Finite Group Databasebeta

← #6473415

Subgroups — #6473415

Order 512.

2501 conjugacy classes of subgroups.

The subgroup lattice has 1442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3203C211yesmaximal, characteristic, complemented
2C2×#3198C211yesmaximal, characteristic, complemented
3C2×#3062C211yesmaximal, characteristic, complemented
4C2×#3061C211yesmaximal, characteristic, complemented
5#37300C211yesmaximal, characteristic, complemented
6#37296C211yesmaximal, characteristic, complemented
7#33187C211yesmaximal, characteristic, complemented
8#33185C211yesmaximal, characteristic, complemented
9#33182C211yesmaximal, characteristic, complemented
10#33174C211yesmaximal, characteristic, complemented
11#30255C211yesmaximal, characteristic, complemented
12#30251C211yesmaximal, characteristic, complemented
13#30244C211yesmaximal, characteristic, complemented
14#30239C211yesmaximal, characteristic, complemented
15#28364C211yesmaximal, characteristic, complemented
16#28360C211yesmaximal, characteristic, complemented
17#28358C211yesmaximal, characteristic, complemented
18#28354C211yesmaximal, characteristic, complemented
19#28349C211yesmaximal, characteristic, complemented
20#28342C211yesmaximal, characteristic, complemented
21#28338C211yesmaximal, characteristic, complemented
22#28329C211yesmaximal, characteristic, complemented
23#27945C211yesmaximal, characteristic, complemented
24#27944C211yesmaximal, characteristic, complemented
25#27938C211yesmaximal, characteristic, complemented
26#27929C211yesmaximal, characteristic, complemented
27#25793C211yesmaximal, characteristic, complemented
28#25791C211yesmaximal, characteristic, complemented
29#25785C211yesmaximal, characteristic, complemented
30#25775C211yesmaximal, characteristic, complemented
31#20387C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic, complemented
34C22×#131C2211yescharacteristic
35C2×#537C2211yescharacteristic
36C2×#537C2211yescharacteristic
37C2×#537C2211yescharacteristic
38C2×#535C2211yescharacteristic
39#3203—28no—
40#3198—28no—
41C2×#496C2211yescharacteristic
42C2×#496C2211yescharacteristic
43C2×#495C2211yescharacteristic
44C2×#492C2211yescharacteristic
45C2×#484C2211yescharacteristic
46C2×#484C2211yescharacteristic, complemented
47C2×#481C2211yescharacteristic
48C2×#485C2211yescharacteristic
49C2×#482C2211yescharacteristic
50C2×#480C2211yescharacteristic
51C2×#480C2211yescharacteristic
52C2×#480C2211yescharacteristic, complemented
53#3062—28no—
54#3061—28no—
55C2×#469C2211yescharacteristic
56C2×#469C2211yescharacteristic
57C2×#469C2211yescharacteristic
58C2×#468C2211yescharacteristic
59C2×#468C2211yescharacteristic
60C2×#468C2211yescharacteristic
61C2×#468C2211yescharacteristic
62C2×#468C2211yescharacteristic
63C2×#468C2211yescharacteristic, complemented
64C2×#468C2211yescharacteristic, complemented
65C2×#468C2211yescharacteristic, complemented
66C2×#468C2211yescharacteristic, complemented
67C2×#467C2211yescharacteristic
68C2×#467C2211yescharacteristic, complemented
69C2×#467C2211yescharacteristic, complemented
70C2×#466C2211yescharacteristic
71C2×#466C2211yescharacteristic
72C2×#466C2211yescharacteristic
73C2×#466C2211yescharacteristic
74C2×#466C2211yescharacteristic, complemented
75C2×#466C2211yescharacteristic, complemented
76C2×#465C2211yescharacteristic
77C2×#465C2211yescharacteristic
78C2×#465C2211yescharacteristic
