Finite Group Databasebeta

← #25972545

Subgroups — #25972545

Order 11008.

2674 conjugacy classes of subgroups.

The subgroup lattice has 1074 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583714C211yesmaximal, characteristic, complemented
2C2×#14583707C211yesmaximal, characteristic, complemented
3#19148382C211yesmaximal, characteristic, complemented
4#19146166C214yesmaximal, complemented
5#19146146C214yesmaximal, complemented
6#19146121C214yesmaximal, complemented
7#19146106C214yesmaximal, complemented
8C2×#14583291C211yesmaximal, characteristic, complemented
9#19144247C211yesmaximal, characteristic, complemented
10#19144236C211yesmaximal, characteristic, complemented
11#19144089C211yesmaximal, characteristic, complemented
12#19144078C211yesmaximal, characteristic, complemented
13#19143890C211yesmaximal, characteristic, complemented
14#19143888C211yesmaximal, characteristic, complemented
15#19143881C211yesmaximal, characteristic, complemented
16#19143870C211yesmaximal, characteristic, complemented
17#19143393C211yesmaximal, characteristic, complemented
18#19143313C211yesmaximal, characteristic, complemented
19C43×#3499C211yesmaximal, characteristic, complemented
20C2×#13063372C2211yescharacteristic
21C2×#13063371C2211yescharacteristic
22#14583714—28no—
23#14583707—28no—
24C2×#13063356C2211yescharacteristic
25C2×#13063356C2212yes—
26C2×#13063356C2211yescharacteristic
27C2×#13063356C2212yescomplemented
28C2×#13063355C2211yescharacteristic, complemented
29C2×#13063355C2212yescomplemented
30C2×#13063350C2212yes—
31C2×#13063350C2211yescharacteristic
32C2×#13063345C2212yes—
33C2×#13063345C2211yescharacteristic
34C2×#13063345C2212yescomplemented
35C22×#10621885C2211yescharacteristic, complemented
36C22×#10621885C2212yescomplemented
37C22×#10621885C2211yescharacteristic, complemented
38C22×#10621884C2211yescharacteristic
39C22×#10621884C2212yes—
40C22×#10621884C2211yescharacteristic
41C2×#13063332C2211yescharacteristic
42C2×#13063332C2211yescharacteristic, complemented
43#14583558C2214yes—
44#14583545C2214yes—
45#14583538—24no—
46#14583474—21no—
47#14583470C2211yescharacteristic
48#14583463C2211yescharacteristic
49#14583462—21no—
50#14583448—21no—
51C2×#13063313C2211yescharacteristic
52#124×D43—21no—
53C4×#10621898C2211yescharacteristic
54#14583291C2214yescomplemented
55#14583291C2214yescomplemented
56#14583155C2214yescomplemented
57#14583147C2214yescomplemented
58#14583138C2214yescomplemented
59#14583130C2214yescomplemented
60#14583121C2214yescomplemented
61#14583114C2214yescomplemented
62#14583106C2214yescomplemented
63#14583101C2214yescomplemented
64#14583061C2214yescomplemented
65#14583059C2214yes—
66#14583059C2214yescomplemented
67#14583055C2214yescomplemented
68#14583054C2214yescomplemented
69#14583049C2214yes—
70#14583044C2214yescomplemented
71#14583038C2214yescomplemented
72#14583009C2212yescomplemented
73#14583004C2212yescomplemented
74#14582999C2212yescomplemented
75#14582997C2212yescomplemented
76#14582971C2214yescomplemented
77#14582971C2214yescomplemented
78#14582935C2211yescharacteristic, complemented
79#14582923C2211yescharacteristic, complemented
