Finite Group Databasebeta

← #873899

Subgroups — #873899

Order 512.

3262 conjugacy classes of subgroups.

The subgroup lattice has 869 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2862C211yesmaximal, characteristic, complemented
2C2×#2492C211yesmaximal, characteristic
3C2×#2434C211yesmaximal, characteristic
4C2×#2434C211yesmaximal, characteristic
5#16524C214yesmaximal, complemented
6#15510C214yesmaximal, complemented
7#15378C214yesmaximal
8#15191C211yesmaximal, characteristic, complemented
9#15190C211yesmaximal, characteristic, complemented
10#15190C211yesmaximal, characteristic, complemented
11#15182C211yesmaximal, characteristic
12#15180C211yesmaximal, characteristic, complemented
13#15178C211yesmaximal, characteristic
14#14714C211yesmaximal, characteristic, complemented
15#14403C214yesmaximal
16#14155C211yesmaximal, characteristic, complemented
17#14000C211yesmaximal, characteristic, complemented
18#13922C211yesmaximal, characteristic
19C4×#388C211yesmaximal, characteristic
20C24×Q8C2211yescharacteristic
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C22×C4⋊Q8C2211yescharacteristic
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×C4⋊Q8C2211yescharacteristic
27C22×C22⋊Q8C2211yescharacteristic
28C22×C22⋊Q8C2211yescharacteristic
29#2862—28no—
30#2492—28no—
31#2434—28no—
32#2434—28no—
33C2×#400C2212yes—
34C2×#395C2212yes—
35C2×#395C2214yes—
36C2×#395C2212yes—
37C2×#393C2212yes—
38C2×#391C2214yes—
39C2×#391C2211yescharacteristic
40C2×#391C2211yescharacteristic
41C2×#391C2211yescharacteristic
42C2×#391C2211yescharacteristic
43C2×#391C2211yescharacteristic
44C2×#391C2211yescharacteristic
45C2×#391C2211yescharacteristic
46C2×#391C2211yescharacteristic
47C2×#391C2212yes—
48C2×#391C2211yescharacteristic
49C2×#391C2211yescharacteristic
50C2×#391C2211yescharacteristic
51C2×#391C2211yescharacteristic
52C2×#391C2211yescharacteristic
53C2×#391C2211yescharacteristic
54C2×#388C2212yes—
55C2×#388C2212yes—
56C2×#385C2212yes—
57C2×#385C2214yes—
58C2×#385C2212yes—
59C2×#384C2211yescharacteristic
60C2×#382C2214yes—
61C2×#380C2211yescharacteristic
62C2×C4×C4⋊C4C2211yescharacteristic
63C2×C4×C4⋊C4C2211yescharacteristic
64C2×C4×C22⋊C4C2211yescharacteristic
65C2×C4×C22⋊C4C2211yescharacteristic
66C2×C4×C22⋊C4C2211yescharacteristic
67C2×C43C2211yescharacteristic
68#1446C2214yes—
69#1446C2214yes—
70#1445C2214yes—
71#1444C2214yes—
72#1444C2214yes—
73#1444C2214yes—
74#1444C2214yes—
75#1444C2214yes—
76#1442C2214yes—
77#1442C2214yes—
78#1442C2214yes—
79#1441C2214yes—
80#1441C2214yes—
81#1439C2214yes—
82#1439C2214yes—
83#1437C2212yes—
84#1436C2214yes—
85#1436C2212yes—
86C4⋊#95C2214yes—
87C4⋊#95C2214yes—
88C4⋊#95C2214yes—
89C4⋊#95C2211yescharacteristic
90C4⋊#95C2211yescharacteristic
91#1434C2212yes—
92C22⋊#95C2214yes—
93C4×#95C2211yescharacteristic
94C4×#95C2211yescharacteristic
95C23×Q8—24no—
96C23×Q8—24no—
97C23×Q8—24no—
98C23×Q8—42no—
99C23×Q8—42no—
100C23×Q8—42no—
101C23×Q8—42no—
102C23×Q8C2311yescharacteristic
103C23×Q8C2311yescharacteristic
104C23×Q8C2311yescharacteristic
105C23×Q8C2311yescharacteristic
106C23×Q8C2312yes—
107C23×Q8C2312yes—
108C24×C4C2311yescharacteristic
109C24×C4C2312yes—
110C2×C4⋊Q8—24no—
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—42no—
120C2×C4⋊Q8—42no—
121C2×C4⋊Q8—42no—
122C2×C4⋊Q8—42no—
123C2×C4⋊Q8—42no—
124C2×C4⋊Q8—42no—
125C2×C4⋊Q8—42no—
126C2×C4⋊Q8—42no—
127C2×C4⋊Q8—42no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×C22⋊Q8—24no—
