Finite Group Databasebeta

← #6607136

Subgroups — #6607136

Order 512.

2484 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3350C211yesmaximal, characteristic, complemented
2C2×#3326C211yesmaximal, characteristic, complemented
3C2×#3324C211yesmaximal, characteristic, complemented
4C2×#3265C211yesmaximal, characteristic, complemented
5#38091C211yesmaximal, characteristic, complemented
6#38080C211yesmaximal, characteristic, complemented
7#33243C211yesmaximal, characteristic, complemented
8#33187C211yesmaximal, characteristic, complemented
9#33174C211yesmaximal, characteristic, complemented
10#28543C211yesmaximal, characteristic, complemented
11#28480C211yesmaximal, characteristic, complemented
12#28406C211yesmaximal, characteristic, complemented
13#28404C211yesmaximal, characteristic, complemented
14#28393C211yesmaximal, characteristic, complemented
15#28392C211yesmaximal, characteristic, complemented
16#28368C211yesmaximal, characteristic, complemented
17#28367C211yesmaximal, characteristic, complemented
18#28365C211yesmaximal, characteristic, complemented
19#28353C211yesmaximal, characteristic, complemented
20#28323C211yesmaximal, characteristic, complemented
21#28321C211yesmaximal, characteristic, complemented
22#28307C211yesmaximal, characteristic, complemented
23#28302C211yesmaximal, characteristic, complemented
24#27947C211yesmaximal, characteristic, complemented
25#27928C211yesmaximal, characteristic, complemented
26#25791C211yesmaximal, characteristic, complemented
27#25774C211yesmaximal, characteristic, complemented
28#21695C211yesmaximal, characteristic, complemented
29#21236C211yesmaximal, characteristic, complemented
30#21231C211yesmaximal, characteristic, complemented
31#20490C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C23×SD16C2211yescharacteristic
34C2×#556C2211yescharacteristic
35C2×#553C2211yescharacteristic
36C2×#548C2211yescharacteristic
37C2×D42C2211yescharacteristic
38#3350—28no—
39#3326—28no—
40#3324—28no—
41#3265—28no—
42C2×#501C2211yescharacteristic, complemented
43C2×#496C2211yescharacteristic
44C2×#496C2211yescharacteristic, complemented
45C2×#492C2211yescharacteristic
46C2×#492C2211yescharacteristic, complemented
47C2×#488C2211yescharacteristic, complemented
48C2×#486C2211yescharacteristic
49C2×#485C2211yescharacteristic, complemented
50C2×#482C2211yescharacteristic
51C2×#482C2211yescharacteristic
52C2×#482C2211yescharacteristic, complemented
53C2×#482C2211yescharacteristic, complemented
54C2×#482C2211yescharacteristic, complemented
55C2×#483C2211yescharacteristic, complemented
56C2×#483C2211yescharacteristic, complemented
57C2×#479C2211yescharacteristic, complemented
58C2×#479C2211yescharacteristic, complemented
59C2×#476C2211yescharacteristic, complemented
60C2×#474C2211yescharacteristic
61C2×#469C2211yescharacteristic, complemented
62C2×#468C2211yescharacteristic
63C2×#468C2211yescharacteristic
64C2×#468C2211yescharacteristic
65C2×#468C2211yescharacteristic, complemented
66C2×#468C2211yescharacteristic, complemented
67C2×#466C2211yescharacteristic
68C2×#465C2211yescharacteristic, complemented
69C2×#460C2211yescharacteristic
70C2×#460C2211yescharacteristic
71C2×#463C2211yescharacteristic
72C2×#463C2211yescharacteristic, complemented
73C2×#449C2211yescharacteristic
74C2×#449C2211yescharacteristic, complemented
75C2×#448C2211yescharacteristic
76C2×#448C2211yescharacteristic, complemented
77C2×#450C2211yescharacteristic
78C2×#450C2211yescharacteristic
79C2×#450C2211yescharacteristic
