Finite Group Databasebeta

← #6440339

Subgroups — #6440339

Order 512.

4242 conjugacy classes of subgroups.

The subgroup lattice has 1123 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3489C211yesmaximal, characteristic
2C2×#3093C211yesmaximal, characteristic, complemented
3C22×#485C211yesmaximal, characteristic, complemented
4#34044C211yesmaximal, characteristic, complemented
5#24017C214yesmaximal, complemented
6#24016C214yesmaximal, complemented
7#24010C214yesmaximal, complemented
8#24008C214yesmaximal, complemented
9#23489C211yesmaximal, characteristic, complemented
10#23488C211yesmaximal, characteristic, complemented
11#23484C211yesmaximal, characteristic, complemented
12#23484C211yesmaximal, characteristic, complemented
13#20911C211yesmaximal, characteristic, complemented
14#20908C211yesmaximal, characteristic, complemented
15#20848C211yesmaximal, characteristic, complemented
16#20847C211yesmaximal, characteristic, complemented
17#20603C211yesmaximal, characteristic, complemented
18#20603C211yesmaximal, characteristic, complemented
19#20581C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C23×#41C2211yescharacteristic
22#3489—28no—
23#3489—28no—
24C2×D4×Q8—21no—
25C2×#548—21no—
26C2×#547—21no—
27C2×#547—22no—
28C2×#546—22no—
29C2×#546—21no—
30C2×#537C2211yescharacteristic
31C2×#537C2212yes—
32C2×#536C2211yescharacteristic
33C2×#536C2212yes—
34C2×#525C2212yes—
35C2×#525C2211yescharacteristic
36C22×C22⋊Q8C2212yes—
37C22×C22⋊Q8C2211yescharacteristic
38C2×#520C2211yescharacteristic
39C22×#117C2211yescharacteristic
40C22×#117C2211yescharacteristic
41#3093—28no—
42C2×#485—28no—
43C2×#485C2214yes—
44C2×#485C2212yes—
45C2×#485C2214yescomplemented
46C2×#485C2212yescomplemented
47C2×#482C2212yes—
48C2×#482C2212yescomplemented
49C2×#428C2211yescharacteristic, complemented
50C2×#428C2211yescharacteristic, complemented
51C22×#107C2211yescharacteristic, complemented
52C22×#106C2211yescharacteristic, complemented
53C2×#417C2211yescharacteristic, complemented
54C2×#417C2211yescharacteristic, complemented
55C2×#419C2211yescharacteristic, complemented
56C2×#419C2211yescharacteristic, complemented
57C2×#416C2211yescharacteristic, complemented
58C2×#416C2211yescharacteristic, complemented
59C22×#103C2211yescharacteristic, complemented
60C22×#103C2211yescharacteristic, complemented
61C2×#408C2211yescharacteristic
62C2×#408C2211yescharacteristic
63C2×#408C2211yescharacteristic
64C2×#408C2211yescharacteristic
65C2×#407C2211yescharacteristic
66C22×C22⋊C8C2211yescharacteristic
67#2311C2211yescharacteristic
68#2311C2211yescharacteristic
69#2311C2211yescharacteristic
70#2311C2211yescharacteristic
71#2311C2214yes—
72#2310—21no—
73#2309—21no—
74#2308—22no—
75#2297—22no—
76#2297—21no—
77#2297—21no—
78#2280C2214yes—
79#2036C2214yescomplemented
80#2036C2214yescomplemented
81#2036C2214yescomplemented
82#2035C2214yescomplemented
83#2035C2214yescomplemented
84#2035C2214yescomplemented
85#2034C2214yescomplemented
86#2033C2214yescomplemented
87#1875C2212yes—
88#1874C2212yescomplemented
89#1873C2212yes—
