Finite Group Databasebeta

← C2×#19146386 #25972813

Subgroups — C2×#19146386 #25972813

Order 11008.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583710C211yesmaximal, characteristic, complemented
2C2×#14583707C211yesmaximal, characteristic, complemented
3C2×#14583706C211yesmaximal, characteristic, complemented
4#19146386C2116yesmaximal, direct product factor
5C2×#14583270C211yesmaximal, characteristic, complemented
6C2×#14583164C211yesmaximal, characteristic, complemented
7C2×#14583162C211yesmaximal, characteristic, complemented
8C2×#14583160C211yesmaximal, characteristic, complemented
9C2×#14583159C211yesmaximal, characteristic, complemented
10C2×#14583082C211yesmaximal, characteristic, complemented
11C2×#14583080C211yesmaximal, characteristic, complemented
12C2×#14583067C211yesmaximal, characteristic, complemented
13C2×#14583065C211yesmaximal, characteristic, complemented
14C2×#14583016C211yesmaximal, characteristic, complemented
15C2×#14583014C211yesmaximal, characteristic, complemented
16C2×C43×#577C211yesmaximal, characteristic, complemented
17C2×#13063372C2211yescharacteristic
18C2×#13063371C2211yescharacteristic, complemented
19#14583710—24no—
20#14583710C2218yescomplemented
21#14583707—24no—
22#14583707C2218yescomplemented
23#14583706—24no—
24#14583706C2218yescomplemented
25C2×#13063357—21no—
26C2×#13063356—21no—
27C2×#13063356C2211yescharacteristic, complemented
28C2×#13063355—21no—
29C2×#13063355C2211yescharacteristic, complemented
30C2×#13063355C2211yescharacteristic, complemented
31C2×#13063351—21no—
32C2×#13063351C2211yescharacteristic
33C2×#13063350—21no—
34C2×#13063350C2211yescharacteristic
35C2×#13063350C2211yescharacteristic
36C2×#13063349—21no—
37C2×#13063346—21no—
38C2×#13063345—21no—
39C2×#13063345—21no—
40C2×#13063345C2211yescharacteristic
41C22×#10621873C2211yescharacteristic, complemented
42C22×#10621883—21no—
43C22×#10621883C2211yescharacteristic, complemented
44C22×#10621884—21no—
45C22×#10621884C2211yescharacteristic, complemented
46C2×SD16×D43—21no—
47C2×#13063332C2211yescharacteristic, complemented
48C2×#13063332C2211yescharacteristic, complemented
49C2×#13063331C2211yescharacteristic, complemented
50C2×#13063323C2211yescharacteristic, complemented
51C2×#13063321C2211yescharacteristic
52#14583270C2218yescomplemented
53#14583164C2218yescomplemented
54#14583162C2218yescomplemented
55#14583160C2218yescomplemented
56#14583159C2218yescomplemented
57#14583082C2218yescomplemented
58#14583080C2218yescomplemented
59#14583067C2218yescomplemented
60#14583065C2218yescomplemented
61#14583016C2218yescomplemented
62#14583014C2218yescomplemented
63C2×#13063261C2211yescharacteristic, complemented
64C2×#13063260C2211yescharacteristic, complemented
65C2×#13063252C2211yescharacteristic, complemented
66C2×#13063252C2211yescharacteristic, complemented
67C2×#13063252C2211yescharacteristic, complemented
68C2×#13063251C2211yescharacteristic, complemented
69C2×#13063244C2211yescharacteristic, complemented
70C2×#13063243C2211yescharacteristic, complemented
71C2×#13063242C2211yescharacteristic, complemented
72C2×#13063241C2211yescharacteristic, complemented
73C2×C8×Dic43C2211yescharacteristic, complemented
74C2×2−1+4×C43C2211yescharacteristic
75C2×H(5,𝔽2)×C43C2211yescharacteristic, complemented
76C43×#577—24no—
77C43×#577C2218yescomplemented
78C2×#137×C43—21no—
79C2×#137×C43C2211yescharacteristic, complemented
80C2×AGL(1,ℤ/8)×C43—21no—
81C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
82C2×#135×C43—21no—
83C2×#135×C43C2211yescharacteristic
84C22×SD16×C43—21no—
85C22×SD16×C43C2211yescharacteristic, complemented