80C2×#447C2211yescharacteristic
81C2×#440C2211yescharacteristic
82C2×#440C2211yescharacteristic, complemented
83C2×C4×SD16C2211yescharacteristic
84C2×C4×SD16C2211yescharacteristic, complemented
85C2×#436C2211yescharacteristic
86C2×#435C2211yescharacteristic
87C2×#428C2211yescharacteristic, complemented
88C2×#427C2211yescharacteristic, complemented
89C2×#417C2211yescharacteristic, complemented
90C2×#419C2211yescharacteristic, complemented
91C2×#418C2211yescharacteristic
92C2×#418C2211yescharacteristic
93C2×#405C2211yescharacteristic, complemented
94C2×C4×M16C2211yescharacteristic, complemented
95#2857C2211yescharacteristic, complemented
96#2856C2211yescharacteristic
97#2715—22no—
98#2714—22no—
99#2686—22no—
100#2678—22no—
101#2641C2211yescharacteristic
102#2640C2211yescharacteristic, complemented
103#2620C2211yescharacteristic, complemented
104#2619C2211yescharacteristic
105#2567C2211yescharacteristic, complemented
106#2566C2211yescharacteristic
107#2545C2211yescharacteristic, complemented
108#2541C2211yescharacteristic
109#2504C2211yescharacteristic
110#2500C2211yescharacteristic
111#2500C2211yescharacteristic, complemented
112#2499C2211yescharacteristic, complemented
113#2466—22no—
114#2465—22no—
115#2434C2211yescharacteristic, complemented
116#2433C2211yescharacteristic
117#2433C2211yescharacteristic
118#2432C2211yescharacteristic, complemented
119#2424—22no—
120#2410—22no—
121#2328C2211yescharacteristic
122#2327C2211yescharacteristic, complemented
123#2310C2211yescharacteristic, complemented
124#2309C2211yescharacteristic
125#2297C2211yescharacteristic, complemented
126C2×#390C2211yescharacteristic
127#2290C2211yescharacteristic
128#2097C2211yescharacteristic, complemented
129#2097C2211yescharacteristic, complemented
130#2097C2211yescharacteristic, complemented
131#2095C2211yescharacteristic, complemented
132#2094C2211yescharacteristic
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2094C2211yescharacteristic, complemented
136#2093C2211yescharacteristic
137#2092C2211yescharacteristic, complemented
138#2092C2211yescharacteristic, complemented
139#2092C2211yescharacteristic, complemented
140#2014C2211yescharacteristic
141#2014C2211yescharacteristic, complemented
142#2014C2211yescharacteristic, complemented
143#2014C2211yescharacteristic, complemented
144#2013C2211yescharacteristic
145#2013C2211yescharacteristic, complemented
146#2013C2211yescharacteristic, complemented
147#2013C2211yescharacteristic, complemented
148#2012C2211yescharacteristic
149#2012C2211yescharacteristic, complemented
150#2011C2211yescharacteristic
151#2011C2211yescharacteristic, complemented
152#1973C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic, complemented
155#1973C2211yescharacteristic, complemented
156#1973C2211yescharacteristic, complemented
157#1973C2211yescharacteristic, complemented
158#1973C2211yescharacteristic, complemented
159#1973C2211yescharacteristic, complemented
160#1973C2211yescharacteristic, complemented
161#1972C2211yescharacteristic
162#1972C2211yescharacteristic, complemented
163#1972C2211yescharacteristic, complemented
164#1970C2211yescharacteristic
165#1970C2211yescharacteristic, complemented
166#1970C2211yescharacteristic, complemented
167#1970C2211yescharacteristic, complemented
168#1970C2211yescharacteristic, complemented
169#1968C2211yescharacteristic
170#1968C2211yescharacteristic
171#1968C2211yescharacteristic
172#1968C2211yescharacteristic
173#1968C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1968C2211yescharacteristic, complemented
