Finite Group Databasebeta

← #6469952

Subgroups — #6469952

Order 512.

4993 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#525C211yesmaximal, characteristic, complemented
2C2×#3196C211yesmaximal, characteristic, complemented
3C2×#3194C211yesmaximal, characteristic, complemented
4#36614C211yesmaximal, characteristic, complemented
5#32984C211yesmaximal, characteristic, complemented
6#32980C211yesmaximal, characteristic, complemented
7#32883C211yesmaximal, characteristic, complemented
8#32880C211yesmaximal, characteristic, complemented
9#29599C211yesmaximal, characteristic, complemented
10#29598C211yesmaximal, characteristic, complemented
11#29595C211yesmaximal, characteristic, complemented
12#29594C211yesmaximal, characteristic, complemented
13#24389C214yesmaximal, complemented
14#24388C214yesmaximal, complemented
15#24008C214yesmaximal, complemented
16#23923C214yesmaximal, complemented
17#21768C211yesmaximal, characteristic, complemented
18#21767C211yesmaximal, characteristic, complemented
19#20579C211yesmaximal, characteristic, complemented
20C23×#41C2211yescharacteristic
21C25×C4C2211yescharacteristic
22C2×#525—22no—
23C2×#525—22no—
24C2×#525—28no—
25C2×#525—28no—
26C2×#525C2211yescharacteristic
27C2×#525C2214yes—
28C2×#525C2214yes—
29C2×#525C2212yescomplemented
30C22×#123—21no—
31C22×C22⋊Q8C2211yescharacteristic
32C22×C22⋊Q8C2211yescharacteristic
33C22×#121C2211yescharacteristic
34C22×#121C2211yescharacteristic
35C22×#120—21no—
36C22×C4×D4—21no—
37C22×C4×D4—21no—
38C22×#117C2211yescharacteristic
39#3196—28no—
40#3194—28no—
41C2×#484C2211yescharacteristic, complemented
42C2×#481C2211yescharacteristic, complemented
43C2×#485C2212yescomplemented
44C2×#482C2212yescomplemented
45C2×#483C2211yescharacteristic, complemented
46C2×#480C2211yescharacteristic, complemented
47C2×#470C2212yescomplemented
48C2×#469C2212yescomplemented
49C2×#468C2212yescomplemented
50C2×#468C2212yescomplemented
51C2×#452C2212yescomplemented
52C2×#452C2214yescomplemented
53C2×#449C2212yescomplemented
54C2×#449C2214yescomplemented
55C2×#451C2211yescharacteristic, complemented
56C2×#448C2211yescharacteristic, complemented
57C2×#450C2211yescharacteristic, complemented
58C2×#447C2211yescharacteristic, complemented
59C2×#407C2211yescharacteristic
60C2×#407C2211yescharacteristic
61C2×#407C2214yescomplemented
62#2849—21no—
63#2849—22no—
64#2848C2211yescharacteristic
65#2848C2211yescharacteristic
66#2848C2212yescomplemented
67#2847C2211yescharacteristic
68#2847C2211yescharacteristic
69#2847C2212yescomplemented
70#2846—21no—
71C4×#120—21no—
72C4×#120—21no—
73C4×#120—22no—
74#2280C2211yescharacteristic
75#2280C2212yescomplemented
76#2036C2214yescomplemented
77#2035C2214yescomplemented
78#2034C2214yescomplemented
79#2033C2214yescomplemented
80#2001C2214yescomplemented
81#2000C2214yescomplemented
82#2000C2214yescomplemented
83#1999C2214yescomplemented
84#1895C2214yescomplemented
85#1894C2214yescomplemented
86#1875C2214yescomplemented
87#1875C2214yescomplemented
88#1873C2214yescomplemented
89#1873C2214yescomplemented
90#1854C2214yescomplemented
