Finite Group Databasebeta

← #6607073

Subgroups — #6607073

Order 512.

2369 conjugacy classes of subgroups.

The subgroup lattice has 1363 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3347C211yesmaximal, characteristic, complemented
2C2×#3329C211yesmaximal, characteristic, complemented
3C2×#3322C211yesmaximal, characteristic, complemented
4C2×#3266C211yesmaximal, characteristic, complemented
5#38090C211yesmaximal, characteristic, complemented
6#38085C211yesmaximal, characteristic, complemented
7#33244C211yesmaximal, characteristic, complemented
8#33185C211yesmaximal, characteristic, complemented
9#33182C211yesmaximal, characteristic, complemented
10#28545C211yesmaximal, characteristic, complemented
11#28479C211yesmaximal, characteristic, complemented
12#28414C211yesmaximal, characteristic, complemented
13#28412C211yesmaximal, characteristic, complemented
14#28394C211yesmaximal, characteristic, complemented
15#28388C211yesmaximal, characteristic, complemented
16#28365C211yesmaximal, characteristic, complemented
17#28363C211yesmaximal, characteristic, complemented
18#28360C211yesmaximal, characteristic, complemented
19#28359C211yesmaximal, characteristic, complemented
20#28324C211yesmaximal, characteristic, complemented
21#28321C211yesmaximal, characteristic, complemented
22#28318C211yesmaximal, characteristic, complemented
23#28314C211yesmaximal, characteristic, complemented
24#27945C211yesmaximal, characteristic, complemented
25#27936C211yesmaximal, characteristic, complemented
26#25797C211yesmaximal, characteristic, complemented
27#25783C211yesmaximal, characteristic, complemented
28#21704C211yesmaximal, characteristic, complemented
29#21237C211yesmaximal, characteristic, complemented
30#21231C211yesmaximal, characteristic, complemented
31#20487C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C23×SD16C2211yescharacteristic
34C2×#555C2211yescharacteristic
35C2×#553C2211yescharacteristic
36C2×D4×Q8C2211yescharacteristic
37C2×#546C2211yescharacteristic
38#3347—28no—
39#3329—28no—
40#3322—28no—
41#3266—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#497C2211yescharacteristic
44C2×#496C2211yescharacteristic
45C2×#496C2211yescharacteristic
46C2×#495C2211yescharacteristic, complemented
47C2×#488C2211yescharacteristic
48C2×#487C2211yescharacteristic, complemented
49C2×#485C2211yescharacteristic
50C2×#485C2211yescharacteristic
51C2×#485C2211yescharacteristic, complemented
52C2×#482C2211yescharacteristic
53C2×#482C2211yescharacteristic
54C2×#482C2211yescharacteristic, complemented
55C2×#480C2211yescharacteristic
56C2×#480C2211yescharacteristic, complemented
57C2×#477C2211yescharacteristic, complemented
58C2×#478C2211yescharacteristic
59C2×#478C2211yescharacteristic, complemented
60C2×#474C2211yescharacteristic, complemented
61C2×#469C2211yescharacteristic
62C2×#469C2211yescharacteristic, complemented
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#468C2211yescharacteristic
66C2×#468C2211yescharacteristic, complemented
67C2×#467C2211yescharacteristic
68C2×#466C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#463C2211yescharacteristic
71C2×#461C2211yescharacteristic
72C2×#461C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#449C2211yescharacteristic
75C2×#451C2211yescharacteristic
76C2×#448C2211yescharacteristic
77C2×#448C2211yescharacteristic
78C2×#448C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#442C2211yescharacteristic, complemented
82C2×#440C2211yescharacteristic
83C2×C4×SD16C2211yescharacteristic, complemented
84C2×C4×D8C2211yescharacteristic
85C2×#436C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic, complemented
88C2×#427C2211yescharacteristic
89C2×#417C2211yescharacteristic
90C2×#419C2211yescharacteristic
91C2×#419C2211yescharacteristic, complemented
92C2×#418C2211yescharacteristic
93C2×#405C2211yescharacteristic
94C2×C4×M16C2211yescharacteristic, complemented
95#2856C2211yescharacteristic
96#2850C2211yescharacteristic, complemented
97#2716—22no—
98#2687—22no—
99#2676—22no—
100#2668—22no—
101#2642C2211yescharacteristic, complemented
102#2640C2211yescharacteristic
