Finite Group Databasebeta

← #6607129

Subgroups — #6607129

Order 512.

2350 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3356C211yesmaximal, characteristic, complemented
2C2×#3311C211yesmaximal, characteristic, complemented
3C2×#3316C211yesmaximal, characteristic, complemented
4C2×#3275C211yesmaximal, characteristic
5#38091C211yesmaximal, characteristic, complemented
6#38078C211yesmaximal, characteristic, complemented
7#33245C211yesmaximal, characteristic, complemented
8#33181C211yesmaximal, characteristic, complemented
9#33176C211yesmaximal, characteristic, complemented
10#28530C211yesmaximal, characteristic, complemented
11#28466C211yesmaximal, characteristic, complemented
12#28432C211yesmaximal, characteristic, complemented
13#28426C211yesmaximal, characteristic, complemented
14#28396C211yesmaximal, characteristic, complemented
15#28395C211yesmaximal, characteristic, complemented
16#28362C211yesmaximal, characteristic, complemented
17#28361C211yesmaximal, characteristic, complemented
18#28339C211yesmaximal, characteristic, complemented
19#28336C211yesmaximal, characteristic, complemented
20#28328C211yesmaximal, characteristic, complemented
21#28324C211yesmaximal, characteristic, complemented
22#28308C211yesmaximal, characteristic, complemented
23#28302C211yesmaximal, characteristic, complemented
24#27941C211yesmaximal, characteristic, complemented
25#27940C211yesmaximal, characteristic, complemented
26#25796C211yesmaximal, characteristic, complemented
27#25795C211yesmaximal, characteristic, complemented
28#21703C211yesmaximal, characteristic, complemented
29#21236C211yesmaximal, characteristic, complemented
30#21234C211yesmaximal, characteristic, complemented
31#20490C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C22×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#554C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×#546C2211yescharacteristic
38#3356—28no—
39#3316—28no—
40#3311—28no—
41#3275—28no—
42C2×#498C2211yescharacteristic, complemented
43C2×#497C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#495C2211yescharacteristic
46C2×#494C2211yescharacteristic, complemented
47C2×#489C2211yescharacteristic
48C2×#489C2211yescharacteristic, complemented
49C2×#481C2211yescharacteristic, complemented
50C2×#485C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#485C2211yescharacteristic, complemented
53C2×#482C2211yescharacteristic
54C2×#483C2211yescharacteristic
55C2×#483C2211yescharacteristic
56C2×#483C2211yescharacteristic, complemented
57C2×#477C2211yescharacteristic, complemented
58C2×#475C2211yescharacteristic, complemented
59C2×#475C2211yescharacteristic, complemented
60C2×#476C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#470C2211yescharacteristic
63C2×#470C2211yescharacteristic
64C2×#470C2211yescharacteristic
65C2×#470C2211yescharacteristic, complemented
66C2×#469C2211yescharacteristic
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#464C2211yescharacteristic, complemented
72C2×#463C2211yescharacteristic
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic
76C2×#449C2211yescharacteristic
77C2×#451C2211yescharacteristic, complemented
78C2×#448C2211yescharacteristic
79C2×#450C2211yescharacteristic
80C2×#450C2211yescharacteristic
81C2×#441C2211yescharacteristic, complemented
82C2×#440C2211yescharacteristic
83C2×C4×Q16C2211yescharacteristic, complemented
84C2×C4×SD16C2211yescharacteristic
85C2×#436C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic
88C2×#428C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic
90C2×#418C2211yescharacteristic
91C2×#416C2211yescharacteristic
92C22×#103C2211yescharacteristic, complemented
93C2×#405C2211yescharacteristic, complemented
94C2×C4×M16C2211yescharacteristic
95#2857C2211yescharacteristic
96#2857C2211yescharacteristic
97#2715—22no—
98#2694—22no—
99#2686—22no—
100#2681—22no—
101#2640C2211yescharacteristic
102#2640C2211yescharacteristic, complemented
103#2620C2211yescharacteristic
104#2620C2211yescharacteristic, complemented
