Finite Group Databasebeta

← #6473323

Subgroups — #6473323

Order 512.

2448 conjugacy classes of subgroups.

The subgroup lattice has 1419 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3201C211yesmaximal, characteristic, complemented
2C2×#3198C211yesmaximal, characteristic, complemented
3C2×#3060C211yesmaximal, characteristic, complemented
4C2×#3057C211yesmaximal, characteristic, complemented
5#37388C211yesmaximal, characteristic, complemented
6#37300C211yesmaximal, characteristic, complemented
7#33181C211yesmaximal, characteristic, complemented
8#33178C211yesmaximal, characteristic, complemented
9#33173C211yesmaximal, characteristic, complemented
10#33170C211yesmaximal, characteristic, complemented
11#30252C211yesmaximal, characteristic, complemented
12#30251C211yesmaximal, characteristic, complemented
13#30246C211yesmaximal, characteristic, complemented
14#30245C211yesmaximal, characteristic, complemented
15#28368C211yesmaximal, characteristic, complemented
16#28366C211yesmaximal, characteristic, complemented
17#28363C211yesmaximal, characteristic, complemented
18#28361C211yesmaximal, characteristic, complemented
19#28360C211yesmaximal, characteristic, complemented
20#28358C211yesmaximal, characteristic, complemented
21#28355C211yesmaximal, characteristic, complemented
22#28353C211yesmaximal, characteristic, complemented
23#27926C211yesmaximal, characteristic, complemented
24#27925C211yesmaximal, characteristic, complemented
25#27925C211yesmaximal, characteristic, complemented
26#27924C211yesmaximal, characteristic, complemented
27#25776C211yesmaximal, characteristic, complemented
28#25775C211yesmaximal, characteristic, complemented
29#25775C211yesmaximal, characteristic, complemented
30#25774C211yesmaximal, characteristic, complemented
31#20383C211yesmaximal, characteristic, complemented
32C22×#135C2211yescharacteristic, complemented
33C23×SD16C2211yescharacteristic
34C22×#131C2211yescharacteristic
35C2×#537C2211yescharacteristic
36C2×#537C2211yescharacteristic
37C2×#536C2211yescharacteristic
38C2×#535C2211yescharacteristic
39#3201—28no—
40#3198—28no—
41C2×#495C2211yescharacteristic
42C2×#495C2211yescharacteristic
43C2×#492C2211yescharacteristic
44C2×#492C2211yescharacteristic
45C2×#484C2211yescharacteristic, complemented
46C2×#481C2211yescharacteristic
47C2×#485C2211yescharacteristic
48C2×#485C2211yescharacteristic
49C2×#482C2211yescharacteristic
50C2×#482C2211yescharacteristic
51C2×#483C2211yescharacteristic, complemented
52C2×#480C2211yescharacteristic
53#3060—28no—
54#3057—28no—
55C2×#470C2211yescharacteristic
56C2×#470C2211yescharacteristic, complemented
57C2×#470C2211yescharacteristic, complemented
58C2×#469C2211yescharacteristic
59C2×#469C2211yescharacteristic
60C2×#469C2211yescharacteristic, complemented
61C2×#468C2211yescharacteristic
62C2×#468C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#468C2211yescharacteristic
66C2×#468C2211yescharacteristic, complemented
67C2×#467C2211yescharacteristic, complemented
68C2×#466C2211yescharacteristic
69C2×#465C2211yescharacteristic
70C2×#465C2211yescharacteristic
71C2×#465C2211yescharacteristic
72C2×#465C2211yescharacteristic
73C2×#465C2211yescharacteristic
74C2×#465C2211yescharacteristic
