Finite Group Databasebeta

← #25968040

Subgroups — #25968040

Order 11008.

2134 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147889C211yesmaximal, characteristic
2C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
3#19145624C211yesmaximal, characteristic, complemented
4#19145623C212yesmaximal, complemented
5#19145622C211yesmaximal, characteristic, complemented
6#19145619C211yesmaximal, characteristic, complemented
7#19145618C212yesmaximal, complemented
8#19145542C212yesmaximal, complemented
9#19145541C212yesmaximal, complemented
10#19145519C212yesmaximal, complemented
11#19145518C212yesmaximal, complemented
12#19145051C212yesmaximal, complemented
13#19144974C212yesmaximal, complemented
14#19144079C212yesmaximal, complemented
15#19144077C212yesmaximal, complemented
16#19143830C212yesmaximal, complemented
17#19143826C212yesmaximal, complemented
18#19143225C211yesmaximal, characteristic, complemented
19C43×#3218C211yesmaximal, characteristic, complemented
20C22×Q8×D43C2212yes—
21C2×#13063357C2214yes—
22C2×#13063354C2214yes—
23#14583455C2211yescharacteristic
24#14583453C2211yescharacteristic
25#14583451C2211yescharacteristic
26#14583448C2211yescharacteristic
27#14583446C2211yescharacteristic
28#14583444C2211yescharacteristic
29C2×#13063325C2211yescharacteristic
30C2×#13063324—21no—
31C2×#13063324—21no—
32C2×#13063323C2212yes—
33C4⋊Q8×D43—21no—
34C4⋊Q8×D43—21no—
35C4⋊Q8×D43—21no—
36C4⋊Q8×D43—21no—
37C4⋊Q8×D43C2212yes—
38C4⋊Q8×D43C2212yes—
39C4⋊Q8×D43C2212yes—
40C4⋊Q8×D43C2212yes—
41#14583434C2211yescharacteristic
42#14583433C2211yescharacteristic
43#14583432—21no—
44#14583432—21no—
45#14583428C2211yescharacteristic
46#14583427—21no—
47#14583426—21no—
48#14583412C2211yescharacteristic
49#14583409C2211yescharacteristic
50#14583408—21no—
51#14583407—21no—
52C4×#10621902C2211yescharacteristic
53#14583367—21no—
54C4×#10621900—21no—
55C4×#10621900C2211yescharacteristic
56C2×C4⋊C4×D43—21no—
57C2×C4⋊C4×D43—21no—
58C2×C42×D43C2211yescharacteristic
59#14583294C2212yescomplemented
60#14583293C2212yescomplemented
61#14583291C2212yescomplemented
62#14583277C2214yescomplemented
63#14583270C2214yescomplemented
64#14583269C2212yescomplemented
65#14583268C2212yescomplemented
66#14583267C2212yescomplemented
67#14583248C2214yescomplemented
68#14583248C2214yescomplemented
69#14583110C2212yescomplemented
70#14583109C2212yescomplemented
71#14583108C2214yescomplemented
72#14583107C2214yescomplemented
73#14583106C2212yescomplemented
74#14583105C2212yescomplemented
75#14583104C2212yescomplemented
76#14583103C2214yescomplemented
77#14583102C2214yescomplemented
78#14583101C2212yescomplemented
79#14583057C2212yes—
80#14583056C2214yes—
81#14583055C2212yes—
82#14583054C2212yes—
83#14583053C2214yes—
84#14583040C2212yes—
85#14583039C2214yes—
86#14583038C2212yes—
87#14583037C2212yes—
88#14583036C2214yes—
89#14582956C2211yescharacteristic
90#14582954C2212yes—
91#14582951C2212yes—
92#14582949C2212yes—
93#14582921C2212yes—
94#14582906C2214yes—
95#14582906C2214yes—
96#14582861C2212yes—
97#14582851C2212yes—
98C2×C4⋊Q8×C43C2211yescharacteristic
99C43×#529C2211yescharacteristic
