Finite Group Databasebeta

← #6606857

Subgroups — #6606857

Order 512.

2352 conjugacy classes of subgroups.

The subgroup lattice has 1356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3311C211yesmaximal, characteristic, complemented
2C2×#3307C211yesmaximal, characteristic, complemented
3C2×#3302C211yesmaximal, characteristic, complemented
4C2×#3297C211yesmaximal, characteristic, complemented
5#37870C211yesmaximal, characteristic, complemented
6#37682C211yesmaximal, characteristic, complemented
7#33229C211yesmaximal, characteristic, complemented
8#33188C211yesmaximal, characteristic, complemented
9#33173C211yesmaximal, characteristic, complemented
10#28525C211yesmaximal, characteristic, complemented
11#28453C211yesmaximal, characteristic, complemented
12#28427C211yesmaximal, characteristic, complemented
13#28422C211yesmaximal, characteristic, complemented
14#28408C211yesmaximal, characteristic, complemented
15#28398C211yesmaximal, characteristic, complemented
16#28357C211yesmaximal, characteristic, complemented
17#28356C211yesmaximal, characteristic, complemented
18#28352C211yesmaximal, characteristic, complemented
19#28351C211yesmaximal, characteristic, complemented
20#28339C211yesmaximal, characteristic, complemented
21#28338C211yesmaximal, characteristic, complemented
22#28337C211yesmaximal, characteristic, complemented
23#28330C211yesmaximal, characteristic, complemented
24#27922C211yesmaximal, characteristic, complemented
25#27915C211yesmaximal, characteristic, complemented
26#25736C211yesmaximal, characteristic, complemented
27#25727C211yesmaximal, characteristic, complemented
28#21704C211yesmaximal, characteristic, complemented
29#21206C211yesmaximal, characteristic, complemented
30#21195C211yesmaximal, characteristic, complemented
31#20484C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#547C2211yescharacteristic
35C2×#546C2211yescharacteristic
36C2×#535C2211yescharacteristic
37C2×#532C2211yescharacteristic
38#3311—28no—
39#3307—28no—
40#3302—28no—
41#3297—28no—
42C2×#497C2211yescharacteristic, complemented
43C2×#496C2211yescharacteristic
44C2×#495C2211yescharacteristic
45C2×#491C2211yescharacteristic, complemented
46C2×#489C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#487C2211yescharacteristic, complemented
49C2×#484C2211yescharacteristic
50C2×#485C2211yescharacteristic
51C2×#485C2211yescharacteristic
52C2×#485C2211yescharacteristic, complemented
53C2×#485C2211yescharacteristic, complemented
54C2×#482C2211yescharacteristic
55C2×#482C2211yescharacteristic
56C2×#483C2211yescharacteristic
57C2×#478C2211yescharacteristic
58C2×#478C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic
60C2×#474C2211yescharacteristic, complemented
61C2×#470C2211yescharacteristic
62C2×#468C2211yescharacteristic
63C2×#467C2211yescharacteristic
64C2×#467C2211yescharacteristic, complemented
65C2×#466C2211yescharacteristic
66C2×#465C2211yescharacteristic
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic
70C2×#462C2211yescharacteristic, complemented
71C2×#463C2211yescharacteristic
72C2×#461C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#452C2211yescharacteristic, complemented
76C2×#449C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#449C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#442C2211yescharacteristic, complemented
82C2×#440C2211yescharacteristic
83C2×C4×SD16C2211yescharacteristic, complemented
84C2×C4×D8C2211yescharacteristic
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×C4×C8C2211yescharacteristic, complemented
97#2850C2211yescharacteristic