75C2×#465C2211yescharacteristic
76C2×#465C2211yescharacteristic, complemented
77C2×#465C2211yescharacteristic, complemented
78C2×#465C2211yescharacteristic, complemented
79C2×#452C2211yescharacteristic, complemented
80C2×#452C2211yescharacteristic, complemented
81C2×#449C2211yescharacteristic
82C2×#449C2211yescharacteristic
83C2×#451C2211yescharacteristic
84C2×#448C2211yescharacteristic
85C2×#450C2211yescharacteristic
86C2×#447C2211yescharacteristic
87C2×#427C2211yescharacteristic
88C22×#106C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic, complemented
90C2×#417C2211yescharacteristic, complemented
91C2×#419C2211yescharacteristic
92C2×#418C2211yescharacteristic
93C2×#408C2211yescharacteristic
94C2×#405C2211yescharacteristic, complemented
95C22×C4×C8C2211yescharacteristic, complemented
96#2857C2211yescharacteristic, complemented
97#2856C2211yescharacteristic
98#2850C2211yescharacteristic
99#2850C2211yescharacteristic, complemented
100#2730—22no—
101#2729—22no—
102#2708—22no—
103#2701—22no—
104#2686—22no—
105#2678—22no—
106#2673—22no—
107#2668—22no—
108#2621C2211yescharacteristic, complemented
109#2620C2211yescharacteristic
110#2620C2211yescharacteristic, complemented
111#2619C2211yescharacteristic
112#2504C2211yescharacteristic
113#2503C2211yescharacteristic, complemented
114#2502C2211yescharacteristic, complemented
115#2501C2211yescharacteristic
116#2500C2211yescharacteristic
117#2500C2211yescharacteristic
118#2499C2211yescharacteristic
119#2499C2211yescharacteristic
120#2436C2211yescharacteristic
121#2435C2211yescharacteristic
122#2434C2211yescharacteristic
123#2433C2211yescharacteristic
124#2432C2211yescharacteristic, complemented
125#2432C2211yescharacteristic, complemented
126#2431C2211yescharacteristic
127#2431C2211yescharacteristic
128#2297C2211yescharacteristic
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2097C2211yescharacteristic, complemented
132#2097C2211yescharacteristic, complemented
133#2096C2211yescharacteristic, complemented
134#2096C2211yescharacteristic, complemented
135#2095C2211yescharacteristic, complemented
136#2095C2211yescharacteristic, complemented
137#2094C2211yescharacteristic
138#2094C2211yescharacteristic
139#2093C2211yescharacteristic, complemented
140#2093C2211yescharacteristic, complemented
141#2092C2211yescharacteristic
142#2092C2211yescharacteristic
143#2092C2211yescharacteristic, complemented
144#2092C2211yescharacteristic, complemented
145#2016C2211yescharacteristic, complemented
146#2016C2211yescharacteristic, complemented
147#2015C2211yescharacteristic
148#2015C2211yescharacteristic
149#2015C2211yescharacteristic
150#2015C2211yescharacteristic
151#2014C2211yescharacteristic
152#2014C2211yescharacteristic
153#2013C2211yescharacteristic
154#2013C2211yescharacteristic
155#2012C2211yescharacteristic
156#2012C2211yescharacteristic
157#2012C2211yescharacteristic, complemented
158#2012C2211yescharacteristic, complemented
159#2011C2211yescharacteristic
160#2011C2211yescharacteristic
161#1973C2211yescharacteristic
162#1973C2211yescharacteristic, complemented
163#1972C2211yescharacteristic
164#1971C2211yescharacteristic, complemented
165#1970C2211yescharacteristic
166#1969C2211yescharacteristic, complemented