100C43×#497C2212yescomplemented
101C43×#491C2212yescomplemented
102C43×#462C2212yescomplemented
103C43×#461C2212yescomplemented
104C43×#451C2212yes—
105C43×#448C2212yes—
106C43×#432C2211yescharacteristic
107C2×#10621902C2311yescharacteristic
108C2×#10621898—21no—
109C2×#10621900—21no—
110C2×#10621900C2311yescharacteristic
111C22×Dic86—22no—
112C22×Dic86C2312yes—
113C2×Q8×D43—22no—
114C2×Q8×D43—22no—
115C2×Q8×D43—48no—
116C2×Q8×D43C2314yes—
117C2×Q8×D43C2314yes—
118C22×C4×D43—22no—
119C22×C4×D43D411yescharacteristic
120C22×C4×D43D411yescharacteristic
121C22×C4×D43C2311yescharacteristic
122#13063357—48no—
123#13063354—48no—
124C2×Dic172C2314yes—
125C2×#10621885C2314yes—
126C2×#10621885C2314yes—
127C2×#10621873C2314yes—
128C2×#10621883C2314yes—
129C2×#10621884C2314yes—
130C2×#10621872C2314yes—
131#13063325—21no—
132#13063325—21no—
133#13063325C2312yes—
134#13063325C2312yes—
135#13063324—22no—
136#13063324—22no—
137#13063324—22no—
138#13063324—22no—
139#13063324—22no—
140#13063324—22no—
141#13063324—22no—
142#13063324—22no—
143#13063324C2311yescharacteristic
144#13063324C2311yescharacteristic
145#13063323—22no—
146#13063323—22no—
147#13063323C2314yes—
148#13063323C2314yes—
149#13063323C2311yescharacteristic
150#13063321C2311yescharacteristic
151#13063320—21no—
152#13063319—21no—
153#13063318—21no—
154#13063317C2311yescharacteristic
155#13063315—21no—
156#13063315—21no—
157#13063313C2311yescharacteristic
158#13063311—21no—
159#13063311—21no—
160#13063310—21no—
161#13063310—21no—
162#13063308—21no—
163#13063307—21no—
164#13063307—21no—
165#13063305C2311yescharacteristic
166#13063304C2311yescharacteristic
167#13063303—21no—
168#13063303—21no—
169#13063303—21no—
170#13063302—21no—
171#13063301C2311yescharacteristic
172#13063300C2311yescharacteristic
173#13063299C2311yescharacteristic
174#13063298—21no—
175#13063298—21no—
176#13063298—21no—
177#13063297—21no—
178#13063296C2311yescharacteristic
179#13063295—21no—
180#13063293—21no—
181Q8×Dic43C2311yescharacteristic
182C4×Dic86—21no—
183C4×Dic86C2311yescharacteristic
184#13063290—21no—
185#13063290—21no—
186#13063290—21no—
187#13063290C2311yescharacteristic
188C4×D172—21no—
189C4×D172C2311yescharacteristic
190D4×Dic43—21no—
191D4×Dic43C2311yescharacteristic
192#13063287—21no—
193#13063287—21no—
194#13063287—21no—
195#13063287C2311yescharacteristic
196C4×C22⋊D43—21no—
197C4×C22⋊D43—21no—
198C4×C22⋊D43—21no—
199(C22⋊D43)⋊C4—21no—
200(C22⋊D43)⋊C4—21no—
201(C22⋊D43)⋊C4—21no—
202(C22⋊D43)⋊C4—21no—
203(C22⋊D43)⋊C4—21no—
204(C22⋊D43)⋊C4—21no—
205(C22⋊D43)⋊C4—21no—
206#13063283—21no—
207#13063283—21no—
208#13063283C2311yescharacteristic
209#13063283C2311yescharacteristic
210#13063282—21no—
211#13063282—21no—
212#13063281—21no—
213#13063281—21no—
214#13063281—21no—
215C2×C4⋊Dic43—21no—
216C2×C4⋊Dic43—21no—
217C2×Dic43⋊C4—22no—
218C2×Dic43⋊C4—22no—
219C4⋊C4×D43—22no—
220C4⋊C4×D43—22no—
221C4⋊C4×D43—22no—
222C4⋊C4×D43—22no—
223C4⋊C4×D43—22no—
224C4⋊C4×D43—22no—
225C4⋊C4×D43—22no—
226C4⋊C4×D43—22no—
227C2×C4×Dic43—21no—
228C2×C4×Dic43D411yescharacteristic
229C2×C4×Dic43D411yescharacteristic
