Finite Group Databasebeta

← #6606793

Subgroups — #6606793

Order 512.

2406 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3317C211yesmaximal, characteristic, complemented
2C2×#3319C211yesmaximal, characteristic, complemented
3C2×#3305C211yesmaximal, characteristic, complemented
4C2×#3296C211yesmaximal, characteristic, complemented
5#37871C211yesmaximal, characteristic, complemented
6#37681C211yesmaximal, characteristic, complemented
7#33228C211yesmaximal, characteristic, complemented
8#33183C211yesmaximal, characteristic, complemented
9#33182C211yesmaximal, characteristic, complemented
10#28523C211yesmaximal, characteristic, complemented
11#28452C211yesmaximal, characteristic, complemented
12#28424C211yesmaximal, characteristic, complemented
13#28421C211yesmaximal, characteristic, complemented
14#28420C211yesmaximal, characteristic, complemented
15#28410C211yesmaximal, characteristic, complemented
16#28368C211yesmaximal, characteristic, complemented
17#28365C211yesmaximal, characteristic, complemented
18#28352C211yesmaximal, characteristic, complemented
19#28350C211yesmaximal, characteristic, complemented
20#28349C211yesmaximal, characteristic, complemented
21#28341C211yesmaximal, characteristic, complemented
22#28340C211yesmaximal, characteristic, complemented
23#28337C211yesmaximal, characteristic, complemented
24#27920C211yesmaximal, characteristic, complemented
25#27907C211yesmaximal, characteristic, complemented
26#25736C211yesmaximal, characteristic, complemented
27#25723C211yesmaximal, characteristic, complemented
28#21694C211yesmaximal, characteristic, complemented
29#21206C211yesmaximal, characteristic, complemented
30#21199C211yesmaximal, characteristic, complemented
31#20493C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#550C2211yescharacteristic
35C2×#546C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C2×#532C2211yescharacteristic
38#3319—28no—
39#3317—28no—
40#3305—28no—
41#3296—28no—
42C2×#496C2211yescharacteristic
43C2×#495C2211yescharacteristic
44C2×#495C2211yescharacteristic, complemented
45C2×#490C2211yescharacteristic, complemented
46C2×#489C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#486C2211yescharacteristic, complemented
49C2×#481C2211yescharacteristic
50C2×#485C2211yescharacteristic
51C2×#482C2211yescharacteristic
52C2×#482C2211yescharacteristic
53C2×#482C2211yescharacteristic
54C2×#482C2211yescharacteristic, complemented
55C2×#482C2211yescharacteristic, complemented
56C2×#483C2211yescharacteristic
57C2×#479C2211yescharacteristic, complemented
58C2×#477C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic
60C2×#474C2211yescharacteristic
61C2×#468C2211yescharacteristic
62C2×#468C2211yescharacteristic
63C2×#467C2211yescharacteristic
64C2×#466C2211yescharacteristic
65C2×#466C2211yescharacteristic
66C2×#466C2211yescharacteristic, complemented
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic
70C2×#460C2211yescharacteristic, complemented
71C2×#463C2211yescharacteristic
72C2×#459C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic, complemented
76C2×#449C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#449C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#442C2211yescharacteristic
82C2×#441C2211yescharacteristic, complemented
83C2×C4×SD16C2211yescharacteristic
84C2×C4×SD16C2211yescharacteristic, complemented
85C2×#435C2211yescharacteristic
86C2×C8×D4C2211yescharacteristic
87C2×#417C2211yescharacteristic
88C2×#418C2211yescharacteristic
89C2×#416C2211yescharacteristic
90C2×#416C2211yescharacteristic
91C2×#416C2211yescharacteristic
92C2×#416C2211yescharacteristic, complemented
93C2×#416C2211yescharacteristic, complemented
94C22×#102C2211yescharacteristic
95C2×#405C2211yescharacteristic
96C22×#97C2211yescharacteristic, complemented
97#2856C2211yescharacteristic
98#2850C2211yescharacteristic, complemented
99#2715—22no—
100#2708—22no—