90#1873C2214yes—
91#1872C2212yescomplemented
92#1872C2214yescomplemented
93#1854C2214yescomplemented
94#1854C2214yescomplemented
95#1853C2214yescomplemented
96#1852C2214yescomplemented
97#1788C2214yescomplemented
98#1788C2214yescomplemented
99#1787C2214yescomplemented
100#1787C2214yescomplemented
101#1780C2214yes—
102#1779C2214yes—
103#1736C2211yescharacteristic, complemented
104#1736C2211yescharacteristic, complemented
105#1735C2211yescharacteristic, complemented
106#1735C2211yescharacteristic, complemented
107C2×2−1+4—24no—
108C2×2−1+4—24no—
109C2×2−1+4—24no—
110C2×2−1+4—24no—
111C2×2−1+4—42no—
112C2×2−1+4—42no—
113C22×#41—24no—
114C22×#41—24no—
115C22×#41—22no—
116C22×#41—21no—
117C22×#41—24no—
118C22×#41—24no—
119C22×#41—42no—
120C22×#41—42no—
121C22×#41D411yescharacteristic
122C22×#41D412yes—
123C22×#41D411yescharacteristic
124C22×#41C2311yescharacteristic
125C22×#41C2312yes—
126C22×#41C2311yescharacteristic
127C22×#41C2312yes—
128C22×#41C2311yescharacteristic
129C23×Q8—21no—
130C23×Q8D411yescharacteristic
131C23×Q8C2311yescharacteristic
132C23×Q8C2312yes—
133C23×D4D412yes—
134C23×D4D411yescharacteristic
135C24×C4C2312yes—
136C24×C4C2311yescharacteristic
137C22×M16C2311yescharacteristic
138C22×M16C2311yescharacteristic
139C23×C8C2311yescharacteristic
140C23×C8C2311yescharacteristic
141D4×Q8—216no—
142#548—216no—
143#547—216no—
144#547—232no—
145#546—216no—
146#546—232no—
147#537—24no—
148#537—28no—
149#537—28no—
150#537—24no—
151#536—24no—
152#536—28no—
153#536—28no—
154#536—24no—
155C2×C4⋊Q8—21no—
156C2×C4⋊Q8—22no—
157C2×#124—21no—
158C2×#124—22no—
159#525—24no—
160#525—28no—
161#525—28no—
162#525D418yes—
163C2×#123—22no—
164C2×#123—22no—
165C2×#123—22no—
166C2×#123—22no—
167C2×#123—21no—
168C2×C22⋊Q8—21no—
169C2×C22⋊Q8—22no—
170C2×C22⋊Q8—22no—
171C2×C22⋊Q8—21no—
172C2×C22⋊Q8—22no—
173C2×C22⋊Q8—21no—
174C2×C22⋊Q8—24no—
175C2×C22⋊Q8—28no—
176C2×C22⋊Q8—28no—
177C2×C22⋊Q8D418yes—
178C2×C22⋊Q8C2312yes—
179C2×C22⋊Q8C2312yes—
180C2×C22⋊Q8C2312yes—
181C2×C22⋊Q8C2311yescharacteristic
182C2×C22⋊Q8C2312yes—
183C2×C22⋊Q8C2312yes—
184C2×C22⋊Q8C2311yescharacteristic
185C2×#121—22no—
186C2×#121—22no—
187C2×#121—22no—
188C2×#121—21no—
189C2×#121—22no—
190C2×#121C2312yes—
191C2×#121C2311yescharacteristic
192C2×#121C2311yescharacteristic
193C2×#120—22no—
194C2×#120—21no—
195#520—24no—
196#520—24no—
197C2×C4×Q8—21no—
198C2×C4×D4—22no—
199C2×C4×D4—21no—
200C2×C4×D4—22no—
201C2×C4×D4—21no—
202C2×C4×D4—22no—
203C2×C4×D4—21no—
204C2×#117—21no—
205C2×#117—21no—
206C2×#117—21no—
207C2×#117—21no—
208C2×#117—24no—
209C2×#117—24no—
210C2×#117—42no—
211C2×#117—42no—
212C2×#117C2312yes—
213C2×#117C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C2×#117C2312yes—
216C2×#117C2312yes—
217C2×#117C2311yescharacteristic
218C2×#117C2312yes—
219C22×C4⋊C4—22no—
220C22×C4⋊C4—21no—
221C22×C4⋊C4C2311yescharacteristic
222C22×C4⋊C4C2311yescharacteristic
223C22×C4⋊C4C2312yes—
224C22×C4⋊C4C2311yescharacteristic
225C22×C4⋊C4C2312yes—
226C22×C22⋊C4—22no—
227C22×C22⋊C4—21no—
