yes—
57C2×#380C2212yes—
58C2×C4×C4⋊C4C2211yescharacteristic
59C2×C4×C22⋊C4C2212yes—
60C2×C4×C22⋊C4C2212yes—
61C2×#376C2211yescharacteristic
62#1446C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2212yes—
67#1441C2212yes—
68#1441C2212yes—
69#1441C2212yes—
70#1441C2214yes—
71#1440C2214yes—
72#1440C2214yes—
73#1439C2214yes—
74#1439C2214yes—
75#1439C2214yes—
76#1438C2214yes—
77#1438C2214yes—
78#1437C2214yes—
79C4⋊#95C2212yes—
80C4⋊#95C2212yes—
81C4⋊#95C2212yes—
82C4⋊#95C2212yes—
83C4⋊#95C2212yes—
84C4⋊#95C2212yes—
85C22⋊#95C2212yes—
86C22⋊#95C2212yes—
87C22⋊#95C2214yes—
88C22⋊#95C2214yes—
89C23×Q8C2311yescharacteristic
90C23×Q8C2312yes—
91C23×D4C2311yescharacteristic
92C23×D4C2314yes—
93C23×D4C2311yescharacteristic
94C24×C4C2312yes—
95C24×C4C2312yes—
96C24×C4C2312yes—
97C24×C4C2312yes—
98#554—2128no—
99C2×C4⋊Q8—24no—
100C2×C4⋊Q8—24no—
101C2×C4⋊Q8—24no—
102C2×#125—24no—
103C2×#125—24no—
104C2×#125—24no—
105C2×#125—24no—
106C2×#125—24no—
107C2×#125D418yescomplemented
108C2×C22⋊Q8—28no—
109C2×C22⋊Q8—28no—
110C2×C22⋊Q8—28no—
111C2×C22⋊Q8—28no—
112C2×C22⋊Q8—28no—
113C2×C22⋊Q8—28no—
114C2×C22⋊Q8—28no—
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—28no—
117C2×#121—28no—
118C2×#121—28no—
119C2×#121—28no—
120C2×#121—28no—
121C2×#121—48no—
122C2×C4×Q8—24no—
123C2×C4×Q8—24no—
124C2×C4×Q8D418yescomplemented
125C2×C4×D4—24no—
126C2×C4×D4—24no—
127C2×C4×D4—24no—
128C2×C4×D4—24no—
129C2×C4×D4—24no—
130C2×C4×D4—24no—
131C2×C4×D4—24no—
132C2×C4×D4—24no—
133C2×C4×D4—24no—
134C2×C4×D4—24no—
135C2×C4×D4—24no—
136C2×C4×D4D418yes—
137C22×C4⋊C4—28no—
138C22×C4⋊C4—28no—
139C22×C4⋊C4—28no—
140C22×C4⋊C4C2311yescharacteristic
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2312yes—
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2311yescharacteristic
147C22×C4⋊C4C2312yes—
148C22×C4⋊C4C2311yescharacteristic
149C22×C4⋊C4C2311yescharacteristic
150C22×C4⋊C4C2311yescharacteristic
151C22×C4⋊C4C2311yescharacteristic
152C22×C4⋊C4C2311yescharacteristic
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2312yes—
155C22×C4⋊C4C2312yes—
156C22×C22⋊C4C2312yes—
157C22×C22⋊C4C2312yes—
158C22×C22⋊C4C2314yes—
159C22×C22⋊C4C2312yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2314yes—
163C22×C22⋊C4C2314yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2312yes—
166C22×C22⋊C4C2312yes—
167C22×C22⋊C4C2314yes—
168C22×C22⋊C4C2314yes—
169C22×C22⋊C4C2314yes—
170C22×C42C2312yes—
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173C22×C42C2312yes—
174C22×C42C2311yescharacteristic
175#400—28no—
176#400—24no—
177#400—24no—
178#397—28no—
179#394—28no—
180#394—24no—
181#394—24no—
182#394—216no—
183#393—28no—
184#393—48no—
185#391—44no—
186#390—28no—
187#388—216no—
188#386—48no—
189#386—48no—
190#384—24no—
191#380—28no—
192#380—28no—
193#380—28no—
194#380—28no—
195C4×C4⋊C4—24no—
196C4×C22⋊C4—28no—
197C4×C22⋊C4—28no—
198#376—24no—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2311yescharacteristic
203C2×#95C2311yescharacteristic
204C2×#95C2312yes—
205C2×#95C2314yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2314yes—
209C2×#95C2314yes—
210C2×#95C2314yes—
211C2×#95C2314yes—
212C2×#95C2314yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C25C2412yes—
