Finite Group Databasebeta

← #25063500

Subgroups — #25063500

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148157C211yesmaximal, characteristic
2#19143559C211yesmaximal, characteristic, complemented
3#19143160C211yesmaximal, characteristic, complemented
4#19133061C211yesmaximal, characteristic, complemented
5#19133059C211yesmaximal, characteristic, complemented
6#19133048C211yesmaximal, characteristic, complemented
7#19133034C211yesmaximal, characteristic, complemented
8#19133031C211yesmaximal, characteristic, complemented
9#19133018C211yesmaximal, characteristic, complemented
10#19133007C211yesmaximal, characteristic, complemented
11#19133006C211yesmaximal, characteristic, complemented
12#19132996C211yesmaximal, characteristic, complemented
13#19132979C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1477C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583621C411yescharacteristic
18#14583612C411yescharacteristic
19#14583608C411yescharacteristic
20#14583598—21no—
21#14583590C411yescharacteristic
22#14583588C411yescharacteristic
23#14583582—21no—
24#14583578—21no—
25#14583573—21no—
26#14583548C411yescharacteristic
27#14583544C411yescharacteristic
28#14583537C411yescharacteristic
29#14583453C2211yescharacteristic
30#14583436C2211yescharacteristic
31#14583433—21no—
32#14583433C2211yescharacteristic
33#14583429—21no—
34#14583408—21no—
35C4×#10621898C2211yescharacteristic
36C4×#10621900C2211yescharacteristic
37C4×D4×D43C2211yescharacteristic
38C2×#13063282—21no—
39#14583028—21no—
40#14582974—21no—
41#14582973—21no—
42#14582969—21no—
43#14582950C2211yescharacteristic
44#14582950C2211yescharacteristic, complemented
45#14582925—21no—
46#14582924—21no—
47#14582924—21no—
48#14582923C2211yescharacteristic, complemented
49#14582921C2211yescharacteristic
50#14582921C2211yescharacteristic, complemented
51C4⋊C8×D43C2211yescharacteristic
52C4⋊C8×D43C2211yescharacteristic, complemented
53C4×#10621877C2211yescharacteristic, complemented
54C4×#10621872C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic
56#14582631C2211yescharacteristic, complemented
57#14582631C2211yescharacteristic, complemented
58Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
59Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
60#14582629C2211yescharacteristic, complemented
61#14582629C2211yescharacteristic, complemented
62#14582628C2211yescharacteristic
63#14582628C2211yescharacteristic
64D4⋊(C43⋊C8)C2211yescharacteristic
65D4⋊(C43⋊C8)C2211yescharacteristic
66#14582626C2211yescharacteristic
67#14582626C2211yescharacteristic
68C4×#41×C43C2211yescharacteristic
69C43×#431C2211yescharacteristic, complemented
70C2×C4⋊C8×C43C2211yescharacteristic, complemented
71C43×Q8⋊C8C2211yescharacteristic, complemented
72C43×Q8⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic
74C43×D4⋊C8C2211yescharacteristic
75C2×#10621898D411yescharacteristic
76C2×#10621900C2×C411yescharacteristic
77C2×D4×D43C2×C411yescharacteristic
78C22×C4×D43—21no—
79#13063331—44no—
80C2×#10621877—21no—
