Finite Group Databasebeta

← #6520447

Subgroups — #6520447

Order 512.

2371 conjugacy classes of subgroups.

The subgroup lattice has 1385 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3263C211yesmaximal, characteristic, complemented
2C2×#3225C211yesmaximal, characteristic, complemented
3C2×#3118C211yesmaximal, characteristic, complemented
4C2×#3042C211yesmaximal, characteristic, complemented
5#37391C211yesmaximal, characteristic, complemented
6#35536C211yesmaximal, characteristic, complemented
7#28479C211yesmaximal, characteristic, complemented
8#28478C211yesmaximal, characteristic, complemented
9#28465C211yesmaximal, characteristic, complemented
10#28464C211yesmaximal, characteristic, complemented
11#28455C211yesmaximal, characteristic, complemented
12#28453C211yesmaximal, characteristic, complemented
13#28443C211yesmaximal, characteristic, complemented
14#28442C211yesmaximal, characteristic, complemented
15#28434C211yesmaximal, characteristic, complemented
16#28430C211yesmaximal, characteristic, complemented
17#28400C211yesmaximal, characteristic, complemented
18#28398C211yesmaximal, characteristic, complemented
19#28395C211yesmaximal, characteristic, complemented
20#28393C211yesmaximal, characteristic, complemented
21#28372C211yesmaximal, characteristic, complemented
22#28370C211yesmaximal, characteristic, complemented
23#28363C211yesmaximal, characteristic, complemented
24#28355C211yesmaximal, characteristic, complemented
25#28340C211yesmaximal, characteristic, complemented
26#28339C211yesmaximal, characteristic, complemented
27#25796C211yesmaximal, characteristic, complemented
28#25794C211yesmaximal, characteristic
29#25776C211yesmaximal, characteristic, complemented
30#25774C211yesmaximal, characteristic, complemented
31#20552C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C23×SD16C2211yescharacteristic
34C2×#542C2211yescharacteristic
35C2×#542C2211yescharacteristic
36C2×#536C2211yescharacteristic
37C2×#518C2211yescharacteristic
38#3263—28no—
39#3225—28no—
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic, complemented
42C2×#496C2211yescharacteristic
43C2×#495C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#495C2211yescharacteristic
46C2×#495C2211yescharacteristic, complemented
47C2×#493C2211yescharacteristic
48C2×#492C2211yescharacteristic
49C2×#492C2211yescharacteristic
50C2×#489C2211yescharacteristic, complemented
51C2×#487C2211yescharacteristic, complemented
52#3118—28no—
53C2×#485C2211yescharacteristic
54C2×#482C2211yescharacteristic
55C2×#475C2211yescharacteristic, complemented
56C2×#475C2211yescharacteristic, complemented
57C2×#476C2211yescharacteristic
58C2×#476C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic, complemented
60C2×#474C2211yescharacteristic
61C2×#470C2211yescharacteristic
62C2×#469C2211yescharacteristic
63C2×#465C2211yescharacteristic
64C2×#465C2211yescharacteristic
65#3042—28no—
66C2×#464C2211yescharacteristic, complemented
67C2×#464C2211yescharacteristic, complemented
68C2×#464C2211yescharacteristic, complemented
69C2×#462C2211yescharacteristic, complemented
70C2×#463C2211yescharacteristic
71C2×#463C2211yescharacteristic
72C2×#463C2211yescharacteristic
73C2×#463C2211yescharacteristic
74C2×#463C2211yescharacteristic
75C2×#463C2211yescharacteristic
76C2×#463C2211yescharacteristic, complemented
77C2×#463C2211yescharacteristic, complemented
78C2×#463C2211yescharacteristic, complemented
79C2×#461C2211yescharacteristic
80C2×#461C2211yescharacteristic
81C2×#461C2211yescharacteristic
82C2×#461C2211yescharacteristic
83C2×#461C2211yescharacteristic, complemented