98#2850C2211yescharacteristic, complemented
99#2695—22no—
100#2686—22no—
101#2671—22no—
102#2668—22no—
103#2660C2211yescharacteristic, complemented
104#2658C2211yescharacteristic
105#2621C2211yescharacteristic
106#2620C2211yescharacteristic
107#2565C2211yescharacteristic, complemented
108#2563C2211yescharacteristic, complemented
109#2547C2211yescharacteristic
110#2544C2211yescharacteristic
111#2503C2211yescharacteristic
112#2500C2211yescharacteristic
113#2500C2211yescharacteristic, complemented
114#2499C2211yescharacteristic, complemented
115#2469—22no—
116#2468—22no—
117#2443—22no—
118#2435C2211yescharacteristic
119#2432C2211yescharacteristic
120#2432C2211yescharacteristic
121#2431C2211yescharacteristic
122#2418—22no—
123#2328C2211yescharacteristic
124#2326C2211yescharacteristic, complemented
125#2317C2211yescharacteristic
126#2290C2211yescharacteristic
127#2285C2211yescharacteristic, complemented
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2097C2211yescharacteristic, complemented
132#2096C2211yescharacteristic, complemented
133#2095C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2093C2211yescharacteristic
136#2092C2211yescharacteristic
137#2092C2211yescharacteristic
138#2092C2211yescharacteristic
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2015C2211yescharacteristic
144#2015C2211yescharacteristic, complemented
145#2014C2211yescharacteristic
146#2013C2211yescharacteristic, complemented
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic
150#2012C2211yescharacteristic, complemented
151#2011C2211yescharacteristic
152#1973C2211yescharacteristic, complemented
153#1973C2211yescharacteristic, complemented
154#1972C2211yescharacteristic
155#1971C2211yescharacteristic, complemented
156#1970C2211yescharacteristic
157#1970C2211yescharacteristic, complemented
158#1969C2211yescharacteristic, complemented
159#1969C2211yescharacteristic, complemented
160#1968C2211yescharacteristic
161#1968C2211yescharacteristic
162#1968C2211yescharacteristic, complemented
163#1968C2211yescharacteristic, complemented
164#1961C2211yescharacteristic
165#1961C2211yescharacteristic
166#1960C2211yescharacteristic, complemented
167#1960C2211yescharacteristic, complemented
168#1959C2211yescharacteristic
169#1959C2211yescharacteristic
170#1959C2211yescharacteristic
171#1959C2211yescharacteristic
172#1958C2211yescharacteristic
173#1958C2211yescharacteristic
174#1958C2211yescharacteristic
175#1958C2211yescharacteristic
176#1958C2211yescharacteristic
177#1958C2211yescharacteristic, complemented
178#1958C2211yescharacteristic, complemented
179#1958C2211yescharacteristic, complemented
180#1957C2211yescharacteristic
181#1957C2211yescharacteristic
182#1957C2211yescharacteristic
183#1956C2211yescharacteristic, complemented
184#1956C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1846C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1752C2211yescharacteristic, complemented
194C8×C22⋊C4C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C23×D4C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#556—24no—
220#556—24no—
221#553—24no—
222#553—24no—
223#547—24no—
224#547—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×C4⋊Q8C2311yescharacteristic
234C2×C4⋊Q8C2311yescharacteristic
235C2×#127C2311yescharacteristic
236C2×#127C2311yescharacteristic
237C2×#126—21no—
238C2×#126—21no—
239C2×#126—21no—
240C2×#125C2311yescharacteristic
241C2×#124—21no—
242C2×#124C2311yescharacteristic
243C2×#124C2311yescharacteristic
244C2×#124C2311yescharacteristic
245C2×#124C2311yescharacteristic
246C2×#124C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#123—21no—
