Finite Group Databasebeta

← #6520415

Subgroups — #6520415

Order 512.

2311 conjugacy classes of subgroups.

The subgroup lattice has 1361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3252C211yesmaximal, characteristic, complemented
2C2×#3211C211yesmaximal, characteristic, complemented
3C2×#3107C211yesmaximal, characteristic, complemented
4C2×#3040C211yesmaximal, characteristic, complemented
5#37537C211yesmaximal, characteristic, complemented
6#35211C211yesmaximal, characteristic, complemented
7#28469C211yesmaximal, characteristic, complemented
8#28468C211yesmaximal, characteristic, complemented
9#28466C211yesmaximal, characteristic, complemented
10#28464C211yesmaximal, characteristic, complemented
11#28456C211yesmaximal, characteristic, complemented
12#28455C211yesmaximal, characteristic, complemented
13#28453C211yesmaximal, characteristic, complemented
14#28453C211yesmaximal, characteristic, complemented
15#28411C211yesmaximal, characteristic, complemented
16#28410C211yesmaximal, characteristic, complemented
17#28407C211yesmaximal, characteristic, complemented
18#28406C211yesmaximal, characteristic, complemented
19#28396C211yesmaximal, characteristic, complemented
20#28395C211yesmaximal, characteristic, complemented
21#28394C211yesmaximal, characteristic, complemented
22#28393C211yesmaximal, characteristic, complemented
23#28367C211yesmaximal, characteristic, complemented
24#28361C211yesmaximal, characteristic, complemented
25#28357C211yesmaximal, characteristic, complemented
26#28355C211yesmaximal, characteristic, complemented
27#25796C211yesmaximal, characteristic, complemented
28#25795C211yesmaximal, characteristic, complemented
29#25793C211yesmaximal, characteristic
30#25790C211yesmaximal, characteristic, complemented
31#20548C211yesmaximal, characteristic, complemented
32C22×#137C2211yescharacteristic
33C22×AGL(1,ℤ/8)C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C22×#124C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#3252—28no—
39#3211—28no—
40C2×#497C2211yescharacteristic
41C2×#497C2211yescharacteristic, complemented
42C2×#497C2211yescharacteristic, complemented
43C2×#496C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#495C2211yescharacteristic
46C2×#495C2211yescharacteristic
47C2×#495C2211yescharacteristic
48C2×#494C2211yescharacteristic, complemented
49C2×#492C2211yescharacteristic, complemented
50C2×#488C2211yescharacteristic
51C2×#488C2211yescharacteristic
52#3107—28no—
53C2×#485C2211yescharacteristic
54C2×#485C2211yescharacteristic
55C2×#479C2211yescharacteristic, complemented
56C2×#479C2211yescharacteristic, complemented
57C2×#477C2211yescharacteristic, complemented
58C2×#475C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic, complemented
60C2×#474C2211yescharacteristic, complemented
61C2×#470C2211yescharacteristic
62C2×#470C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65#3040—28no—
66C2×#464C2211yescharacteristic
67C2×#464C2211yescharacteristic
68C2×#464C2211yescharacteristic
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#464C2211yescharacteristic
72C2×#464C2211yescharacteristic, complemented
73C2×#464C2211yescharacteristic, complemented
74C2×#462C2211yescharacteristic, complemented
75C2×#462C2211yescharacteristic, complemented
76C2×#463C2211yescharacteristic
77C2×#463C2211yescharacteristic
78C2×#463C2211yescharacteristic
79C2×#463C2211yescharacteristic
80C2×#463C2211yescharacteristic
81C2×#463C2211yescharacteristic
82C2×#461C2211yescharacteristic, complemented
