Finite Group Databasebeta

← #6607144

Subgroups — #6607144

Order 512.

2426 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3343C211yesmaximal, characteristic, complemented
2C2×#3332C211yesmaximal, characteristic, complemented
3C2×#3323C211yesmaximal, characteristic, complemented
4C2×#3268C211yesmaximal, characteristic, complemented
5#38093C211yesmaximal, characteristic, complemented
6#38082C211yesmaximal, characteristic, complemented
7#33243C211yesmaximal, characteristic, complemented
8#33187C211yesmaximal, characteristic, complemented
9#33177C211yesmaximal, characteristic, complemented
10#28549C211yesmaximal, characteristic, complemented
11#28474C211yesmaximal, characteristic, complemented
12#28408C211yesmaximal, characteristic, complemented
13#28399C211yesmaximal, characteristic, complemented
14#28396C211yesmaximal, characteristic, complemented
15#28387C211yesmaximal, characteristic, complemented
16#28368C211yesmaximal, characteristic, complemented
17#28356C211yesmaximal, characteristic, complemented
18#28354C211yesmaximal, characteristic, complemented
19#28353C211yesmaximal, characteristic, complemented
20#28328C211yesmaximal, characteristic, complemented
21#28325C211yesmaximal, characteristic, complemented
22#28309C211yesmaximal, characteristic, complemented
23#28303C211yesmaximal, characteristic, complemented
24#27946C211yesmaximal, characteristic, complemented
25#27932C211yesmaximal, characteristic, complemented
26#25791C211yesmaximal, characteristic, complemented
27#25775C211yesmaximal, characteristic, complemented
28#21695C211yesmaximal, characteristic, complemented
29#21236C211yesmaximal, characteristic, complemented
30#21230C211yesmaximal, characteristic, complemented
31#20490C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C22×#135C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×#550C2211yescharacteristic
36C2×#547C2211yescharacteristic
37C2×#546C2211yescharacteristic
38#3343—28no—
39#3332—28no—
40#3323—28no—
41#3268—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#496C2211yescharacteristic
44C2×#496C2211yescharacteristic
45C2×#495C2211yescharacteristic, complemented
46C2×#492C2211yescharacteristic
47C2×#488C2211yescharacteristic
48C2×#486C2211yescharacteristic, complemented
49C2×#484C2211yescharacteristic
50C2×#481C2211yescharacteristic
51C2×#481C2211yescharacteristic
52C2×#481C2211yescharacteristic, complemented
53C2×#485C2211yescharacteristic
54C2×#482C2211yescharacteristic
55C2×#483C2211yescharacteristic, complemented
56C2×#480C2211yescharacteristic, complemented
57C2×#477C2211yescharacteristic, complemented
58C2×#475C2211yescharacteristic, complemented
59C2×#478C2211yescharacteristic
60C2×#478C2211yescharacteristic, complemented
61C2×#470C2211yescharacteristic
62C2×#469C2211yescharacteristic
63C2×#469C2211yescharacteristic, complemented
64C2×#468C2211yescharacteristic
65C2×#468C2211yescharacteristic
66C2×#468C2211yescharacteristic
67C2×#466C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#464C2211yescharacteristic
70C2×#464C2211yescharacteristic
71C2×#459C2211yescharacteristic
72C2×#459C2211yescharacteristic, complemented
73C2×#452C2211yescharacteristic
74C2×#452C2211yescharacteristic
75C2×#449C2211yescharacteristic
76C2×#449C2211yescharacteristic
77C2×#449C2211yescharacteristic
78C2×#449C2211yescharacteristic, complemented
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#440C2211yescharacteristic
82C2×#440C2211yescharacteristic, complemented
83C2×C4×SD16C2211yescharacteristic
84C2×C4×SD16C2211yescharacteristic, complemented
85C2×#436C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic
88C22×#107C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic
90C2×#417C2211yescharacteristic
91C2×#417C2211yescharacteristic, complemented
92C2×#418C2211yescharacteristic
93C2×#405C2211yescharacteristic, complemented
94C2×C4×M16C2211yescharacteristic
95#2850C2211yescharacteristic
96#2850C2211yescharacteristic
97#2709—22no—
98#2703—22no—
99#2696—22no—