250C2×#123—21no—
251C2×#123—21no—
252C2×#123—21no—
253C2×C22⋊Q8C2311yescharacteristic
254C2×C22⋊Q8C2311yescharacteristic
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×#121—21no—
259C2×#121—21no—
260C2×#121—22no—
261C2×#121—22no—
262C2×#121—21no—
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#120—21no—
267C2×#120—22no—
268C2×C4×Q8—21no—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×D4—21no—
271C2×C4×D4—22no—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×C4×D4C2311yescharacteristic
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C2×#117C2311yescharacteristic
279C2×#117C2311yescharacteristic
280C22×C4⋊C4—21no—
281C22×C4⋊C4C2311yescharacteristic
282C22×C22⋊C4—21no—
283C22×C42C2311yescharacteristic
284#497—42no—
285#496—24no—
286#495—42no—
287#491—24no—
288#489—24no—
289#488—24no—
290#487—24no—
291#485—24no—
292#485—24no—
293#485—24no—
294#485—24no—
295#484—24no—
296#483—24no—
297#482—24no—
298#482—24no—
299#478—24no—
300#478—24no—
301#476—24no—
302#474—24no—
303#470—24no—
304#468—24no—
305#467—24no—
306#467—24no—
307#466—24no—
308#465—24no—
309#465—24no—
310#465—24no—
311#464—24no—
312#463—24no—
313#462—24no—
314#461—24no—
315#452—24no—
316#452—24no—
317#452—24no—
318#450—24no—
319#449—24no—
320#449—24no—
321#449—24no—
322#447—24no—
323#442—24no—
324#440—24no—
325C4×SD16—24no—
326C4×D8—24no—
327#435D418yescomplemented
328C8×D4D418yescomplemented
329C2×#107C2311yescharacteristic
330C2×#107C2311yescharacteristic
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×#106C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×C4⋊C8C2311yescharacteristic
342C2×C4⋊C8C2311yescharacteristic
343#418—24no—
344#417—24no—
345#416—24no—
346#416—24no—
347#416—24no—
348#416—24no—
349#416—24no—
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
368C2×#103C2311yescharacteristic
369C2×#103C2311yescharacteristic
370C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
392C2×C22⋊C8C2311yescharacteristic
393C2×C22⋊C8C2311yescharacteristic
394C2×C22⋊C8C2311yescharacteristic
395#405—42no—
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×#97C2311yescharacteristic
400C2×#97C2311yescharacteristic
401C2×C4×C8—42no—
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406C2×C4×C8C2311yescharacteristic
407C2×C4×C8C2311yescharacteristic
408C2×C4×C8C2311yescharacteristic
409#400—22no—
410#399—22no—
411#399—22no—
412#398—22no—
413#398—22no—
414#398—22no—
415#397—22no—
416#397—22no—
417#397—22no—
418#396—22no—
419#395—22no—
420#394—22no—
421#394—22no—
422#394—22no—
423#394—22no—
424#394—22no—
425#394—22no—
426#394—22no—
427#393—22no—
428#392—22no—
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#391C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#389—22no—
442#388—22no—
443#388—22no—
444#388—22no—
445#388—22no—
446#388—22no—
447#388D412yes—
448#387—22no—
449#387—22no—
450#387D412yes—
451#386—22no—
452#386—22no—
453#386—22no—
454#386—22no—
455#386—22no—
456#386—22no—
457#386D412yes—
458#385—22no—
459#385—22no—
460#385—22no—
461#385—22no—
462#385D412yes—
463#384C2311yescharacteristic
464#384C2311yescharacteristic
465#384C2311yescharacteristic
466#384C2311yescharacteristic
467#382C2311yescharacteristic
468#382C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472#382C2311yescharacteristic
473#381—22no—
474#380—22no—
475#380—22no—
476#380—22no—
477#379—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×Q8C2411yescharacteristic
513C22×D4—22no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—22no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4C2×D412yes—
