Finite Group Databasebeta

← #6393549

Subgroups — #6393549

Order 512.

3137 conjugacy classes of subgroups.

The subgroup lattice has 1065 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3547C211yesmaximal, characteristic
2#60232C211yesmaximal, characteristic, complemented
3#60144C211yesmaximal, characteristic, complemented
4#22483C212yesmaximal, complemented
5#22481C212yesmaximal, complemented
6#22480C214yesmaximal, complemented
7#22411C212yesmaximal, complemented
8#22410C214yesmaximal, complemented
9D4×#101C212yesmaximal, complemented
10#21880C211yesmaximal, characteristic, complemented
11#21879C211yesmaximal, characteristic, complemented
12#21757C212yesmaximal, complemented
13#21756C212yesmaximal, complemented
14#21426C211yesmaximal, characteristic, complemented
15#21425C211yesmaximal, characteristic, complemented
16#20992C212yesmaximal, complemented
17#20991C212yesmaximal, complemented
18C2×#568C2212yes—
19#3547—22no—
20#3547—22no—
21#3547—22no—
22#3547—22no—
23#3547—22no—
24#3547—22no—
25#3547—22no—
26#3547—22no—
27C2×#562C414yes—
28C2×#555C412yes—
29C2×#555C2211yescharacteristic
30C2×#554C2211yescharacteristic
31C2×#553C412yes—
32C2×#552C2212yes—
33C2×D4×Q8C2211yescharacteristic
34C2×#548C2212yes—
35C2×#547C2211yescharacteristic
36C2×#544C412yes—
37C2×#542C414yes—
38C2×#540C412yes—
39C2×#537C2212yes—
40C2×#536C2212yes—
41C2×#533C2211yescharacteristic
42C2×#532C2211yescharacteristic
43C2×#529C2211yescharacteristic
44#2981—22no—
45#2981—22no—
46#2980—22no—
47#2979—22no—
48#2935—22no—
49#2935—22no—
50D4×M16C2212yes—
51D4×M16C2214yes—
52D4×M16C2212yes—
53D4×M16C2212yes—
54D4×M16C2214yes—
55D4×M16C2212yes—
56#2932—22no—
57#2931—22no—
58#2920C2211yescharacteristic
59#2920C2211yescharacteristic
60C2×#423C2211yescharacteristic
61C2×#413C2214yes—
62C22×#101C2214yes—
63#2879C2212yes—
64#2879C2212yes—
65#2879C2212yes—
66C2×C4×M16C2211yescharacteristic
67#1998C2212yes—
68#1998C2212yes—
69#1997C2212yes—
70#1997C2212yes—
71#1967C2212yes—
72#1967C2212yes—
73#1966C2212yes—
74#1966C2212yes—
75#1901C2212yes—
76#1901C2214yes—
77#1901C2212yes—
78#1901C2212yes—
79#1901C2212yes—
80#1901C2214yes—
81#1901C2214yes—
82#1901C2214yes—
83#1901C2214yes—
84#1901C2214yes—
85#1901C2212yes—
86#1901C2211yescharacteristic
87#1901C2211yescharacteristic
88#1900C2211yescharacteristic
89#1900C2212yes—
90#1900C2214yes—
91#1900C2214yes—
92#1900C2211yescharacteristic
93#1822C2214yes—
94#1821C2214yes—
95#1801C2214yes—
96#1801C2212yes—
97#1800C2212yes—
98#1785C2214yes—
99#1784C2214yes—
100C4×#101C2212yes—
101C4×#101C2214yes—
102C4×#100C2212yes—
103#1742C2214yes—
104C2×#343C2214yes—
105C22×#41C2312yes—
106C22×#41C2312yes—
107C23×Q8C2312yes—
108#568—48no—
109C2×#131—24no—
110C2×#131—24no—
111C22×M16C2311yescharacteristic
112C22×M16C2314yes—
113C22×M16C2314yes—
114C22×M16C2311yescharacteristic
115C22×M16C2314yes—
116C22×M16C2314yes—
117C22×M16C2312yes—