100#2691—22no—
101#2641C2211yescharacteristic, complemented
102#2640C2211yescharacteristic
103#2620C2211yescharacteristic, complemented
104#2619C2211yescharacteristic
105#2565C2211yescharacteristic, complemented
106#2563C2211yescharacteristic
107#2548C2211yescharacteristic, complemented
108#2544C2211yescharacteristic
109#2504C2211yescharacteristic
110#2504C2211yescharacteristic, complemented
111#2503C2211yescharacteristic
112#2500C2211yescharacteristic
113#2476—22no—
114#2460—22no—
115#2433C2211yescharacteristic
116#2432C2211yescharacteristic
117#2432C2211yescharacteristic, complemented
118#2431C2211yescharacteristic
119#2412—22no—
120#2404—22no—
121#2328C2211yescharacteristic
122#2327C2211yescharacteristic, complemented
123#2311C2211yescharacteristic
124#2311C2211yescharacteristic, complemented
125#2297C2211yescharacteristic
126C2×#390C2211yescharacteristic
127#2290C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2096C2211yescharacteristic, complemented
132#2094C2211yescharacteristic
133#2092C2211yescharacteristic
134#2092C2211yescharacteristic
135#2092C2211yescharacteristic
136#2092C2211yescharacteristic, complemented
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2092C2211yescharacteristic, complemented
140#2016C2211yescharacteristic, complemented
141#2015C2211yescharacteristic, complemented
142#2015C2211yescharacteristic, complemented
143#2014C2211yescharacteristic
144#2013C2211yescharacteristic
145#2012C2211yescharacteristic
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic, complemented
149#2011C2211yescharacteristic
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic, complemented
156#1973C2211yescharacteristic, complemented
157#1973C2211yescharacteristic, complemented
158#1973C2211yescharacteristic, complemented
159#1972C2211yescharacteristic
160#1972C2211yescharacteristic
161#1972C2211yescharacteristic
162#1972C2211yescharacteristic, complemented
163#1971C2211yescharacteristic, complemented
164#1970C2211yescharacteristic
165#1970C2211yescharacteristic
166#1970C2211yescharacteristic
167#1970C2211yescharacteristic
168#1970C2211yescharacteristic
169#1970C2211yescharacteristic
170#1970C2211yescharacteristic, complemented
171#1969C2211yescharacteristic, complemented
172#1969C2211yescharacteristic, complemented
173#1968C2211yescharacteristic
174#1968C2211yescharacteristic
175#1968C2211yescharacteristic
176#1968C2211yescharacteristic
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1968C2211yescharacteristic, complemented
180#1961C2211yescharacteristic
181#1960C2211yescharacteristic, complemented
182#1958C2211yescharacteristic, complemented
183#1958C2211yescharacteristic, complemented
184#1958C2211yescharacteristic, complemented
185#1957C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1846C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic
198#1726C2211yescharacteristic, complemented
199C22×#41—21no—
200C22×#41C2311yescharacteristic
201C22×#41C2311yescharacteristic
202C22×#41C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C2×AGL(1,ℤ/8)—24no—
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×#135—24no—
208C2×#135—24no—
209C2×#135—42no—
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×D8C2311yescharacteristic
221C22×D8C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C22×M16C2311yescharacteristic
229C23×C8C2311yescharacteristic
230#552—24no—
231#552—24no—
232#550—24no—
233#550—24no—
234#547—24no—
235#547—24no—
236#546—24no—
237#546—24no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×#127—21no—
241C2×#127C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#127C2311yescharacteristic
244C2×#126—21no—
245C2×#125—21no—
246C2×#125C2311yescharacteristic
247C2×#124C2311yescharacteristic
248C2×#124C2311yescharacteristic
249C2×#124C2311yescharacteristic
250C2×#124C2311yescharacteristic
251C2×#123—21no—
252C2×#123—21no—
253C2×#123—21no—
254C2×#123—21no—
255C2×C22⋊Q8—21no—
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×C22⋊Q8C2311yescharacteristic