541C23×C4C2411yescharacteristic
542C23×C4C2411yescharacteristic
543C2×Q16—22no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—22no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—41no—
561C2×SD16—41no—
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×D8—22no—
571C2×D8—22no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C2×D8—41no—
579C2×M16—41no—
580C2×M16—41no—
581C2×M16C2×D414yes—
582C22×C8—41no—
583C22×C8—41no—
584C22×C8—41no—
585C22×C8—41no—
586C22×C8—41no—
587C22×C8—41no—
588C22×C8C2×D414yes—
589C22×C8C2×D414yes—
590C22×C8C2×D414yes—
591C22×C8C2411yescharacteristic
592C22×C8C2411yescharacteristic
593C22×C8C2411yescharacteristic
594C22×C8C2411yescharacteristic
595C22×C8C2411yescharacteristic
596C22×C8C2411yescharacteristic
597C22×C8C2411yescharacteristic
598C22×C8C2411yescharacteristic
599C4⋊Q8—22no—
600C4⋊Q8—22no—
601C4⋊Q8—22no—
602C4⋊Q8—22no—
603C4⋊Q8—22no—
604C4⋊Q8—22no—
605C4⋊Q8—41no—
606C4⋊Q8—41no—
607#127—22no—
608#127—22no—
609#127—41no—
610#127#4114yes—
611#126—44no—
612#126—44no—
613#126—44no—
614#125—22no—
615#125—22no—
616#124—22no—
617#124—22no—
618#124—22no—
619#124—22no—
620#124—22no—
621#124—22no—
622#124—22no—
623#124—22no—
624#124—22no—
625#124—41no—
626#124—41no—
627#124—41no—
628#124—41no—
629#124—41no—
630#124—44no—
631#123—44no—
632#123—44no—
633#123—44no—
634#123—44no—
635C22⋊Q8—22no—
636C22⋊Q8—22no—
637C22⋊Q8—22no—
638C22⋊Q8—22no—
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—48no—
652#121—48no—
653#121—44no—
654#121—44no—
655#121—44no—
656#120—48no—
657#120—44no—
658C4×Q8—22no—
659C4×Q8—22no—
660C4×Q8—44no—
661C4×D4—22no—
662C4×D4—22no—
663C4×D4—22no—
664C4×D4—22no—
665C4×D4—22no—
666C4×D4—22no—
667C4×D4—48no—
668C4×D4—44no—
669C4×D4C2×D414yes—
670C4×D4C2×D414yes—
671#117—22no—
672#117—22no—
673#117—22no—
674#117—22no—
675#117—22no—
676#117—22no—
677#117—22no—
678#117—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—44no—
700C2×C4⋊C4C2×D412yes—
701C2×C4⋊C4C2×D412yes—
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—44no—
740C2×C22⋊C4C2×D412yes—
741C2×C22⋊C4C2×D412yes—
742C2×C22⋊C4C2×D412yes—
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C42—22no—
746C2×C42—22no—
747C2×C42—21no—
748C2×C42—21no—
749C2×C42—21no—
750C2×C42—21no—
751C2×C42C2×D412yes—
752C2×C42C2411yescharacteristic
753C2×C42C2411yescharacteristic
754C2×C42C2411yescharacteristic
755C2×C42C2411yescharacteristic
756C2×C42C2411yescharacteristic
757#107—22no—
758#107—22no—
759#107—22no—
760#107—22no—
761#107—22no—
762#107—22no—
763#106—22no—
764#106—22no—
765#106—22no—
766#106—22no—
767#106—22no—
768#106—22no—
769C4⋊C8C2×D414yes—
770C4⋊C8C2×D414yes—
771#103—22no—
772#103—22no—
773#103—22no—
774#103—22no—
775#103—22no—
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#103—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—
811C22⋊C8C2×D414yes—
812C22⋊C8C2×D414yes—
813C22⋊C8C2×D414yes—
814C22⋊C8C2×D414yes—
815#97—22no—
816#97—22no—
817#97—41no—
818#97—41no—
819#97C2×D414yes—
820C4×C8—22no—
821C4×C8—22no—
822C4×C8—41no—
823C4×C8—41no—
824C4×C8—41no—
825C4×C8—41no—
826C4×C8C2×D414yes—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95C2×D412yes—
840#95C2×D412yes—
841#95C2×D412yes—
842#95C2×D412yes—
843#95C2×D412yes—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—42no—
849C24—42no—
850C24—81no—
851C24—82no—
852C24—82no—
853C24C22×D411yescharacteristic
854C24C22×D411yescharacteristic
855#41—44no—
856#41—44no—
857#41—44no—
858#41—44no—
859#41—44no—
860#41—44no—
861#41—82no—
862#41—82no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
