Finite Group Databasebeta

← #6445368

Subgroups — #6445368

Order 512.

3420 conjugacy classes of subgroups.

The subgroup lattice has 809 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#533C211yesmaximal, characteristic
2C2×#3078C212yesmaximal, complemented
3C2×C4×C22⋊Q8C211yesmaximal, characteristic
4#24307C214yesmaximal, complemented
5#24306C214yesmaximal, complemented
6#24303C214yesmaximal, complemented
7#24302C212yesmaximal, complemented
8#24301C212yesmaximal, complemented
9#23554C212yesmaximal, complemented
10#23455C212yesmaximal, complemented
11#21312C212yesmaximal, complemented
12#20911C212yesmaximal
13#20846C212yesmaximal
14#20626C211yesmaximal, characteristic
15C2×#533—21no—
16C2×#533—21no—
17C2×#533—21no—
18C2×#533—21no—
19C2×#533—216no—
20C2×#533C2212yes—
21C2×#533C2212yes—
22C2×#533C2212yes—
23C2×#533C2212yes—
24C22×C4⋊Q8C2211yescharacteristic
25C22×C4⋊Q8C2211yescharacteristic
26C22×#125C2212yes—
27C22×C22⋊Q8—21no—
28C22×C22⋊Q8—21no—
29C22×C22⋊Q8C2211yescharacteristic
30C22×C4×Q8—21no—
31C22×C4×Q8—21no—
32C22×C4×Q8C2211yescharacteristic
33C22×#117C2212yes—
34C23×C42C2211yescharacteristic
35#3078—216no—
36C2×#479C2218yescomplemented
37C2×#477C2214yescomplemented
38C2×#475C2214yescomplemented
39C2×#428C2214yes—
40C2×#423C2212yes—
41C2×#419C2214yes—
42C2×#407C2212yes—
43C4×C22⋊Q8—21no—
44C4×C22⋊Q8—21no—
45C4×C22⋊Q8—21no—
46C4×C22⋊Q8—21no—
47C4×C22⋊Q8C2212yes—
48C4×C22⋊Q8C2212yes—
49C4×C22⋊Q8C2212yes—
50C4×C22⋊Q8C2212yes—
51C2×#391C2211yescharacteristic
52C2×#389C2211yescharacteristic
53C2×#387—21no—
54C2×#385—21no—
55C2×#380C2211yescharacteristic
56C2×C4×C4⋊C4—21no—
57C2×C4×C4⋊C4C2211yescharacteristic
58C2×C4×C22⋊C4—21no—
59#2059C2218yescomplemented
60#2058C2214yescomplemented
61#2057C2214yescomplemented
62#2026C2218yescomplemented
63#2024C2214yescomplemented
64#2024C2214yescomplemented
65#1989C2218yescomplemented
66#1988C2214yescomplemented
67#1987C2214yescomplemented
68#1873C2218yes—
69#1872C2214yes—
70#1872C2214yes—
71#1854C2218yes—
72#1853C2214yes—
73#1852C2214yes—
74#1797C2212yes—
75#1797C2212yes—
76#1797C2212yes—
77#1797C2212yes—
78#1736C2214yes—
79#1736C2214yes—
80#1728C2212yes—
81C23×Q8—21no—
82C23×Q8—21no—
83C23×Q8C2311yescharacteristic
84C24×C4D411yescharacteristic
85C24×C4D411yescharacteristic
86C24×C4C2311yescharacteristic
87C22×M16C2314yes—
88#533—216no—
89#533—216no—
90#533—216no—
91#533—216no—
92#533—28no—
93#533—28no—
94#533—216no—
95#533—216no—
96#533—28no—
97#533D4116yes—
98C2×C4⋊Q8—28no—
99C2×C4⋊Q8—28no—
100C2×C4⋊Q8—21no—
101C2×C4⋊Q8—21no—
102C2×C4⋊Q8—21no—
103C2×C4⋊Q8—21no—
104C2×C4⋊Q8C2312yes—
105C2×C4⋊Q8C2312yes—
106C2×C4⋊Q8C2312yes—
107C2×C4⋊Q8C2312yes—
108C2×#125—216no—
109C2×#125—22no—
110C2×#125—22no—
111C2×#125C2314yes—
112C2×#125C2314yes—
113C2×C22⋊Q8—216no—
114C2×C22⋊Q8—216no—
115C2×C22⋊Q8—22no—
116C2×C22⋊Q8—22no—
117C2×C22⋊Q8—22no—