91#1854C2214yescomplemented
92#1824C2211yescharacteristic, complemented
93#1824C2211yescharacteristic, complemented
94#1823C2211yescharacteristic, complemented
95#1823C2211yescharacteristic, complemented
96#1788C2214yescomplemented
97#1788C2214yescomplemented
98#1787C2211yescharacteristic, complemented
99#1787C2211yescharacteristic, complemented
100#1786C2211yescharacteristic, complemented
101#1786C2211yescharacteristic, complemented
102#1779C2211yescharacteristic
103#1779C2211yescharacteristic
104#1779C2211yescharacteristic
105#1779C2211yescharacteristic
106#1779C2214yescomplemented
107C26D411yescharacteristic
108C22×#41—24no—
109C22×#41—24no—
110C22×#41—22no—
111C22×#41—48no—
112C22×#41C2314yes—
113C22×#41C2311yescharacteristic
114C23×Q8C2311yescharacteristic
115C23×D4—21no—
116C23×D4—21no—
117C23×D4—21no—
118C23×D4C2311yescharacteristic
119C24×C4—24no—
120C24×C4—24no—
121C24×C4—21no—
122C24×C4—48no—
123C24×C4D411yescharacteristic
124C24×C4D412yes—
125C24×C4D411yescharacteristic
126C24×C4D411yescharacteristic
127C24×C4D412yes—
128C24×C4C2311yescharacteristic
129C24×C4C2312yes—
130C24×C4C2312yes—
131C24×C4C2311yescharacteristic
132C24×C4C2311yescharacteristic
133C22×Q16C2312yescomplemented
134C22×SD16C2312yescomplemented
135C22×SD16C2312yescomplemented
136C22×D8C2312yescomplemented
137C22×M16C2312yes—
138C22×M16C2312yes—
139#525—232no—
140#525—232no—
141#525—216no—
142#525—216no—
143#525—216no—
144#525—216no—
145#525—24no—
146#525—24no—
147#525—48no—
148C2×#123—216no—
149C2×#123—24no—
150C2×#123—24no—
151C2×#123—21no—
152C2×#123—22no—
153C2×C22⋊Q8—24no—
154C2×C22⋊Q8—24no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—24no—
159C2×C22⋊Q8D418yescomplemented
160C2×C22⋊Q8C2311yescharacteristic
161C2×C22⋊Q8C2312yes—
162C2×C22⋊Q8C2311yescharacteristic
163C2×C22⋊Q8C2314yes—
164C2×C22⋊Q8C2312yes—
165C2×C22⋊Q8C2312yes—
166C2×C22⋊Q8C2312yes—
167C2×#121—24no—
168C2×#121—24no—
169C2×#121—22no—
170C2×#121—21no—
171C2×#121—21no—
172C2×#121—24no—
173C2×#121D418yescomplemented
174C2×#121C2311yescharacteristic
175C2×#121C2312yes—
176C2×#121C2311yescharacteristic
177C2×#121C2314yes—
178C2×#121C2312yes—
179C2×#121C2312yes—
180C2×#121C2312yes—
181C2×#120—216no—
182C2×#120—24no—
183C2×#120—24no—
184C2×#120—21no—
185C2×#120—21no—
186C2×#120—22no—
187C2×#120—21no—
188C2×#120—22no—
189C2×C4×D4—216no—
190C2×C4×D4—216no—
191C2×C4×D4—24no—
192C2×C4×D4—24no—
193C2×C4×D4—24no—
194C2×C4×D4—24no—
195C2×C4×D4—21no—
196C2×C4×D4—21no—
197C2×C4×D4—22no—
198C2×C4×D4—22no—
199C2×#117—22no—
200C2×#117—24no—
201C2×#117—24no—
202C2×#117C2311yescharacteristic
203C2×#117C2314yes—
204C2×#117C2312yes—
205C22×C4⋊C4—21no—
206C22×C4⋊C4—21no—
207C22×C4⋊C4C2311yescharacteristic
208C22×C4⋊C4C2311yescharacteristic
209C22×C22⋊C4—21no—
210C22×C22⋊C4—21no—
211C22×C22⋊C4—21no—
212C22×C22⋊C4—21no—
213C22×C22⋊C4—21no—
214C22×C42—21no—
215#485—28no—
216#484—24no—
217#483—24no—
218#482—28no—
219#481—24no—
220#480—24no—
221#470—28no—
222#469—28no—
223#468—28no—
224#468—28no—
225#452—28no—
226#452—48no—
227#451—24no—
228#450—24no—
229#449—28no—
230#449—48no—
231#448—24no—
232#447—24no—