79C2×#452C2211yescharacteristic
80C2×#452C2211yescharacteristic, complemented
81C2×#449C2211yescharacteristic
82C2×#449C2211yescharacteristic
83C2×#449C2211yescharacteristic
84C2×#449C2211yescharacteristic, complemented
85C2×#450C2211yescharacteristic
86C2×#447C2211yescharacteristic
87C2×#428C2211yescharacteristic
88C22×#107C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic, complemented
90C2×#417C2211yescharacteristic, complemented
91C2×#416C2211yescharacteristic
92C22×#102C2211yescharacteristic
93C2×#408C2211yescharacteristic
94C2×#405C2211yescharacteristic, complemented
95C2×C4×M16C2211yescharacteristic, complemented
96#2857C2211yescharacteristic, complemented
97#2856C2211yescharacteristic
98#2856C2211yescharacteristic, complemented
99#2850C2211yescharacteristic
100#2732—22no—
101#2730—22no—
102#2682—22no—
103#2678—22no—
104#2673—22no—
105#2671—22no—
106#2671—22no—
107#2668—22no—
108#2620C2211yescharacteristic
109#2620C2211yescharacteristic, complemented
110#2620C2211yescharacteristic, complemented
111#2619C2211yescharacteristic
112#2504C2211yescharacteristic
113#2502C2211yescharacteristic
114#2502C2211yescharacteristic, complemented
115#2501C2211yescharacteristic
116#2501C2211yescharacteristic
117#2501C2211yescharacteristic, complemented
118#2500C2211yescharacteristic
119#2499C2211yescharacteristic
120#2435C2211yescharacteristic
121#2433C2211yescharacteristic
122#2432C2211yescharacteristic
123#2432C2211yescharacteristic, complemented
124#2431C2211yescharacteristic
125#2431C2211yescharacteristic
126#2431C2211yescharacteristic
127#2431C2211yescharacteristic, complemented
128#2297C2211yescharacteristic
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2097C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2095C2211yescharacteristic, complemented
135#2094C2211yescharacteristic, complemented
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic
138#2093C2211yescharacteristic
139#2093C2211yescharacteristic
140#2093C2211yescharacteristic, complemented
141#2093C2211yescharacteristic, complemented
142#2093C2211yescharacteristic, complemented
143#2093C2211yescharacteristic, complemented
144#2092C2211yescharacteristic, complemented
145#2016C2211yescharacteristic, complemented
146#2015C2211yescharacteristic
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic
149#2015C2211yescharacteristic, complemented
150#2014C2211yescharacteristic
151#2013C2211yescharacteristic
152#2012C2211yescharacteristic
153#2012C2211yescharacteristic
154#2012C2211yescharacteristic
155#2012C2211yescharacteristic, complemented
156#2011C2211yescharacteristic
157#2011C2211yescharacteristic
158#2011C2211yescharacteristic
159#2011C2211yescharacteristic
160#2011C2211yescharacteristic, complemented
161#1973C2211yescharacteristic
162#1973C2211yescharacteristic
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic
165#1973C2211yescharacteristic, complemented
166#1973C2211yescharacteristic, complemented
167#1973C2211yescharacteristic, complemented
168#1972C2211yescharacteristic, complemented
169#1970C2211yescharacteristic
170#1970C2211yescharacteristic
171#1970C2211yescharacteristic
172#1970C2211yescharacteristic
173#1969C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1968C2211yescharacteristic, complemented
176#1968C2211yescharacteristic, complemented
177#1961C2211yescharacteristic, complemented