81C2×#10621877—21no—
82C2×#10621872—21no—
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88#13063324C2×C411yescharacteristic
89#13063323C2×C411yescharacteristic
90#13063320—21no—
91#13063320—21no—
92#13063319—21no—
93#13063319—21no—
94#13063319—21no—
95#13063318—21no—
96#13063317—21no—
97#13063317C2×C411yescharacteristic
98#13063316C2×C411yescharacteristic
99#13063315—21no—
100#13063315—21no—
101#13063314C2×C411yescharacteristic
102#13063313—21no—
103#13063313C2×C411yescharacteristic
104#13063311—21no—
105#13063310—21no—
106#13063310—21no—
107#13063309—21no—
108#13063308—21no—
109#13063308—21no—
110#13063308—21no—
111#13063307—21no—
112#13063306—21no—
113#13063305C2×C411yescharacteristic
114#13063304—21no—
115#13063304C2×C411yescharacteristic
116#13063303—21no—
117#13063303—21no—
118#13063302—21no—
119#13063302—21no—
120#13063301C2×C411yescharacteristic
121#13063301C2×C411yescharacteristic
122#13063300C2×C411yescharacteristic
123#13063299—21no—
124#13063299C2×C411yescharacteristic
125#13063298—21no—
126#13063297—21no—
127#13063297—21no—
128#13063295—21no—
129#13063293—21no—
130C4×Dic86—21no—
131C4×Dic86C2×C411yescharacteristic
132C4×Dic86D411yescharacteristic
133C4×Dic86C2311yescharacteristic
134#13063290C2×C411yescharacteristic
135C4×D172—21no—
136C4×D172C2×C411yescharacteristic
137C4×D172D411yescharacteristic
138C4×D172C2311yescharacteristic
139D4×Dic43C2×C411yescharacteristic
140D4×Dic43C2×C411yescharacteristic
141#13063287C2×C411yescharacteristic
142C4×C22⋊D43—21no—
143C4×C22⋊D43—21no—
144C4×C22⋊D43—21no—
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149(C22⋊D43)⋊C4—21no—
150(C22⋊D43)⋊C4—21no—
151#13063284D411yescharacteristic
152#13063283C2×C411yescharacteristic
153#13063282—21no—
154#13063282—21no—
155#13063282—21no—
156#13063282—21no—
157#13063282—21no—
158#13063282—21no—
159#13063282—21no—
160#13063282D411yescharacteristic
161#13063282D411yescharacteristic
162#13063281—21no—
163C2×Dic43⋊C4—21no—
164C2×Dic43⋊C4—21no—
165C4⋊C4×D43C2×C411yescharacteristic
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C22⋊C4×D43—21no—
169C2×C4×Dic43—21no—
170C42×D43C2311yescharacteristic
171C42×D43C2311yescharacteristic
172C4⋊(C43⋊C8)—21no—
173C4⋊(C43⋊C8)C2311yescharacteristic
174C4⋊(C43⋊C8)C2311yescharacteristic
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177Dic43⋊C8—21no—
178Dic43⋊C8—21no—
179Dic43⋊C8—21no—
180Dic43⋊C8—21no—
181(C2×D43)⋊C8—21no—
182(C2×D43)⋊C8—21no—
183#13063236—21no—
184#13063235—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C2×#41×C43C2×C411yescharacteristic
189C22×C8×C43—21no—
190C4×Q8×C43C2×C411yescharacteristic
191C4×Q8×C43C2311yescharacteristic
192C4×D4×C43—21no—
193C4×D4×C43—21no—
194C4×D4×C43C2×C411yescharacteristic
195C4×D4×C43C2311yescharacteristic
196#117×C43—21no—
197#117×C43C2×C411yescharacteristic
198C2×C42×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43—21no—
201C4⋊C8×C43—21no—
202C4⋊C8×C43C2311yescharacteristic
203C4⋊C8×C43C2311yescharacteristic
204C22⋊C8×C43—21no—
205C4×C8×C43C2311yescharacteristic
