Finite Group Databasebeta

← #25063572

Subgroups — #25063572

Order 11008.

1096 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148201C211yesmaximal, characteristic
2#19143722C211yesmaximal, characteristic, complemented
3C4×#13063331C211yesmaximal, characteristic, complemented
4#19133054C211yesmaximal, characteristic, complemented
5#19133044C211yesmaximal, characteristic, complemented
6#19133037C211yesmaximal, characteristic, complemented
7#19133036C211yesmaximal, characteristic, complemented
8#19133033C211yesmaximal, characteristic, complemented
9#19133010C211yesmaximal, characteristic, complemented
10#19133008C211yesmaximal, characteristic, complemented
11#19133007C211yesmaximal, characteristic, complemented
12#19132976C211yesmaximal, characteristic, complemented
13C2×#14582628C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1494C211yesmaximal, characteristic, complemented
16C2×#13063331—21no—
17#14583631C411yescharacteristic
18#14583607C411yescharacteristic
19#14583605C411yescharacteristic
20#14583602C411yescharacteristic
21#14583601C411yescharacteristic
22#14583600—21no—
23#14583574—21no—
24#14583572—21no—
25#14583542C411yescharacteristic
26#14583541—21no—
27#14583540C411yescharacteristic
28#14583533C411yescharacteristic
29#14583446C2211yescharacteristic
30#14583436C2211yescharacteristic
31#14583427—21no—
32#14583411—21no—
33#14583408—21no—
34C4×#10621902C2211yescharacteristic
35C4×#10621898C2211yescharacteristic
36C2×C4×D172C2211yescharacteristic
37C4×D4×D43—21no—
38C4×D4×D43C2211yescharacteristic
39#14583027—21no—
40#14582972—21no—
41#14582967—21no—
42(C22⋊D43)⋊C8—21no—
43#14582955C2211yescharacteristic, complemented
44#14582951C2211yescharacteristic, complemented
45#14582921C2211yescharacteristic, complemented
46C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
47C4⋊C8×D43C2211yescharacteristic, complemented
48#14582854—21no—
49#14582853—21no—
50#14582853—21no—
51C4×#10621877C2211yescharacteristic, complemented
52C4×#10621872C2211yescharacteristic, complemented
53C4×#10621872C2211yescharacteristic, complemented
54C4×C8×D43C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic, complemented
56Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
57Q8⋊(C43⋊C8)C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic
59#14582628C2211yescharacteristic
60#14582628C2211yescharacteristic, complemented
61#14582628C2211yescharacteristic, complemented
62D4⋊(C43⋊C8)C2211yescharacteristic, complemented
63D4⋊(C43⋊C8)C2211yescharacteristic, complemented
64#14582626C2211yescharacteristic
65#14582626C2211yescharacteristic
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C43×#529C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C2×C4×C8×C43C2211yescharacteristic, complemented
71C43×Q8⋊C8C2211yescharacteristic, complemented
72C43×Q8⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic, complemented
74C43×D4⋊C8C2211yescharacteristic, complemented
75C2×#10621902C2×C411yescharacteristic
76C2×#10621898—21no—
77C2×#10621898D411yescharacteristic
78C22×D172C2×C411yescharacteristic
79C2×D4×D43—21no—