118#562—28no—
119#562—28no—
120#562—28no—
121#562—28no—
122#555—24no—
123#555—24no—
124#555—24no—
125#555—24no—
126#555—22no—
127#555—22no—
128#555—22no—
129#555—22no—
130#554—22no—
131#554—22no—
132#554—22no—
133#554—22no—
134#553—24no—
135#553—24no—
136#553—24no—
137#553—24no—
138#552—24no—
139#552—24no—
140#552—24no—
141#552—24no—
142D4×Q8—22no—
143D4×Q8—22no—
144D4×Q8—22no—
145D4×Q8—22no—
146#548—24no—
147#548—24no—
148#548—24no—
149#548—24no—
150#547—22no—
151#547—22no—
152#547—22no—
153#547—22no—
154#544—24no—
155#544—24no—
156#544—24no—
157#544—24no—
158#542—28no—
159#542—28no—
160#542—28no—
161#542—28no—
162#540—24no—
163#540—24no—
164#540—24no—
165#540—24no—
166#537—24no—
167#537—24no—
168#537—24no—
169#537—24no—
170#536—24no—
171#536—24no—
172#536—24no—
173#536—24no—
174#533—21no—
175#533—21no—
176#533—21no—
177#533—21no—
178#533—21no—
179#533—21no—
180#533—21no—
181#533—21no—
182#532D412yes—
183#532D412yes—
184#532D412yes—
185#532D412yes—
186#532D412yes—
187#532D412yes—
188#532D412yes—
189#532D412yes—
190C2×C4⋊Q8C2×C414yes—
191C2×C4⋊Q8C2×C412yes—
192C2×C4⋊Q8C2×C411yescharacteristic
193C2×C4⋊Q8C2311yescharacteristic
194C2×C4⋊Q8C2311yescharacteristic
195C2×#127C2×C411yescharacteristic
196#529—21no—
197#529—21no—
198#529—21no—
199#529—21no—
200#529—21no—
201#529—21no—
202#529—21no—
203#529—21no—
204C2×#126C2×C412yes—
205C2×#126C2×C414yes—
206C2×#125C2×C412yes—
207C2×#125C2×C414yes—
208C2×#125C2×C412yes—
209C2×#125C2311yescharacteristic
210C2×#124C2×C414yes—
211C2×#124C2×C414yes—
212C2×#124C2×C414yes—
213C2×#124C2×C412yes—
214C2×#124C2311yescharacteristic
215C2×#123C2×C412yes—
216C2×#123C2×C414yes—
217C2×#123C2×C414yes—
218C2×#123C2×C414yes—
219C2×#123C2×C414yes—
220C2×C22⋊Q8C2×C412yes—
221C2×C22⋊Q8C2×C414yes—
222C2×C22⋊Q8C2×C414yes—
223C2×C22⋊Q8C2×C414yes—
224C2×C22⋊Q8C2×C414yes—
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2312yes—
227C2×C22⋊Q8C2312yes—
228C2×C22⋊Q8C2312yes—
229C2×C22⋊Q8C2312yes—
230C2×#121C2×C414yes—
231C2×#121C2×C414yes—
232C2×#121C2×C414yes—
233C2×#121C2×C412yes—
234C2×#121C2×C414yes—
235C2×#121C2×C412yes—
236C2×#121C2×C411yescharacteristic
237C2×#121C2×C411yescharacteristic
238C2×#121C2×C412yes—
239C2×#121C2311yescharacteristic
240C2×#121C2312yes—
241C2×C4×Q8C2×C412yes—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2312yes—
244C2×C4×D4C2×C412yes—
245C2×C4×D4C2×C412yes—
246C2×C4×D4C2×C412yes—
247C2×C4×D4C2×C414yes—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2312yes—
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2×C412yes—
253C2×#117C2×C412yes—
254C2×#117C2×C414yes—
255C2×#117C2×C412yes—
256C2×#117C2312yes—
257C22×C4⋊C4C2×C412yes—
258C22×C4⋊C4C2312yes—
259C22×C42C2311yescharacteristic
260#436—22no—
261#436—24no—
262#436—22no—
263#436—22no—
264#436—24no—
265#436—22no—
266#435—24no—
267#435—24no—
268#435—24no—
269#435—24no—
270#435—24no—
271#435—24no—
272#435—24no—