84C2×#452C2211yescharacteristic
85C2×#449C2211yescharacteristic
86C2×#451C2211yescharacteristic
87C2×#448C2211yescharacteristic
88C2×#450C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×#442C2211yescharacteristic
91C2×#440C2211yescharacteristic
92C2×C4×SD16C2211yescharacteristic
93C2×C4×D8C2211yescharacteristic
94C2×#433C2211yescharacteristic
95C2×#424C2211yescharacteristic
96C2×#419C2211yescharacteristic
97C2×#416C2211yescharacteristic
98#2862C2211yescharacteristic, complemented
99#2858C2211yescharacteristic, complemented
100#2723—22no—
101#2710—22no—
102#2706—22no—
103#2692—22no—
104#2658C2211yescharacteristic, complemented
105#2640C2211yescharacteristic, complemented
106#2563C2211yescharacteristic
107#2547C2211yescharacteristic, complemented
108#2546C2211yescharacteristic, complemented
109#2545C2211yescharacteristic, complemented
110#2544C2211yescharacteristic
111#2544C2211yescharacteristic
112#2544C2211yescharacteristic, complemented
113#2542C2211yescharacteristic
114#2500C2211yescharacteristic
115#2499C2211yescharacteristic
116#2472—22no—
117#2467—22no—
118#2463—22no—
119#2436C2211yescharacteristic
120#2435C2211yescharacteristic
121#2434C2211yescharacteristic
122#2433C2211yescharacteristic
123#2432C2211yescharacteristic
124#2431C2211yescharacteristic
125#2418—22no—
126#2328C2211yescharacteristic
127#2326C2211yescharacteristic
128C4×#127C2211yescharacteristic
129C4×#124C2211yescharacteristic
130#2298C2211yescharacteristic
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2097C2211yescharacteristic, complemented
134#2096C2211yescharacteristic, complemented
135#2096C2211yescharacteristic, complemented
136#2096C2211yescharacteristic, complemented
137#2094C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2016C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic, complemented
145#2014C2211yescharacteristic
146#2014C2211yescharacteristic
147#2014C2211yescharacteristic
148#2014C2211yescharacteristic, complemented
149#2013C2211yescharacteristic
150#2013C2211yescharacteristic
151#2013C2211yescharacteristic
152#2013C2211yescharacteristic, complemented
153#2012C2211yescharacteristic
154#2012C2211yescharacteristic
155#2012C2211yescharacteristic
156#2012C2211yescharacteristic
157#2012C2211yescharacteristic
158#2012C2211yescharacteristic, complemented
159#2012C2211yescharacteristic, complemented
160#2012C2211yescharacteristic, complemented
161#2011C2211yescharacteristic
162#2011C2211yescharacteristic
163#1973C2211yescharacteristic, complemented
164#1972C2211yescharacteristic
165#1972C2211yescharacteristic
166#1971C2211yescharacteristic, complemented
167#1970C2211yescharacteristic, complemented
168#1969C2211yescharacteristic, complemented
169#1969C2211yescharacteristic, complemented
170#1968C2211yescharacteristic
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic
173#1968C2211yescharacteristic
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic, complemented
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1960C2211yescharacteristic, complemented
180#1959C2211yescharacteristic, complemented
181#1958C2211yescharacteristic, complemented
182#1958C2211yescharacteristic, complemented
183#1958C2211yescharacteristic, complemented
184#1957C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1956C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188#1771C2211yescharacteristic, complemented
189C8×C4⋊C4C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1768C2211yescharacteristic, complemented
193C4×C4⋊C8C2211yescharacteristic, complemented
194C4×C4⋊C8C2211yescharacteristic, complemented