131C2×C22⋊Q8—42no—
132C2×C22⋊Q8—42no—
133C2×C22⋊Q8—42no—
134C22×C4⋊C4C2311yescharacteristic
135C22×C4⋊C4C2311yescharacteristic
136C22×C4⋊C4C2311yescharacteristic
137C22×C4⋊C4C2312yes—
138C22×C4⋊C4C2312yes—
139C22×C4⋊C4C2314yes—
140C22×C4⋊C4C2312yes—
141C22×C4⋊C4C2312yes—
142C22×C4⋊C4C2312yes—
143C22×C4⋊C4C2312yes—
144C22×C4⋊C4C2311yescharacteristic
145C22×C4⋊C4C2312yes—
146C22×C4⋊C4C2314yes—
147C22×C4⋊C4C2314yes—
148C22×C4⋊C4C2314yes—
149C22×C4⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C42C2311yescharacteristic
158C22×C42C2311yescharacteristic
159C22×C42C2311yescharacteristic
160C22×C42C2312yes—
161C22×C42C2311yescharacteristic
162C22×C42C2311yescharacteristic
163C22×C42C2311yescharacteristic
164C22×C42C2312yes—
165C22×C42C2312yes—
166#400—28no—
167#395—216no—
168#395—28no—
169#395—28no—
170#393—28no—
171#391—24no—
172#391—24no—
173#391—24no—
174#391—24no—
175#391—24no—
176#391—24no—
177#391—24no—
178#391—24no—
179#391—216no—
180#391—28no—
181#391—42no—
182#391—42no—
183#391—42no—
184#391—42no—
185#391—42no—
186#391D418yes—
187#388—28no—
188#388Q8116yescomplemented
189#385—28no—
190#385—28no—
191#385—216no—
192#384—42no—
193#382—216no—
194#380—24no—
195C4×C4⋊C4—24no—
196C4×C4⋊C4—42no—
197C4×C22⋊C4—24no—
198C4×C22⋊C4—42no—
199C4×C22⋊C4D418yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2314yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2314yes—
214C2×#95C2314yes—
215C2×#95C2314yes—
216C2×#95C2312yes—
217C2×#95C2314yes—
218C2×#95C2314yes—
219C2×#95C2314yes—
220C2×#95C2312yes—
221C2×#95C2312yes—
222C2×#95C2314yes—
223C2×#95C2314yes—
224C2×#95C2314yes—
225C2×#95C2314yes—
226C2×#95C2311yescharacteristic
227C2×#95C2311yescharacteristic
228C2×#95C2314yes—
229C2×#95C2312yes—
230C2×#95C2312yes—
231C43—24no—
232C25C2411yescharacteristic
233C22×Q8—22no—
234C22×Q8—22no—
235C22×Q8—22no—
236C22×Q8—22no—
237C22×Q8—22no—
238C22×Q8—22no—
239C22×Q8—24no—
240C22×Q8—22no—
241C22×Q8—24no—
242C22×Q8—24no—
243C22×Q8—24no—
244C22×Q8—22no—
245C22×Q8—22no—
246C22×Q8—22no—
247C22×Q8—24no—
248C22×Q8—22no—
249C22×Q8—22no—
250C22×Q8—22no—
251C22×Q8—22no—
252C22×Q8—22no—
253C22×Q8—22no—
254C22×Q8—22no—
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—22no—
262C22×Q8—22no—
263C22×Q8—22no—
264C22×Q8—28no—
265C22×Q8—42no—
266C22×Q8—42no—
267C22×Q8—42no—
268C22×Q8—42no—
269C22×Q8—42no—
270C22×Q8—44no—
271C22×Q8—416no—
272C22×Q8—416no—
273C22×Q8—416no—
274C22×Q8—416no—
275C22×Q8—416no—
276C22×Q8—416no—
277C22×Q8—416no—
278C22×Q8C2×D414yes—
279C22×Q8#4114yes—
280C23×C4—22no—
281C23×C4—22no—
282C23×C4—22no—
283C23×C4—22no—
284C23×C4—22no—
285C23×C4—22no—
286C23×C4—24no—
287C23×C4—24no—
288C23×C4—24no—
289C23×C4—42no—
290C23×C4—42no—
291C23×C4—42no—
292C23×C4—42no—
293C23×C4C2×D414yes—
294C23×C4C2412yes—
295C23×C4C2412yes—
296C23×C4C2412yes—
297C23×C4C2412yes—
298C23×C4C2412yes—
299C23×C4C2412yes—
300C23×C4C2411yescharacteristic
301C23×C4C2411yescharacteristic
302C23×C4C2412yes—
303C23×C4C2412yes—
304C23×C4C2412yes—
305C23×C4C2412yes—
306C23×C4C2412yes—
307C23×C4C2411yescharacteristic
308C23×C4C2411yescharacteristic
309C23×C4C2412yes—
310C23×C4C2411yescharacteristic
311C23×C4C2411yescharacteristic
312C4⋊Q8—416no—
313C4⋊Q8—416no—
314C4⋊Q8—416no—
315C4⋊Q8—416no—
316C4⋊Q8—416no—
317C4⋊Q8—416no—
318C22⋊Q8—416no—
319C22⋊Q8—416no—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—22no—
322C2×C4⋊C4—22no—
