Finite Group Databasebeta

← #25063492

Subgroups — #25063492

Order 11008.

1216 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148081C211yesmaximal, characteristic
2#19143557C211yesmaximal, characteristic, complemented
3#19143256C211yesmaximal, characteristic, complemented
4#19133064C211yesmaximal, characteristic, complemented
5#19133062C211yesmaximal, characteristic, complemented
6#19133044C211yesmaximal, characteristic, complemented
7#19133039C211yesmaximal, characteristic, complemented
8#19133036C211yesmaximal, characteristic, complemented
9#19133018C211yesmaximal, characteristic, complemented
10#19133010C211yesmaximal, characteristic, complemented
11#19132992C211yesmaximal, characteristic, complemented
12#19132985C211yesmaximal, characteristic, complemented
13#19132984C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1484C211yesmaximal, characteristic, complemented
16C2×#41×D43—21no—
17#14583569C411yescharacteristic
18#14583564C411yescharacteristic
19#14583557—21no—
20#14583552C411yescharacteristic
21#14583549C411yescharacteristic
22#14583549C411yescharacteristic
23#14583542—21no—
24#14583538—21no—
25#14583538—21no—
26#14583534C411yescharacteristic
27#14583533C411yescharacteristic
28#14583533C411yescharacteristic
29#14583446C2211yescharacteristic
30#14583446C2211yescharacteristic
31#14583408—21no—
32#14583408—21no—
33#14583406—21no—
34C4×#10621898C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C4×D4×D43C2211yescharacteristic
37C4×D4×D43C2211yescharacteristic
38#14583027—21no—
39#14582975—21no—
40#14582972—21no—
41#14582968—21no—
42#14582958—21no—
43#14582957—21no—
44#14582956C2211yescharacteristic, complemented
45#14582955C2211yescharacteristic, complemented
46#14582952C2211yescharacteristic, complemented
47#14582951C2211yescharacteristic, complemented
48#14582950C2211yescharacteristic, complemented
49#14582950C2211yescharacteristic, complemented
50#14582921C2211yescharacteristic, complemented
51C4⋊C8×D43C2211yescharacteristic, complemented
52#14582864—21no—
53#14582853—21no—
54C4×#10621872C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic, complemented
56#14582628C2211yescharacteristic
57#14582628C2211yescharacteristic
58#14582628C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic, complemented
60D4⋊(C43⋊C8)C2211yescharacteristic, complemented
61D4⋊(C43⋊C8)C2211yescharacteristic, complemented
62D4⋊(C43⋊C8)C2211yescharacteristic, complemented
63D4⋊(C43⋊C8)C2211yescharacteristic, complemented
64#14582626C2211yescharacteristic
65#14582626C2211yescharacteristic
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C43×#532C2211yescharacteristic
69C43×#431C2211yescharacteristic, complemented
70C4×M16×C43C2211yescharacteristic, complemented
71C43×D4⋊C8C2211yescharacteristic, complemented
72C43×D4⋊C8C2211yescharacteristic, complemented
73C43×D4⋊C8C2211yescharacteristic, complemented
74C43×D4⋊C8C2211yescharacteristic, complemented
75C2×#10621902—21no—
76C2×#10621898—21no—
77C2×#10621898—21no—
78C2×#10621898D411yescharacteristic
79C2×#10621900—21no—
80C2×#10621900—21no—
81C2×#10621900—21no—
82#41×D43—44no—
83#41×D43—44no—
84C2×Q8×D43—21no—
85C22×D172C2×C411yescharacteristic
86C2×D4×D43—21no—