178#1959C2211yescharacteristic
179#1959C2211yescharacteristic
180#1959C2211yescharacteristic, complemented
181#1958C2211yescharacteristic, complemented
182#1957C2211yescharacteristic
183#1957C2211yescharacteristic
184#1956C2211yescharacteristic, complemented
185#1847C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1845C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1753C2211yescharacteristic
190#1753C2211yescharacteristic
191#1753C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198C2×#336C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C2×AGL(1,ℤ/8)—24no—
205C2×AGL(1,ℤ/8)—42no—
206C2×AGL(1,ℤ/8)—42no—
207C2×#135—24no—
208C2×#135—42no—
209C2×#135—42no—
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C2×#131—42no—
227C2×#131—42no—
228C2×#131D418yescomplemented
229C22×M16C2311yescharacteristic
230C22×M16C2311yescharacteristic
231C22×M16C2311yescharacteristic
232C22×M16C2311yescharacteristic
233C23×C8C2311yescharacteristic
234C23×C8C2311yescharacteristic
235C23×C8C2311yescharacteristic
236C23×C8C2311yescharacteristic
237#537—24no—
238#537—24no—
239#537—24no—
240#537—24no—
241#537—24no—
242#537—24no—
243#535—24no—
244#535—24no—
245C2×C4⋊Q8C2311yescharacteristic
246C2×#127—21no—
247C2×#127C2311yescharacteristic
248C2×#127C2311yescharacteristic
249C2×#127C2311yescharacteristic
250C2×#124—21no—
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#123—22no—
256C2×#123—22no—
257C2×#123—22no—
258C2×C22⋊Q8—21no—
259C2×C22⋊Q8—21no—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8C2311yescharacteristic
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×C22⋊Q8C2311yescharacteristic
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2311yescharacteristic
267C2×#121—21no—
268C2×#121—21no—
269C2×#121—21no—
270C2×#121—21no—
271C2×#121—21no—
272C2×#121—21no—
273C2×#121—21no—
274C2×#121—21no—
275C2×#121—21no—
276C2×#121—22no—
277C2×#121—22no—
278C2×#121C2311yescharacteristic
279C2×#121C2311yescharacteristic
280C2×#121C2311yescharacteristic
281C2×#121C2311yescharacteristic
282C2×#121C2311yescharacteristic
283C2×#121C2311yescharacteristic
284C2×#121C2311yescharacteristic
285C2×#121C2311yescharacteristic
286C2×#121C2311yescharacteristic
287C2×#121C2311yescharacteristic
288C2×#120—21no—
289C2×#120—21no—
290C2×#120—22no—
291C2×#117C2311yescharacteristic
292C2×#117C2311yescharacteristic
293C22×C4⋊C4C2311yescharacteristic
294C22×C4⋊C4C2311yescharacteristic
295C22×C4⋊C4C2311yescharacteristic
296C22×C42C2311yescharacteristic
297#496—42no—
298#496—42no—
299#495—42no—
300#492—42no—
301#485—24no—
302#484—24no—
303#484—24no—
304#482—24no—
305#481—24no—
306#480—24no—
307#480—24no—
308#480—24no—
309#469—24no—
310#469—24no—
311#469—24no—
312#468—24no—
313#468—24no—
314#468—24no—
315#468—24no—
316#468—24no—
317#468—24no—
318#468—24no—
319#468—24no—
320#468—24no—
321#467—24no—
322#467—24no—
323#467—24no—
324#466—24no—
325#466—24no—
326#466—24no—
327#466—24no—
328#466—24no—
329#466—24no—
330#465—24no—
331#465—24no—
332#465—24no—
333#452—24no—
334#452—24no—
335#450—24no—
336#449—24no—
337#449—24no—
338#449—24no—
339#449—24no—
340#447—24no—
341#428—24no—
342C2×#107—24no—
343C2×#107C2311yescharacteristic
344C2×#107C2311yescharacteristic
345C2×#107C2311yescharacteristic
346C2×#107C2311yescharacteristic
347C2×#107C2311yescharacteristic
348C2×#107C2311yescharacteristic
349C2×#107C2311yescharacteristic