80#14582908C2211yescharacteristic, complemented
81#14582908C2211yescharacteristic, complemented
82#14582907C2211yescharacteristic, complemented
83#14582903C2211yescharacteristic
84#14582895C2211yescharacteristic, complemented
85#14582893C2211yescharacteristic
86#14582866C2211yescharacteristic
87#14582866C2211yescharacteristic, complemented
88C2×#13063236C2211yescharacteristic, complemented
89C2×2−1+4×C43C2211yescharacteristic
90C2×2−1+4×C43C2211yescharacteristic, complemented
91D4×Q8×C43C2214yescomplemented
92C43×#547—24no—
93C43×#547C2214yescomplemented
94C43×#536—21no—
95C43×#536—21no—
96C43×#536C2211yescharacteristic
97C43×#536C2211yescharacteristic, complemented
98C43×#532—21no—
99C43×#532C2211yescharacteristic
100C2×C4⋊Q8×C43—21no—
101C2×C4⋊Q8×C43C2211yescharacteristic, complemented
102C4×#41×C43C2211yescharacteristic, complemented
103#13063372—24no—
104#13063372—42no—
105#13063371—24no—
106#13063371—42no—
107C2×#10621902—21no—
108C2×#10621898C2312yes—
109C2×#10621898C2312yes—
110C2×#10621898C2311yescharacteristic
111C2×#10621900—21no—
112C2×#10621900—22no—
113C22×Dic86C2311yescharacteristic
114C22×Dic86C2312yes—
115C2×Q8×D43—21no—
116C22×D172C2311yescharacteristic
117C22×D172C2312yes—
118C2×D4×D43—21no—
119C2×D4×D43—22no—
120#13063356—24no—
121#13063356—24no—
122#13063356—28no—
123#13063356—28no—
124#13063355—24no—
125#13063355—28no—
126#13063350—24no—
127#13063350—28no—
128#13063345—28no—
129#13063345—28no—
130#13063345D418yescomplemented
131C2×#10621885—28no—
132C2×#10621885—24no—
133C2×#10621885—42no—
134C2×#10621885C2312yes—
135C2×#10621885C2312yes—
136C2×#10621885C2312yes—
137C2×#10621885C2312yes—
138C2×#10621885C2312yes—
139C2×#10621885C2314yes—
140C2×#10621885C2311yescharacteristic
141C2×#10621883C2312yes—
142C2×#10621883C2311yescharacteristic
143C2×#10621884—28no—
144C2×#10621884—24no—
145C2×#10621884—42no—
146C2×#10621884C2312yes—
147C2×#10621884C2312yes—
148C2×#10621884C2312yes—
149C2×#10621884C2312yes—
150C2×#10621884C2312yes—
151C2×#10621884C2314yes—
152C2×#10621884C2311yescharacteristic
153C2×#10621882C2312yes—
154C2×#10621882C2311yescharacteristic
155#13063332—24no—
156#13063332—24no—
157C2×#10621877C2311yescharacteristic
158C2×#10621877C2311yescharacteristic
159C2×#10621877C2312yes—
160C2×#10621877C2312yes—
161C22×C43⋊C8C2311yescharacteristic
162C22×C43⋊C8C2312yes—
163C22×C43⋊C8C2312yes—
164C22×C43⋊C8C2311yescharacteristic
165#13063323—21no—
166#13063321—21no—
167#13063314—21no—
168#13063313—21no—
169#13063313—21no—
170#13063313C2314yes—
171#13063312—21no—
172#13063311—24no—
173#13063310—24no—
174#13063306—22no—
175#13063304C2314yes—
176#13063303—24no—
177#13063299C2314yes—
178#13063298—24no—
179#13063297—24no—
180#13063293—24no—
181#13063293—22no—
182C4×Dic86C2312yes—
183C4×D172C2312yes—
184C4×C22⋊D43—22no—
185(C22⋊D43)⋊C4—24no—
186#13063284C2311yescharacteristic
187#13063282—21no—
188C2×(C2×D43)⋊C4—22no—
189C22⋊C4×D43—24no—
190C42×D43—21no—
191#13063258C2312yes—
192#13063256C2312yes—
193C4⋊(C43⋊C8)C2314yes—
194#13063249C2314yes—
195#13063249C2312yes—
196#13063249C2314yes—
197#13063248C2312yes—
198#13063248C2314yes—
199#13063246C2312yes—
200#13063245C2312yes—
