Finite Group Databasebeta

← #649268

Subgroups — #649268

Order 512.

3698 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
1C2×#2546C211yesmaximal, characteristic, complemented
2C2×#2429C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic
5C2×Q8×C22⋊C4C211yesmaximal, characteristic
6C2×C4×C4⋊Q8C211yesmaximal, characteristic, complemented
7#15623C214yesmaximal, complemented
8#15305C214yesmaximal
9#15190C211yesmaximal, characteristic, complemented
10#15184C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic
12#15182C211yesmaximal, characteristic
13#14816C214yesmaximal, complemented
14#14714C211yesmaximal, characteristic, complemented
15#14112C214yesmaximal
16#14024C211yesmaximal, characteristic, complemented
17#14024C211yesmaximal, characteristic, complemented
18#13976C211yesmaximal, characteristic, complemented
19C4×#388C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C22⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31#2546—28no—
32#2434—28no—
33#2434—28no—
34#2429—28no—
35C2×#398C2212yes—
36C2×#398C2214yes—
37C2×#396C2212yes—
38C2×#395C2214yes—
39C2×#395C2214yes—
40Q8×C22⋊C4—28no—
41C4×C4⋊Q8—28no—
42C2×#391C2212yes—
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2212yes—
46C2×#391C2211yescharacteristic
47C2×#391C2211yescharacteristic
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#391C2211yescharacteristic
55C2×#389C2214yes—
56C2×#389C2214yes—
57C2×#389C2211yescharacteristic
58C2×#389C2212yes—
59C2×#388C2212yes—
60C2×#388C2212yes—
61C2×#385C2214yes—
62C2×#385C2214yes—
63C2×#384C2211yescharacteristic
64C2×#384C2211yescharacteristic
65C2×#380C2211yescharacteristic
66C2×#380C2212yes—
67C2×C4×C4⋊C4C2214yes—
68C2×C4×C4⋊C4C2211yescharacteristic
69C2×C4×C22⋊C4C2212yes—
70C2×C4×C22⋊C4C2211yescharacteristic
71C2×C4×C22⋊C4C2211yescharacteristic
72C2×C4×C22⋊C4C2211yescharacteristic
73C2×C43C2211yescharacteristic
74#1444C2214yes—
75#1444C2214yes—
76#1444C2214yes—
77#1441C2214yes—
78#1441C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1441C2214yes—
82#1441C2214yes—
83#1439C2214yes—
84#1439C2214yes—
85#1437C2212yes—
86#1436C2212yes—
87#1436C2214yes—
88#1436C2214yes—
89#1436C2214yes—
90C4⋊#95C2214yes—
91C4⋊#95C2214yes—
92C4⋊#95C2211yescharacteristic
93C4⋊#95C2211yescharacteristic
94#1434C2212yes—
95C4×#95C2211yescharacteristic
96C4×#95C2211yescharacteristic
97C23×Q8—24no—
98C23×Q8—24no—
99C23×Q8—24no—
100C23×Q8—24no—
101C23×Q8—24no—
102C23×Q8—42no—
103C23×Q8—42no—
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2311yescharacteristic
107C23×Q8C2312yes—
108C23×Q8C2311yescharacteristic
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—24no—
115C2×C4⋊Q8—24no—
116C2×C4⋊Q8—24no—
117C2×C4⋊Q8—24no—
118C2×C4⋊Q8—24no—
119C2×C4⋊Q8—24no—
120C2×C4⋊Q8—24no—
121C2×C4⋊Q8—24no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8D418yes—
126C2×C22⋊Q8—24no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—42no—
131C2×C22⋊Q8—42no—
132C2×C4×Q8—24no—
133C2×C4×Q8—24no—
134C2×C4×Q8—24no—
135C2×C4×Q8—24no—
136C2×C4×Q8—24no—
137C2×C4×Q8—24no—
138C2×C4×Q8—42no—
139C2×C4×Q8—42no—
140C2×C4×Q8—42no—
141C22×C4⋊C4C2314yes—
142C22×C4⋊C4C2311yescharacteristic
143C22×C4⋊C4C2311yescharacteristic
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2312yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C4⋊C4C2312yes—
151C22×C4⋊C4C2312yes—
152C22×C4⋊C4C2312yes—
153C22×C4⋊C4C2312yes—
154C22×C4⋊C4C2314yes—
155C22×C4⋊C4C2314yes—
156C22×C4⋊C4C2311yescharacteristic
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2312yes—
159C22×C4⋊C4C2314yes—