103#2620C2211yescharacteristic
104#2620C2211yescharacteristic
105#2565C2211yescharacteristic, complemented
106#2547C2211yescharacteristic, complemented
107#2544C2211yescharacteristic
108#2542C2211yescharacteristic
109#2502C2211yescharacteristic, complemented
110#2500C2211yescharacteristic
111#2499C2211yescharacteristic
112#2499C2211yescharacteristic
113#2472—22no—
114#2471—22no—
115#2450—22no—
116#2444—22no—
117#2436C2211yescharacteristic
118#2436C2211yescharacteristic, complemented
119#2433C2211yescharacteristic
120#2431C2211yescharacteristic
121#2328C2211yescharacteristic
122#2326C2211yescharacteristic, complemented
123#2310C2211yescharacteristic
124#2309C2211yescharacteristic
125#2297C2211yescharacteristic
126C2×#391C2211yescharacteristic, complemented
127#2290C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2095C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2095C2211yescharacteristic, complemented
135#2095C2211yescharacteristic, complemented
136#2094C2211yescharacteristic
137#2093C2211yescharacteristic
138#2093C2211yescharacteristic
139#2092C2211yescharacteristic
140#2015C2211yescharacteristic, complemented
141#2015C2211yescharacteristic, complemented
142#2015C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic
146#2014C2211yescharacteristic
147#2014C2211yescharacteristic
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic
156#1973C2211yescharacteristic
157#1973C2211yescharacteristic
158#1973C2211yescharacteristic
159#1973C2211yescharacteristic
160#1973C2211yescharacteristic, complemented
161#1973C2211yescharacteristic, complemented
162#1973C2211yescharacteristic, complemented
163#1972C2211yescharacteristic
164#1971C2211yescharacteristic, complemented
165#1971C2211yescharacteristic, complemented
166#1971C2211yescharacteristic, complemented
167#1971C2211yescharacteristic, complemented
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic, complemented
170#1969C2211yescharacteristic, complemented
171#1969C2211yescharacteristic, complemented
172#1969C2211yescharacteristic, complemented
173#1968C2211yescharacteristic
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic
178#1968C2211yescharacteristic
179#1968C2211yescharacteristic, complemented
180#1961C2211yescharacteristic
181#1959C2211yescharacteristic, complemented
182#1959C2211yescharacteristic, complemented
183#1959C2211yescharacteristic, complemented
184#1958C2211yescharacteristic, complemented
185#1957C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic, complemented
194#1753C2211yescharacteristic, complemented
195#1752C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C2×#137—24no—
204C2×#137—24no—
205C2×#137—42no—
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16—24no—
210C22×SD16—24no—
211C22×SD16—42no—
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×M16C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C23×C8C2311yescharacteristic
229#555—24no—
230#555—24no—
231#553—24no—
232#553—24no—
233D4×Q8—24no—
234D4×Q8—24no—
235#546—24no—
236#546—24no—
237C2×C4⋊Q8—21no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#126—21no—
243C2×#125C2311yescharacteristic
244C2×#124—21no—
245C2×#124—21no—
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#123—21no—
252C2×#123—21no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×#121—21no—
260C2×#121—21no—
261C2×#121—22no—
262C2×#121—21no—
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#120—21no—
269C2×#120—22no—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×D4—21no—
272C2×C4×D4—21no—
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117—21no—
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C22×C4⋊C4C2311yescharacteristic
283C22×C22⋊C4—21no—
284C22×C42C2311yescharacteristic
285#501—24no—
286#497—24no—
287#496—24no—
288#496—42no—
289#495—42no—
290#488—24no—
291#487—24no—
292#485—24no—
293#485—24no—
294#485—24no—
295#482—24no—
296#482—24no—
297#482—24no—
298#480—24no—
299#480—24no—
300#478—24no—
301#478—24no—
302#477—24no—
303#474—24no—
304#469—24no—
305#469—24no—
306#468—24no—
307#468—24no—
308#468—24no—
309#468—24no—
310#467—24no—
311#466—24no—
