Finite Group Databasebeta

← #6473276

Subgroups — #6473276

Order 512.

2448 conjugacy classes of subgroups.

The subgroup lattice has 1430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3203C211yesmaximal, characteristic, complemented
2C2×#3201C211yesmaximal, characteristic, complemented
3C2×#3200C211yesmaximal, characteristic, complemented
4C2×#3198C211yesmaximal, characteristic, complemented
5#35308C211yesmaximal, characteristic, complemented
6#35256C211yesmaximal, characteristic, complemented
7#33184C211yesmaximal, characteristic, complemented
8#33183C211yesmaximal, characteristic, complemented
9#33177C211yesmaximal, characteristic, complemented
10#33174C211yesmaximal, characteristic, complemented
11#30255C211yesmaximal, characteristic, complemented
12#30254C211yesmaximal, characteristic, complemented
13#30252C211yesmaximal, characteristic, complemented
14#30251C211yesmaximal, characteristic, complemented
15#28318C211yesmaximal, characteristic, complemented
16#28318C211yesmaximal, characteristic, complemented
17#28317C211yesmaximal, characteristic, complemented
18#28316C211yesmaximal, characteristic, complemented
19#28315C211yesmaximal, characteristic, complemented
20#28314C211yesmaximal, characteristic, complemented
21#28312C211yesmaximal, characteristic, complemented
22#28311C211yesmaximal, characteristic, complemented
23#27923C211yesmaximal, characteristic, complemented
24#27922C211yesmaximal, characteristic, complemented
25#27921C211yesmaximal, characteristic, complemented
26#27921C211yesmaximal, characteristic, complemented
27#25737C211yesmaximal, characteristic, complemented
28#25736C211yesmaximal, characteristic, complemented
29#25733C211yesmaximal, characteristic, complemented
30#25732C211yesmaximal, characteristic, complemented
31#20375C211yesmaximal, characteristic, complemented
32C2×#537C2211yescharacteristic
33C2×#537C2211yescharacteristic
34C2×#536C2211yescharacteristic
35C2×#536C2211yescharacteristic, complemented
36C2×#535C2211yescharacteristic
37C2×#535C2211yescharacteristic
38C2×C4×#41C2211yescharacteristic
39#3203—28no—
40#3201—28no—
41#3200—28no—
42#3198—28no—
43C2×#497C2211yescharacteristic
44C2×#496C2211yescharacteristic
45C2×#495C2211yescharacteristic
46C2×#492C2211yescharacteristic
47C2×#484C2211yescharacteristic
48C2×#484C2211yescharacteristic
49C2×#484C2211yescharacteristic, complemented
50C2×#481C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#485C2211yescharacteristic
53C2×#485C2211yescharacteristic
54C2×#485C2211yescharacteristic, complemented
55C2×#482C2211yescharacteristic
56C2×#482C2211yescharacteristic
57C2×#482C2211yescharacteristic
58C2×#482C2211yescharacteristic, complemented
59C2×#483C2211yescharacteristic
60C2×#480C2211yescharacteristic
61C2×#480C2211yescharacteristic
62C2×#480C2211yescharacteristic, complemented
63C2×#470C2211yescharacteristic, complemented
64C2×#469C2211yescharacteristic
65C2×#468C2211yescharacteristic
66C2×#468C2211yescharacteristic
67C2×#468C2211yescharacteristic
68C2×#468C2211yescharacteristic, complemented
69C2×#468C2211yescharacteristic, complemented
70C2×#468C2211yescharacteristic, complemented
71C2×#467C2211yescharacteristic, complemented
72C2×#467C2211yescharacteristic, complemented
73C2×#466C2211yescharacteristic
74C2×#466C2211yescharacteristic, complemented
75C2×#465C2211yescharacteristic
76C2×#465C2211yescharacteristic
77C2×#465C2211yescharacteristic
