Finite Group Databasebeta

← #25063603

Subgroups — #25063603

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148201C211yesmaximal, characteristic
2#19143716C211yesmaximal, characteristic, complemented
3#19143234C211yesmaximal, characteristic, complemented
4#19133062C211yesmaximal, characteristic, complemented
5#19133060C211yesmaximal, characteristic, complemented
6#19133054C211yesmaximal, characteristic, complemented
7#19133036C211yesmaximal, characteristic, complemented
8#19133028C211yesmaximal, characteristic, complemented
9#19133021C211yesmaximal, characteristic, complemented
10#19133007C211yesmaximal, characteristic, complemented
11#19132992C211yesmaximal, characteristic, complemented
12#19132985C211yesmaximal, characteristic, complemented
13#19132981C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1482C211yesmaximal, characteristic, complemented
16#14583631C411yescharacteristic
17#14583607C411yescharacteristic
18#14583605C411yescharacteristic
19#14583602C411yescharacteristic
20#14583601C411yescharacteristic
21#14583600—21no—
22#14583574—21no—
23#14583572—21no—
24#14583542C411yescharacteristic
25#14583541—21no—
26#14583540C411yescharacteristic
27#14583533C411yescharacteristic
28#14583446C2211yescharacteristic
29#14583436C2211yescharacteristic
30#14583427—21no—
31#14583411—21no—
32#14583408—21no—
33C4×#10621902C2211yescharacteristic
34C4×#10621898C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C4×D4×D43—21no—
37C4×D4×D43C2211yescharacteristic
38#14583029—21no—
39#14582973—21no—
40#14582973—21no—
41C8×D172—21no—
42#14582959—21no—
43#14582957—21no—
44#14582955C2211yescharacteristic, complemented
45#14582955C2211yescharacteristic, complemented
46#14582952C2211yescharacteristic, complemented
47#14582950C2211yescharacteristic, complemented
48#14582950C2211yescharacteristic, complemented
49#14582924—21no—
50#14582923C2211yescharacteristic, complemented
51C4⋊C8×D43C2211yescharacteristic, complemented
52C4⋊C8×D43C2211yescharacteristic, complemented
53#14582864—21no—
54C4×#10621872C2211yescharacteristic, 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×#431C2211yescharacteristic, complemented
70C43×#431C2211yescharacteristic, 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—
83C2×#10621877—21no—
84C2×#10621872—21no—
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87C2×C8×D43—21no—
88#13063324C2×C411yescharacteristic
89#13063321C2×C411yescharacteristic
90#13063320—21no—
91#13063320—21no—
92#13063318—21no—
93#13063316C2×C411yescharacteristic
94#13063315—21no—
95#13063314C2×C411yescharacteristic
96#13063311—21no—
97#13063311—21no—
98#13063310—21no—
99#13063310—21no—
100#13063310—21no—
101#13063309—21no—
102#13063309—21no—
103#13063307—21no—
104#13063307—21no—
105#13063305—21no—
106#13063305—21no—
107#13063303—21no—
108#13063303—21no—
109#13063302—21no—
110#13063301C2×C411yescharacteristic
111#13063300—21no—
112#13063300—21no—
113#13063300C2×C411yescharacteristic
114#13063300C2×C411yescharacteristic
115#13063298—21no—
116#13063298—21no—
117#13063298—21no—
118#13063297—21no—
119#13063296C2×C411yescharacteristic
120#13063295—21no—
121#13063295—21no—
122#13063295—21no—
123#13063293—21no—
124Q8×Dic43C2×C411yescharacteristic
125C4×Dic86C2×C411yescharacteristic
126C4×Dic86D411yescharacteristic
127C4×D172—21no—
128C4×D172—21no—