80C2×D4×D43C2×C411yescharacteristic
81C22×C4×D43—21no—
82C22×C4×D43—21no—
83#13063331—28no—
84C2×#10621877—21no—
85C2×#10621872—21no—
86C2×#10621872—21no—
87C2×#10621872—21no—
88C22×C43⋊C8—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91C2×C8×D43—21no—
92#13063324C2×C411yescharacteristic
93#13063321C2×C411yescharacteristic
94#13063320—21no—
95#13063320—21no—
96#13063318—21no—
97#13063316C2×C411yescharacteristic
98#13063315—21no—
99#13063314C2×C411yescharacteristic
100#13063311—21no—
101#13063311—21no—
102#13063310—21no—
103#13063310—21no—
104#13063310—21no—
105#13063309—21no—
106#13063309—21no—
107#13063307—21no—
108#13063307—21no—
109#13063305—21no—
110#13063305—21no—
111#13063303—21no—
112#13063303—21no—
113#13063302—21no—
114#13063301C2×C411yescharacteristic
115#13063300—21no—
116#13063300—21no—
117#13063300C2×C411yescharacteristic
118#13063300C2×C411yescharacteristic
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063296C2×C411yescharacteristic
124#13063295—21no—
125#13063295—21no—
126#13063295—21no—
127#13063293—21no—
128Q8×Dic43C2×C411yescharacteristic
129C4×Dic86C2×C411yescharacteristic
130C4×Dic86D411yescharacteristic
131C4×D172—21no—
132C4×D172—21no—
133C4×D172—21no—
134C4×D172—21no—
135C4×D172C2×C411yescharacteristic
136C4×D172C2×C411yescharacteristic
137C4×D172C2×C411yescharacteristic
138C4×D172D411yescharacteristic
139C4×D172C2311yescharacteristic
140C4×D172C2311yescharacteristic
141D4×Dic43—21no—
142D4×Dic43C2×C411yescharacteristic
143#13063287—21no—
144#13063287—21no—
145#13063287C2×C411yescharacteristic
146#13063287C2×C411yescharacteristic
147C4×C22⋊D43—21no—
148C4×C22⋊D43—21no—
149C4×C22⋊D43C2×C411yescharacteristic
150C4×C22⋊D43C2×C411yescharacteristic
151C4×C22⋊D43D411yescharacteristic
152C4×C22⋊D43D411yescharacteristic
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156#13063284D411yescharacteristic
157#13063283—21no—
158#13063283C2×C411yescharacteristic
159#13063282—21no—
160#13063282D411yescharacteristic
161#13063282D411yescharacteristic
162C2×C4⋊Dic43C2×C411yescharacteristic
163C4⋊C4×D43—21no—
164C4⋊C4×D43C2×C411yescharacteristic
165C2×(C2×D43)⋊C4—21no—
166C22⋊C4×D43—21no—
167C22⋊C4×D43—21no—
168C22⋊C4×D43—21no—
169C42×D43—21no—
170C42×D43C2311yescharacteristic
171C42×D43C2311yescharacteristic
172C4⋊(C43⋊C8)—21no—
173C4⋊(C43⋊C8)C2311yescharacteristic
174C4⋊(C43⋊C8)C2311yescharacteristic
175Dic43⋊C8—21no—
176Dic43⋊C8—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179#13063236—21no—
180#13063235—21no—
181#13063235—21no—
182#13063235—21no—
183C4×C43⋊C8C2311yescharacteristic
184C4×C43⋊C8C2311yescharacteristic
185C8×Dic43—21no—
186C8×Dic43—21no—
187C8×Dic43—21no—
188C22×C8×C43—21no—
189#126×C43—21no—
190#125×C43C2×C411yescharacteristic
191#124×C43C2×C411yescharacteristic
192#123×C43—21no—
193C22⋊Q8×C43C2×C411yescharacteristic
194#121×C43C2×C411yescharacteristic
195C4×Q8×C43C2311yescharacteristic
196C4×D4×C43—21no—
197C4×D4×C43C2311yescharacteristic
198#117×C43—21no—
199C2×C42×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C4⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43—21no—