87C2×D4×D43—21no—
88C2×D4×D43—21no—
89C2×D4×D43C2×C411yescharacteristic
90C2×D4×D43C2×C411yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43—21no—
94C2×#10621872—21no—
95C2×#10621872—21no—
96C2×C8×D43—21no—
97C2×C8×D43—21no—
98#13063324C2×C411yescharacteristic
99#13063324C2×C411yescharacteristic
100#13063321C2×C411yescharacteristic
101#13063321C2×C411yescharacteristic
102#13063311—21no—
103#13063311—21no—
104#13063310—21no—
105#13063310—21no—
106#13063307—21no—
107#13063307—21no—
108#13063306—21no—
109#13063306—21no—
110#13063303—21no—
111#13063303—21no—
112#13063302—21no—
113#13063302—21no—
114#13063301—21no—
115#13063301—21no—
116#13063300C2×C411yescharacteristic
117#13063300C2×C411yescharacteristic
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063298—21no—
122#13063297—21no—
123#13063297—21no—
124#13063296—21no—
125#13063296—21no—
126#13063296C2×C411yescharacteristic
127#13063296C2×C411yescharacteristic
128#13063295—21no—
129#13063295—21no—
130#13063293—21no—
131#13063293—21no—
132#13063293—21no—
133#13063293—21no—
134C4×Dic86C2×C411yescharacteristic
135C4×Dic86D411yescharacteristic
136C4×D172—21no—
137C4×D172—21no—
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141C4×D172D411yescharacteristic
142C4×D172C2311yescharacteristic
143C4×D172C2311yescharacteristic
144D4×Dic43C2×C411yescharacteristic
145D4×Dic43C2×C411yescharacteristic
146#13063287C2×C411yescharacteristic
147#13063287C2×C411yescharacteristic
148C4×C22⋊D43—21no—
149C4×C22⋊D43—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152C4×C22⋊D43C2×C411yescharacteristic
153C4×C22⋊D43C2×C411yescharacteristic
154C4×C22⋊D43D411yescharacteristic
155C4×C22⋊D43D411yescharacteristic
156(C22⋊D43)⋊C4—21no—
157(C22⋊D43)⋊C4—21no—
158#13063284D411yescharacteristic
159#13063282D411yescharacteristic
160#13063282D411yescharacteristic
161C2×C4⋊Dic43C2×C411yescharacteristic
162C4⋊C4×D43C2×C411yescharacteristic
163C4⋊C4×D43C2×C411yescharacteristic
164C2×(C2×D43)⋊C4—21no—
165C22⋊C4×D43—21no—
166C22⋊C4×D43—21no—
167C42×D43C2311yescharacteristic
168C42×D43C2311yescharacteristic
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—
177C22⋊(C43⋊C8)—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181(C2×D43)⋊C8—21no—
182#13063236—21no—
183#13063235—21no—
184#13063235—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C8×Dic43—21no—
189C2×#41×C43—21no—
190C2×M16×C43—21no—
191C4⋊Q8×C43C2×C411yescharacteristic
192#127×C43C2×C411yescharacteristic
193#124×C43—21no—
194#121×C43—21no—
195#121×C43C2×C411yescharacteristic
196#121×C43C2×C411yescharacteristic
197C4×D4×C43—21no—
198C4×D4×C43C2311yescharacteristic
199C4×D4×C43C2311yescharacteristic
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43C2311yescharacteristic
202C4⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43—21no—
204#97×C43—21no—
205C4×C8×C43—21no—
206C4×C8×C43C2311yescharacteristic
207C4×C8×C43C2311yescharacteristic
208C23×D43—21no—
209C23×D43—21no—
210C23×D43—21no—
211#41×C43—42no—
212#41×C43—42no—
213C2×Q8×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43—21no—
218C2×D4×C43C22×C411yescharacteristic
219C2×D4×C43C22×C411yescharacteristic
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—21no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—21no—