118C2×C22⋊Q8—22no—
119C2×C22⋊Q8—22no—
120C2×C22⋊Q8—22no—
121C2×C22⋊Q8—22no—
122C2×C22⋊Q8—22no—
123C2×C22⋊Q8—21no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—24no—
126C2×C22⋊Q8Q818yescomplemented
127C2×C22⋊Q8C2312yes—
128C2×C22⋊Q8C2312yes—
129C2×C4×Q8—216no—
130C2×C4×Q8—216no—
131C2×C4×Q8—22no—
132C2×C4×Q8—22no—
133C2×C4×Q8—22no—
134C2×C4×Q8—22no—
135C2×C4×Q8—22no—
136C2×C4×Q8—22no—
137C2×C4×Q8—22no—
138C2×C4×Q8—22no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8—28no—
142C2×C4×Q8C2312yes—
143C2×C4×Q8C2312yes—
144C2×#117—22no—
145C2×#117—22no—
146C2×#117—216no—
147C2×#117C2314yes—
148C2×#117C2314yes—
149C22×C4⋊C4—22no—
150C22×C4⋊C4—22no—
151C22×C4⋊C4—21no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4—21no—
155C22×C4⋊C4—21no—
156C22×C4⋊C4C2312yes—
157C22×C4⋊C4C2312yes—
158C22×C4⋊C4C2311yescharacteristic
159C22×C4⋊C4C2311yescharacteristic
160C22×C4⋊C4C2311yescharacteristic
161C22×C22⋊C4—22no—
162C22×C22⋊C4—21no—
163C22×C22⋊C4—21no—
164C22×C42—22no—
165C22×C42—28no—
166C22×C42—21no—
167C22×C42—21no—
168C22×C42D411yescharacteristic
169C22×C42D411yescharacteristic
170C22×C42D411yescharacteristic
171C22×C42D411yescharacteristic
172C22×C42D411yescharacteristic
173C22×C42D411yescharacteristic
174C22×C42C2311yescharacteristic
175C22×C42C2311yescharacteristic
176C22×C42C2311yescharacteristic
177C22×C42C2311yescharacteristic
178C22×C42C2311yescharacteristic
179C22×C42C2311yescharacteristic
180#479—232no—
181#477—216no—
182#475—216no—
183#428—216no—
184C2×#107C2318yes—
185C2×#106C2318yes—
186#423—28no—
187C2×C4⋊C8C2314yes—
188C2×C4⋊C8C2314yes—
189#419—216no—
190C2×#103C2318yes—
191C2×#103C2318yes—
192#407—28no—
193C2×C22⋊C8C2314yes—
194C2×C22⋊C8C2314yes—
195#391—21no—
196#391—21no—
197#391C2312yes—
198#391C2312yes—
199#389—21no—
200#389—21no—
201#389C2312yes—
202#389C2312yes—
203#387—22no—
204#387—22no—
205#387—22no—
206#387—22no—
207#385—22no—
208#385—22no—
209#385—22no—
210#385—22no—
211#380—21no—
212#380—21no—
213#380C2312yes—
214#380C2312yes—
215C4×C4⋊C4—22no—
216C4×C4⋊C4—22no—
217C4×C4⋊C4—22no—
218C4×C4⋊C4—22no—
219C4×C4⋊C4—21no—
220C4×C4⋊C4—21no—
221C4×C4⋊C4C2312yes—
222C4×C4⋊C4C2312yes—
223C4×C22⋊C4—22no—
224C4×C22⋊C4—22no—
225C4×C22⋊C4—22no—
226C4×C22⋊C4—22no—
227C2×#95—21no—
228C2×#95—21no—
229C2×#95—21no—
230C2×#95—21no—
231C2×#95—21no—
232#340C2318yes—
233#340C2318yes—
234#340C2318yes—
235#340C2318yes—
236#336C2314yes—
237#336C2314yes—
238C25C2×D411yescharacteristic
239C22×Q8—28no—
240C22×Q8—28no—
241C22×Q8—22no—
242C22×Q8—22no—
243C22×Q8—22no—
244C22×Q8—22no—
245C22×Q8—21no—
246C22×Q8—22no—
247C22×Q8—24no—
248C22×Q8—24no—
249C22×Q8—44no—
250C22×Q8—44no—
251C22×Q8—44no—
252C22×Q8—44no—
253C22×Q8C2×Q814yescomplemented
254C22×Q8C2412yes—
255C23×C4—24no—
256C23×C4—24no—
257C23×C4—22no—
258C23×C4—22no—
259C23×C4—21no—
260C23×C4—21no—