273#435—24no—
274C8×D4—22no—
275C8×D4—24no—
276C8×D4—22no—
277C8×D4—22no—
278C8×D4—24no—
279C8×D4—22no—
280#432—21no—
281#432—21no—
282#432—21no—
283#432—21no—
284#431—21no—
285#431—21no—
286#431—21no—
287#431—21no—
288#423—21no—
289#423—21no—
290#423C2312yes—
291#423C2312yes—
292#423C2312yes—
293#423C2312yes—
294C2×C4⋊C8—21no—
295C2×C4⋊C8—21no—
296#413—48no—
297C2×#101—48no—
298C2×#101C2312yes—
299C2×#101C2314yes—
300C2×#101C2314yes—
301C2×#101C2314yes—
302C2×#101C2314yes—
303C2×#101C2314yes—
304C2×#101C2312yes—
305C2×#100C2312yes—
306C2×#100C2314yes—
307C2×#100C2312yes—
308#408—24no—
309#408—24no—
310#408—24no—
311#408—24no—
312#408—24no—
313#408—24no—
314#407C2314yes—
315#407C2314yes—
316#407C2314yes—
317#407C2314yes—
318#407C2311yescharacteristic
319#407C2312yes—
320#407C2311yescharacteristic
321C4×M16—21no—
322C4×M16—21no—
323C4×M16C2312yes—
324C4×M16C2312yes—
325C4×M16C2312yes—
326C4×M16C2312yes—
327C2×#97—21no—
328C2×C4×C8—21no—
329#343C2314yes—
330#343C2314yes—
331#343C2314yes—
332#343C2314yes—
333#343C2312yes—
334#343C2314yes—
335#343C2312yes—
336#343C2312yes—
337#343C2314yes—
338#343C2312yes—
339C2×#41—24no—
340C2×#41—24no—
341C2×#41—44no—
342C2×#41—44no—
343C2×#41—44no—
344C2×#41—44no—
345C2×#41C2×D414yes—
346C2×#41C2×D414yes—
347C2×#41C2×D414yes—
348C2×#41C2×D414yes—
349C22×Q8—24no—
350C22×Q8—24no—
351C22×Q8—44no—
352C22×Q8—44no—
353C22×Q8C22×C414yes—
354C22×Q8C22×C412yes—
355C22×Q8C22×C412yes—
356C22×Q8C2411yescharacteristic
357C22×Q8C2412yes—
358C22×D4C22×C414yes—
359C22×D4C22×C412yes—
360C22×D4C22×C414yes—
361C22×D4C22×C411yescharacteristic
362C22×D4C22×C411yescharacteristic
363C22×D4C22×C412yes—
364C22×D4C22×C412yes—
365C22×D4C22×C412yes—
366C22×D4C22×C412yes—
367C22×D4C2411yescharacteristic
368C23×C4C22×C412yes—
369C23×C4C22×C414yes—
370C23×C4C22×C414yes—
371C23×C4C22×C414yes—
372C23×C4C22×C411yescharacteristic
373C23×C4C22×C411yescharacteristic
374C23×C4C2412yes—
375C23×C4C2412yes—
376C23×C4C2411yescharacteristic
377#131—416no—
378#131—416no—
379C2×M16—21no—
380C2×M16—24no—
381C2×M16—22no—
382C2×M16—24no—
383C2×M16—24no—
384C2×M16—21no—
385C2×M16—24no—
386C2×M16—24no—
387C2×M16—28no—
388C2×M16—28no—
389C2×M16—42no—
390C2×M16—44no—
391C2×M16—44no—
392C2×M16—44no—
393C2×M16—44no—
394C2×M16—44no—
395C2×M16—44no—
396C2×M16—44no—
397C2×M16C2414yes—
398C2×M16C2412yes—
399C2×M16C2414yes—
400C2×M16C2412yes—
401C2×M16C2412yes—
402C2×M16C2412yes—
403C22×C8—21no—
404C22×C8—22no—
405C22×C8—24no—
406C22×C8—24no—
407C22×C8—21no—
408C22×C8—24no—
409C22×C8—24no—
410C4⋊Q8—28no—
411C4⋊Q8—28no—
412C4⋊Q8—24no—
413C4⋊Q8—24no—
414C4⋊Q8—21no—
415C4⋊Q8—21no—
416C4⋊Q8—21no—
417C4⋊Q8—21no—
418C4⋊Q8—21no—
419C4⋊Q8—21no—
420C4⋊Q8—21no—
421C4⋊Q8—21no—
422C4⋊Q8C22⋊C412yes—
423C4⋊Q8C22⋊C412yes—
424C4⋊Q8C22⋊C412yes—
425C4⋊Q8C22⋊C412yes—
426#127C22⋊C412yes—
427#127C22⋊C412yes—
428#127C22⋊C412yes—
429#127C22⋊C412yes—
430#126—28no—
431#126—28no—