201#13063245C2314yes—
202C22⋊(C43⋊C8)C2314yes—
203C22⋊(C43⋊C8)C2314yes—
204#13063236C2312yes—
205#13063236C2312yes—
2062−1+4×C43—24no—
2072−1+4×C43—24no—
2082−1+4×C43—42no—
2092−1+4×C43—42no—
210C2×#41×C43—21no—
211C2×#41×C43—21no—
212C2×#41×C43—22no—
213C2×#41×C43—22no—
214C2×#41×C43C2312yes—
215C2×#41×C43C2312yes—
216C2×#41×C43C2311yescharacteristic
217C2×#41×C43C2311yescharacteristic
218C2×#41×C43C2311yescharacteristic
219C22×Q8×C43—21no—
220C22×Q8×C43—21no—
221C22×Q8×C43C2311yescharacteristic
222C22×Q8×C43C2311yescharacteristic
223C22×Q8×C43C2312yes—
224C22×Q8×C43C2312yes—
225C4⋊Q8×C43—21no—
226C4⋊Q8×C43—21no—
227C4⋊Q8×C43—24no—
228C4⋊Q8×C43—21no—
229C4⋊Q8×C43—21no—
230C4⋊Q8×C43D411yescharacteristic
231C4⋊Q8×C43C2314yes—
232#127×C43D411yescharacteristic
233#124×C43—21no—
234#124×C43—21no—
235#124×C43D411yescharacteristic
236#124×C43D411yescharacteristic
237#123×C43—22no—
238#123×C43—22no—
239#123×C43—24no—
240#123×C43—24no—
241C22⋊Q8×C43—24no—
242C22⋊Q8×C43—24no—
243C22⋊Q8×C43C2314yes—
244C22⋊Q8×C43C2314yes—
245#121×C43—24no—
246#121×C43D414yes—
247C4×Q8×C43C2312yes—
248C4×D4×C43—24no—
249C4×D4×C43—22no—
250C4×D4×C43C2312yes—
251C4×D4×C43C2314yes—
252#117×C43—21no—
253#117×C43C2311yescharacteristic
254C2×C4⋊C4×C43—22no—
255C2×C4⋊C4×C43—24no—
256C2×C42×C43—21no—
257C2×C42×C43C2311yescharacteristic
258C23×D43—22no—
259C23×D43—21no—
260#41×C43—22no—
261#41×C43—22no—
262#41×C43—22no—
263#41×C43—22no—
264#41×C43—22no—
265#41×C43—24no—
266#41×C43—24no—
267#41×C43—42no—
268#41×C43—42no—
269#41×C43—44no—
270#41×C43—44no—
271#41×C43—48no—
272#41×C43—48no—
273#41×C43C2×D414yes—
274C2×Q8×C43—22no—
275C2×Q8×C43—22no—
276C2×Q8×C43—21no—
277C2×Q8×C43—21no—
278C2×Q8×C43—24no—
279C2×Q8×C43—24no—
280C2×Q8×C43—22no—
281C2×Q8×C43—22no—
282C2×Q8×C43—22no—
283C2×Q8×C43—22no—
284C2×Q8×C43—42no—
285C2×Q8×C43—42no—
286C2×Q8×C43—44no—
287C2×Q8×C43—44no—
288C2×Q8×C43C2×D411yescharacteristic
289C2×Q8×C43C2×D411yescharacteristic
290C2×Q8×C43C2412yes—
291C2×Q8×C43C2412yes—
292C2×Q8×C43C2411yescharacteristic
293C2×D4×C43—21no—
294C2×D4×C43—22no—
295C2×D4×C43—22no—
296C2×D4×C43C2×D412yes—
297C2×D4×C43C2×D412yes—
298C2×D4×C43C2×D411yescharacteristic
299C2×D4×C43C2×D411yescharacteristic
300C2×D4×C43C2×D414yes—
301C2×D4×C43C2411yescharacteristic
302C22×C4×C43—21no—
303C22×C4×C43—22no—
304C22×C4×C43—22no—
305C22×C4×C43—22no—
306C22×C4×C43—21no—
307C22×C4×C43—21no—
308C22×C4×C43—22no—
309C22×C4×C43—22no—
310C22×C4×C43C2×D412yes—
311C22×C4×C43C2412yes—
312C22×C4×C43C2412yes—
313C22×C4×C43C2411yescharacteristic
314C2×C22⋊D43—21no—
315C2×C22⋊D43—22no—
316C2×C22⋊D43—22no—
317C2×C22⋊D43—24no—
318C22×Dic43—21no—
319C22×Dic43—22no—
320#10621902—44no—
321Q8×D43—44no—
322#10621900—44no—
323#10621900—48no—
324D4×D43—44no—
325D4×D43—48no—
326#10621898—22no—
327#10621898—24no—
328#10621898—24no—
329#10621898—42no—
330#10621898—42no—
331#10621898C2×D414yes—
332C2×D172—22no—
333C2×D172—21no—
334C2×D172—22no—
335C2×D172—22no—
336C2×D172—24no—
337C2×D172—42no—
338C2×D172C2412yes—
339C2×D172C2411yescharacteristic
340C2×C4×D43—21no—
341C2×C4×D43—22no—
342C2×C4×D43—22no—
343C2×C4×D43—22no—
344C2×Dic86—22no—
345C2×Dic86—22no—