261C23×C4—24no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4C2×D411yescharacteristic
270C23×C4C2×D411yescharacteristic
271C23×C4C2×D411yescharacteristic
272C23×C4C2×D411yescharacteristic
273C23×C4C2×D411yescharacteristic
274C23×C4C2×D411yescharacteristic
275C23×C4C2×D411yescharacteristic
276C23×C4C2×D411yescharacteristic
277C23×C4C2×D411yescharacteristic
278C23×C4C2×D411yescharacteristic
279C23×C4C2×D411yescharacteristic
280C23×C4C2×D411yescharacteristic
281C23×C4C2×D411yescharacteristic
282C23×C4C2×D411yescharacteristic
283C23×C4C2×D411yescharacteristic
284C23×C4C2×Q814yes—
285C23×C4#4114yes—
286C23×C4C2411yescharacteristic
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C2×M16—28no—
290C2×M16—28no—
291C2×M16—28no—
292C22×C8C2418yes—
293C4⋊Q8—28no—
294C4⋊Q8—28no—
295C4⋊Q8—28no—
296C4⋊Q8—28no—
297C4⋊Q8—28no—
298C4⋊Q8—28no—
299C4⋊Q8—24no—
300C4⋊Q8—24no—
301C4⋊Q8C2×D418yes—
302C4⋊Q8C2×D418yes—
303#125—216no—
304#125—216no—
305#125—28no—
306#125—28no—
307#125—28no—
308#125C2×D4116yes—
309C22⋊Q8—216no—
310C22⋊Q8—216no—
311C22⋊Q8—216no—
312C22⋊Q8—216no—
313C22⋊Q8—216no—
314C22⋊Q8—216no—
315C22⋊Q8—216no—
316C22⋊Q8—216no—
317C22⋊Q8—28no—
318C22⋊Q8—28no—
319C22⋊Q8—24no—
320C22⋊Q8—24no—
321C22⋊Q8C2×Q818yes—
322C22⋊Q8C2×Q818yescomplemented
323C4×Q8—216no—
324C4×Q8—216no—
325C4×Q8—216no—
326C4×Q8—216no—
327C4×Q8—216no—
328C4×Q8—216no—
329C4×Q8—216no—
330C4×Q8—216no—
331C4×Q8—28no—
332C4×Q8—28no—
333C4×Q8—44no—
334C4×Q8—44no—
335#117—216no—
336#117—216no—
337#117—28no—
338#117—28no—
339#117—28no—
340#117C2×D4116yes—
341C2×C4⋊C4—216no—
342C2×C4⋊C4—216no—
343C2×C4⋊C4—28no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—24no—
347C2×C4⋊C4—24no—
348C2×C4⋊C4—24no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—28no—
361C2×C4⋊C4—28no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—24no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4C2×Q814yescomplemented
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2414yes—
376C2×C4⋊C4C2414yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—216no—
379C2×C22⋊C4—28no—
380C2×C22⋊C4—24no—
381C2×C22⋊C4—24no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—44no—
387C2×C42—216no—
388C2×C42—24no—
389C2×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—24no—
394C2×C42—24no—
395C2×C42—24no—
396C2×C42—24no—
397C2×C42—24no—
398C2×C42—24no—
399C2×C42—24no—
400C2×C42—24no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—44no—
406C2×C42—44no—
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D418yes—
420C2×C42C2411yescharacteristic
421C2×C42C2411yescharacteristic
422C2×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424#107—216no—
425#106—216no—
426C4⋊C8—28no—
427C4⋊C8—28no—
428#103—216no—
429#103—216no—
430C22⋊C8—28no—
431C22⋊C8—28no—
432#95—22no—
433#95—22no—
434#95—22no—
435#95—22no—
436#95—22no—
437#95—22no—
438#95—22no—
439#95—22no—