86C2×#131×C43C2211yescharacteristic, complemented
87#13063372—22no—
88#13063372—22no—
89#13063372—41no—
90#13063372C2314yes—
91#13063371—22no—
92#13063371—22no—
93#13063371—41no—
94#13063371C2314yescomplemented
95C2×#10621902—21no—
96C2×#10621898—21no—
97C2×#10621898—21no—
98C2×#10621898C2311yescharacteristic
99C2×#10621900—21no—
100C2×#10621900—41no—
101C22×Dic86—21no—
102C22×Dic86C2311yescharacteristic
103C2×Q8×D43—21no—
104C22×D172—21no—
105C22×D172C2311yescharacteristic
106C22×C22⋊D43—41no—
107C2×D4×D43—21no—
108C2×D4×D43—41no—
109#13063357—28no—
110#13063356—22no—
111#13063356—28no—
112#13063356C2314yescomplemented
113#13063355—22no—
114#13063355—22no—
115#13063355—28no—
116#13063355C2314yescomplemented
117#13063355C2314yescomplemented
118#13063351—22no—
119#13063351—28no—
120#13063351C2314yes—
121#13063350—22no—
122#13063350—22no—
123#13063350—28no—
124#13063350C2314yes—
125#13063350C2314yes—
126#13063349—28no—
127#13063346—28no—
128#13063345—28no—
129#13063345—28no—
130#13063345D414yescomplemented
131#13063345C2314yes—
132C2×#10621885—21no—
133C2×#10621885—21no—
134C2×#10621885—21no—
135C2×#10621885D411yescharacteristic, complemented
136C2×#10621873—21no—
137C2×#10621873—21no—
138C2×#10621873—22no—
139C2×#10621873C2314yescomplemented
140C2×#10621883—21no—
141C2×#10621883—21no—
142C2×#10621883—21no—
143C2×#10621883—28no—
144C2×#10621883—21no—
145C2×#10621883—21no—
146C2×#10621883—22no—
147C2×#10621883D411yescharacteristic, complemented
148C2×#10621883C2314yescomplemented
149C2×#10621884—21no—
150C2×#10621884—21no—
151C2×#10621884—21no—
152C2×#10621884—28no—
153C2×#10621884—21no—
154C2×#10621884—21no—
155C2×#10621884—22no—
156C2×#10621884D411yescharacteristic, complemented
157C2×#10621884C2314yescomplemented
158SD16×D43—28no—
159C2×#10621882—21no—
160C2×#10621882—21no—
161C2×#10621882—21no—
162C2×#10621882D411yescharacteristic, complemented
163#13063332—22no—
164#13063332—22no—
165#13063332C2314yescomplemented
166#13063332C2314yescomplemented
167#13063331—22no—
168#13063331C2314yescomplemented
169C2×#10621877—21no—
170C2×#10621877—21no—
171C2×#10621877C2311yescharacteristic
172C2×#10621877C2311yescharacteristic
173C2×#10621877C2311yescharacteristic
174C2×#10621872—21no—
175C22×C43⋊C8—21no—
176C22×C43⋊C8—21no—
177C22×C43⋊C8C2311yescharacteristic
178C2×C8×D43—21no—
179#13063323—41no—
180#13063323C2314yescomplemented
181#13063321—41no—
182#13063321C2314yes—
183C2×Dic43⋊C4—41no—
184C2×C4×Dic43C2311yescharacteristic
185#13063261C2314yescomplemented
186#13063260C2314yescomplemented
187#13063252C2314yescomplemented
188#13063252C2314yescomplemented
189#13063252C2314yescomplemented
190#13063251C2314yescomplemented
191#13063244C2314yescomplemented
192#13063243C2314yescomplemented
193#13063242C2314yescomplemented
194#13063241C2314yescomplemented
195C8×Dic43C2314yescomplemented
1962−1+4×C43—22no—
1972−1+4×C43—22no—
1982−1+4×C43—41no—
1992−1+4×C43C2314yes—
200H(5,𝔽2)×C43—22no—
201H(5,𝔽2)×C43—22no—
202H(5,𝔽2)×C43—41no—
203H(5,𝔽2)×C43C2314yescomplemented
204C2×#41×C43—21no—
205C2×#41×C43—21no—
206C2×#41×C43—21no—
207C2×#41×C43—21no—
208C2×#41×C43—41no—
209C2×#41×C43C2311yescharacteristic
210C2×#41×C43C2311yescharacteristic
211C2×#41×C43C2311yescharacteristic
212C22×Q8×C43—21no—
213C22×Q8×C43—21no—
214C22×Q8×C43C2311yescharacteristic
215C22×D4×C43—21no—
216C22×D4×C43—21no—
217C22×D4×C43—41no—
218C22×D4×C43C2311yescharacteristic
219#137×C43—22no—
220#137×C43—28no—
221#137×C43C2314yescomplemented
222AGL(1,ℤ/8)×C43—22no—
223AGL(1,ℤ/8)×C43—28no—
224AGL(1,ℤ/8)×C43C2314yes—
225#135×C43—28no—
226#135×C43D414yescomplemented
227#135×C43C2314yes—
228C2×Q16×C43—21no—