230C2×C4×Dic43C2311yescharacteristic
231C42×D43—21no—
232C42×D43D411yescharacteristic
233C42×D43D411yescharacteristic
234C42×D43D411yescharacteristic
235C42×D43D411yescharacteristic
236C42×D43C2311yescharacteristic
237C42×D43C2311yescharacteristic
238C42×D43C2311yescharacteristic
239C42×D43C2311yescharacteristic
240C4⋊(C43⋊C8)C2312yes—
241Dic43⋊C8C2314yes—
242#13063250C2314yes—
243#13063250C2314yes—
244#13063249C2314yes—
245#13063249C2314yes—
246#13063248C2314yes—
247#13063248C2314yes—
248C22⋊(C43⋊C8)C2312yes—
249(C2×D43)⋊C8C2314yes—
250#13063236C2312yes—
251C8×Dic43C2314yes—
252C22×Q8×C43C2312yes—
253C2×Q16×C43C2314yes—
254C2×SD16×C43C2314yes—
255C4⋊Q8×C43—21no—
256C4⋊Q8×C43—21no—
257C4⋊Q8×C43C2312yes—
258C4⋊Q8×C43C2312yes—
259#126×C43—21no—
260#125×C43C2311yescharacteristic
261#124×C43C2311yescharacteristic
262#123×C43—21no—
263C22⋊Q8×C43C2311yescharacteristic
264#121×C43C2311yescharacteristic
265C4×Q8×C43C2311yescharacteristic
266C4×D4×C43—21no—
267C4×D4×C43C2311yescharacteristic
268#117×C43—21no—
269C2×C4⋊C4×C43—21no—
270C2×C4⋊C4×C43—21no—
271C2×C42×C43C2311yescharacteristic
272C4⋊C8×C43C2312yes—
273#103×C43C2314yes—
274#103×C43C2314yes—
275C22⋊C8×C43C2312yes—
276#97×C43C2312yes—
277C23×D43C2×D411yescharacteristic
278C2×Q8×C43—22no—
279C2×Q8×C43—44no—
280C2×Q8×C43C2414yes—
281C2×Q8×C43C2411yescharacteristic
282C2×D4×C43—21no—
283C2×D4×C43C2411yescharacteristic
284C22×C4×C43—21no—
285C22×C4×C43—22no—
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2×D411yescharacteristic
288C22×C4×C43C2411yescharacteristic
289C2×C22⋊D43—21no—
290C2×C22⋊D43—21no—
291C2×C22⋊D43—21no—
292C2×C22⋊D43—21no—
293C2×C22⋊D43—21no—
294C22×Dic43—21no—
295C22×Dic43—21no—
296C22×Dic43—22no—
297C22×Dic43C2×D411yescharacteristic
298C22×Dic43C2×D411yescharacteristic
299C22×Dic43C2×D411yescharacteristic
300#10621902—24no—
301Q8×D43—28no—
302Q8×D43—28no—
303Q8×D43—44no—
304Q8×D43—44no—
305Q8×D43—48no—
306Q8×D43—48no—
307#10621900—24no—
308#10621900—44no—
309#10621898—44no—
310C2×D172—21no—
311C2×D172—21no—
312C2×D172C2411yescharacteristic
313C2×C4×D43—24no—
314C2×C4×D43—24no—
315C2×C4×D43—24no—
316C2×C4×D43—21no—
317C2×C4×D43—21no—
318C2×C4×D43—21no—
319C2×C4×D43—24no—
320C2×C4×D43—24no—
321C2×C4×D43—48no—
322C2×C4×D43C2×D411yescharacteristic
323C2×C4×D43C2×D411yescharacteristic
324C2×C4×D43C2×D411yescharacteristic
325C2×C4×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2×D411yescharacteristic
328C2×C4×D43C2×D411yescharacteristic
329C2×C4×D43C2×D411yescharacteristic
330C2×C4×D43C2×D411yescharacteristic
331C2×C4×D43C2×D411yescharacteristic
332C2×C4×D43C2411yescharacteristic
333C2×C4×D43C2411yescharacteristic
334C2×Dic86—22no—
335C2×Dic86—21no—
336C2×Dic86—21no—
337C2×Dic86—24no—
338C2×Dic86—24no—
339C2×Dic86—44no—
340C2×Dic86—48no—
341C2×Dic86C2414yes—
342C2×Dic86C2411yescharacteristic
343Q16×C43—44no—
344SD16×C43—44no—
345C2×C8×C43C2414yes—
346C4⋊C4×C43—22no—
347C4⋊C4×C43—22no—
348C4⋊C4×C43—22no—
349C4⋊C4×C43—22no—
350C4⋊C4×C43—21no—
351C4⋊C4×C43—21no—
352C4⋊C4×C43—21no—
353C4⋊C4×C43—21no—
354C4⋊C4×C43C2411yescharacteristic
355C4⋊C4×C43C2411yescharacteristic
356C22⋊C4×C43—21no—