346C2×Dic86—24no—
347C2×Dic86—22no—
348C2×Dic86—21no—
349C2×Dic86—42no—
350C2×Dic86C2412yes—
351C2×Dic86C2411yescharacteristic
352C4⋊C4×C43—24no—
353C4⋊C4×C43—24no—
354C4⋊C4×C43—24no—
355C4⋊C4×C43—24no—
356C4⋊C4×C43—22no—
357C4⋊C4×C43C2×D414yes—
358C4⋊C4×C43C2412yes—
359C22⋊C4×C43—22no—
360C22⋊C4×C43—21no—
361C22⋊C4×C43—24no—
362C22⋊C4×C43—24no—
363C22⋊C4×C43C2×D414yes—
364C22⋊C4×C43C2×D414yes—
365C42×C43—21no—
366C42×C43—22no—
367C42×C43C2×D411yescharacteristic
368C42×C43C2×D411yescharacteristic
369C42×C43C2412yes—
370C22⋊Dic43—24no—
371C22⋊Dic43—21no—
372#10621885—24no—
373#10621885—24no—
374#10621885—24no—
375#10621885—24no—
376#10621885—24no—
377#10621885—44no—
378#10621885C2×D414yes—
379#10621884—24no—
380#10621884—24no—
381#10621884—24no—
382#10621884—24no—
383#10621884—24no—
384#10621884—44no—
385#10621884C2×D414yes—
386#10621883—24no—
387#10621883C2×D414yes—
388#10621882—24no—
389#10621882C2×D414yes—
390(C2×D43)⋊C4—24no—
391(C2×D43)⋊C4—24no—
392(C2×D43)⋊C4—24no—
393(C2×D43)⋊C4—22no—
394C4⋊Dic43C2412yes—
395Dic43⋊C4—22no—
396Dic43⋊C4—24no—
397C4×Dic43—21no—
398C4×Dic43—22no—
399#10621877—22no—
400#10621877—22no—
401#10621877—24no—
402#10621877—24no—
403C2×C43⋊C8—22no—
404C2×C43⋊C8—24no—
405C2×C43⋊C8—24no—
406C2×C43⋊C8C2×D414yes—
407C2×C43⋊C8C2412yes—
408C2×C43⋊C8C2412yes—
409C2×C43⋊C8C2412yes—
410C2×C43⋊C8C2411yescharacteristic
411C2×C43⋊C8C2411yescharacteristic
412C23×C43—21no—
413C23×C43C22×D412yes—
414C23×C43C22×D412yes—
415C23×C43C22×D411yescharacteristic
416C22×D43—21no—
417C22×D43—22no—
418C22×D43—44no—
419C22×D43—42no—
420C22×D43—84no—
421C22×D43—82no—
422Q8×C43—22no—
423Q8×C43—22no—
424Q8×C43—21no—
425Q8×C43—22no—
426Q8×C43—22no—
427Q8×C43—22no—
428Q8×C43—22no—
429Q8×C43—44no—
430Q8×C43—44no—
431Q8×C43—42no—
432Q8×C43—42no—
433Q8×C43C22×D412yes—
434D4×C43—24no—
435D4×C43—24no—
436D4×C43—24no—
437D4×C43—22no—
438D4×C43—22no—
439D4×C43—21no—
440D4×C43—44no—
441D4×C43—44no—
442D4×C43—44no—
443D4×C43C22×D412yes—
444C2×C4×C43—21no—
445C2×C4×C43—24no—
446C2×C4×C43—22no—
447C2×C4×C43—22no—
448C2×C4×C43—22no—
449C2×C4×C43—22no—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—22no—
453C2×C4×C43—42no—
454C2×C4×C43—44no—
455C2×C4×C43—44no—
456C2×C4×C43—44no—
457C2×C4×C43—44no—
458C2×C4×C43—44no—
459C2×C4×C43—42no—
460C2×C4×C43—42no—
461C2×C4×C43C22×D412yes—
462C2×C4×C43C22×D412yes—
463C2×C4×C43C22×D412yes—
464C2×C4×C43C22×D412yes—
465C2×C4×C43C22×D412yes—
466C2×C4×C43C22×D411yescharacteristic
467C2×C4×C43H(5,𝔽2)12yes—
468C2×C4×C43C2511yescharacteristic
469C22⋊D43—24no—
470C22⋊D43—44no—
471C22⋊D43—44no—
472C22⋊D43—84no—
473C2×Dic43—21no—
474C2×Dic43—22no—
475C2×Dic43—22no—
476C2×Dic43—44no—
477C2×Dic43—42no—
478D172—22no—
479D172—21no—
480D172—22no—
481D172—44no—
482D172—42no—
483D172C22×D412yes—
484C4×D43—24no—
485C4×D43—44no—
486C4×D43—44no—
487C4×D43—82no—
488Dic86—21no—
489Dic86—22no—
490Dic86—22no—
491Dic86—44no—
492Dic86—42no—
493Dic86C22×D412yes—
494C43⋊C8—22no—
495C43⋊C8—22no—
496C43⋊C8—22no—
497C43⋊C8C22×D412yes—
498C43⋊C8C22×D412yes—
499#61083—431nomaximal, Sylow
500C22×C43—22no—
501C22×C43—24no—
502C22×C43—24no—
503C22×C43—22no—
504C22×C43—22no—