432#126—22no—
433#126—22no—
434#126—22no—
435#126—22no—
436#125—28no—
437#125—28no—
438#125—24no—
439#125—24no—
440#125—22no—
441#125—22no—
442#125—22no—
443#125—22no—
444#125—21no—
445#125—21no—
446#125—21no—
447#125—21no—
448#124—28no—
449#124—28no—
450#124—28no—
451#124—28no—
452#124—28no—
453#124—28no—
454#124—21no—
455#124—21no—
456#124—21no—
457#124—21no—
458#124C22⋊C414yes—
459#124C22⋊C414yes—
460#124C22⋊C414yes—
461#124C22⋊C414yes—
462#123—28no—
463#123—28no—
464#123—28no—
465#123—28no—
466#123—28no—
467#123—28no—
468#123—22no—
469#123—22no—
470#123—22no—
471#123—22no—
472#123—28no—
473#123—28no—
474C22⋊Q8—28no—
475C22⋊Q8—28no—
476C22⋊Q8—22no—
477C22⋊Q8—22no—
478C22⋊Q8—22no—
479C22⋊Q8—22no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488C22⋊Q8—24no—
489C22⋊Q8—24no—
490C22⋊Q8—24no—
491C22⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8—24no—
494C22⋊Q8—28no—
495C22⋊Q8—28no—
496C22⋊Q8—28no—
497C22⋊Q8—28no—
498C22⋊Q8—28no—
499C22⋊Q8—28no—
500#121—28no—
501#121—28no—
502#121—28no—
503#121—28no—
504#121—28no—
505#121—28no—
506#121—24no—
507#121—24no—
508#121—28no—
509#121—28no—
510#121—24no—
511#121—24no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—24no—
517#121—24no—
518#121C22⋊C412yes—
519#121C22⋊C412yes—
520#121C22⋊C412yes—
521#121C22⋊C412yes—
522#121C22⋊C412yes—
523#121C22⋊C412yes—
524#121C22⋊C412yes—
525#121C22⋊C412yes—
526#121C22⋊C414yes—
527#121C22⋊C414yes—
528#121C22⋊C414yes—
529#121C22⋊C414yes—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—21no—
535C4×Q8—21no—
536C4×Q8—21no—
537C4×Q8—21no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×D4—24no—
543C4×D4—24no—
544C4×D4—24no—
545C4×D4—24no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—28no—
551C4×D4—28no—
552C4×D4—21no—
553C4×D4—21no—
554C4×D4—21no—
555C4×D4—21no—
556C4×D4C2×D412yes—
557C4×D4C2×D412yes—
558C4×D4C2×D412yes—
559C4×D4C2×D412yes—
560C4×D4C2×D414yes—
561C4×D4C2×D414yes—
562C4×D4C2×D414yes—
563C4×D4C2×D414yes—
564C4×D4C2×D412yes—
565C4×D4C2×D412yes—
566C4×D4C2×D412yes—
567C4×D4C2×D412yes—
568#117—22no—
569#117—22no—
570#117—22no—
571#117—22no—
572#117—24no—
573#117—24no—
574#117—24no—
575#117—24no—
576#117—28no—
577#117—28no—
578#117—22no—
579#117—22no—
580#117—22no—
581#117—22no—
582C2×C4⋊C4—24no—
583C2×C4⋊C4—24no—
584C2×C4⋊C4—24no—
585C2×C4⋊C4—24no—
586C2×C4⋊C4C22×C412yes—
587C2×C4⋊C4C22×C414yes—
588C2×C4⋊C4C22×C414yes—
589C2×C4⋊C4C22×C412yes—
590C2×C4⋊C4C22×C412yes—
591C2×C4⋊C4C22×C414yes—
592C2×C4⋊C4C22×C412yes—
593C2×C4⋊C4C22×C412yes—
594C2×C4⋊C4C22×C414yes—
595C2×C4⋊C4C22×C414yes—
596C2×C4⋊C4C22×C412yes—
597C2×C4⋊C4C22×C414yes—
598C2×C4⋊C4C22×C412yes—
599C2×C4⋊C4C22×C411yescharacteristic
600C2×C4⋊C4C22×C411yescharacteristic
601C2×C4⋊C4C22×C412yes—
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2412yes—
604C2×C4⋊C4C2411yescharacteristic
605C2×C22⋊C4C22×C412yes—
606C2×C22⋊C4C22×C412yes—
607C2×C22⋊C4C22×C414yes—