105#2567C2211yescharacteristic, complemented
106#2545C2211yescharacteristic
107#2545C2211yescharacteristic, complemented
108#2542C2211yescharacteristic
109#2502C2211yescharacteristic
110#2501C2211yescharacteristic
111#2500C2211yescharacteristic, complemented
112#2499C2211yescharacteristic
113#2466—22no—
114#2465—22no—
115#2437—22no—
116#2435C2211yescharacteristic
117#2434C2211yescharacteristic, complemented
118#2432C2211yescharacteristic
119#2432C2211yescharacteristic
120#2418—22no—
121#2327C2211yescharacteristic, complemented
122#2326C2211yescharacteristic
123#2311C2211yescharacteristic
124#2310C2211yescharacteristic, complemented
125#2297C2211yescharacteristic
126C2×#390C2211yescharacteristic
127#2290C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2096C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2094C2211yescharacteristic
135#2094C2211yescharacteristic
136#2094C2211yescharacteristic
137#2094C2211yescharacteristic, complemented
138#2093C2211yescharacteristic, complemented
139#2092C2211yescharacteristic
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic, complemented
146#2013C2211yescharacteristic
147#2013C2211yescharacteristic
148#2013C2211yescharacteristic
149#2013C2211yescharacteristic, complemented
150#2012C2211yescharacteristic
151#2012C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1972C2211yescharacteristic
156#1972C2211yescharacteristic
157#1972C2211yescharacteristic
158#1971C2211yescharacteristic, complemented
159#1971C2211yescharacteristic, complemented
160#1971C2211yescharacteristic, complemented
161#1971C2211yescharacteristic, complemented
162#1971C2211yescharacteristic, complemented
163#1971C2211yescharacteristic, complemented
164#1970C2211yescharacteristic
165#1970C2211yescharacteristic
166#1969C2211yescharacteristic, complemented
167#1969C2211yescharacteristic, complemented
168#1969C2211yescharacteristic, complemented
169#1968C2211yescharacteristic
170#1968C2211yescharacteristic
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic
173#1968C2211yescharacteristic
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1968C2211yescharacteristic, complemented
180#1959C2211yescharacteristic
181#1959C2211yescharacteristic, complemented
182#1958C2211yescharacteristic
183#1956C2211yescharacteristic, complemented
184#1956C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1844C2211yescharacteristic, complemented
188#1844C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C23×Q8C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C2×#137—24no—
204C2×#137—24no—
205C2×#137—42no—
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—24no—
208C2×AGL(1,ℤ/8)—42no—
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×M16C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C23×C8C2311yescharacteristic
229#556—24no—
230#556—24no—
231#554—24no—
232#554—24no—
233#548—24no—
234#548—24no—
235#546—24no—
236#546—24no—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×#126—21no—
243C2×#126—21no—
244C2×#125—21no—
245C2×#124—21no—
246C2×#124—21no—
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#124C2311yescharacteristic
252C2×#123—21no—
253C2×#123—22no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8—22no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×#121—21no—
265C2×#121—21no—
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#120—21no—
269C2×C4×Q8—21no—
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×D4—21no—
274C2×C4×D4—21no—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C4⋊C4C2311yescharacteristic
282C22×C22⋊C4—22no—
283C22×C22⋊C4—21no—
284C22×C42C2311yescharacteristic
285#498—24no—
286#497—24no—
287#495—24no—
288#495—42no—
289#494—42no—
290#489—24no—
291#489—24no—
292#485—24no—
293#485—24no—
294#485—24no—
295#483—24no—
296#483—24no—
297#483—24no—
298#482—24no—
299#481—24no—
300#477—24no—
301#476—24no—
302#475—24no—
303#475—24no—
304#470—24no—
305#470—24no—
306#470—24no—
307#470—24no—
308#470—24no—
309#469—24no—
310#465—24no—
311#465—24no—
312#464—24no—
313#464—24no—
314#464—24no—
315#463—24no—