505C22×C43—22no—
506C22×C43—42no—
507C22×C43D4212yes—
508C22×C43C23×D411yescharacteristic
509C2×D43—22no—
510C2×D43—42no—
511C2×D43—44no—
512C2×D43—42no—
513C2×D43—164no—
514C2×D43—162no—
515C4×C43—22no—
516C4×C43—22no—
517C4×C43—22no—
518C4×C43—22no—
519C4×C43—22no—
520C4×C43—42no—
521C4×C43—42no—
522C4×C43—42no—
523C4×C43D4212yes—
524C4×C43C23×D411yescharacteristic
525C4×C43C2×H(5,𝔽2)11yescharacteristic
526Dic43—22no—
527Dic43—42no—
528Dic43—42no—
529C2×#578—431no—
530C2×#577—431no—
531#3500—431no—
532#3499D4311yescharacteristic, complemented
533#3270—434no—
534#3269—434no—
535#3267—434no—
536#3266—434no—
537C2×#497—431no—
538#3059—431no—
539#3057—431no—
540#3040—431no—
541#3039—431no—
542#3011—431no—
543#3011—431no—
544#3010—431no—
545#3009—431no—
546#2943—431no—
547#2932—431no—
548C2×C43—22no—
549C2×C43—42no—
550C2×C43—42no—
551C2×C43—42no—
552C2×C43C2×D4211yescharacteristic
553C2×C43#358612yes—
554D43—42no—
555D43—82no—
556C2×2−1+4—431no—
557C2×2−1+4C2×D4311yescharacteristic
558C2×2−1+4C2×D4311yescharacteristic, complemented
559C2×H(5,𝔽2)—431no—
560#578—868no—
561#577—868no—
562C2×#137—431no—
563C2×#137—432no—
564C2×#137—431no—
565C2×#137—431no—
566C2×#137—432no—
567C2×#137—432no—
568C2×AGL(1,ℤ/8)—431no—
569C2×AGL(1,ℤ/8)—432no—
570C2×#135—431no—
571C2×#135—432no—
572C2×#135—432no—
573C22×Q16—431no—
574C22×Q16—432no—
575C22×Q16—431no—
576C22×SD16—431no—
577C22×SD16—432no—
578C22×SD16—431no—
579C2×#131—431no—
580C2×#131—431no—
581D4×Q8C2×D4314yescomplemented
582#548—434no—
583#547—24no—
584#547C2×D4314yescomplemented
585#546—434no—
586#546—864no—
587#536—21no—
588#536—21no—
589#536—431no—
590#536—861no—
591#536C2×D4311yescharacteristic
592#536C2×D4311yescharacteristic, complemented
593#535—431no—
594#535—861no—
595#532—21no—
596#532—861no—
597#532C2×D4311yescharacteristic
598C2×C4⋊Q8—21no—
599C2×C4⋊Q8C2×D4311yescharacteristic, complemented
600C2×#124—431no—
601C2×#124—861no—
602C4×#41—431no—
603C4×#41C2×D4311yescharacteristic, complemented
604#497—434no—
605#497—434no—
606#470—434no—
607#468—434no—
608#467—434no—
609#465—434no—
610#464—434no—
611#463—434no—
612#462—434no—
613#461—434no—
614#452—434no—
615#452—434no—
616#452—434no—
617#451—434no—
618#451—434no—
619#450—434no—
620#449—434no—
621#448—434no—
622#442—432no—
623#441—432no—
624#440—432no—
625#440—432no—
626#435—434no—
627#435—434no—
628#427—431no—
629#423—431no—
630#419—431no—
631#419—431no—
632#419—431no—
633#418—431no—
634#416—431no—
635#416—431no—
636#408—431no—
637#408—431no—
638C2×#97—431no—
639C43#6108311yescharacteristic, complemented, Sylow
6402−1+4—24no—
6412−1+4—24no—
6422−1+4—42no—
6432−1+4—42no—
6442−1+4—864no—
6452−1+4—1722no—
646H(5,𝔽2)—864no—
647H(5,𝔽2)—1722no—
648C2×#41—21no—
649C2×#41—21no—
650C2×#41—22no—
651C2×#41—22no—
652C2×#41—431no—
653C2×#41—432no—
654C2×#41—432no—
655C2×#41—861no—
656C2×#41—861no—
657C2×#41—862no—
658C2×#41C22×D4312yes—
659C2×#41C22×D4312yes—
660C2×#41C22×D4311yescharacteristic
661C2×#41C22×D4311yescharacteristic
662C2×#41C22×D4311yescharacteristic
663C22×Q8—21no—
664C22×Q8—21no—
665C22×Q8—431no—
666C22×Q8—432no—
667C22×Q8—861no—
668C22×Q8C22×D4311yescharacteristic