167#1968C2211yescharacteristic
168#1968C2211yescharacteristic
169#1968C2211yescharacteristic
170#1968C2211yescharacteristic
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic, complemented
173#1968C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1968C2211yescharacteristic, complemented
176#1968C2211yescharacteristic, complemented
177#1961C2211yescharacteristic
178#1960C2211yescharacteristic, complemented
179#1959C2211yescharacteristic
180#1959C2211yescharacteristic, complemented
181#1958C2211yescharacteristic
182#1958C2211yescharacteristic, complemented
183#1957C2211yescharacteristic
184#1956C2211yescharacteristic, complemented
185#1846C2211yescharacteristic, complemented
186#1846C2211yescharacteristic, complemented
187#1844C2211yescharacteristic, complemented
188#1844C2211yescharacteristic, complemented
189#1753C2211yescharacteristic
190#1753C2211yescharacteristic
191#1753C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193C8×C22⋊C4C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic, complemented
196C8×C22⋊C4C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198#1728C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C23×Q8C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C2×#135—24no—
205C2×#135—42no—
206C2×#135—42no—
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16—24no—
211C22×SD16—42no—
212C22×SD16—42no—
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×SD16C2311yescharacteristic
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#536—24no—
242#536—24no—
243#535—24no—
244#535—24no—
245C2×C4⋊Q8—21no—
246C2×C4⋊Q8C2311yescharacteristic
247C2×C4⋊Q8C2311yescharacteristic
248C2×#127—21no—
249C2×#127C2311yescharacteristic
250C2×#127C2311yescharacteristic
251C2×#124—21no—
252C2×#124—21no—
253C2×#124C2311yescharacteristic
254C2×#124C2311yescharacteristic
255C2×#124C2311yescharacteristic
256C2×#124C2311yescharacteristic
257C2×#123—21no—
258C2×#123—21no—
259C2×#123—22no—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8—21no—
262C2×C22⋊Q8C2311yescharacteristic
263C2×C22⋊Q8C2311yescharacteristic
264C2×C22⋊Q8C2311yescharacteristic
265C2×C22⋊Q8C2311yescharacteristic
266C2×C22⋊Q8C2311yescharacteristic
267C2×C22⋊Q8C2311yescharacteristic
268C2×C22⋊Q8C2311yescharacteristic
269C2×C22⋊Q8C2311yescharacteristic
270C2×#121—21no—
271C2×#121—21no—
272C2×#121—21no—
273C2×#121—21no—
274C2×#121—21no—
275C2×#121—21no—
276C2×#121—22no—
277C2×#121C2311yescharacteristic
278C2×#121C2311yescharacteristic
279C2×#121C2311yescharacteristic
280C2×#121C2311yescharacteristic
281C2×#121C2311yescharacteristic
282C2×#121C2311yescharacteristic
283C2×#121C2311yescharacteristic
284C2×#121C2311yescharacteristic
285C2×#120—21no—
286C2×#120—21no—
287C2×#120—22no—
288C2×#117C2311yescharacteristic
289C2×#117C2311yescharacteristic
290C2×#117C2311yescharacteristic
291C22×C4⋊C4C2311yescharacteristic
292C22×C4⋊C4C2311yescharacteristic
293C22×C42C2311yescharacteristic
294#495—42no—
295#495—42no—
296#492—42no—
297#492—42no—
298#485—24no—
299#485—24no—
300#484—24no—
301#483—24no—
302#482—24no—
303#482—24no—
304#481—24no—
305#480—24no—
306#470—24no—
307#470—24no—
308#470—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#467—24no—
319#466—24no—
320#465—24no—
321#465—24no—