229C2×C22⋊D43—21no—
230C2×C22⋊D43—21no—
231C2×C22⋊D43—21no—
232C2×C22⋊D43—21no—
233C2×C22⋊D43C22⋊C411yescharacteristic
234C2×C22⋊D43C22⋊C411yescharacteristic
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238#10621902—44no—
239Q8×D43—44no—
240#10621900—44no—
241#10621900—44no—
242#10621900—44no—
243D4×D43—22no—
244D4×D43—22no—
245D4×D43—41no—
246D4×D43—41no—
247D4×D43—44no—
248D4×D43—44no—
249D4×D43—44no—
250#10621898—22no—
251#10621898—22no—
252#10621898—42no—
253#10621898—42no—
254#10621898—42no—
255#10621898—42no—
256C2×D172—21no—
257C2×D172—21no—
258C2×D172—21no—
259C2×D172—22no—
260C2×D172—41no—
261C2×D172C22⋊C411yescharacteristic
262C2×D172C22×C411yescharacteristic
263C2×D172C22×C411yescharacteristic
264C2×C4×D43—21no—
265C2×C4×D43—21no—
266C2×C4×D43—21no—
267C2×C4×D43—21no—
268C2×C4×D43—21no—
269C2×C4×D43—21no—
270C2×C4×D43—21no—
271C2×C4×D43—21no—
272C2×C4×D43—42no—
273C2×C4×D43—42no—
274C2×C4×D43—42no—
275C2×C4×D43—42no—
276C2×C4×D43—42no—
277C2×C4×D43—42no—
278C2×C4×D43C22×C411yescharacteristic
279C2×C4×D43C22×C411yescharacteristic
280C2×C4×D43C2×D411yescharacteristic
281C2×C4×D43C2×D411yescharacteristic
282C2×C4×D43C2×D411yescharacteristic
283C2×C4×D43C2×D411yescharacteristic
284C2×Dic86—21no—
285C2×Dic86—21no—
286C2×Dic86C22⋊C411yescharacteristic
287M16×C43—42no—
288C2×C8×C43—21no—
289C2×C8×C43—21no—
290C2×C8×C43—21no—
291C2×C8×C43—21no—
292C4⋊C4×C43—21no—
293C4⋊C4×C43C22×C411yescharacteristic
294C4⋊C4×C43C22×C411yescharacteristic
295C22⋊C4×C43—21no—
296C22⋊C4×C43—21no—
297C22⋊C4×C43—21no—
298C22⋊C4×C43—21no—
299C42×C43C22×C411yescharacteristic
300C42×C43C2×D411yescharacteristic
301C42×C43C2×D411yescharacteristic
302C42×C43C2411yescharacteristic
303C22⋊Dic43—21no—
304C22⋊Dic43—21no—
305C22⋊Dic43—21no—
306C22⋊Dic43—21no—
307C22⋊Dic43C22⋊C411yescharacteristic
308C22⋊Dic43C22⋊C411yescharacteristic
309(C2×D43)⋊C4—21no—
310(C2×D43)⋊C4—21no—
311(C2×D43)⋊C4—21no—
312(C2×D43)⋊C4—21no—
313(C2×D43)⋊C4—21no—
314(C2×D43)⋊C4—21no—
315(C2×D43)⋊C4—21no—
316(C2×D43)⋊C4—21no—
317(C2×D43)⋊C4C22⋊C411yescharacteristic
318(C2×D43)⋊C4C22⋊C411yescharacteristic
319(C2×D43)⋊C4C22⋊C411yescharacteristic
320(C2×D43)⋊C4C22⋊C411yescharacteristic
321C4⋊Dic43—21no—
322C4⋊Dic43C22⋊C411yescharacteristic
323C4⋊Dic43C22⋊C411yescharacteristic
324C4⋊Dic43C22×C411yescharacteristic
325C4⋊Dic43C22×C411yescharacteristic
326Dic43⋊C4—21no—
327Dic43⋊C4—21no—
328Dic43⋊C4—21no—
329Dic43⋊C4—21no—
330Dic43⋊C4C22⋊C411yescharacteristic
331Dic43⋊C4C22⋊C411yescharacteristic
332Dic43⋊C4C22⋊C411yescharacteristic
333Dic43⋊C4C22⋊C411yescharacteristic
334C4×Dic43C22×C411yescharacteristic
335C4×Dic43C22×C411yescharacteristic
336C4×Dic43C2×D411yescharacteristic
337C4×Dic43C2×D411yescharacteristic
338C4×Dic43C2×D411yescharacteristic
339C4×Dic43C2×D411yescharacteristic
340C2×C43⋊C8—21no—
341C2×C43⋊C8—21no—
342C2×C43⋊C8—21no—
343C2×C43⋊C8—21no—
344#10621872—42no—
345#10621872—42no—
346C8×D43—42no—
347C8×D43—42no—
348C23×C43—21no—
349C23×C43—21no—
350C23×C43C2×C22⋊C411yescharacteristic
351C22×D43—21no—
352C22×D43—21no—
353C22×D43—42no—
354C22×D43—42no—
355C22×D43—42no—
356C22×D43—42no—
357C22×D43—42no—