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197C8×C22⋊C4C2211yescharacteristic
198C8×C22⋊C4C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C2×AGL(1,ℤ/8)—24no—
203C2×AGL(1,ℤ/8)—42no—
204C2×AGL(1,ℤ/8)—42no—
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16—24no—
210C22×SD16—42no—
211C22×SD16—42no—
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C22×SD16C2311yescharacteristic
225C22×SD16C2311yescharacteristic
226C22×D8C2311yescharacteristic
227C22×D8C2311yescharacteristic
228C22×D8C2311yescharacteristic
229C22×D8C2311yescharacteristic
230C22×D8C2311yescharacteristic
231C22×D8C2311yescharacteristic
232C22×M16C2311yescharacteristic
233C23×C8C2311yescharacteristic
234#542—24no—
235#542—24no—
236#542—24no—
237#542—24no—
238#536—24no—
239#536—24no—
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×C4⋊Q8C2311yescharacteristic
244C2×C4⋊Q8C2311yescharacteristic
245C2×C4⋊Q8C2311yescharacteristic
246C2×C4⋊Q8C2311yescharacteristic
247C2×#127C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#127C2311yescharacteristic
250C2×#126—21no—
251C2×#126—21no—
252C2×#124—21no—
253C2×#124—21no—
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#124C2311yescharacteristic
264C2×#123—21no—
265C2×#123—21no—
266C2×#123—21no—
267C2×#123—21no—
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8—21no—
270C2×C22⋊Q8—21no—
271C2×C22⋊Q8—21no—
272C2×C22⋊Q8—22no—
273C2×C22⋊Q8C2311yescharacteristic
274C2×C22⋊Q8C2311yescharacteristic
275C2×#121C2311yescharacteristic
276C2×#121C2311yescharacteristic
277C2×#120—22no—
278#518—24no—
279#518—24no—
280C2×C4×Q8C2311yescharacteristic
281C2×C4×Q8C2311yescharacteristic
282C2×C4×D4—21no—
283C2×C4×D4—21no—
284C2×C4×D4—22no—
285C2×C4×D4C2311yescharacteristic
286C2×C4×D4C2311yescharacteristic
287C2×C4×D4C2311yescharacteristic
288C2×C4×D4C2311yescharacteristic
289C2×C4×D4C2311yescharacteristic
290C2×C4×D4C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C22×C22⋊C4—21no—
294C22×C22⋊C4—21no—
295#497—24no—
296#497—42no—
297#496—42no—
298#495—24no—
299#495—42no—
300#495—42no—
301#495—42no—
302#493—42no—
303#492—42no—
304#492—42no—
305#489—24no—
306#487—24no—
307#485—24no—
308#482—24no—
309#476—24no—
310#476—24no—
311#476—24no—
312#475—24no—
313#475—24no—
314#474—24no—
315#470—24no—
316#469—24no—
317#465—24no—
318#465—24no—
319#464—24no—
320#464—24no—
321#464—24no—
322#463—24no—
323#463—24no—
324#463—24no—
325#463—24no—
326#463—24no—
327#463—24no—
328#463—24no—
329#463—24no—
330#463—24no—
331#462—24no—
332#461—24no—
333#461—24no—
334#461—24no—
335#461—24no—
336#461—24no—
337#452—24no—
338#451—24no—
339#450—24no—
340#449—24no—
341#448—24no—
342#447—24no—
343#442—24no—
344#440—24no—
345C4×SD16—24no—
346C4×D8—24no—
347#433D418yescomplemented
348C2×#107C2311yescharacteristic
349C2×#107C2311yescharacteristic
350C2×#106C2311yescharacteristic
351C2×#106C2311yescharacteristic
352C2×#106C2311yescharacteristic
353C2×#106C2311yescharacteristic
354C2×#106C2311yescharacteristic
355C2×#106C2311yescharacteristic
356#424D418yescomplemented
357C2×C4⋊C8C2311yescharacteristic
358C2×C4⋊C8C2311yescharacteristic
359C2×C4⋊C8C2311yescharacteristic
360C2×C4⋊C8C2311yescharacteristic
361C2×C4⋊C8C2311yescharacteristic
362C2×C4⋊C8C2311yescharacteristic
363#419—24no—
364#416—24no—
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#103C2311yescharacteristic
379C2×#103C2311yescharacteristic
380C2×#103C2311yescharacteristic
381C2×#103C2311yescharacteristic
382C2×#103C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×#102C2311yescharacteristic
394C2×#102C2311yescharacteristic
395C2×#102C2311yescharacteristic