101#2675—22no—
102#2669—22no—
103#2660C2211yescharacteristic, complemented
104#2657C2211yescharacteristic
105#2620C2211yescharacteristic
106#2620C2211yescharacteristic
107#2568C2211yescharacteristic, complemented
108#2566C2211yescharacteristic, complemented
109#2545C2211yescharacteristic
110#2541C2211yescharacteristic
111#2504C2211yescharacteristic
112#2500C2211yescharacteristic, complemented
113#2499C2211yescharacteristic
114#2499C2211yescharacteristic, complemented
115#2475—22no—
116#2474—22no—
117#2456—22no—
118#2433C2211yescharacteristic
119#2432C2211yescharacteristic
120#2431C2211yescharacteristic
121#2431C2211yescharacteristic
122#2424—22no—
123#2326C2211yescharacteristic
124#2326C2211yescharacteristic, complemented
125#2317C2211yescharacteristic
126#2290C2211yescharacteristic
127#2285C2211yescharacteristic, complemented
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2096C2211yescharacteristic, complemented
131#2095C2211yescharacteristic, complemented
132#2094C2211yescharacteristic, complemented
133#2093C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic, complemented
143#2014C2211yescharacteristic
144#2014C2211yescharacteristic
145#2014C2211yescharacteristic
146#2013C2211yescharacteristic, complemented
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic, complemented
149#2011C2211yescharacteristic
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic, complemented
154#1973C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1972C2211yescharacteristic
157#1972C2211yescharacteristic
158#1972C2211yescharacteristic, complemented
159#1971C2211yescharacteristic, complemented
160#1970C2211yescharacteristic, complemented
161#1969C2211yescharacteristic, complemented
162#1968C2211yescharacteristic
163#1968C2211yescharacteristic, complemented
164#1961C2211yescharacteristic
165#1961C2211yescharacteristic
166#1961C2211yescharacteristic
167#1961C2211yescharacteristic
168#1961C2211yescharacteristic
169#1960C2211yescharacteristic, complemented
170#1960C2211yescharacteristic, complemented
171#1959C2211yescharacteristic
172#1959C2211yescharacteristic
173#1959C2211yescharacteristic
174#1959C2211yescharacteristic, complemented
175#1959C2211yescharacteristic, complemented
176#1959C2211yescharacteristic, complemented
177#1959C2211yescharacteristic, complemented
178#1958C2211yescharacteristic
179#1958C2211yescharacteristic
180#1958C2211yescharacteristic, complemented
181#1958C2211yescharacteristic, complemented
182#1957C2211yescharacteristic
183#1957C2211yescharacteristic
184#1957C2211yescharacteristic
185#1957C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1845C2211yescharacteristic, complemented
188#1844C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1770C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic
197C4×C22⋊C8C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#555—24no—
220#555—24no—
221#552—24no—
222#552—24no—
223#550—24no—
224#550—24no—
225#546—24no—
226#546—24no—
227#535—24no—
228#535—42no—
229#532—24no—
230#532—42no—
231C2×C4⋊Q8C2311yescharacteristic
232C2×C4⋊Q8C2311yescharacteristic
233C2×#127—21no—
234C2×#127C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#127C2311yescharacteristic
237C2×#127C2311yescharacteristic
238C2×#127C2311yescharacteristic
239C2×#126—21no—
240C2×#125—21no—
241C2×#125C2311yescharacteristic
242C2×#124—21no—
243C2×#124—21no—
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#123—21no—
251C2×#123—21no—
252C2×C22⋊Q8C2311yescharacteristic
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×#121—21no—
256C2×#121—22no—
257C2×#121—22no—
258C2×#121—22no—
259C2×#121—22no—
260C2×#121—21no—
261C2×#121—21no—
262C2×#121—21no—
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#120—21no—
269C2×#120—22no—
270C2×#120—22no—
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×D4—21no—
274C2×C4×D4—22no—
275C2×C4×D4C2311yescharacteristic
276C2×C4×D4C2311yescharacteristic