358C22×D43—42no—
359C22×D43—81no—
360C22×D43—81no—
361C22×D43—81no—
362C22×D43C2×C22⋊C411yescharacteristic
363C22×D43C2×C22⋊C411yescharacteristic
364Q8×C43—42no—
365D4×C43—21no—
366D4×C43—21no—
367D4×C43—21no—
368D4×C43—21no—
369D4×C43—42no—
370D4×C43—42no—
371D4×C43—42no—
372D4×C43—81no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—21no—
376C2×C4×C43—21no—
377C2×C4×C43—21no—
378C2×C4×C43—21no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C23×C411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C22⋊D43—22no—
391C22⋊D43—22no—
392C22⋊D43—42no—
393C22⋊D43—42no—
394C22⋊D43—42no—
395C22⋊D43—42no—
396C22⋊D43—42no—
397C22⋊D43—42no—
398C22⋊D43—81no—
399C22⋊D43—81no—
400C2×Dic43—21no—
401C2×Dic43—21no—
402C2×Dic43—42no—
403C2×Dic43—42no—
404C2×Dic43—42no—
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C2×Dic43C2×C22⋊C411yescharacteristic
408C2×Dic43C2×C22⋊C411yescharacteristic
409C2×Dic43C2×C22⋊C411yescharacteristic
410C2×Dic43C2×C22⋊C411yescharacteristic
411D172—22no—
412D172—21no—
413D172—21no—
414D172—21no—
415D172—42no—
416D172—42no—
417D172—42no—
418D172#13112yes—
419C4×D43—21no—
420C4×D43—21no—
421C4×D43—21no—
422C4×D43—21no—
423C4×D43—21no—
424C4×D43—21no—
425C4×D43—41no—
426C4×D43—41no—
427C4×D43—42no—
428C4×D43—42no—
429C4×D43—42no—
430C4×D43—42no—
431C4×D43—42no—
432C4×D43—41no—
433C4×D43—41no—
434C4×D43—41no—
435C4×D43—41no—
436C4×D43—42no—
437C4×D43AGL(1,ℤ/8)12yes—
438C4×D43AGL(1,ℤ/8)12yes—
439Dic86—22no—
440Dic86—42no—
441Dic86—42no—
442C8×C43—22no—
443C8×C43—41no—
444C8×C43—41no—
445C8×C43—41no—
446C43⋊C8—41no—
447C43⋊C8—41no—
448C43⋊C8—41no—
449C43⋊C8—41no—
450#17511—431nomaximal, Sylow
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—41no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43C22×C22⋊C411yescharacteristic
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—22no—
464C2×D43—21no—
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—84no—
473C2×D43—84no—
474C2×D43—84no—
475C2×D43#41812yes—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—41no—
481C4×C43—41no—
482C4×C43C2×#13111yescharacteristic
483C4×C43#56811yescharacteristic
484C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
485C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—21no—
490Dic43—21no—
491Dic43—41no—
492Dic43—41no—
493Dic43#41812yes—
494D4×#41—431no—
495#2965—431no—
496#2925—431no—
497#1496—431no—
498#1496—431no—
499#1492—431no—
500#1490—431no—
501#1490—431no—
502#1486—431no—
503#1484—431no—
504#1484D4311yescharacteristic, complemented
505#1480—431no—
506#1478—431no—
507#1478—431no—
508C2×D4⋊C8—431no—
509C2×C43—41no—
510C2×C43—81no—
511C2×C43—81no—
512C2×C43#288011yescharacteristic
513C2×C43C2×#41811yescharacteristic
514C2×C43#290111yescharacteristic
515D43—22no—
516D43—41no—
517D43—42no—
518D43—81no—
519C22×#41—861no—
520#550—431no—
521D4×Q8—431no—
522#548—861no—
523#547—431no—
524#547—431no—
525#547—431no—
526#546—861no—
527#546—861no—
528#546—861no—
529D42—431no—
530D42—431no—
531D42—431no—
532#532—431no—
533#532—431no—
534#532C2×D4311yescharacteristic
535#525—861no—
536#525—861no—
537#525—861no—
538C4×#41—431no—
539C2×C4×D4—431no—
540C2×C4×D4—431no—
541C2×C4×D4—431no—
542#446—861no—
543#436—861no—