233C2×#107C2312yescomplemented
234C2×#107C2312yescomplemented
235C2×#106C2312yescomplemented
236C2×#106C2312yescomplemented
237C2×#103C2312yescomplemented
238C2×#103C2312yescomplemented
239C2×#103C2312yescomplemented
240C2×#103C2312yescomplemented
241C2×#103C2314yescomplemented
242C2×#103C2314yescomplemented
243C2×#102C2312yescomplemented
244C2×#102C2312yescomplemented
245C2×#102C2312yescomplemented
246C2×#102C2312yescomplemented
247C2×#102C2314yescomplemented
248C2×#102C2314yescomplemented
249#407—24no—
250#407—24no—
251#407—48no—
252C2×C22⋊C8C2311yescharacteristic
253C2×C22⋊C8C2311yescharacteristic
254C2×C22⋊C8C2312yes—
255C2×C22⋊C8C2312yes—
256C2×C22⋊C8C2311yescharacteristic
257C2×C22⋊C8C2311yescharacteristic
258C2×C22⋊C8C2314yes—
259C2×C22⋊C8C2314yes—
260C2×C22⋊C8C2314yes—
261C2×C22⋊C8C2314yes—
262#386—22no—
263#386—21no—
264#386—21no—
265#386—22no—
266#386—22no—
267#386—22no—
268#386—22no—
269#385—22no—
270#385—21no—
271#385—21no—
272#385—22no—
273#385—22no—
274#385—22no—
275#385—22no—
276#381—21no—
277#381—22no—
278#380C2311yescharacteristic
279#380C2311yescharacteristic
280#380C2312yes—
281#380C2312yes—
282#380C2312yes—
283#380C2312yes—
284#380C2312yes—
285#379—21no—
286#379—21no—
287#379—22no—
288#379—21no—
289#379—22no—
290C4×C22⋊C4—21no—
291C4×C22⋊C4—21no—
292C4×C22⋊C4—22no—
293C4×C22⋊C4—22no—
294#340C2314yescomplemented
295#340C2314yescomplemented
296#340C2314yescomplemented
297#340C2314yescomplemented
298C25—24no—
299C25—21no—
300C25—44no—
301C25—44no—
302C25—42no—
303C25—42no—
304C25C2×D411yescharacteristic
305C25C2×D411yescharacteristic
306C25C2×D412yes—
307C25C2×D412yes—
308C25C2×D411yescharacteristic
309C2×#41—216no—
310C2×#41—28no—
311C2×#41—28no—
312C2×#41—22no—
313C2×#41—22no—
314C2×#41—28no—
315C2×#41—28no—
316C2×#41—44no—
317C2×#41—44no—
318C2×#41—44no—
319C2×#41—432no—
320C2×#41—432no—
321C2×#41—48no—
322C2×#41—48no—
323C22×Q8—22no—
324C22×Q8—21no—
325C22×Q8—44no—
326C22×Q8C2×D414yes—
327C22×Q8C2411yescharacteristic
328C22×Q8C2412yes—
329C22×D4—28no—
330C22×D4—28no—
331C22×D4—28no—
332C22×D4—24no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—24no—
336C22×D4—22no—
337C22×D4—21no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—22no—
343C22×D4—44no—
344C22×D4—48no—
345C22×D4—44no—
346C22×D4—44no—
347C22×D4—48no—
348C22×D4C2×D414yes—
349C22×D4C2411yescharacteristic
350C22×D4C2412yes—
351C23×C4—22no—
352C23×C4—22no—
353C23×C4—28no—
354C23×C4—28no—
355C23×C4—24no—
356C23×C4—21no—
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—28no—
362C23×C4—28no—
363C23×C4—24no—
364C23×C4—22no—
365C23×C4—22no—
366C23×C4—24no—
367C23×C4—24no—
368C23×C4—24no—
369C23×C4—24no—
370C23×C4—28no—
371C23×C4—28no—
372C23×C4—21no—
373C23×C4—44no—
374C23×C4—44no—
375C23×C4—44no—
376C23×C4—44no—
377C23×C4—44no—
378C23×C4—44no—
379C23×C4—44no—
380C23×C4—44no—
381C23×C4—44no—
382C23×C4—44no—
383C23×C4—44no—
384C23×C4—432no—
385C23×C4—432no—
386C23×C4—48no—
387C23×C4C2×D412yes—
388C23×C4C2×D411yescharacteristic
389C23×C4C2×D412yes—
390C23×C4C2×D412yes—
391C23×C4C2×D412yes—
392C23×C4C2×D412yes—
393C23×C4C2×D412yes—
394C23×C4C2×D412yes—