277C2×C4×D4C2311yescharacteristic
278C2×#117—21no—
279C2×#117—21no—
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C22⋊C4—21no—
286C22×C42C2311yescharacteristic
287#496—42no—
288#495—24no—
289#495—42no—
290#490—24no—
291#489—24no—
292#488—24no—
293#486—24no—
294#485—24no—
295#483—24no—
296#482—24no—
297#482—24no—
298#482—24no—
299#482—24no—
300#482—24no—
301#481—24no—
302#479—24no—
303#478—24no—
304#477—24no—
305#474—24no—
306#468—24no—
307#468—24no—
308#467—24no—
309#466—24no—
310#466—24no—
311#466—24no—
312#465—24no—
313#465—24no—
314#464—24no—
315#463—24no—
316#460—24no—
317#459—24no—
318#452—24no—
319#452—24no—
320#452—24no—
321#450—24no—
322#449—24no—
323#449—24no—
324#449—24no—
325#447—24no—
326#442—24no—
327#441—24no—
328C4×SD16—24no—
329C4×SD16—24no—
330#435D418yescomplemented
331C8×D4D418yescomplemented
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×C4⋊C8C2311yescharacteristic
345C2×C4⋊C8C2311yescharacteristic
346#418—24no—
347#417—24no—
348#416—24no—
349#416—24no—
350#416—24no—
351#416—24no—
352#416—24no—
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
355C2×#103C2311yescharacteristic
356C2×#103C2311yescharacteristic
357C2×#103C2311yescharacteristic
358C2×#103C2311yescharacteristic
359C2×#103C2311yescharacteristic
360C2×#103C2311yescharacteristic
361C2×#103C2311yescharacteristic
362C2×#103C2311yescharacteristic
363C2×#103C2311yescharacteristic
364C2×#103C2311yescharacteristic
365C2×#103C2311yescharacteristic
366C2×#103C2311yescharacteristic
367C2×#102—24no—
368C2×#102C2311yescharacteristic
369C2×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
395C2×C22⋊C8C2311yescharacteristic
396C2×C22⋊C8C2311yescharacteristic
397C2×C22⋊C8C2311yescharacteristic
398#405—42no—
399C2×#97—42no—
400C2×#97C2311yescharacteristic
401C2×#97C2311yescharacteristic
402C2×#97C2311yescharacteristic
403C2×#97C2311yescharacteristic
404C2×#97C2311yescharacteristic
405C2×#97C2311yescharacteristic
406C2×#97C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409C2×C4×C8C2311yescharacteristic
410C2×C4×C8C2311yescharacteristic
411C2×C4×C8C2311yescharacteristic
412#400—22no—
413#398—22no—
414#397—22no—
415#397—22no—
416#397—22no—
417#396—22no—
418#396—22no—
419#396—22no—
420#396—22no—
421#395—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#392—22no—
427#392—22no—
428#392—22no—
429#392—22no—
430#392—22no—
431#392—22no—
432#391—22no—
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#391C2311yescharacteristic
436#391C2311yescharacteristic
437#391C2311yescharacteristic
438#390—22no—
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#389—22no—
447#388—22no—
448#388—22no—
449#388—22no—
450#388—22no—
451#388—22no—
452#388D412yes—
453#387—22no—
454#387—22no—
455#387D412yes—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386D412yes—
461#385—22no—
462#385—22no—
463#385—22no—
464#385—22no—
465#385—22no—
466#385D412yes—
467#384C2311yescharacteristic
468#384C2311yescharacteristic
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#382C2311yescharacteristic
476#382C2311yescharacteristic
477#380—22no—
478C4×C4⋊C4—22no—
479C4×C4⋊C4C2311yescharacteristic
480C4×C22⋊C4C2311yescharacteristic
481C4×C22⋊C4C2311yescharacteristic
482#376C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489C25—21no—
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
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—
508C22×Q8—21no—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×Q8C2411yescharacteristic
512C22×D4—22no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—22no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C2×D411yescharacteristic
534C22×D4C2411yescharacteristic
535C22×D4C2411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C2×D412yes—
546C23×C4C2411yescharacteristic
547C23×C4C2411yescharacteristic
548C2×Q16—22no—
549C2×Q16—22no—
550C2×Q16—22no—
551C2×Q16—41no—
552C2×Q16—41no—