350C2×#107C2311yescharacteristic
351C2×#107C2311yescharacteristic
352C2×#107C2311yescharacteristic
353C2×#107C2311yescharacteristic
354C2×#107C2311yescharacteristic
355C2×#106C2311yescharacteristic
356C2×#106C2311yescharacteristic
357C2×#106C2311yescharacteristic
358C2×#106C2311yescharacteristic
359#417—24no—
360#417—24no—
361#416—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×#102—24no—
375C2×#102C2311yescharacteristic
376C2×#102C2311yescharacteristic
377C2×#102C2311yescharacteristic
378C2×#102C2311yescharacteristic
379C2×#102C2311yescharacteristic
380C2×#102C2311yescharacteristic
381C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
395#408D418yescomplemented
396C2×C22⋊C8C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398C2×C22⋊C8C2311yescharacteristic
399C2×C22⋊C8C2311yescharacteristic
400#405—42no—
401C4×M16—42no—
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410#399—22no—
411#399—22no—
412#399—22no—
413#398—22no—
414#398—22no—
415#397—22no—
416#397—22no—
417#396—22no—
418#396—22no—
419#396—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#394—22no—
428#392—22no—
429#392—22no—
430#392—22no—
431#392—22no—
432#392—22no—
433#392—22no—
434#391D412yes—
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#391C2311yescharacteristic
441#390—22no—
442#390—22no—
443#390D412yes—
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#390C2311yescharacteristic
451#390C2311yescharacteristic
452#390C2311yescharacteristic
453#390C2311yescharacteristic
454#389—22no—
455#388—22no—
456#388—22no—
457#387—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386—22no—
462#386—22no—
463#386—22no—
464#386D412yes—
465#386D412yes—
466#385—22no—
467#385—22no—
468#385—22no—
469#385—22no—
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#384C2311yescharacteristic
474#384C2311yescharacteristic
475#384C2311yescharacteristic
476#382C2311yescharacteristic
477#382C2311yescharacteristic
478#380—22no—
479#379—22no—
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482C4×C22⋊C4C2311yescharacteristic
483C4×C22⋊C4C2311yescharacteristic
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—22no—
498C2×#41—22no—
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×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×D414yes—
516C2×#41C2×D414yes—
517C22×Q8C2×D411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×D4—21no—
522C22×D4—21no—
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—21no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—22no—
540C22×D4—41no—
541C22×D4—41no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4C2×D411yescharacteristic
545C22×D4C2×D411yescharacteristic
546C22×D4C2×D411yescharacteristic
547C22×D4C2411yescharacteristic
548C22×D4C2411yescharacteristic
549C22×D4C2411yescharacteristic
550C22×D4C2411yescharacteristic
551C22×D4C2411yescharacteristic
552C23×C4—21no—
553C23×C4—21no—
554C23×C4—21no—
555C23×C4—21no—
556C23×C4—21no—
557C23×C4—21no—
558C23×C4C2×D412yes—
559C23×C4C2411yescharacteristic
560C23×C4C2411yescharacteristic
561C23×C4C2411yescharacteristic
562AGL(1,ℤ/8)—416no—
563#135—416no—
564C2×Q16—22no—
565C2×Q16—22no—
566C2×Q16—41no—
567C2×Q16—41no—
568C2×Q16—41no—
569C2×Q16—41no—
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—22no—
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
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×D8—22no—