395C23×C4C2×D411yescharacteristic
396C23×C4C2×D412yes—
397C23×C4C2×D411yescharacteristic
398C23×C4C2×D411yescharacteristic
399C23×C4C2×D411yescharacteristic
400C23×C4C2×D414yes—
401C23×C4C2×D414yes—
402C23×C4C2412yes—
403C23×C4C2411yescharacteristic
404C23×C4C2411yescharacteristic
405C23×C4C2411yescharacteristic
406C23×C4C2412yes—
407C2×Q16—24no—
408C2×Q16—44no—
409C2×SD16—24no—
410C2×SD16—24no—
411C2×SD16—44no—
412C2×SD16—44no—
413C2×D8—24no—
414C2×D8—44no—
415C2×M16—24no—
416C2×M16—24no—
417C2×M16—44no—
418C2×M16—44no—
419C22×C8C2412yes—
420C22×C8C2412yes—
421C22×C8C2412yes—
422C22×C8C2412yes—
423#123—232no—
424#123—232no—
425#123—48no—
426#123—44no—
427C22⋊Q8—216no—
428C22⋊Q8—28no—
429C22⋊Q8—28no—
430C22⋊Q8—28no—
431C22⋊Q8—24no—
432C22⋊Q8—24no—
433C22⋊Q8—28no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—28no—
439C22⋊Q8—44no—
440C22⋊Q8C2×D418yes—
441C22⋊Q8C2×D418yes—
442#121—216no—
443#121—28no—
444#121—28no—
445#121—28no—
446#121—24no—
447#121—24no—
448#121—28no—
449#121—22no—
450#121—22no—
451#121—22no—
452#121—22no—
453#121—28no—
454#121—44no—
455#121C2×D418yes—
456#121C2×D418yes—
457#120—232no—
458#120—232no—
459#120—44no—
460#120—44no—
461#120—48no—
462#120—48no—
463#120—44no—
464C4×D4—232no—
465C4×D4—232no—
466C4×D4—232no—
467C4×D4—232no—
468C4×D4—48no—
469C4×D4—48no—
470C4×D4—44no—
471C4×D4—44no—
472#117—216no—
473#117—28no—
474#117—28no—
475#117—22no—
476#117—22no—
477#117—44no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—28no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—22no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—22no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—22no—
491C2×C4⋊C4C2×D414yes—
492C2×C4⋊C4C2×D414yes—
493C2×C4⋊C4C2412yes—
494C2×C4⋊C4C2412yes—
495C2×C4⋊C4C2411yescharacteristic
496C2×C4⋊C4C2411yescharacteristic
497C2×C4⋊C4C2412yes—
498C2×C4⋊C4C2412yes—
499C2×C22⋊C4—28no—
500C2×C22⋊C4—28no—
501C2×C22⋊C4—28no—
502C2×C22⋊C4—28no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—28no—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—22no—
528C2×C42—28no—
529C2×C42—24no—
530C2×C42—22no—
531C2×C42—21no—
532#107—24no—
533#107—24no—
534#106—24no—
535#106—24no—
536#103—24no—
537#103—24no—
538#103—24no—
539#103—24no—
540#103—44no—
541#103—44no—
542#102—24no—
543#102—24no—
544#102—24no—
545#102—24no—
546#102—44no—
547#102—44no—
548C22⋊C8—22no—
549C22⋊C8—22no—
550C22⋊C8—24no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553C22⋊C8—24no—
554C22⋊C8—28no—
555C22⋊C8—28no—
556C22⋊C8—44no—
557C22⋊C8—44no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—21no—
562#95—21no—
563#95—22no—
564#95—22no—
565C24—22no—
566C24—22no—
567C24—24no—
568C24—24no—
569C24—22no—
570C24—22no—
571C24—24no—
572C24—24no—
573C24—24no—
574C24—24no—
575C24—24no—
576C24—24no—
577C24—22no—
578C24—22no—
579C24—24no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—42no—
589C24—42no—
590C24—42no—
591C24—42no—
592C24—42no—
593C24—42no—
594C24—42no—
595C24—42no—
596C24—416no—
597C24—416no—
598C24—416no—
599C24—44no—
600C24—44no—
601C24—432no—
602C24—432no—
603C24—42no—
604C24—42no—