669C22×Q8C22×D4311yescharacteristic
670C22×Q8C22×D4312yes—
671C22×Q8C22×D4312yes—
672C22×D4—431no—
673C22×D4—432no—
674C22×D4—861no—
675C22×D4—862no—
676#137—868no—
677#137—868no—
678#137—868no—
679#137—864no—
680#137—864no—
681#137—864no—
682AGL(1,ℤ/8)—868no—
683AGL(1,ℤ/8)—864no—
684#135—438no—
685#135—868no—
686#135—868no—
687C2×Q16—431no—
688C2×Q16—432no—
689C2×Q16—432no—
690C2×Q16—432no—
691C2×Q16—432no—
692C2×Q16—432no—
693C2×Q16—434no—
694C2×Q16—864no—
695C2×Q16—868no—
696C2×Q16—1722no—
697C2×SD16—431no—
698C2×SD16—431no—
699C2×SD16—432no—
700C2×SD16—432no—
701C2×SD16—432no—
702C2×SD16—432no—
703C2×SD16—432no—
704C2×SD16—432no—
705C2×SD16—434no—
706C2×SD16—864no—
707C2×SD16—868no—
708C2×SD16—1722no—
709C2×D8—431no—
710C2×D8—432no—
711#131—864no—
712#131—864no—
713C2×M16—431no—
714C2×M16—432no—
715C2×M16—431no—
716C2×M16—432no—
717C22×C8—431no—
718C22×C8—432no—
719C22×C8—432no—
720C22×C8—431no—
721C4⋊Q8—21no—
722C4⋊Q8—21no—
723C4⋊Q8—24no—
724C4⋊Q8—21no—
725C4⋊Q8—21no—
726C4⋊Q8—861no—
727C4⋊Q8C22⋊D4311yescharacteristic
728C4⋊Q8C22×D4314yes—
729#127—861no—
730#127C22⋊D4311yescharacteristic
731#124—21no—
732#124—21no—
733#124—434no—
734#124—861no—
735#124—861no—
736#124—864no—
737#124—861no—
738#124—861no—
739#124C22⋊D4311yescharacteristic
740#124C22⋊D4311yescharacteristic
741#123—22no—
742#123—22no—
743#123—24no—
744#123—24no—
745#123—862no—
746#123—864no—
747C22⋊Q8—24no—
748C22⋊Q8—24no—
749C22⋊Q8—434no—
750C22⋊Q8—864no—
751C22⋊Q8C22×D4314yes—
752C22⋊Q8C22×D4314yes—
753#121—24no—
754#121—434no—
755#121—864no—
756#121—864no—
757#121C22⋊D4314yes—
758#120—862no—
759#120—864no—
760C4×Q8—432no—
761C4×Q8C22×D4312yes—
762C4×D4—24no—
763C4×D4—22no—
764C4×D4—432no—
765C4×D4—862no—
766C4×D4—864no—
767C4×D4C22×D4312yes—
768C4×D4C22×D4314yes—
769#117—21no—
770#117—431no—
771#117—861no—
772#117C22×D4311yescharacteristic
773C2×C4⋊C4—22no—
774C2×C4⋊C4—24no—
775C2×C22⋊C4—862no—
776C2×C22⋊C4—864no—
777C2×C42—21no—
778C2×C42—861no—
779C2×C42C22×D4311yescharacteristic
780#107—432no—
781#106—432no—
782C4⋊C8—434no—
783#103—432no—
784#103—434no—
785#103—434no—
786#103—432no—
787#103—434no—
788#102—432no—
789#102—432no—
790#102—434no—
791C22⋊C8—434no—
792C22⋊C8—434no—
793#97—432no—
794#97—432no—
795C24—862no—
796C24—861no—
797#41—22no—
798#41—22no—
799#41—22no—
800#41—22no—
801#41—22no—
802#41—24no—
803#41—24no—
804#41—42no—
805#41—42no—
806#41—44no—
807#41—44no—
808#41—48no—
809#41—48no—
810#41—434no—
811#41—864no—
812#41—864no—
813#41—862no—
814#41—1722no—
815#41—1722no—
816#41—1724no—
817#41—1724no—
818#41—1728no—
819#41D4×D4314yes—
820C2×Q8—22no—
821C2×Q8—22no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—24no—
825C2×Q8—24no—
826C2×Q8—22no—
827C2×Q8—22no—
828C2×Q8—22no—
829C2×Q8—22no—
830C2×Q8—42no—
831C2×Q8—42no—
832C2×Q8—44no—
833C2×Q8—44no—
834C2×Q8—431no—
835C2×Q8—432no—
836C2×Q8—864no—
837C2×Q8—862no—
838C2×Q8—861no—
839C2×Q8—862no—
840C2×Q8—862no—
841C2×Q8—1722no—
842C2×Q8—1724no—
843C2×Q8C2×C22⋊D4311yescharacteristic
844C2×Q8C2×C22⋊D4311yescharacteristic
845C2×Q8C23×D4312yes—
846C2×Q8C23×D4312yes—
847C2×Q8C23×D4311yescharacteristic
848C2×D4—21no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—431no—