544#435—861no—
545#435—861no—
546#433—861no—
547#433—861no—
548#432—431no—
549#432—431no—
550#431—431no—
551#431—431no—
552#431—431no—
553#431—431no—
554#431C2×D4311yescharacteristic, complemented
555#423—431no—
556C2×C4⋊C8—431no—
557#408—861no—
558#405—861no—
559C4×M16—431no—
560C4×M16C2×D4311yescharacteristic, complemented
561C2×C4×C8—431no—
562D4⋊C8—431no—
563D4⋊C8—431no—
564D4⋊C8—431no—
565D4⋊C8—431no—
566D4⋊C8—431no—
567D4⋊C8—431no—
568D4⋊C8—431no—
569D4⋊C8—431no—
570D4⋊C8—431no—
571D4⋊C8—431no—
572D4⋊C8—431no—
573D4⋊C8—431no—
574D4⋊C8C2×D4311yescharacteristic, complemented
575D4⋊C8C2×D4311yescharacteristic, complemented
576D4⋊C8C2×D4311yescharacteristic, complemented
577D4⋊C8C2×D4311yescharacteristic, complemented
578C43#1751111yescharacteristic, complemented, Sylow
579C2×#41—21no—
580C2×#41—431no—
581C2×#41—861no—
582C2×#41—861no—
583C2×#41—861no—
584C2×#41—861no—
585C2×#41—861no—
586C2×#41—861no—
587C2×#41—1724no—
588C2×#41—1724no—
589C22×Q8—861no—
590C22×D4—431no—
591C22×D4—431no—
592C22×D4—431no—
593C22×D4—861no—
594C22×D4—861no—
595C22×D4—861no—
596C23×C4—861no—
597C23×C4—861no—
598C23×C4—861no—
599C2×M16—21no—
600C2×M16—861no—
601C2×M16—861no—
602C22×C8—861no—
603C22×C8—861no—
604C4⋊Q8—431no—
605C4⋊Q8—431no—
606C4⋊Q8C4×D4311yescharacteristic
607#127—431no—
608#127—431no—
609#127C4×D4311yescharacteristic
610#124—21no—
611#124—861no—
612#124—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616#123—861no—
617#123—861no—
618#123—861no—
619C22⋊Q8—861no—
620C22⋊Q8—861no—
621C22⋊Q8—861no—
622C22⋊Q8—861no—
623C22⋊Q8—861no—
624C22⋊Q8—861no—
625#121—21no—
626#121—431no—
627#121—431no—
628#121—431no—
629#121—431no—
630#121—861no—
631#121—861no—
632#121—861no—
633#121—861no—
634#121—861no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121C4×D4311yescharacteristic
639#121C4×D4311yescharacteristic
640#120—861no—
641#120—861no—
642#120—861no—
643#120—861no—
644#120—861no—
645#120—861no—
646C4×Q8—431no—
647C4×Q8—431no—
648C4×D4—21no—
649C4×D4—431no—
650C4×D4—431no—
651C4×D4—431no—
652C4×D4—431no—
653C4×D4—431no—
654C4×D4—431no—
655C4×D4—431no—
656C4×D4—431no—
657C4×D4—431no—
658C4×D4—431no—
659C4×D4—431no—
660C4×D4—431no—
661C4×D4—431no—
662C4×D4—431no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669C4×D4—861no—
670C4×D4—861no—
671C4×D4C22×D4311yescharacteristic
672C4×D4C22×D4311yescharacteristic
673#117—431no—
674#117—431no—
675#117—431no—
676C2×C4⋊C4—431no—
677C2×C4⋊C4—431no—
678C2×C4⋊C4—431no—
679C2×C22⋊C4—861no—
680C2×C22⋊C4—861no—
681C2×C22⋊C4—861no—
682C2×C42—431no—
683C2×C42—431no—
684C2×C42C22×D4311yescharacteristic
685C4⋊C8—431no—
686C4⋊C8—431no—
687C4⋊C8—861no—
688C4⋊C8—861no—
689C4⋊C8—861no—
690C4⋊C8—861no—
691C4⋊C8—861no—
692C4⋊C8C22×D4311yescharacteristic
693C4⋊C8C22×D4311yescharacteristic
694C22⋊C8—21no—
695C22⋊C8—861no—
696C22⋊C8—861no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8—861no—
700C22⋊C8—861no—
701#97—21no—
702#97—861no—
703#97—861no—
704#97—861no—
705C4×C8—21no—
706C4×C8—431no—
707C4×C8—431no—
708C4×C8—861no—
709C4×C8—861no—
710C4×C8C22×D4311yescharacteristic
711C4×C8C22×D4311yescharacteristic
712C24—861no—
713C24—861no—
714C24—861no—
715#41—42no—
716#41—42no—
717#41—862no—