176#1968C2211yescharacteristic, complemented
177#1968C2211yescharacteristic, complemented
178#1968C2211yescharacteristic, complemented
179#1968C2211yescharacteristic, complemented
180#1961C2211yescharacteristic
181#1960C2211yescharacteristic, complemented
182#1958C2211yescharacteristic, complemented
183#1957C2211yescharacteristic, complemented
184#1957C2211yescharacteristic, complemented
185#1956C2211yescharacteristic, complemented
186#1847C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, complemented
188#1845C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191#1768C2211yescharacteristic, complemented
192#1753C2211yescharacteristic, complemented
193#1753C2211yescharacteristic, complemented
194#1753C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic, complemented
196#1750C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic, complemented
198#1726C2211yescharacteristic, complemented
199C22×#41C2311yescharacteristic
200C23×Q8C2311yescharacteristic
201C23×D4—21no—
202C23×D4C2311yescharacteristic
203C23×D4C2311yescharacteristic
204C2×AGL(1,ℤ/8)—24no—
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C22×SD16—24no—
208C22×SD16—24no—
209C22×SD16—42no—
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×SD16C2311yescharacteristic
218C22×SD16C2311yescharacteristic
219C22×SD16C2311yescharacteristic
220C22×SD16C2311yescharacteristic
221C22×SD16C2311yescharacteristic
222C22×D8C2311yescharacteristic
223C22×D8C2311yescharacteristic
224C22×D8C2311yescharacteristic
225C22×D8C2311yescharacteristic
226C22×M16C2311yescharacteristic
227C22×M16C2311yescharacteristic
228C22×M16C2311yescharacteristic
229C23×C8C2311yescharacteristic
230#556—24no—
231#556—24no—
232#553—24no—
233#553—24no—
234#548—24no—
235#548—24no—
236D42—24no—
237D42—24no—
238C2×C4⋊Q8C2311yescharacteristic
239C2×C4⋊Q8C2311yescharacteristic
240C2×C4⋊Q8C2311yescharacteristic
241C2×#127C2311yescharacteristic
242C2×#127C2311yescharacteristic
243C2×#127C2311yescharacteristic
244C2×#127C2311yescharacteristic
245C2×#126—21no—
246C2×#126—21no—
247C2×#126—21no—
248C2×#125C2311yescharacteristic
249C2×#124—21no—
250C2×#124—21no—
251C2×#124C2311yescharacteristic
252C2×#124C2311yescharacteristic
253C2×#123—21no—
254C2×C22⋊Q8—21no—
255C2×C22⋊Q8C2311yescharacteristic
256C2×C22⋊Q8C2311yescharacteristic
257C2×C22⋊Q8C2311yescharacteristic
258C2×#121—21no—
259C2×#121—21no—
260C2×#121—22no—
261C2×#121—21no—
262C2×#121—22no—
263C2×#121C2311yescharacteristic
264C2×#121C2311yescharacteristic
265C2×#121C2311yescharacteristic
266C2×#121C2311yescharacteristic
267C2×#121C2311yescharacteristic
268C2×#120—21no—
269C2×#120—21no—
270C2×#120—22no—
271C2×#120—22no—
272C2×C4×Q8—21no—
273C2×C4×Q8C2311yescharacteristic
274C2×C4×Q8C2311yescharacteristic
275C2×C4×D4—21no—
276C2×C4×D4—21no—
277C2×C4×D4C2311yescharacteristic
278C2×C4×D4C2311yescharacteristic
279C2×C4×D4C2311yescharacteristic
280C2×#117C2311yescharacteristic
281C2×#117C2311yescharacteristic
282C2×#117C2311yescharacteristic
283C2×#117C2311yescharacteristic
284C22×C4⋊C4C2311yescharacteristic
285C22×C22⋊C4—22no—
286C22×C42C2311yescharacteristic
287#501—24no—
288#496—24no—
289#496—42no—
290#492—24no—
291#492—42no—
292#488—24no—
293#486—24no—
294#485—24no—
295#483—24no—
296#483—24no—
297#482—24no—
298#482—24no—
299#482—24no—
300#482—24no—
301#482—24no—
302#479—24no—
303#479—24no—
304#476—24no—
305#474—24no—
306#469—24no—
307#468—24no—
308#468—24no—
309#468—24no—
310#468—24no—
311#468—24no—
312#466—24no—
313#465—24no—