357C22⋊C4×C43—21no—
358C22⋊C4×C43—21no—
359C22⋊C4×C43—21no—
360C22⋊C4×C43—21no—
361C42×C43—21no—
362C42×C43C2×D411yescharacteristic
363C42×C43C2×D411yescharacteristic
364C42×C43C2411yescharacteristic
365C42×C43C2411yescharacteristic
366C22⋊Dic43—21no—
367C22⋊Dic43—21no—
368C22⋊Dic43—21no—
369#10621885—44no—
370#10621885—44no—
371#10621884—44no—
372#10621883—44no—
373(C2×D43)⋊C4—21no—
374(C2×D43)⋊C4—21no—
375(C2×D43)⋊C4—21no—
376(C2×D43)⋊C4—21no—
377(C2×D43)⋊C4—21no—
378(C2×D43)⋊C4—21no—
379(C2×D43)⋊C4—21no—
380(C2×D43)⋊C4—21no—
381(C2×D43)⋊C4—21no—
382(C2×D43)⋊C4—21no—
383C4⋊Dic43—22no—
384C4⋊Dic43—22no—
385C4⋊Dic43—22no—
386C4⋊Dic43—22no—
387C4⋊Dic43—21no—
388C4⋊Dic43—21no—
389C4⋊Dic43C2411yescharacteristic
390C4⋊Dic43C2411yescharacteristic
391Dic43⋊C4—21no—
392Dic43⋊C4—21no—
393Dic43⋊C4—21no—
394Dic43⋊C4—21no—
395Dic43⋊C4—24no—
396Dic43⋊C4—24no—
397Dic43⋊C4—24no—
398Dic43⋊C4—24no—
399Dic43⋊C4—21no—
400Dic43⋊C4—21no—
401Dic43⋊C4—21no—
402Dic43⋊C4—21no—
403Dic43⋊C4—21no—
404Dic43⋊C4—21no—
405C4×Dic43—21no—
406C4×Dic43—21no—
407C4×Dic43—21no—
408C4×Dic43—21no—
409C4×Dic43—21no—
410C4×Dic43C2×D411yescharacteristic
411C4×Dic43C2×D411yescharacteristic
412C4×Dic43C2×D411yescharacteristic
413C4×Dic43C2×D411yescharacteristic
414C4×Dic43C2×D411yescharacteristic
415C4×Dic43C2×D411yescharacteristic
416C4×Dic43C2×D411yescharacteristic
417C4×Dic43C2×D411yescharacteristic
418C4×Dic43C2×D411yescharacteristic
419C4×Dic43C2×D411yescharacteristic
420C4×Dic43C2411yescharacteristic
421C4×Dic43C2411yescharacteristic
422C2×C43⋊C8C2414yes—
423Dic172—44no—
424#10621873—44no—
425#10621872—28no—
426C23×C43—21no—
427C23×C43C22×D411yescharacteristic
428C22×D43—22no—
429C22×D43—22no—
430C22×D43—22no—
431C22×D43—21no—
432C22×D43C22×D411yescharacteristic
433C22×D43C22×D411yescharacteristic
434Q8×C43—24no—
435Q8×C43—22no—
436Q8×C43—24no—
437Q8×C43—44no—
438D4×C43—22no—
439D4×C43—42no—
440C2×C4×C43—22no—
441C2×C4×C43—22no—
442C2×C4×C43—22no—
443C2×C4×C43—21no—
444C2×C4×C43—21no—
445C2×C4×C43—21no—
446C2×C4×C43—24no—
447C2×C4×C43—44no—
448C2×C4×C43—42no—
449C2×C4×C43C22×D411yescharacteristic
450C2×C4×C43C22×D411yescharacteristic
451C2×C4×C43C22×D411yescharacteristic
452C2×C4×C43C22×D411yescharacteristic
453C2×C4×C43C22×D411yescharacteristic
454C2×C4×C43C2511yescharacteristic
455C22⋊D43—42no—
456C22⋊D43—42no—
457C22⋊D43—42no—
458C22⋊D43—42no—
459C22⋊D43—42no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—21no—
463C2×Dic43—21no—
464C2×Dic43—21no—
465C2×Dic43—24no—
466C2×Dic43—44no—
467C2×Dic43—42no—
468C2×Dic43—42no—
469C2×Dic43#13714yescomplemented
470C2×Dic43C22×D411yescharacteristic
471C2×Dic43C22×D411yescharacteristic
472C2×Dic43C22×D411yescharacteristic
473C2×Dic43C22×D411yescharacteristic
474C2×Dic43C22×D411yescharacteristic
475C2×Dic43C22×D411yescharacteristic
476D172—22no—
477D172—42no—
478D172—42no—
479C4×D43—22no—
480C4×D43—22no—
481C4×D43—22no—
482C4×D43—22no—
483C4×D43—22no—
484C4×D43—22no—
485C4×D43—22no—
486C4×D43—22no—
487C4×D43—22no—
488C4×D43—22no—
489C4×D43—48no—
490C4×D43—48no—
491C4×D43—42no—
492C4×D43—42no—
493C4×D43—42no—
494C4×D43#13714yescomplemented
