Finite Group Databasebeta

← #25063495

Subgroups — #25063495

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
1D4×#10621898C211yesmaximal, characteristic
2#19143557C211yesmaximal, characteristic, complemented
3#19143262C211yesmaximal, characteristic, complemented
4#19133063C211yesmaximal, characteristic, complemented
5#19133062C211yesmaximal, characteristic, complemented
6#19133044C211yesmaximal, characteristic, complemented
7#19133036C211yesmaximal, characteristic, complemented
8#19133018C211yesmaximal, characteristic, complemented
9#19133013C211yesmaximal, characteristic, complemented
10#19133010C211yesmaximal, characteristic, complemented
11#19132992C211yesmaximal, characteristic, complemented
12#19132986C211yesmaximal, characteristic, complemented
13#19132984C211yesmaximal, characteristic, complemented
14D4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#1490C211yesmaximal, characteristic, complemented
16C22×#10621898—21no—
17#14583570C411yescharacteristic
18D4×Dic86C411yescharacteristic
19#14583558—21no—
20#14583554C411yescharacteristic
21#14583550C411yescharacteristic
22#14583550C411yescharacteristic
23#14583545—21no—
24#14583539—21no—
25#14583539—21no—
26D4×D172C411yescharacteristic
27D4×C22⋊D43C411yescharacteristic
28D4×C22⋊D43C411yescharacteristic
29#14583449C2211yescharacteristic
30#14583446C2211yescharacteristic
31#14583446C2211yescharacteristic
32#14583410—21no—
33#14583408—21no—
34#14583408—21no—
35C4×#10621898C2211yescharacteristic
36C4×D4×D43C2211yescharacteristic
37C4×D4×D43C2211yescharacteristic
38#14583027—21no—
39#14582975—21no—
40#14582972—21no—
41#14582968—21no—
42#14582961—21no—
43#14582957—21no—
44#14582955C2211yescharacteristic, complemented
45#14582952C2211yescharacteristic, complemented
46#14582952C2211yescharacteristic, complemented
47#14582951C2211yescharacteristic, complemented
48#14582950C2211yescharacteristic, complemented
49#14582950C2211yescharacteristic, complemented
50#14582921C2211yescharacteristic, complemented
51C4⋊C8×D43C2211yescharacteristic, complemented
52#14582864—21no—
53#14582856—21no—
54C4×#10621872C2211yescharacteristic, complemented
55C4×C8×D43C2211yescharacteristic, complemented
56#14582628C2211yescharacteristic, complemented
57#14582628C2211yescharacteristic, complemented
58#14582628C2211yescharacteristic, complemented
59#14582628C2211yescharacteristic, complemented
60D4⋊(C43⋊C8)C2211yescharacteristic
61D4⋊(C43⋊C8)C2211yescharacteristic
62D4⋊(C43⋊C8)C2211yescharacteristic, complemented
63D4⋊(C43⋊C8)C2211yescharacteristic, complemented
64#14582626C2211yescharacteristic, complemented
65#14582626C2211yescharacteristic, complemented
66#14582626C2211yescharacteristic, complemented
67#14582626C2211yescharacteristic, complemented
68C2×C4×D4×C43C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C4×M16×C43C2211yescharacteristic, complemented
71C43×D4⋊C8C2211yescharacteristic
72C43×D4⋊C8C2211yescharacteristic
73C43×D4⋊C8C2211yescharacteristic, complemented
74C43×D4⋊C8C2211yescharacteristic, complemented
75C2×#10621898—21no—
76C2×#10621898—21no—
77C2×#10621898—21no—
78C2×#10621898—21no—
79C2×#10621898—21no—
80C2×#10621898—21no—
81C2×#10621898—21no—
82C2×#10621898—44no—