322#465—24no—
323#465—24no—
324#465—24no—
325#465—24no—
326#465—24no—
327#465—24no—
328#465—24no—
329#465—24no—
330#452—24no—
331#452—24no—
332#451—24no—
333#450—24no—
334#449—24no—
335#449—24no—
336#448—24no—
337#447—24no—
338#427—24no—
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#107C2311yescharacteristic
342C2×#107C2311yescharacteristic
343C2×#107C2311yescharacteristic
344C2×#107C2311yescharacteristic
345C2×#106—24no—
346C2×#106C2311yescharacteristic
347C2×#106C2311yescharacteristic
348C2×#106C2311yescharacteristic
349C2×#106C2311yescharacteristic
350C2×#106C2311yescharacteristic
351C2×#106C2311yescharacteristic
352C2×#106C2311yescharacteristic
353C2×#106C2311yescharacteristic
354C2×#106C2311yescharacteristic
355C2×#106C2311yescharacteristic
356#419—24no—
357#418—24no—
358#417—24no—
359#417—24no—
360C2×#103C2311yescharacteristic
361C2×#103C2311yescharacteristic
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#103C2311yescharacteristic
371C2×#103C2311yescharacteristic
372C2×#103C2311yescharacteristic
373C2×#103C2311yescharacteristic
374C2×#103C2311yescharacteristic
375C2×#103C2311yescharacteristic
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
392#408D418yescomplemented
393C2×C22⋊C8C2311yescharacteristic
394C2×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397#405—42no—
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×C4×C8—42no—
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407#400—22no—
408#399—22no—
409#398—22no—
410#398—22no—
411#397—22no—
412#397—22no—
413#397—22no—
414#397—22no—
415#396—22no—
416#396—22no—
417#395—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#393—22no—
427#392—22no—
428#392—22no—
429#392—22no—
430#392—22no—
431#391D412yes—
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#391C2311yescharacteristic
439#391C2311yescharacteristic
440#390—22no—
441#390D412yes—
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#389—22no—
451#388—22no—
452#388—22no—
453#388—22no—
454#388—22no—
455#387—22no—
456#387—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386—22no—
462#386—22no—
463#386D412yes—
464#386D412yes—
465#385—22no—
466#385—22no—
467#385—22no—
468#385—22no—
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#384C2311yescharacteristic
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#382C2311yescharacteristic
477#381—22no—
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—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—22no—
536C22×D4—21no—
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×C4C2411yescharacteristic
556C23×C4C2411yescharacteristic
557C23×C4C2411yescharacteristic
558#135—416no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—22no—
562C2×Q16—41no—
563C2×Q16—41no—
564C2×Q16—41no—
565C2×Q16—41no—
566C2×Q16—41no—
567C2×Q16—41no—
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—22no—
580C2×SD16—22no—
581C2×SD16—22no—
582C2×SD16—22no—
583C2×SD16—22no—
584C2×SD16—22no—
585C2×SD16—22no—
586C2×SD16—41no—
587C2×SD16—41no—
588C2×SD16—41no—
589C2×SD16—41no—
590C2×SD16—416no—
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—
608#131—416no—
609C2×M16—41no—
610C2×M16—41no—
611C2×M16—41no—
612C2×M16—41no—
613C2×M16—41no—
614C2×M16—41no—
615C2×M16—41no—