129C4×D172—21no—
130C4×D172—21no—
131C4×D172C2×C411yescharacteristic
132C4×D172C2×C411yescharacteristic
133C4×D172C2×C411yescharacteristic
134C4×D172D411yescharacteristic
135C4×D172C2311yescharacteristic
136C4×D172C2311yescharacteristic
137D4×Dic43—21no—
138D4×Dic43C2×C411yescharacteristic
139#13063287—21no—
140#13063287—21no—
141#13063287C2×C411yescharacteristic
142#13063287C2×C411yescharacteristic
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(C22⋊D43)⋊C4—21no—
152#13063284D411yescharacteristic
153#13063283—21no—
154#13063283C2×C411yescharacteristic
155#13063282—21no—
156#13063282D411yescharacteristic
157#13063282D411yescharacteristic
158C2×C4⋊Dic43C2×C411yescharacteristic
159C4⋊C4×D43—21no—
160C4⋊C4×D43C2×C411yescharacteristic
161C2×(C2×D43)⋊C4—21no—
162C22⋊C4×D43—21no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—21no—
165C42×D43—21no—
166C42×D43C2311yescharacteristic
167C42×D43C2311yescharacteristic
168C4⋊(C43⋊C8)—21no—
169C4⋊(C43⋊C8)—21no—
170C4⋊(C43⋊C8)C2311yescharacteristic
171C4⋊(C43⋊C8)C2311yescharacteristic
172Dic43⋊C8—21no—
173Dic43⋊C8—21no—
174Dic43⋊C8—21no—
175Dic43⋊C8—21no—
176C22⋊(C43⋊C8)—21no—
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181#13063235—21no—
182#13063235—21no—
183#13063235—21no—
184C4×C43⋊C8C2311yescharacteristic
185C4×C43⋊C8C2311yescharacteristic
186C8×Dic43—21no—
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic
189#124×C43C2×C411yescharacteristic
190#123×C43—21no—
191C22⋊Q8×C43C2×C411yescharacteristic
192#121×C43C2×C411yescharacteristic
193C4×Q8×C43C2311yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2311yescharacteristic
196#117×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C4⋊C8×C43C2311yescharacteristic
200C4⋊C8×C43C2311yescharacteristic
201C22⋊C8×C43—21no—
202C22⋊C8×C43—21no—
203C4×C8×C43—21no—
204C4×C8×C43C2311yescharacteristic
205C4×C8×C43C2311yescharacteristic
206C23×D43—21no—
207C23×D43—21no—
208C2×Q8×C43C22×C411yescharacteristic
209C2×D4×C43—21no—
210C2×D4×C43C22×C411yescharacteristic
211C22×C4×C43—21no—
212C22×C4×C43C22×C411yescharacteristic
213C22×C4×C43C2×D411yescharacteristic
214C22×C4×C43C2×D411yescharacteristic
215C2×C22⋊D43—21no—
216C2×C22⋊D43—21no—
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43C22⋊C411yescharacteristic
220C2×C22⋊D43C22⋊C411yescharacteristic
221C22×Dic43—21no—
222C22×Dic43—21no—
223#10621902—22no—
224#10621902—41no—
225D4×D43—22no—
226D4×D43—41no—
227D4×D43—44no—
228#10621898—42no—
229#10621898—81no—
230#10621898—81no—
231C2×D172—21no—
232C2×D172—21no—
233C2×D172—21no—
234C2×D172—21no—
235C2×D172—22no—
236C2×D172—41no—
237C2×D172C22⋊C411yescharacteristic
238C2×D172C22×C411yescharacteristic
239C2×D172C22×C411yescharacteristic
240C2×C4×D43—21no—
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—81no—
249C2×C4×D43—81no—
250C2×C4×D43—81no—
251C2×C4×D43—81no—
252C2×C4×D43C22×C411yescharacteristic
253C2×C4×D43C22×C411yescharacteristic
254C2×C4×D43C2×D411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×Dic86—21no—
259C2×Dic86C22⋊C411yescharacteristic
260C2×C8×C43—21no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C2×C8×C43—21no—
264C4⋊C4×C43—21no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43—21no—
268C4⋊C4×C43C22×C411yescharacteristic
269C4⋊C4×C43C22×C411yescharacteristic
270C22⋊C4×C43—21no—