78C2×#465C2211yescharacteristic, complemented
79C2×#452C2211yescharacteristic
80C2×#452C2211yescharacteristic
81C2×#452C2211yescharacteristic
82C2×#452C2211yescharacteristic, complemented
83C2×#449C2211yescharacteristic
84C2×#449C2211yescharacteristic
85C2×#449C2211yescharacteristic
86C2×#449C2211yescharacteristic, complemented
87C2×#451C2211yescharacteristic, complemented
88C2×#448C2211yescharacteristic
89C2×#448C2211yescharacteristic
90C2×#448C2211yescharacteristic, complemented
91C2×#450C2211yescharacteristic
92C2×#450C2211yescharacteristic
93C2×#450C2211yescharacteristic
94C2×#447C2211yescharacteristic
95C2×#408C2211yescharacteristic
96C2×#408C2211yescharacteristic
97C2×C4×M16C2211yescharacteristic, complemented
98C22×#97C2211yescharacteristic, complemented
99#2857C2211yescharacteristic
100#2857C2211yescharacteristic, complemented
101#2856C2211yescharacteristic
102#2856C2211yescharacteristic
103#2850C2211yescharacteristic
104#2850C2211yescharacteristic
105#2850C2211yescharacteristic
106#2850C2211yescharacteristic, complemented
107#2621C2211yescharacteristic
108#2621C2211yescharacteristic, complemented
109#2620C2211yescharacteristic
110#2620C2211yescharacteristic
111#2620C2211yescharacteristic
112#2620C2211yescharacteristic, complemented
113#2619C2211yescharacteristic
114#2619C2211yescharacteristic
115#2429—22no—
116#2428—22no—
117#2427—22no—
118#2426—22no—
119#2425—22no—
120#2425—22no—
121#2424—22no—
122#2424—22no—
123#2317C2211yescharacteristic
124#2317C2211yescharacteristic, complemented
125#2297C2211yescharacteristic
126#2297C2211yescharacteristic, complemented
127C2×#391C2211yescharacteristic, complemented
128C2×#390C2211yescharacteristic
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2096C2211yescharacteristic, complemented
134#2095C2211yescharacteristic, complemented
135#2095C2211yescharacteristic, complemented
136#2095C2211yescharacteristic, complemented
137#2094C2211yescharacteristic, complemented
138#2093C2211yescharacteristic
139#2093C2211yescharacteristic
140#2093C2211yescharacteristic, complemented
141#2092C2211yescharacteristic
142#2092C2211yescharacteristic
143#2092C2211yescharacteristic, complemented
144#2092C2211yescharacteristic, complemented
145#2016C2211yescharacteristic, complemented
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic
149#2015C2211yescharacteristic, complemented
150#2014C2211yescharacteristic
151#2014C2211yescharacteristic
152#2014C2211yescharacteristic
153#2013C2211yescharacteristic
154#2013C2211yescharacteristic
155#2013C2211yescharacteristic, complemented
156#2012C2211yescharacteristic
157#2012C2211yescharacteristic
158#2012C2211yescharacteristic
159#2012C2211yescharacteristic, complemented
160#2011C2211yescharacteristic
161#1973C2211yescharacteristic
162#1973C2211yescharacteristic
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic
166#1973C2211yescharacteristic
167#1973C2211yescharacteristic, complemented
168#1973C2211yescharacteristic, complemented
169#1973C2211yescharacteristic, complemented
170#1973C2211yescharacteristic, complemented
171#1972C2211yescharacteristic
172#1972C2211yescharacteristic
173#1972C2211yescharacteristic, complemented
174#1971C2211yescharacteristic, complemented
175#1971C2211yescharacteristic, complemented
176#1971C2211yescharacteristic, complemented
177#1961C2211yescharacteristic
178#1960C2211yescharacteristic, complemented
179#1959C2211yescharacteristic