229C2×Q16×C43D411yescharacteristic, complemented
230C2×SD16×C43—21no—
231C2×SD16×C43—21no—
232C2×SD16×C43—28no—
233C2×SD16×C43—21no—
234C2×SD16×C43—21no—
235C2×SD16×C43—22no—
236C2×SD16×C43D411yescharacteristic, complemented
237C2×SD16×C43D411yescharacteristic, complemented
238C2×SD16×C43C2314yescomplemented
239C2×D8×C43—21no—
240C2×D8×C43D411yescharacteristic, complemented
241#131×C43—22no—
242#131×C43C2314yescomplemented
243C2×M16×C43—21no—
244C2×M16×C43C2311yescharacteristic
245C22×C8×C43—21no—
246C22×C8×C43C2311yescharacteristic
247C24×C43—21no—
248C24×C43—41no—
249C23×D43—21no—
250C23×D43—41no—
251#41×C43—21no—
252#41×C43—21no—
253#41×C43—21no—
254#41×C43—21no—
255#41×C43—21no—
256#41×C43—21no—
257#41×C43—24no—
258#41×C43—24no—
259#41×C43—24no—
260#41×C43—24no—
261#41×C43—44no—
262#41×C43—42no—
263#41×C43—42no—
264#41×C43—42no—
265#41×C43—42no—
266#41×C43—44no—
267#41×C43C2×D412yes—
268#41×C43C2×D412yes—
269#41×C43C2×D412yes—
270#41×C43C2412yes—
271#41×C43C2412yes—
272#41×C43C2412yes—
273C2×Q8×C43—21no—
274C2×Q8×C43—24no—
275C2×Q8×C43—24no—
276C2×Q8×C43—21no—
277C2×Q8×C43—21no—
278C2×Q8×C43—21no—
279C2×Q8×C43—21no—
280C2×Q8×C43—41no—
281C2×Q8×C43—42no—
282C2×Q8×C43—42no—
283C2×Q8×C43C2×D411yescharacteristic
284C2×Q8×C43C2×D411yescharacteristic
285C2×Q8×C43C2×D411yescharacteristic
286C2×Q8×C43C2412yes—
287C2×D4×C43—21no—
288C2×D4×C43—21no—
289C2×D4×C43—21no—
290C2×D4×C43—21no—
291C2×D4×C43—24no—
292C2×D4×C43—24no—
293C2×D4×C43—21no—
294C2×D4×C43—21no—
295C2×D4×C43—21no—
296C2×D4×C43—21no—
297C2×D4×C43—41no—
298C2×D4×C43—41no—
299C2×D4×C43—41no—
300C2×D4×C43—44no—
301C2×D4×C43—42no—
302C2×D4×C43—42no—
303C2×D4×C43—44no—
304C2×D4×C43C2×D411yescharacteristic
305C2×D4×C43C2×D411yescharacteristic
306C2×D4×C43C2×D411yescharacteristic
307C2×D4×C43C2412yes—
308C22×C4×C43—21no—
309C22×C4×C43—21no—
310C22×C4×C43—21no—
311C22×C4×C43—21no—
312C22×C4×C43—41no—
313C22×C4×C43—41no—
314C22×C4×C43—41no—
315C22×C4×C43C2411yescharacteristic
316C2×C22⋊D43—21no—
317C2×C22⋊D43—44no—
318C2×C22⋊D43—41no—
319C2×C22⋊D43—41no—
320C2×C22⋊D43—84no—
321C22×Dic43—21no—
322C22×Dic43—21no—
323C22×Dic43—41no—
324#10621902—24no—
325#10621902—42no—
326Q8×D43—24no—
327Q8×D43—42no—
328#10621900—24no—
329#10621900—42no—
330#10621900—44no—
331#10621900—44no—
332D4×D43—24no—
333D4×D43—44no—
334D4×D43—42no—
335D4×D43—44no—
336#10621898—21no—
337#10621898—21no—
338#10621898—24no—
339#10621898—24no—
340#10621898—42no—
341#10621898—42no—
342#10621898C2×D412yes—
343#10621898C2412yes—
344C2×D172—21no—
345C2×D172—21no—
346C2×D172—21no—
347C2×D172—21no—
348C2×D172—21no—
349C2×D172—24no—
350C2×D172—41no—
351C2×D172—42no—
352C2×D172C2×D411yescharacteristic
353C2×D172C2412yes—
354C2×C4×D43—21no—
355C2×C4×D43—41no—
356C2×C4×D43—41no—
357C2×Dic86—21no—
358C2×Dic86—21no—
359C2×Dic86—21no—
360C2×Dic86—21no—
361C2×Dic86—24no—
362C2×Dic86—21no—
363C2×Dic86—42no—
364C2×Dic86—41no—
365C2×Dic86C2×D411yescharacteristic
366C2×Dic86C2412yes—
367Q16×C43—24no—
368Q16×C43C2×D414yescomplemented
369SD16×C43—24no—
370SD16×C43—24no—
371SD16×C43—24no—
372SD16×C43—24no—
373SD16×C43C2×D414yescomplemented
374SD16×C43C2×D414yescomplemented
375D8×C43—24no—
376D8×C43C2×D414yescomplemented
377M16×C43—21no—
378M16×C43—24no—
379M16×C43C2412yes—
380C2×C8×C43—21no—
381C2×C8×C43—24no—
382C2×C8×C43C2×D411yescharacteristic
383C2×C8×C43C2×D411yescharacteristic
384C2×C8×C43C2×D412yes—
385C2×C8×C43C2412yes—
386#10621885—24no—
387#10621885—24no—
388#10621885—24no—
389#10621885C2×D414yescomplemented
390#10621884—24no—
391#10621884—24no—
392#10621884—24no—
393#10621884—24no—
394#10621884—24no—
395#10621884C2×D414yescomplemented