314#463—24no—
315#463—24no—
316#460—24no—
317#460—24no—
318#450—24no—
319#450—24no—
320#450—24no—
321#449—24no—
322#449—24no—
323#448—24no—
324#448—24no—
325#447—24no—
326#440—24no—
327#440—24no—
328C4×SD16—24no—
329C4×SD16—24no—
330#436D418yescomplemented
331#435D418yescomplemented
332#428—24no—
333#427—24no—
334C2×#107C2311yescharacteristic
335C2×#107C2311yescharacteristic
336C2×#107C2311yescharacteristic
337C2×#107C2311yescharacteristic
338C2×#107C2311yescharacteristic
339C2×#107C2311yescharacteristic
340C2×#107C2311yescharacteristic
341C2×#107C2311yescharacteristic
342C2×#106C2311yescharacteristic
343C2×#106C2311yescharacteristic
344C2×#106C2311yescharacteristic
345C2×#106C2311yescharacteristic
346C2×#106C2311yescharacteristic
347C2×#106C2311yescharacteristic
348C2×#106C2311yescharacteristic
349C2×#106C2311yescharacteristic
350C2×C4⋊C8C2311yescharacteristic
351C2×C4⋊C8C2311yescharacteristic
352#419—24no—
353#418—24no—
354#418—24no—
355#417—24no—
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×#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×C22⋊C8C2311yescharacteristic
389C2×C22⋊C8C2311yescharacteristic
390C2×C22⋊C8C2311yescharacteristic
391C2×C22⋊C8C2311yescharacteristic
392#405—42no—
393C4×M16—42no—
394C2×#97C2311yescharacteristic
395C2×#97C2311yescharacteristic
396C2×#97C2311yescharacteristic
397C2×#97C2311yescharacteristic
398C2×#97C2311yescharacteristic
399C2×C4×C8C2311yescharacteristic
400C2×C4×C8C2311yescharacteristic
401C2×C4×C8C2311yescharacteristic
402C2×C4×C8C2311yescharacteristic
403C2×C4×C8C2311yescharacteristic
404C2×C4×C8C2311yescharacteristic
405C2×C4×C8C2311yescharacteristic
406#397—22no—
407#397—22no—
408#397—22no—
409#396—22no—
410#396—22no—
411#396—22no—
412#395—22no—
413#395—22no—
414#394—22no—
415#394—22no—
416#394—22no—
417#394—22no—
418#394—22no—
419#394—22no—
420#394—22no—
421#393—22no—
422#392—22no—
423#392—22no—
424#392—22no—
425#392—22no—
426#391—22no—
427#391C2311yescharacteristic
428#391C2311yescharacteristic
429#391C2311yescharacteristic
430#391C2311yescharacteristic
431#391C2311yescharacteristic
432#391C2311yescharacteristic
433#391C2311yescharacteristic
434#390—22no—
435#390—22no—
436#390—22no—
437#390C2311yescharacteristic
438#390C2311yescharacteristic
439#390C2311yescharacteristic
440#390C2311yescharacteristic
441#390C2311yescharacteristic
442#390C2311yescharacteristic
443#390C2311yescharacteristic
444#390C2311yescharacteristic
445#390C2311yescharacteristic
446#390C2311yescharacteristic
447#390C2311yescharacteristic
448#390C2311yescharacteristic
449#390C2311yescharacteristic
450#389—22no—
451#389—22no—
452#388—22no—
453#388—22no—
454#388—22no—
455#388D412yes—
456#387—22no—
457#387—22no—
458#387—22no—
459#387D412yes—
460#386—22no—
461#386—22no—
462#386—22no—
463#386—22no—
464#386D412yes—
465#385—22no—
466#385—22no—
467#385—22no—
468#385D412yes—
469#384C2311yescharacteristic
470#384C2311yescharacteristic
471#384C2311yescharacteristic
472#382C2311yescharacteristic
473#382C2311yescharacteristic
474#382C2311yescharacteristic
475#381—22no—
476#380—22no—
477#379—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—
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—22no—
500C22×Q8—22no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—22no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—44no—
534C22×D4—84no—
535C22×D4C2×D411yescharacteristic
536C22×D4C2411yescharacteristic
537C22×D4C2411yescharacteristic
538C22×D4C2411yescharacteristic
539C22×D4C2411yescharacteristic