180#1959C2211yescharacteristic, complemented
181#1958C2211yescharacteristic
182#1958C2211yescharacteristic, complemented
183#1957C2211yescharacteristic
184#1956C2211yescharacteristic, complemented
185#1847C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1750C2211yescharacteristic
190#1750C2211yescharacteristic
191#1750C2211yescharacteristic, complemented
192#1750C2211yescharacteristic, complemented
193#1749C2211yescharacteristic
194#1749C2211yescharacteristic
195#1749C2211yescharacteristic, complemented
196#1749C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198#1729C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×M16C2311yescharacteristic
221C22×M16C2311yescharacteristic
222C23×C8C2311yescharacteristic
223C23×C8C2311yescharacteristic
224#537—24no—
225#537—24no—
226#537—24no—
227#537—24no—
228#536—24no—
229#536—24no—
230#536—42no—
231#536—42no—
232#535—24no—
233#535—24no—
234#535—42no—
235#535—42no—
236C2×C4⋊Q8—21no—
237C2×C4⋊Q8C2311yescharacteristic
238C2×C4⋊Q8C2311yescharacteristic
239C2×#127—21no—
240C2×#127C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#124—21no—
243C2×#124—21no—
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#123—21no—
249C2×#123—21no—
250C2×#123—22no—
251C2×C22⋊Q8—21no—
252C2×C22⋊Q8—21no—
253C2×C22⋊Q8—22no—
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×C22⋊Q8C2311yescharacteristic
260C2×C22⋊Q8C2311yescharacteristic
261C2×C22⋊Q8C2311yescharacteristic
262C2×#121—21no—
263C2×#121—21no—
264C2×#121—21no—
265C2×#121—21no—
266C2×#121—21no—
267C2×#121—21no—
268C2×#121—22no—
269C2×#121—22no—
270C2×#121—22no—
271C2×#121C2311yescharacteristic
272C2×#121C2311yescharacteristic
273C2×#121C2311yescharacteristic
274C2×#121C2311yescharacteristic
275C2×#121C2311yescharacteristic
276C2×#121C2311yescharacteristic
277C2×#121C2311yescharacteristic
278C2×#121C2311yescharacteristic
279C2×#120—21no—
280C2×#120—21no—
281C2×#120—22no—
282C4×#41—42no—
283C4×#41—42no—
284C2×C4×Q8D412yes—
285C2×C4×D4D412yes—
286C2×C4×D4D412yes—
287C2×C4×D4D412yes—
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2311yescharacteristic
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C22⋊C4—22no—
296C22×C42C2311yescharacteristic
297C22×C42C2311yescharacteristic
298C22×C42C2311yescharacteristic
299#497—42no—
300#496—42no—
301#495—42no—
302#492—42no—
303#485—24no—
304#485—24no—
305#485—24no—
306#485—24no—
307#484—24no—
308#484—24no—
309#484—24no—
310#483—24no—
311#482—24no—
312#482—24no—
313#482—24no—
314#482—24no—
315#481—24no—
316#480—24no—
317#480—24no—
318#480—24no—
319#470—24no—
320#469—24no—
321#468—24no—
322#468—24no—
323#468—24no—
324#468—24no—
325#468—24no—
326#468—24no—
327#467—24no—
328#467—24no—
329#466—24no—
330#466—24no—
331#465—24no—
332#465—24no—
333#465—24no—
334#465—24no—
335#452—24no—
336#452—24no—
337#452—24no—
338#452—24no—
339#451—24no—
340#450—24no—
341#450—24no—
342#450—24no—
343#449—24no—
344#449—24no—
345#449—24no—
346#449—24no—
347#448—24no—
348#448—24no—
349#448—24no—
350#447—24no—
351C2×#107C2311yescharacteristic
352C2×#107C2311yescharacteristic
353C2×#107C2311yescharacteristic
354C2×#107C2311yescharacteristic
355C2×#107C2311yescharacteristic
356C2×#107C2311yescharacteristic
357C2×#107C2311yescharacteristic
358C2×#107C2311yescharacteristic
359C2×#107C2311yescharacteristic
360C2×#107C2311yescharacteristic
361C2×#106C2311yescharacteristic
362C2×#106C2311yescharacteristic
363C2×#106C2311yescharacteristic
364C2×#106C2311yescharacteristic