271C22⋊C4×C43—21no—
272C22⋊C4×C43—21no—
273C22⋊C4×C43—21no—
274C22⋊C4×C43—21no—
275C42×C43—21no—
276C42×C43C22×C411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2×D411yescharacteristic
279C42×C43C2411yescharacteristic
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43C22⋊C411yescharacteristic
283C22⋊Dic43C22⋊C411yescharacteristic
284(C2×D43)⋊C4—21no—
285(C2×D43)⋊C4—21no—
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)⋊C4C22⋊C411yescharacteristic
297(C2×D43)⋊C4C22⋊C411yescharacteristic
298(C2×D43)⋊C4C22⋊C411yescharacteristic
299(C2×D43)⋊C4C22⋊C411yescharacteristic
300C4⋊Dic43—21no—
301C4⋊Dic43—21no—
302C4⋊Dic43—21no—
303C4⋊Dic43C22⋊C411yescharacteristic
304C4⋊Dic43C22⋊C411yescharacteristic
305C4⋊Dic43C22×C411yescharacteristic
306C4⋊Dic43C22×C411yescharacteristic
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4C22⋊C411yescharacteristic
312Dic43⋊C4C22⋊C411yescharacteristic
313Dic43⋊C4C22⋊C411yescharacteristic
314Dic43⋊C4C22⋊C411yescharacteristic
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43C22×C411yescharacteristic
318C4×Dic43C22×C411yescharacteristic
319C4×Dic43C2×D411yescharacteristic
320C4×Dic43C2×D411yescharacteristic
321C4×Dic43C2×D411yescharacteristic
322C4×Dic43C2×D411yescharacteristic
323#10621877—81no—
324C2×C43⋊C8—21no—
325C2×C43⋊C8—21no—
326C2×C43⋊C8—21no—
327C2×C43⋊C8—21no—
328#10621872—42no—
329C8×D43—42no—
330C8×D43—81no—
331C8×D43—81no—
332C23×C43—21no—
333C23×C43C2×C22⋊C411yescharacteristic
334C22×D43—21no—
335C22×D43—21no—
336C22×D43—42no—
337C22×D43—42no—
338C22×D43—42no—
339C22×D43—42no—
340C22×D43—81no—
341C22×D43—81no—
342C22×D43C2×C22⋊C411yescharacteristic
343C22×D43C2×C22⋊C411yescharacteristic
344Q8×C43—21no—
345Q8×C43—21no—
346D4×C43—21no—
347D4×C43—21no—
348D4×C43—42no—
349C2×C4×C43—21no—
350C2×C4×C43—21no—
351C2×C4×C43—21no—
352C2×C4×C43—21no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—21no—
356C2×C4×C43—41no—
357C2×C4×C43—41no—
358C2×C4×C43—41no—
359C2×C4×C43C2×C22⋊C411yescharacteristic
360C2×C4×C43C2×C22⋊C411yescharacteristic
361C2×C4×C43C2×C22⋊C411yescharacteristic
362C2×C4×C43C23×C411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C22⋊D43—22no—
366C22⋊D43—41no—
367C22⋊D43—42no—
368C22⋊D43—42no—
369C22⋊D43—81no—
370C22⋊D43—81no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—81no—
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—21no—
385D172—42no—
386D172—42no—
387D172—42no—
388D172—81no—
389D172#13112yes—
390C4×D43—22no—
391C4×D43—21no—
392C4×D43—21no—
393C4×D43—21no—
394C4×D43—21no—
395C4×D43—21no—
396C4×D43—21no—
397C4×D43—21no—
398C4×D43—21no—
399C4×D43—41no—
400C4×D43—42no—
401C4×D43—42no—
402C4×D43—41no—
403C4×D43—41no—
404C4×D43—41no—
405C4×D43—41no—
406C4×D43—81no—
407C4×D43—81no—
408C4×D43—81no—
409C4×D43—81no—
410Dic86—41no—
411Dic86—81no—
412C8×C43—41no—
413C8×C43—41no—
414C8×C43—41no—
415C8×C43—41no—
416C43⋊C8—41no—
417C43⋊C8—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17521—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—41no—
425C22×C43—41no—
426C22×C43—41no—
427C22×C43C22×C22⋊C411yescharacteristic
428C2×D43—21no—
429C2×D43—21no—
430C2×D43—22no—
431C2×D43—21no—
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—41no—
435C2×D43—41no—
436C2×D43—41no—
437C2×D43—41no—
438C2×D43—41no—
439C2×D43—84no—
440C2×D43—84no—
441C2×D43#42112yes—