203#97×C43—21no—
204C4×C8×C43—21no—
205C4×C8×C43C2311yescharacteristic
206C4×C8×C43C2311yescharacteristic
207C23×D43—21no—
208C23×D43—21no—
209C2×Q8×C43C22×C411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43C22×C411yescharacteristic
212C22×C4×C43—21no—
213C22×C4×C43C22×C411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C2×C22⋊D43C22⋊C411yescharacteristic
221C2×C22⋊D43C22⋊C411yescharacteristic
222C22×Dic43—21no—
223C22×Dic43—21no—
224#10621902—22no—
225#10621902—41no—
226D4×D43—22no—
227D4×D43—41no—
228D4×D43—44no—
229#10621898—24no—
230#10621898—81no—
231#10621898—81no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172—21no—
236C2×D172—22no—
237C2×D172—41no—
238C2×D172C22⋊C411yescharacteristic
239C2×D172C22×C411yescharacteristic
240C2×D172C22×C411yescharacteristic
241C2×C4×D43—21no—
242C2×C4×D43—21no—
243C2×C4×D43—21no—
244C2×C4×D43—21no—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—21no—
249C2×C4×D43—81no—
250C2×C4×D43—81no—
251C2×C4×D43—81no—
252C2×C4×D43—81no—
253C2×C4×D43C22×C411yescharacteristic
254C2×C4×D43C22×C411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×D411yescharacteristic
259C2×Dic86—21no—
260C2×Dic86C22⋊C411yescharacteristic
261C2×C8×C43—24no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C2×C8×C43—21no—
265C2×C8×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43—21no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43C22×C411yescharacteristic
271C4⋊C4×C43C22×C411yescharacteristic
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C22⋊C4×C43—21no—
276C22⋊C4×C43—21no—
277C42×C43—21no—
278C42×C43C22×C411yescharacteristic
279C42×C43C2×D411yescharacteristic
280C42×C43C2×D411yescharacteristic
281C42×C43C2411yescharacteristic
282C22⋊Dic43—21no—
283C22⋊Dic43—21no—
284C22⋊Dic43C22⋊C411yescharacteristic
285C22⋊Dic43C22⋊C411yescharacteristic
286(C2×D43)⋊C4—21no—
287(C2×D43)⋊C4—21no—
288(C2×D43)⋊C4—21no—
289(C2×D43)⋊C4—21no—
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—21no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—21no—
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300(C2×D43)⋊C4C22⋊C411yescharacteristic
301(C2×D43)⋊C4C22⋊C411yescharacteristic
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43C22⋊C411yescharacteristic
306C4⋊Dic43C22⋊C411yescharacteristic
307C4⋊Dic43C22×C411yescharacteristic
308C4⋊Dic43C22×C411yescharacteristic
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315Dic43⋊C4C22⋊C411yescharacteristic
316Dic43⋊C4C22⋊C411yescharacteristic
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43C22×C411yescharacteristic
320C4×Dic43C22×C411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323C4×Dic43C2×D411yescharacteristic
324C4×Dic43C2×D411yescharacteristic
325#10621877—24no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328C2×C43⋊C8—21no—
329C2×C43⋊C8—21no—
330C2×C43⋊C8—81no—
331#10621872—24no—
332#10621872—24no—
333#10621872—81no—
334C8×D43—24no—
335C8×D43—24no—
336C8×D43—81no—
337C23×C43—21no—
338C23×C43C2×C22⋊C411yescharacteristic
339C22×D43—21no—
340C22×D43—21no—