365C2×#106C2311yescharacteristic
366C2×#106C2311yescharacteristic
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×#102C2311yescharacteristic
398C2×#102C2311yescharacteristic
399#408D418yescomplemented
400#408D418yescomplemented
401C2×C22⋊C8C2311yescharacteristic
402C2×C22⋊C8C2311yescharacteristic
403C2×C22⋊C8C2311yescharacteristic
404C2×C22⋊C8C2311yescharacteristic
405C2×C22⋊C8C2311yescharacteristic
406C2×C22⋊C8C2311yescharacteristic
407C2×C22⋊C8C2311yescharacteristic
408C2×C22⋊C8C2311yescharacteristic
409C4×M16—42no—
410C2×#97—42no—
411C2×#97C2311yescharacteristic
412C2×#97C2311yescharacteristic
413C2×#97C2311yescharacteristic
414C2×#97C2311yescharacteristic
415C2×#97C2311yescharacteristic
416C2×#97C2311yescharacteristic
417C2×C4×C8C2311yescharacteristic
418C2×C4×C8C2311yescharacteristic
419#398—22no—
420#398—22no—
421#397—22no—
422#397—22no—
423#396—22no—
424#396—22no—
425#396—22no—
426#396—22no—
427#394—22no—
428#394—22no—
429#394—22no—
430#394—22no—
431#394—22no—
432#394—22no—
433#392—22no—
434#392—22no—
435#391—22no—
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#391C2311yescharacteristic
442#391C2311yescharacteristic
443#391C2311yescharacteristic
444#390—22no—
445#390—22no—
446#390—22no—
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2311yescharacteristic
452#390C2311yescharacteristic
453#390C2311yescharacteristic
454#390C2311yescharacteristic
455#389—22no—
456#389—22no—
457#389—22no—
458#389—22no—
459#388—22no—
460#388—22no—
461#388—22no—
462#388—22no—
463#386—22no—
464#386—22no—
465#386—22no—
466#386—22no—
467#386—22no—
468#386—22no—
469#385—22no—
470#385—22no—
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#382C2311yescharacteristic
476#382C2311yescharacteristic
477#382C2311yescharacteristic
478#382C2311yescharacteristic
479#380—22no—
480#380—22no—
481C4×C22⋊C4—22no—
482C4×C22⋊C4—22no—
483C2×#95—22no—
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—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41C2×D414yes—
510C2×#41C2×D414yes—
511C22×Q8—21no—
512C22×Q8—22no—
513C22×Q8—22no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8—41no—
517C22×Q8—41no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×Q8C2411yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—41no—
539C22×D4—41no—
540C22×D4—41no—
541C22×D4—41no—
542C22×D4C2×D411yescharacteristic
543C22×D4C2×D411yescharacteristic
544C22×D4C2×D411yescharacteristic
545C22×D4C2411yescharacteristic
546C22×D4C2411yescharacteristic
547C22×D4C2411yescharacteristic
548C22×D4C2411yescharacteristic
549C23×C4—21no—
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4—21no—
554C23×C4C2×D412yes—
555C23×C4C2×D412yes—
556C23×C4C2×D412yes—
557C23×C4C2411yescharacteristic
558C23×C4C2411yescharacteristic
559C23×C4C2411yescharacteristic
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—22no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×Q16—41no—
567C2×Q16—41no—
568C2×Q16—41no—
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×SD16—41no—
598C2×SD16—41no—
599C2×D8—22no—
600C2×D8—22no—
601C2×D8—22no—
602C2×D8—41no—
603C2×D8—41no—
604C2×D8—41no—
605C2×D8—41no—
606C2×D8—41no—
607C2×D8—41no—
608C2×M16—41no—
609C2×M16—41no—
610C2×M16—41no—
611C2×M16—41no—
612C2×M16C2×D414yes—
613C2×M16C2×D414yes—
614C22×C8—41no—
615C22×C8—41no—
616C22×C8—41no—
617C22×C8—41no—
618C22×C8C2×D414yes—
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—41no—
631C4⋊Q8—41no—