259C2×#121—21no—
260C2×#121—21no—
261C2×#121—21no—
262C2×#121C2311yescharacteristic
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#120—21no—
268C2×#120—22no—
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×D4—21no—
272C2×C4×D4C2311yescharacteristic
273C2×C4×D4C2311yescharacteristic
274C2×C4×D4C2311yescharacteristic
275C2×#117—21no—
276C2×#117C2311yescharacteristic
277C2×#117C2311yescharacteristic
278C22×C4⋊C4C2311yescharacteristic
279C22×C4⋊C4C2311yescharacteristic
280C22×C4⋊C4C2311yescharacteristic
281C22×C22⋊C4—22no—
282C22×C22⋊C4—21no—
283C22×C42C2311yescharacteristic
284#501—24no—
285#496—24no—
286#496—42no—
287#495—42no—
288#492—24no—
289#488—24no—
290#486—24no—
291#485—24no—
292#484—24no—
293#483—24no—
294#482—24no—
295#481—24no—
296#481—24no—
297#481—24no—
298#480—24no—
299#478—24no—
300#478—24no—
301#477—24no—
302#475—24no—
303#470—24no—
304#469—24no—
305#469—24no—
306#468—24no—
307#468—24no—
308#468—24no—
309#466—24no—
310#465—24no—
311#464—24no—
312#464—24no—
313#459—24no—
314#459—24no—
315#452—24no—
316#452—24no—
317#450—24no—
318#449—24no—
319#449—24no—
320#449—24no—
321#449—24no—
322#447—24no—
323#440—24no—
324#440—24no—
325C4×SD16—24no—
326C4×SD16—24no—
327#436D418yescomplemented
328#435D418yescomplemented
329#428—24no—
330C2×#107—24no—
331C2×#107C2311yescharacteristic
332C2×#107C2311yescharacteristic
333C2×#107C2311yescharacteristic
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#106C2311yescharacteristic
340C2×#106C2311yescharacteristic
341C2×#106C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×C4⋊C8C2311yescharacteristic
348C2×C4⋊C8C2311yescharacteristic
349#418—24no—
350#417—24no—
351#417—24no—
352#417—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×#102C2311yescharacteristic
366C2×#102C2311yescharacteristic
367C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
386C2×C22⋊C8C2311yescharacteristic
387C2×C22⋊C8C2311yescharacteristic
388C2×C22⋊C8C2311yescharacteristic
389#405—42no—
390C4×M16—42no—
391C2×#97C2311yescharacteristic
392C2×#97C2311yescharacteristic
393C2×#97C2311yescharacteristic
394C2×#97C2311yescharacteristic
395C2×#97C2311yescharacteristic
396C2×C4×C8C2311yescharacteristic
397C2×C4×C8C2311yescharacteristic
398C2×C4×C8C2311yescharacteristic
399C2×C4×C8C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403#400—22no—
404#398—22no—
405#397—22no—
406#397—22no—
407#397—22no—
408#396—22no—
409#394—22no—
410#394—22no—
411#394—22no—
412#394—22no—
413#394—22no—
414#394—22no—
415#394—22no—
416#394—22no—
417#394—22no—
418#393—22no—
419#393—22no—
420#392—22no—
421#392—22no—
422#392—22no—
423#391C2311yescharacteristic
424#391C2311yescharacteristic
425#391C2311yescharacteristic
426#391C2311yescharacteristic
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#390—22no—
431#390—22no—
432#390C2311yescharacteristic
433#390C2311yescharacteristic
434#390C2311yescharacteristic
435#390C2311yescharacteristic
436#390C2311yescharacteristic
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#388—22no—
446#388—22no—
447#388—22no—
448#388D412yes—
449#387—22no—
450#387—22no—
451#387—22no—
452#387D412yes—
453#386—22no—
454#386—22no—
455#386—22no—
456#386—22no—
457#386—22no—
458#386—22no—
459#386—22no—
460#386—22no—
461#386—22no—
462#386—22no—
463#386—22no—
464#386D412yes—
465#385—22no—
466#385—22no—
467#385D412yes—
468#384C2311yescharacteristic
469#382C2311yescharacteristic
470#382C2311yescharacteristic
471#382C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#381—22no—
475#380—22no—
476#380—22no—
477#380—22no—
478C4×C4⋊C4C2311yescharacteristic
479C4×C22⋊C4—22no—
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—
508C2×#41—44no—
509C2×#41—84no—
510C22×Q8—21no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
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×C4—21no—
546C23×C4—21no—
547C23×C4C2×D412yes—
548C23×C4C2411yescharacteristic
549C23×C4C2411yescharacteristic
550AGL(1,ℤ/8)—416no—
551#135—416no—