608C2×C22⋊C4C22×C414yes—
609C2×C22⋊C4C22×C414yes—
610C2×C22⋊C4C22×C414yes—
611C2×C22⋊C4C22×C412yes—
612C2×C22⋊C4C22×C414yes—
613C2×C22⋊C4C22×C414yes—
614C2×C22⋊C4C22×C412yes—
615C2×C22⋊C4C22×C412yes—
616C2×C22⋊C4C22×C412yes—
617C2×C22⋊C4C22×C412yes—
618C2×C22⋊C4C22×C412yes—
619C2×C22⋊C4C22×C412yes—
620C2×C42C22×C414yes—
621C2×C42C22×C414yes—
622C2×C42C22×C412yes—
623C2×C42C22×C411yescharacteristic
624C2×C42C22×C411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C4⋊C8—22no—
636C4⋊C8—22no—
637C4⋊C8—22no—
638C4⋊C8—22no—
639C4⋊C8—22no—
640C4⋊C8—22no—
641C4⋊C8—22no—
642C4⋊C8—22no—
643#101—24no—
644#101—28no—
645#101—44no—
646#101—44no—
647#101—42no—
648#101—44no—
649#101—44no—
650#100—24no—
651#100—42no—
652#100—44no—
653C22⋊C8—21no—
654C22⋊C8—22no—
655C22⋊C8—21no—
656C22⋊C8—21no—
657C22⋊C8—22no—
658C22⋊C8—21no—
659C22⋊C8—24no—
660C22⋊C8—24no—
661C22⋊C8—24no—
662C22⋊C8—24no—
663C22⋊C8—24no—
664C22⋊C8—24no—
665C22⋊C8—24no—
666C22⋊C8—24no—
667#97—22no—
668#97—22no—
669#97—22no—
670#97—22no—
671C4×C8—22no—
672C4×C8—22no—
673C4×C8—22no—
674C4×C8—22no—
675C24C23×C412yes—
676C24C23×C412yes—
677C24C23×C411yescharacteristic
678C24C23×C412yes—
679#41—44no—
680#41—44no—
681#41—44no—
682#41—44no—
683#41—44no—
684#41—44no—
685#41—44no—
686#41—44no—
687#41—84no—
688#41—84no—
689#41—84no—
690#41—84no—
691C2×Q8—22no—
692C2×Q8—22no—
693C2×Q8—28no—
694C2×Q8—21no—
695C2×Q8—21no—
696C2×Q8—22no—
697C2×Q8—22no—
698C2×Q8—22no—
699C2×Q8—24no—
700C2×Q8—22no—
701C2×Q8—24no—
702C2×Q8—44no—
703C2×Q8—48no—
704C2×Q8—84no—
705C2×Q8—84no—
706C2×Q8—84no—
707C2×Q8—84no—
708C2×Q8—82no—
709C2×Q8C2×C22⋊C414yes—
710C2×Q8C2×C22⋊C414yes—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—28no—
714C2×D4—28no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—44no—
724C2×D4—48no—
725C2×D4—82no—
726C2×D4—82no—
727C2×D4—84no—
728C2×D4C2×C22⋊C412yes—
729C2×D4C2×C22⋊C412yes—
730C2×D4C2×C22⋊C412yes—
731C2×D4C2×C22⋊C412yes—
732C2×D4C2×C22⋊C414yes—
733C2×D4C2×C22⋊C414yes—
734C2×D4C2×C22⋊C414yes—
735C2×D4C2×C22⋊C414yes—
736C2×D4C2×C22⋊C414yes—
737C2×D4C2×C22⋊C414yes—
738C2×D4C2×C22⋊C414yes—
739C2×D4C2×C22⋊C414yes—
740C22×C4—24no—
741C22×C4—24no—
742C22×C4—22no—
743C22×C4—24no—
744C22×C4—24no—
745C22×C4—22no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—28no—
751C22×C4—42no—
752C22×C4—48no—
753C22×C4—48no—
754C22×C4—44no—
755C22×C4—81no—
756C22×C4—84no—
757C22×C4C2×C22⋊C411yescharacteristic
758C22×C4C2×C22⋊C411yescharacteristic
759C22×C4C2×C22⋊C411yescharacteristic
760C22×C4C2×C22⋊C411yescharacteristic
761C22×C4C2×C22⋊C411yescharacteristic
762C22×C4C2×C22⋊C411yescharacteristic
763C22×C4C2×C22⋊C411yescharacteristic
764C22×C4C2×C22⋊C411yescharacteristic
765C22×C4C23×C412yes—
766C22×C4C23×C414yes—
767C22×C4C23×C411yescharacteristic
768C22×C4C23×C412yes—
769C22×C4C23×C411yescharacteristic
770C22×C4C23×C412yes—
771C22×C4C23×C412yes—
772C22×C4C23×C414yes—
