Finite Group Databasebeta

← #949906

Subgroups — #949906

Order 512.

2796 conjugacy classes of subgroups.

The subgroup lattice has 965 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17296C212yesmaximal, complemented
2#17153C212yesmaximal, complemented
3#16987C211yesmaximal, characteristic, complemented
4#16951C212yesmaximal, complemented
5#16823C211yesmaximal, characteristic, complemented
6#16707C211yesmaximal, characteristic, complemented
7#16609C212yesmaximal, complemented
8#16339C211yesmaximal, characteristic, complemented
9#16118C212yesmaximal, complemented
10#15378C212yesmaximal, complemented
11#14934C212yesmaximal, complemented
12#14767C212yesmaximal, complemented
13#14717C212yesmaximal
14#14263C212yesmaximal, complemented
15#14127C212yesmaximal
16#14052C212yesmaximal, complemented
17#13903C211yesmaximal, characteristic
18#13869C211yesmaximal, characteristic
19C2×#1439C211yesmaximal, characteristic
20C22×C22⋊Q8C2212yes—
21C23×C4⋊C4C2211yescharacteristic
22C23×C22⋊C4C2212yes—
23C23×C22⋊C4C2211yescharacteristic
24C23×C22⋊C4C2211yescharacteristic
25C2×#400C2212yescomplemented
26C2×#393C2212yes—
27C2×#393C2212yes—
28C2×#391C2212yescomplemented
29C2×#385C2212yes—
30C2×#385C2212yes—
31C2×#385C2212yes—
32C2×#385C2212yes—
33C2×#381C2212yes—
34C2×#381C2212yes—
35C2×#380C2211yescharacteristic
36C2×#379C2212yes—
37C2×#379C2211yescharacteristic
38C2×C4×C22⋊C4C2211yescharacteristic
39C22×#95C2211yescharacteristic
40C22×#95C2212yes—
41#1446C2212yescomplemented
42#1446C2212yescomplemented
43#1446C2212yescomplemented
44#1445C2212yescomplemented
45#1445C2212yescomplemented
46#1444C2212yescomplemented
47#1444C2212yescomplemented
48#1444C2212yescomplemented
49#1444C2212yescomplemented
50#1443C2212yescomplemented
51#1443C2212yescomplemented
52#1442C2212yescomplemented
53#1442C2212yescomplemented
54#1442C2212yescomplemented
55#1442C2212yescomplemented
56#1442C2212yescomplemented
57#1442C2212yescomplemented
58#1442C2212yescomplemented
59#1442C2212yescomplemented
60#1442C2212yescomplemented
61#1442C2212yescomplemented
62#1442C2212yescomplemented
63#1442C2212yescomplemented
64#1442C2212yescomplemented
65#1441C2212yescomplemented
66#1441C2212yescomplemented
67#1441C2212yescomplemented
68#1440C2212yes—
69#1440C2212yes—
70#1439C2211yescharacteristic
71#1439C2212yes—
72#1439C2212yes—
73#1439C2212yes—
74#1439C2212yes—
75#1439C2212yes—
76#1439C2211yescharacteristic
77#1439C2211yescharacteristic
78#1439C2211yescharacteristic
79#1439C2211yescharacteristic
80#1439C2212yes—
81#1439C2212yes—
82#1439C2212yes—
83#1439C2212yes—
84#1439C2211yescharacteristic
85#1439C2211yescharacteristic
86#1439C2211yescharacteristic
87#1439C2212yes—
88#1439C2212yes—
89#1439C2212yes—
90#1437C2212yes—
91#1437C2212yes—
92#1436C2212yescomplemented
93#1436C2212yescomplemented
94C4⋊#95C2212yescomplemented
95C22⋊#95C2211yescharacteristic
96C22⋊#95C2211yescharacteristic
97C22⋊#95C2211yescharacteristic
98C22⋊#95C2212yes—
99C22⋊#95C2211yescharacteristic
100C22⋊#95C2212yes—
101C22⋊#95C2212yes—
102C22⋊#95C2212yes—
103C22⋊#95C2212yes—
104C22⋊#95C2212yes—
105C22⋊#95C2212yes—
106C22⋊#95C2212yes—
107C26C2311yescharacteristic
108C23×Q8C2312yes—
109C24×C4C2311yescharacteristic
110C24×C4C2312yes—
111C24×C4C2312yes—
112C24×C4C2311yescharacteristic
113C24×C4C2311yescharacteristic