83C2×#461C2211yescharacteristic, complemented
84C2×#452C2211yescharacteristic
85C2×#452C2211yescharacteristic
86C2×#451C2211yescharacteristic
87C2×#448C2211yescharacteristic
88C2×#450C2211yescharacteristic
89C2×#447C2211yescharacteristic
90C2×C4×Q16C2211yescharacteristic, complemented
91C2×C4×Q16C2211yescharacteristic, complemented
92C2×C4×SD16C2211yescharacteristic, complemented
93C2×C4×SD16C2211yescharacteristic, complemented
94C2×#431C2211yescharacteristic
95C2×#423C2211yescharacteristic
96C2×#419C2211yescharacteristic
97C2×#418C2211yescharacteristic
98#2852—22no—
99#2820—22no—
100#2658C2211yescharacteristic
101#2658C2211yescharacteristic
102#2640C2211yescharacteristic
103#2640C2211yescharacteristic
104#2632—22no—
105#2630—22no—
106#2626—22no—
107#2609—22no—
108#2600—22no—
109#2566C2211yescharacteristic, complemented
110#2565C2211yescharacteristic, complemented
111#2545C2211yescharacteristic
112#2545C2211yescharacteristic
113#2545C2211yescharacteristic
114#2545C2211yescharacteristic
115#2545C2211yescharacteristic, complemented
116#2544C2211yescharacteristic, complemented
117#2500C2211yescharacteristic
118#2499C2211yescharacteristic
119#2482—22no—
120#2435C2211yescharacteristic
121#2435C2211yescharacteristic
122#2434C2211yescharacteristic
123#2434C2211yescharacteristic
124#2432C2211yescharacteristic
125#2431C2211yescharacteristic
126#2328C2211yescharacteristic, complemented
127#2327C2211yescharacteristic, complemented
128#2326C2211yescharacteristic, complemented
129#2326C2211yescharacteristic, complemented
130#2283C2211yescharacteristic
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2096C2211yescharacteristic, complemented
134#2095C2211yescharacteristic, complemented
135#2094C2211yescharacteristic
136#2093C2211yescharacteristic
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2016C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2016C2211yescharacteristic, complemented
142#2016C2211yescharacteristic, complemented
143#2016C2211yescharacteristic, complemented
144#2015C2211yescharacteristic
145#2015C2211yescharacteristic
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic, complemented
149#2015C2211yescharacteristic, complemented
150#2014C2211yescharacteristic, complemented
151#2013C2211yescharacteristic
152#2013C2211yescharacteristic, complemented
153#2013C2211yescharacteristic, complemented
154#2013C2211yescharacteristic, complemented
155#2013C2211yescharacteristic, complemented
156#2012C2211yescharacteristic
157#2012C2211yescharacteristic
158#2012C2211yescharacteristic
159#2012C2211yescharacteristic
160#2012C2211yescharacteristic
161#2012C2211yescharacteristic
162#2011C2211yescharacteristic
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic, complemented
166#1973C2211yescharacteristic, complemented
167#1972C2211yescharacteristic
168#1972C2211yescharacteristic
169#1971C2211yescharacteristic, complemented
170#1971C2211yescharacteristic, complemented
171#1970C2211yescharacteristic
172#1970C2211yescharacteristic
173#1969C2211yescharacteristic, complemented
174#1969C2211yescharacteristic, complemented
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1960C2211yescharacteristic, complemented
180#1960C2211yescharacteristic, complemented
181#1959C2211yescharacteristic
182#1959C2211yescharacteristic
183#1958C2211yescharacteristic
184#1958C2211yescharacteristic
185#1956C2211yescharacteristic, complemented
186#1956C2211yescharacteristic, complemented
187#1770C2211yescharacteristic, complemented