316#452—24no—
317#452—24no—
318#452—24no—
319#451—24no—
320#450—24no—
321#450—24no—
322#449—24no—
323#448—24no—
324#441—24no—
325#440—24no—
326C4×Q16—24no—
327C4×SD16—24no—
328#436D418yes—
329#435D418yes—
330#428—24no—
331#428—24no—
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×#106C2311yescharacteristic
348C2×C4⋊C8C2311yescharacteristic
349C2×C4⋊C8C2311yescharacteristic
350#418—24no—
351#417—24no—
352#416—24no—
353C2×#103—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×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
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×C4×C8C2311yescharacteristic
398C2×C4×C8C2311yescharacteristic
399C2×C4×C8C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404#399—22no—
405#399—22no—
406#398—22no—
407#397—22no—
408#397—22no—
409#397—22no—
410#396—22no—
411#396—22no—
412#396—22no—
413#396—22no—
414#395—22no—
415#395—22no—
416#394—22no—
417#394—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#393—22no—
423#393—22no—
424#391—22no—
425#391C2311yescharacteristic
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#390—22no—
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#389—22no—
447#389—22no—
448#389—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388—22no—
453#388D412yes—
454#387—22no—
455#387—22no—
456#387—22no—
457#387D412yes—
458#386—22no—
459#386—22no—
460#386D412yes—
461#385—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#385—22no—
466#385D412yes—
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#382C2311yescharacteristic
473#381—22no—
474#380—22no—
475#380—22no—
476#380—22no—
477#379—22no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—22no—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
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—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C2×D411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2×D412yes—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540#137—416no—
541AGL(1,ℤ/8)—416no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—22no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
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—41no—
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#4114yes—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—22no—
588C2×D8—22no—
589C2×D8—41no—
590C2×M16—22no—
591C2×M16—22no—
592C2×M16—22no—
593C2×M16—22no—
594C2×M16—41no—
595C2×M16—41no—
596C2×M16C2×D414yes—
597C2×M16C2×D414yes—
598C2×M16C2×D414yes—
599C22×C8—41no—
600C22×C8—41no—
601C22×C8C2×D414yes—
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C22×C8C2411yescharacteristic
605C22×C8C2411yescharacteristic
606C22×C8C2411yescharacteristic
607C22×C8C2411yescharacteristic
608C22×C8C2411yescharacteristic
609C22×C8C2411yescharacteristic
610C4⋊Q8—22no—
611C4⋊Q8—22no—
612C4⋊Q8—22no—
613C4⋊Q8—22no—
614C4⋊Q8—22no—
615C4⋊Q8—41no—
616C4⋊Q8—41no—
617C4⋊Q8—41no—
618C4⋊Q8—41no—
619C4⋊Q8—41no—
620#126—44no—
621#126—44no—
622#125—44no—
623#124—22no—
624#124—22no—
625#124—22no—
626#124—22no—
627#124—22no—
628#124—41no—
629#124—41no—
630#124—41no—
631#124—41no—
632#124—41no—
633#124—44no—
634#124—44no—
635#123—44no—
636#123—84no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—44no—
650C22⋊Q8—44no—
651C22⋊Q8—44no—
652C22⋊Q8—84no—
653#121—22no—
654#121—22no—
655#121—22no—
656#121—22no—
657#121—44no—
658#121—44no—
659#120—44no—
660C4×Q8—22no—
661C4×Q8—22no—
662C4×Q8—22no—
663C4×Q8—22no—
664C4×Q8—22no—
665C4×Q8—22no—
666C4×Q8—44no—
667C4×D4—22no—
668C4×D4—22no—
669C4×D4—44no—
670C4×D4—44no—
671C4×D4C2×D414yes—
672C4×D4C2×D414yes—
673#117—22no—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—41no—
678#117—41no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4C2×D412yes—
705C2×C4⋊C4C2×D412yes—
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
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—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
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⋊C4—84no—
744C2×C22⋊C4C2×D412yes—
745C2×C22⋊C4C2×D412yes—
746C2×C22⋊C4C2×D412yes—