114C24×C4C2311yescharacteristic
115C2×C22⋊Q8—28no—
116C2×C22⋊Q8—44no—
117C2×C22⋊Q8—44no—
118C22×C4⋊C4—42no—
119C22×C4⋊C4—44no—
120C22×C4⋊C4C2312yes—
121C22×C4⋊C4C2312yes—
122C22×C4⋊C4C2312yes—
123C22×C4⋊C4C2311yescharacteristic
124C22×C4⋊C4C2312yes—
125C22×C4⋊C4C2312yes—
126C22×C4⋊C4C2311yescharacteristic
127C22×C4⋊C4C2311yescharacteristic
128C22×C4⋊C4C2312yes—
129C22×C4⋊C4C2311yescharacteristic
130C22×C4⋊C4C2312yes—
131C22×C4⋊C4C2312yes—
132C22×C22⋊C4—44no—
133C22×C22⋊C4—44no—
134C22×C22⋊C4—42no—
135C22×C22⋊C4—44no—
136C22×C22⋊C4—42no—
137C22×C22⋊C4—42no—
138C22×C22⋊C4—44no—
139C22×C22⋊C4Q818yescomplemented
140C22×C22⋊C4C2312yes—
141C22×C22⋊C4C2312yes—
142C22×C22⋊C4C2312yes—
143C22×C22⋊C4C2312yes—
144C22×C22⋊C4C2312yes—
145C22×C22⋊C4C2312yes—
146C22×C22⋊C4C2312yes—
147C22×C22⋊C4C2311yescharacteristic
148C22×C22⋊C4C2312yes—
149C22×C22⋊C4C2312yes—
150C22×C22⋊C4C2312yes—
151C22×C22⋊C4C2311yescharacteristic
152C22×C22⋊C4C2312yes—
153C22×C22⋊C4C2312yes—
154C22×C22⋊C4C2312yes—
155C22×C22⋊C4C2312yes—
156C22×C22⋊C4C2311yescharacteristic
157C22×C22⋊C4C2311yescharacteristic
158C22×C22⋊C4C2311yescharacteristic
159C22×C22⋊C4C2311yescharacteristic
160C22×C42C2312yes—
161#400—44no—
162#393—44no—
163#393—44no—
164#391—44no—
165#385—44no—
166#385—44no—
167#385—44no—
168#385—44no—
169#381—28no—
170#381—44no—
171#380—42no—
172#379—28no—
173#379—42no—
174C4×C22⋊C4—42no—
175C2×#95—44no—
176C2×#95—42no—
177C2×#95C2312yes—
178C2×#95C2312yes—
179C2×#95C2312yes—
180C2×#95C2312yes—
181C2×#95C2312yes—
182C2×#95C2312yes—
183C2×#95C2312yes—
184C2×#95C2312yes—
185C2×#95C2312yes—
186C2×#95C2312yes—
187C2×#95C2312yes—
188C2×#95C2312yes—
189C2×#95C2312yes—
190C2×#95C2312yes—
191C2×#95C2312yes—
192C2×#95C2312yes—
193C2×#95C2312yes—
194C2×#95C2312yes—
195C2×#95C2312yes—
196C2×#95C2312yes—
197C2×#95C2312yes—
198C2×#95C2312yes—
199C2×#95C2312yes—
200C2×#95C2312yes—
201C2×#95C2312yes—
202C2×#95C2312yes—
203C2×#95C2312yes—
204C2×#95C2312yes—
205C2×#95C2312yes—
206C2×#95C2312yes—
207C2×#95C2312yes—
208C2×#95C2312yes—
209C2×#95C2312yes—
210C2×#95C2312yes—
211C2×#95C2312yes—
212C2×#95C2312yes—
213C2×#95C2312yes—
214C2×#95C2312yes—
215C2×#95C2312yes—
216C2×#95C2312yes—
217C2×#95C2312yes—
218C2×#95C2311yescharacteristic
219C2×#95C2311yescharacteristic
220C2×#95C2311yescharacteristic
221C2×#95C2312yes—
222C2×#95C2311yescharacteristic
223C25—22no—
224C25—22no—
225C25—24no—
226C25—22no—
227C25—24no—
228C25—22no—
229C25—42no—
230C25—41no—
231C25—41no—
232C25—42no—
233C25C2×Q814yes—
234C25C2411yescharacteristic
235C25C2411yescharacteristic
236C25C2411yescharacteristic
237C22×Q8—24no—
238C22×Q8—24no—
239C22×Q8—42no—
240C22×Q8—42no—
241C22×Q8—42no—
242C22×Q8—42no—
243C22×Q8—42no—
244C23×C4—24no—
245C23×C4—22no—
246C23×C4—22no—
247C23×C4—24no—
248C23×C4—22no—
249C23×C4—22no—
250C23×C4—24no—
251C23×C4—24no—
252C23×C4—24no—
253C23×C4—24no—
254C23×C4—24no—
255C23×C4—24no—
256C23×C4—22no—
257C23×C4—22no—
258C23×C4—24no—
259C23×C4—42no—
260C23×C4—42no—
261C23×C4—41no—
262C23×C4—42no—
263C23×C4—42no—
264C23×C4—42no—
265C23×C4—41no—
266C23×C4—42no—
267C23×C4—42no—
268C23×C4—42no—
269C23×C4—42no—
270C23×C4—42no—
271C23×C4—42no—
272C23×C4—41no—
273C23×C4—42no—
274C23×C4—41no—
275C23×C4—42no—
276C23×C4C2×Q814yes—
277C23×C4C2×Q814yes—
278C23×C4C2412yes—
279C23×C4C2412yes—
280C23×C4C2412yes—