221C25C2412yes—
222C22×Q8—22no—
223C22×Q8—22no—
224C22×Q8—24no—
225C22×Q8—24no—
226C22×Q8—24no—
227C22×Q8—22no—
228C22×Q8—22no—
229C22×Q8—41no—
230C22×Q8—41no—
231C22×Q8—44no—
232C22×Q8—44no—
233C22×Q8C2×D414yes—
234C22×D4—24no—
235C22×D4—28no—
236C22×D4—28no—
237C22×D4—28no—
238C22×D4—28no—
239C22×D4—22no—
240C22×D4—22no—
241C22×D4—22no—
242C22×D4—22no—
243C22×D4—22no—
244C22×D4—24no—
245C22×D4—42no—
246C22×D4—44no—
247C22×D4—44no—
248C22×D4—44no—
249C22×D4C2×D414yes—
250C22×D4#4118yes—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—24no—
258C23×C4—24no—
259C23×C4—24no—
260C23×C4—24no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—24no—
265C23×C4—24no—
266C23×C4—24no—
267C23×C4—24no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—44no—
271C23×C4—44no—
272C23×C4—44no—
273C23×C4—44no—
274C23×C4C2×D418yes—
275C23×C4C2414yes—
276C23×C4C2412yes—
277C23×C4C2412yes—
278C23×C4C2412yes—
279C23×C4C2414yes—
280C23×C4C2411yescharacteristic
281C23×C4C2411yescharacteristic
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2411yescharacteristic
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C4⋊Q8—232no—
291#125—232no—
292#125—232no—
293C22⋊Q8—264no—
294C22⋊Q8—264no—
295C22⋊Q8—264no—
296#121—432no—
297#121—432no—
298C4×Q8—232no—
299C4×D4—232no—
300C4×D4—232no—
301C4×D4—232no—
302C4×D4—416no—
303C2×C4⋊C4—264no—
304C2×C4⋊C4—22no—
305C2×C4⋊C4—22no—
306C2×C4⋊C4—24no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4—24no—
311C2×C4⋊C4—24no—
312C2×C4⋊C4—24no—
313C2×C4⋊C4—24no—
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—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—24no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—22no—
330C2×C4⋊C4—22no—
331C2×C4⋊C4—22no—
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—44no—
341C2×C4⋊C4—42no—
342C2×C4⋊C4—42no—
343C2×C4⋊C4C2×D414yes—
344C2×C4⋊C4C2×D418yes—
345C2×C4⋊C4C2×D414yes—
346C2×C4⋊C4C2×D414yes—
347C2×C4⋊C4C2×D414yes—
348C2×C4⋊C4C2×D414yes—
349C2×C4⋊C4C2×D414yes—
350C2×C4⋊C4C2×D418yes—
351C2×C22⋊C4—24no—
352C2×C22⋊C4—24no—
353C2×C22⋊C4—24no—
354C2×C22⋊C4—24no—
355C2×C22⋊C4—24no—
356C2×C22⋊C4—24no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—28no—
360C2×C22⋊C4—28no—
361C2×C22⋊C4—28no—
362C2×C22⋊C4—28no—
363C2×C22⋊C4—24no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—24no—
366C2×C22⋊C4—24no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—28no—
375C2×C22⋊C4—24no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—28no—
378C2×C22⋊C4—28no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—44no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—44no—
386C2×C22⋊C4—44no—
387C2×C22⋊C4—44no—
388C2×C22⋊C4—44no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—44no—
391C2×C22⋊C4—44no—
392C2×C22⋊C4C2×D418yes—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42C2×D414yes—
404C2×C42C2×D414yes—
405C2×C42C2×D414yes—
406C2×C42C2×D414yes—
407C2×C42C2×D414yes—
408#95—24no—
409#95—22no—
410#95—22no—
411#95—24no—
412#95—24no—
413#95—24no—
414#95—24no—
415#95—24no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—28no—
420#95—44no—
421#95—44no—
422#95—44no—
423#95—44no—
424#95—44no—