632C4⋊Q8—44no—
633#127—22no—
634#127—22no—
635#127—41no—
636#127—41no—
637#127—44no—
638#124—22no—
639#124—22no—
640#124—22no—
641#124—22no—
642#124—41no—
643#124—41no—
644#124—41no—
645#124—41no—
646#124—44no—
647#124—44no—
648#123—48no—
649#123—44no—
650#123—44no—
651C22⋊Q8—22no—
652C22⋊Q8—22no—
653C22⋊Q8—22no—
654C22⋊Q8—22no—
655C22⋊Q8—22no—
656C22⋊Q8—22no—
657C22⋊Q8—22no—
658C22⋊Q8—22no—
659C22⋊Q8—22no—
660C22⋊Q8—22no—
661C22⋊Q8—22no—
662C22⋊Q8—22no—
663C22⋊Q8—22no—
664C22⋊Q8—22no—
665C22⋊Q8—22no—
666C22⋊Q8—22no—
667C22⋊Q8—48no—
668C22⋊Q8—44no—
669C22⋊Q8—44no—
670#121—22no—
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—22no—
680#121—22no—
681#121—22no—
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—48no—
687#121—44no—
688#121—44no—
689#121—44no—
690#121—44no—
691#121—44no—
692#121—44no—
693#121—84no—
694#121—84no—
695#120—48no—
696#120—44no—
697#120—44no—
698C4×Q8—44no—
699C4×D4—44no—
700C4×D4—44no—
701C4×D4—44no—
702#117—22no—
703#117—22no—
704#117—22no—
705#117—22no—
706#117—22no—
707#117—22no—
708#117—22no—
709#117—22no—
710#117—41no—
711#117—41no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
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—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—21no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—22no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4C2×D412yes—
733C2×C4⋊C4C2×D412yes—
734C2×C4⋊C4C2×D412yes—
735C2×C4⋊C4C2411yescharacteristic
736C2×C4⋊C4C2411yescharacteristic
737C2×C4⋊C4C2411yescharacteristic
738C2×C4⋊C4C2411yescharacteristic
739C2×C4⋊C4C2411yescharacteristic
740C2×C4⋊C4C2411yescharacteristic
741C2×C4⋊C4C2411yescharacteristic
742C2×C4⋊C4C2411yescharacteristic
743C2×C22⋊C4—21no—
744C2×C22⋊C4—21no—
745C2×C22⋊C4—21no—
746C2×C22⋊C4—21no—
747C2×C22⋊C4—21no—
748C2×C22⋊C4—21no—
749C2×C22⋊C4—21no—
750C2×C22⋊C4—21no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—22no—
756C2×C22⋊C4—22no—
757C2×C22⋊C4—21no—
758C2×C22⋊C4—21no—
759C2×C22⋊C4—21no—
760C2×C22⋊C4—21no—
761C2×C22⋊C4—22no—
762C2×C22⋊C4—21no—
763C2×C22⋊C4—21no—
764C2×C22⋊C4—21no—
765C2×C22⋊C4—21no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—84no—
774C2×C22⋊C4C2×D412yes—
775C2×C22⋊C4C2×D412yes—
776C2×C22⋊C4C2×D412yes—
777C2×C42—22no—
778C2×C42—22no—
779C2×C42—21no—
780C2×C42—21no—
781C2×C42—41no—
782C2×C42—41no—
783C2×C42—41no—
784C2×C42—41no—
785C2×C42C2×D412yes—
786C2×C42C2×D412yes—
787C2×C42C2×D412yes—
788C2×C42C2411yescharacteristic
789C2×C42C2411yescharacteristic
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792#107—22no—
793#107—22no—
794#107—22no—
795#107—22no—
796#107—22no—
797#107—22no—
798#107—22no—
799#107—22no—
800#107—22no—
801#107—22no—
802#106—22no—
803#106—22no—
804#106—22no—
805#106—22no—
806#106—22no—
807#106—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#103—22no—
821#103—22no—
822#103—22no—
823#103—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—
834#102—22no—
835#102—22no—
836#102—22no—
837#102—22no—
838#102—22no—
839#102—22no—
840C22⋊C8C2×D414yes—
841C22⋊C8C2×D414yes—
842C22⋊C8C2×D414yes—
843C22⋊C8C2×D414yes—
844C22⋊C8C2×D414yes—
845C22⋊C8C2×D414yes—
846C22⋊C8C2×D414yes—
847C22⋊C8C2×D414yes—
848#97—22no—
849#97—22no—
850#97—41no—
851#97—41no—
852#97—41no—
853#97—41no—
854C4×C8—22no—
855C4×C8—22no—
856#95—22no—
857#95—22no—
858#95—22no—
859#95—22no—
860#95—22no—
861#95—22no—
862#95—22no—
863#95—22no—
864#95—22no—
865#95—22no—
866#95—22no—