188#1770C2211yescharacteristic, complemented
189C8×C4⋊C4C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1768C2211yescharacteristic, complemented
193#1768C2211yescharacteristic, complemented
194#1768C2211yescharacteristic, complemented
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C2×#137—24no—
203C2×#137—42no—
204C2×#137—42no—
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C22×Q16C2311yescharacteristic
214C22×Q16C2311yescharacteristic
215C22×Q16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
223C22×SD16C2311yescharacteristic
224C22×SD16C2311yescharacteristic
225C22×SD16C2311yescharacteristic
226C22×SD16C2311yescharacteristic
227C22×SD16C2311yescharacteristic
228C22×D8C2311yescharacteristic
229C22×D8C2311yescharacteristic
230C22×D8C2311yescharacteristic
231C22×D8C2311yescharacteristic
232C22×M16C2311yescharacteristic
233C22×M16C2311yescharacteristic
234#533—24no—
235#533—24no—
236C2×C4⋊Q8C2311yescharacteristic
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×C4⋊Q8C2311yescharacteristic
242C2×C4⋊Q8C2311yescharacteristic
243C2×#127C2311yescharacteristic
244#529—24no—
245#529—24no—
246C2×#126—21no—
247C2×#125—21no—
248C2×#125C2311yescharacteristic
249C2×#124—21no—
250C2×#124—21no—
251C2×#124—24no—
252C2×#124—24no—
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#124C2311yescharacteristic
258C2×#124C2311yescharacteristic
259C2×#124C2311yescharacteristic
260C2×#124C2311yescharacteristic
261C2×#124C2311yescharacteristic
262C2×#124C2311yescharacteristic
263C2×#124C2311yescharacteristic
264C2×#123—21no—
265C2×C22⋊Q8—21no—
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2311yescharacteristic
269C2×#121C2311yescharacteristic
270C4×#41—24no—
271C4×#41—24no—
272C2×C4×Q8—21no—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×Q8C2311yescharacteristic
276C2×C4×Q8C2311yescharacteristic
277C2×C4×Q8C2311yescharacteristic
278C2×C4×D4—21no—
279C2×C4×D4—21no—
280C2×C4×D4—21no—
281C2×C4×D4C2311yescharacteristic
282C2×C4×D4C2311yescharacteristic
283C2×C4×D4C2311yescharacteristic
284C2×#117—21no—
285C2×#117—21no—
286C2×#117—21no—
287C2×#117C2311yescharacteristic
288C22×C22⋊C4—21no—
289C22×C22⋊C4—21no—
290C22×C42—21no—
291C22×C42C2311yescharacteristic
292#497—42no—
293#497—42no—
294#497—42no—
295#496—42no—
296#495—24no—
297#495—24no—
298#495—42no—
299#495—42no—
300#494—42no—
301#492—42no—
302#488—24no—
303#488—24no—
304#485—24no—
305#485—24no—
306#479—24no—
307#479—24no—
308#477—24no—
309#476—24no—
310#475—24no—
311#474—24no—
312#470—24no—
313#470—24no—
314#468—24no—
315#468—24no—
316#464—24no—
317#464—24no—
318#464—24no—
319#464—24no—
320#464—24no—
321#464—24no—
322#464—24no—
323#464—24no—
324#463—24no—
325#463—24no—
326#463—24no—
327#463—24no—
328#463—24no—
329#463—24no—
330#462—24no—
331#462—24no—
332#461—24no—
333#461—24no—
334#452—24no—
335#452—24no—
336#451—24no—
337#450—24no—
338#448—24no—
339#447—24no—
340C4×Q16—24no—
341C4×Q16—24no—
342C4×SD16—24no—
343C4×SD16—24no—
344#431D418yescomplemented
345C2×#107C2311yescharacteristic
346C2×#107C2311yescharacteristic
347C2×#107C2311yescharacteristic
348C2×#107C2311yescharacteristic
349C2×#106C2311yescharacteristic
350C2×#106C2311yescharacteristic
351C2×#106C2311yescharacteristic
352C2×#106C2311yescharacteristic
353#423D418yescomplemented
354C2×C4⋊C8C2311yescharacteristic
355C2×C4⋊C8C2311yescharacteristic
356C2×C4⋊C8C2311yescharacteristic
357C2×C4⋊C8C2311yescharacteristic
358C2×C4⋊C8C2311yescharacteristic