312#464—24no—
313#463—24no—
314#461—24no—
315#461—24no—
316#452—24no—
317#451—24no—
318#450—24no—
319#449—24no—
320#448—24no—
321#448—24no—
322#448—24no—
323#447—24no—
324#442—24no—
325#440—24no—
326C4×SD16—24no—
327C4×D8—24no—
328#436D418yescomplemented
329#435D418yescomplemented
330#428—24no—
331#427—24no—
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#107C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×#106C2311yescharacteristic
348C2×C4⋊C8C2311yescharacteristic
349C2×C4⋊C8C2311yescharacteristic
350#419—24no—
351#419—24no—
352#418—24no—
353#417—24no—
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#103C2311yescharacteristic
357C2×#103C2311yescharacteristic
358C2×#103C2311yescharacteristic
359C2×#103C2311yescharacteristic
360C2×#103C2311yescharacteristic
361C2×#103C2311yescharacteristic
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×C22⋊C8C2311yescharacteristic
387C2×C22⋊C8C2311yescharacteristic
388C2×C22⋊C8C2311yescharacteristic
389C2×C22⋊C8C2311yescharacteristic
390#405—42no—
391C4×M16—42no—
392C2×#97C2311yescharacteristic
393C2×#97C2311yescharacteristic
394C2×#97C2311yescharacteristic
395C2×#97C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×C4×C8C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404#400—22no—
405#400—22no—
406#399—22no—
407#398—22no—
408#398—22no—
409#397—22no—
410#397—22no—
411#397—22no—
412#397—22no—
413#396—22no—
414#396—22no—
415#394—22no—
416#394—22no—
417#394—22no—
418#394—22no—
419#393—22no—
420#393—22no—
421#393—22no—
422#392—22no—
423#392—22no—
424#391—22no—
425#391—22no—
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390—22no—
439#390—22no—
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#388—22no—
449#388—22no—
450#388—22no—
451#388D412yes—
452#387—22no—
453#387—22no—
454#387—22no—
455#387D412yes—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386—22no—
462#386—22no—
463#386—22no—
464#386D412yes—
465#385—22no—
466#385—22no—
467#385D412yes—
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#381—22no—
475#380—22no—
476#379—22no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C22⋊C4—22no—
479C4×C22⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481#376C2311yescharacteristic
482C2×#95—22no—
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C25—21no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4C2×D411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C2×D412yes—
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545#137—416no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—416no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16#4114yes—
586C2×D8—22no—
587C2×D8—22no—
588C2×D8—22no—
589C2×D8—22no—
590C2×D8—22no—
591C2×D8—22no—
592C2×D8—41no—
593C2×D8—41no—
594C2×D8—41no—
595C2×M16—22no—
596C2×M16—22no—
597C2×M16—41no—
598C2×M16—41no—
599C2×M16—41no—
600C2×M16—41no—
601C2×M16C2×D414yes—
602C2×M16C2×D414yes—
603C2×M16C2×D414yes—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8C2×D414yes—
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C22×C8C2411yescharacteristic
611C22×C8C2411yescharacteristic
612C22×C8C2411yescharacteristic
613C22×C8C2411yescharacteristic
614C22×C8C2411yescharacteristic
615C4⋊Q8—22no—
616C4⋊Q8—22no—
617C4⋊Q8—22no—
618C4⋊Q8—22no—
619C4⋊Q8—44no—
620#127—22no—
621#127—41no—
622#127—41no—
623#127—41no—
624#126—44no—
625#125—22no—
626#125—22no—
627#124—22no—
628#124—22no—
629#124—22no—
630#124—41no—
631#124—41no—
632#124—41no—
633#124—41no—
634#124—41no—
635#124—41no—
636#124—41no—
637#124—44no—
638#124—44no—
639#123—44no—
640#123—44no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—44no—
648C22⋊Q8—44no—
649C22⋊Q8—84no—
650#121—22no—
651#121—22no—
652#121—22no—
653#121—22no—
654#121—22no—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—22no—
659#121—22no—
660#121—44no—
661#121—44no—
662#121—44no—
663#121—84no—
664#120—44no—
665#120—84no—
666C4×Q8—22no—
667C4×Q8—22no—
668C4×D4—22no—
669C4×D4—22no—
670C4×D4—22no—
671C4×D4—22no—
672C4×D4—22no—
673C4×D4—22no—
674C4×D4—44no—
675C4×D4—44no—
676C4×D4C2×D414yes—
677C4×D4C2×D414yes—
678#117—22no—
679#117—22no—
680#117—22no—