495C4×D43H(5,𝔽2)14yes—
496Dic86—24no—
497Dic86—22no—
498Dic86—24no—
499Dic86—48no—
500Dic86—44no—
501Dic86—48no—
502Dic86—42no—
503Dic86—42no—
504C8×C43—24no—
505C43⋊C8—24no—
506#60800—431nomaximal, Sylow
507C22×C43—21no—
508C22×C43—21no—
509C22×C43—41no—
510C22×C43—41no—
511C22×C43—41no—
512C22×C43C2×#13712yes—
513C22×C43C23×D411yescharacteristic
514C2×D43—28no—
515C2×D43—21no—
516C2×D43—21no—
517C2×D43—21no—
518C2×D43—21no—
519C2×D43—41no—
520C2×D43—41no—
521C2×D43—41no—
522C2×D43#53512yes—
523C2×D43C2×#13712yes—
524C4×C43—21no—
525C4×C43—21no—
526C4×C43—21no—
527C4×C43—21no—
528C4×C43—44no—
529C4×C43—41no—
530C4×C43—41no—
531C4×C43—41no—
532C4×C43C2×#13712yes—
533C4×C43C2×H(5,𝔽2)12yes—
534Dic43—21no—
535Dic43—21no—
536Dic43—44no—
537Dic43—41no—
538Dic43—41no—
539Dic43—41no—
540Dic43#53512yes—
541Dic43C2×#13712yes—
542Dic43C2×#13712yes—
543Dic43C2×#13712yes—
544#3444—431no—
545C22×C4⋊Q8—431no—
546#3218—432no—
547#3218—432no—
548#3218—431no—
549#3218—431no—
550#3218—431no—
551#3218D4311yescharacteristic, complemented
552#3209—432no—
553#3209—432no—
554#3206—432no—
555#3206—432no—
556#3152—432no—
557#3139—432no—
558#3039—432no—
559#3039—432no—
560#3004—432no—
561#3004—432no—
562#2920—431no—
563C2×C43—22no—
564C2×C43—81no—
565C2×C43C2×#53511yescharacteristic
566C2×C43C22×#13711yescharacteristic
567C2×C43C22×#13711yescharacteristic
568D43—22no—
569D43—22no—
570D43—81no—
571C23×Q8—432no—
572C2×#137—434no—
573C2×#137—434no—
574#533—431no—
575#533—431no—
576#533—431no—
577#532—431no—
578#532—431no—
579#532—431no—
580C2×C4⋊Q8—432no—
581C2×C4⋊Q8—432no—
582C2×C4⋊Q8—432no—
583C2×C4⋊Q8—432no—
584C2×C4⋊Q8—432no—
585C2×C4⋊Q8—431no—
586C2×C4⋊Q8—861no—
587C2×C4⋊Q8—861no—
588C2×C4⋊Q8—861no—
589C2×C4⋊Q8—861no—
590C2×C4⋊Q8—861no—
591C2×C4⋊Q8—861no—
592C2×C4⋊Q8C2×D4311yescharacteristic
593#529—431no—
594#529—431no—
595#529—431no—
596#529—861no—
597#529—861no—
598#529—861no—
599#529—861no—
600#529C2×D4311yescharacteristic
601#525—431no—
602#525—431no—
603#525—861no—
604#525—861no—
605C4×#41—431no—
606C4×#41—431no—
607C4×#41—861no—
608C4×#41—861no—
609C22×C4⋊C4—861no—
610C22×C4⋊C4—861no—
611C22×C42—431no—
612#497—432no—
613#497—432no—
614#497—432no—
615#497C2×D4312yescomplemented
616#494—434no—
617#492—434no—
618#491—432no—
619#491—432no—
620#491—432no—
621#491C2×D4312yescomplemented
622#487—434no—
623#487—434no—
624#462—434no—
625#462—432no—
626#462—432no—
627#462—432no—
628#462—434no—
629#462C2×D4312yescomplemented
630#461—434no—
631#461—432no—
632#461—432no—
633#461—432no—
634#461—434no—
635#461C2×D4312yescomplemented
636#451—432no—
637#451—434no—
638#451—432no—
639#451—434no—
640#451—432no—
641#451C2×D4312yes—
642#448—432no—
643#448—434no—
644#448—432no—
645#448—434no—
646#448—432no—
647#448C2×D4312yes—
648#432—431no—
649#432—432no—
650#432C2×D4311yescharacteristic
651#431—432no—
652#431—432no—
653#423—432no—
654#419—434no—
655#419—434no—
656#407—432no—
657C4×M16—432no—
658C43#6080011yescharacteristic, complemented, Sylow
659C2×#41—431no—
660C2×#41—431no—
661C2×#41—861no—
662C2×#41—861no—
663C22×Q8—434no—
664C22×Q8—434no—
665C22×Q8—432no—