852C2×D4—432no—
853C2×D4—864no—
854C2×D4—861no—
855C2×D4—864no—
856C2×D4—862no—
857C2×D4—862no—
858C2×D4—862no—
859C2×D4—862no—
860C2×D4—861no—
861C2×D4—862no—
862C2×D4—1722no—
863C2×D4—1724no—
864C2×D4—1728no—
865C2×D4C2×C22⋊D4312yes—
866C2×D4C2×C22⋊D4312yes—
867C2×D4C2×C22⋊D4311yescharacteristic
868C2×D4C2×C22⋊D4311yescharacteristic
869C2×D4C2×C22⋊D4314yes—
870C2×D4C23×D4311yescharacteristic
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—22no—
877C22×C4—22no—
878C22×C4—22no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—862no—
882C22×C4—862no—
883C22×C4—862no—
884C22×C4—862no—
885C22×C4C2×C22⋊D4312yes—
886C22×C4C23×D4312yes—
887C22×C4C23×D4312yes—
888C22×C4C23×D4311yescharacteristic
889Q16—434no—
890Q16—864no—
891Q16—864no—
892Q16—864no—
893Q16—864no—
894Q16—864no—
895Q16—1724no—
896SD16—434no—
897SD16—434no—
898SD16—864no—
899SD16—864no—
900SD16—864no—
901SD16—864no—
902SD16—864no—
903SD16—864no—
904SD16—1724no—
905D8—434no—
906D8—864no—
907M16—864no—
908M16—864no—
909M16—862no—
910M16—862no—
911C2×C8—434no—
912C2×C8—431no—
913C2×C8—431no—
914C2×C8—432no—
915C2×C8—432no—
916C2×C8—432no—
917C2×C8—864no—
918C2×C8—864no—
919C2×C8—862no—
920C4⋊C4—24no—
921C4⋊C4—24no—
922C4⋊C4—24no—
923C4⋊C4—24no—
924C4⋊C4—22no—
925C4⋊C4—432no—
926C4⋊C4—862no—
927C4⋊C4—864no—
928C4⋊C4C2×C22⋊D4314yes—
929C4⋊C4C23×D4312yes—
930C22⋊C4—21no—
931C22⋊C4—24no—
932C22⋊C4—24no—
933C22⋊C4—22no—
934C22⋊C4—864no—
935C22⋊C4—861no—
936C22⋊C4—864no—
937C22⋊C4—864no—
938C22⋊C4—864no—
939C22⋊C4—862no—
940C22⋊C4C2×C22⋊D4314yes—
941C22⋊C4C2×C22⋊D4314yes—
942C42—21no—
943C42—22no—
944C42—861no—
945C42—862no—
946C42C2×C22⋊D4311yescharacteristic
947C42C2×C22⋊D4311yescharacteristic
948C42C23×D4312yes—
949C23—21no—
950C23—861no—
951C23—862no—
952C23—3442no—
953C23—3444no—
954C23—1724no—
955C23—1722no—
956C23C22×C22⋊D4312yes—
957C23C22×C22⋊D4312yes—
958C23C22×C22⋊D4311yescharacteristic
959Q8—21no—
960Q8—22no—
961Q8—22no—
962Q8—22no—
963Q8—22no—
964Q8—22no—
965Q8—22no—
966Q8—44no—
967Q8—44no—
968Q8—42no—
969Q8—42no—
970Q8—432no—
971Q8—861no—
972Q8—862no—
973Q8—862no—
974Q8—1724no—
975Q8—1722no—
976Q8C2×D4×D4312yes—
977D4—24no—
978D4—24no—
979D4—24no—
980D4—21no—
981D4—22no—
982D4—22no—
983D4—44no—
984D4—44no—
985D4—44no—
986D4—432no—
987D4—864no—
988D4—862no—
989D4—861no—
990D4—862no—
991D4—3444no—
992D4—1724no—
993D4—1724no—
994D4—1724no—
995D4—1722no—
996D4C2×D4×D4312yes—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—24no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—42no—
1007C2×C4—44no—
1008C2×C4—44no—
1009C2×C4—44no—
1010C2×C4—44no—
1011C2×C4—44no—
1012C2×C4—42no—
1013C2×C4—42no—
1014C2×C4—861no—
1015C2×C4—864no—
1016C2×C4—862no—
1017C2×C4—862no—
1018C2×C4—3442no—
1019C2×C4—1724no—
1020C2×C4—1724no—
1021C2×C4—1724no—
1022C2×C4—1722no—
1023C2×C4C2×D4×D4312yes—
1024C2×C4C22×C22⋊D4312yes—
1025C2×C4C22×C22⋊D4312yes—
1026C2×C4C22×C22⋊D4312yes—
1027C2×C4C22×C22⋊D4312yes—
1028C2×C4C22×C22⋊D4311yescharacteristic
1029C2×C4#1306337012yes—
1030C2×C4C24×D4311yescharacteristic
1031C8—432no—
1032C8—432no—
1033C8—862no—
1034C8—862no—
1035C8—862no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—22no—