396#10621883—24no—
397#10621883—24no—
398#10621883—24no—
399#10621883—24no—
400#10621883—24no—
401#10621883C2×D414yescomplemented
402#10621882—24no—
403#10621882—24no—
404#10621882—24no—
405#10621882C2×D414yescomplemented
406Dic43⋊C4—44no—
407C4×Dic43—21no—
408C4×Dic43C2412yes—
409#10621877—21no—
410#10621877—21no—
411#10621877—21no—
412#10621877—24no—
413#10621877—24no—
414#10621877C2412yes—
415#10621877C2412yes—
416#10621877C2412yes—
417C2×C43⋊C8—21no—
418C2×C43⋊C8—21no—
419C2×C43⋊C8—21no—
420C2×C43⋊C8—24no—
421C2×C43⋊C8—24no—
422C2×C43⋊C8C2×D411yescharacteristic
423C2×C43⋊C8C2×D411yescharacteristic
424C2×C43⋊C8C2×D412yes—
425C2×C43⋊C8C2412yes—
426#10621873—24no—
427#10621873—24no—
428#10621872—24no—
429C8×D43—24no—
430C23×C43—21no—
431C23×C43—21no—
432C23×C43—21no—
433C23×C43—22no—
434C23×C43—44no—
435C23×C43—41no—
436C23×C43—41no—
437C23×C43—82no—
438C23×C43—162no—
439C23×C43H(5,𝔽2)11yescharacteristic
440C22×D43—21no—
441C22×D43—22no—
442C22×D43—44no—
443C22×D43—41no—
444C22×D43—41no—
445C22×D43—82no—
446C22×D43—162no—
447Q8×C43—21no—
448Q8×C43—21no—
449Q8×C43—21no—
450Q8×C43—22no—
451Q8×C43—22no—
452Q8×C43—44no—
453Q8×C43—41no—
454Q8×C43—41no—
455Q8×C43C22×D412yes—
456Q8×C43C22×D412yes—
457Q8×C43C22×D412yes—
458D4×C43—22no—
459D4×C43—22no—
460D4×C43—22no—
461D4×C43—22no—
462D4×C43—22no—
463D4×C43—22no—
464D4×C43—21no—
465D4×C43—21no—
466D4×C43—21no—
467D4×C43—22no—
468D4×C43—22no—
469D4×C43—44no—
470D4×C43—44no—
471D4×C43—44no—
472D4×C43—41no—
473D4×C43—41no—
474D4×C43C22×D412yes—
475D4×C43C22×D412yes—
476D4×C43C22×D412yes—
477C2×C4×C43—21no—
478C2×C4×C43—21no—
479C2×C4×C43—21no—
480C2×C4×C43—22no—
481C2×C4×C43—22no—
482C2×C4×C43—22no—
483C2×C4×C43—22no—
484C2×C4×C43—22no—
485C2×C4×C43—22no—
486C2×C4×C43—22no—
487C2×C4×C43—44no—
488C2×C4×C43—44no—
489C2×C4×C43—44no—
490C2×C4×C43—41no—
491C2×C4×C43—41no—
492C2×C4×C43C22×D411yescharacteristic
493C2×C4×C43C22×D411yescharacteristic
494C2×C4×C43C22×D411yescharacteristic
495C2×C4×C43C22×D411yescharacteristic
496C2×C4×C43H(5,𝔽2)11yescharacteristic
497C2×C4×C43C2511yescharacteristic
498C22⋊D43—22no—
499C22⋊D43—22no—
500C22⋊D43—44no—
501C22⋊D43—44no—
502C22⋊D43—88no—
503C2×Dic43—24no—
504C2×Dic43—21no—
505C2×Dic43—22no—
506C2×Dic43—22no—
507C2×Dic43—44no—
508C2×Dic43—41no—
509C2×Dic43—41no—
510D172—21no—
511D172—22no—
512D172—22no—
513D172—44no—
514D172—41no—
515D172—41no—
516D172C22×D412yes—
517C4×D43—22no—
518C4×D43—22no—
519C4×D43—44no—
520C4×D43—44no—
521Dic86—21no—
522Dic86—22no—
523Dic86—22no—
524Dic86—44no—
525Dic86—41no—
526Dic86—41no—
527Dic86C22×D412yes—
528C8×C43—22no—
529C8×C43C22×D412yes—
530C8×C43C22×D412yes—
531C43⋊C8—22no—
532C43⋊C8—22no—
533C43⋊C8—22no—
534C43⋊C8C22×D412yes—
535C43⋊C8C22×D412yes—
536C2×#3291—431nomaximal, Sylow
537C22×C43—22no—
538C22×C43—22no—
539C22×C43—22no—
540C22×C43—22no—
541C22×C43—42no—
542C22×C43—42no—
543C22×C43—42no—
544C22×C43—42no—
545C22×C43—82no—
546C22×C43—82no—
547C22×C43—161no—
548C22×C43—164no—
549C22×C43D4211yescharacteristic
550C22×C43D4211yescharacteristic
551C22×C43C2×H(5,𝔽2)11yescharacteristic
552C2×D43—22no—
553C2×D43—42no—
554C2×D43—42no—
555C2×D43—82no—
556C2×D43—82no—
557C2×D43—164no—
558C2×D43—161no—
559C4×C43—22no—
560C4×C43—22no—
561C4×C43—22no—
562C4×C43—42no—
563C4×C43D4211yescharacteristic
564C4×C43D4211yescharacteristic
565C4×C43C23×D411yescharacteristic
566C4×C43C23×D411yescharacteristic
567Dic43—24no—
568Dic43—22no—
569Dic43—42no—
570C2×#577—431no—
571C2×#577—431no—
572C2×#577—431no—
573C2×#577D4311yescharacteristic, complemented
574#3291—4316no—
575C2×#492—431no—
576C2×#471—431no—
577C2×#471—431no—
578C2×#471—431no—