396C2×#102C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398C2×C22⋊C8C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409#399—22no—
410#399—22no—
411#399—22no—
412#398—22no—
413#397—22no—
414#397—22no—
415#397—22no—
416#396—22no—
417#395—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#393—22no—
425#393—22no—
426#393—22no—
427#392—22no—
428#392—22no—
429#391—22no—
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390—22no—
439#390—22no—
440#390—22no—
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#389—22no—
450#388—22no—
451#388—22no—
452#388—22no—
453#388—22no—
454#388D412yes—
455#388D412yes—
456#387—22no—
457#387D412yes—
458#387D412yes—
459#386—22no—
460#386—22no—
461#386—22no—
462#386—22no—
463#386—22no—
464#386—22no—
465#386—22no—
466#385—22no—
467#385—22no—
468#385—22no—
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#382—22no—
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#380—22no—
475#380—22no—
476#379—22no—
477C4×C4⋊C4C2311yescharacteristic
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—22no—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483C43C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492C25—21no—
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
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×C4—21no—
538C23×C4—21no—
539C23×C4C2411yescharacteristic
540AGL(1,ℤ/8)—416no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×SD16—22no—
554C2×SD16—22no—
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—22no—
573C2×SD16—22no—
574C2×SD16—22no—
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—41no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—41no—
591C2×SD16—41no—
592C2×SD16—41no—
593C2×SD16—41no—
594C2×SD16—41no—
595C2×SD16—416no—
596C2×D8—22no—
597C2×D8—22no—
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—22no—
603C2×D8—22no—
604C2×D8—22no—
605C2×D8—22no—
606C2×D8—41no—
607C2×D8—41no—
608C2×D8—41no—
609C2×D8—41no—
610C2×D8—41no—
611C2×D8—41no—
612C2×D8—41no—
613C2×D8—41no—
614C2×M16—41no—
615C2×M16—41no—
616C2×M16C2×D414yes—
617C22×C8—41no—
618C22×C8—41no—
619C22×C8C2×D414yes—
620C22×C8C2411yescharacteristic
621C22×C8C2411yescharacteristic
622C22×C8C2411yescharacteristic
623C22×C8C2411yescharacteristic
624C22×C8C2411yescharacteristic
625C22×C8C2411yescharacteristic
626C22×C8C2411yescharacteristic
627C22×C8C2411yescharacteristic
628C4⋊Q8—22no—
629C4⋊Q8—22no—
630C4⋊Q8—22no—
631C4⋊Q8—22no—
632C4⋊Q8—22no—
633C4⋊Q8—22no—
634C4⋊Q8—22no—
635C4⋊Q8—22no—
636C4⋊Q8—41no—
637C4⋊Q8—41no—
638C4⋊Q8—41no—
639C4⋊Q8—41no—
640C4⋊Q8—41no—
641C4⋊Q8—41no—
642#127—22no—
643#127—22no—
644#127—41no—
645#127—41no—
646#127—41no—
647#127—41no—
648#126—44no—
649#126—44no—
650#124—22no—
651#124—22no—
652#124—22no—
653#124—22no—
654#124—22no—
655#124—22no—
656#124—22no—
657#124—22no—
658#124—22no—
659#124—22no—
660#124—41no—
661#124—41no—
662#124—41no—
663#124—41no—
664#124—41no—
665#124—41no—
666#124—41no—
667#124—41no—
668#124—41no—
669#124—41no—
670#124—44no—
671#124—44no—
672#123—44no—
673#123—44no—
674#123—44no—
675#123—44no—
676C22⋊Q8—22no—
677C22⋊Q8—22no—
678C22⋊Q8—22no—
679C22⋊Q8—22no—
680C22⋊Q8—44no—
681C22⋊Q8—44no—
682C22⋊Q8—44no—
683C22⋊Q8—44no—
684C22⋊Q8—84no—
685#121—22no—
686#121—22no—
687#121—22no—
688#121—22no—
689#120—84no—
690C4×Q8—22no—
691C4×Q8—22no—
692C4×Q8—22no—
693C4×Q8—22no—
694C4×D4—22no—
695C4×D4—22no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—22no—
699C4×D4—22no—
700C4×D4—22no—
701C4×D4—22no—
702C4×D4—22no—
703C4×D4—22no—
704C4×D4—22no—
705C4×D4—22no—
706C4×D4—44no—
707C4×D4—44no—
708C4×D4—84no—