1040C22—24no—
1041C22—24no—
1042C22—42no—
1043C22—862no—
1044C22—1722no—
1045C22—1724no—
1046C22—1722no—
1047C22—6882no—
1048C22—6884no—
1049C22D4×C22⋊D4312yes—
1050C22C23×C22⋊D4311yescharacteristic
1051C4—22no—
1052C4—22no—
1053C4—22no—
1054C4—22no—
1055C4—22no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—862no—
1060C4—1722no—
1061C4—1722no—
1062C4D4×C22⋊D4312yes—
1063C4C22×D4×D4311yescharacteristic
1064C4C2×#1306337011yescharacteristic
1065C2—22no—
1066C2—42no—
1067C2—42no—
1068C2—42no—
1069C2—3442no—
1070C2—1722no—
1071C2C2×D4×C22⋊D4311yescharacteristic
1072C2#1914938212yes—
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3499C2
socleC22×C43C23×D4
hypercenter#3499D43
hypocenterC43#61083
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #532 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×#14583714C2semidirect
2. C2×#14583707C2semidirect
3. #19148382C2semidirect
4. #19146166C2semidirect
5. #19146146C2semidirect
6. #19146121C2semidirect
7. #19146106C2semidirect
8. C2×#14583291C2semidirect
9. #19144247C2semidirect
10. #19144236C2semidirect
11. #19144089C2semidirect
12. #19144078C2semidirect
13. #19143890C2semidirect
14. #19143888C2semidirect
15. #19143881C2semidirect
16. #19143870C2semidirect
17. #19143393C2semidirect
18. #19143313C2semidirect
19. C43×#3499C2semidirect
27. C2×#13063356C22semidirect
28. C2×#13063355C22semidirect
29. C2×#13063355C22semidirect
34. C2×#13063345C22semidirect
35. C22×#10621885C22semidirect
36. C22×#10621885C22semidirect
37. C22×#10621885C22semidirect
42. C2×#13063332C22semidirect
54. #14583291C22semidirect
55. #14583291C22semidirect
56. #14583155C22semidirect
57. #14583147C22semidirect
58. #14583138C22semidirect
59. #14583130C22semidirect
60. #14583121C22semidirect
61. #14583114C22semidirect
62. #14583106C22semidirect
63. #14583101C22semidirect
64. #14583061C22semidirect
66. #14583059C22semidirect
67. #14583055C22semidirect
68. #14583054C22semidirect
70. #14583044C22semidirect
71. #14583038C22semidirect
72. #14583009C22semidirect
73. #14583004C22semidirect
74. #14582999C22semidirect
75. #14582997C22semidirect
76. #14582971C22semidirect
77. #14582971C22semidirect
78. #14582935C22semidirect
79. #14582923C22semidirect
80. #14582908C22semidirect
81. #14582908C22semidirect
82. #14582907C22semidirect
84. #14582895C22semidirect
87. #14582866C22semidirect
88. C2×#13063236C22semidirect
90. C2×2−1+4×C43C22semidirect
91. D4×Q8×C43C22semidirect
93. C43×#547C22semidirect
97. C43×#536C22semidirect
101. C2×C4⋊Q8×C43C22semidirect
102. C4×#41×C43C22semidirect
130. #13063345D4semidirect
532. #3499D43semidirect
558. C2×2−1+4C2×D43semidirect
581. D4×Q8C2×D43semidirect
584. #547C2×D43semidirect
592. #536C2×D43semidirect
599. C2×C4⋊Q8C2×D43semidirect
603. C4×#41C2×D43semidirect
639. C43#61083semidirect

Maximal subgroups

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

subgroupindex
C2×#145837142
C2×#145837072
#191483822
#191461662
#191461462
#191461212
#191461062
C2×#145832912
#191442472
#191442362
#191440892
#191440782
#191438902
#191438882
#191438812
#191438702
#191433932
#191433132
C43×#34992
#6108343