Finite Group Databasebeta

← #6569709

Subgroups — #6569709

Order 512.

2172 conjugacy classes of subgroups.

The subgroup lattice has 867 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3356C211yesmaximal, characteristic, complemented
2C2×#3342C211yesmaximal, characteristic, complemented
3C2×#3324C211yesmaximal, characteristic
4C2×#3295C211yesmaximal, characteristic
5#39490C211yesmaximal, characteristic, complemented
6#38957C211yesmaximal, characteristic
7#30278C211yesmaximal, characteristic, complemented
8#30252C212yesmaximal, complemented
9#28540C211yesmaximal, characteristic, complemented
10#28530C211yesmaximal, characteristic, complemented
11#28510C211yesmaximal, characteristic, complemented
12#28418C211yesmaximal, characteristic, complemented
13#28402C211yesmaximal, characteristic, complemented
14#28374C211yesmaximal, characteristic, complemented
15#28361C212yesmaximal, complemented
16#28330C212yesmaximal, complemented
17#28320C212yesmaximal, complemented
18#27946C212yesmaximal, complemented
19#27925C212yesmaximal, complemented
20#27920C212yesmaximal, complemented
21#23797C211yesmaximal, characteristic, complemented
22#23735C212yesmaximal, complemented
23#20562C211yesmaximal, characteristic, complemented
24C2×#556C2211yescharacteristic
25C2×#556C2211yescharacteristic
26C2×#554C2211yescharacteristic
27C2×D42C2211yescharacteristic
28#3356—28no—
29#3342—28no—
30#3324—28no—
31#3295—28no—
32C2×#500C2211yescharacteristic, complemented
33C2×#498C2211yescharacteristic, complemented
34C2×#486C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#481C2212yes—
37C2×#485C2212yescomplemented
38C2×#485C2212yescomplemented
39C2×#485C2212yescomplemented
40C2×#482C2212yes—
41C2×#483C2212yescomplemented
42C2×#477C2211yescharacteristic, complemented
43C2×#475C2211yescharacteristic, complemented
44C2×#475C2211yescharacteristic, complemented
45C2×#475C2211yescharacteristic, complemented
46C2×#476C2211yescharacteristic
47C2×#474C2211yescharacteristic
48C2×#470C2212yescomplemented
49C2×#468C2212yes—
50C2×#467C2212yescomplemented
51C2×#465C2212yes—
52C2×#460C2211yescharacteristic
53C2×#460C2211yescharacteristic
54C2×#450C2212yes—
55C2×#450C2212yes—
56C2×C4×Q16C2211yescharacteristic, complemented
57C2×C4×Q16C2211yescharacteristic, complemented
58C2×C4×SD16C2211yescharacteristic
59C2×C4×SD16C2211yescharacteristic
60C2×#436C2211yescharacteristic
61C2×C8×D4C2211yescharacteristic
62C2×#428C2212yescomplemented
63C2×#427C2212yescomplemented
64C2×#418C2212yes—
65C22×#102C2212yes—
66#2862C2211yescharacteristic, complemented
67#2858C2211yescharacteristic
68#2689—24no—
69#2685—24no—
70#2621C2212yescomplemented
71#2620C2212yes—
72#2568C2211yescharacteristic, complemented
73#2567C2211yescharacteristic, complemented
74#2548C2211yescharacteristic
75#2542C2211yescharacteristic
76#2503C2212yescomplemented
77#2500C2212yes—
78#2499C2212yescomplemented
79#2453—22no—
80#2447—22no—
81#2435—22no—
82#2435C2212yes—
83#2426—22no—
84#2317C2212yescomplemented
85#2309C2212yes—
86C4×C4⋊Q8C2211yescharacteristic, complemented
87C4×#124C2211yescharacteristic
88#2293C2211yescharacteristic
89#2097C2212yescomplemented
90#2097C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2096C2212yescomplemented
94#2095C2212yescomplemented
95#2094C2212yes—
96#2094C2212yescomplemented
97#2093C2211yescharacteristic
98#2093C2212yescomplemented
99#2092C2212yes—
100#2092C2212yes—
101#2092C2212yescomplemented
102#2092C2212yescomplemented
103#2092C2212yescomplemented