595C2×D8—22no—
596C2×D8—22no—
597C2×D8—22no—
598C2×D8—22no—
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×D8—41no—
609C2×D8—41no—
610C2×D8—41no—
611C2×D8—41no—
612#131—416no—
613C2×M16—22no—
614C2×M16—22no—
615C2×M16—22no—
616C2×M16—22no—
617C2×M16—41no—
618C2×M16—41no—
619C2×M16—41no—
620C2×M16—41no—
621C2×M16C2×D414yes—
622C2×M16C2×D414yes—
623C2×M16C2×D414yes—
624C2×M16C2×D414yes—
625C22×C8—22no—
626C22×C8—22no—
627C22×C8—41no—
628C22×C8—41no—
629C22×C8—41no—
630C22×C8—41no—
631C22×C8—41no—
632C22×C8—41no—
633C22×C8C2×D414yes—
634C22×C8C2×D414yes—
635C22×C8C2×D414yes—
636C22×C8C2×D414yes—
637C22×C8C2411yescharacteristic
638C22×C8C2411yescharacteristic
639C22×C8C2411yescharacteristic
640C22×C8C2411yescharacteristic
641C22×C8C2411yescharacteristic
642C22×C8C2411yescharacteristic
643C22×C8C2411yescharacteristic
644C22×C8C2411yescharacteristic
645C4⋊Q8—41no—
646C4⋊Q8—41no—
647#127—41no—
648#127—41no—
649#127—41no—
650#127—41no—
651#127—41no—
652#127—41no—
653#127—44no—
654#124—41no—
655#124—41no—
656#124—41no—
657#124—41no—
658#124—41no—
659#124—41no—
660#124—41no—
661#124—41no—
662#124—44no—
663#123—84no—
664#123—84no—
665#123—84no—
666C22⋊Q8—22no—
667C22⋊Q8—22no—
668C22⋊Q8—22no—
669C22⋊Q8—22no—
670C22⋊Q8—22no—
671C22⋊Q8—22no—
672C22⋊Q8—22no—
673C22⋊Q8—22no—
674C22⋊Q8—22no—
675C22⋊Q8—22no—
676C22⋊Q8—22no—
677C22⋊Q8—22no—
678C22⋊Q8—44no—
679C22⋊Q8—44no—
680C22⋊Q8—44no—
681#121—22no—
682#121—22no—
683#121—22no—
684#121—22no—
685#121—22no—
686#121—22no—
687#121—22no—
688#121—22no—
689#121—22no—
690#121—22no—
691#121—22no—
692#121—22no—
693#121—22no—
694#121—22no—
695#121—22no—
696#121—22no—
697#121—22no—
698#121—22no—
699#121—22no—
700#121—22no—
701#121—44no—
702#121—44no—
703#121—44no—
704#121—44no—
705#121—44no—
706#121—44no—
707#121—44no—
708#121—44no—
709#121—44no—
710#121—84no—
711#121—84no—
712#120—44no—
713#120—44no—
714#120—84no—
715#117—22no—
716#117—22no—
717#117—41no—
718#117—41no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—21no—
729C2×C4⋊C4—21no—
730C2×C4⋊C4—21no—
731C2×C4⋊C4—21no—
732C2×C4⋊C4—21no—
733C2×C4⋊C4—21no—
734C2×C4⋊C4—22no—
735C2×C4⋊C4—22no—
736C2×C4⋊C4—22no—
737C2×C4⋊C4—22no—
738C2×C4⋊C4—22no—
739C2×C4⋊C4—22no—
740C2×C4⋊C4—22no—
741C2×C4⋊C4C2×D412yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2411yescharacteristic
745C2×C4⋊C4C2411yescharacteristic
746C2×C4⋊C4C2411yescharacteristic
747C2×C4⋊C4C2411yescharacteristic
748C2×C4⋊C4C2411yescharacteristic
749C2×C4⋊C4C2411yescharacteristic
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—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—21no—
767C2×C22⋊C4—21no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4C2×D412yes—
782C2×C22⋊C4C2×D412yes—
783C2×C22⋊C4C2×D412yes—
784C2×C22⋊C4C2×D412yes—
785C2×C22⋊C4C2×D412yes—
786C2×C42—21no—
787C2×C42—41no—
788C2×C42—41no—
789C2×C42C2×D412yes—
790C2×C42C2411yescharacteristic
791C2×C42C2411yescharacteristic
792C2×C42C2411yescharacteristic
793C2×C42C2411yescharacteristic
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#107—22no—
803#107—22no—
804#107—22no—
805#107—22no—
806#106—22no—
807#106—22no—
808#106—22no—
809#106—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#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—
834#102—22no—
835#102—22no—
836#102—22no—
837#102—22no—
838#102—22no—
839#102—22no—
840#102—22no—
841#102—22no—