867#95—22no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—42no—
873C24—42no—
874C24—42no—
875C24—82no—
876C24—82no—
877C24C22×D411yescharacteristic
878C24C22×D411yescharacteristic
879C24C22×D411yescharacteristic
880#41—44no—
881#41—44no—
882#41—44no—
883#41—44no—
884#41—82no—
885#41—82no—
886#41—82no—
887#41—82no—
888#41—82no—
889#41—82no—
890#41—82no—
891#41—82no—
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—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—21no—
912C2×Q8—21no—
913C2×Q8—21no—
914C2×Q8—21no—
915C2×Q8—21no—
916C2×Q8—41no—
917C2×Q8—41no—
918C2×Q8—42no—
919C2×Q8—42no—
920C2×Q8—42no—
921C2×Q8—82no—
922C2×Q8—82no—
923C2×Q8—82no—
924C2×Q8—82no—
925C2×Q8#12714yes—
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—21no—
948C2×D4—21no—
949C2×D4—21no—
950C2×D4—41no—
951C2×D4—41no—
952C2×D4—41no—
953C2×D4—41no—
954C2×D4—41no—
955C2×D4—41no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—44no—
959C2×D4—42no—
960C2×D4—42no—
961C2×D4—42no—
962C2×D4—42no—
963C2×D4—42no—
964C2×D4—42no—
965C2×D4—42no—
966C2×D4—42no—
967C2×D4—42no—
968C2×D4—42no—
969C2×D4—42no—
970C2×D4—42no—
971C2×D4—42no—
972C2×D4—42no—
973C2×D4—42no—
974C2×D4—44no—
975C2×D4—82no—
976C2×D4—82no—
977C2×D4—82no—
978C2×D4—82no—
979C2×D4—82no—
980C2×D4—82no—
981C2×D4—82no—
982C2×D4—82no—
983C2×D4—82no—
984C2×D4—82no—
985C2×D4—82no—
986C2×D4—82no—
987C2×D4—82no—
988C2×D4—82no—
989C2×D4—82no—
990C2×D4—82no—
991C2×D4#12714yes—
992C2×D4#12714yes—
993C2×D4#12714yes—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—24no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—21no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—21no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—42no—
1022C22×C4—42no—
1023C22×C4—42no—
1024C22×C4—42no—
1025C22×C4—42no—
1026C22×C4—42no—
1027C22×C4—42no—
1028C22×C4—42no—
1029C22×C4—42no—
1030C22×C4—42no—
1031C22×C4—42no—
1032C22×C4—42no—
1033C22×C4—42no—
1034C22×C4—42no—
1035C22×C4—42no—
1036C22×C4—42no—
1037C22×C4—42no—
1038C22×C4—82no—
1039C22×C4—82no—
1040C22×C4C22×D412yes—
1041C22×C4C22×D412yes—
1042C22×C4C22×D412yes—
1043C22×C4C22×D411yescharacteristic
1044C22×C4C22×D411yescharacteristic
1045C22×C4C22×D411yescharacteristic
1046C22×C4C22×D412yes—
1047C22×C4C22×D412yes—
1048C22×C4C22×D412yes—
1049C22×C4C22×D412yes—
1050C22×C4C22×D412yes—
1051C22×C4C22×D412yes—
1052C22×C4C22×D412yes—
1053C22×C4C2511yescharacteristic
1054Q16—82no—
1055Q16—82no—
1056Q16—82no—
1057SD16—82no—
1058SD16—82no—
1059SD16—82no—
1060SD16—82no—
1061SD16—82no—
1062SD16—82no—
1063SD16—82no—
1064SD16—82no—
1065SD16—82no—
1066SD16—82no—
1067D8—82no—
1068D8—82no—
1069D8—82no—
1070M16—44no—
1071M16—44no—
1072C2×C8—21no—
1073C2×C8—21no—
1074C2×C8—21no—
1075C2×C8—21no—
1076C2×C8—21no—
1077C2×C8—21no—
1078C2×C8—21no—
1079C2×C8—21no—
1080C2×C8—21no—
1081C2×C8—21no—
1082C2×C8—21no—
1083C2×C8—21no—
1084C2×C8—21no—
1085C2×C8—21no—
1086C2×C8—21no—
1087C2×C8—21no—
1088C2×C8—44no—
1089C2×C8—44no—
1090C2×C8C22×D412yes—
1091C2×C8C22×D412yes—
1092C2×C8C22×D412yes—
1093C2×C8C22×D412yes—
1094C2×C8C22×D412yes—
1095C2×C8C22×D412yes—
1096C2×C8C22×D412yes—
1097C2×C8C22×D412yes—
1098C4⋊C4—24no—
1099C4⋊C4—24no—
1100C4⋊C4—21no—
1101C4⋊C4—21no—
1102C4⋊C4—21no—
1103C4⋊C4—21no—
1104C4⋊C4—21no—
1105C4⋊C4—21no—
1106C4⋊C4—21no—
1107C4⋊C4—21no—
1108C4⋊C4—21no—
1109C4⋊C4—21no—
1110C4⋊C4—21no—
1111C4⋊C4—21no—
1112C4⋊C4—21no—
1113C4⋊C4—21no—
1114C4⋊C4—21no—
1115C4⋊C4—21no—