160C22×C22⋊C4C2312yes—
161C22×C22⋊C4C2312yes—
162C22×C22⋊C4C2312yes—
163C22×C22⋊C4C2312yes—
164C22×C22⋊C4C2312yes—
165C22×C22⋊C4C2311yescharacteristic
166C22×C22⋊C4C2311yescharacteristic
167C22×C42C2311yescharacteristic
168C22×C42C2311yescharacteristic
169C22×C42C2312yes—
170C22×C42C2312yes—
171C22×C42C2312yes—
172C22×C42C2312yes—
173C22×C42C2311yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2312yes—
178#398—216no—
179#398—28no—
180#396—28no—
181#395—216no—
182#395—216no—
183#391—24no—
184#391—24no—
185#391—24no—
186#391—24no—
187#391—24no—
188#391—24no—
189#391—24no—
190#391—24no—
191#391—24no—
192#391—28no—
193#391—28no—
194#391—42no—
195#391D418yes—
196#389—216no—
197#389—24no—
198#389—216no—
199#389—28no—
200#388—28no—
201#388Q8116yescomplemented
202#385—216no—
203#385—216no—
204#384—24no—
205#384—42no—
206#380—24no—
207#380—28no—
208C4×C4⋊C4—24no—
209C4×C4⋊C4—216no—
210C4×C22⋊C4—28no—
211C4×C22⋊C4—24no—
212C4×C22⋊C4—24no—
213C4×C22⋊C4D418yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2314yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2312yes—
220C2×#95C2312yes—
221C2×#95C2314yes—
222C2×#95C2312yes—
223C2×#95C2314yes—
224C2×#95C2312yes—
225C2×#95C2312yes—
226C2×#95C2312yes—
227C2×#95C2312yes—
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C2×#95C2312yes—
232C2×#95C2312yes—
233C2×#95C2314yes—
234C2×#95C2314yes—
235C2×#95C2314yes—
236C2×#95C2314yes—
237C2×#95C2311yescharacteristic
238C2×#95C2311yescharacteristic
239C2×#95C2312yes—
240C2×#95C2312yes—
241C43—24no—
242C25C2411yescharacteristic
243C22×Q8—232no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—22no—
248C22×Q8—22no—
249C22×Q8—24no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—24no—
255C22×Q8—24no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—24no—
260C22×Q8—24no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—22no—
265C22×Q8—22no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—22no—
269C22×Q8—22no—
270C22×Q8—22no—
271C22×Q8—22no—
272C22×Q8—42no—
273C22×Q8—42no—
274C22×Q8—416no—
275C22×Q8—416no—
276C22×Q8—416no—
277C22×Q8—416no—
278C22×Q8—416no—
279C22×Q8—416no—
280C22×Q8C2×D414yes—
281C22×Q8C2×D414yes—
282C22×Q8C2×D414yes—
283C22×Q8#4114yes—
284C22×Q8#4114yes—
285C23×C4—24no—
286C23×C4—22no—
287C23×C4—22no—
288C23×C4—24no—
289C23×C4—24no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—24no—
295C23×C4—24no—
296C23×C4—42no—
297C23×C4—42no—
298C23×C4C2×D414yes—
299C23×C4C2412yes—
300C23×C4C2412yes—
301C23×C4C2412yes—
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2411yescharacteristic
305C23×C4C2412yes—
306C23×C4C2411yescharacteristic
307C23×C4C2411yescharacteristic
308C23×C4C2412yes—
309C23×C4C2412yes—
310C23×C4C2412yes—
311C23×C4C2412yes—
312C23×C4C2411yescharacteristic
313C23×C4C2411yescharacteristic
314C23×C4C2412yes—
315C23×C4C2412yes—
316C23×C4C2411yescharacteristic
317C4⋊Q8—232no—
318C4⋊Q8—416no—
319C4⋊Q8—416no—
320C4⋊Q8—416no—
321C4⋊Q8—416no—
322C22⋊Q8—416no—
323C22⋊Q8—416no—
324C4×Q8—416no—
325C4×Q8—416no—
326C4×Q8—416no—
327C2×C4⋊C4—22no—
328C2×C4⋊C4—28no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—22no—
332C2×C4⋊C4—24no—
333C2×C4⋊C4—24no—
334C2×C4⋊C4—24no—
335C2×C4⋊C4—22no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—22no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—28no—
350C2×C4⋊C4—28no—
351C2×C4⋊C4—28no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—28no—
356C2×C4⋊C4—24no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—24no—
359C2×C4⋊C4—28no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—28no—