281C23×C4C2412yes—
282C23×C4C2412yes—
283C23×C4C2412yes—
284C23×C4C2412yes—
285C23×C4C2412yes—
286C23×C4C2412yes—
287C23×C4C2411yescharacteristic
288C23×C4C2411yescharacteristic
289C23×C4C2411yescharacteristic
290C23×C4C2411yescharacteristic
291C23×C4C2412yes—
292C23×C4C2412yes—
293C23×C4C2412yes—
294C22⋊Q8—432no—
295C2×C4⋊C4—24no—
296C2×C4⋊C4—24no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—42no—
299C2×C4⋊C4—42no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—42no—
306C2×C4⋊C4—42no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—42no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—416no—
312C2×C4⋊C4—42no—
313C2×C4⋊C4—42no—
314C2×C4⋊C4—42no—
315C2×C4⋊C4—41no—
316C2×C4⋊C4—41no—
317C2×C4⋊C4—42no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4—42no—
320C2×C4⋊C4—42no—
321C2×C4⋊C4—42no—
322C2×C4⋊C4—42no—
323C2×C4⋊C4—42no—
324C2×C4⋊C4—42no—
325C2×C4⋊C4—42no—
326C2×C4⋊C4—42no—
327C2×C4⋊C4—42no—
328C2×C22⋊C4—24no—
329C2×C22⋊C4—24no—
330C2×C22⋊C4—24no—
331C2×C22⋊C4—24no—
332C2×C22⋊C4—24no—
333C2×C22⋊C4—24no—
334C2×C22⋊C4—24no—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—24no—
338C2×C22⋊C4—24no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—24no—
341C2×C22⋊C4—24no—
342C2×C22⋊C4—24no—
343C2×C22⋊C4—24no—
344C2×C22⋊C4—24no—
345C2×C22⋊C4—24no—
346C2×C22⋊C4—24no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—24no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—416no—
352C2×C22⋊C4—41no—
353C2×C22⋊C4—41no—
354C2×C22⋊C4—41no—
355C2×C22⋊C4—41no—
356C2×C22⋊C4—41no—
357C2×C22⋊C4—41no—
358C2×C22⋊C4—41no—
359C2×C22⋊C4—41no—
360C2×C22⋊C4—42no—
361C2×C22⋊C4—42no—
362C2×C22⋊C4—42no—
363C2×C22⋊C4—42no—
364C2×C22⋊C4—42no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C2×C22⋊C4—42no—
368C2×C22⋊C4—42no—
369C2×C22⋊C4—42no—
370C2×C22⋊C4—42no—
371C2×C22⋊C4—42no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—432no—
374C2×C22⋊C4—416no—
375C2×C22⋊C4—42no—
376C2×C22⋊C4—42no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—41no—
379C2×C22⋊C4—41no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—41no—
382C2×C22⋊C4—41no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4C2×Q814yes—
387C2×C22⋊C4C2×Q814yes—
388C2×C22⋊C4C2×Q814yes—
389C2×C22⋊C4C2×Q814yes—
390C2×C22⋊C4#4118yes—
391C2×C42—42no—
392C2×C42—42no—
393C2×C42—42no—
394#95—24no—
395#95—24no—
396#95—24no—
397#95—24no—
398#95—24no—
399#95—24no—
400#95—24no—
401#95—24no—
402#95—24no—
403#95—42no—
404#95—42no—
405#95—41no—
406#95—42no—
407#95—41no—
408#95—42no—
409#95—42no—
410#95—42no—
411#95—42no—
412#95—42no—
413#95—42no—
414#95—42no—
415#95—42no—
416#95—42no—
417#95—42no—
418#95—41no—
419#95—41no—
420#95—42no—
421#95—42no—
422#95—42no—
423#95—42no—
424#95—42no—
425#95—42no—
426#95—42no—
427#95—42no—
428#95—42no—
429#95—42no—
430#95—42no—
431#95—42no—
432#95—42no—
433#95—42no—
434#95—42no—
435#95—42no—
436#95—42no—
437#95—42no—
438#95—42no—
439#95—42no—
440C24—22no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—21no—
445C24—22no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—21no—
450C24—22no—
451C24—21no—
452C24—21no—
453C24—22no—
454C24—28no—
455C24—22no—
456C24—22no—
457C24—21no—
458C24—21no—
459C24—21no—
460C24—22no—
461C24—21no—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—28no—
466C24—216no—
467C24—44no—
468C24—48no—