666C22×Q8—862no—
667C22×Q8—862no—
668C22×Q8—862no—
669C22×Q8—1728no—
670C22×Q8C22×D4312yes—
671C23×C4—431no—
672C23×C4—431no—
673C23×C4—431no—
674C23×C4—862no—
675#137—1728no—
676#137—1728no—
677C2×Q16—434no—
678C2×Q16—434no—
679C2×Q16—434no—
680C2×Q16C22×D4314yes—
681C2×SD16—434no—
682C2×SD16—434no—
683C2×SD16—434no—
684C2×SD16C22×D4314yes—
685C2×M16—434no—
686C4⋊Q8—21no—
687C4⋊Q8—21no—
688C4⋊Q8—431no—
689C4⋊Q8—431no—
690C4⋊Q8—434no—
691C4⋊Q8—434no—
692C4⋊Q8—431no—
693C4⋊Q8—432no—
694C4⋊Q8—432no—
695C4⋊Q8—862no—
696C4⋊Q8—862no—
697C4⋊Q8—862no—
698C4⋊Q8—862no—
699C4⋊Q8—862no—
700C4⋊Q8—862no—
701C4⋊Q8—862no—
702C4⋊Q8—862no—
703C4⋊Q8—862no—
704C4⋊Q8—862no—
705C4⋊Q8—861no—
706C4⋊Q8—861no—
707C4⋊Q8C22×D4312yes—
708C4⋊Q8C22×D4312yes—
709#127—431no—
710#126—21no—
711#126—861no—
712#126—861no—
713#126—861no—
714#125—431no—
715#125—861no—
716#125—861no—
717#125C22×D4311yescharacteristic
718#124—431no—
719#124—861no—
720#124—861no—
721#124C22×D4311yescharacteristic
722#123—21no—
723#123—861no—
724#123—861no—
725#123—861no—
726#123—861no—
727#123—861no—
728C22⋊Q8—431no—
729C22⋊Q8—431no—
730C22⋊Q8—431no—
731C22⋊Q8—861no—
732C22⋊Q8—861no—
733C22⋊Q8—861no—
734C22⋊Q8—861no—
735C22⋊Q8C22×D4311yescharacteristic
736#121—431no—
737#121—431no—
738#121—431no—
739#121—861no—
740#121—861no—
741#121—861no—
742#121—861no—
743#121C22×D4311yescharacteristic
744#120—861no—
745#120—861no—
746C4×Q8—431no—
747C4×Q8—431no—
748C4×Q8—431no—
749C4×Q8—861no—
750C4×Q8—861no—
751C4×Q8—861no—
752C4×Q8—861no—
753C4×Q8C22×D4311yescharacteristic
754C4×D4—21no—
755C4×D4—431no—
756C4×D4—431no—
757C4×D4—431no—
758C4×D4—861no—
759C4×D4—861no—
760C4×D4—861no—
761C4×D4—861no—
762C4×D4—861no—
763C4×D4—861no—
764C4×D4—861no—
765C4×D4—861no—
766C4×D4—861no—
767C4×D4—861no—
768C4×D4—861no—
769C4×D4—861no—
770C4×D4—861no—
771C4×D4—861no—
772C4×D4—861no—
773C4×D4C22×D4311yescharacteristic
774#117—21no—
775#117—431no—
776#117—431no—
777#117—861no—
778#117—861no—
779#117—861no—
780#117—861no—
781#117—861no—
782#117—861no—
783#117—861no—
784C2×C4⋊C4—21no—
785C2×C4⋊C4—21no—
786C2×C4⋊C4—862no—
787C2×C4⋊C4—862no—
788C2×C4⋊C4—862no—
789C2×C4⋊C4—862no—
790C2×C4⋊C4—862no—
791C2×C4⋊C4—862no—
792C2×C4⋊C4—862no—
793C2×C4⋊C4—862no—
794C2×C4⋊C4—862no—
795C2×C4⋊C4—862no—
796C2×C4⋊C4—861no—
797C2×C4⋊C4—861no—
798C2×C42—431no—
799C2×C42—431no—
800C2×C42—431no—
801C2×C42—431no—
802C2×C42—431no—
803C2×C42—431no—
804C2×C42—431no—
805C2×C42—431no—
806C2×C42—431no—
807C2×C42—431no—
808C2×C42—431no—
809C2×C42—861no—
810C2×C42—861no—
811C2×C42C22×D4311yescharacteristic
812C4⋊C8—434no—
813C4⋊C8—432no—
814C4⋊C8C22×D4312yes—
815#103—434no—
816#103—434no—
817#103—434no—
818#103—434no—
819#103—434no—
820#103—434no—
821#103C22×D4314yes—
822#103C22×D4314yes—
823C22⋊C8—432no—
824C22⋊C8—434no—
825C22⋊C8C22×D4312yes—
826#97—432no—
827#97C22×D4312yes—
828C4×C8—434no—
829C24—431no—
830#41—864no—
831#41—864no—
832#41—1724no—
833#41—1724no—
834C2×Q8—22no—
835C2×Q8—44no—
836C2×Q8—434no—
837C2×Q8—431no—
838C2×Q8—861no—
839C2×Q8—861no—
840C2×Q8—864no—
841C2×Q8—864no—
842C2×Q8—868no—
843C2×Q8—868no—
844C2×Q8—862no—
845C2×Q8—1724no—