540C22×D4C2411yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C2×D412yes—
547C23×C4C2411yescharacteristic
548C23×C4C2411yescharacteristic
549AGL(1,ℤ/8)—416no—
550C2×SD16—22no—
551C2×SD16—22no—
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—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—416no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×SD16—41no—
577C2×SD16—41no—
578C2×SD16—41no—
579C2×SD16—41no—
580C2×SD16—41no—
581C2×SD16—41no—
582C2×SD16—41no—
583C2×SD16—41no—
584C2×SD16—41no—
585C2×SD16—41no—
586C2×SD16#4114yes—
587C2×D8—22no—
588C2×D8—22no—
589C2×D8—22no—
590C2×D8—22no—
591C2×D8—22no—
592C2×D8—22no—
593C2×D8—22no—
594C2×D8—41no—
595C2×D8—41no—
596C2×D8—41no—
597C2×D8—41no—
598C2×D8—41no—
599C2×M16—22no—
600C2×M16—22no—
601C2×M16—41no—
602C2×M16—41no—
603C2×M16—41no—
604C2×M16—41no—
605C2×M16C2×D414yes—
606C2×M16C2×D414yes—
607C2×M16C2×D414yes—
608C22×C8—22no—
609C22×C8—22no—
610C22×C8C2×D414yes—
611C22×C8C2411yescharacteristic
612C22×C8C2411yescharacteristic
613C22×C8C2411yescharacteristic
614C22×C8C2411yescharacteristic
615C22×C8C2411yescharacteristic
616C22×C8C2411yescharacteristic
617C22×C8C2411yescharacteristic
618C22×C8C2411yescharacteristic
619C4⋊Q8—22no—
620C4⋊Q8—22no—
621C4⋊Q8—22no—
622C4⋊Q8—41no—
623C4⋊Q8—41no—
624C4⋊Q8—41no—
625#127—22no—
626#127—22no—
627#127—22no—
628#127—41no—
629#127—41no—
630#127—41no—
631#127—41no—
632#127—41no—
633#126—44no—
634#126—44no—
635#126—44no—
636#125—22no—
637#125—22no—
638#124—22no—
639#124—22no—
640#124—41no—
641#124—41no—
642#124—44no—
643#124—44no—
644#123—44no—
645C22⋊Q8—22no—
646C22⋊Q8—22no—
647C22⋊Q8—22no—
648C22⋊Q8—22no—
649C22⋊Q8—22no—
650C22⋊Q8—22no—
651C22⋊Q8—44no—
652#121—22no—
653#121—22no—
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—44no—
663#121—44no—
664#121—44no—
665#121—84no—
666#121—84no—
667#120—44no—
668#120—44no—
669#120—84no—
670#120—84no—
671C4×Q8—22no—
672C4×Q8—22no—
673C4×Q8—22no—
674C4×Q8—22no—
675C4×Q8—44no—
676C4×D4—22no—
677C4×D4—22no—
678C4×D4—22no—
679C4×D4—22no—
680C4×D4—44no—
681C4×D4—44no—
682C4×D4C2×D414yes—
683C4×D4C2×D414yes—
684#117—22no—
685#117—22no—
686#117—22no—
687#117—22no—
688#117—22no—
689#117—22no—
690#117—41no—
691#117—41no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
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—21no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4C2×D412yes—
709C2×C4⋊C4C2×D412yes—
710C2×C4⋊C4C2×D411yescharacteristic
711C2×C4⋊C4C2411yescharacteristic
712C2×C4⋊C4C2411yescharacteristic
713C2×C4⋊C4C2411yescharacteristic
714C2×C4⋊C4C2411yescharacteristic
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2411yescharacteristic
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2411yescharacteristic
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—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
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—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—84no—
749C2×C22⋊C4C2×D412yes—
750C2×C22⋊C4C2×D412yes—
751C2×C22⋊C4C2×D412yes—
752C2×C22⋊C4C2×D411yescharacteristic
753C2×C22⋊C4C2×D411yescharacteristic
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42—41no—
760C2×C42—41no—
761C2×C42C2×D412yes—
762C2×C42C2411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767#107—22no—
768#107—22no—
769#107—22no—
770#107—22no—
771#107—22no—
772#107—22no—
773#107—22no—
774#107—22no—
775#106—22no—
776#106—22no—
777#106—22no—
778#106—22no—
779#106—22no—
780#106—22no—
781#106—22no—
782#106—22no—
783C4⋊C8C2×D414yes—