83C2×#10621898—44no—
84C2×#10621898D411yescharacteristic
85C22×Dic86—21no—
86C22×D172—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C2×D4×D43C2×C411yescharacteristic
90C2×D4×D43C2×C411yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C2×#10621872—21no—
94C2×#10621872—21no—
95C2×C8×D43—21no—
96C2×C8×D43—21no—
97#13063325C2×C411yescharacteristic
98#13063324C2×C411yescharacteristic
99#13063324C2×C411yescharacteristic
100#13063322C2×C411yescharacteristic
101#13063321C2×C411yescharacteristic
102#13063321C2×C411yescharacteristic
103#13063313—21no—
104#13063311—21no—
105#13063311—21no—
106#13063310—21no—
107#13063310—21no—
108#13063308—21no—
109#13063308—21no—
110#13063307—21no—
111#13063307—21no—
112#13063304—21no—
113#13063304—21no—
114#13063303—21no—
115#13063303—21no—
116#13063302—21no—
117#13063302—21no—
118#13063300C2×C411yescharacteristic
119#13063300C2×C411yescharacteristic
120#13063299—21no—
121#13063299—21no—
122#13063299—21no—
123#13063299C2×C411yescharacteristic
124#13063299C2×C411yescharacteristic
125#13063298—21no—
126#13063298—21no—
127#13063298—21no—
128#13063298—21no—
129#13063297—21no—
130#13063297—21no—
131#13063296C2×C411yescharacteristic
132#13063296C2×C411yescharacteristic
133#13063295—21no—
134#13063295—21no—
135#13063294—21no—
136#13063294—21no—
137#13063293—21no—
138#13063293—21no—
139C4×Dic86C2×C411yescharacteristic
140C4×Dic86D411yescharacteristic
141C4×D172—21no—
142C4×D172C2×C411yescharacteristic
143C4×D172D411yescharacteristic
144C4×D172C2311yescharacteristic
145C4×D172C2311yescharacteristic
146D4×Dic43C2×C411yescharacteristic
147D4×Dic43C2×C411yescharacteristic
148#13063287C2×C411yescharacteristic
149#13063287C2×C411yescharacteristic
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152C4×C22⋊D43—21no—
153C4×C22⋊D43—21no—
154C4×C22⋊D43C2×C411yescharacteristic
155C4×C22⋊D43C2×C411yescharacteristic
156C4×C22⋊D43D411yescharacteristic
157C4×C22⋊D43D411yescharacteristic
158(C22⋊D43)⋊C4—21no—
159(C22⋊D43)⋊C4—21no—
160#13063284D411yescharacteristic
161#13063282D411yescharacteristic
162#13063282D411yescharacteristic
163C4⋊C4×D43C2×C411yescharacteristic
164C4⋊C4×D43C2×C411yescharacteristic
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#13063235—21no—
183#13063235—21no—
184C4×C43⋊C8—21no—
185C4×C43⋊C8C2311yescharacteristic
186C4×C43⋊C8C2311yescharacteristic
187C8×Dic43—21no—
188C8×Dic43—21no—
189C22×D4×C43C2×C411yescharacteristic
190C23×C4×C43—21no—
191C2×M16×C43—21no—
192C4×D4×C43—21no—
193C4×D4×C43—21no—
194C4×D4×C43C2×C411yescharacteristic
195C4×D4×C43C2×C411yescharacteristic
196C4×D4×C43C2311yescharacteristic
197C4×D4×C43C2311yescharacteristic
198C2×C4⋊C4×C43C2×C411yescharacteristic
199C2×C22⋊C4×C43—21no—
200C2×C42×C43C2311yescharacteristic
201C4⋊C8×C43C2311yescharacteristic
202C4⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43—21no—
204#97×C43—21no—
205#97×C43—21no—
206C4×C8×C43C2311yescharacteristic
207C4×C8×C43C2311yescharacteristic
208C24×C43—21no—
209C23×D43—21no—
210C23×D43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—22no—
213C2×D4×C43—41no—
214C2×D4×C43C22×C411yescharacteristic
215C2×D4×C43C22×C411yescharacteristic
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—42no—