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—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—42no—
892C2×Q8—82no—
893C2×D4—28no—
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—44no—
917C2×D4—44no—
918C2×D4—42no—
919C2×D4—42no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—42no—
927C2×D4—42no—
928C2×D4—42no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—82no—
932C2×D4—82no—
933C2×D4—82no—
934C2×D4—82no—
935C2×D4—81no—
936C2×D4—82no—
937C2×D4—82no—
938C2×D4—82no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—82no—
943C2×D4—82no—
944C2×D4#12714yes—
945C2×D4C2×#4112yes—
946C2×D4C2×#4112yes—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—24no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—82no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—82no—
985C22×C4—82no—
986C22×C4—82no—
987C22×C4C22×D412yes—
988C22×C4C22×D412yes—
989C22×C4C22×D412yes—
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D412yes—
995C22×C4C22×D412yes—
996C22×C4C22×D412yes—
997C22×C4C22×D412yes—
998C22×C4C22×D412yes—
999C22×C4C2511yescharacteristic
1000Q16—82no—
1001Q16—82no—
1002Q16—82no—
1003SD16—44no—
1004SD16—44no—
1005SD16—82no—
1006SD16—82no—
1007SD16—82no—
1008SD16—82no—
1009D8—44no—
1010D8—44no—
1011D8—82no—
1012M16—44no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—44no—
1030C2×C8—44no—
1031C2×C8—44no—
1032C2×C8C22×D412yes—
1033C2×C8C22×D412yes—
1034C2×C8C22×D412yes—
1035C2×C8C22×D412yes—
1036C2×C8C22×D412yes—
1037C2×C8C22×D412yes—
1038C2×C8C22×D412yes—
1039C2×C8C22×D412yes—
1040C4⋊C4—24no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—44no—
1071C4⋊C4—82no—
1072C4⋊C4—82no—
1073C4⋊C4—82no—
1074C4⋊C4—82no—
1075C4⋊C4—82no—
1076C4⋊C4#12714yes—
1077C22⋊C4—24no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—44no—
1081C22⋊C4—44no—
1082C22⋊C4—44no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—44no—
1100C22⋊C4—44no—
1101C22⋊C4—82no—
1102C22⋊C4—82no—
1103C22⋊C4—82no—
1104C22⋊C4—82no—
1105C22⋊C4—82no—
1106C22⋊C4—82no—
1107C22⋊C4—82no—
1108C22⋊C4#12714yes—
1109C22⋊C4#12714yes—
1110C42—24no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42C22×D412yes—
1122C42C22×D412yes—
1123C42C2×#4112yes—
1124C42H(5,𝔽2)12yes—
1125C23—22no—
1126C23—22no—
1127C23—22no—
1128C23—22no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—22no—
1134C23—22no—
1135C23—42no—
1136C23—42no—
1137C23—42no—
1138C23—42no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—42no—
1144C23—42no—
1145C23—42no—
1146C23—42no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—84no—
1154C23—84no—
1155C23—162no—
1156C23—164no—
1157C23—164no—
1158C23C2×#12712yes—
1159C23C2×#12712yes—
1160C23C23×D411yescharacteristic
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—84no—
1178D4—22no—
1179D4—22no—
1180D4—22no—
1181D4—22no—
1182D4—44no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—88no—
1196D4—84no—
1197D4—84no—
1198D4—84no—
1199D4—84no—
1200D4—84no—
1201D4—164no—
1202D4—162no—
1203D4—162no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—22no—
1214C2×C4—22no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—22no—
1222C2×C4—22no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—22no—
1228C2×C4—22no—
1229C2×C4—48no—
1230C2×C4—42no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—42no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—84no—
1259C2×C4—84no—
1260C2×C4—84no—
1261C2×C4—84no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4C2×#12712yes—
1266C2×C4C2×#12712yes—
1267C2×C4C2×#12712yes—
1268C2×C4C2×#12712yes—
1269C2×C4#54614yes—
1270C2×C4C23×D411yescharacteristic
1271C2×C4C23×D411yescharacteristic