359C2×C4⋊C8C2311yescharacteristic
360#419—24no—
361#418—24no—
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×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
376C2×#103C2311yescharacteristic
377C2×#103C2311yescharacteristic
378C2×#103C2311yescharacteristic
379C2×#103C2311yescharacteristic
380C2×#103C2311yescharacteristic
381C2×#103C2311yescharacteristic
382C2×#102C2311yescharacteristic
383C2×#102C2311yescharacteristic
384C2×#102C2311yescharacteristic
385C2×#102C2311yescharacteristic
386C2×#102C2311yescharacteristic
387C2×#102C2311yescharacteristic
388C2×#102C2311yescharacteristic
389C2×#102C2311yescharacteristic
390C2×#102C2311yescharacteristic
391C2×#102C2311yescharacteristic
392C2×#102C2311yescharacteristic
393C2×#102C2311yescharacteristic
394C2×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406#399—22no—
407#399—22no—
408#399—22no—
409#399—22no—
410#398—22no—
411#397—22no—
412#397—22no—
413#397—22no—
414#396—22no—
415#396—22no—
416#396—22no—
417#396—22no—
418#396—22no—
419#396—22no—
420#395—22no—
421#395—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#393—22no—
428#393—22no—
429#392—22no—
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#388—22no—
447#388—22no—
448#388—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388—22no—
453#388—22no—
454#387—22no—
455#387—22no—
456#387—22no—
457#387—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#385—22no—
466#385—22no—
467#385—22no—
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#383D412yes—
471#382D412yes—
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#381D412yes—
475#380D412yes—
476#379—22no—
477#379—22no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483#376C2311yescharacteristic
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—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535#137—416no—
536AGL(1,ℤ/8)—416no—
537C2×Q16—22no—
538C2×Q16—22no—
539C2×Q16—22no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16—22no—
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×Q16—22no—
548C2×Q16—22no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×Q16—41no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×Q16—41no—
559C2×Q16—41no—
560C2×Q16—41no—
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—22no—
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—22no—
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—41no—
596C2×SD16—41no—
597C2×D8—22no—
598C2×D8—22no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—22no—
603C2×D8—41no—
604C2×D8—41no—
605C2×D8—41no—
606C2×D8—41no—
607C2×D8—41no—
608C2×D8—41no—
609C2×M16—41no—
610C2×M16—41no—
611C2×M16—41no—
612C2×M16—41no—
613C2×M16C2×D414yes—
614C2×M16C2×D414yes—
615C22×C8C2411yescharacteristic
616C22×C8C2411yescharacteristic
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C22×C8C2411yescharacteristic
620C22×C8C2411yescharacteristic
621C22×C8C2411yescharacteristic
622C22×C8C2411yescharacteristic
623C4⋊Q8—22no—
624C4⋊Q8—22no—
625C4⋊Q8—22no—
626C4⋊Q8—22no—
627C4⋊Q8—22no—
628C4⋊Q8—41no—
629C4⋊Q8—41no—
630C4⋊Q8—41no—
631C4⋊Q8—41no—
632C4⋊Q8—41no—
633C4⋊Q8—41no—
634C4⋊Q8—41no—
635C4⋊Q8—41no—
636C4⋊Q8—41no—
637#127—22no—
638#127—41no—
639#126—44no—
640#125—22no—
641#125—22no—
642#125—44no—
643#124—22no—
644#124—22no—
645#124—22no—
646#124—22no—
647#124—22no—
648#124—22no—
649#124—22no—
650#124—22no—
651#124—22no—
652#124—22no—
653#124—22no—
654#124—22no—
655#124—41no—
656#124—41no—
657#124—41no—
658#124—41no—
659#124—41no—
660#124—41no—
661#124—41no—
662#124—41no—