442C4×C43—21no—
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—41no—
447C4×C43—41no—
448C4×C43—41no—
449C4×C43C2×#13111yescharacteristic
450C4×C43#56811yescharacteristic
451C4×C43#57611yescharacteristic
452C4×C43#57711yescharacteristic
453Dic43—21no—
454Dic43—21no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—21no—
459Dic43—41no—
460Dic43—41no—
461#3481—431no—
462#2990—431no—
463#2922—431no—
464#1496—431no—
465#1495—431no—
466#1494—431no—
467#1490—431no—
468#1488—431no—
469#1486—431no—
470#1483—431no—
471#1482D4311yescharacteristic, complemented
472#1480—431no—
473#1478—431no—
474#1477—431no—
475C2×D4⋊C8—431no—
476C2×C43—41no—
477C2×C43—81no—
478C2×C43#288011yescharacteristic
479C2×C43#289711yescharacteristic
480C2×C43C2×#42111yescharacteristic
481D43—22no—
482D43—41no—
483D43—42no—
484D43—81no—
485#559—431no—
486#554—431no—
487#554—431no—
488#553—431no—
489#553—431no—
490#553—861no—
491#551—861no—
492#551—861no—
493#546—431no—
494#546—431no—
495#546—861no—
496D42—431no—
497#532—431no—
498#529—431no—
499#529—861no—
500#529C2×D4311yescharacteristic
501#525—861no—
502#525—861no—
503C4×#41—431no—
504C4×#41—431no—
505C2×C4×D4—431no—
506C2×C4×D4—431no—
507C2×C4×D4—861no—
508#446—861no—
509#435—861no—
510#435—861no—
511C8×D4—861no—
512#433—861no—
513#433—861no—
514#432—431no—
515#432—431no—
516#431—431no—
517#431—431no—
518#431—431no—
519#431C2×D4311yescharacteristic, complemented
520#431C2×D4311yescharacteristic, complemented
521#424—861no—
522#423—431no—
523C2×C4⋊C8—431no—
524C2×C4⋊C8—431no—
525#408—861no—
526C4×M16—431no—
527C2×C4×C8—431no—
528Q8⋊C8—431no—
529Q8⋊C8—431no—
530Q8⋊C8C2×D4311yescharacteristic, complemented
531Q8⋊C8C2×D4311yescharacteristic, complemented
532D4⋊C8—431no—
533D4⋊C8—431no—
534D4⋊C8—431no—
535D4⋊C8—431no—
536D4⋊C8—431no—
537D4⋊C8—431no—
538D4⋊C8—431no—
539D4⋊C8—431no—
540D4⋊C8—431no—
541D4⋊C8—431no—
542D4⋊C8C2×D4311yescharacteristic, complemented
543D4⋊C8C2×D4311yescharacteristic, complemented
544C43#1752111yescharacteristic, complemented, Sylow
545C2×#41—431no—
546C2×#41—431no—
547C2×#41—861no—
548C22×D4—431no—
549C22×D4—431no—
550C22×D4—861no—
551C23×C4—861no—
552C23×C4—861no—
553C2×M16—861no—
554C2×M16—861no—
555C22×C8—861no—
556C22×C8—861no—
557C22×C8—861no—
558C4⋊Q8—431no—
559#127—431no—
560#126—21no—
561#126—861no—
562#126—861no—
563#126—861no—
564#125—431no—
565#125—861no—
566#125C4×D4311yescharacteristic
567#124—431no—
568#124—861no—
569#124—861no—
570#124C4×D4311yescharacteristic
571#123—21no—
572#123—861no—
573#123—861no—
574#123—861no—
575#123—861no—
576#123—861no—
577#123—861no—
578#123—861no—
579C22⋊Q8—431no—
580C22⋊Q8—861no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C22⋊Q8—861no—
584C22⋊Q8—861no—
585C22⋊Q8C4×D4311yescharacteristic
586#121—431no—
587#121—431no—
588#121—431no—
589#121—861no—
590#121—861no—
591#121—861no—
592#121—861no—
593#121—861no—
594#121—861no—
595#121C4×D4311yescharacteristic
596#120—861no—
597#120—861no—
598#120—861no—
599#120—861no—
600C4×Q8—431no—
601C4×Q8—431no—
602C4×Q8—431no—
603C4×Q8C22×D4311yescharacteristic
604C4×D4—21no—
605C4×D4—431no—
606C4×D4—431no—
607C4×D4—431no—
608C4×D4—431no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—431no—
612C4×D4—431no—
613C4×D4—431no—
614C4×D4—431no—
615C4×D4—431no—
616C4×D4—431no—
617C4×D4—431no—