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—28no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—28no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—28no—
348C2×C4⋊C4—42no—
349C2×C4⋊C4—42no—
350C2×C4⋊C4—42no—
351C2×C4⋊C4—42no—
352C2×C4⋊C4—42no—
353C2×C4⋊C4—42no—
354C2×C4⋊C4—44no—
355C2×C4⋊C4—42no—
356C2×C4⋊C4—42no—
357C2×C4⋊C4—42no—
358C2×C4⋊C4—44no—
359C2×C4⋊C4—44no—
360C2×C4⋊C4—44no—
361C2×C4⋊C4—44no—
362C2×C4⋊C4—44no—
363C2×C4⋊C4—42no—
364C2×C4⋊C4—44no—
365C2×C4⋊C4—44no—
366C2×C4⋊C4C2×D414yes—
367C2×C4⋊C4C2×Q818yescomplemented
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—24no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—42no—
379C2×C22⋊C4—42no—
380C2×C22⋊C4—44no—
381C2×C22⋊C4C2×D414yes—
382C2×C22⋊C4C2×D414yes—
383C2×C22⋊C4C2×Q818yes—
384C2×C22⋊C4C2×Q818yes—
385C2×C22⋊C4C2×Q818yes—
386C2×C42—22no—
387C2×C42—24no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—22no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—24no—
394C2×C42—22no—
395C2×C42—24no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—24no—
405C2×C42—24no—
406C2×C42—42no—
407C2×C42—44no—
408C2×C42C2×D414yes—
409C2×C42C2×D414yes—
410C2×C42C2×D414yes—
411C2×C42C2×Q818yescomplemented
412#95—24no—
413#95—24no—
414#95—24no—
415#95—28no—
416#95—28no—
417#95—28no—
418#95—28no—
419#95—24no—
420#95—24no—
421#95—24no—
422#95—24no—
423#95—24no—
424#95—24no—
425#95—24no—
426#95—24no—
427#95—24no—
428#95—24no—
429#95—44no—
430#95—44no—
431#95—42no—
432#95—42no—
433#95—44no—
434#95—44no—
435#95—44no—
436#95—44no—
437#95—44no—
438#95C2×D414yes—
439#95C2×D414yes—
440#95C2×D4116yes—
441#95C2×Q818yescomplemented
442#95C2×Q818yescomplemented
443C24—21no—
444C24—21no—
445C24—21no—
446C24—21no—
447C24—21no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24C22×D412yes—
453C24C22×Q814yes—
454C24C2511yescharacteristic
455C2×Q8—28no—
456C2×Q8—28no—
457C2×Q8—28no—
458C2×Q8—28no—
459C2×Q8—28no—
460C2×Q8—28no—
461C2×Q8—48no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—48no—
465C2×Q8—416no—
466C2×Q8—48no—
467C2×Q8—48no—
468C2×Q8—48no—
469C2×Q8—4128no—
470C2×Q8—48no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—44no—
475C2×Q8—44no—
476C2×Q8—44no—
477C2×Q8—44no—
478C2×Q8—48no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—44no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8—44no—
488C2×Q8—44no—
489C2×Q8—44no—
490C2×Q8—44no—
491C2×Q8—44no—
492C2×Q8—44no—
493C2×Q8—44no—
494C2×Q8—84no—
495C2×Q8—88no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
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—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—24no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—24no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—28no—
555C22×C4—28no—
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—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—24no—
580C22×C4—24no—
581C22×C4—24no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—48no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4C22×D412yes—
597C22×C4C22×D414yes—
598C22×C4C22×D414yes—
599C22×C4C22×D412yes—
600C22×C4C22×D412yes—
601C22×C4C22×D412yes—
602C22×C4C22×D412yes—
603C22×C4C22×D414yes—
604C22×C4C22×D412yes—
605C22×C4C22×D412yes—
606C22×C4C22×Q814yes—
607C22×C4C22×Q814yes—
608C22×C4C22×Q814yes—
609C22×C4C22×Q814yes—
610C22×C4C22×Q814yes—
611C22×C4C22×Q814yes—
612C22×C4C2×#4114yes—
613C22×C4C2×#4112yes—
614C22×C4H(5,𝔽2)12yes—
615C22×C4H(5,𝔽2)12yes—
616C22×C4H(5,𝔽2)12yes—
617C22×C4H(5,𝔽2)12yes—
618C22×C42−1+414yes—