663#124—41no—
664#124—41no—
665#124—44no—
666#124—44no—
667#123—44no—
668C22⋊Q8—22no—
669C22⋊Q8—22no—
670C22⋊Q8—22no—
671C22⋊Q8—22no—
672C22⋊Q8—22no—
673C22⋊Q8—22no—
674C22⋊Q8—44no—
675#121—22no—
676#121—22no—
677C4×Q8—22no—
678C4×Q8—22no—
679C4×Q8—22no—
680C4×Q8—22no—
681C4×Q8—22no—
682C4×Q8—22no—
683C4×Q8—22no—
684C4×Q8—22no—
685C4×Q8—22no—
686C4×Q8—22no—
687C4×Q8—44no—
688C4×D4—22no—
689C4×D4—22no—
690C4×D4—22no—
691C4×D4—22no—
692C4×D4—22no—
693C4×D4—22no—
694C4×D4—44no—
695C4×D4—44no—
696C4×D4—44no—
697#117—22no—
698#117—22no—
699#117—44no—
700#117—44no—
701#117—44no—
702C2×C4⋊C4—21no—
703C2×C4⋊C4—21no—
704C2×C4⋊C4—21no—
705C2×C4⋊C4—21no—
706C2×C4⋊C4—21no—
707C2×C4⋊C4—21no—
708C2×C4⋊C4—21no—
709C2×C4⋊C4—21no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—21no—
712C2×C4⋊C4—21no—
713C2×C4⋊C4—21no—
714C2×C4⋊C4—21no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4C2×D412yes—
723C2×C4⋊C4C2×D412yes—
724C2×C4⋊C4C2411yescharacteristic
725C2×C4⋊C4C2411yescharacteristic
726C2×C4⋊C4C2411yescharacteristic
727C2×C4⋊C4C2411yescharacteristic
728C2×C4⋊C4C2411yescharacteristic
729C2×C4⋊C4C2411yescharacteristic
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
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—21no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—22no—
759C2×C22⋊C4—22no—
760C2×C22⋊C4—22no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—44no—
763C2×C22⋊C4—44no—
764C2×C22⋊C4C2×D412yes—
765C2×C22⋊C4C2×D412yes—
766C2×C42—21no—
767C2×C42—21no—
768C2×C42—21no—
769C2×C42—21no—
770C2×C42—21no—
771C2×C42—21no—
772C2×C42—44no—
773C2×C42C2×D411yescharacteristic
774C2×C42C2×D411yescharacteristic
775C2×C42C2×D414yes—
776C2×C42C2×D414yes—
777C2×C42C2411yescharacteristic
778C2×C42C2411yescharacteristic
779C2×C42C2411yescharacteristic
780C2×C42C2411yescharacteristic
781C2×C42C2411yescharacteristic
782C2×C42C2411yescharacteristic
783#107—22no—
784#107—22no—
785#107—22no—
786#107—22no—
787#106—22no—
788#106—22no—
789#106—22no—
790#106—22no—
791C4⋊C8C2×D414yes—
792C4⋊C8C2×D414yes—
793C4⋊C8C2×D414yes—
794C4⋊C8C2×D414yes—
795C4⋊C8C2×D414yes—
796C4⋊C8C2×D414yes—
797#103—22no—
798#103—22no—
799#103—22no—
800#103—22no—
801#103—22no—
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#102—22no—
818#102—22no—
819#102—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—
829C22⋊C8C2×D414yes—
830C22⋊C8C2×D414yes—
831#97—41no—
832#97—41no—
833#97—41no—
834#97—41no—
835C4×C8—41no—
836C4×C8—41no—
837C4×C8—41no—
838C4×C8—41no—
839C4×C8C2×D414yes—
840C4×C8C2×D414yes—
841#95—22no—
842#95—22no—
843#95—22no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95C2×D412yes—
852#95C2×D412yes—
853#95C2×D412yes—
854#95C2×D412yes—
855#95C2×D412yes—
856#95C2×D412yes—
857#95C2×D412yes—
858#95C2×D412yes—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—44no—
864C24—42no—
865C24—81no—
866C24—81no—
867C24—82no—
868C24C22×D411yescharacteristic
869#41—28no—
870#41—44no—
871#41—44no—
872#41—44no—
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—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—21no—
908C2×Q8—44no—
909C2×Q8—44no—
910C2×Q8—42no—
911C2×Q8—42no—
912C2×Q8—82no—
913C2×Q8—81no—
914C2×Q8—81no—
915C2×Q8—82no—
916C2×Q8—82no—
917C2×Q8H(5,𝔽2)12yes—
918C2×D4—21no—
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—42no—
942C2×D4—44no—
943C2×D4—44no—
944C2×D4—44no—
945C2×D4—42no—
946C2×D4—42no—
947C2×D4—42no—
948C2×D4—42no—
949C2×D4—82no—
950C2×D4—82no—
951C2×D4—81no—
952C2×D4—81no—
953C2×D4—82no—