773C22×C4C23×C412yes—
774C22×C4C23×C411yescharacteristic
775C22×C4C23×C411yescharacteristic
776C22×C4C23×C411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D414yes—
780C22×C4C22×D414yes—
781C22×C4C22×D414yes—
782C22×C4C22×D414yes—
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C2511yescharacteristic
786M16—24no—
787M16—22no—
788M16—22no—
789M16—24no—
790M16—24no—
791M16—22no—
792M16—24no—
793M16—22no—
794M16—22no—
795M16—22no—
796M16—22no—
797M16—24no—
798M16—48no—
799M16—48no—
800M16—42no—
801M16—44no—
802M16—84no—
803M16—84no—
804M16H(5,𝔽2)14yes—
805C2×C8—24no—
806C2×C8—22no—
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—24no—
810C2×C8—22no—
811C2×C8—24no—
812C2×C8—48no—
813C2×C8—48no—
814C2×C8—42no—
815C2×C8—44no—
816C2×C8—84no—
817C2×C8—84no—
818C4⋊C4—22no—
819C4⋊C4—22no—
820C4⋊C4—28no—
821C4⋊C4—28no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—28no—
827C4⋊C4—22no—
828C4⋊C4—22no—
829C4⋊C4—22no—
830C4⋊C4—22no—
831C4⋊C4—28no—
832C4⋊C4—24no—
833C4⋊C4—24no—
834C4⋊C4—24no—
835C4⋊C4—24no—
836C4⋊C4—22no—
837C4⋊C4—22no—
838C4⋊C4—22no—
839C4⋊C4—22no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—22no—
843C4⋊C4—22no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4C2×C22⋊C412yes—
847C4⋊C4C2×C22⋊C412yes—
848C4⋊C4C2×C22⋊C412yes—
849C4⋊C4C2×C22⋊C412yes—
850C4⋊C4C2×C22⋊C414yes—
851C4⋊C4C2×C22⋊C414yes—
852C22⋊C4—24no—
853C22⋊C4—24no—
854C22⋊C4—28no—
855C22⋊C4—28no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—22no—
859C22⋊C4—22no—
860C22⋊C4—22no—
861C22⋊C4—22no—
862C22⋊C4—22no—
863C22⋊C4—22no—
864C22⋊C4—28no—
865C22⋊C4—22no—
866C22⋊C4—22no—
867C22⋊C4—22no—
868C22⋊C4—22no—
869C22⋊C4C2×C22⋊C414yes—
870C22⋊C4C2×C22⋊C414yes—
871C22⋊C4C2×C22⋊C414yes—
872C22⋊C4C2×C22⋊C414yes—
873C22⋊C4C2×C22⋊C414yes—
874C22⋊C4C2×C22⋊C414yes—
875C22⋊C4C2×C22⋊C414yes—
876C22⋊C4C2×C22⋊C414yes—
877C42—28no—
878C42—24no—
879C42—24no—
880C42—22no—
881C42—22no—
882C42C2×C22⋊C411yescharacteristic
883C42C2×C22⋊C411yescharacteristic
884C42C2×C22⋊C411yescharacteristic
885C42C2×C22⋊C411yescharacteristic
886C42C2×C22⋊C411yescharacteristic
887C42C2×C22⋊C411yescharacteristic
888C42C2×C22⋊C411yescharacteristic
889C42C2×C22⋊C411yescharacteristic
890C42C22×D411yescharacteristic
891C42C22×D411yescharacteristic
892C42C22×D411yescharacteristic
893C42C22×D411yescharacteristic
894C42C22×D411yescharacteristic
895C42C22×D411yescharacteristic
896C42C22×D411yescharacteristic
897C42C22×D411yescharacteristic
898C23—24no—
899C23—22no—
900C23—24no—
901C23—22no—
902C23—24no—
903C23—41no—
904C23—42no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23C22×C22⋊C411yescharacteristic
912C23C22×C22⋊C411yescharacteristic
913C23C22×C22⋊C414yes—
914C23C22×C22⋊C414yes—
915C23C24×C411yescharacteristic
916Q8—44no—
917Q8—44no—
918Q8—41no—
919Q8—42no—
920Q8—41no—
921Q8—42no—
922Q8—42no—
923Q8—44no—
924Q8—88no—
925Q8—82no—
926Q8—82no—
927D4—24no—
928D4—24no—