718#41—862no—
719#41—1722no—
720#41—1722no—
721#41—1722no—
722#41—1722no—
723#41—1724no—
724#41—1724no—
725#41—1724no—
726#41—1724no—
727C2×Q8—21no—
728C2×Q8—431no—
729C2×Q8—861no—
730C2×Q8—861no—
731C2×Q8—1724no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—431no—
737C2×D4—431no—
738C2×D4—431no—
739C2×D4—431no—
740C2×D4—431no—
741C2×D4—862no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4—861no—
747C2×D4—861no—
748C2×D4—861no—
749C2×D4—861no—
750C2×D4—862no—
751C2×D4—862no—
752C2×D4—861no—
753C2×D4—861no—
754C2×D4—861no—
755C2×D4—1721no—
756C2×D4—1721no—
757C2×D4—1721no—
758C2×D4—1724no—
759C2×D4—1724no—
760C2×D4—1724no—
761C2×D4C2×C4×D4311yescharacteristic
762C2×D4C2×C4×D4311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—431no—
766C22×C4—431no—
767C22×C4—431no—
768C22×C4—431no—
769C22×C4—431no—
770C22×C4—431no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—861no—
774C22×C4—861no—
775C22×C4—861no—
776C22×C4—861no—
777C22×C4—861no—
778C22×C4—861no—
779C22×C4—861no—
780C22×C4—861no—
781C22×C4—861no—
782C22×C4—1722no—
783C22×C4—1722no—
784C22×C4—1722no—
785C22×C4—1722no—
786C22×C4—1722no—
787C22×C4—1722no—
788C22×C4C2×C4×D4311yescharacteristic
789C22×C4D4×D4311yescharacteristic
790C22×C4D4×D4311yescharacteristic
791M16—42no—
792M16—1722no—
793M16—1722no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—861no—
799C2×C8—861no—
800C2×C8—861no—
801C2×C8—861no—
802C2×C8—1722no—
803C2×C8—1722no—
804C4⋊C4—21no—
805C4⋊C4—431no—
806C4⋊C4—431no—
807C4⋊C4—431no—
808C4⋊C4—431no—
809C4⋊C4—431no—
810C4⋊C4—431no—
811C4⋊C4—431no—
812C4⋊C4—431no—
813C4⋊C4—861no—
814C4⋊C4—861no—
815C4⋊C4—861no—
816C4⋊C4—861no—
817C4⋊C4—861no—
818C4⋊C4C2×C4×D4311yescharacteristic
819C4⋊C4C2×C4×D4311yescharacteristic
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—431no—
825C22⋊C4—431no—
826C22⋊C4—431no—
827C22⋊C4—431no—
828C22⋊C4—431no—
829C22⋊C4—431no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—861no—
836C22⋊C4—861no—
837C22⋊C4—861no—
838C22⋊C4—861no—
839C22⋊C4—861no—
840C22⋊C4—861no—
841C22⋊C4—861no—
842C42—431no—
843C42—431no—
844C42—431no—
845C42—431no—
846C42—431no—
847C42—431no—
848C42C2×C4×D4311yescharacteristic
849C42D4×D4311yescharacteristic
850C42D4×D4311yescharacteristic
851C42C23×D4311yescharacteristic
852C23—21no—
853C23—21no—
854C23—431no—
855C23—431no—
856C23—861no—
857C23—861no—
858C23—3441no—
859C23—3441no—
860C23—3441no—
861C23—1722no—
862C23—1722no—
863C23—1722no—
864C23—1722no—
865C23—1722no—
866C23—1722no—
867C23C22⋊C4×D4311yescharacteristic
868Q8—42no—
869Q8—862no—
870Q8—1722no—
871Q8—1722no—
872D4—21no—
873D4—21no—
874D4—21no—
875D4—21no—
876D4—42no—
877D4—42no—
878D4—42no—
879D4—81no—
880D4—432no—
881D4—862no—
882D4—862no—
883D4—862no—
884D4—861no—
885D4—861no—
886D4—861no—
887D4—3441no—
888D4—3441no—
889D4—1722no—
890D4—1722no—
891D4—1722no—
892D4—1722no—
893D4—1722no—
894D4—1722no—
895D4—1722no—
896D4—1722no—
897D4—1722no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—431no—
910C2×C4—432no—
911C2×C4—432no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—431no—
917C2×C4—861no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—861no—
921C2×C4—861no—
922C2×C4—861no—
923C2×C4—861no—