616C2×M16—41no—
617C2×M16C2×D414yes—
618C2×M16C2×D414yes—
619C2×M16C2×D414yes—
620C2×M16C2×D414yes—
621C22×C8—22no—
622C22×C8—22no—
623C22×C8—22no—
624C22×C8—22no—
625C22×C8—22no—
626C22×C8—22no—
627C22×C8—41no—
628C22×C8—41no—
629C22×C8C2×D414yes—
630C22×C8C2×D414yes—
631C22×C8C2×D414yes—
632C22×C8C2×D414yes—
633C22×C8C2411yescharacteristic
634C22×C8C2411yescharacteristic
635C22×C8C2411yescharacteristic
636C22×C8C2411yescharacteristic
637C22×C8C2411yescharacteristic
638C22×C8C2411yescharacteristic
639C22×C8C2411yescharacteristic
640C22×C8C2411yescharacteristic
641C4⋊Q8—41no—
642C4⋊Q8—41no—
643C4⋊Q8—41no—
644C4⋊Q8—41no—
645C4⋊Q8—44no—
646#127—41no—
647#127—41no—
648#127—41no—
649#127—41no—
650#127—44no—
651#124—41no—
652#124—41no—
653#124—41no—
654#124—41no—
655#124—41no—
656#124—41no—
657#124—41no—
658#124—41no—
659#124—44no—
660#124—44no—
661#123—44no—
662#123—44no—
663#123—84no—
664C22⋊Q8—22no—
665C22⋊Q8—22no—
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—22no—
679C22⋊Q8—22no—
680C22⋊Q8—44no—
681C22⋊Q8—44no—
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—44no—
699#121—44no—
700#121—44no—
701#121—44no—
702#121—44no—
703#121—44no—
704#121—84no—
705#120—44no—
706#120—44no—
707#120—84no—
708#117—22no—
709#117—22no—
710#117—22no—
711#117—22no—
712#117—41no—
713#117—41no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4—21no—
719C2×C4⋊C4—21no—
720C2×C4⋊C4—21no—
721C2×C4⋊C4—21no—
722C2×C4⋊C4—21no—
723C2×C4⋊C4—21no—
724C2×C4⋊C4—22no—
725C2×C4⋊C4—21no—
726C2×C4⋊C4—21no—
727C2×C4⋊C4—21no—
728C2×C4⋊C4—21no—
729C2×C4⋊C4—22no—
730C2×C4⋊C4—22no—
731C2×C4⋊C4—22no—
732C2×C4⋊C4—22no—
733C2×C4⋊C4—22no—
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—21no—
754C2×C22⋊C4—21no—
755C2×C22⋊C4—21no—
756C2×C22⋊C4—21no—
757C2×C22⋊C4—22no—
758C2×C22⋊C4—21no—
759C2×C22⋊C4—21no—
760C2×C22⋊C4—21no—
761C2×C22⋊C4—21no—
762C2×C22⋊C4—22no—
763C2×C22⋊C4—22no—
764C2×C22⋊C4—22no—
765C2×C22⋊C4—22no—
766C2×C22⋊C4—22no—
767C2×C22⋊C4—22no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—22no—
773C2×C22⋊C4C2×D412yes—
774C2×C22⋊C4C2×D412yes—
775C2×C22⋊C4C2×D412yes—
776C2×C22⋊C4C2×D412yes—
777C2×C22⋊C4C2×D412yes—
778C2×C42—21no—
779C2×C42—21no—
780C2×C42—41no—
781C2×C42—41no—
782C2×C42C2×D412yes—
783C2×C42C2411yescharacteristic
784C2×C42C2411yescharacteristic
785C2×C42C2411yescharacteristic
786C2×C42C2411yescharacteristic
787#107—22no—
788#107—22no—
789#107—22no—
790#107—22no—
791#107—22no—
792#107—22no—
793#106—22no—
794#106—22no—
795#106—22no—
796#106—22no—
797#106—22no—
798#106—22no—
799#106—22no—
800#106—22no—
801#106—22no—
802#106—22no—
803#103—22no—
804#103—22no—
805#103—22no—
806#103—22no—
807#103—22no—
808#103—22no—
809#103—22no—
810#103—22no—
811#103—22no—
812#103—22no—
813#103—22no—
814#103—22no—
815#103—22no—
816#103—22no—
817#103—22no—
818#103—22no—
819#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—
829#102—22no—
830#102—22no—
831#102—22no—
832#102—22no—
833#102—22no—
834#102—22no—
835C22⋊C8C2×D414yes—
836C22⋊C8C2×D414yes—
837C22⋊C8C2×D414yes—
838C22⋊C8C2×D414yes—
839#97—41no—
840#97—41no—
841C4×C8—22no—
842C4×C8—22no—
843C4×C8—22no—
844C4×C8—22no—
845C4×C8—41no—
846C4×C8—41no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—22no—
854#95—22no—