440#95—22no—
441#95—22no—
442C24—22no—
443C24—22no—
444C24—22no—
445C24—22no—
446C24—41no—
447C24—41no—
448C24C22⋊Q814yes—
449C24C22×D411yescharacteristic
450C24C22×D411yescharacteristic
451C24C22×D411yescharacteristic
452C2×Q8—28no—
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—24no—
457C2×Q8—22no—
458C2×Q8—216no—
459C2×Q8—24no—
460C2×Q8—24no—
461C2×Q8—432no—
462C2×Q8—44no—
463C2×Q8—44no—
464C2×Q8—44no—
465C2×Q8—44no—
466C2×Q8—432no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×Q8—48no—
470C2×Q8—44no—
471C2×Q8—44no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8C22×Q814yes—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—216no—
485C22×C4—216no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—28no—
495C22×C4—28no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—41no—
524C22×C4—41no—
525C22×C4—41no—
526C22×C4—41no—
527C22×C4—41no—
528C22×C4—41no—
529C22×C4—41no—
530C22×C4—416no—
531C22×C4—416no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—44no—
539C22×C4—44no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—42no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4#12014yes—
547C22×C4#12014yes—
548C22×C4C22⋊Q814yes—
549C22×C4C22⋊Q814yes—
550C22×C4C22⋊Q814yes—
551C22×C4#13714yes—
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C22×D411yescharacteristic
559C22×C4C22×D411yescharacteristic
560C22×C4C22×D411yescharacteristic
561C22×C4C22×D411yescharacteristic
562C22×C4C22×D411yescharacteristic
563C22×C4C22×D414yes—
564C22×C4C22×Q812yes—
565C22×C4C22×Q812yes—
566C22×C4C22×Q812yes—
567C22×C4C2×#4112yes—
568C22×C4C2×#4112yes—
569C22×C4C2×#4112yes—
570C22×C42−1+414yes—
571C22×C4C2511yescharacteristic
572M16—416no—
573C2×C8—28no—
574C2×C8—28no—
575C2×C8—28no—
576C4⋊C4—28no—
577C4⋊C4—28no—
578C4⋊C4—216no—
579C4⋊C4—216no—
580C4⋊C4—28no—
581C4⋊C4—28no—
582C4⋊C4—216no—
583C4⋊C4—216no—
584C4⋊C4—28no—
585C4⋊C4—28no—
586C4⋊C4—28no—
587C4⋊C4—28no—
588C4⋊C4—24no—
589C4⋊C4—24no—
590C4⋊C4—24no—
591C4⋊C4—22no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—44no—
595C4⋊C4—42no—
596C4⋊C4—44no—
597C4⋊C4—44no—
598C4⋊C4—42no—
599C4⋊C4—44no—
600C4⋊C4C22×D418yes—
601C4⋊C4C22×D418yes—
602C4⋊C4C22×Q814yes—
603C22⋊C4—216no—
604C22⋊C4—216no—
605C22⋊C4—28no—
606C22⋊C4—28no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C42—216no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—216no—
621C42—22no—
622C42—22no—
623C42—44no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42#12014yes—
628C42#12014yes—
629C42C22×D414yes—
630C42C22×D414yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—28no—
640C23—21no—
641C23—28no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23C2×#12012yes—
653C23C2×C22⋊Q812yes—
654C23C2×C22⋊Q812yes—
655C23C2×C22⋊Q812yes—
656C23#53612yes—
657C23C2×#13712yes—
658C23#57512yes—
659C23C23×D411yescharacteristic
660Q8—28no—
661Q8—416no—