618C4×D4—861no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629C4×D4—861no—
630C4×D4C22×D4311yescharacteristic
631#117—21no—
632#117—431no—
633#117—431no—
634#117—431no—
635#117—431no—
636#117—861no—
637#117—861no—
638C2×C4⋊C4—431no—
639C2×C4⋊C4—431no—
640C2×C4⋊C4—861no—
641C2×C22⋊C4—861no—
642C2×C22⋊C4—861no—
643C2×C22⋊C4—861no—
644C2×C22⋊C4—861no—
645C2×C42—431no—
646C2×C42—431no—
647C2×C42—861no—
648C2×C42C22×D4311yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—431no—
651C4⋊C8—431no—
652C4⋊C8—861no—
653C4⋊C8—861no—
654C4⋊C8—861no—
655C4⋊C8—861no—
656C4⋊C8—861no—
657C4⋊C8—861no—
658C4⋊C8C22×D4311yescharacteristic
659C4⋊C8C22×D4311yescharacteristic
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—861no—
663C22⋊C8—861no—
664C22⋊C8—861no—
665C22⋊C8—861no—
666C22⋊C8—861no—
667#97—861no—
668#97—861no—
669#97—861no—
670C4×C8—21no—
671C4×C8—431no—
672C4×C8—431no—
673C4×C8—861no—
674C4×C8C22×D4311yescharacteristic
675C4×C8C22×D4311yescharacteristic
676C24—861no—
677C24—861no—
678#41—862no—
679#41—3441no—
680#41—3441no—
681#41—1722no—
682#41—1721no—
683C2×Q8—431no—
684C2×Q8—861no—
685C2×Q8C2×C4×D4311yescharacteristic
686C2×D4—21no—
687C2×D4—431no—
688C2×D4—431no—
689C2×D4—431no—
690C2×D4—431no—
691C2×D4—431no—
692C2×D4—862no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—861no—
696C2×D4—861no—
697C2×D4—861no—
698C2×D4—861no—
699C2×D4—862no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—1721no—
703C2×D4—1721no—
704C2×D4—1724no—
705C2×D4C2×C4×D4311yescharacteristic
706C22×C4—21no—
707C22×C4—431no—
708C22×C4—431no—
709C22×C4—431no—
710C22×C4—431no—
711C22×C4—431no—
712C22×C4—431no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—861no—
716C22×C4—861no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—3441no—
724C22×C4—3441no—
725C22×C4—3441no—
726C22×C4—3441no—
727C22×C4C2×C4×D4311yescharacteristic
728C22×C4D4×D4311yescharacteristic
729C22×C4D4×D4311yescharacteristic
730M16—3441no—
731M16—1722no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—861no—
737C2×C8—861no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—3441no—
741C2×C8—3441no—
742C2×C8—1722no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—21no—
746C4⋊C4—21no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—431no—
753C4⋊C4—431no—
754C4⋊C4—431no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4C2×C4×D4311yescharacteristic
763C4⋊C4C2×C4×D4311yescharacteristic
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—431no—
770C22⋊C4—431no—
771C22⋊C4—431no—
772C22⋊C4—431no—
773C22⋊C4—431no—
774C22⋊C4—431no—
775C22⋊C4—861no—
776C22⋊C4—861no—
777C22⋊C4—861no—
778C22⋊C4—861no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C42—21no—
790C42—431no—
791C42—431no—
792C42—431no—
793C42—431no—
794C42—431no—
795C42—431no—
796C42—861no—
797C42—861no—
798C42C2×C4×D4311yescharacteristic
799C42D4×D4311yescharacteristic
800C42D4×D4311yescharacteristic
801C42C23×D4311yescharacteristic
802C23—21no—
803C23—431no—
804C23—431no—
805C23—861no—
806C23—861no—
807C23—3441no—
808C23—3441no—
809C23—1722no—
810C23—1722no—
811C23—1722no—
812C23—1722no—
813C23C22⋊C4×D4311yescharacteristic
814Q8—21no—
815Q8—21no—
816Q8—3441no—
817Q8—1721no—
818D4—21no—
819D4—21no—
820D4—42no—
821D4—432no—
822D4—862no—
823D4—862no—
824D4—861no—
825D4—861no—
826D4—861no—
827D4—3441no—