605C24#12014yes—
606C24C22×D411yescharacteristic
607C24C22×D411yescharacteristic
608C24C22×D412yes—
609C24C22×D412yes—
610C24C22×D411yescharacteristic
611#41—416no—
612#41—416no—
613#41—416no—
614#41—416no—
615#41—464no—
616#41—84no—
617#41—84no—
618C2×Q8—24no—
619C2×Q8—22no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—24no—
623C2×Q8—24no—
624C2×Q8—24no—
625C2×Q8—48no—
626C2×Q8—44no—
627C2×Q8—48no—
628C2×Q8C22×D414yes—
629C2×D4—216no—
630C2×D4—216no—
631C2×D4—28no—
632C2×D4—28no—
633C2×D4—24no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—24no—
640C2×D4—48no—
641C2×D4—44no—
642C2×D4—48no—
643C2×D4—432no—
644C2×D4—432no—
645C2×D4—44no—
646C2×D4—44no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—48no—
650C2×D4—432no—
651C2×D4—48no—
652C2×D4—48no—
653C2×D4—48no—
654C2×D4—44no—
655C2×D4—44no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—44no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—44no—
664C2×D4—44no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4C22×D414yes—
668C22×C4—216no—
669C22×C4—216no—
670C22×C4—22no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—24no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—216no—
682C22×C4—24no—
683C22×C4—24no—
684C22×C4—22no—
685C22×C4—24no—
686C22×C4—24no—
687C22×C4—24no—
688C22×C4—24no—
689C22×C4—24no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—24no—
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—24no—
697C22×C4—24no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—24no—
702C22×C4—22no—
703C22×C4—22no—
704C22×C4—24no—
705C22×C4—24no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—21no—
711C22×C4—48no—
712C22×C4—48no—
713C22×C4—42no—
714C22×C4—42no—
715C22×C4—42no—
716C22×C4—42no—
717C22×C4—42no—
718C22×C4—42no—
719C22×C4—42no—
720C22×C4—42no—
721C22×C4—42no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—416no—
726C22×C4—416no—
727C22×C4—416no—
728C22×C4—416no—
729C22×C4—416no—
730C22×C4—416no—
731C22×C4—432no—
732C22×C4—432no—
733C22×C4—48no—
734C22×C4—48no—
735C22×C4—432no—
736C22×C4—48no—
737C22×C4—44no—
738C22×C4—416no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—42no—
742C22×C4—42no—
743C22×C4—48no—
744C22×C4—42no—
745C22×C4#12014yes—
746C22×C4#12014yes—
747C22×C4#12014yes—
748C22×C4C22×D412yes—
749C22×C4C22×D411yescharacteristic
750C22×C4C22×D411yescharacteristic
751C22×C4C22×D411yescharacteristic
752C22×C4C22×D412yes—
753C22×C4C22×D412yes—
754C22×C4C22×D412yes—
755C22×C4C22×D412yes—
756C22×C4C22×D412yes—
757C22×C4C22×D412yes—
758C22×C4C22×D412yes—
759C22×C4H(5,𝔽2)18yes—
760C22×C4C2511yescharacteristic
761Q16—84no—
762SD16—84no—
763SD16—84no—
764D8—84no—
765M16—84no—
766M16—84no—
767C2×C8—22no—
768C2×C8—22no—
769C2×C8—22no—
770C2×C8—22no—
771C2×C8—24no—
772C2×C8—24no—
773C2×C8—24no—
774C2×C8—24no—
775C4⋊C4—216no—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—24no—
779C4⋊C4—24no—
780C4⋊C4—22no—
781C4⋊C4—22no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—24no—
787C4⋊C4—24no—
788C4⋊C4—44no—
789C4⋊C4—42no—
790C4⋊C4—42no—
791C4⋊C4—44no—
792C4⋊C4C22×D414yes—
793C4⋊C4C22×D414yes—