469C24—48no—
470C24—48no—
471C24—48no—
472C24—44no—
473C24—44no—
474C24—44no—
475C24—44no—
476C24—48no—
477C24—48no—
478C24—44no—
479C24—44no—
480C24—84no—
481C24—84no—
482C24—84no—
483C24—84no—
484C24—82no—
485C24—82no—
486C24—84no—
487C24C22×Q812yes—
488C24C22×Q812yes—
489C24C22×Q812yes—
490C24C2×#4114yes—
491C24H(5,𝔽2)12yes—
492C24H(5,𝔽2)12yes—
493C24H(5,𝔽2)14yes—
494C24H(5,𝔽2)12yes—
495C242−1+412yes—
496C24C2511yescharacteristic
497C2×Q8—48no—
498C2×Q8—48no—
499C2×Q8—84no—
500C2×Q8—84no—
501C2×Q8—84no—
502C2×Q8—84no—
503C2×Q8—84no—
504C22×C4—28no—
505C22×C4—216no—
506C22×C4—22no—
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—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—28no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
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—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—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—48no—
605C22×C4—48no—
606C22×C4—48no—
607C22×C4—48no—
608C22×C4—48no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—44no—
614C22×C4—44no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—84no—
618C22×C4—84no—
619C22×C4—84no—
620C22×C4—82no—
621C22×C4—82no—
622C22×C4—84no—
623C22×C4—84no—
624C22×C4—84no—
625C22×C4—82no—
626C22×C4—84no—
627C22×C4—82no—
628C22×C4—84no—
629C22×C4—84no—
630C22×C4—84no—
631C22×C4—84no—
632C22×C4—82no—
633C22×C4—82no—
634C22×C4—84no—
635C22×C4C22×Q812yes—
636C22×C4C22×Q812yes—
637C22×C4C22×Q812yes—
638C22×C4C22×Q812yes—
639C22×C4C2×#4114yes—
640C22×C4C2×#4114yes—
641C22×C4H(5,𝔽2)14yes—
642C4⋊C4—48no—
643C4⋊C4—48no—
644C4⋊C4—48no—
645C4⋊C4—44no—
646C4⋊C4—48no—
647C4⋊C4—44no—
648C4⋊C4—84no—
649C4⋊C4—84no—
650C4⋊C4—82no—
651C4⋊C4—82no—
652C4⋊C4—84no—
653C4⋊C4—84no—
654C22⋊C4—216no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C22⋊C4—44no—
658C22⋊C4—44no—
659C22⋊C4—48no—
660C22⋊C4—48no—
661C22⋊C4—48no—
662C22⋊C4—48no—
663C22⋊C4—48no—
664C22⋊C4—48no—
665C22⋊C4—48no—
666C22⋊C4—48no—
667C22⋊C4—48no—
668C22⋊C4—48no—
669C22⋊C4—84no—
670C22⋊C4—84no—
671C22⋊C4—82no—
672C22⋊C4—82no—
673C22⋊C4—84no—
674C42—84no—
675C23—22no—
676C23—22no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—24no—
689C23—24no—
690C23—22no—
691C23—22no—
692C23—24no—
693C23—22no—
694C23—22no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—24no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—24no—
709C23—24no—
710C23—416no—
711C23—432no—
712C23—42no—
713C23—41no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—42no—
722C23—42no—
723C23—41no—
724C23—42no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—41no—
729C23—42no—
730C23—42no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—41no—
738C23—41no—
739C23—42no—
740C23—416no—
741C23—88no—
742C23—816no—
743C23—88no—
744C23—88no—
745C23—88no—
746C23—816no—
747C23—816no—
748C23—88no—
749C23#53818yes—
750C23#54314yes—
751C23#54414yes—
752C23#55418yes—
753C23#55914yes—
754C23H(3,𝔽4)14yes—
755C23C23×Q811yescharacteristic
756C23C22×#4112yes—
757C23C2×H(5,𝔽2)11yescharacteristic
758C23C2×H(5,𝔽2)12yes—
759C23C2×H(5,𝔽2)11yescharacteristic
760C23C2×H(5,𝔽2)11yescharacteristic
761C23C2×H(5,𝔽2)12yes—
762C23C2×2−1+411yescharacteristic
763C23#58511yescharacteristic
764C23#58511yescharacteristic
765C23#58512yes—
766Q8—816no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—24no—