619C22×C42−1+414yes—
620C4⋊C4—28no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—48no—
625C4⋊C4—48no—
626C4⋊C4—48no—
627C4⋊C4—416no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C4⋊C4—416no—
631C4⋊C4—416no—
632C4⋊C4—44no—
633C4⋊C4—44no—
634C4⋊C4—44no—
635C4⋊C4—88no—
636C22⋊C4—28no—
637C22⋊C4—216no—
638C22⋊C4—48no—
639C22⋊C4—48no—
640C22⋊C4—48no—
641C22⋊C4—84no—
642C22⋊C4C4⋊Q8116yescomplemented
643C42—28no—
644C42—28no—
645C42—28no—
646C42—216no—
647C42—48no—
648C42—44no—
649C42—44no—
650C42—44no—
651C42—84no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—41no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23C2×C4⋊Q814yes—
675C23C23×D411yescharacteristic
676C23C23×D411yescharacteristic
677C23C23×Q812yes—
678C23C22×#4111yescharacteristic
679C23C2×H(5,𝔽2)11yescharacteristic
680C23C2×H(5,𝔽2)11yescharacteristic
681C23C2×H(5,𝔽2)11yescharacteristic
682C23C2×H(5,𝔽2)11yescharacteristic
683C23C2×2−1+412yes—
684C23C2×2−1+412yes—
685C23#58512yes—
686Q8—432no—
687Q8—416no—
688Q8—416no—
689Q8—816no—
690Q8—88no—
691Q8—88no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—28no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—432no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—41no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—416no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—44no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4C2×C4⋊Q814yes—
794C2×C4C2×C4⋊Q814yes—
795C2×C4#53514yes—
796C2×C4#53514yes—
797C2×C4#53614yes—
798C2×C4#53814yes—
799C2×C4D4214yes—
800C2×C4#54614yes—
801C2×C4#54614yes—
802C2×C4D4×Q818yes—
803C2×C4H(3,𝔽4)14yes—
804C22—24no—
805C22—24no—
806C22—24no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—44no—
813C22—44no—
814C22—44no—
815C22C22×C4⋊Q811yescharacteristic
816C22C2×#53511yescharacteristic
817C22C2×#53511yescharacteristic
818C22C2×#53611yescharacteristic
819C22C2×#53811yescharacteristic
820C22C2×D4211yescharacteristic
821C22C2×#54611yescharacteristic
822C22C2×#54611yescharacteristic
823C22C2×D4×Q812yes—
824C22Q8×#4112yes—
825C22#348912yes—
826C22#349911yescharacteristic
827C22#350011yescharacteristic
828C22#350112yes—
829C22#350312yes—
830C22#350312yes—
831C22#350312yes—
832C22#352312yes—
833C22C2×H(3,𝔽4)11yescharacteristic
834C22#355012yes—
835C22#355412yes—
836C22#356112yes—
837C22#356112yes—
838C4—24no—
839C4—24no—
840C4—24no—
841C4—28no—
842C4—42no—
843C4—44no—
844C4—42no—
845C4—44no—
846C4—44no—
847C4—44no—
848C4—44no—
849C4—44no—
850C4—82no—
851C4—82no—
852C4—82no—
853C4—82no—
854C4—82no—
855C4#267018yes—
856C2—44no—
857C2#3528111yescharacteristic
858C2D4×C4⋊Q811yescharacteristic
859C2#3627611yescharacteristic
860C2#3739111yescharacteristic
861C2#3767611yescharacteristic
862C2#3895411yescharacteristic
863C2#3959612yes—
864C2#3966312yes—
865C2#4600412yes—
866C2C2×#267011yescharacteristic
867C2#5909612yes—
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×#2862C2semidirect
5. #16524C2semidirect
6. #15510C2semidirect
8. #15191C2semidirect
9. #15190C2semidirect
10. #15190C2semidirect
12. #15180C2semidirect
14. #14714C2semidirect
16. #14155C2semidirect
17. #14000C2semidirect
188. #388Q8semidirect
367. C2×C4⋊C4C2×Q8semidirect
411. C2×C42C2×Q8semidirect
441. #95C2×Q8semidirect
442. #95C2×Q8semidirect
642. C22⋊C4C4⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#28622
C2×#24922
C2×#24342
#165242
#155102
#153782
#151912
#151902
#151822
#151802
#151782
#147142
#144032
#141552
#140002
#139222
C4×#3882