222C22×C4×C43—42no—
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
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⋊D43—21no—
234C2×C22⋊D43—21no—
235C2×C22⋊D43—21no—
236C2×C22⋊D43—44no—
237C2×C22⋊D43—44no—
238C2×C22⋊D43C22⋊C411yescharacteristic
239C2×C22⋊D43C22⋊C411yescharacteristic
240C22×Dic43—21no—
241C22×Dic43—21no—
242D4×D43—22no—
243D4×D43—22no—
244D4×D43—41no—
245D4×D43—41no—
246#10621898—22no—
247#10621898—22no—
248#10621898—44no—
249#10621898—42no—
250#10621898—42no—
251#10621898—44no—
252#10621898—44no—
253#10621898—44no—
254#10621898—42no—
255#10621898—42no—
256#10621898—42no—
257#10621898—42no—
258C2×D172—21no—
259C2×D172—21no—
260C2×D172—21no—
261C2×D172—21no—
262C2×D172—44no—
263C2×D172C22⋊C411yescharacteristic
264C2×D172C22×C411yescharacteristic
265C2×D172C22×C411yescharacteristic
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×D43C22×C411yescharacteristic
277C2×C4×D43C22×C411yescharacteristic
278C2×C4×D43C2×D411yescharacteristic
279C2×C4×D43C2×D411yescharacteristic
280C2×C4×D43C2×D411yescharacteristic
281C2×C4×D43C2×D411yescharacteristic
282C2×Dic86—21no—
283C2×Dic86—21no—
284C2×Dic86—21no—
285C2×Dic86—44no—
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×C43—42no—
351C23×C43—42no—
352C23×C43—81no—
353C23×C43C2×C22⋊C411yescharacteristic
354C22×D43—21no—
355C22×D43—21no—
356C22×D43—42no—
357C22×D43—42no—
358C22×D43—42no—
359C22×D43—42no—
360C22×D43—81no—
361C22×D43—81no—
362C22×D43C2×C22⋊C411yescharacteristic
363C22×D43C2×C22⋊C411yescharacteristic
364D4×C43—21no—
365D4×C43—21no—
366D4×C43—21no—
367D4×C43—42no—
368D4×C43#13112yes—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—41no—
376C2×C4×C43—42no—
377C2×C4×C43—42no—
378C2×C4×C43—42no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C2×C22⋊C411yescharacteristic
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C23×C411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C22⋊D43—22no—
390C22⋊D43—22no—
391C22⋊D43—42no—
392C22⋊D43—42no—
393C22⋊D43—42no—
394C22⋊D43—42no—
395C22⋊D43—42no—
396C22⋊D43—42no—
397C22⋊D43—42no—
398C22⋊D43—42no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C2×Dic43—21no—
402C2×Dic43—21no—
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—21no—
416D172—42no—
417D172—42no—
418D172—42no—
419D172—81no—
420C4×D43—21no—
421C4×D43—21no—
422C4×D43—21no—
423C4×D43—21no—
424C4×D43—21no—
425C4×D43—21no—
426C4×D43—41no—
427C4×D43—41no—
428C4×D43—42no—
429C4×D43—42no—
430C4×D43—42no—
431C4×D43—41no—
432C4×D43—41no—
433C4×D43—41no—
434C4×D43—41no—
435C4×D43—42no—
436C4×D43AGL(1,ℤ/8)12yes—
437C4×D43AGL(1,ℤ/8)12yes—
438Dic86—22no—
439Dic86—42no—
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—22no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43—21no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—41no—
459C22×C43—41no—
460C22×C43—84no—
461C22×C43C22×C22⋊C411yescharacteristic
462C2×D43—21no—
463C2×D43—21no—
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—41no—
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#1490D4311yescharacteristic, complemented
502#1486—431no—
503#1484—431no—
504#1484—431no—
505#1480—431no—
506#1478—431no—
507#1478—431no—
508C2×D4⋊C8—431no—
509C2×C43—42no—
510C2×C43—41no—