425#95—44no—
426#95—44no—
427#95—44no—
428#95—44no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—24no—
433C24—22no—
434C24—24no—
435C24—22no—
436C24—24no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24C22×D414yes—
453C24C2×#4118yes—
454C24H(5,𝔽2)14yes—
455C24C2511yescharacteristic
456C2×Q8—216no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—44no—
460C2×Q8—44no—
461C2×Q8—44no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—84no—
465C2×Q8—84no—
466C2×Q8—88no—
467C2×Q8—88no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—216no—
472C2×D4—216no—
473C2×D4—48no—
474C2×D4—48no—
475C2×D4—44no—
476C2×D4—416no—
477C2×D4—416no—
478C2×D4—416no—
479C2×D4—416no—
480C2×D4—44no—
481C2×D4—88no—
482C2×D4—88no—
483C2×D4—88no—
484C2×D4#124116yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—216no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—24no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—24no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—24no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—22no—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—216no—
525C22×C4—216no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—22no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—24no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—24no—
547C22×C4—24no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—48no—
562C22×C4—48no—
563C22×C4—48no—
564C22×C4—48no—
565C22×C4—48no—
566C22×C4—48no—
567C22×C4—48no—
568C22×C4—48no—
569C22×C4—48no—
570C22×C4—48no—
571C22×C4—48no—
572C22×C4—48no—
573C22×C4—48no—
574C22×C4—48no—
575C22×C4—48no—
576C22×C4—88no—
577C22×C4—88no—
578C22×C4—88no—
579C22×C4—88no—
580C22×C4—84no—
581C22×C4—84no—
582C22×C4C22×D412yes—
583C22×C4C22×D412yes—
584C22×C4C22×D412yes—
585C22×C4C22×D414yes—
586C22×C4C22×D414yes—
587C22×C4C22×D414yes—
588C22×C4C22×D412yes—
589C22×C4C22×D412yes—
590C22×C4C22×D412yes—
591C22×C4C22×D412yes—
592C22×C4C22×D412yes—
593C22×C4C22×D412yes—
594C22×C4C22×D412yes—
595C22×C4C22×D412yes—
596C22×C4C22×D412yes—
597C22×C4C22×D412yes—
598C22×C4C2×#4114yes—
599C22×C4H(5,𝔽2)12yes—
600C22×C42−1+412yes—
601C22×C42−1+414yes—
602C4⋊C4—216no—
603C4⋊C4—216no—
604C4⋊C4—216no—
605C4⋊C4—28no—
606C4⋊C4—216no—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—216no—
613C4⋊C4—48no—
614C4⋊C4—44no—
615C4⋊C4—48no—
616C4⋊C4—48no—
617C4⋊C4—84no—
618C22⋊C4—216no—
619C22⋊C4—216no—
620C22⋊C4—216no—
621C22⋊C4—48no—
622C22⋊C4—416no—
623C22⋊C4—48no—
624C22⋊C4—416no—
625C22⋊C4—48no—
626C22⋊C4—416no—
627C22⋊C4—48no—
628C22⋊C4—48no—
629C22⋊C4—88no—
630C22⋊C4—88no—
631C22⋊C4—88no—
632C42—28no—
633C42—28no—
634C42—48no—
635C42—84no—
636C42#120116yes—
637C23—24no—
638C23—24no—
639C23—28no—
640C23—28no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—28no—
646C23—28no—
647C23—28no—
648C23—28no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—44no—
660C23—44no—
661C23—42no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—42no—
693C23—42no—
694C23C2×#12418yes—
695C23C23×D411yescharacteristic
696C23C23×D411yescharacteristic
697C23C23×D411yescharacteristic
698C23C22×#4112yes—
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)12yes—