206C4×C8×C43C2311yescharacteristic
207C23×D43—21no—
208#41×C43—22no—
209#41×C43—41no—
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43C22×C411yescharacteristic
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C22×C411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2×D411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43C22⋊C411yescharacteristic
223C2×C22⋊D43C22⋊C411yescharacteristic
224C22×Dic43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227#10621900—22no—
228#10621900—41no—
229D4×D43—22no—
230D4×D43—41no—
231#10621898—22no—
232#10621898—22no—
233C2×D172—21no—
234C2×D172C22⋊C411yescharacteristic
235C2×D172C22×C411yescharacteristic
236C2×C4×D43—21no—
237C2×C4×D43—21no—
238C2×C4×D43—21no—
239C2×C4×D43—42no—
240C2×C4×D43—42no—
241C2×C4×D43C22×C411yescharacteristic
242C2×C4×D43C22×C411yescharacteristic
243C2×C4×D43C2×D411yescharacteristic
244C2×C4×D43C2×D411yescharacteristic
245C2×C4×D43C2×D411yescharacteristic
246C2×C4×D43C2×D411yescharacteristic
247C2×Dic86—21no—
248C2×Dic86C22⋊C411yescharacteristic
249C2×Dic86C22×C411yescharacteristic
250C2×C8×C43—21no—
251C2×C8×C43—21no—
252C2×C8×C43—21no—
253C2×C8×C43—21no—
254C2×C8×C43—42no—
255C4⋊C4×C43—21no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43C22×C411yescharacteristic
258C4⋊C4×C43C22×C411yescharacteristic
259C22⋊C4×C43—21no—
260C22⋊C4×C43—21no—
261C22⋊C4×C43—21no—
262C42×C43—21no—
263C42×C43—21no—
264C42×C43—21no—
265C42×C43C22×C411yescharacteristic
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2411yescharacteristic
269C22⋊Dic43—21no—
270C22⋊Dic43—21no—
271C22⋊Dic43—21no—
272C22⋊Dic43C22⋊C411yescharacteristic
273C22⋊Dic43C22⋊C411yescharacteristic
274(C2×D43)⋊C4—21no—
275(C2×D43)⋊C4—21no—
276(C2×D43)⋊C4—21no—
277(C2×D43)⋊C4—21no—
278(C2×D43)⋊C4—21no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—21no—
282(C2×D43)⋊C4—21no—
283(C2×D43)⋊C4—21no—
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
286(C2×D43)⋊C4C22⋊C411yescharacteristic
287(C2×D43)⋊C4C22⋊C411yescharacteristic
288(C2×D43)⋊C4C22⋊C411yescharacteristic
289(C2×D43)⋊C4C22⋊C411yescharacteristic
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292C4⋊Dic43C22⋊C411yescharacteristic
293C4⋊Dic43C22⋊C411yescharacteristic
294C4⋊Dic43C22×C411yescharacteristic
295C4⋊Dic43C22×C411yescharacteristic
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—21no—
299Dic43⋊C4—21no—
300Dic43⋊C4—21no—
301Dic43⋊C4—21no—
302Dic43⋊C4—21no—
303Dic43⋊C4—21no—
304Dic43⋊C4—21no—
305Dic43⋊C4—21no—
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4C22⋊C411yescharacteristic
309Dic43⋊C4C22⋊C411yescharacteristic
310Dic43⋊C4C22⋊C411yescharacteristic
311Dic43⋊C4C22⋊C411yescharacteristic
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43C22×C411yescharacteristic
316C4×Dic43C22×C411yescharacteristic
317C4×Dic43C2×D411yescharacteristic
318C4×Dic43C2×D411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321#10621877—42no—
322#10621877—42no—
323C2×C43⋊C8—21no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327#10621872—42no—