784C4⋊C8C2×D414yes—
785#103—22no—
786#103—22no—
787#103—22no—
788#103—22no—
789#103—22no—
790#103—22no—
791#103—22no—
792#103—22no—
793#103—22no—
794#103—22no—
795#103—22no—
796#103—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—
816#102—22no—
817C22⋊C8C2×D414yes—
818C22⋊C8C2×D414yes—
819C22⋊C8C2×D414yes—
820C22⋊C8C2×D414yes—
821#97—22no—
822#97—22no—
823#97—41no—
824#97—41no—
825#97C2×D414yes—
826C4×C8—22no—
827C4×C8—22no—
828C4×C8—41no—
829C4×C8—41no—
830C4×C8—41no—
831C4×C8—41no—
832C4×C8C2×D414yes—
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#95—22no—
843#95C2×D412yes—
844#95C2×D412yes—
845#95C2×D412yes—
846#95C2×D412yes—
847#95C2×D412yes—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—42no—
854C24—42no—
855C24—44no—
856C24—42no—
857C24—42no—
858C24—82no—
859C24—81no—
860C24—81no—
861C24—82no—
862C24—82no—
863C24C22×D411yescharacteristic
864C24C22×D411yescharacteristic
865#41—44no—
866#41—44no—
867#41—82no—
868#41—82no—
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—42no—
887C2×Q8—44no—
888C2×Q8—44no—
889C2×Q8—42no—
890C2×Q8—42no—
891C2×Q8—82no—
892C2×Q8—81no—
893C2×Q8—82no—
894C2×Q8—82no—
895C2×Q8C2×#4112yes—
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—21no—
921C2×D4—21no—
922C2×D4—21no—
923C2×D4—21no—
924C2×D4—21no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—42no—
930C2×D4—42no—
931C2×D4—42no—
932C2×D4—42no—
933C2×D4—44no—
934C2×D4—44no—
935C2×D4—44no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—42no—
943C2×D4—42no—
944C2×D4—42no—
945C2×D4—42no—
946C2×D4—44no—
947C2×D4—82no—
948C2×D4—82no—
949C2×D4—82no—
950C2×D4—82no—
951C2×D4—81no—
952C2×D4—81no—
953C2×D4—82no—
954C2×D4—82no—
955C2×D4—82no—
956C2×D4—82no—
957C2×D4—82no—
958C2×D4—82no—
959C2×D4—82no—
960C2×D4—82no—
961C2×D4—82no—
962C2×D4—82no—
963C2×D4—82no—
964C2×D4—81no—
965C2×D4—82no—
966C2×D4—816no—
967C2×D4#12714yes—
968C2×D4C2×#4112yes—
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—21no—
978C22×C4—24no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—42no—
990C22×C4—42no—
991C22×C4—42no—
992C22×C4—42no—
993C22×C4—42no—
994C22×C4—42no—
995C22×C4—42no—
996C22×C4—42no—
997C22×C4—42no—
998C22×C4—82no—
999C22×C4—81no—
1000C22×C4—82no—
1001C22×C4—81no—
1002C22×C4—82no—
1003C22×C4C22×D412yes—
1004C22×C4C22×D412yes—
1005C22×C4C22×D412yes—
1006C22×C4C22×D411yescharacteristic
1007C22×C4C22×D411yescharacteristic
1008C22×C4C22×D411yescharacteristic
1009C22×C4C22×D411yescharacteristic
1010C22×C4C22×D412yes—
1011C22×C4C22×D412yes—
1012C22×C4C22×D412yes—
1013C22×C4C22×D412yes—
1014C22×C4C22×D412yes—
1015C22×C4C2511yescharacteristic
1016SD16—28no—
1017SD16—44no—
1018SD16—44no—
1019SD16—44no—
1020SD16—44no—
1021SD16—44no—
1022SD16—44no—
1023SD16—44no—
1024SD16—82no—
1025SD16—82no—
1026SD16—82no—
1027SD16—82no—
1028D8—44no—
1029D8—44no—
1030D8—82no—
1031D8—82no—
1032M16—28no—
1033M16—44no—
1034M16—44no—
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—21no—
1046C2×C8—21no—
1047C2×C8—21no—
1048C2×C8—21no—
1049C2×C8—28no—
1050C2×C8C22×D412yes—
1051C2×C8C22×D412yes—
1052C2×C8C22×D412yes—
1053C2×C8C22×D412yes—
1054C2×C8C22×D412yes—
1055C2×C8C22×D412yes—
1056C2×C8C22×D412yes—
1057C2×C8C22×D412yes—
1058C2×C8C2×#4112yes—
1059C2×C8H(5,𝔽2)12yes—
1060C4⋊C4—24no—
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—21no—
1073C4⋊C4—21no—
1074C4⋊C4—21no—
1075C4⋊C4—21no—
1076C4⋊C4—21no—
1077C4⋊C4—42no—
1078C4⋊C4—44no—
1079C4⋊C4—42no—
1080C4⋊C4—42no—
1081C4⋊C4—42no—
1082C4⋊C4—42no—
1083C4⋊C4—42no—
1084C4⋊C4—42no—
1085C4⋊C4—42no—