367C2×C4⋊C4—44no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—42no—
371C2×C4⋊C4—42no—
372C2×C4⋊C4—42no—
373C2×C4⋊C4—42no—
374C2×C4⋊C4—42no—
375C2×C4⋊C4—44no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4—42no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4C2×D414yes—
381C2×C4⋊C4C2×D4116yes—
382C2×C4⋊C4C2×Q818yescomplemented
383C2×C22⋊C4—24no—
384C2×C22⋊C4—24no—
385C2×C22⋊C4—24no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—24no—
390C2×C22⋊C4—24no—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—42no—
393C2×C22⋊C4—44no—
394C2×C22⋊C4—42no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4C2×D414yes—
397C2×C22⋊C4C2×D414yes—
398C2×C22⋊C4C2×Q818yes—
399C2×C22⋊C4C2×Q818yes—
400C2×C22⋊C4C2×Q818yes—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—24no—
411C2×C42—24no—
412C2×C42—24no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—24no—
416C2×C42—24no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—22no—
420C2×C42—24no—
421C2×C42—22no—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—24no—
425C2×C42—42no—
426C2×C42—42no—
427C2×C42—42no—
428C2×C42—42no—
429C2×C42C2×D414yes—
430C2×C42C2×D414yes—
431C2×C42C2×D414yes—
432C2×C42C2×D414yes—
433C2×C42C2×Q818yescomplemented
434#95—24no—
435#95—24no—
436#95—24no—
437#95—24no—
438#95—28no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—28no—
444#95—28no—
445#95—28no—
446#95—24no—
447#95—24no—
448#95—28no—
449#95—28no—
450#95—24no—
451#95—24no—
452#95—42no—
453#95—44no—
454#95—44no—
455#95—44no—
456#95C2×D414yes—
457#95C2×D414yes—
458#95C2×D4116yes—
459#95C2×Q818yescomplemented
460#95C2×Q818yescomplemented
461C24—21no—
462C24—21no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24—22no—
468C24—22no—
469C24—22no—
470C24C22×D412yes—
471C24C22×Q814yes—
472C24C2511yescharacteristic
473C2×Q8—216no—
474C2×Q8—28no—
475C2×Q8—28no—
476C2×Q8—28no—
477C2×Q8—28no—
478C2×Q8—28no—
479C2×Q8—28no—
480C2×Q8—28no—
481C2×Q8—28no—
482C2×Q8—28no—
483C2×Q8—28no—
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—48no—
487C2×Q8—48no—
488C2×Q8—48no—
489C2×Q8—48no—
490C2×Q8—48no—
491C2×Q8—4128no—
492C2×Q8—48no—
493C2×Q8—44no—
494C2×Q8—44no—
495C2×Q8—44no—
496C2×Q8—44no—
497C2×Q8—44no—
498C2×Q8—44no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—44no—
503C2×Q8—44no—
504C2×Q8—44no—
505C2×Q8—44no—
506C2×Q8—44no—
507C2×Q8—44no—
508C2×Q8#121116yes—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—216no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—24no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—24no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—48no—
596C22×C4—48no—
597C22×C4—48no—
598C22×C4—48no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—44no—
605C22×C4C22×D412yes—
606C22×C4C22×D414yes—
607C22×C4C22×D412yes—
608C22×C4C22×D412yes—
609C22×C4C22×D414yes—
610C22×C4C22×D414yes—
611C22×C4C22×D414yes—
612C22×C4C22×D412yes—
613C22×C4C22×D412yes—
614C22×C4C22×D414yes—
615C22×C4C22×D414yes—
616C22×C4C22×D412yes—
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×Q814yes—
620C22×C4C22×Q814yes—
621C22×C4C22×Q814yes—
622C22×C4C22×Q814yes—
623C22×C4C22×Q814yes—
624C22×C4C22×Q814yes—
625C22×C4C2×#4114yes—
626C22×C4C2×#4114yes—
627C22×C4C2×#4112yes—
628C22×C4C2×#4112yes—
629C22×C4H(5,𝔽2)12yes—
630C22×C4H(5,𝔽2)12yes—
631C22×C42−1+414yes—
632C22×C42−1+414yes—
633C4⋊C4—232no—
634C4⋊C4—28no—
635C4⋊C4—216no—
636C4⋊C4—416no—
637C4⋊C4—48no—
638C4⋊C4—48no—
639C4⋊C4—48no—
640C4⋊C4—48no—
641C4⋊C4—48no—
642C4⋊C4—48no—
643C4⋊C4—416no—
644C4⋊C4—48no—
645C4⋊C4—416no—