511C2×C43—81no—
512C2×C43#288011yescharacteristic
513C2×C43C2×#41811yescharacteristic
514C2×C43#290111yescharacteristic
515D43—22no—
516D43—41no—
517D43—81no—
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#532—431no—
535#525—861no—
536#525—861no—
537#525—861no—
538C4×#41—431no—
539C2×C4×D4—431no—
540C2×C4×D4—431no—
541C2×C4×D4C2×D4311yescharacteristic
542#446—861no—
543#436—861no—
544#435—861no—
545#435—861no—
546#433—861no—
547#433—861no—
548#432—431no—
549#432C2×D4311yescharacteristic, complemented
550#431—431no—
551#431—431no—
552#431—431no—
553#431—431no—
554#431—431no—
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
575D4⋊C8C2×D4311yescharacteristic
576D4⋊C8C2×D4311yescharacteristic, complemented
577D4⋊C8C2×D4311yescharacteristic, complemented
578C43#1751111yescharacteristic, complemented, Sylow
579C2×#41—431no—
580C2×#41—861no—
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—861no—
593C22×D4—861no—
594C22×D4—861no—
595C22×D4C4×D4311yescharacteristic
596C23×C4—21no—
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⋊Q8—431no—
607#127—431no—
608#127—431no—
609#127—431no—
610#124—861no—
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—431no—
626#121—431no—
627#121—431no—
628#121—431no—
629#121—431no—
630#121—431no—
631#121—861no—
632#121—861no—
633#121—861no—
634#121—861no—
635#121—861no—
636#121—861no—
637#121—861no—
638#121—861no—
639#121—861no—
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—21no—
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—861no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669C4×D4C4×D4311yescharacteristic
670C4×D4C4×D4311yescharacteristic
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⋊C4C4×D4311yescharacteristic
679C2×C22⋊C4—21no—
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—21no—
703#97—861no—
704#97—861no—
705C4×C8—431no—
706C4×C8—431no—
707C4×C8—861no—
708C4×C8—861no—
709C4×C8—861no—
710C4×C8C22×D4311yescharacteristic
711C4×C8C22×D4311yescharacteristic
712C24—21no—
713C24—861no—
714C24—861no—
715#41—862no—
716#41—862no—
717#41—1722no—
718#41—1722no—
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—431no—
728C2×Q8—861no—
729C2×Q8—861no—
730C2×Q8—861no—
731C2×Q8—1724no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—41no—
735C2×D4—431no—
736C2×D4—431no—
737C2×D4—431no—
738C2×D4—431no—
739C2×D4—431no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—861no—
743C2×D4—861no—
744C2×D4—861no—
745C2×D4—861no—
746C2×D4—861no—
747C2×D4—861no—
748C2×D4—862no—
749C2×D4—862no—
750C2×D4—861no—
751C2×D4—861no—
752C2×D4—861no—
753C2×D4—861no—
754C2×D4—861no—
755C2×D4—861no—
756C2×D4—1724no—
757C2×D4—1721no—
758C2×D4—1721no—
759C2×D4—1724no—
760C2×D4—1724no—
761C2×D4C2×C4×D4311yescharacteristic
762C2×D4C2×C4×D4311yescharacteristic
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—42no—
769C22×C4—42no—
770C22×C4—431no—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—431no—
775C22×C4—431no—
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—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—42no—
855C23—42no—
856C23—81no—
857C23—431no—
858C23—431no—
859C23—861no—
860C23—861no—
861C23—3441no—
862C23—3441no—
863C23—1722no—
864C23—1722no—