709#117—22no—
710#117—22no—
711#117C2×D414yes—
712#117C2×D414yes—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—21no—
716C2×C4⋊C4—21no—
717C2×C4⋊C4—21no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—21no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—22no—
726C2×C4⋊C4—22no—
727C2×C4⋊C4—22no—
728C2×C4⋊C4C2×D412yes—
729C2×C4⋊C4C2×D412yes—
730C2×C4⋊C4C2×D411yescharacteristic
731C2×C4⋊C4C2×D411yescharacteristic
732C2×C4⋊C4C2411yescharacteristic
733C2×C4⋊C4C2411yescharacteristic
734C2×C4⋊C4C2411yescharacteristic
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C22⋊C4—21no—
739C2×C22⋊C4—21no—
740C2×C22⋊C4—21no—
741C2×C22⋊C4—21no—
742C2×C22⋊C4—21no—
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—21no—
757C2×C22⋊C4—21no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—44no—
772C2×C22⋊C4—44no—
773C2×C22⋊C4C2×D412yes—
774C2×C22⋊C4C2×D412yes—
775C2×C22⋊C4C2×D411yescharacteristic
776C2×C22⋊C4C2×D411yescharacteristic
777C2×C42—21no—
778C2×C42—21no—
779C2×C42—21no—
780C2×C42C2×D412yes—
781C2×C42C2×D412yes—
782C2×C42C2411yescharacteristic
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787C2×C42C2411yescharacteristic
788#107—22no—
789#107—22no—
790#106—22no—
791#106—22no—
792#106—22no—
793#106—22no—
794#106—22no—
795#106—22no—
796C4⋊C8C2×D414yes—
797C4⋊C8C2×D414yes—
798C4⋊C8C2×D414yes—
799C4⋊C8C2×D414yes—
800C4⋊C8C2×D414yes—
801C4⋊C8C2×D414yes—
802#103—22no—
803#103—22no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—22no—
815#103—22no—
816#103—22no—
817#103—22no—
818#103—22no—
819#103—22no—
820#102—22no—
821#102—22no—
822#102—22no—
823#102—22no—
824#102—22no—
825#102—22no—
826#102—22no—
827#102—22no—
828#102—22no—
829#102—22no—
830#102—22no—
831#102—22no—
832#102—22no—
833#102—22no—
834C22⋊C8C2×D414yes—
835C22⋊C8C2×D414yes—
836#97—41no—
837#97—41no—
838#97C2×D414yes—
839C4×C8—41no—
840C4×C8—41no—
841C4×C8—41no—
842C4×C8—41no—
843C4×C8—41no—
844C4×C8—41no—
845C4×C8C2×D414yes—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95C2×D412yes—
857#95C2×D412yes—
858#95C2×D412yes—
859#95C2×D412yes—
860#95C2×D412yes—
861#95C2×D412yes—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—42no—
868C24—42no—
869C24—42no—
870C24—82no—
871C24—82no—
872C24C22×D411yescharacteristic
873#41—44no—
874#41—44no—
875#41—82no—
876#41—82no—
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—21no—
893C2×Q8—21no—
894C2×Q8—21no—
895C2×Q8—21no—
896C2×Q8—21no—
897C2×Q8—21no—
898C2×Q8—21no—
899C2×Q8—21no—
900C2×Q8—21no—
901C2×Q8—21no—
902C2×Q8—21no—
903C2×Q8—21no—
904C2×Q8—21no—
905C2×Q8—21no—
906C2×Q8—21no—
907C2×Q8—44no—
908C2×Q8—44no—
909C2×Q8—42no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—81no—
913C2×Q8—81no—
914C2×Q8—82no—
915C2×Q8—82no—
916C2×Q8—82no—
917C2×Q8—82no—
918C2×D4—28no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—21no—
926C2×D4—21no—
927C2×D4—21no—
928C2×D4—21no—
929C2×D4—21no—
930C2×D4—21no—
931C2×D4—21no—
932C2×D4—21no—
933C2×D4—21no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—21no—
937C2×D4—21no—
938C2×D4—21no—
939C2×D4—21no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—21no—
945C2×D4—21no—
946C2×D4—21no—
947C2×D4—44no—
948C2×D4—44no—
949C2×D4—42no—
950C2×D4—42no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—42no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—44no—
959C2×D4—44no—
960C2×D4—82no—
961C2×D4—82no—
962C2×D4—82no—
963C2×D4—82no—
964C2×D4—82no—
965C2×D4—81no—
966C2×D4—81no—
967C2×D4—82no—
968C2×D4—82no—
969C2×D4H(5,𝔽2)12yes—
970C2×D4H(5,𝔽2)12yes—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—81no—
995C22×C4—81no—