646C4⋊C4—48no—
647C4⋊C4—416no—
648C4⋊C4—44no—
649C4⋊C4—44no—
650C4⋊C4—44no—
651C4⋊C4—88no—
652C22⋊C4—216no—
653C22⋊C4—216no—
654C22⋊C4—44no—
655C22⋊C4—48no—
656C22⋊C4—48no—
657C22⋊C4—48no—
658C22⋊C4C4⋊Q8116yescomplemented
659C42—28no—
660C42—28no—
661C42—28no—
662C42—28no—
663C42—216no—
664C42—48no—
665C42—48no—
666C42—48no—
667C42—48no—
668C42—44no—
669C42—44no—
670C23—22no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—22no—
680C23—24no—
681C23—24no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C2×C4⋊Q814yes—
693C23C23×D411yescharacteristic
694C23C23×D411yescharacteristic
695C23C23×D411yescharacteristic
696C23C23×Q812yes—
697C23C22×#4111yescharacteristic
698C23C22×#4111yescharacteristic
699C23C2×H(5,𝔽2)11yescharacteristic
700C23C2×H(5,𝔽2)11yescharacteristic
701C23C2×2−1+412yes—
702C23C2×2−1+412yes—
703C23#58512yes—
704Q8—232no—
705Q8—432no—
706Q8—416no—
707Q8—416no—
708Q8—88no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—28no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—24no—
758C2×C4—432no—
759C2×C4—42no—
760C2×C4—41no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—41no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—42no—
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—42no—
784C2×C4—44no—
785C2×C4—42no—
786C2×C4—416no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—44no—
807C2×C4—44no—
808C2×C4—44no—
809C2×C4C2×#12118yes—
810C2×C4C2×#12114yes—
811C2×C4#52514yes—
812C2×C4C2×C4⋊Q814yes—
813C2×C4C2×C4⋊Q814yes—
814C2×C4#53814yes—
815C2×C4D4214yes—
816C2×C4D4214yes—
817C2×C4#54614yes—
818C2×C4#54614yes—
819C2×C4D4×Q818yes—
820C2×C4D4×Q818yes—
821C22—24no—
822C22—24no—
823C22—24no—
824C22—44no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—44no—
830C22—44no—
831C22—44no—
832C22C22×#12111yescharacteristic
833C22C2×#52511yescharacteristic
834C22C22×C4⋊Q811yescharacteristic
835C22#344911yescharacteristic
836C22C2×#53811yescharacteristic
837C22C2×D4211yescharacteristic
838C22C2×D4211yescharacteristic
839C22C2×#54611yescharacteristic
840C22C2×#54611yescharacteristic
841C22C2×D4×Q812yes—
842C22C2×D4×Q812yes—
843C22Q8×#4112yes—
844C22Q8×#4112yes—
845C22#348912yes—
846C22#349712yes—
847C22#349911yescharacteristic
848C22#349911yescharacteristic
849C22#350312yes—
850C22#350312yes—
851C22#352312yes—
852C22#352312yes—
853C22#355412yes—
854C22#356112yes—
855C4—24no—
856C4—24no—
857C4—28no—
858C4—28no—
859C4—28no—
860C4—44no—
861C4—42no—
862C4—44no—
863C4—42no—
864C4—44no—
865C4—44no—
866C4—42no—
867C4—44no—
868C4—82no—
869C4—82no—
870C4—82no—
871C4—82no—
872C4#242418yes—
873C2—44no—
874C2C2×#242411yescharacteristic
875C2#3495311yescharacteristic
876C2#3567011yescharacteristic
877C2D4×C4⋊Q811yescharacteristic
878C2D4×C4⋊Q811yescharacteristic
879C2Q8×#12112yes—
880C2#3768011yescharacteristic
881C2#3935611yescharacteristic
882C2#3966312yes—
883C2#5909612yes—
884C2#5941312yes—
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC25C24
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×#2546C2semidirect
6. C2×C4×C4⋊Q8C2semidirect
7. #15623C2semidirect
9. #15190C2semidirect
10. #15184C2semidirect
13. #14816C2semidirect
14. #14714C2semidirect
16. #14024C2semidirect
17. #14024C2semidirect
18. #13976C2semidirect
201. #388Q8semidirect
382. C2×C4⋊C4C2×Q8semidirect
433. C2×C42C2×Q8semidirect
459. #95C2×Q8semidirect
460. #95C2×Q8semidirect
658. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#24292
C2×#24342
C2×Q8×C22⋊C42
C2×C4×C4⋊Q82
#156232
#153052
#151902
#151842
#151822
#148162
#147142
#141122
#140242
#139762
C4×#3882