579C2×#471—431no—
580C2×#456—431no—
581C2×#456—431no—
582C2×#453—431no—
583C2×#453—431no—
584C2×#443—431no—
585C2×#443—431no—
586C2×C43—21no—
587C2×C43—21no—
588C2×C43—42no—
589C2×C43—42no—
590C2×C43—42no—
591C2×C43—82no—
592C2×C43#329112yescomplemented
593C2×C43C2×D4211yescharacteristic
594D43—42no—
595D43—82no—
596C2×2−1+4—431no—
597C2×2−1+4C2×D4311yescharacteristic
598C2×H(5,𝔽2)—431no—
599C2×H(5,𝔽2)C2×D4311yescharacteristic, complemented
600#577—24no—
601#577—438no—
602#577—438no—
603#577—438no—
604#577—864no—
605#577—864no—
606#577—864no—
607#577C2×D4318yescomplemented
608C2×#137—21no—
609C2×#137—431no—
610C2×#137—431no—
611C2×#137—431no—
612C2×#137—861no—
613C2×#137—861no—
614C2×#137—861no—
615C2×#137C2×D4311yescharacteristic, complemented
616C2×AGL(1,ℤ/8)—21no—
617C2×AGL(1,ℤ/8)—431no—
618C2×AGL(1,ℤ/8)—431no—
619C2×AGL(1,ℤ/8)—431no—
620C2×AGL(1,ℤ/8)—861no—
621C2×AGL(1,ℤ/8)—861no—
622C2×AGL(1,ℤ/8)—861no—
623C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
624C2×#135—21no—
625C2×#135—431no—
626C2×#135—861no—
627C2×#135—861no—
628C2×#135—861no—
629C2×#135C2×D4311yescharacteristic
630C22×SD16—21no—
631C22×SD16—431no—
632C22×SD16—431no—
633C22×SD16—431no—
634C22×SD16—861no—
635C22×SD16—861no—
636C22×SD16—861no—
637C22×SD16C2×D4311yescharacteristic, complemented
638C2×#131—431no—
639C2×#131—431no—
640C2×#131—431no—
641C2×#131C2×D4311yescharacteristic, complemented
642C2×C4⋊Q8—431no—
643C2×#127—431no—
644#492—438no—
645#471—438no—
646#471—438no—
647#471—438no—
648#471—438no—
649#456—438no—
650#456—438no—
651#453—438no—
652#453—438no—
653#443—438no—
654#443—438no—
655C2×#108—431no—
656C2×#108—431no—
657C2×#104—431no—
658C2×#104—431no—
659C2×#104—431no—
660C2×#104—431no—
661C2×#101—431no—
662C2×#101—431no—
663C2×#100—431no—
664C2×#100—431no—
665C2×C4×C8—431no—
666C43C2×#329111yescharacteristic, complemented, Sylow
6672−1+4—22no—
6682−1+4—22no—
6692−1+4—41no—
6702−1+4—434no—
6712−1+4—862no—
6722−1+4—862no—
6732−1+4—1721no—
6742−1+4C22×D4314yes—
675H(5,𝔽2)—22no—
676H(5,𝔽2)—22no—
677H(5,𝔽2)—41no—
678H(5,𝔽2)—434no—
679H(5,𝔽2)—862no—
680H(5,𝔽2)—862no—
681H(5,𝔽2)—1721no—
682H(5,𝔽2)C22×D4314yescomplemented
683C2×#41—21no—
684C2×#41—21no—
685C2×#41—21no—
686C2×#41—21no—
687C2×#41—41no—
688C2×#41—431no—
689C2×#41—861no—
690C2×#41—861no—
691C2×#41—861no—
692C2×#41—861no—
693C2×#41—1721no—
694C2×#41C22×D4311yescharacteristic
695C2×#41C22×D4311yescharacteristic
696C2×#41C22×D4311yescharacteristic
697C22×Q8—21no—
698C22×Q8—21no—
699C22×Q8—431no—
700C22×Q8—861no—
701C22×Q8—861no—
702C22×Q8C22×D4311yescharacteristic
703C22×D4—21no—
704C22×D4—21no—
705C22×D4—41no—
706C22×D4—431no—
707C22×D4—861no—
708C22×D4—861no—
709C22×D4—1721no—
710C22×D4—1721no—
711C22×D4C22×D4311yescharacteristic
712#137—22no—
713#137—28no—
714#137—434no—
715#137—434no—
716#137—434no—
717#137—868no—
718#137—868no—
719#137—862no—
720#137—862no—
721#137—862no—
722#137—868no—
723#137C22×D4314yescomplemented
724AGL(1,ℤ/8)—22no—
725AGL(1,ℤ/8)—28no—
726AGL(1,ℤ/8)—434no—
727AGL(1,ℤ/8)—434no—
728AGL(1,ℤ/8)—434no—
729AGL(1,ℤ/8)—868no—
730AGL(1,ℤ/8)—868no—
731AGL(1,ℤ/8)—862no—
732AGL(1,ℤ/8)—862no—
733AGL(1,ℤ/8)—862no—
734AGL(1,ℤ/8)—868no—
735AGL(1,ℤ/8)C22×D4314yes—
736#135—28no—
737#135—434no—
738#135—434no—
739#135—868no—
740#135—868no—
741#135—868no—
742#135C22⋊D4314yescomplemented
743#135C22×D4314yes—
744C2×Q16—21no—
745C2×Q16—431no—
746C2×Q16—861no—
747C2×Q16—861no—
748C2×Q16—861no—
749C2×Q16C22⋊D4311yescharacteristic, complemented
750C2×SD16—21no—
751C2×SD16—21no—
752C2×SD16—28no—
753C2×SD16—21no—
754C2×SD16—21no—
755C2×SD16—22no—
756C2×SD16—431no—
757C2×SD16—431no—
758C2×SD16—434no—