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230C22×C42—21no—
231C22×C42—21no—
232#485—216no—
233#485—216no—
234#485—28no—
235#485—28no—
236#482—28no—
237#482—28no—
238#428—24no—
239#428—24no—
240C2×#107—24no—
241C2×#107C2312yes—
242C2×#107C2312yes—
243C2×#107C2314yes—
244C2×#106—24no—
245C2×#106C2312yes—
246C2×#106C2312yes—
247C2×#106C2314yes—
248#419—42no—
249#419—42no—
250#417—24no—
251#417—24no—
252#416—42no—
253#416—42no—
254C2×#103—24no—
255C2×#103—24no—
256C2×#103C2314yes—
257C2×#103C2314yes—
258C2×#103C2312yes—
259C2×#103C2312yes—
260C2×#103C2312yes—
261C2×#103C2312yes—
262C2×#103C2314yes—
263C2×#103C2314yes—
264C2×#102C2312yes—
265C2×#102C2312yes—
266C2×#102C2312yes—
267C2×#102C2312yes—
268#408—24no—
269#408—24no—
270#408—42no—
271#408—42no—
272#407—24no—
273C2×C22⋊C8—24no—
274C2×C22⋊C8C2312yes—
275C2×C22⋊C8C2312yes—
276C2×C22⋊C8C2312yes—
277C2×C22⋊C8C2312yes—
278C2×C22⋊C8C2314yes—
279C2×C22⋊C8C2314yes—
280C2×C22⋊C8C2314yes—
281C2×C22⋊C8C2314yes—
282#391—21no—
283#391—21no—
284#391—24no—
285#391—21no—
286#391—21no—
287#390—21no—
288#390—21no—
289#390—24no—
290#390—21no—
291#390—21no—
292#386—22no—
293#386—22no—
294#386—24no—
295#386—24no—
296#386—22no—
297#386—22no—
298#381—24no—
299#380C2314yes—
300#380C2314yes—
301#380C2314yes—
302#380C2314yes—
303#379—24no—
304C4×C22⋊C4—24no—
305C4×C22⋊C4—24no—
306#340C2312yes—
307#340C2314yes—
308#340C2312yes—
309#340C2314yes—
310#340C2312yes—
311#340C2312yes—
312C25C2×D412yes—
313C25C2×D411yescharacteristic
3142−1+4—416no—
3152−1+4—416no—
3162−1+4—416no—
3172−1+4—416no—
318C2×#41—28no—
319C2×#41—216no—
320C2×#41—24no—
321C2×#41—24no—
322C2×#41—28no—
323C2×#41—24no—
324C2×#41—24no—
325C2×#41—24no—
326C2×#41—28no—
327C2×#41—24no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41—22no—
331C2×#41—24no—
332C2×#41—24no—
333C2×#41—22no—
334C2×#41—22no—
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—22no—
338C2×#41—22no—
339C2×#41—22no—
340C2×#41—22no—
341C2×#41—22no—
342C2×#41—22no—
343C2×#41—22no—
344C2×#41—22no—
345C2×#41—24no—
346C2×#41—24no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—42no—
350C2×#41—42no—
351C2×#41—44no—
352C2×#41—42no—
353C2×#41—42no—
354C2×#41—42no—
355C2×#41—42no—
356C2×#41—416no—
357C2×#41—416no—
358C2×#41—416no—
359C2×#41—416no—
360C2×#41—48no—
361C2×#41—44no—
362C2×#41—44no—
363C2×#41—48no—
364C2×#41C2×D414yes—
365C2×#41#4114yes—
366C2×#41#4114yes—
367C22×Q8—28no—
368C22×Q8—24no—
369C22×Q8—24no—
370C22×Q8—24no—
371C22×Q8—24no—
372C22×Q8—22no—
373C22×Q8—21no—
374C22×Q8—22no—
375C22×Q8—22no—
376C22×Q8—22no—
377C22×Q8—24no—
378C22×Q8—24no—
379C22×Q8—22no—
380C22×Q8—22no—
381C22×Q8—42no—
382C22×Q8—42no—
383C22×Q8—42no—
384C22×Q8—44no—
385C22×Q8—44no—
386C22×Q8C2×D414yes—
387C22×Q8C2×D411yescharacteristic
388C22×Q8C2×D412yes—
389C22×Q8C2×D411yescharacteristic
390C22×Q8C2412yes—
391C22×Q8C2411yescharacteristic
392C22×D4—28no—
393C22×D4—21no—
394C22×D4—22no—
395C22×D4—21no—
396C22×D4—22no—
397C22×D4—21no—
398C22×D4—24no—
399C22×D4—28no—
400C22×D4—24no—
401C22×D4—42no—
402C22×D4—44no—
403C22×D4C2×D412yes—
404C22×D4C2×D411yescharacteristic