341C22×D43—42no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345C22×D43—81no—
346C22×D43—81no—
347C22×D43C2×C22⋊C411yescharacteristic
348C22×D43C2×C22⋊C411yescharacteristic
349Q8×C43—21no—
350Q8×C43—21no—
351D4×C43—21no—
352D4×C43—21no—
353D4×C43—42no—
354C2×C4×C43—22no—
355C2×C4×C43—21no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—21no—
359C2×C4×C43—21no—
360C2×C4×C43—21no—
361C2×C4×C43—21no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43C2×C22⋊C411yescharacteristic
365C2×C4×C43C2×C22⋊C411yescharacteristic
366C2×C4×C43C2×C22⋊C411yescharacteristic
367C2×C4×C43C23×C411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C22⋊D43—22no—
371C22⋊D43—42no—
372C22⋊D43—42no—
373C22⋊D43—81no—
374C22⋊D43—81no—
375C22⋊D43#10414yes—
376C2×Dic43—21no—
377C2×Dic43—21no—
378C2×Dic43—81no—
379C2×Dic43—81no—
380C2×Dic43C2×C22⋊C411yescharacteristic
381C2×Dic43C2×C22⋊C411yescharacteristic
382C2×Dic43C2×C22⋊C411yescharacteristic
383C2×Dic43C2×C22⋊C411yescharacteristic
384C2×Dic43C2×C22⋊C411yescharacteristic
385C2×Dic43C2×C22⋊C411yescharacteristic
386D172—22no—
387D172—21no—
388D172—21no—
389D172—21no—
390D172—42no—
391D172—42no—
392D172—42no—
393D172—81no—
394D172#13112yescomplemented
395C4×D43—22no—
396C4×D43—21no—
397C4×D43—21no—
398C4×D43—21no—
399C4×D43—21no—
400C4×D43—21no—
401C4×D43—21no—
402C4×D43—21no—
403C4×D43—21no—
404C4×D43—22no—
405C4×D43—42no—
406C4×D43—41no—
407C4×D43—41no—
408C4×D43—41no—
409C4×D43—41no—
410C4×D43—42no—
411C4×D43—81no—
412C4×D43—81no—
413C4×D43—81no—
414C4×D43—81no—
415Dic86—22no—
416Dic86—81no—
417C8×C43—22no—
418C8×C43—22no—
419C8×C43—41no—
420C8×C43—41no—
421C43⋊C8—22no—
422C43⋊C8—22no—
423C43⋊C8—41no—
424C43⋊C8—41no—
425#17517—431nomaximal, Sylow
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—41no—
429C22×C43—41no—
430C22×C43—41no—
431C22×C43C2×#10412yes—
432C22×C43C22×C22⋊C411yescharacteristic
433C2×D43—21no—
434C2×D43—21no—
435C2×D43—22no—
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—21no—
439C2×D43—41no—
440C2×D43—41no—
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—41no—
444C2×D43—84no—
445C2×D43—84no—
446C2×D43C2×#10412yes—
447C4×C43—21no—
448C4×C43—21no—
449C4×C43—21no—
450C4×C43—21no—
451C4×C43—41no—
452C4×C43—41no—
453C4×C43—41no—
454C4×C43C2×#13111yescharacteristic
455C4×C43#56811yescharacteristic
456C4×C43#57611yescharacteristic
457C4×C43#57711yescharacteristic
458Dic43—21no—
459Dic43—21no—
460Dic43—21no—
461Dic43—21no—
462Dic43—21no—
463Dic43—41no—
464Dic43—41no—
465Dic43C2×#10412yes—
466#3481—431no—
467#2990—431no—
468C4×#131—431no—
469#1494—431no—
470#1494D4311yescharacteristic, complemented
471#1492—431no—
472#1490—431no—
473#1490—431no—
474#1489—431no—
475#1484—431no—
476#1483—431no—
477#1483—431no—
478#1476—431no—
479C2×D4⋊C8—431no—
480C2×D4⋊C8—431no—
481C2×C43—22no—
482C2×C43—81no—
483C2×C43#288011yescharacteristic
484C2×C43#289711yescharacteristic
485C2×C43C22×#10411yescharacteristic
486D43—22no—
487D43—41no—
488D43—42no—
489D43—81no—
490C2×#131—861no—
491#559—431no—
492#554—431no—
493#554—431no—
494#553—431no—
495#553—431no—
496#553—861no—
497#551—861no—
498#551—861no—