552C2×Q16—22no—
553C2×Q16—22no—
554C2×Q16—22no—
555C2×Q16—41no—
556C2×Q16—41no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—22no—
563C2×SD16—22no—
564C2×SD16—22no—
565C2×SD16—22no—
566C2×SD16—22no—
567C2×SD16—22no—
568C2×SD16—22no—
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16#4114yescomplemented
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—22no—
585C2×D8—22no—
586C2×D8—22no—
587C2×D8—22no—
588C2×D8—22no—
589C2×D8—22no—
590C2×D8—22no—
591C2×D8—22no—
592C2×D8—41no—
593C2×D8—41no—
594C2×D8—41no—
595C2×D8—41no—
596C2×D8—41no—
597C2×D8—41no—
598C2×D8—41no—
599C2×D8—41no—
600C2×M16—22no—
601C2×M16—22no—
602C2×M16—41no—
603C2×M16—41no—
604C2×M16—41no—
605C2×M16—41no—
606C2×M16C2×D414yes—
607C2×M16C2×D414yes—
608C2×M16C2×D414yes—
609C22×C8—22no—
610C22×C8—22no—
611C22×C8C2×D414yes—
612C22×C8C2411yescharacteristic
613C22×C8C2411yescharacteristic
614C22×C8C2411yescharacteristic
615C22×C8C2411yescharacteristic
616C22×C8C2411yescharacteristic
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C22×C8C2411yescharacteristic
620C4⋊Q8—22no—
621C4⋊Q8—22no—
622C4⋊Q8—22no—
623C4⋊Q8—41no—
624#127—22no—
625#127—22no—
626#127—22no—
627#127—41no—
628#127—41no—
629#127—41no—
630#127—44no—
631#126—44no—
632#125—22no—
633#125—22no—
634#125—44no—
635#124—22no—
636#124—22no—
637#124—41no—
638#124—41no—
639#124—41no—
640#124—41no—
641#124—41no—
642#124—41no—
643#123—44no—
644#123—44no—
645#123—44no—
646#123—44no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—22no—
652C22⋊Q8—22no—
653C22⋊Q8—44no—
654#121—22no—
655#121—22no—
656#121—22no—
657#121—22no—
658#121—22no—
659#121—22no—
660#121—22no—
661#121—22no—
662#121—22no—
663#121—22no—
664#121—44no—
665#121—44no—
666#121—44no—
667#120—44no—
668#120—84no—
669C4×Q8—22no—
670C4×Q8—22no—
671C4×Q8—22no—
672C4×Q8—22no—
673C4×D4—22no—
674C4×D4—22no—
675C4×D4—22no—
676C4×D4—22no—
677C4×D4—44no—
678C4×D4C2×D414yes—
679C4×D4C2×D414yes—
680#117—22no—
681#117—22no—
682#117—41no—
683#117—41no—
684#117—44no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—21no—
693C2×C4⋊C4—21no—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—21no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4—21no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4C2×D412yes—
705C2×C4⋊C4C2×D412yes—
706C2×C4⋊C4C2×D411yescharacteristic
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2411yescharacteristic
710C2×C4⋊C4C2411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
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—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—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
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—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—44no—
745C2×C22⋊C4—84no—
746C2×C22⋊C4C2×D412yes—
747C2×C22⋊C4C2×D412yes—
748C2×C22⋊C4C2×D412yes—
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C22⋊C4C2×D411yescharacteristic
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—41no—
755C2×C42—41no—
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#107—22no—
769#107—22no—
770#106—22no—
771#106—22no—
772#106—22no—
773#106—22no—
774#106—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778C4⋊C8C2×D414yes—
779C4⋊C8C2×D414yes—
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#103—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—
812C22⋊C8C2×D414yes—
813C22⋊C8C2×D414yes—
814C22⋊C8C2×D414yes—
815C22⋊C8C2×D414yes—
816#97—22no—
817#97—22no—
818#97—41no—
819#97—41no—
820#97C2×D414yes—
821C4×C8—22no—
822C4×C8—22no—
823C4×C8—41no—
824C4×C8—41no—
825C4×C8—41no—
826C4×C8—41no—
827C4×C8C2×D414yes—
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#95—22no—
840#95C2×D412yes—
841#95C2×D412yes—
842#95C2×D412yes—
843#95C2×D412yes—
844#95C2×D412yes—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—42no—
851C24—44no—
852C24—42no—
853C24—81no—
854C24—82no—
855C24C22×D411yescharacteristic
856C24C22×D411yescharacteristic
857#41—44no—
858#41—44no—
859#41—44no—
860#41—44no—