828D4—3441no—
829D4—3441no—
830D4—1722no—
831D4—1722no—
832D4—1722no—
833D4—1721no—
834D4—1722no—
835D4—1722no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—431no—
847C2×C4—431no—
848C2×C4—431no—
849C2×C4—431no—
850C2×C4—431no—
851C2×C4—431no—
852C2×C4—862no—
853C2×C4—861no—
854C2×C4—861no—
855C2×C4—861no—
856C2×C4—861no—
857C2×C4—861no—
858C2×C4—861no—
859C2×C4—861no—
860C2×C4—861no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—3441no—
864C2×C4—3441no—
865C2×C4—3441no—
866C2×C4—3441no—
867C2×C4—3441no—
868C2×C4—3441no—
869C2×C4—1721no—
870C2×C4—1722no—
871C2×C4—1722no—
872C2×C4—1721no—
873C2×C4—1721no—
874C2×C4—1721no—
875C2×C4—1721no—
876C2×C4C22⋊C4×D4311yescharacteristic
877C2×C4C22⋊C4×D4311yescharacteristic
878C2×C4C22⋊C4×D4311yescharacteristic
879C2×C4C22×C4×D4311yescharacteristic
880C2×C4C2×D4×D4311yescharacteristic
881C2×C4C2×D4×D4311yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—1721no—
887C8—1721no—
888C8—1721no—
889C8—1721no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—432no—
897C22—861no—
898C22—861no—
899C22—861no—
900C22—862no—
901C22—861no—
902C22—861no—
903C22—3444no—
904C22—3444no—
905C22—1721no—
906C22—1721no—
907C22—1721no—
908C22—1721no—
909C22—1721no—
910C22C2×C22⋊C4×D4311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—41no—
916C4—41no—
917C4—41no—
918C4—861no—
919C4—861no—
920C4—861no—
921C4—861no—
922C4—861no—
923C4—861no—
924C4—1721no—
925C4—1721no—
926C4#131×D4311yescharacteristic
927C4#1458366411yescharacteristic
928C4#1458370111yescharacteristic
929C4#1458370611yescharacteristic
930C2—41no—
931C2—81no—
932C2—862no—
933C2—3441no—
934C2—1721no—
935C2—1722no—
936C2#1914304311yescharacteristic
937C2#1914311711yescharacteristic
938C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1482C2
socleC22×C43C22×C22⋊C4
prime radical#19148201C2
cosocleC42×C43C24
hypercenter#1482D43
hypocenterC43#17521
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1482

Complements

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

NH ≅ G/Ntype
2. #19143716C2semidirect
3. #19143234C2semidirect
4. #19133062C2semidirect
5. #19133060C2semidirect
6. #19133054C2semidirect
7. #19133036C2semidirect
8. #19133028C2semidirect
9. #19133021C2semidirect
10. #19133007C2semidirect
11. #19132992C2semidirect
12. #19132985C2semidirect
13. #19132981C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1482C2semidirect
44. #14582955C22semidirect
45. #14582955C22semidirect
46. #14582952C22semidirect
47. #14582950C22semidirect
48. #14582950C22semidirect
50. #14582923C22semidirect
51. C4⋊C8×D43C22semidirect
52. C4⋊C8×D43C22semidirect
54. C4×#10621872C22semidirect
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×#431C22semidirect
70. C43×#431C22semidirect
71. C43×Q8⋊C8C22semidirect
72. C43×Q8⋊C8C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
471. #1482D43semidirect
519. #431C2×D43semidirect
520. #431C2×D43semidirect
530. Q8⋊C8C2×D43semidirect
531. Q8⋊C8C2×D43semidirect
542. D4⋊C8C2×D43semidirect
543. D4⋊C8C2×D43semidirect
544. C43#17521semidirect

Maximal subgroups

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

subgroupindex
#191482012
#191437162
#191432342
#191330622
#191330602
#191330542
#191330362
#191330282
#191330212
#191330072
#191329922
#191329852
#191329812
D4⋊C8×D432
C43×#14822
#1752143