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—41no—
755C2×C42—41no—
756C2×C42C2×D412yes—
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#106—22no—
767#106—22no—
768#106—22no—
769#106—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778C4⋊C8C2×D414yes—
779C4⋊C8C2×D414yes—
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#103—22no—
795#103—22no—
796#103—22no—
797#103—22no—
798#103—22no—
799#103—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—
810#102—22no—
811#102—22no—
812C22⋊C8C2×D414yes—
813C22⋊C8C2×D414yes—
814C22⋊C8C2×D414yes—
815C22⋊C8C2×D414yes—
816#97—22no—
817#97—22no—
818#97—41no—
819#97—41no—
820#97C2×D414yes—
821C4×C8—22no—
822C4×C8—22no—
823C4×C8—41no—
824C4×C8—41no—
825C4×C8—41no—
826C4×C8—41no—
827C4×C8C2×D414yes—
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—42no—
849C24—44no—
850C24—42no—
851C24—82no—
852C24—81no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855#41—44no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—82no—
860#41—82no—
861#41—82no—
862#41—82no—
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—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—42no—
893C2×Q8—44no—
894C2×Q8—44no—
895C2×Q8—42no—
896C2×Q8—42no—
897C2×Q8—42no—
898C2×Q8—82no—
899C2×Q8—81no—
900C2×Q8—82no—
901C2×Q8—82no—
902C2×Q8—82no—
903C2×Q8C2×#4112yes—
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—44no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—82no—
933C2×D4—82no—
934C2×D4—81no—
935C2×D4—82no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—82no—
939C2×D4#12714yes—
940C2×D4C2×#4112yes—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—24no—
951C22×C4—21no—
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—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—82no—
977C22×C4—81no—
978C22×C4—82no—
979C22×C4—82no—
980C22×C4C22×D412yes—
981C22×C4C22×D412yes—
982C22×C4C22×D412yes—
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C22×D412yes—
991C22×C4C22×D412yes—
992C22×C4C2511yescharacteristic
993Q16—44no—
994Q16—44no—
995Q16—44no—
996Q16—44no—
997Q16—82no—
998Q16—82no—
999SD16—28no—
1000SD16—44no—
1001SD16—44no—
1002SD16—44no—
1003SD16—82no—
1004SD16—82no—
1005SD16—82no—
1006SD16—82no—
1007D8—44no—
1008D8—44no—
1009M16—28no—
1010M16—28no—
1011M16—44no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—44no—
1027C2×C8C22×D412yes—
1028C2×C8C22×D412yes—
1029C2×C8C22×D412yes—
1030C2×C8C22×D412yes—
1031C2×C8C22×D412yes—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C2×#4112yes—
1036C2×C8H(5,𝔽2)12yes—
1037C4⋊C4—24no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—42no—
1055C4⋊C4—44no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—44no—
1070C4⋊C4—82no—
1071C4⋊C4—82no—
1072C4⋊C4—82no—
1073C4⋊C4—82no—
1074C4⋊C4—82no—
1075C4⋊C4—82no—
1076C4⋊C4#12714yes—
1077C22⋊C4—24no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—44no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
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—44no—
1097C22⋊C4—44no—
1098C22⋊C4—44no—
1099C22⋊C4—82no—
1100C22⋊C4—82no—
1101C22⋊C4—82no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4—82no—
1105C22⋊C4—82no—
1106C22⋊C4—82no—
1107C22⋊C4#12714yes—
1108C22⋊C4#12714yes—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42C22×D412yes—
1124C42C22×D412yes—
1125C23—22no—
1126C23—22no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—22no—
1132C23—22no—
1133C23—22no—
1134C23—42no—
1135C23—41no—
1136C23—41no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—42no—
1147C23—42no—
1148C23—84no—
1149C23—84no—
1150C23—88no—
1151C23—162no—
1152C23—164no—
1153C23C2×#12712yes—
1154C23C2×#12712yes—
1155C23C23×D411yescharacteristic
1156Q8—22no—
1157Q8—22no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—84no—
1177Q8—84no—
1178Q8—162no—
1179D4—22no—
1180D4—22no—
1181D4—44no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196D4—162no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—42no—
1226C2×C4—42no—
1227C2×C4—42no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—42no—