846C2×Q8—1728no—
847C2×Q8—1724no—
848C2×Q8—1724no—
849C2×Q8—1728no—
850C2×Q8—1728no—
851C2×Q8C23×D4314yes—
852C2×Q8C23×D4311yescharacteristic
853C2×D4—21no—
854C2×D4—431no—
855C2×D4—861no—
856C2×D4—861no—
857C2×D4—861no—
858C2×D4—861no—
859C2×D4—861no—
860C2×D4—861no—
861C2×D4—861no—
862C2×D4C23×D4311yescharacteristic
863C22×C4—22no—
864C22×C4—21no—
865C22×C4—431no—
866C22×C4—431no—
867C22×C4—431no—
868C22×C4—431no—
869C22×C4—431no—
870C22×C4—431no—
871C22×C4—431no—
872C22×C4—431no—
873C22×C4—431no—
874C22×C4—431no—
875C22×C4—431no—
876C22×C4—431no—
877C22×C4—431no—
878C22×C4—431no—
879C22×C4—431no—
880C22×C4—864no—
881C22×C4—864no—
882C22×C4—864no—
883C22×C4—861no—
884C22×C4—861no—
885C22×C4—864no—
886C22×C4—864no—
887C22×C4—861no—
888C22×C4—861no—
889C22×C4—862no—
890C22×C4—861no—
891C22×C4—1728no—
892C22×C4D4×D4311yescharacteristic
893C22×C4D4×D4311yescharacteristic
894C22×C4C23×D4311yescharacteristic
895Q16—44no—
896Q16—1724no—
897Q16—1724no—
898Q16—1724no—
899SD16—44no—
900SD16—1724no—
901SD16—1724no—
902SD16—1724no—
903M16—868no—
904C2×C8—434no—
905C2×C8C23×D4314yes—
906C4⋊C4—22no—
907C4⋊C4—22no—
908C4⋊C4—22no—
909C4⋊C4—22no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—431no—
915C4⋊C4—431no—
916C4⋊C4—864no—
917C4⋊C4—864no—
918C4⋊C4—864no—
919C4⋊C4—864no—
920C4⋊C4—861no—
921C4⋊C4—861no—
922C4⋊C4—861no—
923C4⋊C4—861no—
924C4⋊C4—861no—
925C4⋊C4—861no—
926C4⋊C4—861no—
927C4⋊C4—861no—
928C4⋊C4—862no—
929C4⋊C4—862no—
930C4⋊C4—862no—
931C4⋊C4—862no—
932C4⋊C4—861no—
933C4⋊C4—861no—
934C4⋊C4—861no—
935C4⋊C4—861no—
936C4⋊C4C23×D4311yescharacteristic
937C4⋊C4C23×D4311yescharacteristic
938C22⋊C4—21no—
939C22⋊C4—21no—
940C22⋊C4—21no—
941C22⋊C4—21no—
942C22⋊C4—21no—
943C22⋊C4—861no—
944C22⋊C4—861no—
945C22⋊C4—861no—
946C22⋊C4—861no—
947C22⋊C4—861no—
948C22⋊C4—861no—
949C22⋊C4—861no—
950C22⋊C4—861no—
951C22⋊C4—861no—
952C22⋊C4—861no—
953C22⋊C4—861no—
954C22⋊C4—861no—
955C22⋊C4—861no—
956C42—21no—
957C42—431no—
958C42—431no—
959C42—431no—
960C42—431no—
961C42—431no—
962C42—431no—
963C42—431no—
964C42—431no—
965C42—431no—
966C42—431no—
967C42—431no—
968C42—431no—
969C42—861no—
970C42—861no—
971C42—861no—
972C42—861no—
973C42—861no—
974C42D4×D4311yescharacteristic
975C42D4×D4311yescharacteristic
976C42C23×D4311yescharacteristic
977C42C23×D4311yescharacteristic
978C23—21no—
979C23—431no—
980C23—431no—
981C23—862no—
982C23—862no—
983C23—862no—
984C23—861no—
985C23C2×D4×D4311yescharacteristic
986Q8—24no—
987Q8—24no—
988Q8—22no—
989Q8—44no—
990Q8—864no—
991Q8—864no—
992Q8—862no—
993Q8—1724no—
994Q8—1728no—
995Q8—1722no—
996Q8—1722no—
997Q8—1728no—
998D4—22no—
999D4—42no—
1000D4—862no—
1001D4—1722no—
1002D4—1722no—
1003D4—1722no—
1004D4—1722no—
1005D4—1722no—
1006D4—1722no—
1007D4—1722no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—24no—
1015C2×C4—44no—
1016C2×C4—42no—
1017C2×C4—434no—
1018C2×C4—431no—
1019C2×C4—431no—
1020C2×C4—431no—
1021C2×C4—431no—
1022C2×C4—434no—
1023C2×C4—434no—
1024C2×C4—431no—
1025C2×C4—431no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—862no—
1029C2×C4—862no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—862no—