929D4—42no—
930D4—42no—
931D4—44no—
932D4—44no—
933D4—44no—
934D4—44no—
935D4—44no—
936D4—44no—
937D4—44no—
938D4—44no—
939D4—41no—
940D4—41no—
941D4—42no—
942D4—88no—
943D4—82no—
944D4—82no—
945D4—88no—
946C2×C4—24no—
947C2×C4—22no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—24no—
955C2×C4—24no—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—24no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—24no—
971C2×C4—28no—
972C2×C4—24no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—44no—
983C2×C4—44no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—44no—
987C2×C4—88no—
988C2×C4—88no—
989C2×C4—88no—
990C2×C4C22×C22⋊C411yescharacteristic
991C2×C4C22×C22⋊C411yescharacteristic
992C2×C4C22×C22⋊C411yescharacteristic
993C2×C4C22×C22⋊C414yes—
994C2×C4C22×C22⋊C411yescharacteristic
995C2×C4C22×C22⋊C411yescharacteristic
996C2×C4C22×C22⋊C411yescharacteristic
997C2×C4C22×C22⋊C411yescharacteristic
998C2×C4C22×C22⋊C411yescharacteristic
999C2×C4C22×C22⋊C411yescharacteristic
1000C2×C4C22×C22⋊C414yes—
1001C2×C4C22×C22⋊C411yescharacteristic
1002C2×C4C23×D411yescharacteristic
1003C2×C4C23×D411yescharacteristic
1004C2×C4C2×H(5,𝔽2)12yes—
1005C2×C4#58512yes—
1006C8—24no—
1007C8—44no—
1008C8—42no—
1009C8—42no—
1010C8—44no—
1011C8—42no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—24no—
1017C22—24no—
1018C22—21no—
1019C22—21no—
1020C22—24no—
1021C22—24no—
1022C22—24no—
1023C22—21no—
1024C22—21no—
1025C22—24no—
1026C22—42no—
1027C22—42no—
1028C22—42no—
1029C22—84no—
1030C22—82no—
1031C22—84no—
1032C22—84no—
1033C22C23×C22⋊C411yescharacteristic
1034C22C4×H(5,𝔽2)12yes—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—21no—
1041C4—21no—
1042C4—24no—
1043C4—21no—
1044C4—21no—
1045C4—24no—
1046C4—42no—
1047C4—42no—
1048C4—44no—
1049C4—44no—
1050C4—42no—
1051C4#288912yes—
1052C4#348411yescharacteristic
1053C4#348511yescharacteristic
1054C4#349612yes—
1055C2—22no—
1056C2—41no—
1057C2—41no—
1058C2—44no—
1059C2—44no—
1060C2—82no—
1061C2#3425611yescharacteristic
1062C2C2×#288911yescharacteristic
1063C2#6007611yescharacteristic
subgroupG/H
center, socleC22C23×C22⋊C4
commutatorC23C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#3547C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×#532 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #60232C2semidirect
3. #60144C2semidirect
4. #22483C2semidirect
5. #22481C2semidirect
6. #22480C2semidirect
7. #22411C2semidirect
8. #22410C2semidirect
9. D4×#101C2semidirect
10. #21880C2semidirect
11. #21879C2semidirect
12. #21757C2semidirect
13. #21756C2semidirect
14. #21426C2semidirect
15. #21425C2semidirect
16. #20992C2semidirect
17. #20991C2semidirect

Maximal subgroups

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

subgroupindex
C2×#35472
#602322
#601442
#224832
#224812
#224802
#224112
#224102
D4×#1012
#218802
#218792
#217572
#217562
#214262
#214252
#209922
#209912