794C22⋊C4—216no—
795C22⋊C4—216no—
796C22⋊C4—216no—
797C22⋊C4—28no—
798C22⋊C4—28no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4—44no—
806C22⋊C4—44no—
807C22⋊C4—44no—
808C22⋊C4—42no—
809C22⋊C4—42no—
810C22⋊C4—42no—
811C22⋊C4—44no—
812C22⋊C4—44no—
813C22⋊C4—42no—
814C22⋊C4—42no—
815C22⋊C4—42no—
816C22⋊C4—42no—
817C22⋊C4—44no—
818C42—216no—
819C42—44no—
820C42—42no—
821C23—22no—
822C23—22no—
823C23—28no—
824C23—28no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—28no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—24no—
847C23—44no—
848C23—44no—
849C23—48no—
850C23—48no—
851C23—48no—
852C23—48no—
853C23—48no—
854C23—48no—
855C23—48no—
856C23—48no—
857C23—48no—
858C23—48no—
859C23—44no—
860C23—48no—
861C23—48no—
862C23—44no—
863C23—48no—
864C23—48no—
865C23—48no—
866C23—48no—
867C23—48no—
868C23—48no—
869C23—48no—
870C23—48no—
871C23—4128no—
872C23—48no—
873C23—48no—
874C23—44no—
875C23—44no—
876C23—44no—
877C23—48no—
878C23—42no—
879C23—42no—
880C23—44no—
881C23—41no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—88no—
887C23—88no—
888C23C2×#12012yes—
889C23C2×#12012yes—
890C23C2×#12012yes—
891C23#53414yes—
892C23#57514yes—
893C23#57512yes—
894C23#57512yes—
895C23C23×D411yescharacteristic
896Q8—24no—
897Q8—24no—
898Q8—48no—
899Q8—44no—
900Q8—42no—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—48no—
905D4—416no—
906D4—416no—
907D4—432no—
908D4—432no—
909D4—44no—
910D4—42no—
911D4—42no—
912D4—88no—
913D4—88no—
914D4—84no—
915D4—84no—
916D4—84no—
917C2×C4—28no—
918C2×C4—216no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—24no—
925C2×C4—24no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—28no—
929C2×C4—28no—
930C2×C4—24no—
931C2×C4—24no—
932C2×C4—24no—
933C2×C4—24no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—22no—
937C2×C4—22no—
938C2×C4—44no—
939C2×C4—44no—
940C2×C4—44no—
941C2×C4—48no—
942C2×C4—48no—
943C2×C4—48no—
944C2×C4—48no—
945C2×C4—48no—
946C2×C4—48no—
947C2×C4—48no—
948C2×C4—432no—
949C2×C4—44no—
950C2×C4—48no—
951C2×C4—48no—
952C2×C4—44no—
953C2×C4—48no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4—44no—
957C2×C4—44no—
958C2×C4—44no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—42no—
972C2×C4—84no—
973C2×C4C2×#12012yes—
974C2×C4C2×#12012yes—
975C2×C4C2×#12012yes—
976C2×C4#53414yes—
977C2×C4C23×D411yescharacteristic
978C2×C4C23×D411yescharacteristic
979C2×C4C2×H(5,𝔽2)14yes—
980C8—42no—
981C8—42no—
982C8—42no—
983C8—42no—
984C22—24no—
985C22—24no—
986C22—22no—
987C22—22no—
988C22—24no—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—22no—
994C22—22no—
995C22—22no—
996C22—22no—
997C22—24no—
998C22—22no—
999C22—22no—
1000C22—416no—
1001C22—416no—
1002C22—416no—
1003C22—432no—
1004C22—432no—
1005C22—42no—
1006C22—42no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—42no—
1012C22—42no—
1013C22—42no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—816no—
1021C22—84no—
1022C22—84no—
1023C22—82no—
1024C22—82no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22#300514yes—
1029C22C22×#12011yescharacteristic
1030C22C2×#53412yes—
1031C22C2×#57511yescharacteristic