1086C4⋊C4—42no—
1087C4⋊C4—42no—
1088C4⋊C4—82no—
1089C4⋊C4—82no—
1090C4⋊C4—82no—
1091C4⋊C4—82no—
1092C4⋊C4#12714yes—
1093C22⋊C4—24no—
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—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—44no—
1114C22⋊C4—82no—
1115C22⋊C4—82no—
1116C22⋊C4—82no—
1117C22⋊C4—82no—
1118C22⋊C4—82no—
1119C22⋊C4—82no—
1120C22⋊C4—82no—
1121C22⋊C4—82no—
1122C22⋊C4—82no—
1123C22⋊C4—82no—
1124C22⋊C4—82no—
1125C22⋊C4#12714yes—
1126C22⋊C4#12714yes—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—42no—
1136C42—42no—
1137C42—42no—
1138C42—42no—
1139C42—42no—
1140C42—42no—
1141C42C22×D412yes—
1142C42C22×D412yes—
1143C23—22no—
1144C23—22no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—22no—
1150C23—22no—
1151C23—22no—
1152C23—42no—
1153C23—41no—
1154C23—41no—
1155C23—42no—
1156C23—42no—
1157C23—42no—
1158C23—42no—
1159C23—42no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—42no—
1173C23—42no—
1174C23—42no—
1175C23—42no—
1176C23—84no—
1177C23—84no—
1178C23—84no—
1179C23—84no—
1180C23—88no—
1181C23—162no—
1182C23—162no—
1183C23—164no—
1184C23—164no—
1185C23—164no—
1186C23C2×#12712yes—
1187C23C2×#12712yes—
1188C23C23×D411yescharacteristic
1189Q8—22no—
1190Q8—22no—
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—41no—
1200Q8—41no—
1201Q8—84no—
1202Q8—84no—
1203D4—22no—
1204D4—22no—
1205D4—44no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—84no—
1225D4—84no—
1226D4—84no—
1227D4—84no—
1228D4—84no—
1229D4—84no—
1230D4—84no—
1231D4—84no—
1232D4—164no—
1233D4—162no—
1234D4—164no—
1235D4—164no—
1236D4—162no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
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—22no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—22no—
1259C2×C4—22no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—42no—
1266C2×C4—42no—
1267C2×C4—42no—
1268C2×C4—42no—
1269C2×C4—42no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—42no—
1285C2×C4—42no—
1286C2×C4—42no—
1287C2×C4—84no—
1288C2×C4—84no—
1289C2×C4—84no—
1290C2×C4—84no—
1291C2×C4—162no—
1292C2×C4—162no—
1293C2×C4C2×#12712yes—
1294C2×C4C2×#12712yes—
1295C2×C4C2×#12712yes—
1296C2×C4C2×#12712yes—
1297C2×C4#57714yes—
1298C2×C4C23×D411yescharacteristic
1299C2×C4C23×D411yescharacteristic
1300C2×C4C22×#4111yescharacteristic
1301C2×C4C2×H(5,𝔽2)11yescharacteristic
1302C2×C4#58511yescharacteristic
1303C2×C4#58511yescharacteristic
1304C8—22no—
1305C8—22no—
1306C8—22no—
1307C8—22no—
1308C8—22no—
1309C8—22no—
1310C8—22no—
1311C8#54614yes—
1312C22—22no—
1313C22—22no—
1314C22—22no—
1315C22—22no—
1316C22—22no—
1317C22—22no—
1318C22—42no—
1319C22—42no—
1320C22—42no—
1321C22—42no—
1322C22—44no—
1323C22—42no—
1324C22—82no—
1325C22—81no—
1326C22—81no—
1327C22—82no—
1328C22—82no—
1329C22—82no—
1330C22—82no—
1331C22—82no—
1332C22—82no—
1333C22—82no—
1334C22—82no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—168no—
1348C22—168no—
1349C22C22×#12711yescharacteristic
1350C22D4×#4111yescharacteristic
1351C22#349611yescharacteristic
1352C22C2×#57712yes—
1353C22#358512yes—
1354C4—24no—
1355C4—22no—
1356C4—22no—
1357C4—22no—
1358C4—22no—
1359C4—42no—
1360C4—42no—
1361C4—42no—
1362C4—42no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4C2×#54611yescharacteristic
1374C4D4×#4111yescharacteristic
1375C4#349611yescharacteristic
1376C4#350011yescharacteristic
1377C2—42no—
1378C2—42no—
1379C2—82no—
1380C2—161no—
1381C2—161no—
1382C2—161no—
1383C2—161no—
1384C2#3626011yescharacteristic
1385C2#6064411yescharacteristic