842C22⋊C8C2×D414yes—
843C22⋊C8C2×D414yes—
844C22⋊C8C2×D414yes—
845C22⋊C8C2×D414yes—
846#97—22no—
847#97—22no—
848#97—41no—
849#97—41no—
850C4×C8—22no—
851C4×C8—22no—
852C4×C8—41no—
853C4×C8—41no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—22no—
858#95—22no—
859#95—22no—
860#95—22no—
861#95—22no—
862#95C2×D412yes—
863#95C2×D412yes—
864#95C2×D412yes—
865#95C2×D412yes—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—42no—
872C24—81no—
873C24—81no—
874C24—82no—
875C24—82no—
876C24C22×D411yescharacteristic
877C24C22×D411yescharacteristic
878C24C22×D411yescharacteristic
879#41—44no—
880#41—44no—
881#41—44no—
882#41—44no—
883#41—44no—
884#41—44no—
885#41—44no—
886#41—44no—
887#41—44no—
888#41—44no—
889#41—82no—
890#41—82no—
891#41—82no—
892#41—82no—
893#41—82no—
894#41—82no—
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—41no—
914C2×Q8—41no—
915C2×Q8#12714yes—
916C2×D4—21no—
917C2×D4—21no—
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—21no—
942C2×D4—21no—
943C2×D4—21no—
944C2×D4—21no—
945C2×D4—21no—
946C2×D4—41no—
947C2×D4—41no—
948C2×D4—41no—
949C2×D4—41no—
950C2×D4—41no—
951C2×D4—41no—
952C2×D4—44no—
953C2×D4—44no—
954C2×D4—44no—
955C2×D4—42no—
956C2×D4—42no—
957C2×D4—42no—
958C2×D4—42no—
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—44no—
970C2×D4—82no—
971C2×D4—82no—
972C2×D4—81no—
973C2×D4—81no—
974C2×D4—82no—
975C2×D4—82no—
976C2×D4—82no—
977C2×D4—82no—
978C2×D4—82no—
979C2×D4—82no—
980C2×D4—82no—
981C2×D4—81no—
982C2×D4—81no—
983C2×D4—81no—
984C2×D4—81no—
985C2×D4—81no—
986C2×D4—81no—
987C2×D4—82no—
988C2×D4—82no—
989C2×D4—82no—
990C2×D4—82no—
991C2×D4—82no—
992C2×D4—82no—
993C2×D4—82no—
994C2×D4—82no—
995C2×D4—82no—
996C2×D4—82no—
997C2×D4#12714yes—
998C2×D4#12714yes—
999C2×D4#12714yes—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—21no—
1008C22×C4—21no—
1009C22×C4—21no—
1010C22×C4—21no—
1011C22×C4—21no—
1012C22×C4—24no—
1013C22×C4—21no—
1014C22×C4—21no—
1015C22×C4—21no—
1016C22×C4—21no—
1017C22×C4—21no—
1018C22×C4—21no—
1019C22×C4—21no—
1020C22×C4—21no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—21no—
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—81no—
1033C22×C4—81no—
1034C22×C4—81no—
1035C22×C4—81no—
1036C22×C4—81no—
1037C22×C4—81no—
1038C22×C4—82no—
1039C22×C4—82no—
1040C22×C4—82no—
1041C22×C4C22×D412yes—
1042C22×C4C22×D412yes—
1043C22×C4C22×D412yes—
1044C22×C4C22×D411yescharacteristic
1045C22×C4C22×D411yescharacteristic
1046C22×C4C22×D411yescharacteristic
1047C22×C4C22×D412yes—
1048C22×C4C22×D412yes—
1049C22×C4C22×D412yes—
1050C22×C4C22×D412yes—
1051C22×C4C22×D412yes—
1052C22×C4C22×D412yes—
1053C22×C4C22×D412yes—
1054C22×C4C2511yescharacteristic
1055Q16—44no—
1056Q16—82no—
1057SD16—44no—
1058SD16—44no—
1059SD16—44no—
1060SD16—44no—
1061SD16—82no—
1062SD16—82no—
1063SD16—82no—
1064SD16—82no—
1065D8—44no—
1066D8—44no—
1067D8—44no—
1068D8—82no—
1069D8—82no—
1070D8—82no—
1071M16—28no—
1072M16—28no—
1073M16—44no—
1074M16—44no—
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—21no—
1089C2×C8—28no—
1090C2×C8—44no—
1091C2×C8—44no—
1092C2×C8—44no—
1093C2×C8C22×D412yes—
1094C2×C8C22×D412yes—
1095C2×C8C22×D412yes—
1096C2×C8C22×D412yes—
1097C2×C8C22×D412yes—
1098C2×C8C22×D412yes—
1099C2×C8C22×D412yes—
1100C2×C8C22×D412yes—
1101C2×C8H(5,𝔽2)12yes—
1102C2×C8H(5,𝔽2)12yes—
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—21no—