681#117—22no—
682#117—22no—
683#117—22no—
684#117—41no—
685#117—41no—
686#117—44no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4C2×D412yes—
704C2×C4⋊C4C2×D412yes—
705C2×C4⋊C4C2×D411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—44no—
743C2×C22⋊C4C2×D412yes—
744C2×C22⋊C4C2×D412yes—
745C2×C22⋊C4C2×D412yes—
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—41no—
753C2×C42—41no—
754C2×C42C2×D412yes—
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760#107—22no—
761#107—22no—
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#107—22no—
769#107—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776C4⋊C8C2×D414yes—
777C4⋊C8C2×D414yes—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810C22⋊C8C2×D414yes—
811C22⋊C8C2×D414yes—
812C22⋊C8C2×D414yes—
813C22⋊C8C2×D414yes—
814#97—22no—
815#97—22no—
816#97—41no—
817#97—41no—
818#97—41no—
819#97—41no—
820#97C2×D414yes—
821C4×C8—22no—
822C4×C8—22no—
823C4×C8—41no—
824C4×C8—41no—
825C4×C8C2×D414yes—
826#95—22no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95C2×D412yes—
841#95C2×D412yes—
842#95C2×D412yes—
843#95C2×D412yes—
844#95C2×D412yes—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—42no—
850C24—42no—
851C24—81no—
852C24—82no—
853C24—82no—
854C24C22×D411yescharacteristic
855C24C22×D411yescharacteristic
856#41—44no—
857#41—44no—
858#41—82no—
859#41—82no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—42no—
884C2×Q8—42no—
885C2×Q8—44no—
886C2×Q8—44no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—42no—
892C2×Q8—81no—
893C2×Q8—81no—
894C2×Q8—82no—
895C2×Q8—82no—
896C2×Q8—82no—
897C2×Q8—82no—
898C2×Q8—82no—
899C2×Q8C2×#4112yes—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—44no—
924C2×D4—44no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—44no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—82no—
939C2×D4—82no—
940C2×D4—81no—
941C2×D4—82no—
942C2×D4—82no—
943C2×D4—82no—
944C2×D4—82no—
945C2×D4—81no—
946C2×D4—82no—
947C2×D4—82no—
948C2×D4—82no—
949C2×D4—82no—
950C2×D4#12714yes—
951C2×D4C2×#4112yes—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—42no—
985C22×C4—82no—
986C22×C4—81no—
987C22×C4—82no—
988C22×C4—82no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—82no—
992C22×C4C22×D412yes—
993C22×C4C22×D412yes—
994C22×C4C22×D412yes—
995C22×C4C22×D412yes—
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D412yes—
1001C22×C4C22×D412yes—
1002C22×C4C22×D412yes—
1003C22×C4C22×D412yes—
1004C22×C4C2511yescharacteristic
1005Q16—44no—
1006Q16—44no—
1007Q16—82no—
1008SD16—28no—
1009SD16—44no—
1010SD16—44no—
1011SD16—44no—
1012SD16—44no—
1013SD16—44no—
1014SD16—82no—
1015SD16—82no—
1016SD16—82no—
1017SD16—82no—
1018D8—44no—
1019D8—44no—
1020D8—82no—
1021M16—28no—
1022M16—44no—
1023M16—44no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—28no—
1039C2×C8C22×D412yes—
1040C2×C8C22×D412yes—
1041C2×C8C22×D412yes—
1042C2×C8C22×D412yes—
1043C2×C8C22×D412yes—
1044C2×C8C22×D412yes—
1045C2×C8C22×D412yes—
1046C2×C8C22×D412yes—
1047C2×C8C2×#4112yes—
1048C2×C8H(5,𝔽2)12yes—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—44no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—82no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4#12714yes—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—44no—
1086C22⋊C4—44no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—82no—
1104C22⋊C4—82no—
1105C22⋊C4—82no—
1106C22⋊C4—82no—
1107C22⋊C4—82no—
1108C22⋊C4—82no—
1109C22⋊C4—82no—
1110C22⋊C4—82no—
1111C22⋊C4—82no—
1112C22⋊C4—82no—
1113C22⋊C4#12714yes—
1114C22⋊C4#12714yes—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42C22×D412yes—
1129C42C22×D412yes—
1130C23—22no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—22no—
1139C23—42no—
1140C23—42no—
1141C23—41no—
1142C23—41no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—42no—
1148C23—42no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—84no—
1159C23—84no—
1160C23—162no—
1161C23—164no—
1162C23—164no—
1163C23C2×#12712yes—
1164C23C2×#12712yes—
1165C23C23×D411yescharacteristic
1166Q8—22no—
1167Q8—22no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—84no—