328#10621872—42no—
329#10621872—42no—
330C8×D43—42no—
331C8×D43—42no—
332C8×D43—42no—
333C23×C43—21no—
334C23×C43C2×C22⋊C411yescharacteristic
335C22×D43—21no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—81no—
339C22×D43C2×C22⋊C411yescharacteristic
340C22×D43C2×C22⋊C411yescharacteristic
341Q8×C43—21no—
342Q8×C43—21no—
343D4×C43—21no—
344D4×C43—42no—
345D4×C43#13112yescomplemented
346C2×C4×C43—21no—
347C2×C4×C43—21no—
348C2×C4×C43—21no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—41no—
354C2×C4×C43—42no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—81no—
358C2×C4×C43C2×C22⋊C411yescharacteristic
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C23×C411yescharacteristic
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C22⋊D43—22no—
365C22⋊D43—22no—
366C22⋊D43—42no—
367C22⋊D43—42no—
368C22⋊D43—81no—
369C2×Dic43—21no—
370C2×Dic43—21no—
371C2×Dic43—21no—
372C2×Dic43—42no—
373C2×Dic43—42no—
374C2×Dic43—81no—
375C2×Dic43C2×C22⋊C411yescharacteristic
376C2×Dic43C2×C22⋊C411yescharacteristic
377C2×Dic43C2×C22⋊C411yescharacteristic
378C2×Dic43C2×C22⋊C411yescharacteristic
379C2×Dic43C2×C22⋊C411yescharacteristic
380C2×Dic43C2×C22⋊C411yescharacteristic
381D172—22no—
382D172—21no—
383D172—21no—
384D172—81no—
385C4×D43—21no—
386C4×D43—21no—
387C4×D43—21no—
388C4×D43—21no—
389C4×D43—21no—
390C4×D43—21no—
391C4×D43—41no—
392C4×D43—41no—
393C4×D43—42no—
394C4×D43—41no—
395C4×D43—41no—
396C4×D43—42no—
397C4×D43AGL(1,ℤ/8)12yes—
398C4×D43#13712yes—
399Dic86—22no—
400Dic86—21no—
401Dic86—21no—
402Dic86—81no—
403C8×C43—41no—
404C8×C43—41no—
405C8×C43—41no—
406C8×C43—41no—
407C43⋊C8—22no—
408C43⋊C8—41no—
409C43⋊C8—41no—
410C43⋊C8—41no—
411#17512—431nomaximal, Sylow
412C22×C43—22no—
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—21no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43C22×C22⋊C411yescharacteristic
419C2×D43—21no—
420C2×D43—21no—
421C2×D43—21no—
422C2×D43—21no—
423C2×D43—21no—
424C2×D43—41no—
425C2×D43—41no—
426C2×D43—41no—
427C2×D43—84no—
428C2×D43#41712yes—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—21no—
432C4×C43—21no—
433C4×C43—41no—
434C4×C43—41no—
435C4×C43—41no—
436C4×C43C2×#13111yescharacteristic
437C4×C43#56811yescharacteristic
438C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
439C4×C43C2×#13711yescharacteristic
440Dic43—21no—
441Dic43—21no—
442Dic43—21no—
443Dic43—21no—
444Dic43—21no—
445Dic43—41no—
446Dic43—41no—
447Dic43—41no—
448Dic43#41712yes—
449#3475—431no—
450#2965—431no—
451#2906—431no—
452#1495—431no—
453#1495—431no—
454#1493—431no—
455#1489—431no—
456#1489—431no—
457#1486—431no—
458#1483—431no—
459#1483—431no—
460#1481—431no—
461#1477—431no—
462#1477D4311yescharacteristic, complemented
463C2×D4⋊C8—431no—
464C2×C43—42no—
465C2×C43—41no—
466C2×C43#288011yescharacteristic
467C2×C43C2×#41711yescharacteristic
468C2×C43#290111yescharacteristic
469D43—22no—
470D43—41no—
471D43—81no—
472C2×#131—861no—
473#556—431no—
474#555—431no—
475#554—431no—
476#553—861no—
477#552—431no—
478#552—431no—
479#552—861no—