405C22×D4C2×D412yes—
406C22×D4C2×D412yes—
407C22×D4C2×D412yes—
408C22×D4C2×D412yes—
409C22×D4C2×D411yescharacteristic
410C22×D4C2411yescharacteristic
411C23×C4—22no—
412C23×C4—22no—
413C23×C4—22no—
414C23×C4—22no—
415C23×C4—22no—
416C23×C4—21no—
417C23×C4—22no—
418C23×C4—21no—
419C23×C4—22no—
420C23×C4—21no—
421C23×C4—24no—
422C23×C4—24no—
423C23×C4—24no—
424C23×C4—24no—
425C23×C4—22no—
426C23×C4—21no—
427C23×C4—21no—
428C23×C4—42no—
429C23×C4—42no—
430C23×C4C2×D412yes—
431C23×C4C2×D412yes—
432C23×C4C2×D412yes—
433C23×C4C2×D411yescharacteristic
434C23×C4C2×D411yescharacteristic
435C23×C4C2×D411yescharacteristic
436C23×C4C2×D414yes—
437C23×C4C2×D414yes—
438C23×C4C2412yes—
439C23×C4C2411yescharacteristic
440C23×C4C2411yescharacteristic
441C23×C4C2412yes—
442C23×C4C2411yescharacteristic
443C2×M16—22no—
444C2×M16—22no—
445C2×M16—22no—
446C2×M16—22no—
447C2×M16—22no—
448C2×M16—22no—
449C22×C8—22no—
450C22×C8—22no—
451C22×C8—22no—
452C22×C8—22no—
453C22×C8—22no—
454C22×C8—22no—
455C22×C8C2412yes—
456C22×C8C2412yes—
457C22×C8C2412yes—
458C22×C8C2412yes—
459C4⋊Q8—216no—
460C4⋊Q8—28no—
461#124—216no—
462#124—28no—
463#123—216no—
464#123—216no—
465#123—216no—
466#123—216no—
467#123—28no—
468C22⋊Q8—216no—
469C22⋊Q8—216no—
470C22⋊Q8—28no—
471C22⋊Q8—216no—
472C22⋊Q8—24no—
473C22⋊Q8—24no—
474C22⋊Q8—24no—
475C22⋊Q8—28no—
476C22⋊Q8—28no—
477C22⋊Q8—22no—
478C22⋊Q8—24no—
479C22⋊Q8—24no—
480C22⋊Q8—22no—
481C22⋊Q8—24no—
482C22⋊Q8—24no—
483C22⋊Q8—24no—
484C22⋊Q8C2×D414yes—
485C22⋊Q8C2×D418yes—
486C22⋊Q8C2×D418yes—
487C22⋊Q8C2×D414yes—
488#121—216no—
489#121—216no—
490#121—216no—
491#121—28no—
492#121—216no—
493#121—24no—
494#121—22no—
495#121—22no—
496#121—24no—
497#121C2×D414yes—
498#121C2×D414yes—
499#120—216no—
500#120—28no—
501C4×Q8—28no—
502C4×D4—216no—
503C4×D4—28no—
504C4×D4—216no—
505C4×D4—216no—
506C4×D4—28no—
507C4×D4—28no—
508#117—22no—
509#117—24no—
510#117—24no—
511#117—24no—
512#117—24no—
513#117—24no—
514#117—24no—
515#117—22no—
516#117—22no—
517#117—22no—
518#117—22no—
519#117—42no—
520#117—42no—
521#117—44no—
522#117—44no—
523#117—44no—
524#117—44no—
525#117C2×D414yes—
526C2×C4⋊C4—216no—
527C2×C4⋊C4—28no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—22no—
544C2×C4⋊C4—22no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—42no—
548C2×C4⋊C4—42no—
549C2×C4⋊C4C2×D414yes—
550C2×C4⋊C4C2412yes—
551C2×C4⋊C4C2412yes—
552C2×C4⋊C4C2412yes—
553C2×C4⋊C4C2412yes—
554C2×C4⋊C4C2411yescharacteristic
555C2×C4⋊C4C2412yes—
556C2×C4⋊C4C2411yescharacteristic
557C2×C22⋊C4—216no—
558C2×C22⋊C4—28no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—24no—
577C2×C22⋊C4—24no—
578C2×C22⋊C4—24no—
579C2×C22⋊C4—24no—
580C2×C22⋊C4—44no—
581C2×C22⋊C4—44no—
582C2×C42—22no—
583C2×C42—21no—
584C2×C42—22no—
585C2×C42—22no—
586C2×C42—22no—
587C2×C42—21no—
588C2×C42—21no—
589C2×C42—44no—
590C2×C42—44no—
591#107—28no—
592#107—24no—
593#107—24no—
594#106—28no—
595#106—24no—
596#106—24no—
597#103—28no—
598#103—28no—
599#103—24no—
600#103—24no—
601#103—42no—
602#103—42no—
603#103—44no—
604#103—44no—