1116C4⋊C4—42no—
1117C4⋊C4—44no—
1118C4⋊C4—42no—
1119C4⋊C4—42no—
1120C4⋊C4—42no—
1121C4⋊C4—42no—
1122C4⋊C4—42no—
1123C4⋊C4—42no—
1124C4⋊C4—42no—
1125C4⋊C4—42no—
1126C4⋊C4—42no—
1127C4⋊C4—42no—
1128C4⋊C4—44no—
1129C4⋊C4—82no—
1130C4⋊C4—82no—
1131C4⋊C4—82no—
1132C4⋊C4—82no—
1133C22⋊C4—24no—
1134C22⋊C4—24no—
1135C22⋊C4—42no—
1136C22⋊C4—44no—
1137C22⋊C4—44no—
1138C22⋊C4—44no—
1139C22⋊C4—44no—
1140C22⋊C4—44no—
1141C22⋊C4—44no—
1142C22⋊C4—42no—
1143C22⋊C4—42no—
1144C22⋊C4—42no—
1145C22⋊C4—42no—
1146C22⋊C4—42no—
1147C22⋊C4—42no—
1148C22⋊C4—42no—
1149C22⋊C4—42no—
1150C22⋊C4—42no—
1151C22⋊C4—42no—
1152C22⋊C4—42no—
1153C22⋊C4—42no—
1154C22⋊C4—42no—
1155C22⋊C4—42no—
1156C22⋊C4—42no—
1157C22⋊C4—42no—
1158C22⋊C4—42no—
1159C22⋊C4—42no—
1160C22⋊C4—44no—
1161C22⋊C4—44no—
1162C22⋊C4—82no—
1163C22⋊C4—82no—
1164C22⋊C4—82no—
1165C22⋊C4—82no—
1166C42—24no—
1167C42—21no—
1168C42—21no—
1169C42—21no—
1170C42—21no—
1171C42—21no—
1172C42—21no—
1173C42—42no—
1174C42—42no—
1175C42—42no—
1176C42—42no—
1177C42H(5,𝔽2)12yes—
1178C42H(5,𝔽2)12yes—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—42no—
1192C23—42no—
1193C23—42no—
1194C23—42no—
1195C23—42no—
1196C23—42no—
1197C23—42no—
1198C23—42no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—41no—
1206C23—41no—
1207C23—41no—
1208C23—41no—
1209C23—41no—
1210C23—41no—
1211C23—84no—
1212C23—88no—
1213C23—162no—
1214C23—162no—
1215C23—164no—
1216C23C2×#12712yes—
1217C23C2×#12712yes—
1218C23C2×#12712yes—
1219C23C23×D411yescharacteristic
1220Q8—44no—
1221Q8—41no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—41no—
1226Q8—41no—
1227Q8—41no—
1228Q8—41no—
1229Q8—41no—
1230Q8—41no—
1231Q8—41no—
1232Q8—41no—
1233Q8—41no—
1234Q8—41no—
1235Q8—41no—
1236Q8—41no—
1237Q8—84no—
1238D4—44no—
1239D4—44no—
1240D4—44no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—41no—
1247D4—41no—
1248D4—41no—
1249D4—41no—
1250D4—41no—
1251D4—41no—
1252D4—41no—
1253D4—41no—
1254D4—41no—
1255D4—41no—
1256D4—41no—
1257D4—84no—
1258D4—84no—
1259D4—84no—
1260D4—164no—
1261D4—164no—
1262D4—162no—
1263D4—162no—
1264D4—162no—
1265D4—162no—
1266D4—162no—
1267D4—162no—
1268D4—162no—
1269D4—162no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—22no—
1279C2×C4—22no—
1280C2×C4—22no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—22no—
1284C2×C4—22no—
1285C2×C4—22no—
1286C2×C4—22no—
1287C2×C4—22no—
1288C2×C4—22no—
1289C2×C4—22no—
1290C2×C4—22no—
1291C2×C4—22no—
1292C2×C4—22no—
1293C2×C4—22no—
1294C2×C4—22no—
1295C2×C4—22no—
1296C2×C4—22no—
1297C2×C4—22no—
1298C2×C4—22no—
1299C2×C4—42no—
1300C2×C4—42no—
1301C2×C4—42no—
1302C2×C4—42no—
1303C2×C4—42no—
1304C2×C4—42no—
1305C2×C4—42no—
1306C2×C4—42no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—84no—
1328C2×C4—84no—
1329C2×C4—84no—
1330C2×C4—84no—
1331C2×C4—84no—
1332C2×C4—84no—
1333C2×C4—162no—
1334C2×C4—162no—
1335C2×C4C2×#12712yes—
1336C2×C4C2×#12712yes—
1337C2×C4C2×#12712yes—
1338C2×C4#53414yes—
1339C2×C4C23×D411yescharacteristic
1340C2×C4C23×D411yescharacteristic
1341C2×C4C2×H(5,𝔽2)11yescharacteristic
1342C2×C4C2×H(5,𝔽2)11yescharacteristic
1343C2×C4#58511yescharacteristic
1344C2×C4#58511yescharacteristic
1345C8—22no—
1346C8—22no—
1347C8—22no—
1348C8—22no—
1349C8—22no—
1350C8—22no—
1351C8—22no—
1352C8—22no—
1353C22—22no—
1354C22—22no—
1355C22—22no—
1356C22—22no—
1357C22—22no—
1358C22—22no—
1359C22—22no—
1360C22—22no—
1361C22—22no—
1362C22—42no—
1363C22—42no—
1364C22—42no—
1365C22—42no—
1366C22—42no—