104#2092C2212yescomplemented
105#2092C2212yescomplemented
106#2016C2211yescharacteristic, complemented
107#2015C2211yescharacteristic
108#2015C2211yescharacteristic
109#2015C2212yescomplemented
110#2015C2212yescomplemented
111#2013C2211yescharacteristic
112#2013C2212yescomplemented
113#1973C2212yes—
114#1973C2212yescomplemented
115#1968C2212yes—
116#1968C2212yescomplemented
117#1968C2212yescomplemented
118#1968C2212yescomplemented
119#1959C2212yescomplemented
120#1958C2212yes—
121#1958C2212yescomplemented
122#1847C2212yescomplemented
123#1846C2212yescomplemented
124#1844C2212yescomplemented
125#1770C2211yescharacteristic, complemented
126C8×C4⋊C4C2211yescharacteristic, complemented
127C4×C4⋊C8C2211yescharacteristic, complemented
128#1753C2212yescomplemented
129C8×C22⋊C4C2212yescomplemented
130#1750C2212yescomplemented
131#1744C2211yescharacteristic, complemented
132#1729C2212yescomplemented
133C23×D4—21no—
134C23×D4C2312yes—
135C22×Q16C2311yescharacteristic
136C22×Q16C2311yescharacteristic
137C22×SD16C2311yescharacteristic
138C22×SD16C2311yescharacteristic
139C22×SD16C2312yes—
140C22×SD16C2312yes—
141C22×M16C2312yes—
142C23×C8C2312yes—
143#556—24no—
144#556—24no—
145#556—24no—
146#556—24no—
147#554—24no—
148#554—24no—
149D42—24no—
150D42—24no—
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2311yescharacteristic
153C2×C4⋊Q8C2311yescharacteristic
154C2×C4⋊Q8C2311yescharacteristic
155C2×#127C2311yescharacteristic
156C2×#126—22no—
157C2×#126—22no—
158C2×#125—21no—
159C2×#124—21no—
160C2×#124—21no—
161C2×#124—22no—
162C2×#124C2311yescharacteristic
163C2×#124C2312yes—
164C2×C22⋊Q8—22no—
165C2×C22⋊Q8—22no—
166C2×C22⋊Q8C2312yes—
167C2×C22⋊Q8C2312yes—
168C2×C22⋊Q8C2312yes—
169C2×#121—21no—
170C2×#121C2312yes—
171C2×#120—22no—
172C2×C4×Q8—21no—
173C2×C4×Q8—21no—
174C2×C4×Q8C2311yescharacteristic
175C2×C4×Q8C2311yescharacteristic
176C2×C4×Q8C2311yescharacteristic
177C2×C4×D4—21no—
178C2×C4×D4C2311yescharacteristic
179C2×C4×D4C2311yescharacteristic
180C2×#117C2312yes—
181C2×#117C2312yes—
182C2×#117C2312yes—
183C22×C4⋊C4C2312yes—
184#500—24no—
185#498—24no—
186#486—24no—
187#486—24no—
188#485—28no—
189#485—28no—
190#485—28no—
191#483—28no—
192#482—28no—
193#481—28no—
194#477—24no—
195#476—24no—
196#475—24no—
197#475—24no—
198#475—24no—
199#474—24no—
200#470—28no—
201#468—28no—
202#467—28no—
203#465—28no—
204#460—24no—
205#460—24no—
206#450—28no—
207#450—28no—
208C4×Q16—24no—
209C4×Q16—24no—
210C4×SD16—24no—
211C4×SD16—24no—
212#436D418yes—
213C8×D4D418yes—
214#428—28no—
215#427—28no—
216C2×#107C2312yes—
217C2×#107C2312yes—
218C2×#107C2312yes—
219C2×#107C2312yes—
220C2×#107C2311yescharacteristic
221C2×#107C2311yescharacteristic
222C2×#106C2312yes—
223C2×#106C2312yes—
224C2×#106C2312yes—
225C2×#106C2312yes—
226C2×#106C2311yescharacteristic
227C2×#106C2311yescharacteristic
228C2×#106C2312yes—
229C2×#106C2312yes—
230C2×C4⋊C8C2311yescharacteristic
231C2×C4⋊C8C2311yescharacteristic
232#418—28no—
233C2×#103C2312yes—
234C2×#103C2312yes—
235C2×#103C2312yes—
236C2×#103C2312yes—
237C2×#103C2311yescharacteristic
238C2×#103C2311yescharacteristic
239C2×#103C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#102—28no—
244C2×#102C2312yes—
245C2×#102C2312yes—
246C2×#102C2312yes—
247C2×#102C2312yes—
248C2×#102C2311yescharacteristic
249C2×#102C2312yes—
250C2×#102C2312yes—
251C2×#102C2312yes—
252C2×#102C2312yes—
253C2×#102C2311yescharacteristic
254C2×C22⋊C8C2312yes—
255C2×C22⋊C8C2312yes—
256C2×#97C2312yes—
257C2×C4×C8C2312yes—