662Q8—416no—
663Q8—416no—
664Q8—48no—
665Q8—44no—
666Q8—416no—
667C2×C4—28no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—28no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—28no—
690C2×C4—28no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—28no—
694C2×C4—28no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—48no—
710C2×C4—416no—
711C2×C4—416no—
712C2×C4—42no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—44no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—84no—
729C2×C4—84no—
730C2×C4C2×#12012yes—
731C2×C4C2×#12012yes—
732C2×C4C2×#12012yes—
733C2×C4C2×#12012yes—
734C2×C4C2×#12012yes—
735C2×C4C2×C22⋊Q812yes—
736C2×C4C2×C22⋊Q812yes—
737C2×C4C2×C22⋊Q812yes—
738C2×C4#53612yes—
739C2×C4#54818yes—
740C2×C4D4×Q818yes—
741C2×C4C2×#13712yes—
742C2×C4C2×#13712yes—
743C2×C4#57512yes—
744C2×C4#57512yes—
745C2×C4C23×D412yes—
746C2×C4C23×Q811yescharacteristic
747C2×C4C22×#4111yescharacteristic
748C2×C4C2×2−1+412yes—
749C8—48no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—416no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22#240914yes—
771C22#307814yescomplemented
772C22C22×#12011yescharacteristic
773C22C22×C22⋊Q811yescharacteristic
774C22C2×#53611yescharacteristic
775C22C22×#13711yescharacteristic
776C22C2×#57511yescharacteristic
777C22C2×#57511yescharacteristic
778C22C2×#57511yescharacteristic
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—22no—
785C4—22no—
786C4—44no—
787C4—44no—
788C4—41no—
789C4—48no—
790C4—41no—
791C4—48no—
792C4—82no—
793C4—82no—
794C4#240914yes—
795C4#300714yes—
796C4C2×#54812yes—
797C4C2×D4×Q812yes—
798C2—24no—
799C2—24no—
800C2—42no—
801C2C2×#240911yescharacteristic
802C2C2×#300711yescharacteristic
803C2#6035911yescharacteristic
804C2C2×#307811yescharacteristic
805C2#6048411yescharacteristic
806C2#6086511yescharacteristic
807C2#6086611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC25C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C42 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#3078C2semidirect
4. #24307C2semidirect
5. #24306C2semidirect
6. #24303C2semidirect
7. #24302C2semidirect
8. #24301C2semidirect
9. #23554C2semidirect
10. #23455C2semidirect
11. #21312C2semidirect
36. C2×#479C22semidirect
37. C2×#477C22semidirect
38. C2×#475C22semidirect
59. #2059C22semidirect
60. #2058C22semidirect
61. #2057C22semidirect
62. #2026C22semidirect
63. #2024C22semidirect
64. #2024C22semidirect
65. #1989C22semidirect
66. #1988C22semidirect
67. #1987C22semidirect
126. C2×C22⋊Q8Q8semidirect
253. C22×Q8C2×Q8semidirect
322. C22⋊Q8C2×Q8semidirect
372. C2×C4⋊C4C2×Q8semidirect
771. C22#3078semidirect

Maximal subgroups

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

subgroupindex
C22×#5332
C2×#30782
C2×C4×C22⋊Q82
#243072
#243062
#243032
#243022
#243012
#235542
#234552
#213122
#209112
#208462
#206262