1117C4⋊C4—21no—
1118C4⋊C4—21no—
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—42no—
1129C4⋊C4—44no—
1130C4⋊C4—44no—
1131C4⋊C4—82no—
1132C4⋊C4—82no—
1133C4⋊C4—82no—
1134C4⋊C4—82no—
1135C4⋊C4—82no—
1136C22⋊C4—24no—
1137C22⋊C4—24no—
1138C22⋊C4—42no—
1139C22⋊C4—42no—
1140C22⋊C4—42no—
1141C22⋊C4—42no—
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—44no—
1159C22⋊C4—44no—
1160C22⋊C4—44no—
1161C22⋊C4—82no—
1162C22⋊C4—82no—
1163C22⋊C4—82no—
1164C22⋊C4—82no—
1165C22⋊C4—82no—
1166C22⋊C4—82no—
1167C22⋊C4—82no—
1168C22⋊C4—82no—
1169C22⋊C4—82no—
1170C22⋊C4—82no—
1171C22⋊C4—82no—
1172C42—21no—
1173C42—21no—
1174C42—21no—
1175C42—21no—
1176C42—21no—
1177C42—21no—
1178C42—21no—
1179C42—21no—
1180C42—42no—
1181C42—42no—
1182C23—22no—
1183C23—22no—
1184C23—22no—
1185C23—21no—
1186C23—21no—
1187C23—21no—
1188C23—21no—
1189C23—21no—
1190C23—21no—
1191C23—22no—
1192C23—22no—
1193C23—22no—
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—41no—
1212C23—41no—
1213C23—41no—
1214C23—42no—
1215C23—42no—
1216C23—42no—
1217C23—42no—
1218C23—42no—
1219C23—84no—
1220C23—162no—
1221C23—162no—
1222C23—164no—
1223C23—164no—
1224C23C2×#12712yes—
1225C23C2×#12712yes—
1226C23C2×#12712yes—
1227C23C23×D411yescharacteristic
1228Q8—44no—
1229Q8—41no—
1230Q8—41no—
1231Q8—41no—
1232Q8—41no—
1233Q8—41no—
1234Q8—41no—
1235Q8—41no—
1236Q8—41no—
1237Q8—41no—
1238Q8—41no—
1239Q8—41no—
1240Q8—41no—
1241D4—44no—
1242D4—44no—
1243D4—44no—
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—41no—
1258D4—41no—
1259D4—41no—
1260D4—41no—
1261D4—41no—
1262D4—41no—
1263D4—41no—
1264D4—84no—
1265D4—84no—
1266D4—84no—
1267D4—84no—
1268D4—164no—
1269D4—164no—
1270D4—164no—
1271D4—162no—
1272D4—162no—
1273D4—162no—
1274D4—162no—
1275D4—162no—
1276D4—162no—
1277D4—162no—
1278D4—162no—
1279D4—162no—
1280D4—162no—
1281C2×C4—22no—
1282C2×C4—22no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
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—22no—
1300C2×C4—22no—
1301C2×C4—22no—
1302C2×C4—22no—
1303C2×C4—22no—
1304C2×C4—22no—
1305C2×C4—22no—
1306C2×C4—22no—
1307C2×C4—22no—
1308C2×C4—22no—
1309C2×C4—22no—
1310C2×C4—42no—
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—41no—
1328C2×C4—42no—
1329C2×C4—42no—
1330C2×C4—42no—
1331C2×C4—42no—
1332C2×C4—42no—
1333C2×C4—42no—
1334C2×C4—42no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—84no—
1338C2×C4—84no—
1339C2×C4—162no—
1340C2×C4—162no—
1341C2×C4—162no—
1342C2×C4C2×#12712yes—
1343C2×C4C2×#12712yes—
1344C2×C4C2×#12712yes—
1345C2×C4#57614yes—
1346C2×C4C23×D411yescharacteristic
1347C2×C4C23×D411yescharacteristic
1348C2×C4C2×H(5,𝔽2)11yescharacteristic
1349C2×C4C2×H(5,𝔽2)11yescharacteristic
1350C2×C4#58511yescharacteristic
1351C2×C4#58511yescharacteristic
1352C8—22no—
1353C8—22no—
1354C8—22no—
1355C8—22no—
1356C8—22no—
1357C8—22no—
1358C8—22no—
1359C8#53414yes—
1360C22—22no—
1361C22—22no—
1362C22—22no—
1363C22—22no—
1364C22—22no—
1365C22—22no—
1366C22—22no—
1367C22—22no—
1368C22—22no—
1369C22—42no—
1370C22—42no—
1371C22—42no—
1372C22—42no—
1373C22—42no—
1374C22—42no—
1375C22—82no—
1376C22—82no—
1377C22—82no—
1378C22—82no—
1379C22—82no—
1380C22—82no—
1381C22—82no—
1382C22—82no—
1383C22—82no—
1384C22—82no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—81no—
1398C22—81no—
1399C22—81no—
1400C22—168no—
1401C22C22×#12711yescharacteristic
1402C22#349611yescharacteristic