759C2×SD16—434no—
760C2×SD16—434no—
761C2×SD16—861no—
762C2×SD16—861no—
763C2×SD16—862no—
764C2×SD16—861no—
765C2×SD16—861no—
766C2×SD16—862no—
767C2×SD16—868no—
768C2×SD16—868no—
769C2×SD16—861no—
770C2×SD16—861no—
771C2×SD16—861no—
772C2×SD16—861no—
773C2×SD16—861no—
774C2×SD16—861no—
775C2×SD16—868no—
776C2×SD16—861no—
777C2×SD16—861no—
778C2×SD16—862no—
779C2×SD16C22⋊D4311yescharacteristic, complemented
780C2×SD16C22⋊D4311yescharacteristic, complemented
781C2×SD16C22×D4314yescomplemented
782C2×D8—21no—
783C2×D8—431no—
784C2×D8—861no—
785C2×D8—861no—
786C2×D8—861no—
787C2×D8C22⋊D4311yescharacteristic, complemented
788#131—22no—
789#131—434no—
790#131—434no—
791#131—434no—
792#131—862no—
793#131—862no—
794#131—862no—
795#131C22×D4314yescomplemented
796C2×M16—21no—
797C2×M16—431no—
798C2×M16—431no—
799C2×M16—431no—
800C2×M16—861no—
801C2×M16—861no—
802C2×M16—861no—
803C2×M16C22×D4311yescharacteristic
804C22×C8—21no—
805C22×C8—431no—
806C22×C8—861no—
807C22×C8—861no—
808C22×C8—861no—
809C22×C8C22×D4311yescharacteristic
810C4⋊Q8—434no—
811C4⋊Q8—1721no—
812#127—434no—
813#127—1721no—
814C2×C4⋊C4—1721no—
815C2×C42—431no—
816#108—434no—
817#108—434no—
818#104—434no—
819#104—434no—
820#104—434no—
821#104—434no—
822#101—434no—
823#101—434no—
824#100—434no—
825#100—434no—
826C4×C8—434no—
827C24—21no—
828C24—41no—
829C24—861no—
830C24—1721no—
831#41—21no—
832#41—21no—
833#41—21no—
834#41—21no—
835#41—21no—
836#41—21no—
837#41—24no—
838#41—24no—
839#41—24no—
840#41—24no—
841#41—44no—
842#41—42no—
843#41—42no—
844#41—42no—
845#41—42no—
846#41—44no—
847#41—432no—
848#41—432no—
849#41—864no—
850#41—864no—
851#41—861no—
852#41—861no—
853#41—864no—
854#41—864no—
855#41—1722no—
856#41—1722no—
857#41—1724no—
858#41—1722no—
859#41—1722no—
860#41—1724no—
861#41D4×D4312yes—
862#41C2×C22⋊D4312yes—
863#41C2×C22⋊D4312yes—
864#41C23×D4312yes—
865#41C23×D4312yes—
866#41C23×D4312yes—
867C2×Q8—21no—
868C2×Q8—24no—
869C2×Q8—24no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—41no—
875C2×Q8—42no—
876C2×Q8—42no—
877C2×Q8—431no—
878C2×Q8—432no—
879C2×Q8—864no—
880C2×Q8—861no—
881C2×Q8—864no—
882C2×Q8—861no—
883C2×Q8—861no—
884C2×Q8—861no—
885C2×Q8—861no—
886C2×Q8—1721no—
887C2×Q8—1722no—
888C2×Q8—1722no—
889C2×Q8D4×D4311yescharacteristic
890C2×Q8C2×C22⋊D4311yescharacteristic
891C2×Q8C2×C22⋊D4311yescharacteristic
892C2×Q8C23×D4312yes—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—24no—
897C2×D4—24no—
898C2×D4—21no—
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—41no—
906C2×D4—41no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—41no—
910C2×D4—431no—
911C2×D4—432no—
912C2×D4—864no—
913C2×D4—861no—
914C2×D4—864no—
915C2×D4—861no—
916C2×D4—861no—
917C2×D4—861no—
918C2×D4—861no—
919C2×D4—861no—
920C2×D4—3444no—
921C2×D4—1722no—
922C2×D4—1721no—
923C2×D4—1722no—
924C2×D4—1724no—
925C2×D4—1721no—
926C2×D4—1724no—
927C2×D4—1724no—
928C2×D4—1721no—
929C2×D4D4×D4311yescharacteristic
930C2×D4C2×C22⋊D4311yescharacteristic
931C2×D4C2×C22⋊D4311yescharacteristic
932C2×D4C23×D4312yes—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—861no—
941C22×C4—861no—
942C22×C4—861no—
943C22×C4—1721no—
944C22×C4—1721no—
945C22×C4—1721no—
946C22×C4C23×D4311yescharacteristic
947Q16—24no—
948Q16—434no—
949Q16—864no—
950Q16—864no—
951Q16—864no—
952Q16C2×C22⋊D4314yescomplemented
953SD16—24no—
954SD16—24no—
955SD16—24no—
956SD16—24no—
957SD16—434no—
958SD16—434no—
959SD16—864no—
960SD16—864no—
961SD16—864no—
962SD16—864no—
963SD16—864no—
964SD16—864no—
965SD16—864no—
966SD16—864no—
967SD16—864no—
968SD16—864no—
969SD16—864no—
970SD16—864no—
971SD16C2×C22⋊D4314yescomplemented