1386C2#6064611yescharacteristic
1387C2#6154312yes—
1388C2#6230812yes—
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×#3350C2semidirect
2. C2×#3326C2semidirect
3. C2×#3324C2semidirect
4. C2×#3265C2semidirect
5. #38091C2semidirect
6. #38080C2semidirect
7. #33243C2semidirect
8. #33187C2semidirect
9. #33174C2semidirect
10. #28543C2semidirect
11. #28480C2semidirect
12. #28406C2semidirect
13. #28404C2semidirect
14. #28393C2semidirect
15. #28392C2semidirect
16. #28368C2semidirect
17. #28367C2semidirect
18. #28365C2semidirect
19. #28353C2semidirect
20. #28323C2semidirect
21. #28321C2semidirect
22. #28307C2semidirect
23. #28302C2semidirect
24. #27947C2semidirect
25. #27928C2semidirect
26. #25791C2semidirect
27. #25774C2semidirect
28. #21695C2semidirect
29. #21236C2semidirect
30. #21231C2semidirect
31. #20490C2semidirect
42. C2×#501C22semidirect
44. C2×#496C22semidirect
46. C2×#492C22semidirect
47. C2×#488C22semidirect
49. C2×#485C22semidirect
52. C2×#482C22semidirect
53. C2×#482C22semidirect
54. C2×#482C22semidirect
55. C2×#483C22semidirect
56. C2×#483C22semidirect
57. C2×#479C22semidirect
58. C2×#479C22semidirect
59. C2×#476C22semidirect
61. C2×#469C22semidirect
65. C2×#468C22semidirect
66. C2×#468C22semidirect
68. C2×#465C22semidirect
72. C2×#463C22semidirect
74. C2×#449C22semidirect
76. C2×#448C22semidirect
82. C2×#440C22semidirect
84. C2×C4×SD16C22semidirect
87. C2×#428C22semidirect
88. C2×#427C22semidirect
89. C2×#417C22semidirect
90. C2×#419C22semidirect
93. C2×#405C22semidirect
94. C2×C4×M16C22semidirect
95. #2857C22semidirect
102. #2640C22semidirect
103. #2620C22semidirect
105. #2567C22semidirect
107. #2545C22semidirect
111. #2500C22semidirect
112. #2499C22semidirect
115. #2434C22semidirect
118. #2432C22semidirect
122. #2327C22semidirect
123. #2310C22semidirect
125. #2297C22semidirect
128. #2097C22semidirect
129. #2097C22semidirect
130. #2097C22semidirect
131. #2095C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
135. #2094C22semidirect
137. #2092C22semidirect
138. #2092C22semidirect
139. #2092C22semidirect
141. #2014C22semidirect
142. #2014C22semidirect
143. #2014C22semidirect
145. #2013C22semidirect
146. #2013C22semidirect
147. #2013C22semidirect
149. #2012C22semidirect
151. #2011C22semidirect
154. #1973C22semidirect
155. #1973C22semidirect
156. #1973C22semidirect
157. #1973C22semidirect
158. #1973C22semidirect
159. #1973C22semidirect
160. #1973C22semidirect
162. #1972C22semidirect
163. #1972C22semidirect
165. #1970C22semidirect
166. #1970C22semidirect
167. #1970C22semidirect
168. #1970C22semidirect
173. #1968C22semidirect
174. #1968C22semidirect
175. #1968C22semidirect
176. #1968C22semidirect
177. #1968C22semidirect
178. #1968C22semidirect
179. #1968C22semidirect
181. #1960C22semidirect
182. #1958C22semidirect
183. #1957C22semidirect
184. #1957C22semidirect
185. #1956C22semidirect
186. #1847C22semidirect
187. #1846C22semidirect
188. #1845C22semidirect
189. #1771C22semidirect
190. C8×C4⋊C4C22semidirect
191. #1768C22semidirect
192. #1753C22semidirect
193. #1753C22semidirect
194. #1753C22semidirect
195. C8×C22⋊C4C22semidirect
196. #1750C22semidirect
197. C4×C22⋊C8C22semidirect
198. #1726C22semidirect
330. #436D4semidirect
331. #435D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33502
C2×#33262
C2×#33242
C2×#32652
#380912
#380802
#332432
#331872
#331742
#285432
#284802
#284062
#284042
#283932
#283922
#283682
#283672
#283652
#283532
#283232
#283212
#283072
#283022
#279472
#279282
#257912
#257742
#216952
#212362
#212312
#204902