1367C22—42no—
1368C22—82no—
1369C22—82no—
1370C22—82no—
1371C22—82no—
1372C22—82no—
1373C22—82no—
1374C22—82no—
1375C22—82no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—168no—
1389C22C22×#12711yescharacteristic
1390C22C2×#53411yescharacteristic
1391C22#344911yescharacteristic
1392C22#358512yes—
1393C22#358612yes—
1394C4—24no—
1395C4—22no—
1396C4—22no—
1397C4—22no—
1398C4—42no—
1399C4—42no—
1400C4—42no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4—81no—
1412C4—81no—
1413C4#349611yescharacteristic
1414C4#349611yescharacteristic
1415C4#349611yescharacteristic
1416C4#349611yescharacteristic
1417C2—42no—
1418C2—42no—
1419C2—42no—
1420C2—161no—
1421C2—161no—
1422C2—161no—
1423C2—161no—
1424C2#3500111yescharacteristic
1425C2#6065011yescharacteristic
1426C2#6065111yescharacteristic
1427C2#6077212yes—
1428C2#6097312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3203C2semidirect
2. C2×#3201C2semidirect
3. C2×#3200C2semidirect
4. C2×#3198C2semidirect
5. #35308C2semidirect
6. #35256C2semidirect
7. #33184C2semidirect
8. #33183C2semidirect
9. #33177C2semidirect
10. #33174C2semidirect
11. #30255C2semidirect
12. #30254C2semidirect
13. #30252C2semidirect
14. #30251C2semidirect
15. #28318C2semidirect
16. #28318C2semidirect
17. #28317C2semidirect
18. #28316C2semidirect
19. #28315C2semidirect
20. #28314C2semidirect
21. #28312C2semidirect
22. #28311C2semidirect
23. #27923C2semidirect
24. #27922C2semidirect
25. #27921C2semidirect
26. #27921C2semidirect
27. #25737C2semidirect
28. #25736C2semidirect
29. #25733C2semidirect
30. #25732C2semidirect
31. #20375C2semidirect
35. C2×#536C22semidirect
49. C2×#484C22semidirect
54. C2×#485C22semidirect
58. C2×#482C22semidirect
62. C2×#480C22semidirect
63. C2×#470C22semidirect
68. C2×#468C22semidirect
69. C2×#468C22semidirect
70. C2×#468C22semidirect
71. C2×#467C22semidirect
72. C2×#467C22semidirect
74. C2×#466C22semidirect
78. C2×#465C22semidirect
82. C2×#452C22semidirect
86. C2×#449C22semidirect
87. C2×#451C22semidirect
90. C2×#448C22semidirect
97. C2×C4×M16C22semidirect
98. C22×#97C22semidirect
100. #2857C22semidirect
106. #2850C22semidirect
108. #2621C22semidirect
112. #2620C22semidirect
124. #2317C22semidirect
126. #2297C22semidirect
127. C2×#391C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
133. #2096C22semidirect
134. #2095C22semidirect
135. #2095C22semidirect
136. #2095C22semidirect
137. #2094C22semidirect
140. #2093C22semidirect
143. #2092C22semidirect
144. #2092C22semidirect
145. #2016C22semidirect
149. #2015C22semidirect
155. #2013C22semidirect
159. #2012C22semidirect
167. #1973C22semidirect
168. #1973C22semidirect
169. #1973C22semidirect
170. #1973C22semidirect
173. #1972C22semidirect
174. #1971C22semidirect
175. #1971C22semidirect
176. #1971C22semidirect
178. #1960C22semidirect
180. #1959C22semidirect
182. #1958C22semidirect
184. #1956C22semidirect
185. #1847C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1845C22semidirect
191. #1750C22semidirect
192. #1750C22semidirect
195. #1749C22semidirect
196. #1749C22semidirect
197. #1729C22semidirect
198. #1729C22semidirect
399. #408D4semidirect
400. #408D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32032
C2×#32012
C2×#32002
C2×#31982
#353082
#352562
#331842
#331832
#331772
#331742
#302552
#302542
#302522
#302512
#283182
#283172
#283162
#283152
#283142
#283122
#283112
#279232
#279222
#279212
#257372
#257362
#257332
#257322
#203752