972SD16C2×C22⋊D4314yescomplemented
973D8—24no—
974D8—434no—
975D8—864no—
976D8—864no—
977D8—864no—
978D8C2×C22⋊D4314yescomplemented
979M16—21no—
980M16—24no—
981M16—432no—
982M16—432no—
983M16—432no—
984M16—864no—
985M16—864no—
986M16—861no—
987M16—861no—
988M16—861no—
989M16—864no—
990M16C23×D4312yes—
991C2×C8—21no—
992C2×C8—24no—
993C2×C8—431no—
994C2×C8—431no—
995C2×C8—432no—
996C2×C8—432no—
997C2×C8—864no—
998C2×C8—864no—
999C2×C8—861no—
1000C2×C8—861no—
1001C2×C8—861no—
1002C2×C8—864no—
1003C2×C8C2×C22⋊D4311yescharacteristic
1004C2×C8C2×C22⋊D4311yescharacteristic
1005C2×C8C2×C22⋊D4312yes—
1006C2×C8C23×D4312yes—
1007C4⋊C4—1724no—
1008C42—432no—
1009C42—861no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—44no—
1015C23—41no—
1016C23—41no—
1017C23—82no—
1018C23—162no—
1019C23—861no—
1020C23—862no—
1021C23—3442no—
1022C23—1724no—
1023C23—1721no—
1024C23—1721no—
1025C23—6882no—
1026C23#1306337011yescharacteristic
1027Q8—21no—
1028Q8—21no—
1029Q8—21no—
1030Q8—22no—
1031Q8—22no—
1032Q8—44no—
1033Q8—41no—
1034Q8—41no—
1035Q8—432no—
1036Q8—861no—
1037Q8—862no—
1038Q8—862no—
1039Q8—1724no—
1040Q8—1721no—
1041Q8—1721no—
1042Q8C2×D4×D4312yes—
1043Q8C22×C22⋊D4312yes—
1044Q8C22×C22⋊D4312yes—
1045D4—22no—
1046D4—22no—
1047D4—22no—
1048D4—22no—
1049D4—22no—
1050D4—22no—
1051D4—22no—
1052D4—22no—
1053D4—21no—
1054D4—21no—
1055D4—21no—
1056D4—44no—
1057D4—44no—
1058D4—44no—
1059D4—41no—
1060D4—41no—
1061D4—432no—
1062D4—862no—
1063D4—862no—
1064D4—862no—
1065D4—862no—
1066D4—861no—
1067D4—3448no—
1068D4—1724no—
1069D4—1724no—
1070D4—1724no—
1071D4—1721no—
1072D4—1721no—
1073D4C2×D4×D4312yes—
1074D4C22×C22⋊D4312yes—
1075D4C22×C22⋊D4312yes—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—44no—
1087C2×C4—44no—
1088C2×C4—44no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—864no—
1092C2×C4—862no—
1093C2×C4—861no—
1094C2×C4—862no—
1095C2×C4—862no—
1096C2×C4—862no—
1097C2×C4—1724no—
1098C2×C4—1724no—
1099C2×C4—1724no—
1100C2×C4—1721no—
1101C2×C4—1721no—
1102C2×C4C2×D4×D4311yescharacteristic
1103C2×C4C2×D4×D4311yescharacteristic
1104C2×C4C22×C22⋊D4311yescharacteristic
1105C2×C4C22×C22⋊D4311yescharacteristic
1106C2×C4#1306337011yescharacteristic
1107C2×C4C24×D4311yescharacteristic
1108C8—22no—
1109C8—432no—
1110C8—432no—
1111C8—862no—
1112C8—862no—
1113C8—862no—
1114C8C22×C22⋊D4312yes—
1115C8C22×C22⋊D4312yes—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—22no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—82no—
1125C22—82no—
1126C22—161no—
1127C22—164no—
1128C22—862no—
1129C22—3442no—
1130C22—3442no—
1131C22—1722no—
1132C22—1722no—
1133C22—6881no—
1134C22—6884no—
1135C22D4×C22⋊D4311yescharacteristic
1136C22D4×C22⋊D4311yescharacteristic
1137C22C2×#1306337011yescharacteristic
1138C4—22no—
1139C4—22no—
1140C4—22no—
1141C4—42no—
1142C4—864no—
1143C4—862no—
1144C4—1722no—
1145C4D4×C22⋊D4311yescharacteristic
1146C4D4×C22⋊D4311yescharacteristic
1147C4C22×D4×D4311yescharacteristic
1148C4C23×C22⋊D4311yescharacteristic
1149C2—21no—
1150C2—21no—
1151C2—42no—
1152C2—42no—
1153C2—42no—
1154C2—82no—
1155C2—3442no—
1156C2—1722no—
1157C2#1914638612yesdirect product factor
1158C2C2×D4×C22⋊D4311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#577C2
socleC22×C43D42
hypercenterC2×#577D43
hypocenterC43C2×#3291
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#577

Complements

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

NH ≅ G/Ntype
1. C2×#14583710C2semidirect
2. C2×#14583707C2semidirect
3. C2×#14583706C2semidirect
4. #19146386C2direct (N × H)
5. C2×#14583270C2semidirect
6. C2×#14583164C2semidirect
7. C2×#14583162C2semidirect