924C2×C4—861no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1722no—
928C2×C4—1722no—
929C2×C4—1722no—
930C2×C4—1722no—
931C2×C4—1722no—
932C2×C4—1722no—
933C2×C4—1722no—
934C2×C4—1722no—
935C2×C4—1722no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4—1721no—
939C2×C4—1721no—
940C2×C4C22⋊C4×D4311yescharacteristic
941C2×C4C22⋊C4×D4311yescharacteristic
942C2×C4C22⋊C4×D4311yescharacteristic
943C2×C4C22×C4×D4311yescharacteristic
944C2×C4C2×D4×D4311yescharacteristic
945C2×C4C2×D4×D4311yescharacteristic
946C8—22no—
947C8—41no—
948C8—41no—
949C8—41no—
950C8—1721no—
951C8—1721no—
952C8—1721no—
953C8—1721no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—432no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—862no—
968C22—861no—
969C22—861no—
970C22—3444no—
971C22—3444no—
972C22—3444no—
973C22—1721no—
974C22—1721no—
975C22—1721no—
976C22—1721no—
977C22—1721no—
978C22C2×C22⋊C4×D4311yescharacteristic
979C4—21no—
980C4—21no—
981C4—21no—
982C4—21no—
983C4—41no—
984C4—41no—
985C4—432no—
986C4—861no—
987C4—861no—
988C4—861no—
989C4—861no—
990C4—861no—
991C4—1721no—
992C4—1721no—
993C4#131×D4311yescharacteristic
994C4#1458366411yescharacteristic
995C4AGL(1,ℤ/8)×D4311yescharacteristic
996C4AGL(1,ℤ/8)×D4311yescharacteristic
997C2—41no—
998C2—81no—
999C2—81no—
1000C2—862no—
1001C2—3441no—
1002C2—1721no—
1003C2—1722no—
1004C2#1914304311yescharacteristic
1005C2#418×D4311yescharacteristic
1006C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1484C2
socleC22×C43C22×C22⋊C4
prime radical#19148081C2
cosocleC42×C43C24
hypercenter#1484D43
hypocenterC43#17511
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1484

Complements

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

NH ≅ G/Ntype
2. #19143557C2semidirect
3. #19143256C2semidirect
4. #19133064C2semidirect
5. #19133062C2semidirect
6. #19133044C2semidirect
7. #19133039C2semidirect
8. #19133036C2semidirect
9. #19133018C2semidirect
10. #19133010C2semidirect
11. #19132992C2semidirect
12. #19132985C2semidirect
13. #19132984C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1484C2semidirect
44. #14582956C22semidirect
45. #14582955C22semidirect
46. #14582952C22semidirect
47. #14582951C22semidirect
48. #14582950C22semidirect
49. #14582950C22semidirect
50. #14582921C22semidirect
51. C4⋊C8×D43C22semidirect
54. C4×#10621872C22semidirect
55. C4×C8×D43C22semidirect
58. #14582628C22semidirect
59. #14582628C22semidirect
60. D4⋊(C43⋊C8)C22semidirect
61. D4⋊(C43⋊C8)C22semidirect
62. D4⋊(C43⋊C8)C22semidirect
63. D4⋊(C43⋊C8)C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#431C22semidirect
70. C4×M16×C43C22semidirect
71. C43×D4⋊C8C22semidirect
72. C43×D4⋊C8C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
504. #1484D43semidirect
554. #431C2×D43semidirect
560. C4×M16C2×D43semidirect
574. D4⋊C8C2×D43semidirect
575. D4⋊C8C2×D43semidirect
576. D4⋊C8C2×D43semidirect
577. D4⋊C8C2×D43semidirect
578. C43#17511semidirect

Maximal subgroups

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

subgroupindex
#191480812
#191435572
#191432562
#191330642
#191330622
#191330442
#191330392
#191330362
#191330182
#191330102
#191329922
#191329852
#191329842
D4⋊C8×D432
C43×#14842
#1751143