258C2×C4×C8C2312yes—
259C2×C4×C8C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261#400—22no—
262#400—24no—
263#399—22no—
264#398—24no—
265#397—24no—
266#397—24no—
267#396—24no—
268#395—22no—
269#394—24no—
270#394—24no—
271#394—24no—
272#394—22no—
273#391—22no—
274#391—22no—
275#391—22no—
276#391C2311yescharacteristic
277#391C2311yescharacteristic
278#391C2312yes—
279#391C2312yes—
280#391C2311yescharacteristic
281#390—24no—
282#390—22no—
283#390—22no—
284#390D412yes—
285#390C2311yescharacteristic
286#390C2312yes—
287#390C2312yes—
288#390C2312yes—
289#390C2312yes—
290#389—22no—
291#389—24no—
292#389—22no—
293#389D412yes—
294#388—22no—
295#388—24no—
296#388D414yes—
297#387—24no—
298#385—24no—
299#384C2311yescharacteristic
300#384C2312yes—
301#384C2312yes—
302#382C2312yes—
303#382C2312yes—
304#382C2312yes—
305#382C2311yescharacteristic
306#381—24no—
307#379—24no—
308#379—24no—
309C4×C4⋊C4—22no—
310C4×C4⋊C4C2311yescharacteristic
311C4×C22⋊C4—22no—
312C4×C22⋊C4C2312yes—
313C43C2311yescharacteristic
314#336C2312yes—
315#336C2312yes—
316#336C2311yescharacteristic
317#336C2311yescharacteristic
318#336C2311yescharacteristic
319#336C2311yescharacteristic
320#336C2312yes—
321C25—22no—
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8C2411yescharacteristic
326C22×Q8C2411yescharacteristic
327C22×Q8C2411yescharacteristic
328C22×D4—24no—
329C22×D4—22no—
330C22×D4—24no—
331C22×D4—24no—
332C22×D4—21no—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4—42no—
336C22×D4—42no—
337C22×D4—42no—
338C22×D4—44no—
339C22×D4—84no—
340C22×D4C2×D411yescharacteristic
341C22×D4C2412yes—
342C22×D4C2411yescharacteristic
343C23×C4—22no—
344C23×C4—21no—
345C23×C4C2412yes—
346C2×Q16—22no—
347C2×Q16—22no—
348C2×Q16—41no—
349C2×Q16—41no—
350C2×Q16—41no—
351C2×Q16—41no—
352C2×SD16—22no—
353C2×SD16—22no—
354C2×SD16—22no—
355C2×SD16—22no—
356C2×SD16—24no—
357C2×SD16—24no—
358C2×SD16—41no—
359C2×SD16—41no—
360C2×SD16—42no—
361C2×SD16—42no—
362C2×SD16—42no—
363C2×SD16—42no—
364C2×M16—42no—
365C2×M16—42no—
366C2×M16C2×D418yes—
367C22×C8—42no—
368C22×C8—42no—
369C22×C8C2×D418yes—
370C22×C8C2411yescharacteristic
371C22×C8C2412yes—
372C22×C8C2411yescharacteristic
373C22×C8C2412yes—
374C22×C8C2411yescharacteristic
375C22×C8C2411yescharacteristic
376C4⋊Q8—22no—
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379C4⋊Q8—22no—
380C4⋊Q8—22no—
381C4⋊Q8—22no—
382C4⋊Q8—41no—
383C4⋊Q8—41no—
384#127—22no—
385#127—22no—
386#126—48no—
387#126—48no—
388#125—44no—
389#124—22no—
390#124—41no—
391#124—42no—
392#124—42no—
393#124—44no—
394#124—44no—
395#124—84no—
396C22⋊Q8—24no—
397C22⋊Q8—24no—
398C22⋊Q8—24no—
399C22⋊Q8—24no—
400C22⋊Q8—24no—
401C22⋊Q8—24no—
402C22⋊Q8—48no—
403C22⋊Q8—84no—
404#121—24no—
405#121—24no—
406#121—44no—
407#120—48no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×Q8—22no—
414C4×Q8—44no—
415C4×Q8—44no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—44no—
419C4×D4C2×D414yes—
420C4×D4C2×D414yes—
421#117—24no—
422#117—24no—
423#117—24no—
424#117—24no—
425#117—42no—
426#117—42no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—24no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—24no—
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2×D414yes—
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C22⋊C4—22no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—22no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4C2×D414yes—
468C2×C22⋊C4C2×D414yes—
469C2×C22⋊C4C2×D412yes—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C2×D412yes—