865C23—1722no—
866C23—1722no—
867C23C22⋊C4×D4311yescharacteristic
868Q8—862no—
869Q8—1722no—
870Q8—1722no—
871Q8—1722no—
872D4—21no—
873D4—21no—
874D4—21no—
875D4—42no—
876D4—862no—
877D4—862no—
878D4—862no—
879D4—861no—
880D4—861no—
881D4—861no—
882D4—861no—
883D4—3441no—
884D4—3441no—
885D4—3441no—
886D4—1722no—
887D4—1722no—
888D4—1722no—
889D4—1722no—
890D4—1722no—
891D4—1722no—
892D4—1722no—
893D4—1722no—
894D4—1722no—
895D4—1722no—
896D4—1722no—
897D4#1306333312yes—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—41no—
905C2×C4—42no—
906C2×C4—42no—
907C2×C4—42no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—431no—
913C2×C4—432no—
914C2×C4—432no—
915C2×C4—431no—
916C2×C4—431no—
917C2×C4—431no—
918C2×C4—431no—
919C2×C4—431no—
920C2×C4—861no—
921C2×C4—861no—
922C2×C4—861no—
923C2×C4—861no—
924C2×C4—861no—
925C2×C4—861no—
926C2×C4—861no—
927C2×C4—861no—
928C2×C4—1721no—
929C2×C4—1721no—
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—22no—
956C22—21no—
957C22—21no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—84no—
964C22—432no—
965C22—861no—
966C22—861no—
967C22—861no—
968C22—861no—
969C22—861no—
970C22—3444no—
971C22—3444no—
972C22—1721no—
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—
993C4C2×#1306333311yescharacteristic
994C4#1458366511yescharacteristic
995C4AGL(1,ℤ/8)×D4311yescharacteristic
996C4AGL(1,ℤ/8)×D4311yescharacteristic
997C2—41no—
998C2—42no—
999C2—81no—
1000C2—862no—
1001C2—3441no—
1002C2—3441no—
1003C2—1721no—
1004C2#1914304511yescharacteristic
1005C2#418×D4311yescharacteristic
1006C2#1914313911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1490C2
socleC22×C43C22×C22⋊C4
prime radicalD4×#10621898C2
cosocleC42×C43C24
hypercenter#1490D43
hypocenterC43#17511
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1490

Complements

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

NH ≅ G/Ntype
2. #19143557C2semidirect
3. #19143262C2semidirect
4. #19133063C2semidirect
5. #19133062C2semidirect
6. #19133044C2semidirect
7. #19133036C2semidirect
8. #19133018C2semidirect
9. #19133013C2semidirect
10. #19133010C2semidirect
11. #19132992C2semidirect
12. #19132986C2semidirect
13. #19132984C2semidirect
14. D4⋊C8×D43C2semidirect
15. C43×#1490C2semidirect
44. #14582955C22semidirect
45. #14582952C22semidirect
46. #14582952C22semidirect
47. #14582951C22semidirect
48. #14582950C22semidirect
49. #14582950C22semidirect
50. #14582921C22semidirect
51. C4⋊C8×D43C22semidirect
54. C4×#10621872C22semidirect
55. C4×C8×D43C22semidirect
56. #14582628C22semidirect
57. #14582628C22semidirect
58. #14582628C22semidirect
59. #14582628C22semidirect
62. D4⋊(C43⋊C8)C22semidirect
63. D4⋊(C43⋊C8)C22semidirect
64. #14582626C22semidirect
65. #14582626C22semidirect
66. #14582626C22semidirect
67. #14582626C22semidirect
69. C43×#432C22semidirect
70. C4×M16×C43C22semidirect
73. C43×D4⋊C8C22semidirect
74. C43×D4⋊C8C22semidirect
501. #1490D43semidirect
549. #432C2×D43semidirect
560. C4×M16C2×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
D4×#106218982
#191435572
#191432622
#191330632
#191330622
#191330442
#191330362
#191330182
#191330132
#191330102
#191329922
#191329862
#191329842
D4⋊C8×D432
C43×#14902
#1751143