781C2×C4—24no—
782C2×C4—24no—
783C2×C4—24no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
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—42no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—416no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—88no—
873C2×C4—816no—
874C2×C4—816no—
875C2×C4—88no—
876C2×C4—88no—
877C22—24no—
878C22—24no—
879C22—28no—
880C22—24no—
881C22—24no—
882C22—24no—
883C22—28no—
884C22—28no—
885C22—24no—
886C22—28no—
887C22—24no—
888C22—28no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—44no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—44no—
901C22—42no—
902C22—44no—
903C22—832no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—82no—
908C22—82no—
909C22—81no—
910C22#280418yes—
911C22C2×#53812yes—
912C22C2×#54311yescharacteristic
913C22C2×#54411yescharacteristic
914C22#345811yescharacteristic
915C22C2×#55412yes—
916C22C2×#55911yescharacteristic
917C22#350112yes—
918C22#351312yes—
919C22#351312yes—
920C22#352012yes—
921C22#352112yes—
922C22C2×H(3,𝔽4)11yescharacteristic
923C22#353212yes—
924C22#353412yes—
925C22#353411yescharacteristic
926C22#353411yescharacteristic
927C22#353511yescharacteristic
928C22#353511yescharacteristic
929C22#353512yes—
930C22#354212yes—
931C22#354311yescharacteristic
932C22#354511yescharacteristic
933C22#354512yes—
934C4—42no—
935C4—42no—
936C4—42no—
937C4—42no—
938C4—44no—
939C4—44no—
940C4—44no—
941C4—82no—
942C4—82no—
943C4—82no—
944C4—82no—
945C4—82no—
946C4—82no—
947C4—82no—
948C4—82no—
949C4—82no—
950C2—28no—
951C2—44no—
952C2—82no—
953C2#3713411yescharacteristic
954C2#3747811yescharacteristic
955C2#3809712yes—
956C2#3895912yes—
957C2#4080812yes—
958C2#4083712yes—
959C2#4328811yescharacteristic
960C2#4332511yescharacteristic
961C2C2×#280411yescharacteristic
962C2#5231011yescharacteristic
963C2#5292511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC24C25
prime radicalC26C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #17296C2semidirect
2. #17153C2semidirect
3. #16987C2semidirect
4. #16951C2semidirect
5. #16823C2semidirect
6. #16707C2semidirect
7. #16609C2semidirect
8. #16339C2semidirect
9. #16118C2semidirect
10. #15378C2semidirect
11. #14934C2semidirect
12. #14767C2semidirect
14. #14263C2semidirect
16. #14052C2semidirect
25. C2×#400C22semidirect
28. C2×#391C22semidirect
41. #1446C22semidirect
42. #1446C22semidirect
43. #1446C22semidirect
44. #1445C22semidirect
45. #1445C22semidirect
46. #1444C22semidirect
47. #1444C22semidirect
48. #1444C22semidirect
49. #1444C22semidirect
50. #1443C22semidirect
51. #1443C22semidirect
52. #1442C22semidirect
53. #1442C22semidirect
54. #1442C22semidirect
55. #1442C22semidirect
56. #1442C22semidirect
57. #1442C22semidirect
58. #1442C22semidirect
59. #1442C22semidirect
60. #1442C22semidirect
61. #1442C22semidirect
62. #1442C22semidirect
63. #1442C22semidirect
64. #1442C22semidirect
65. #1441C22semidirect
66. #1441C22semidirect
67. #1441C22semidirect
92. #1436C22semidirect
93. #1436C22semidirect
94. C4⋊#95C22semidirect
139. C22×C22⋊C4Q8semidirect

Maximal subgroups

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

subgroupindex
#172962
#171532
#169872
#169512
#168232
#167072
#166092
#163392
#161182
#153782
#149342
#147672
#147172
#142632
#141272
#140522
#139032
#138692
C2×#14392