855#95—22no—
856#95—22no—
857#95—22no—
858#95—22no—
859#95C2×D412yes—
860#95C2×D412yes—
861#95C2×D412yes—
862#95C2×D412yes—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—42no—
868C24—81no—
869C24—81no—
870C24—82no—
871C24—82no—
872C24C22×D411yescharacteristic
873C24C22×D411yescharacteristic
874C24C22×D411yescharacteristic
875#41—44no—
876#41—44no—
877#41—44no—
878#41—44no—
879#41—44no—
880#41—44no—
881#41—44no—
882#41—44no—
883#41—82no—
884#41—82no—
885#41—82no—
886#41—82no—
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—21no—
909C2×Q8—21no—
910C2×Q8—21no—
911C2×Q8—41no—
912C2×Q8—41no—
913C2×Q8—44no—
914C2×Q8—44no—
915C2×Q8—42no—
916C2×Q8—81no—
917C2×Q8—81no—
918C2×Q8—82no—
919C2×Q8—82no—
920C2×Q8#12714yes—
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—41no—
946C2×D4—41no—
947C2×D4—41no—
948C2×D4—41no—
949C2×D4—41no—
950C2×D4—41no—
951C2×D4—44no—
952C2×D4—44no—
953C2×D4—42no—
954C2×D4—42no—
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—44no—
965C2×D4—82no—
966C2×D4—82no—
967C2×D4—81no—
968C2×D4—81no—
969C2×D4—82no—
970C2×D4—82no—
971C2×D4—82no—
972C2×D4—82no—
973C2×D4—82no—
974C2×D4—81no—
975C2×D4—81no—
976C2×D4—81no—
977C2×D4—81no—
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#12714yes—
987C2×D4#12714yes—
988C2×D4#12714yes—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—24no—
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—21no—
1013C22×C4—21no—
1014C22×C4—42no—
1015C22×C4—42no—
1016C22×C4—42no—
1017C22×C4—42no—
1018C22×C4—42no—
1019C22×C4—42no—
1020C22×C4—42no—
1021C22×C4—81no—
1022C22×C4—81no—
1023C22×C4—81no—
1024C22×C4—81no—
1025C22×C4—81no—
1026C22×C4—81no—
1027C22×C4—82no—
1028C22×C4—82no—
1029C22×C4C22×D412yes—
1030C22×C4C22×D412yes—
1031C22×C4C22×D412yes—
1032C22×C4C22×D411yescharacteristic
1033C22×C4C22×D411yescharacteristic
1034C22×C4C22×D411yescharacteristic
1035C22×C4C22×D412yes—
1036C22×C4C22×D412yes—
1037C22×C4C22×D412yes—
1038C22×C4C22×D412yes—
1039C22×C4C22×D412yes—
1040C22×C4C22×D412yes—
1041C22×C4C22×D412yes—
1042C22×C4C2511yescharacteristic
1043Q16—44no—
1044Q16—82no—
1045Q16—82no—
1046SD16—44no—
1047SD16—44no—
1048SD16—44no—
1049SD16—44no—
1050SD16—44no—
1051SD16—44no—
1052SD16—82no—
1053SD16—82no—
1054SD16—82no—
1055SD16—82no—
1056D8—44no—
1057D8—82no—
1058D8—82no—
1059M16—44no—
1060M16—44no—
1061M16—44no—
1062M16—44no—
1063C2×C8—21no—
1064C2×C8—21no—
1065C2×C8—21no—
1066C2×C8—21no—
1067C2×C8—21no—
1068C2×C8—21no—
1069C2×C8—21no—
1070C2×C8—21no—
1071C2×C8—21no—
1072C2×C8—21no—
1073C2×C8—21no—
1074C2×C8—21no—
1075C2×C8—21no—
1076C2×C8—21no—
1077C2×C8—28no—
1078C2×C8—28no—
1079C2×C8—28no—
1080C2×C8—44no—
1081C2×C8C22×D412yes—
1082C2×C8C22×D412yes—
1083C2×C8C22×D412yes—
1084C2×C8C22×D412yes—
1085C2×C8C22×D412yes—
1086C2×C8C22×D412yes—
1087C2×C8C22×D412yes—
1088C2×C8C22×D412yes—
1089C2×C8H(5,𝔽2)12yes—
1090C2×C8H(5,𝔽2)12yes—
1091C4⋊C4—21no—
1092C4⋊C4—21no—
1093C4⋊C4—21no—
1094C4⋊C4—21no—
1095C4⋊C4—21no—
1096C4⋊C4—21no—
1097C4⋊C4—21no—
1098C4⋊C4—21no—
1099C4⋊C4—21no—
1100C4⋊C4—21no—
1101C4⋊C4—21no—
1102C4⋊C4—21no—
1103C4⋊C4—21no—
1104C4⋊C4—21no—
1105C4⋊C4—21no—
1106C4⋊C4—21no—
1107C4⋊C4—42no—
1108C4⋊C4—42no—
1109C4⋊C4—42no—
1110C4⋊C4—42no—
1111C4⋊C4—42no—
1112C4⋊C4—42no—
1113C4⋊C4—42no—
1114C4⋊C4—42no—