996C22×C4—82no—
997C22×C4—82no—
998C22×C4—82no—
999C22×C4—82no—
1000C22×C4—82no—
1001C22×C4—82no—
1002C22×C4—81no—
1003C22×C4—81no—
1004C22×C4C22×D412yes—
1005C22×C4C22×D412yes—
1006C22×C4C22×D412yes—
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D411yescharacteristic
1011C22×C4C22×D411yescharacteristic
1012C22×C4C22×D412yes—
1013C22×C4C22×D412yes—
1014C22×C4C22×D412yes—
1015C22×C4C2511yescharacteristic
1016Q16—82no—
1017Q16—82no—
1018Q16—82no—
1019Q16—82no—
1020SD16—44no—
1021SD16—44no—
1022SD16—44no—
1023SD16—44no—
1024SD16—44no—
1025SD16—44no—
1026SD16—44no—
1027SD16—44no—
1028SD16—82no—
1029SD16—82no—
1030SD16—82no—
1031SD16—82no—
1032SD16—82no—
1033SD16—82no—
1034D8—44no—
1035D8—44no—
1036D8—44no—
1037D8—44no—
1038D8—82no—
1039D8—82no—
1040M16—44no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—21no—
1045C2×C8—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—21no—
1051C2×C8—21no—
1052C2×C8—21no—
1053C2×C8—21no—
1054C2×C8—21no—
1055C2×C8—21no—
1056C2×C8—21no—
1057C2×C8—44no—
1058C2×C8C22×D412yes—
1059C2×C8C22×D412yes—
1060C2×C8C22×D412yes—
1061C2×C8C22×D412yes—
1062C2×C8C22×D412yes—
1063C2×C8C22×D412yes—
1064C2×C8C22×D412yes—
1065C2×C8C22×D412yes—
1066C4⋊C4—24no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—21no—
1078C4⋊C4—21no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—42no—
1089C4⋊C4—42no—
1090C4⋊C4—44no—
1091C4⋊C4—82no—
1092C4⋊C4—82no—
1093C4⋊C4—82no—
1094C4⋊C4—82no—
1095C4⋊C4#12714yes—
1096C4⋊C4#12714yes—
1097C22⋊C4—24no—
1098C22⋊C4—42no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—42no—
1114C22⋊C4—42no—
1115C22⋊C4—42no—
1116C22⋊C4—42no—
1117C22⋊C4—42no—
1118C22⋊C4—42no—
1119C22⋊C4—42no—
1120C22⋊C4—44no—
1121C22⋊C4—82no—
1122C22⋊C4—82no—
1123C22⋊C4—82no—
1124C22⋊C4—82no—
1125C22⋊C4—82no—
1126C22⋊C4—82no—
1127C22⋊C4—82no—
1128C22⋊C4—82no—
1129C22⋊C4—82no—
1130C22⋊C4—82no—
1131C22⋊C4—82no—
1132C22⋊C4#12714yes—
1133C22⋊C4#12714yes—
1134C42—24no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—42no—
1144C42—42no—
1145C42—42no—
1146C42—42no—
1147C42C22×D412yes—
1148C42C22×D412yes—
1149C42C22×D412yes—
1150C42C22×D412yes—
1151C23—22no—
1152C23—21no—
1153C23—21no—
1154C23—22no—
1155C23—22no—
1156C23—22no—
1157C23—48no—
1158C23—42no—
1159C23—42no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—42no—
1165C23—42no—
1166C23—42no—
1167C23—42no—
1168C23—42no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—42no—
1179C23—42no—
1180C23—42no—
1181C23—162no—
1182C23—162no—
1183C23—164no—
1184C23—164no—
1185C23C2×#12712yes—
1186C23C23×D411yescharacteristic
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—84no—
1208Q8—162no—
1209Q8—162no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—48no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—88no—
1232D4—84no—
1233D4—164no—
1234D4—164no—
1235D4—162no—
1236D4—162no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—42no—
1283C2×C4—42no—
1284C2×C4—42no—
1285C2×C4—84no—
1286C2×C4—84no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4—162no—
1290C2×C4—162no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4C2×#12712yes—
1294C2×C4C2×#12712yes—
1295C2×C4C2×#12712yes—
1296C2×C4C2×#12712yes—
1297C2×C4C2×#12712yes—
1298C2×C4#57714yes—
1299C2×C4C23×D411yescharacteristic
1300C2×C4C23×D411yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4C2×H(5,𝔽2)11yescharacteristic
1303C2×C4#58511yescharacteristic
1304C2×C4#58511yescharacteristic
1305C8—22no—
1306C8—22no—
1307C8—22no—
1308C8—22no—
1309C8—22no—
1310C8—22no—
1311C8—22no—
1312C8—22no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—42no—
1317C22—42no—