480#551—861no—
481#551—861no—
482#547—431no—
483#546—431no—
484#546—431no—
485#533—431no—
486#529—431no—
487#529—431no—
488#529—861no—
489#529—861no—
490#525—861no—
491C4×#41—431no—
492C4×#41—431no—
493C4×#41C2×D4311yescharacteristic
494C2×C4×D4—431no—
495C2×#117—861no—
496#446—861no—
497#436—861no—
498#435—861no—
499#435—861no—
500#431—431no—
501#431—431no—
502#431C2×D4311yescharacteristic, complemented
503#424—861no—
504#424—861no—
505#424—861no—
506#423—431no—
507#423—431no—
508#423—431no—
509C2×C4⋊C8—431no—
510C2×C4⋊C8—431no—
511C2×C4⋊C8C2×D4311yescharacteristic, complemented
512C4×M16—431no—
513C4×M16—431no—
514C2×C4×C8—431no—
515Q8⋊C8—431no—
516Q8⋊C8—431no—
517Q8⋊C8—431no—
518Q8⋊C8—431no—
519Q8⋊C8—431no—
520Q8⋊C8—431no—
521Q8⋊C8C2×D4311yescharacteristic, complemented
522Q8⋊C8C2×D4311yescharacteristic, complemented
523D4⋊C8—431no—
524D4⋊C8—431no—
525D4⋊C8—431no—
526D4⋊C8—431no—
527D4⋊C8—431no—
528D4⋊C8—431no—
529D4⋊C8C2×D4311yescharacteristic
530D4⋊C8C2×D4311yescharacteristic
531C43#1751211yescharacteristic, complemented, Sylow
532C2×#41—431no—
533C2×#41—431no—
534C2×#41C4×D4311yescharacteristic
535C22×D4—431no—
536C23×C4—861no—
537#131—1724no—
538C2×M16—861no—
539C2×M16—861no—
540C2×M16—861no—
541C2×M16—861no—
542C2×M16—861no—
543C22×C8—21no—
544C22×C8—861no—
545C22×C8—861no—
546C22×C8—861no—
547C4⋊Q8—431no—
548C4⋊Q8—431no—
549#126—861no—
550#126—861no—
551#126—861no—
552#126—861no—
553#126—861no—
554#126—861no—
555#125—431no—
556#125—431no—
557#125—861no—
558#125—861no—
559#125—861no—
560#124—431no—
561#124—431no—
562#124—861no—
563#124—861no—
564#123—861no—
565#123—861no—
566#123—861no—
567#123—861no—
568#123—861no—
569#123—861no—
570#123—861no—
571#123—861no—
572C22⋊Q8—431no—
573C22⋊Q8—431no—
574C22⋊Q8—431no—
575C22⋊Q8—431no—
576C22⋊Q8—861no—
577C22⋊Q8—861no—
578C22⋊Q8—861no—
579C22⋊Q8—861no—
580C22⋊Q8—861no—
581#121—431no—
582#121—431no—
583#121—861no—
584#121—861no—
585#121—861no—
586#121—861no—
587#120—861no—
588#120—861no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—431no—
592C4×Q8—431no—
593C4×Q8—861no—
594C4×Q8C4×D4311yescharacteristic
595C4×Q8C22×D4311yescharacteristic
596C4×D4—21no—
597C4×D4—21no—
598C4×D4—431no—
599C4×D4—431no—
600C4×D4—431no—
601C4×D4—431no—
602C4×D4—431no—
603C4×D4—431no—
604C4×D4—431no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—861no—
609C4×D4—861no—
610C4×D4—861no—
611C4×D4—861no—
612C4×D4—861no—
613C4×D4—861no—
614C4×D4C4×D4311yescharacteristic
615C4×D4C22×D4311yescharacteristic
616#117—21no—
617#117—431no—
618#117—431no—
619#117—431no—
620#117—431no—
621#117—861no—
622#117—861no—
623#117—861no—
624#117—861no—
625#117—861no—
626#117—861no—
627#117—861no—
628#117—861no—
629#117C4×D4311yescharacteristic
630C2×C4⋊C4—431no—
631C2×C4⋊C4—861no—
632C2×C4⋊C4—861no—
633C2×C22⋊C4—861no—
634C2×C22⋊C4—861no—
635C2×C22⋊C4—861no—
636C2×C42—21no—
637C2×C42—431no—
638C2×C42—431no—
639C2×C42—861no—
640C2×C42C22×D4311yescharacteristic
641C4⋊C8—21no—
642C4⋊C8—21no—
643C4⋊C8—431no—
644C4⋊C8—431no—
645C4⋊C8—861no—