1252C2×C4—42no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4C2×#12712yes—
1261C2×C4C2×#12712yes—
1262C2×C4C2×#12712yes—
1263C2×C4C2×#12712yes—
1264C2×C4#57714yes—
1265C2×C4C23×D411yescharacteristic
1266C2×C4C23×D411yescharacteristic
1267C2×C4C22×#4111yescharacteristic
1268C2×C4C2×H(5,𝔽2)11yescharacteristic
1269C2×C4#58511yescharacteristic
1270C2×C4#58511yescharacteristic
1271C8—22no—
1272C8—22no—
1273C8—22no—
1274C8—22no—
1275C8—22no—
1276C8—22no—
1277C8—22no—
1278C8#54614yes—
1279C22—22no—
1280C22—22no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—22no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—44no—
1290C22—42no—
1291C22—82no—
1292C22—81no—
1293C22—81no—
1294C22—82no—
1295C22—82no—
1296C22—82no—
1297C22—82no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—168no—
1305C22C22×#12711yescharacteristic
1306C22D4×#4111yescharacteristic
1307C22#349611yescharacteristic
1308C22C2×#57712yes—
1309C22#358612yes—
1310C4—24no—
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—42no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4C2×#54611yescharacteristic
1332C4D4×#4111yescharacteristic
1333C4#349611yescharacteristic
1334C4#350011yescharacteristic
1335C2—42no—
1336C2—42no—
1337C2—82no—
1338C2—161no—
1339C2—161no—
1340C2#3626011yescharacteristic
1341C2#6064511yescharacteristic
1342C2#6064611yescharacteristic
1343C2#6155712yes—
1344C2#6232112yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#3275C2
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×#3356C2semidirect
2. C2×#3311C2semidirect
3. C2×#3316C2semidirect
5. #38091C2semidirect
6. #38078C2semidirect
7. #33245C2semidirect
8. #33181C2semidirect
9. #33176C2semidirect
10. #28530C2semidirect
11. #28466C2semidirect
12. #28432C2semidirect
13. #28426C2semidirect
14. #28396C2semidirect
15. #28395C2semidirect
16. #28362C2semidirect
17. #28361C2semidirect
18. #28339C2semidirect
19. #28336C2semidirect
20. #28328C2semidirect
21. #28324C2semidirect
22. #28308C2semidirect
23. #28302C2semidirect
24. #27941C2semidirect
25. #27940C2semidirect
26. #25796C2semidirect
27. #25795C2semidirect
28. #21703C2semidirect
29. #21236C2semidirect
30. #21234C2semidirect
31. #20490C2semidirect
42. C2×#498C22semidirect
46. C2×#494C22semidirect
48. C2×#489C22semidirect
49. C2×#481C22semidirect
52. C2×#485C22semidirect
56. C2×#483C22semidirect
57. C2×#477C22semidirect
58. C2×#475C22semidirect
59. C2×#475C22semidirect
65. C2×#470C22semidirect
68. C2×#465C22semidirect
71. C2×#464C22semidirect
77. C2×#451C22semidirect
81. C2×#441C22semidirect
83. C2×C4×Q16C22semidirect
88. C2×#428C22semidirect
92. C22×#103C22semidirect
93. C2×#405C22semidirect
102. #2640C22semidirect
104. #2620C22semidirect
105. #2567C22semidirect
107. #2545C22semidirect
111. #2500C22semidirect
117. #2434C22semidirect
121. #2327C22semidirect
124. #2310C22semidirect
128. #2097C22semidirect
129. #2096C22semidirect
130. #2096C22semidirect
131. #2096C22semidirect
132. #2096C22semidirect
133. #2095C22semidirect
137. #2094C22semidirect
138. #2093C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
145. #2015C22semidirect
149. #2013C22semidirect
158. #1971C22semidirect
159. #1971C22semidirect
160. #1971C22semidirect
161. #1971C22semidirect
162. #1971C22semidirect
163. #1971C22semidirect
166. #1969C22semidirect
167. #1969C22semidirect
168. #1969C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1968C22semidirect
181. #1959C22semidirect
183. #1956C22semidirect
184. #1956C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1844C22semidirect
188. #1844C22semidirect
189. #1771C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
194. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
196. #1750C22semidirect
198. #1726C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33562
C2×#33112
C2×#33162
C2×#32752
#380912
#380782
#332452
#331812
#331762
#285302
#284662
#284322
#284262
#283962
#283952
#283622
#283612
#283392
#283362
#283282
#283242
#283082
#283022
#279412
#279402
#257962
#257952
#217032
#212362
#212342
#204902