1403C22#349611yescharacteristic
1404C22C2×#57612yes—
1405C22#358612yes—
1406C4—24no—
1407C4—22no—
1408C4—22no—
1409C4—22no—
1410C4—42no—
1411C4—42no—
1412C4—42no—
1413C4—81no—
1414C4—81no—
1415C4—81no—
1416C4—81no—
1417C4—81no—
1418C4—81no—
1419C4—81no—
1420C4—81no—
1421C4—81no—
1422C4—81no—
1423C4—81no—
1424C4C2×#53411yescharacteristic
1425C4#344911yescharacteristic
1426C4#349611yescharacteristic
1427C4#349611yescharacteristic
1428C2—42no—
1429C2—42no—
1430C2—42no—
1431C2—161no—
1432C2—161no—
1433C2—161no—
1434C2—161no—
1435C2—161no—
1436C2#3500111yescharacteristic
1437C2#6064711yescharacteristic
1438C2#6065111yescharacteristic
1439C2#6231112yes—
1440C2#6235312yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2297 ◁ 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×#3198C2semidirect
3. C2×#3062C2semidirect
4. C2×#3061C2semidirect
5. #37300C2semidirect
6. #37296C2semidirect
7. #33187C2semidirect
8. #33185C2semidirect
9. #33182C2semidirect
10. #33174C2semidirect
11. #30255C2semidirect
12. #30251C2semidirect
13. #30244C2semidirect
14. #30239C2semidirect
15. #28364C2semidirect
16. #28360C2semidirect
17. #28358C2semidirect
18. #28354C2semidirect
19. #28349C2semidirect
20. #28342C2semidirect
21. #28338C2semidirect
22. #28329C2semidirect
23. #27945C2semidirect
24. #27944C2semidirect
25. #27938C2semidirect
26. #27929C2semidirect
27. #25793C2semidirect
28. #25791C2semidirect
29. #25785C2semidirect
30. #25775C2semidirect
31. #20387C2semidirect
33. C22×#135C22semidirect
46. C2×#484C22semidirect
52. C2×#480C22semidirect
63. C2×#468C22semidirect
64. C2×#468C22semidirect
65. C2×#468C22semidirect
66. C2×#468C22semidirect
68. C2×#467C22semidirect
69. C2×#467C22semidirect
74. C2×#466C22semidirect
75. C2×#466C22semidirect
80. C2×#452C22semidirect
84. C2×#449C22semidirect
88. C22×#107C22semidirect
89. C2×#417C22semidirect
90. C2×#417C22semidirect
94. C2×#405C22semidirect
95. C2×C4×M16C22semidirect
96. #2857C22semidirect
98. #2856C22semidirect
109. #2620C22semidirect
110. #2620C22semidirect
114. #2502C22semidirect
117. #2501C22semidirect
123. #2432C22semidirect
127. #2431C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2097C22semidirect
132. #2096C22semidirect
133. #2095C22semidirect
134. #2095C22semidirect
135. #2094C22semidirect
140. #2093C22semidirect
141. #2093C22semidirect
142. #2093C22semidirect
143. #2093C22semidirect
144. #2092C22semidirect
145. #2016C22semidirect
149. #2015C22semidirect
155. #2012C22semidirect
160. #2011C22semidirect
165. #1973C22semidirect
166. #1973C22semidirect
167. #1973C22semidirect
168. #1972C22semidirect
173. #1969C22semidirect
174. #1968C22semidirect
175. #1968C22semidirect
176. #1968C22semidirect
177. #1961C22semidirect
180. #1959C22semidirect
181. #1958C22semidirect
184. #1956C22semidirect
185. #1847C22semidirect
186. #1847C22semidirect
187. #1845C22semidirect
188. #1845C22semidirect
191. #1753C22semidirect
192. #1753C22semidirect
194. #1752C22semidirect
196. C8×C22⋊C4C22semidirect
197. #1729C22semidirect
198. C2×#336C22semidirect
228. C2×#131D4semidirect
395. #408D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32032
C2×#31982
C2×#30622
C2×#30612
#373002
#372962
#331872
#331852
#331822
#331742
#302552
#302512
#302442
#302392
#283642
#283602
#283582
#283542
#283492
#283422
#283382
#283292
#279452
#279442
#279382
#279292
#257932
#257912
#257852
#257752
#203872