646C4⋊C8—861no—
647C4⋊C8—861no—
648C4⋊C8—861no—
649C4⋊C8—861no—
650C4⋊C8—861no—
651C4⋊C8—861no—
652C4⋊C8C22×D4311yescharacteristic
653C4⋊C8C22×D4311yescharacteristic
654C22⋊C8—21no—
655C22⋊C8—861no—
656C22⋊C8—861no—
657#97—861no—
658#97—861no—
659C4×C8—431no—
660C4×C8—431no—
661C4×C8—861no—
662C4×C8C22×D4311yescharacteristic
663C4×C8C22×D4311yescharacteristic
664C24—861no—
665#41—22no—
666#41—41no—
667#41—862no—
668#41—862no—
669#41—862no—
670#41—1721no—
671C2×Q8—431no—
672C2×Q8—431no—
673C2×Q8—861no—
674C2×Q8C2×C4×D4311yescharacteristic
675C2×D4—21no—
676C2×D4—431no—
677C2×D4—431no—
678C2×D4—431no—
679C2×D4—431no—
680C2×D4—861no—
681C2×D4—861no—
682C2×D4—862no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—1721no—
686C2×D4C2×C4×D4311yescharacteristic
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—431no—
691C22×C4—431no—
692C22×C4—431no—
693C22×C4—431no—
694C22×C4—431no—
695C22×C4—431no—
696C22×C4—861no—
697C22×C4—861no—
698C22×C4—861no—
699C22×C4—861no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—1722no—
703C22×C4—1722no—
704C22×C4C2×C4×D4311yescharacteristic
705C22×C4D4×D4311yescharacteristic
706C22×C4D4×D4311yescharacteristic
707M16—1722no—
708M16—1722no—
709M16—1722no—
710M16—1722no—
711M16—1722no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—42no—
717C2×C8—861no—
718C2×C8—861no—
719C2×C8—861no—
720C2×C8—861no—
721C2×C8—1722no—
722C2×C8—1722no—
723C2×C8—1722no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—431no—
727C4⋊C4—431no—
728C4⋊C4—431no—
729C4⋊C4—431no—
730C4⋊C4—431no—
731C4⋊C4—431no—
732C4⋊C4—431no—
733C4⋊C4—431no—
734C4⋊C4—861no—
735C4⋊C4—861no—
736C4⋊C4—861no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—861no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4—861no—
744C4⋊C4—861no—
745C4⋊C4—861no—
746C4⋊C4—861no—
747C4⋊C4—861no—
748C4⋊C4C2×C4×D4311yescharacteristic
749C4⋊C4C2×C4×D4311yescharacteristic
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—431no—
754C22⋊C4—431no—
755C22⋊C4—431no—
756C22⋊C4—431no—
757C22⋊C4—431no—
758C22⋊C4—431no—
759C22⋊C4—861no—
760C22⋊C4—861no—
761C22⋊C4—861no—
762C22⋊C4—861no—
763C22⋊C4—861no—
764C22⋊C4—861no—
765C22⋊C4—861no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—861no—
769C22⋊C4—861no—
770C22⋊C4—861no—
771C22⋊C4—861no—
772C22⋊C4—861no—
773C22⋊C4—861no—
774C42—21no—
775C42—21no—
776C42—21no—
777C42—431no—
778C42—431no—
779C42—431no—
780C42—431no—
781C42—431no—
782C42—431no—
783C42—861no—
784C42—861no—
785C42—861no—
786C42C2×C4×D4311yescharacteristic
787C42D4×D4311yescharacteristic
788C42D4×D4311yescharacteristic
789C42C23×D4311yescharacteristic
790C23—21no—
791C23—431no—
792C23—431no—
793C23—861no—
794C23—3441no—
795C23—1722no—
796C23—1722no—
797C23C22⋊C4×D4311yescharacteristic
798Q8—21no—
799Q8—21no—
800Q8—862no—
801Q8—861no—
802Q8—861no—
803Q8—3441no—
804D4—21no—
805D4—42no—
806D4—862no—
807D4—862no—
808D4—862no—
809D4—861no—
810D4—861no—
811D4—3441no—
812D4—3441no—
813D4—1722no—
814D4—1722no—
815D4#1306333112yescomplemented