954C2×D4—82no—
955C2×D4—82no—
956C2×D4H(5,𝔽2)12yes—
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—21no—
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—82no—
983C22×C4—82no—
984C22×C4—82no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4#12714yes—
988C22×C4#12714yes—
989C22×C4C22×D412yes—
990C22×C4C22×D412yes—
991C22×C4C22×D412yes—
992C22×C4C22×D412yes—
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D412yes—
999C22×C4C22×D412yes—
1000C22×C4C2511yescharacteristic
1001Q16—44no—
1002Q16—44no—
1003Q16—44no—
1004Q16—44no—
1005Q16—82no—
1006Q16—82no—
1007Q16—82no—
1008Q16—82no—
1009SD16—44no—
1010SD16—44no—
1011SD16—44no—
1012SD16—44no—
1013SD16—44no—
1014SD16—44no—
1015SD16—82no—
1016SD16—82no—
1017SD16—82no—
1018SD16—82no—
1019SD16—82no—
1020SD16—82no—
1021D8—44no—
1022D8—44no—
1023D8—82no—
1024D8—82no—
1025M16—44no—
1026M16—44no—
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—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8C22×D412yes—
1044C2×C8C22×D412yes—
1045C2×C8C22×D412yes—
1046C2×C8C22×D412yes—
1047C2×C8C22×D412yes—
1048C2×C8C22×D412yes—
1049C2×C8C22×D412yes—
1050C2×C8C22×D412yes—
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—42no—
1064C4⋊C4—42no—
1065C4⋊C4—44no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
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—42no—
1079C4⋊C4—82no—
1080C4⋊C4—82no—
1081C4⋊C4—82no—
1082C4⋊C4—82no—
1083C4⋊C4—82no—
1084C4⋊C4—82no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—44no—
1088C22⋊C4—44no—
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—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—82no—
1108C22⋊C4—82no—
1109C22⋊C4—82no—
1110C22⋊C4—82no—
1111C22⋊C4—82no—
1112C22⋊C4—82no—
1113C22⋊C4—82no—
1114C22⋊C4—82no—
1115C22⋊C4—82no—
1116C22⋊C4—82no—
1117C22⋊C4—82no—
1118C22⋊C4—82no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42#12714yes—
1134C42#12714yes—
1135C42C22×D412yes—
1136C42C22×D412yes—
1137C42C22×D412yes—
1138C42C22×D412yes—
1139C23—22no—
1140C23—22no—
1141C23—21no—
1142C23—21no—
1143C23—22no—
1144C23—42no—
1145C23—42no—
1146C23—41no—
1147C23—41no—
1148C23—42no—
1149C23—42no—
1150C23—42no—
1151C23—42no—
1152C23—42no—
1153C23—42no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—84no—
1164C23—84no—
1165C23—84no—
1166C23—164no—
1167C23—164no—
1168C23C2×#12712yes—
1169C23C23×D411yescharacteristic
1170Q8—22no—
1171Q8—22no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—41no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—84no—
1195Q8—84no—
1196D4—22no—
1197D4—22no—
1198D4—48no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—84no—
1214D4—84no—
1215D4—164no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
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—22no—
1239C2×C4—44no—
1240C2×C4—44no—
1241C2×C4—48no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—42no—
1245C2×C4—42no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
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—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—84no—
1272C2×C4—84no—
1273C2×C4—84no—
1274C2×C4—84no—
1275C2×C4C2×#12712yes—
1276C2×C4C2×#12712yes—
1277C2×C4C2×#12712yes—
1278C2×C4C2×#12712yes—
1279C2×C4C2×#12712yes—
1280C2×C4C23×D411yescharacteristic
1281C2×C4C23×D411yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C8—22no—
1287C8—22no—
1288C8—22no—
1289C8—22no—
1290C8—22no—
1291C8—22no—
1292C8—22no—
1293C8—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—42no—
1298C22—42no—