1318C22—44no—
1319C22—44no—
1320C22—42no—
1321C22—42no—
1322C22—82no—
1323C22—82no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—82no—
1329C22—82no—
1330C22—82no—
1331C22—82no—
1332C22—82no—
1333C22—82no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—168no—
1344C22C22×#12711yescharacteristic
1345C22#348811yescharacteristic
1346C22#348811yescharacteristic
1347C22C2×#57712yes—
1348C22#358412yes—
1349C4—24no—
1350C4—22no—
1351C4—22no—
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—42no—
1356C4—42no—
1357C4—42no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4#348411yescharacteristic
1370C4#348711yescharacteristic
1371C4#348811yescharacteristic
1372C4#348811yescharacteristic
1373C2—42no—
1374C2—82no—
1375C2—82no—
1376C2—161no—
1377C2—161no—
1378C2—161no—
1379C2#3556511yescharacteristic
1380C2#6064611yescharacteristic
1381C2#6064911yescharacteristic
1382C2#6206312yes—
1383C2#6206812yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25794C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3263C2semidirect
2. C2×#3225C2semidirect
3. C2×#3118C2semidirect
4. C2×#3042C2semidirect
5. #37391C2semidirect
6. #35536C2semidirect
7. #28479C2semidirect
8. #28478C2semidirect
9. #28465C2semidirect
10. #28464C2semidirect
11. #28455C2semidirect
12. #28453C2semidirect
13. #28443C2semidirect
14. #28442C2semidirect
15. #28434C2semidirect
16. #28430C2semidirect
17. #28400C2semidirect
18. #28398C2semidirect
19. #28395C2semidirect
20. #28393C2semidirect
21. #28372C2semidirect
22. #28370C2semidirect
23. #28363C2semidirect
24. #28355C2semidirect
25. #28340C2semidirect
26. #28339C2semidirect
27. #25796C2semidirect
29. #25776C2semidirect
30. #25774C2semidirect
31. #20552C2semidirect
41. C2×#497C22semidirect
46. C2×#495C22semidirect
50. C2×#489C22semidirect
51. C2×#487C22semidirect
55. C2×#475C22semidirect
56. C2×#475C22semidirect
58. C2×#476C22semidirect
59. C2×#476C22semidirect
66. C2×#464C22semidirect
67. C2×#464C22semidirect
68. C2×#464C22semidirect
69. C2×#462C22semidirect
76. C2×#463C22semidirect
77. C2×#463C22semidirect
78. C2×#463C22semidirect
83. C2×#461C22semidirect
98. #2862C22semidirect
99. #2858C22semidirect
104. #2658C22semidirect
105. #2640C22semidirect
107. #2547C22semidirect
108. #2546C22semidirect
109. #2545C22semidirect
112. #2544C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
133. #2097C22semidirect
134. #2096C22semidirect
135. #2096C22semidirect
136. #2096C22semidirect
137. #2094C22semidirect
138. #2092C22semidirect
139. #2016C22semidirect
140. #2016C22semidirect
144. #2015C22semidirect
148. #2014C22semidirect
152. #2013C22semidirect
158. #2012C22semidirect
159. #2012C22semidirect
160. #2012C22semidirect
163. #1973C22semidirect
166. #1971C22semidirect
167. #1970C22semidirect
168. #1969C22semidirect
169. #1969C22semidirect
176. #1968C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1960C22semidirect
180. #1959C22semidirect
181. #1958C22semidirect
182. #1958C22semidirect
183. #1958C22semidirect
184. #1957C22semidirect
185. #1956C22semidirect
186. #1956C22semidirect
187. #1771C22semidirect
188. #1771C22semidirect
189. C8×C4⋊C4C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
192. #1768C22semidirect
193. C4×C4⋊C8C22semidirect
194. C4×C4⋊C8C22semidirect
347. #433D4semidirect
356. #424D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32632
C2×#32252
C2×#31182
C2×#30422
#373912
#355362
#284792
#284782
#284652
#284642
#284552
#284532
#284432
#284422
#284342
#284302
#284002
#283982
#283952
#283932
#283722
#283702
#283632
#283552
#283402
#283392
#257962
#257942
#257762
#257742
#205522