553C2×Q16—41no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×D8—41no—
579C2×D8—41no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×D8—41no—
584C2×M16—41no—
585C2×M16—41no—
586C2×M16C2×D414yes—
587C22×C8—41no—
588C22×C8—41no—
589C22×C8—41no—
590C22×C8—41no—
591C22×C8—41no—
592C22×C8—41no—
593C22×C8C2×D414yes—
594C22×C8C2×D414yes—
595C22×C8C2×D414yes—
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C22×C8C2411yescharacteristic
600C22×C8C2411yescharacteristic
601C22×C8C2411yescharacteristic
602C22×C8C2411yescharacteristic
603C22×C8C2411yescharacteristic
604C4⋊Q8—22no—
605C4⋊Q8—22no—
606C4⋊Q8—22no—
607C4⋊Q8—41no—
608#127—22no—
609#127—22no—
610#127—22no—
611#127—22no—
612#127—22no—
613#127—22no—
614#127—41no—
615#127—41no—
616#127—41no—
617#127—41no—
618#127—44no—
619#126—44no—
620#125—22no—
621#125—22no—
622#125—44no—
623#124—22no—
624#124—22no—
625#124—22no—
626#124—22no—
627#124—22no—
628#124—22no—
629#124—22no—
630#124—22no—
631#124—41no—
632#124—41no—
633#124—41no—
634#124—44no—
635#124—44no—
636#124#4114yes—
637#123—44no—
638#123—44no—
639C22⋊Q8—22no—
640C22⋊Q8—22no—
641C22⋊Q8—22no—
642C22⋊Q8—22no—
643C22⋊Q8—22no—
644C22⋊Q8—22no—
645#121—22no—
646#121—22no—
647#121—22no—
648#121—22no—
649#121—22no—
650#121—22no—
651#121—22no—
652#121—22no—
653#121—22no—
654#121—22no—
655#121—48no—
656#121—48no—
657#121—44no—
658#121—44no—
659#121—44no—
660#121—44no—
661#121—84no—
662#121—84no—
663#120—48no—
664#120—44no—
665#120—84no—
666C4×Q8—22no—
667C4×Q8—22no—
668C4×Q8—22no—
669C4×Q8—22no—
670C4×D4—22no—
671C4×D4—22no—
672C4×D4—22no—
673C4×D4—22no—
674C4×D4—48no—
675C4×D4—44no—
676C4×D4C2×D414yes—
677C4×D4C2×D414yes—
678#117—22no—
679#117—22no—
680#117—22no—
681#117—22no—
682#117—22no—
683#117—22no—
684#117—22no—
685#117—22no—
686#117—44no—
687#117—44no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4C2×D412yes—
706C2×C4⋊C4C2×D412yes—
707C2×C4⋊C4C2×D411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C22⋊C4—22no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—44no—
744C2×C22⋊C4C2×D412yes—
745C2×C22⋊C4C2×D412yes—
746C2×C22⋊C4C2×D412yes—
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C42—22no—
750C2×C42—22no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42C2×D412yes—
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761C2×C42C2411yescharacteristic
762#107—22no—
763#107—22no—
764#107—22no—
765#107—22no—
766#107—22no—
767#107—22no—
768#106—22no—
769#106—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774C4⋊C8C2×D414yes—
775C4⋊C8C2×D414yes—
776#103—22no—
777#103—22no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—22no—
782#103—22no—
783#103—22no—
784#103—22no—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#102—22no—
791#102—22no—
792#102—22no—
793#102—22no—
794#102—22no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—22no—
805#102—22no—
806#102—22no—
807#102—22no—
808#102—22no—
809#102—22no—
810#102—22no—
811#102—22no—
812#102—22no—
813#102—22no—
814#102—22no—
815#102—22no—
816C22⋊C8C2×D414yes—
817C22⋊C8C2×D414yes—
818C22⋊C8C2×D414yes—
819C22⋊C8C2×D414yes—
820#97—22no—
821#97—22no—
822#97—41no—
823#97—41no—
824#97—41no—
825#97—41no—
826#97C2×D414yes—
827C4×C8—22no—
828C4×C8—22no—
829C4×C8—41no—
830C4×C8—41no—
831C4×C8C2×D414yes—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—22no—
842#95C2×D412yes—
843#95C2×D412yes—
844#95C2×D412yes—
845#95C2×D412yes—
846#95C2×D412yes—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—42no—
853C24—42no—
854C24—81no—
855C24—82no—
856C24—82no—
857C24C22×D411yescharacteristic
858C24C22×D411yescharacteristic
859#41—44no—
860#41—44no—
861#41—44no—
862#41—44no—
863#41—44no—
864#41—44no—
865#41—82no—
866#41—82no—
867#41—82no—
868#41—82no—
869#41—82no—
870#41—82no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—42no—
889C2×Q8—82no—
890C2×Q8C2×#4112yes—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—42no—