499#546—431no—
500#546—431no—
501#546—861no—
502D42—431no—
503#532—431no—
504#529—431no—
505#529—861no—
506#529C2×D4311yescharacteristic
507#525—861no—
508#525—861no—
509C4×#41—431no—
510C4×#41—431no—
511C2×C4×D4—431no—
512C2×C4×D4—431no—
513C2×C4×D4—861no—
514#446—861no—
515#435—861no—
516#435—861no—
517C8×D4—861no—
518#432—431no—
519#432C2×D4311yescharacteristic, complemented
520#431—431no—
521#423—431no—
522C2×C4⋊C8—431no—
523C2×C4⋊C8—431no—
524#405—861no—
525#405—861no—
526#405—861no—
527C4×M16—431no—
528C4×M16—431no—
529C4×M16—431no—
530C2×C4×C8—431no—
531C2×C4×C8—431no—
532C2×C4×C8C2×D4311yescharacteristic, complemented
533Q8⋊C8—431no—
534Q8⋊C8—431no—
535Q8⋊C8C2×D4311yescharacteristic, complemented
536Q8⋊C8C2×D4311yescharacteristic, complemented
537D4⋊C8—431no—
538D4⋊C8—431no—
539D4⋊C8—431no—
540D4⋊C8—431no—
541D4⋊C8—431no—
542D4⋊C8—431no—
543D4⋊C8—431no—
544D4⋊C8—431no—
545D4⋊C8—431no—
546D4⋊C8—431no—
547D4⋊C8C2×D4311yescharacteristic, complemented
548D4⋊C8C2×D4311yescharacteristic, complemented
549C43#1751711yescharacteristic, complemented, Sylow
550C2×#41—431no—
551C2×#41—431no—
552C2×#41—861no—
553C22×D4—431no—
554C22×D4—431no—
555C22×D4—861no—
556C23×C4—861no—
557C23×C4—861no—
558#131—868no—
559C2×M16—861no—
560C2×M16—861no—
561C2×M16—861no—
562C2×M16—861no—
563C22×C8—21no—
564C22×C8—861no—
565C22×C8—861no—
566C22×C8—861no—
567C22×C8—861no—
568C4⋊Q8—431no—
569#127—431no—
570#126—21no—
571#126—861no—
572#126—861no—
573#126—861no—
574#125—431no—
575#125—861no—
576#125C4×D4311yescharacteristic
577#124—431no—
578#124—861no—
579#124—861no—
580#124C4×D4311yescharacteristic
581#123—21no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586#123—861no—
587#123—861no—
588#123—861no—
589C22⋊Q8—431no—
590C22⋊Q8—861no—
591C22⋊Q8—861no—
592C22⋊Q8—861no—
593C22⋊Q8—861no—
594C22⋊Q8—861no—
595C22⋊Q8C4×D4311yescharacteristic
596#121—431no—
597#121—431no—
598#121—431no—
599#121—861no—
600#121—861no—
601#121—861no—
602#121—861no—
603#121—861no—
604#121—861no—
605#121C4×D4311yescharacteristic
606#120—861no—
607#120—861no—
608#120—861no—
609#120—861no—
610C4×Q8—431no—
611C4×Q8—431no—
612C4×Q8—431no—
613C4×Q8C22×D4311yescharacteristic
614C4×D4—21no—
615C4×D4—431no—
616C4×D4—431no—
617C4×D4—431no—
618C4×D4—431no—
619C4×D4—431no—
620C4×D4—431no—
621C4×D4—431no—
622C4×D4—431no—
623C4×D4—431no—
624C4×D4—431no—
625C4×D4—431no—
626C4×D4—431no—
627C4×D4—431no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4—861no—
631C4×D4—861no—
632C4×D4—861no—
633C4×D4—861no—
634C4×D4—861no—
635C4×D4—861no—
636C4×D4—861no—
637C4×D4—861no—
638C4×D4—861no—
639C4×D4—861no—
640C4×D4C22×D4311yescharacteristic
641#117—21no—
642#117—431no—
643#117—431no—
644#117—431no—
645#117—431no—
646#117—861no—
647#117—861no—
648C2×C4⋊C4—431no—
649C2×C4⋊C4—431no—
650C2×C4⋊C4—861no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4—861no—
653C2×C22⋊C4—861no—
654C2×C22⋊C4—861no—
655C2×C42—431no—
656C2×C42—431no—
657C2×C42—861no—
658C2×C42C22×D4311yescharacteristic
659C4⋊C8—431no—
660C4⋊C8—431no—
661C4⋊C8—861no—
662C4⋊C8—861no—
663C4⋊C8—861no—
664C4⋊C8C22×D4311yescharacteristic