605#102—24no—
606#102—24no—
607#102—42no—
608#102—42no—
609C22⋊C8—24no—
610C22⋊C8—24no—
611C22⋊C8—24no—
612C22⋊C8—24no—
613C22⋊C8—28no—
614C22⋊C8—28no—
615C22⋊C8—44no—
616C22⋊C8—44no—
617#95—24no—
618#95—24no—
619#95—24no—
620#95—24no—
621C24—22no—
622C24—22no—
623C24—21no—
624C24—24no—
625C24—24no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—44no—
630C24—44no—
631C24#12014yes—
632C24C22×D412yes—
633C24C22×D411yescharacteristic
634C24C22×D411yescharacteristic
635C24C22×D412yes—
636C24C22×D411yescharacteristic
637#41—28no—
638#41—28no—
639#41—28no—
640#41—28no—
641#41—28no—
642#41—28no—
643#41—48no—
644#41—48no—
645#41—48no—
646#41—48no—
647#41—432no—
648#41—416no—
649#41—48no—
650#41—48no—
651#41—416no—
652#41—48no—
653#41—48no—
654#41—464no—
655#41—432no—
656#41—44no—
657#41—44no—
658#41—44no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—28no—
663C2×Q8—22no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—22no—
667C2×Q8—24no—
668C2×Q8—22no—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—28no—
674C2×Q8—28no—
675C2×Q8—22no—
676C2×Q8—22no—
677C2×Q8—21no—
678C2×Q8—21no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—21no—
682C2×Q8—21no—
683C2×Q8—42no—
684C2×Q8—416no—
685C2×Q8—48no—
686C2×Q8—48no—
687C2×Q8—48no—
688C2×Q8—48no—
689C2×Q8—44no—
690C2×Q8—432no—
691C2×Q8—44no—
692C2×Q8—42no—
693C2×Q8—42no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8#12314yes—
697C2×Q8C22×D412yes—
698C2×Q8C22×D414yes—
699C2×D4—24no—
700C2×D4—24no—
701C2×D4—28no—
702C2×D4—24no—
703C2×D4—24no—
704C2×D4—24no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—28no—
712C2×D4—24no—
713C2×D4—22no—
714C2×D4—24no—
715C2×D4—22no—
716C2×D4—24no—
717C2×D4—22no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—416no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—432no—
730C2×D4—44no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—42no—
734C2×D4—42no—
735C2×D4—82no—
736C2×D4—84no—
737C2×D4#12318yes—
738C2×D4#12314yes—
739C2×D4C22×D412yes—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—28no—
747C22×C4—28no—
748C22×C4—28no—
749C22×C4—28no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—28no—
763C22×C4—28no—
764C22×C4—24no—
765C22×C4—24no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—28no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—24no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—42no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—44no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—44no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—82no—
808C22×C4—84no—
809C22×C4—82no—
810C22×C4—82no—
811C22×C4—82no—
812C22×C4—82no—
813C22×C4#12014yes—
814C22×C4#12014yes—
815C22×C4#12014yes—
816C22×C4C22×D412yes—
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D412yes—
820C22×C4C22×D412yes—
821C22×C4C22×D412yes—
822C22×C4C22×D412yes—
823C22×C4C22×D412yes—
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D412yes—
826C22×C4C22×D412yes—
827C22×C4C2×#4114yes—
828C22×C4C2×#4114yes—
829C22×C4C2×#4112yes—
830C22×C4C2×#4112yes—