476C2×C42C2×D412yes—
477C2×C42C2411yescharacteristic
478C2×C42C2412yes—
479C2×C42C2411yescharacteristic
480C2×C42C2411yescharacteristic
481#107—22no—
482#107—24no—
483#107—22no—
484#107—24no—
485#107—24no—
486#107—24no—
487#106—24no—
488#106—24no—
489#106—24no—
490#106—24no—
491#106—22no—
492#106—22no—
493#106—24no—
494#106—24no—
495C4⋊C8C2×D414yes—
496C4⋊C8C2×D414yes—
497#103—22no—
498#103—22no—
499#103—22no—
500#103—22no—
501#103—22no—
502#103—22no—
503#103—24no—
504#103—24no—
505#103—24no—
506#103—24no—
507#102—22no—
508#102—24no—
509#102—24no—
510#102—24no—
511#102—22no—
512#102—24no—
513#102—24no—
514#102—24no—
515#102—24no—
516#102—24no—
517C22⋊C8C2×D418yes—
518C22⋊C8C2×D418yes—
519#97—42no—
520C4×C8—42no—
521C4×C8—42no—
522C4×C8C2×D414yes—
523C4×C8C2×D414yes—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—24no—
529#95—24no—
530#95—24no—
531#95—24no—
532#95—24no—
533#95C2×D414yes—
534#95C2×D412yes—
535C24—21no—
536C24—22no—
537C24—44no—
538C24—44no—
539C24—82no—
540C24—84no—
541C24—84no—
542C24C22×D412yes—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—42no—
562C2×Q8—42no—
563C2×Q8—42no—
564C2×Q8—44no—
565C2×Q8—44no—
566C2×Q8—82no—
567C2×D4—24no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—48no—
580C2×D4—48no—
581C2×D4—44no—
582C2×D4—44no—
583C2×D4—44no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—44no—
587C2×D4—84no—
588C2×D4—84no—
589C2×D4—82no—
590C2×D4—82no—
591C2×D4—84no—
592C2×D4—816no—
593C2×D4#12714yes—
594C2×D42−1+412yes—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—44no—
610C22×C4—42no—
611C22×C4—44no—
612C22×C4—84no—
613C22×C4C22×D412yes—
614C22×C4C22×D414yes—
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D414yes—
619C22×C4C22×D414yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C2511yescharacteristic
622Q16—44no—
623Q16—44no—
624SD16—44no—
625SD16—44no—
626SD16—84no—
627SD16—84no—
628M16—48no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—48no—
642C2×C8C22×D412yes—
643C2×C8C22×D412yes—
644C2×C8C22×D412yes—
645C2×C8C22×D412yes—
646C2×C8C22×D414yes—
647C2×C8C22×D414yes—
648C4⋊C4—24no—
649C4⋊C4—21no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—44no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—82no—
676C4⋊C4—84no—
677C4⋊C4—84no—
678C4⋊C4#12714yes—
679C22⋊C4—44no—
680C22⋊C4—44no—
681C22⋊C4—44no—
682C22⋊C4—44no—
683C22⋊C4—44no—
684C22⋊C4—44no—
685C22⋊C4—44no—
686C22⋊C4—44no—
687C22⋊C4—42no—
688C22⋊C4—44no—
689C22⋊C4—82no—
690C22⋊C4—84no—
691C22⋊C4—84no—
692C22⋊C4—84no—
693C22⋊C4—84no—
694C22⋊C4—84no—
695C22⋊C4#12718yes—
696C42—24no—
697C42—21no—
698C42—21no—
699C42—22no—
700C42—22no—
701C42—21no—
702C42—21no—
703C42—42no—
704C42—44no—
705C42—44no—
706C42—42no—
707C42—42no—
708C42—42no—
709C42C22×D412yes—
710C42C22×D412yes—
711C23—24no—
712C23—22no—
713C23—22no—
714C23—24no—
715C23—22no—
716C23—42no—
717C23—41no—
718C23—41no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—44no—
725C23—88no—
726C23—88no—
727C23—164no—
728C23—168no—
729C23—168no—
730C23C2×#12714yes—
731C23C23×D411yescharacteristic
732Q8—41no—
733Q8—41no—
734Q8—41no—
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—84no—
745Q8—84no—
746Q8—162no—
747D4—28no—
748D4—22no—
749D4—22no—
750D4—41no—
751D4—41no—
752D4—42no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—88no—
757D4—88no—
758D4—84no—
759D4—162no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—24no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—44no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—44no—