665C4⋊C8C22×D4311yescharacteristic
666C22⋊C8—21no—
667C22⋊C8—861no—
668C22⋊C8—861no—
669#97—21no—
670#97—861no—
671#97—861no—
672#97—861no—
673#97—861no—
674C4×C8—21no—
675C4×C8—431no—
676C4×C8—431no—
677C4×C8—861no—
678C4×C8—861no—
679C4×C8—861no—
680C4×C8C22×D4311yescharacteristic
681C4×C8C22×D4311yescharacteristic
682C24—861no—
683C24—861no—
684#41—864no—
685#41—862no—
686#41—3441no—
687#41—3441no—
688#41—1721no—
689C2×Q8—431no—
690C2×Q8—861no—
691C2×Q8C2×C4×D4311yescharacteristic
692C2×D4—21no—
693C2×D4—431no—
694C2×D4—431no—
695C2×D4—431no—
696C2×D4—431no—
697C2×D4—431no—
698C2×D4—862no—
699C2×D4—861no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—862no—
706C2×D4—861no—
707C2×D4—861no—
708C2×D4—1721no—
709C2×D4—1721no—
710C2×D4—1724no—
711C2×D4C2×C4×D4311yescharacteristic
712C22×C4—21no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—431no—
718C22×C4—431no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—861no—
727C22×C4—861no—
728C22×C4—861no—
729C22×C4—3441no—
730C22×C4—3441no—
731C22×C4—3441no—
732C22×C4—3441no—
733C22×C4C2×C4×D4311yescharacteristic
734C22×C4D4×D4311yescharacteristic
735C22×C4D4×D4311yescharacteristic
736M16—864no—
737M16—864no—
738M16—864no—
739M16—3441no—
740C2×C8—24no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—864no—
746C2×C8—864no—
747C2×C8—861no—
748C2×C8—861no—
749C2×C8—861no—
750C2×C8—861no—
751C2×C8—3441no—
752C2×C8—3441no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—431no—
758C4⋊C4—431no—
759C4⋊C4—431no—
760C4⋊C4—431no—
761C4⋊C4—431no—
762C4⋊C4—431no—
763C4⋊C4—431no—
764C4⋊C4—431no—
765C4⋊C4—861no—
766C4⋊C4—861no—
767C4⋊C4—861no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—861no—
771C4⋊C4—861no—
772C4⋊C4C2×C4×D4311yescharacteristic
773C4⋊C4C2×C4×D4311yescharacteristic
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—431no—
780C22⋊C4—431no—
781C22⋊C4—431no—
782C22⋊C4—431no—
783C22⋊C4—431no—
784C22⋊C4—431no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C22⋊C4—861no—
795C22⋊C4—861no—
796C22⋊C4—861no—
797C22⋊C4—861no—
798C22⋊C4—861no—
799C42—21no—
800C42—431no—
801C42—431no—
802C42—431no—
803C42—431no—
804C42—431no—
805C42—431no—
806C42—861no—
807C42—861no—
808C42C2×C4×D4311yescharacteristic
809C42D4×D4311yescharacteristic
810C42D4×D4311yescharacteristic
811C42C23×D4311yescharacteristic
812C23—21no—
813C23—431no—
814C23—431no—
815C23—861no—
816C23—861no—
817C23—3441no—
818C23—3441no—
819C23—1722no—
820C23—1722no—
821C23—1722no—
822C23—1722no—
823C23C22⋊C4×D4311yescharacteristic
824Q8—21no—
825Q8—21no—
826Q8—862no—
827Q8—3441no—
828D4—21no—
829D4—21no—
830D4—42no—
831D4—434no—
832D4—432no—
833D4—862no—
834D4—862no—
835D4—861no—
836D4—861no—
837D4—861no—
838D4—3441no—
839D4—3441no—
840D4—3441no—
841D4—1722no—
842D4—1722no—
843D4—1722no—
844D4—1722no—
845D4—1722no—
846C2×C4—22no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—431no—
860C2×C4—431no—
861C2×C4—431no—
862C2×C4—862no—
863C2×C4—862no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—861no—
869C2×C4—861no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—861no—