1115C4⋊C4—42no—
1116C4⋊C4—42no—
1117C4⋊C4—42no—
1118C4⋊C4—44no—
1119C4⋊C4—82no—
1120C4⋊C4—82no—
1121C4⋊C4—82no—
1122C4⋊C4—82no—
1123C4⋊C4—82no—
1124C22⋊C4—24no—
1125C22⋊C4—24no—
1126C22⋊C4—42no—
1127C22⋊C4—42no—
1128C22⋊C4—42no—
1129C22⋊C4—42no—
1130C22⋊C4—42no—
1131C22⋊C4—42no—
1132C22⋊C4—42no—
1133C22⋊C4—42no—
1134C22⋊C4—42no—
1135C22⋊C4—42no—
1136C22⋊C4—42no—
1137C22⋊C4—42no—
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—44no—
1148C22⋊C4—44no—
1149C22⋊C4—82no—
1150C22⋊C4—82no—
1151C22⋊C4—82no—
1152C22⋊C4—82no—
1153C22⋊C4—82no—
1154C22⋊C4—82no—
1155C22⋊C4—82no—
1156C22⋊C4—82no—
1157C22⋊C4—82no—
1158C22⋊C4—82no—
1159C42—21no—
1160C42—21no—
1161C42—21no—
1162C42—21no—
1163C42—21no—
1164C42—21no—
1165C42—21no—
1166C42—21no—
1167C42—42no—
1168C42—42no—
1169C42—42no—
1170C23—22no—
1171C23—22no—
1172C23—22no—
1173C23—21no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—21no—
1179C23—22no—
1180C23—22no—
1181C23—22no—
1182C23—42no—
1183C23—42no—
1184C23—42no—
1185C23—42no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—42no—
1199C23—42no—
1200C23—42no—
1201C23—42no—
1202C23—84no—
1203C23—162no—
1204C23—162no—
1205C23—164no—
1206C23—164no—
1207C23C2×#12712yes—
1208C23C2×#12712yes—
1209C23C2×#12712yes—
1210C23C23×D411yescharacteristic
1211Q8—44no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—41no—
1219Q8—41no—
1220Q8—41no—
1221Q8—41no—
1222Q8—41no—
1223Q8—41no—
1224Q8—41no—
1225Q8—41no—
1226Q8—41no—
1227Q8—41no—
1228Q8—84no—
1229D4—44no—
1230D4—44no—
1231D4—44no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—41no—
1237D4—41no—
1238D4—41no—
1239D4—41no—
1240D4—41no—
1241D4—41no—
1242D4—41no—
1243D4—41no—
1244D4—41no—
1245D4—41no—
1246D4—41no—
1247D4—41no—
1248D4—84no—
1249D4—84no—
1250D4—84no—
1251D4—164no—
1252D4—164no—
1253D4—162no—
1254D4—162no—
1255D4—162no—
1256D4—162no—
1257D4—162no—
1258D4—162no—
1259D4—162no—
1260D4—162no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—22no—
1276C2×C4—22no—
1277C2×C4—22no—
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—48no—
1291C2×C4—42no—
1292C2×C4—42no—
1293C2×C4—42no—
1294C2×C4—42no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
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—42no—
1316C2×C4—42no—
1317C2×C4—42no—
1318C2×C4—42no—
1319C2×C4—84no—
1320C2×C4—84no—
1321C2×C4—84no—
1322C2×C4—162no—
1323C2×C4—162no—
1324C2×C4C2×#12712yes—
1325C2×C4C2×#12712yes—
1326C2×C4C2×#12712yes—
1327C2×C4#57714yes—
1328C2×C4C23×D411yescharacteristic
1329C2×C4C23×D411yescharacteristic
1330C2×C4C2×H(5,𝔽2)11yescharacteristic
1331C2×C4C2×H(5,𝔽2)11yescharacteristic
1332C2×C4#58511yescharacteristic
1333C2×C4#58511yescharacteristic
1334C8—22no—
1335C8—22no—
1336C8—22no—
1337C8—22no—
1338C8—22no—
1339C8—22no—
1340C8—22no—
1341C8#53414yes—
1342C22—22no—
1343C22—22no—
1344C22—22no—
1345C22—22no—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—42no—
1352C22—42no—
1353C22—42no—
1354C22—42no—
1355C22—42no—
1356C22—42no—
1357C22—82no—
1358C22—82no—
1359C22—82no—
1360C22—82no—
1361C22—82no—
1362C22—82no—
1363C22—82no—
1364C22—82no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—168no—
1378C22C22×#12711yescharacteristic
1379C22#349611yescharacteristic
1380C22#349611yescharacteristic