831C22×C4H(5,𝔽2)12yes—
832C22×C4H(5,𝔽2)12yes—
833C22×C4C2511yescharacteristic
834M16—44no—
835M16—44no—
836C2×C8—22no—
837C2×C8—22no—
838C2×C8—22no—
839C2×C8—22no—
840C2×C8—22no—
841C2×C8—22no—
842C2×C8—22no—
843C2×C8—22no—
844C2×C8—22no—
845C2×C8—22no—
846C2×C8—22no—
847C2×C8—22no—
848C2×C8—44no—
849C2×C8—44no—
850C4⋊C4—28no—
851C4⋊C4—28no—
852C4⋊C4—28no—
853C4⋊C4—28no—
854C4⋊C4—24no—
855C4⋊C4—28no—
856C4⋊C4—28no—
857C4⋊C4—24no—
858C4⋊C4—24no—
859C4⋊C4—21no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—44no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4C22×D412yes—
874C4⋊C4C22×D414yes—
875C4⋊C4C22×D412yes—
876C22⋊C4—28no—
877C22⋊C4—28no—
878C22⋊C4—28no—
879C22⋊C4—28no—
880C22⋊C4—28no—
881C22⋊C4—24no—
882C22⋊C4—28no—
883C22⋊C4—28no—
884C22⋊C4—24no—
885C22⋊C4—24no—
886C22⋊C4—24no—
887C22⋊C4—24no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—42no—
892C22⋊C4—42no—
893C22⋊C4—84no—
894C22⋊C4—84no—
895C22⋊C4—84no—
896C22⋊C4—84no—
897C42—28no—
898C42—24no—
899C42—44no—
900C42—44no—
901C42—44no—
902C42—42no—
903C42—42no—
904C23—22no—
905C23—22no—
906C23—24no—
907C23—22no—
908C23—22no—
909C23—24no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—21no—
914C23—21no—
915C23—21no—
916C23—21no—
917C23—22no—
918C23—28no—
919C23—24no—
920C23—24no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—44no—
926C23—44no—
927C23—48no—
928C23—48no—
929C23—42no—
930C23—42no—
931C23—41no—
932C23—41no—
933C23—84no—
934C23—84no—
935C23—88no—
936C23—84no—
937C23—88no—
938C23C2×#12012yes—
939C23C2×#12012yes—
940C23C2×#12012yes—
941C23C2×#12314yes—
942C23C2×#12312yes—
943C23#53412yes—
944C23C23×D411yescharacteristic
945Q8—28no—
946Q8—24no—
947Q8—24no—
948Q8—22no—
949Q8—22no—
950Q8—48no—
951Q8—416no—
952Q8—48no—
953Q8—44no—
954Q8—42no—
955Q8—42no—
956Q8—41no—
957Q8—41no—
958D4—216no—
959D4—28no—
960D4—22no—
961D4—22no—
962D4—48no—
963D4—48no—
964D4—48no—
965D4—48no—
966D4—416no—
967D4—48no—
968D4—48no—
969D4—44no—
970D4—41no—
971D4—41no—
972D4—84no—
973D4—88no—
974C2×C4—28no—
975C2×C4—22no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—22no—
981C2×C4—28no—
982C2×C4—28no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—24no—
992C2×C4—24no—
993C2×C4—24no—
994C2×C4—24no—
995C2×C4—22no—
996C2×C4—24no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—24no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—48no—
1004C2×C4—48no—
1005C2×C4—48no—
1006C2×C4—416no—
1007C2×C4—416no—
1008C2×C4—44no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—48no—
1012C2×C4—42no—
1013C2×C4—41no—
1014C2×C4—42no—
1015C2×C4—41no—
1016C2×C4—48no—
1017C2×C4—42no—
1018C2×C4—42no—
1019C2×C4—42no—
1020C2×C4—42no—
1021C2×C4—42no—
1022C2×C4—42no—
1023C2×C4—44no—
1024C2×C4—42no—
1025C2×C4—42no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—42no—
1029C2×C4—42no—
1030C2×C4—42no—
1031C2×C4—84no—
1032C2×C4—88no—
1033C2×C4—84no—
1034C2×C4—84no—
1035C2×C4—88no—
1036C2×C4C2×#12012yes—
1037C2×C4C2×#12012yes—
1038C2×C4C2×#12012yes—
1039C2×C4C2×#12314yes—
1040C2×C4C2×#12312yes—
1041C2×C4#53412yes—