861#41—44no—
862#41—44no—
863#41—82no—
864#41—82no—
865#41—82no—
866#41—82no—
867#41—82no—
868#41—82no—
869#41—816no—
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—42no—
888C2×Q8—82no—
889C2×Q8C2×#4112yes—
890C2×D4—21no—
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—44no—
920C2×D4—44no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—42no—
927C2×D4—44no—
928C2×D4—42no—
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—82no—
940C2×D4—82no—
941C2×D4—82no—
942C2×D4—81no—
943C2×D4—82no—
944C2×D4—82no—
945C2×D4—82no—
946C2×D4—82no—
947C2×D4—82no—
948C2×D4—82no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4—81no—
952C2×D4—82no—
953C2×D4—82no—
954C2×D4—82no—
955C2×D4—82no—
956C2×D4#12714yes—
957C2×D4C2×#4112yes—
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—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—44no—
984C22×C4—42no—
985C22×C4—42no—
986C22×C4—42no—
987C22×C4—42no—
988C22×C4—42no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4—82no—
996C22×C4—82no—
997C22×C4—82no—
998C22×C4—82no—
999C22×C4C22×D412yes—
1000C22×C4C22×D412yes—
1001C22×C4C22×D412yes—
1002C22×C4C22×D412yes—
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D412yes—
1008C22×C4C22×D412yes—
1009C22×C4C22×D412yes—
1010C22×C4C22×D412yes—
1011C22×C4C2511yescharacteristic
1012Q16—44no—
1013Q16—82no—
1014SD16—28no—
1015SD16—44no—
1016SD16—44no—
1017SD16—44no—
1018SD16—44no—
1019SD16—44no—
1020SD16—82no—
1021SD16—82no—
1022D8—44no—
1023D8—44no—
1024D8—44no—
1025D8—82no—
1026D8—82no—
1027D8—82no—
1028M16—28no—
1029M16—44no—
1030M16—44no—
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—21no—
1045C2×C8—28no—
1046C2×C8C22×D412yes—
1047C2×C8C22×D412yes—
1048C2×C8C22×D412yes—
1049C2×C8C22×D412yes—
1050C2×C8C22×D412yes—
1051C2×C8C22×D412yes—
1052C2×C8C22×D412yes—
1053C2×C8C22×D412yes—
1054C2×C8C2×#4112yes—
1055C2×C8H(5,𝔽2)12yes—
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—42no—
1074C4⋊C4—44no—
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—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—82no—
1087C4⋊C4#12714yes—
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—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—82no—
1105C22⋊C4—82no—
1106C22⋊C4—82no—
1107C22⋊C4—82no—
1108C22⋊C4—82no—
1109C22⋊C4—82no—
1110C22⋊C4—82no—
1111C22⋊C4—82no—
1112C22⋊C4—82no—
1113C22⋊C4—82no—
1114C22⋊C4—82no—
1115C22⋊C4—82no—
1116C22⋊C4—82no—
1117C22⋊C4—82no—
1118C22⋊C4—82no—
1119C22⋊C4—82no—
1120C22⋊C4#12714yes—
1121C22⋊C4#12714yes—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—42no—
1131C42—42no—
1132C42—42no—
1133C42—42no—
1134C42C22×D412yes—
1135C42C22×D412yes—
1136C23—22no—
1137C23—22no—
1138C23—22no—
1139C23—22no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—22no—
1145C23—42no—
1146C23—42no—
1147C23—41no—
1148C23—41no—
1149C23—42no—
1150C23—42no—
1151C23—42no—
1152C23—42no—
1153C23—42no—
1154C23—42no—
1155C23—42no—
1156C23—42no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—84no—
1170C23—84no—
1171C23—88no—
1172C23—162no—
1173C23—164no—
1174C23C2×#12712yes—
1175C23C2×#12712yes—
1176C23C23×D411yescharacteristic
1177Q8—22no—
1178Q8—22no—
1179Q8—41no—
1180Q8—41no—
1181Q8—41no—
1182Q8—41no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189Q8—84no—
1190D4—22no—
1191D4—22no—
1192D4—44no—
1193D4—41no—
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—84no—
1212D4—84no—
1213D4—84no—
1214D4—84no—
1215D4—84no—
1216D4—84no—
1217D4—84no—
1218D4—162no—
1219D4—164no—
1220D4—164no—
1221D4—162no—
1222D4—162no—
1223D4—162no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—22no—
1231C2×C4—22no—
1232C2×C4—22no—
1233C2×C4—22no—
1234C2×C4—22no—
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—41no—
1252C2×C4—41no—
1253C2×C4—42no—
1254C2×C4—42no—
1255C2×C4—42no—
1256C2×C4—42no—
1257C2×C4—42no—
1258C2×C4—42no—
1259C2×C4—42no—
1260C2×C4—42no—
1261C2×C4—41no—
1262C2×C4—41no—
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—84no—
1276C2×C4—84no—