873C2×C4—861no—
874C2×C4—3441no—
875C2×C4—3441no—
876C2×C4—3441no—
877C2×C4—3441no—
878C2×C4—3441no—
879C2×C4—3441no—
880C2×C4—1722no—
881C2×C4—1722no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4C22⋊C4×D4311yescharacteristic
887C2×C4C22⋊C4×D4311yescharacteristic
888C2×C4C22⋊C4×D4311yescharacteristic
889C2×C4C22×C4×D4311yescharacteristic
890C2×C4C2×D4×D4311yescharacteristic
891C2×C4C2×D4×D4311yescharacteristic
892C8—22no—
893C8—22no—
894C8—41no—
895C8—41no—
896C8—862no—
897C8—862no—
898C8—1721no—
899C8—1721no—
900C22—21no—
901C22—21no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—432no—
906C22—861no—
907C22—861no—
908C22—861no—
909C22—862no—
910C22—861no—
911C22—861no—
912C22—3444no—
913C22—3444no—
914C22—1721no—
915C22—1721no—
916C22—1721no—
917C22—1721no—
918C22—1721no—
919C22#104×D4312yes—
920C22C2×C22⋊C4×D4311yescharacteristic
921C4—21no—
922C4—21no—
923C4—21no—
924C4—21no—
925C4—41no—
926C4—41no—
927C4—41no—
928C4—432no—
929C4—861no—
930C4—861no—
931C4—861no—
932C4—861no—
933C4—861no—
934C4—1721no—
935C4—1721no—
936C4#131×D4311yescharacteristic
937C4#1458366411yescharacteristic
938C4#1458370111yescharacteristic
939C4#1458370611yescharacteristic
940C2—22no—
941C2—81no—
942C2—862no—
943C2—3441no—
944C2—1721no—
945C2—1722no—
946C2#1914304311yescharacteristic
947C2#1914311711yescharacteristic
948C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1494C2
socleC22×C43C22×C22⋊C4
prime radical#19148201C2
cosocleC42×C43C24
hypercenter#1494D43
hypocenterC43#17517
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
2. #19143722C2semidirect
3. C4×#13063331C2semidirect
4. #19133054C2semidirect
5. #19133044C2semidirect
6. #19133037C2semidirect
7. #19133036C2semidirect
8. #19133033C2semidirect
9. #19133010C2semidirect
10. #19133008C2semidirect
11. #19133007C2semidirect
12. #19132976C2semidirect
13. C2×#14582628C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1494C2semidirect
43. #14582955C22semidirect
44. #14582951C22semidirect
45. #14582921C22semidirect
46. C2×C4⋊(C43⋊C8)C22semidirect
47. C4⋊C8×D43C22semidirect
51. C4×#10621877C22semidirect
52. C4×#10621872C22semidirect
53. C4×#10621872C22semidirect
54. C4×C8×D43C22semidirect
55. C4×C8×D43C22semidirect
56. Q8⋊(C43⋊C8)C22semidirect
57. Q8⋊(C43⋊C8)C22semidirect
60. #14582628C22semidirect
61. #14582628C22semidirect
62. D4⋊(C43⋊C8)C22semidirect
63. D4⋊(C43⋊C8)C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#432C22semidirect
70. C2×C4×C8×C43C22semidirect
71. C43×Q8⋊C8C22semidirect
72. C43×Q8⋊C8C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
394. D172#131semidirect
470. #1494D43semidirect
519. #432C2×D43semidirect
532. C2×C4×C8C2×D43semidirect
535. Q8⋊C8C2×D43semidirect
536. Q8⋊C8C2×D43semidirect
547. D4⋊C8C2×D43semidirect
548. D4⋊C8C2×D43semidirect
549. C43#17517semidirect

Maximal subgroups

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

subgroupindex
#191482012
#191437222
C4×#130633312
#191330542
#191330442
#191330372
#191330362
#191330332
#191330102
#191330082
#191330072
#191329762
C2×#145826282
D4⋊C8×D432
C43×#14942
#1751743