1042C2×C4#54614yes—
1043C2×C4#54614yes—
1044C2×C4#54614yes—
1045C2×C4#54614yes—
1046C2×C4C23×D411yescharacteristic
1047C2×C4C23×D411yescharacteristic
1048C2×C4C22×#4111yescharacteristic
1049C2×C4C22×#4111yescharacteristic
1050C2×C4C2×H(5,𝔽2)11yescharacteristic
1051C2×C4C2×H(5,𝔽2)11yescharacteristic
1052C8—42no—
1053C8—42no—
1054C8—42no—
1055C8—42no—
1056C22—24no—
1057C22—24no—
1058C22—22no—
1059C22—22no—
1060C22—22no—
1061C22—22no—
1062C22—24no—
1063C22—28no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—22no—
1068C22—42no—
1069C22—44no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—44no—
1076C22—42no—
1077C22—42no—
1078C22—44no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—88no—
1084C22—816no—
1085C22—82no—
1086C22—82no—
1087C22#240514yes—
1088C22C22×#12011yescharacteristic
1089C22C22×#12311yescharacteristic
1090C22C2×#53411yescharacteristic
1091C22#358412yes—
1092C22#358612yes—
1093C4—22no—
1094C4—22no—
1095C4—24no—
1096C4—42no—
1097C4—44no—
1098C4—42no—
1099C4—44no—
1100C4—42no—
1101C4—42no—
1102C4—82no—
1103C4—82no—
1104C4—82no—
1105C4—82no—
1106C4#240514yes—
1107C4C2×#54611yescharacteristic
1108C4C2×#54611yescharacteristic
1109C4C2×#54611yescharacteristic
1110C4C2×#54611yescharacteristic
1111C2—24no—
1112C2—42no—
1113C2—44no—
1114C2—42no—
1115C2—82no—
1116C2—82no—
1117C2C2×#240511yescharacteristic
1118C2#6036611yescharacteristic
1119C2#6036811yescharacteristic
1120C2#6052412yes—
1121C2#6076612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#3093C2semidirect
3. C22×#485C2semidirect
4. #34044C2semidirect
5. #24017C2semidirect
6. #24016C2semidirect
7. #24010C2semidirect
8. #24008C2semidirect
9. #23489C2semidirect
10. #23488C2semidirect
11. #23484C2semidirect
12. #23484C2semidirect
13. #20911C2semidirect
14. #20908C2semidirect
15. #20848C2semidirect
16. #20847C2semidirect
17. #20603C2semidirect
18. #20603C2semidirect
19. #20581C2semidirect
45. C2×#485C22semidirect
46. C2×#485C22semidirect
48. C2×#482C22semidirect
49. C2×#428C22semidirect
50. C2×#428C22semidirect
51. C22×#107C22semidirect
52. C22×#106C22semidirect
53. C2×#417C22semidirect
54. C2×#417C22semidirect
55. C2×#419C22semidirect
56. C2×#419C22semidirect
57. C2×#416C22semidirect
58. C2×#416C22semidirect
59. C22×#103C22semidirect
60. C22×#103C22semidirect
79. #2036C22semidirect
80. #2036C22semidirect
81. #2036C22semidirect
82. #2035C22semidirect
83. #2035C22semidirect
84. #2035C22semidirect
85. #2034C22semidirect
86. #2033C22semidirect
88. #1874C22semidirect
91. #1872C22semidirect
92. #1872C22semidirect
93. #1854C22semidirect
94. #1854C22semidirect
95. #1853C22semidirect
96. #1852C22semidirect
97. #1788C22semidirect
98. #1788C22semidirect
99. #1787C22semidirect
100. #1787C22semidirect
103. #1736C22semidirect
104. #1736C22semidirect
105. #1735C22semidirect
106. #1735C22semidirect

Maximal subgroups

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

subgroupindex
C2×#34892
C2×#30932
C22×#4852
#340442
#240172
#240162
#240102
#240082
#234892
#234882
#234842
#209112
#209082
#208482
#208472
#206032
#205812