1033C2×C4—862no—
1034C2×C4—862no—
1035C2×C4—862no—
1036C2×C4—862no—
1037C2×C4—862no—
1038C2×C4—861no—
1039C2×C4—861no—
1040C2×C4—861no—
1041C2×C4—864no—
1042C2×C4—1722no—
1043C2×C4—1722no—
1044C2×C4—1728no—
1045C2×C4—1728no—
1046C2×C4—1722no—
1047C2×C4—1722no—
1048C2×C4—1724no—
1049C2×C4—1722no—
1050C2×C4C2×D4×D4311yescharacteristic
1051C2×C4C2×D4×D4311yescharacteristic
1052C2×C4C2×D4×D4311yescharacteristic
1053C2×C4C2×D4×D4311yescharacteristic
1054C2×C4C2×D4×D4311yescharacteristic
1055C2×C4C24×D4311yescharacteristic
1056C8—24no—
1057C8—864no—
1058C22—21no—
1059C22—21no—
1060C22—41no—
1061C22—41no—
1062C22—41no—
1063C22—432no—
1064C22—432no—
1065C22—868no—
1066C22—861no—
1067C22—861no—
1068C22—861no—
1069C22—861no—
1070C22—1721no—
1071C22—1721no—
1072C22—1721no—
1073C22#137×D4312yes—
1074C22C22×D4×D4311yescharacteristic
1075C4—21no—
1076C4—21no—
1077C4—21no—
1078C4—21no—
1079C4—41no—
1080C4—41no—
1081C4—44no—
1082C4—41no—
1083C4—432no—
1084C4—432no—
1085C4—432no—
1086C4—432no—
1087C4—861no—
1088C4—861no—
1089C4—1721no—
1090C4—1721no—
1091C4—1724no—
1092C4—1721no—
1093C4#137×D4312yes—
1094C4H(5,𝔽2)×D4312yes—
1095C2—22no—
1096C2—81no—
1097C2—862no—
1098C2—862no—
1099C2—3441no—
1100C2#535×D4311yescharacteristic
1101C2C2×#137×D4311yescharacteristic
1102C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3218C2
socleC22×C43C23×D4
prime radical#19147889C2
hypercenter#3218D43
hypocenterC43#60800
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Q8×D43C2semidirect
3. #19145624C2semidirect
4. #19145623C2semidirect
5. #19145622C2semidirect
6. #19145619C2semidirect
7. #19145618C2semidirect
8. #19145542C2semidirect
9. #19145541C2semidirect
10. #19145519C2semidirect
11. #19145518C2semidirect
12. #19145051C2semidirect
13. #19144974C2semidirect
14. #19144079C2semidirect
15. #19144077C2semidirect
16. #19143830C2semidirect
17. #19143826C2semidirect
18. #19143225C2semidirect
19. C43×#3218C2semidirect
59. #14583294C22semidirect
60. #14583293C22semidirect
61. #14583291C22semidirect
62. #14583277C22semidirect
63. #14583270C22semidirect
64. #14583269C22semidirect
65. #14583268C22semidirect
66. #14583267C22semidirect
67. #14583248C22semidirect
68. #14583248C22semidirect
69. #14583110C22semidirect
70. #14583109C22semidirect
71. #14583108C22semidirect
72. #14583107C22semidirect
73. #14583106C22semidirect
74. #14583105C22semidirect
75. #14583104C22semidirect
76. #14583103C22semidirect
77. #14583102C22semidirect
78. #14583101C22semidirect
100. C43×#497C22semidirect
101. C43×#491C22semidirect
102. C43×#462C22semidirect
103. C43×#461C22semidirect
469. C2×Dic43#137semidirect
494. C4×D43#137semidirect
551. #3218D43semidirect
615. #497C2×D43semidirect
621. #491C2×D43semidirect
629. #462C2×D43semidirect
635. #461C2×D43semidirect
658. C43#60800semidirect

Maximal subgroups

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

subgroupindex
#191478892
C2×C4⋊Q8×D432
#191456242
#191456232
#191456222
#191456192
#191456182
#191455422
#191455412
#191455192
#191455182
#191450512
#191449742
#191440792
#191440772
#191438302
#191438262
#191432252
C43×#32182
#6080043