1381C22C2×#57712yes—
1382C22#358412yes—
1383C4—24no—
1384C4—22no—
1385C4—22no—
1386C4—22no—
1387C4—42no—
1388C4—42no—
1389C4—42no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4C2×#53411yescharacteristic
1403C4#344911yescharacteristic
1404C4#349611yescharacteristic
1405C4#349611yescharacteristic
1406C2—42no—
1407C2—42no—
1408C2—42no—
1409C2—161no—
1410C2—161no—
1411C2—161no—
1412C2—161no—
1413C2#3500111yescharacteristic
1414C2#6064611yescharacteristic
1415C2#6064911yescharacteristic
1416C2#6226512yes—
1417C2#6232312yes—
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×#3201C2semidirect
2. C2×#3198C2semidirect
3. C2×#3060C2semidirect
4. C2×#3057C2semidirect
5. #37388C2semidirect
6. #37300C2semidirect
7. #33181C2semidirect
8. #33178C2semidirect
9. #33173C2semidirect
10. #33170C2semidirect
11. #30252C2semidirect
12. #30251C2semidirect
13. #30246C2semidirect
14. #30245C2semidirect
15. #28368C2semidirect
16. #28366C2semidirect
17. #28363C2semidirect
18. #28361C2semidirect
19. #28360C2semidirect
20. #28358C2semidirect
21. #28355C2semidirect
22. #28353C2semidirect
23. #27926C2semidirect
24. #27925C2semidirect
25. #27925C2semidirect
26. #27924C2semidirect
27. #25776C2semidirect
28. #25775C2semidirect
29. #25775C2semidirect
30. #25774C2semidirect
31. #20383C2semidirect
32. C22×#135C22semidirect
45. C2×#484C22semidirect
51. C2×#483C22semidirect
56. C2×#470C22semidirect
57. C2×#470C22semidirect
60. C2×#469C22semidirect
66. C2×#468C22semidirect
67. C2×#467C22semidirect
76. C2×#465C22semidirect
77. C2×#465C22semidirect
78. C2×#465C22semidirect
79. C2×#452C22semidirect
80. C2×#452C22semidirect
88. C22×#106C22semidirect
89. C2×#417C22semidirect
90. C2×#417C22semidirect
94. C2×#405C22semidirect
95. C22×C4×C8C22semidirect
96. #2857C22semidirect
99. #2850C22semidirect
108. #2621C22semidirect
110. #2620C22semidirect
113. #2503C22semidirect
114. #2502C22semidirect
124. #2432C22semidirect
125. #2432C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2097C22semidirect
132. #2097C22semidirect
133. #2096C22semidirect
134. #2096C22semidirect
135. #2095C22semidirect
136. #2095C22semidirect
139. #2093C22semidirect
140. #2093C22semidirect
143. #2092C22semidirect
144. #2092C22semidirect
145. #2016C22semidirect
146. #2016C22semidirect
157. #2012C22semidirect
158. #2012C22semidirect
162. #1973C22semidirect
164. #1971C22semidirect
166. #1969C22semidirect
172. #1968C22semidirect
173. #1968C22semidirect
174. #1968C22semidirect
175. #1968C22semidirect
176. #1968C22semidirect
178. #1960C22semidirect
180. #1959C22semidirect
182. #1958C22semidirect
184. #1956C22semidirect
185. #1846C22semidirect
186. #1846C22semidirect
187. #1844C22semidirect
188. #1844C22semidirect
191. #1753C22semidirect
192. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
196. C8×C22⋊C4C22semidirect
197. #1729C22semidirect
198. #1728C22semidirect
228. C2×#131D4semidirect
392. #408D4semidirect

Maximal subgroups

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

subgroupindex
C2×#32012
C2×#31982
C2×#30602
C2×#30572
#373882
#373002
#331812
#331782
#331732
#331702
#302522
#302512
#302462
#302452
#283682
#283662
#283632
#283612
#283602
#283582
#283552
#283532
#279262
#279252
#279242
#257762
#257752
#257742
#203832