923C2×D4—44no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—42no—
934C2×D4—42no—
935C2×D4—42no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—44no—
942C2×D4—82no—
943C2×D4—82no—
944C2×D4—82no—
945C2×D4—82no—
946C2×D4—81no—
947C2×D4—82no—
948C2×D4—82no—
949C2×D4—82no—
950C2×D4—82no—
951C2×D4—82no—
952C2×D4—82no—
953C2×D4—82no—
954C2×D4—82no—
955C2×D4—81no—
956C2×D4—81no—
957C2×D4—81no—
958C2×D4—82no—
959C2×D4—82no—
960C2×D4—82no—
961C2×D4—82no—
962C2×D4—82no—
963C2×D4#12714yes—
964C2×D4C2×#4112yes—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—24no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—82no—
997C22×C4—81no—
998C22×C4—81no—
999C22×C4—81no—
1000C22×C4—82no—
1001C22×C4—82no—
1002C22×C4C22×D412yes—
1003C22×C4C22×D412yes—
1004C22×C4C22×D412yes—
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D412yes—
1010C22×C4C22×D412yes—
1011C22×C4C22×D412yes—
1012C22×C4C22×D412yes—
1013C22×C4C22×D412yes—
1014C22×C4C2511yescharacteristic
1015Q16—44no—
1016Q16—82no—
1017SD16—44no—
1018SD16—44no—
1019SD16—82no—
1020SD16—82no—
1021SD16—82no—
1022SD16—82no—
1023D8—44no—
1024D8—82no—
1025D8—82no—
1026D8—82no—
1027M16—44no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—21no—
1043C2×C8—21no—
1044C2×C8—44no—
1045C2×C8—44no—
1046C2×C8—44no—
1047C2×C8C22×D412yes—
1048C2×C8C22×D412yes—
1049C2×C8C22×D412yes—
1050C2×C8C22×D412yes—
1051C2×C8C22×D412yes—
1052C2×C8C22×D412yes—
1053C2×C8C22×D412yes—
1054C2×C8C22×D412yes—
1055C4⋊C4—24no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—21no—
1068C4⋊C4—21no—
1069C4⋊C4—21no—
1070C4⋊C4—21no—
1071C4⋊C4—21no—
1072C4⋊C4—42no—
1073C4⋊C4—44no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—42no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—82no—
1084C4⋊C4—82no—
1085C4⋊C4—82no—
1086C4⋊C4—82no—
1087C4⋊C4—82no—
1088C4⋊C4#12714yes—
1089C22⋊C4—28no—
1090C22⋊C4—24no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—44no—
1094C22⋊C4—44no—
1095C22⋊C4—44no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—44no—
1112C22⋊C4—44no—
1113C22⋊C4—82no—
1114C22⋊C4—82no—
1115C22⋊C4—82no—
1116C22⋊C4—82no—
1117C22⋊C4—82no—
1118C22⋊C4—82no—
1119C22⋊C4#12714yes—
1120C22⋊C4#12714yes—
1121C42—24no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—42no—
1129C42—42no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42C22×D412yes—
1134C42C22×D412yes—
1135C42C2×#4112yes—
1136C42H(5,𝔽2)12yes—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—22no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—42no—
1147C23—42no—
1148C23—41no—
1149C23—41no—
1150C23—42no—
1151C23—42no—
1152C23—42no—
1153C23—42no—
1154C23—42no—
1155C23—42no—
1156C23—42no—
1157C23—42no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—84no—
1171C23—84no—
1172C23—162no—
1173C23—164no—
1174C23—164no—
1175C23C2×#12712yes—
1176C23C2×#12712yes—
1177C23C23×D411yescharacteristic
1178Q8—22no—
1179Q8—22no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—41no—
1190Q8—162no—
1191D4—22no—
1192D4—22no—
1193D4—44no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—84no—
1213D4—84no—
1214D4—84no—
1215D4—84no—
1216D4—88no—
1217D4—84no—
1218D4—164no—
1219D4—162no—
1220D4—164no—
1221D4—164no—
1222D4—162no—
1223D4—162no—
1224D4—162no—
1225D4—162no—
1226D4—162no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—22no—
1230C2×C4—22no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—22no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—22no—
1241C2×C4—22no—
1242C2×C4—22no—
1243C2×C4—22no—
1244C2×C4—22no—
1245C2×C4—22no—
1246C2×C4—22no—
1247C2×C4—22no—
1248C2×C4—22no—
1249C2×C4—22no—
1250C2×C4—22no—
1251C2×C4—22no—
1252C2×C4—22no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—42no—
1262C2×C4—42no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—84no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—162no—
1284C2×C4C2×#12712yes—
1285C2×C4C2×#12712yes—
1286C2×C4C2×#12712yes—