701C23C2×2−1+412yes—
702C23C2×2−1+411yescharacteristic
703C23#58511yescharacteristic
704C23#58511yescharacteristic
705C23#58512yes—
706Q8—416no—
707Q8—816no—
708D4—232no—
709D4—416no—
710D4—832no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—28no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—432no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—44no—
754C2×C4—44no—
755C2×C4—44no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—44no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—44no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—44no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—44no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—42no—
790C2×C4—44no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—44no—
794C2×C4—42no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—816no—
798C2×C4—816no—
799C2×C4—816no—
800C2×C4C2×#12014yes—
801C2×C4C2×#12014yes—
802C2×C4C2×#12014yes—
803C2×C4C2×#12414yes—
804C2×C4#53614yes—
805C2×C4#53714yes—
806C2×C4#54818yes—
807C2×C4#54818yes—
808C22—28no—
809C22—28no—
810C22—28no—
811C22—48no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22—48no—
816C22—48no—
817C22—44no—
818C22—48no—
819C22—44no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—82no—
827C22—82no—
828C22—82no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—82no—
833C22—82no—
834C22C22×#12011yescharacteristic
835C22C22×#12411yescharacteristic
836C22C2×#53611yescharacteristic
837C22C2×#53711yescharacteristic
838C22#344911yescharacteristic
839C22C2×#54812yes—
840C22C2×#54812yes—
841C22#348411yescharacteristic
842C22#348511yescharacteristic
843C22#348812yes—
844C22#348811yescharacteristic
845C22#348811yescharacteristic
846C22#348812yes—
847C22#348911yescharacteristic
848C22#348911yescharacteristic
849C22#351312yes—
850C22#351512yes—
851C22#351912yes—
852C22#352112yes—
853C22#354412yes—
854C22#354712yes—
855C22#355912yes—
856C22#356512yes—
857C4—24no—
858C4—24no—
859C4—24no—
860C4—44no—
861C4—42no—
862C4—42no—
863C4—44no—
864C4—44no—
865C4—42no—
866C4—84no—
867C4—82no—
868C4—82no—
869C4—82no—
870C4—84no—
871C4#243618yes—
872C2—48no—
873C2—84no—
874C2C2×#243611yescharacteristic
875C2#3525111yescharacteristic
876C2#3551211yescharacteristic
877C2#3590311yescharacteristic
878C2#3604211yescharacteristic
879C2#3911812yes—
880C2#3912612yes—
881C2#4248211yescharacteristic
882C2#4268111yescharacteristic
883C2#4504212yes—
884C2#4507112yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC2×#2537C2
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×#554C2semidirect
3. C2×#2562C2semidirect
4. C2×#2398C2semidirect
5. #16366C2semidirect
6. #16253C2semidirect
7. #15613C2semidirect
8. #15275C2semidirect
9. #15216C2semidirect
10. #15125C2semidirect
11. #14822C2semidirect
12. #14719C2semidirect
13. #14283C2semidirect
14. #13970C2semidirect
15. #13970C2semidirect
16. #13926C2semidirect
17. #13785C2semidirect
107. C2×#125D4semidirect
124. C2×C4×Q8D4semidirect

Maximal subgroups

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

subgroupindex
C22×#5542
C2×#25372
C2×#25622
C2×#23982
#163662
#162532
#156132
#152752
#152162
#151252
#148222
#147192
#142832
#139702
#139262
#137852