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—81no—
828C2×C4—431no—
829C2×C4—432no—
830C2×C4—432no—
831C2×C4—431no—
832C2×C4—431no—
833C2×C4—431no—
834C2×C4—431no—
835C2×C4—431no—
836C2×C4—861no—
837C2×C4—861no—
838C2×C4—861no—
839C2×C4—861no—
840C2×C4—861no—
841C2×C4—861no—
842C2×C4—861no—
843C2×C4—861no—
844C2×C4—861no—
845C2×C4—3441no—
846C2×C4—1721no—
847C2×C4—1721no—
848C2×C4—1722no—
849C2×C4—1722no—
850C2×C4—1722no—
851C2×C4—1722no—
852C2×C4—1721no—
853C2×C4—1721no—
854C2×C4C22⋊C4×D4311yescharacteristic
855C2×C4C22⋊C4×D4311yescharacteristic
856C2×C4C22⋊C4×D4311yescharacteristic
857C2×C4C22×C4×D4311yescharacteristic
858C2×C4C2×D4×D4311yescharacteristic
859C2×C4C2×D4×D4311yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C8—862no—
865C8—1721no—
866C8—1721no—
867C8—1721no—
868C22—21no—
869C22—22no—
870C22—21no—
871C22—21no—
872C22—41no—
873C22—41no—
874C22—432no—
875C22—861no—
876C22—861no—
877C22—861no—
878C22—861no—
879C22—861no—
880C22—3444no—
881C22—1721no—
882C22—1721no—
883C22—1721no—
884C22C2×C22⋊C4×D4311yescharacteristic
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—41no—
890C4—41no—
891C4—41no—
892C4—432no—
893C4—861no—
894C4—861no—
895C4—861no—
896C4—861no—
897C4—861no—
898C4—1721no—
899C4—1721no—
900C4—1721no—
901C4C2×#1306333111yescharacteristic
902C4#1458366511yescharacteristic
903C4AGL(1,ℤ/8)×D4311yescharacteristic
904C4#137×D4311yescharacteristic
905C2—41no—
906C2—42no—
907C2—862no—
908C2—3441no—
909C2—1721no—
910C2#1914304111yescharacteristic
911C2#417×D4311yescharacteristic
912C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1477C2
socleC22×C43C22×C22⋊C4
prime radical#19148157C2
cosocleC42×C43C24
hypercenter#1477D43
hypocenterC43#17512
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #19143559C2semidirect
3. #19143160C2semidirect
4. #19133061C2semidirect
5. #19133059C2semidirect
6. #19133048C2semidirect
7. #19133034C2semidirect
8. #19133031C2semidirect
9. #19133018C2semidirect
10. #19133007C2semidirect
11. #19133006C2semidirect
12. #19132996C2semidirect
13. #19132979C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1477C2semidirect
44. #14582950C22semidirect
48. #14582923C22semidirect
50. #14582921C22semidirect
52. C4⋊C8×D43C22semidirect
53. C4×#10621877C22semidirect
54. C4×#10621872C22semidirect
56. #14582631C22semidirect
57. #14582631C22semidirect
58. Q8⋊(C43⋊C8)C22semidirect
59. Q8⋊(C43⋊C8)C22semidirect
60. #14582629C22semidirect
61. #14582629C22semidirect
69. C43×#431C22semidirect
70. C2×C4⋊C8×C43C22semidirect
71. C43×Q8⋊C8C22semidirect
72. C43×Q8⋊C8C22semidirect
345. D4×C43#131semidirect
462. #1477D43semidirect
502. #431C2×D43semidirect
511. C2×C4⋊C8C2×D43semidirect
521. Q8⋊C8C2×D43semidirect
522. Q8⋊C8C2×D43semidirect
531. C43#17512semidirect
815. D4#13063331semidirect

Maximal subgroups

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

subgroupindex
#191481572
#191435592
#191431602
#191330612
#191330592
#191330482
#191330342
#191330312
#191330182
#191330072
#191330062
#191329962
#191329792
D4⋊C8×D432
C43×#14772
#1751243