1032C22C2×#57512yes—
1033C22C2×#57511yescharacteristic
1034C4—24no—
1035C4—22no—
1036C4—22no—
1037C4—22no—
1038C4—42no—
1039C4—44no—
1040C4—44no—
1041C4—44no—
1042C4—82no—
1043C4—82no—
1044C4—81no—
1045C4—81no—
1046C4—81no—
1047C4#348412yes—
1048C4#348412yes—
1049C2—24no—
1050C2—44no—
1051C2—44no—
1052C2—42no—
1053C2—42no—
1054C2—84no—
1055C2—161no—
1056C2#3498011yescharacteristic
1057C2C2×#300511yescharacteristic
1058C2#6035911yescharacteristic
1059C2#6074112yes—
1060C2#6075212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#525C2semidirect
2. C2×#3196C2semidirect
3. C2×#3194C2semidirect
4. #36614C2semidirect
5. #32984C2semidirect
6. #32980C2semidirect
7. #32883C2semidirect
8. #32880C2semidirect
9. #29599C2semidirect
10. #29598C2semidirect
11. #29595C2semidirect
12. #29594C2semidirect
13. #24389C2semidirect
14. #24388C2semidirect
15. #24008C2semidirect
16. #23923C2semidirect
17. #21768C2semidirect
18. #21767C2semidirect
19. #20579C2semidirect
29. C2×#525C22semidirect
41. C2×#484C22semidirect
42. C2×#481C22semidirect
43. C2×#485C22semidirect
44. C2×#482C22semidirect
45. C2×#483C22semidirect
46. C2×#480C22semidirect
47. C2×#470C22semidirect
48. C2×#469C22semidirect
49. C2×#468C22semidirect
50. C2×#468C22semidirect
51. C2×#452C22semidirect
52. C2×#452C22semidirect
53. C2×#449C22semidirect
54. C2×#449C22semidirect
55. C2×#451C22semidirect
56. C2×#448C22semidirect
57. C2×#450C22semidirect
58. C2×#447C22semidirect
61. C2×#407C22semidirect
66. #2848C22semidirect
69. #2847C22semidirect
75. #2280C22semidirect
76. #2036C22semidirect
77. #2035C22semidirect
78. #2034C22semidirect
79. #2033C22semidirect
80. #2001C22semidirect
81. #2000C22semidirect
82. #2000C22semidirect
83. #1999C22semidirect
84. #1895C22semidirect
85. #1894C22semidirect
86. #1875C22semidirect
87. #1875C22semidirect
88. #1873C22semidirect
89. #1873C22semidirect
90. #1854C22semidirect
91. #1854C22semidirect
92. #1824C22semidirect
93. #1824C22semidirect
94. #1823C22semidirect
95. #1823C22semidirect
96. #1788C22semidirect
97. #1788C22semidirect
98. #1787C22semidirect
99. #1787C22semidirect
100. #1786C22semidirect
101. #1786C22semidirect
106. #1779C22semidirect
133. C22×Q16C23semidirect
134. C22×SD16C23semidirect
135. C22×SD16C23semidirect
136. C22×D8C23semidirect
159. C2×C22⋊Q8D4semidirect
173. C2×#121D4semidirect
233. C2×#107C23semidirect
234. C2×#107C23semidirect
235. C2×#106C23semidirect
236. C2×#106C23semidirect
237. C2×#103C23semidirect
238. C2×#103C23semidirect
239. C2×#103C23semidirect
240. C2×#103C23semidirect
241. C2×#103C23semidirect
242. C2×#103C23semidirect
243. C2×#102C23semidirect
244. C2×#102C23semidirect
245. C2×#102C23semidirect
246. C2×#102C23semidirect
247. C2×#102C23semidirect
248. C2×#102C23semidirect
294. #340C23semidirect
295. #340C23semidirect
296. #340C23semidirect
297. #340C23semidirect

Maximal subgroups

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

subgroupindex
C22×#5252
C2×#31962
C2×#31942
#366142
#329842
#329802
#328832
#328802
#295992
#295982
#295952
#295942
#243892
#243882
#240082
#239232
#217682
#217672
#205792