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C8—22no—
1277C8—22no—
1278C8—22no—
1279C8—22no—
1280C8—22no—
1281C8—22no—
1282C8—22no—
1283C8—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—44no—
1297C22—44no—
1298C22—82no—
1299C22—82no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—82no—
1305C22—82no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—82no—
1313C22—82no—
1314C22—168no—
1315C22C22×#12711yescharacteristic
1316C22C2×#54611yescharacteristic
1317C22#350011yescharacteristic
1318C22#358412yes—
1319C22#358412yes—
1320C4—22no—
1321C4—22no—
1322C4—22no—
1323C4—22no—
1324C4—24no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4D4×#4111yescharacteristic
1341C4D4×#4111yescharacteristic
1342C4#349611yescharacteristic
1343C4#349611yescharacteristic
1344C2—42no—
1345C2—42no—
1346C2—82no—
1347C2—82no—
1348C2—161no—
1349C2—161no—
1350C2#3626011yescharacteristic
1351C2#6064311yescharacteristic
1352C2#6064911yescharacteristic
1353C2#6116912yes—
1354C2#6255412yes—
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×#3311C2semidirect
2. C2×#3307C2semidirect
3. C2×#3302C2semidirect
4. C2×#3297C2semidirect
5. #37870C2semidirect
6. #37682C2semidirect
7. #33229C2semidirect
8. #33188C2semidirect
9. #33173C2semidirect
10. #28525C2semidirect
11. #28453C2semidirect
12. #28427C2semidirect
13. #28422C2semidirect
14. #28408C2semidirect
15. #28398C2semidirect
16. #28357C2semidirect
17. #28356C2semidirect
18. #28352C2semidirect
19. #28351C2semidirect
20. #28339C2semidirect
21. #28338C2semidirect
22. #28337C2semidirect
23. #28330C2semidirect
24. #27922C2semidirect
25. #27915C2semidirect
26. #25736C2semidirect
27. #25727C2semidirect
28. #21704C2semidirect
29. #21206C2semidirect
30. #21195C2semidirect
31. #20484C2semidirect
42. C2×#497C22semidirect
45. C2×#491C22semidirect
48. C2×#487C22semidirect
52. C2×#485C22semidirect
53. C2×#485C22semidirect
58. C2×#478C22semidirect
60. C2×#474C22semidirect
64. C2×#467C22semidirect
68. C2×#465C22semidirect
70. C2×#462C22semidirect
72. C2×#461C22semidirect
75. C2×#452C22semidirect
78. C2×#449C22semidirect
81. C2×#442C22semidirect
83. C2×C4×SD16C22semidirect
92. C2×#416C22semidirect
93. C2×#416C22semidirect
96. C22×C4×C8C22semidirect
98. #2850C22semidirect
103. #2660C22semidirect
107. #2565C22semidirect
108. #2563C22semidirect
113. #2500C22semidirect
114. #2499C22semidirect
124. #2326C22semidirect
127. #2285C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2097C22semidirect
132. #2096C22semidirect
133. #2095C22semidirect
134. #2094C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
144. #2015C22semidirect
146. #2013C22semidirect
150. #2012C22semidirect
152. #1973C22semidirect
153. #1973C22semidirect
155. #1971C22semidirect
157. #1970C22semidirect
158. #1969C22semidirect
159. #1969C22semidirect
162. #1968C22semidirect
163. #1968C22semidirect
166. #1960C22semidirect
167. #1960C22semidirect
177. #1958C22semidirect
178. #1958C22semidirect
179. #1958C22semidirect
183. #1956C22semidirect
184. #1956C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1846C22semidirect
189. #1771C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
193. #1752C22semidirect
195. C8×C22⋊C4C22semidirect
197. #1749C22semidirect
198. #1726C22semidirect
327. #435D4semidirect
328. C8×D4D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33112
C2×#33072
C2×#33022
C2×#32972
#378702
#376822
#332292
#331882
#331732
#285252
#284532
#284272
#284222
#284082
#283982
#283572
#283562
#283522
#283512
#283392
#283382
#283372
#283302
#279222
#279152
#257362
#257272
#217042
#212062
#211952
#204842