1299C22—44no—
1300C22—42no—
1301C22—82no—
1302C22—81no—
1303C22—81no—
1304C22—82no—
1305C22—82no—
1306C22—82no—
1307C22—82no—
1308C22—82no—
1309C22—82no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—168no—
1320C22C22×#12711yescharacteristic
1321C22#348811yescharacteristic
1322C22#348811yescharacteristic
1323C22#358412yes—
1324C22#358612yes—
1325C4—22no—
1326C4—22no—
1327C4—22no—
1328C4—22no—
1329C4—22no—
1330C4—42no—
1331C4—42no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4#348411yescharacteristic
1347C4#348711yescharacteristic
1348C4#348811yescharacteristic
1349C4#348811yescharacteristic
1350C2—42no—
1351C2—82no—
1352C2—161no—
1353C2—161no—
1354C2—161no—
1355C2#3556511yescharacteristic
1356C2#6064311yescharacteristic
1357C2#6064511yescharacteristic
1358C2#6204812yes—
1359C2#6205012yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25793C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3252C2semidirect
2. C2×#3211C2semidirect
3. C2×#3107C2semidirect
4. C2×#3040C2semidirect
5. #37537C2semidirect
6. #35211C2semidirect
7. #28469C2semidirect
8. #28468C2semidirect
9. #28466C2semidirect
10. #28464C2semidirect
11. #28456C2semidirect
12. #28455C2semidirect
13. #28453C2semidirect
14. #28453C2semidirect
15. #28411C2semidirect
16. #28410C2semidirect
17. #28407C2semidirect
18. #28406C2semidirect
19. #28396C2semidirect
20. #28395C2semidirect
21. #28394C2semidirect
22. #28393C2semidirect
23. #28367C2semidirect
24. #28361C2semidirect
25. #28357C2semidirect
26. #28355C2semidirect
27. #25796C2semidirect
28. #25795C2semidirect
30. #25790C2semidirect
31. #20548C2semidirect
41. C2×#497C22semidirect
42. C2×#497C22semidirect
48. C2×#494C22semidirect
49. C2×#492C22semidirect
55. C2×#479C22semidirect
56. C2×#479C22semidirect
57. C2×#477C22semidirect
58. C2×#475C22semidirect
59. C2×#476C22semidirect
60. C2×#474C22semidirect
72. C2×#464C22semidirect
73. C2×#464C22semidirect
74. C2×#462C22semidirect
75. C2×#462C22semidirect
82. C2×#461C22semidirect
83. C2×#461C22semidirect
90. C2×C4×Q16C22semidirect
91. C2×C4×Q16C22semidirect
92. C2×C4×SD16C22semidirect
93. C2×C4×SD16C22semidirect
109. #2566C22semidirect
110. #2565C22semidirect
115. #2545C22semidirect
116. #2544C22semidirect
126. #2328C22semidirect
127. #2327C22semidirect
128. #2326C22semidirect
129. #2326C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
133. #2096C22semidirect
134. #2095C22semidirect
139. #2016C22semidirect
140. #2016C22semidirect
141. #2016C22semidirect
142. #2016C22semidirect
143. #2016C22semidirect
148. #2015C22semidirect
149. #2015C22semidirect
150. #2014C22semidirect
152. #2013C22semidirect
153. #2013C22semidirect
154. #2013C22semidirect
155. #2013C22semidirect
165. #1973C22semidirect
166. #1973C22semidirect
169. #1971C22semidirect
170. #1971C22semidirect
173. #1969C22semidirect
174. #1969C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1960C22semidirect
180. #1960C22semidirect
185. #1956C22semidirect
186. #1956C22semidirect
187. #1770C22semidirect
188. #1770C22semidirect
189. C8×C4⋊C4C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
192. #1768C22semidirect
193. #1768C22semidirect
194. #1768C22semidirect
344. #431D4semidirect
353. #423D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32522
C2×#32112
C2×#31072
C2×#30402
#375372
#352112
#284692
#284682
#284662
#284642
#284562
#284552
#284532
#284112
#284102
#284072
#284062
#283962
#283952
#283942
#283932
#283672
#283612
#283572
#283552
#257962
#257952
#257932
#257902
#205482