797C2×C4—42no—
798C2×C4—44no—
799C2×C4—84no—
800C2×C4—164no—
801C2×C4C2×#12714yes—
802C2×C4C2×#12712yes—
803C2×C4C2×#12712yes—
804C2×C4#57714yes—
805C2×C4C23×D411yescharacteristic
806C2×C4C23×D411yescharacteristic
807C2×C4C2×2−1+411yescharacteristic
808C2×C4#58511yescharacteristic
809C2×C4#58511yescharacteristic
810C2×C4#58511yescharacteristic
811C8—22no—
812C8—24no—
813C8—22no—
814C8—24no—
815C8—22no—
816C8—22no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—44no—
821C22—44no—
822C22—44no—
823C22—42no—
824C22—82no—
825C22—81no—
826C22—81no—
827C22—84no—
828C22—84no—
829C22—82no—
830C22—82no—
831C22—82no—
832C22—1616no—
833C22C22×#12711yescharacteristic
834C22#348511yescharacteristic
835C22#348911yescharacteristic
836C22C2×#57712yes—
837C22#358412yes—
838C4—24no—
839C4—22no—
840C4—42no—
841C4—42no—
842C4—44no—
843C4—81no—
844C4—81no—
845C4—81no—
846C4—81no—
847C4—82no—
848C4—82no—
849C4—81no—
850C4—81no—
851C4—81no—
852C4—82no—
853C4#315414yes—
854C4#348511yescharacteristic
855C4#348511yescharacteristic
856C4#348911yescharacteristic
857C4#348911yescharacteristic
858C2—44no—
859C2—82no—
860C2—162no—
861C2#3606011yescharacteristic
862C2C2×#315411yescharacteristic
863C2#6064911yescharacteristic
864C2#6178612yes—
865C2#6221612yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3356C2semidirect
2. C2×#3342C2semidirect
5. #39490C2semidirect
7. #30278C2semidirect
8. #30252C2semidirect
9. #28540C2semidirect
10. #28530C2semidirect
11. #28510C2semidirect
12. #28418C2semidirect
13. #28402C2semidirect
14. #28374C2semidirect
15. #28361C2semidirect
16. #28330C2semidirect
17. #28320C2semidirect
18. #27946C2semidirect
19. #27925C2semidirect
20. #27920C2semidirect
21. #23797C2semidirect
22. #23735C2semidirect
23. #20562C2semidirect
32. C2×#500C22semidirect
33. C2×#498C22semidirect
37. C2×#485C22semidirect
38. C2×#485C22semidirect
39. C2×#485C22semidirect
41. C2×#483C22semidirect
42. C2×#477C22semidirect
43. C2×#475C22semidirect
44. C2×#475C22semidirect
45. C2×#475C22semidirect
48. C2×#470C22semidirect
50. C2×#467C22semidirect
56. C2×C4×Q16C22semidirect
57. C2×C4×Q16C22semidirect
62. C2×#428C22semidirect
63. C2×#427C22semidirect
66. #2862C22semidirect
70. #2621C22semidirect
72. #2568C22semidirect
73. #2567C22semidirect
76. #2503C22semidirect
78. #2499C22semidirect
84. #2317C22semidirect
86. C4×C4⋊Q8C22semidirect
89. #2097C22semidirect
90. #2097C22semidirect
91. #2097C22semidirect
92. #2096C22semidirect
93. #2096C22semidirect
94. #2095C22semidirect
96. #2094C22semidirect
98. #2093C22semidirect
101. #2092C22semidirect
102. #2092C22semidirect
103. #2092C22semidirect
104. #2092C22semidirect
105. #2092C22semidirect
106. #2016C22semidirect
109. #2015C22semidirect
110. #2015C22semidirect
112. #2013C22semidirect
114. #1973C22semidirect
116. #1968C22semidirect
117. #1968C22semidirect
118. #1968C22semidirect
119. #1959C22semidirect
121. #1958C22semidirect
122. #1847C22semidirect
123. #1846C22semidirect
124. #1844C22semidirect
125. #1770C22semidirect
126. C8×C4⋊C4C22semidirect
127. C4×C4⋊C8C22semidirect
128. #1753C22semidirect
129. C8×C22⋊C4C22semidirect
130. #1750C22semidirect
131. #1744C22semidirect
132. #1729C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33562
C2×#33422
C2×#33242
C2×#32952
#394902
#389572
#302782
#302522
#285402
#285302
#285102
#284182
#284022
#283742
#283612
#283302
#283202
#279462
#279252
#279202
#237972
#237352
#205622