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×C4C23×D411yescharacteristic
1289C2×C4C23×D411yescharacteristic
1290C2×C4C22×#4111yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4#58511yescharacteristic
1293C2×C4#58511yescharacteristic
1294C8—22no—
1295C8—22no—
1296C8—22no—
1297C8—22no—
1298C8—22no—
1299C8—22no—
1300C8—22no—
1301C8#54614yes—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—42no—
1312C22—44no—
1313C22—42no—
1314C22—82no—
1315C22—81no—
1316C22—81no—
1317C22—82no—
1318C22—82no—
1319C22—82no—
1320C22—82no—
1321C22—82no—
1322C22—82no—
1323C22—82no—
1324C22—82no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—168no—
1338C22C22×#12711yescharacteristic
1339C22D4×#4111yescharacteristic
1340C22#349611yescharacteristic
1341C22#358412yes—
1342C22#358512yes—
1343C4—22no—
1344C4—22no—
1345C4—22no—
1346C4—22no—
1347C4—42no—
1348C4—42no—
1349C4—42no—
1350C4—42no—
1351C4—42no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4C2×#54611yescharacteristic
1363C4D4×#4111yescharacteristic
1364C4#349611yescharacteristic
1365C4#350011yescharacteristic
1366C2—42no—
1367C2—42no—
1368C2—82no—
1369C2—161no—
1370C2—161no—
1371C2—161no—
1372C2—161no—
1373C2#3626011yescharacteristic
1374C2#6064411yescharacteristic
1375C2#6064911yescharacteristic
1376C2#6153512yes—
1377C2#6231312yes—
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×#3343C2semidirect
2. C2×#3332C2semidirect
3. C2×#3323C2semidirect
4. C2×#3268C2semidirect
5. #38093C2semidirect
6. #38082C2semidirect
7. #33243C2semidirect
8. #33187C2semidirect
9. #33177C2semidirect
10. #28549C2semidirect
11. #28474C2semidirect
12. #28408C2semidirect
13. #28399C2semidirect
14. #28396C2semidirect
15. #28387C2semidirect
16. #28368C2semidirect
17. #28356C2semidirect
18. #28354C2semidirect
19. #28353C2semidirect
20. #28328C2semidirect
21. #28325C2semidirect
22. #28309C2semidirect
23. #28303C2semidirect
24. #27946C2semidirect
25. #27932C2semidirect
26. #25791C2semidirect
27. #25775C2semidirect
28. #21695C2semidirect
29. #21236C2semidirect
30. #21230C2semidirect
31. #20490C2semidirect
42. C2×#501C22semidirect
45. C2×#495C22semidirect
48. C2×#486C22semidirect
52. C2×#481C22semidirect
55. C2×#483C22semidirect
56. C2×#480C22semidirect
57. C2×#477C22semidirect
58. C2×#475C22semidirect
60. C2×#478C22semidirect
63. C2×#469C22semidirect
68. C2×#465C22semidirect
72. C2×#459C22semidirect
78. C2×#449C22semidirect
82. C2×#440C22semidirect
84. C2×C4×SD16C22semidirect
88. C22×#107C22semidirect
91. C2×#417C22semidirect
93. C2×#405C22semidirect
101. #2641C22semidirect
103. #2620C22semidirect
105. #2565C22semidirect
107. #2548C22semidirect
110. #2504C22semidirect
117. #2432C22semidirect
122. #2327C22semidirect
124. #2311C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2096C22semidirect
136. #2092C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2092C22semidirect
140. #2016C22semidirect
141. #2015C22semidirect
142. #2015C22semidirect
148. #2012C22semidirect
155. #1973C22semidirect
156. #1973C22semidirect
157. #1973C22semidirect
158. #1973C22semidirect
162. #1972C22semidirect
163. #1971C22semidirect
170. #1970C22semidirect
171. #1969C22semidirect
172. #1969C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1968C22semidirect
181. #1960C22semidirect
182. #1958C22semidirect
183. #1958C22semidirect
184. #1958C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1846C22semidirect
189. #1771C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
194. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
196. #1750C22semidirect
198. #1726C22semidirect
327. #436D4semidirect
328. #435D4semidirect
581. C2×SD16#41semidirect

Maximal subgroups

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

subgroupindex
C2×#33432
C2×#33322
C2×#33232
C2×#32682
#380932
#380822
#332432
#331872
#331772
#285492
#284742
#284082
#283992
#283962
#283872
#283682
#283562
#283542
#283532
#283282
#283252
#283092
#283032
#279462
#279322
#257912
#257752
#216952
#212362
#212302
#204902