1183Q8—84no—
1184Q8—162no—
1185D4—22no—
1186D4—22no—
1187D4—44no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—84no—
1203D4—84no—
1204D4—84no—
1205D4—164no—
1206D4—164no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—42no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—42no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4C2×#12712yes—
1274C2×C4C2×#12712yes—
1275C2×C4C2×#12712yes—
1276C2×C4C2×#12712yes—
1277C2×C4C23×D411yescharacteristic
1278C2×C4C23×D411yescharacteristic
1279C2×C4C22×#4111yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—22no—
1284C8—22no—
1285C8—22no—
1286C8—22no—
1287C8—22no—
1288C8—22no—
1289C8—22no—
1290C8#54614yes—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—42no—
1301C22—44no—
1302C22—42no—
1303C22—82no—
1304C22—81no—
1305C22—81no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—82no—
1311C22—82no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22C22×#12711yescharacteristic
1323C22D4×#4111yescharacteristic
1324C22#349611yescharacteristic
1325C22#358512yes—
1326C22#358612yes—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—22no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4C2×#54611yescharacteristic
1348C4D4×#4111yescharacteristic
1349C4#349611yescharacteristic
1350C4#350011yescharacteristic
1351C2—42no—
1352C2—42no—
1353C2—82no—
1354C2—161no—
1355C2—161no—
1356C2—161no—
1357C2#3626011yescharacteristic
1358C2#6064511yescharacteristic
1359C2#6065011yescharacteristic
1360C2#6151312yes—
1361C2#6228512yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3347C2semidirect
2. C2×#3329C2semidirect
3. C2×#3322C2semidirect
4. C2×#3266C2semidirect
5. #38090C2semidirect
6. #38085C2semidirect
7. #33244C2semidirect
8. #33185C2semidirect
9. #33182C2semidirect
10. #28545C2semidirect
11. #28479C2semidirect
12. #28414C2semidirect
13. #28412C2semidirect
14. #28394C2semidirect
15. #28388C2semidirect
16. #28365C2semidirect
17. #28363C2semidirect
18. #28360C2semidirect
19. #28359C2semidirect
20. #28324C2semidirect
21. #28321C2semidirect
22. #28318C2semidirect
23. #28314C2semidirect
24. #27945C2semidirect
25. #27936C2semidirect
26. #25797C2semidirect
27. #25783C2semidirect
28. #21704C2semidirect
29. #21237C2semidirect
30. #21231C2semidirect
31. #20487C2semidirect
42. C2×#501C22semidirect
46. C2×#495C22semidirect
48. C2×#487C22semidirect
51. C2×#485C22semidirect
54. C2×#482C22semidirect
56. C2×#480C22semidirect
57. C2×#477C22semidirect
59. C2×#478C22semidirect
60. C2×#474C22semidirect
62. C2×#469C22semidirect
66. C2×#468C22semidirect
72. C2×#461C22semidirect
78. C2×#448C22semidirect
81. C2×#442C22semidirect
83. C2×C4×SD16C22semidirect
87. C2×#428C22semidirect
91. C2×#419C22semidirect
94. C2×C4×M16C22semidirect
96. #2850C22semidirect
101. #2642C22semidirect
105. #2565C22semidirect
106. #2547C22semidirect
109. #2502C22semidirect
118. #2436C22semidirect
122. #2326C22semidirect
126. C2×#391C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2096C22semidirect
132. #2095C22semidirect
133. #2095C22semidirect
134. #2095C22semidirect
135. #2095C22semidirect
140. #2015C22semidirect
141. #2015C22semidirect
142. #2015C22semidirect
143. #2015C22semidirect
160. #1973C22semidirect
161. #1973C22semidirect
162. #1973C22semidirect
164. #1971C22semidirect
165. #1971C22semidirect
166. #1971C22semidirect
167. #1971C22semidirect
169. #1970C22semidirect
170. #1969C22semidirect
171. #1969C22semidirect
172. #1969C22semidirect
179. #1968C22semidirect
181. #1959C22semidirect
182. #1959C22semidirect
183. #1959C22semidirect
184. #1958C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1845C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1768C22semidirect
193. #1753C22semidirect
194. #1753C22semidirect
197. #1749C22semidirect
198. #1726C22semidirect
328. #436D4semidirect
329. #435D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33472
C2×#33292
C2×#33222
C2×#32662
#380902
#380852
#332442
#331852
#331822
#285452
#284792
#284142
#284122
#283942
#283882
#283652
#283632
#283602
#283592
#283242
#283212
#283182
#283142
#279452
#279362
#257972
#257832
#217042
#212372
#212312
#204872