1287C2×C4C2×#12712yes—
1288C2×C4#54614yes—
1289C2×C4C23×D411yescharacteristic
1290C2×C4C23×D411yescharacteristic
1291C2×C4C22×#4111yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4#58511yescharacteristic
1294C2×C4#58511yescharacteristic
1295C8—22no—
1296C8—22no—
1297C8—22no—
1298C8—22no—
1299C8—22no—
1300C8—22no—
1301C8—22no—
1302C8—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—42no—
1313C22—44no—
1314C22—42no—
1315C22—82no—
1316C22—81no—
1317C22—81no—
1318C22—82no—
1319C22—82no—
1320C22—82no—
1321C22—82no—
1322C22—82no—
1323C22—82no—
1324C22—82no—
1325C22—82no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—168no—
1339C22C22×#12711yescharacteristic
1340C22C2×#54611yescharacteristic
1341C22#350011yescharacteristic
1342C22#358412yes—
1343C22#358512yes—
1344C4—24no—
1345C4—22no—
1346C4—22no—
1347C4—22no—
1348C4—22no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—42no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4D4×#4111yescharacteristic
1364C4D4×#4111yescharacteristic
1365C4#349611yescharacteristic
1366C4#349611yescharacteristic
1367C2—42no—
1368C2—42no—
1369C2—82no—
1370C2—161no—
1371C2—161no—
1372C2—161no—
1373C2—161no—
1374C2#3626011yescharacteristic
1375C2#6064311yescharacteristic
1376C2#6065011yescharacteristic
1377C2#6119612yes—
1378C2#6260712yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3317C2semidirect
2. C2×#3319C2semidirect
3. C2×#3305C2semidirect
4. C2×#3296C2semidirect
5. #37871C2semidirect
6. #37681C2semidirect
7. #33228C2semidirect
8. #33183C2semidirect
9. #33182C2semidirect
10. #28523C2semidirect
11. #28452C2semidirect
12. #28424C2semidirect
13. #28421C2semidirect
14. #28420C2semidirect
15. #28410C2semidirect
16. #28368C2semidirect
17. #28365C2semidirect
18. #28352C2semidirect
19. #28350C2semidirect
20. #28349C2semidirect
21. #28341C2semidirect
22. #28340C2semidirect
23. #28337C2semidirect
24. #27920C2semidirect
25. #27907C2semidirect
26. #25736C2semidirect
27. #25723C2semidirect
28. #21694C2semidirect
29. #21206C2semidirect
30. #21199C2semidirect
31. #20493C2semidirect
44. C2×#495C22semidirect
45. C2×#490C22semidirect
48. C2×#486C22semidirect
54. C2×#482C22semidirect
55. C2×#482C22semidirect
57. C2×#479C22semidirect
58. C2×#477C22semidirect
66. C2×#466C22semidirect
68. C2×#465C22semidirect
70. C2×#460C22semidirect
72. C2×#459C22semidirect
75. C2×#452C22semidirect
78. C2×#449C22semidirect
82. C2×#441C22semidirect
84. C2×C4×SD16C22semidirect
92. C2×#416C22semidirect
93. C2×#416C22semidirect
96. C22×#97C22semidirect
98. #2850C22semidirect
103. #2660C22semidirect
107. #2568C22semidirect
108. #2566C22semidirect
112. #2500C22semidirect
114. #2499C22semidirect
124. #2326C22semidirect
127. #2285C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2096C22semidirect
131. #2095C22semidirect
132. #2094C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
142. #2015C22semidirect
146. #2013C22semidirect
148. #2012C22semidirect
153. #1973C22semidirect
154. #1973C22semidirect
155. #1973C22semidirect
158. #1972C22semidirect
159. #1971C22semidirect
160. #1970C22semidirect
161. #1969C22semidirect
163. #1968C22semidirect
169. #1960C22semidirect
170. #1960C22semidirect
174. #1959C22semidirect
175. #1959C22semidirect
176. #1959C22semidirect
177. #1959C22semidirect
180. #1958C22semidirect
181. #1958C22semidirect
186. #1847C22semidirect
187. #1845C22semidirect
188. #1844C22semidirect
189. #1771C22semidirect
190. #1770C22semidirect
191. #1768C22semidirect
194. #1752C22semidirect
195. C8×C22⋊C4C22semidirect
197. C4×C22⋊C8C22semidirect
198. #1726C22semidirect
330. #435D4semidirect
331. C8×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33172
C2×#33192
C2×#33052
C2×#32962
#378712
#376812
#332282
#331832
#331822
#285232
#284522
#284242
#284212
#284202
#284102
#283682
#283652
#283522
#283502
#283492
#283412
#283402
#283372
#279202
#279072
#257362
#257232
#216942
#212062
#211992
#204932