8. C2×#14583160C2semidirect
9. C2×#14583159C2semidirect
10. C2×#14583082C2semidirect
11. C2×#14583080C2semidirect
12. C2×#14583067C2semidirect
13. C2×#14583065C2semidirect
14. C2×#14583016C2semidirect
15. C2×#14583014C2semidirect
16. C2×C43×#577C2semidirect
18. C2×#13063371C22semidirect
20. #14583710C22semidirect
22. #14583707C22semidirect
24. #14583706C22semidirect
27. C2×#13063356C22semidirect
29. C2×#13063355C22semidirect
30. C2×#13063355C22semidirect
41. C22×#10621873C22semidirect
43. C22×#10621883C22semidirect
45. C22×#10621884C22semidirect
47. C2×#13063332C22semidirect
48. C2×#13063332C22semidirect
49. C2×#13063331C22semidirect
50. C2×#13063323C22semidirect
52. #14583270C22semidirect
53. #14583164C22semidirect
54. #14583162C22semidirect
55. #14583160C22semidirect
56. #14583159C22semidirect
57. #14583082C22semidirect
58. #14583080C22semidirect
59. #14583067C22semidirect
60. #14583065C22semidirect
61. #14583016C22semidirect
62. #14583014C22semidirect
63. C2×#13063261C22semidirect
64. C2×#13063260C22semidirect
65. C2×#13063252C22semidirect
66. C2×#13063252C22semidirect
67. C2×#13063252C22semidirect
68. C2×#13063251C22semidirect
69. C2×#13063244C22semidirect
70. C2×#13063243C22semidirect
71. C2×#13063242C22semidirect
72. C2×#13063241C22semidirect
73. C2×C8×Dic43C22semidirect
75. C2×H(5,𝔽2)×C43C22semidirect
77. C43×#577C22semidirect
79. C2×#137×C43C22semidirect
85. C22×SD16×C43C22semidirect
86. C2×#131×C43C22semidirect
94. #13063371C23semidirect
112. #13063356C23semidirect
116. #13063355C23semidirect
117. #13063355C23semidirect
130. #13063345D4semidirect
135. C2×#10621885D4semidirect
139. C2×#10621873C23semidirect
147. C2×#10621883D4semidirect
148. C2×#10621883C23semidirect
156. C2×#10621884D4semidirect
157. C2×#10621884C23semidirect
162. C2×#10621882D4semidirect
165. #13063332C23semidirect
166. #13063332C23semidirect
168. #13063331C23semidirect
180. #13063323C23semidirect
185. #13063261C23semidirect
186. #13063260C23semidirect
187. #13063252C23semidirect
188. #13063252C23semidirect
189. #13063252C23semidirect
190. #13063251C23semidirect
191. #13063244C23semidirect
192. #13063243C23semidirect
193. #13063242C23semidirect
194. #13063241C23semidirect
195. C8×Dic43C23semidirect
203. H(5,𝔽2)×C43C23semidirect
221. #137×C43C23semidirect
226. #135×C43D4semidirect
229. C2×Q16×C43D4semidirect
236. C2×SD16×C43D4semidirect
237. C2×SD16×C43D4semidirect
238. C2×SD16×C43C23semidirect
240. C2×D8×C43D4semidirect
242. #131×C43C23semidirect
368. Q16×C43C2×D4semidirect
373. SD16×C43C2×D4semidirect
374. SD16×C43C2×D4semidirect
376. D8×C43C2×D4semidirect
389. #10621885C2×D4semidirect
395. #10621884C2×D4semidirect
401. #10621883C2×D4semidirect
405. #10621882C2×D4semidirect
573. C2×#577D43semidirect
592. C2×C43#3291semidirect
599. C2×H(5,𝔽2)C2×D43semidirect
607. #577C2×D43semidirect
615. C2×#137C2×D43semidirect
637. C22×SD16C2×D43semidirect
641. C2×#131C2×D43semidirect
666. C43C2×#3291semidirect
682. H(5,𝔽2)C22×D43semidirect
723. #137C22×D43semidirect
742. #135C22⋊D43semidirect
749. C2×Q16C22⋊D43semidirect
779. C2×SD16C22⋊D43semidirect
780. C2×SD16C22⋊D43semidirect
781. C2×SD16C22×D43semidirect
787. C2×D8C22⋊D43semidirect
795. #131C22×D43semidirect
952. Q16C2×C22⋊D43semidirect
971. SD16C2×C22⋊D43semidirect
972. SD16C2×C22⋊D43semidirect
978. D8C2×C22⋊D43semidirect
1157. C2#19146386direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145837102
C2×#145837072
C2×#145837062
#191463862
C2×#145832702
C2×#145831642
C2×#145831622
C2×#145831602
C2×#145831592
C2×#145830822
C2×#145830802
C2×#145830672
C2×#145830652
C2×#145830162
C2×#145830142
C2×C43×#5772
C2×#329143