Finite Group Databasebeta

← #25064129

Subgroups — #25064129

Order 11008.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148622C211yesmaximal, characteristic
2#19143632C211yesmaximal, characteristic, complemented
3#19137226C211yesmaximal, characteristic, complemented
4#19133170C211yesmaximal, characteristic, complemented
5#19133161C211yesmaximal, characteristic, complemented
6#19133155C211yesmaximal, characteristic, complemented
7#19133148C211yesmaximal, characteristic, complemented
8#19133135C211yesmaximal, characteristic, complemented
9#19133134C211yesmaximal, characteristic, complemented
10#19133122C211yesmaximal, characteristic, complemented
11#19133109C211yesmaximal, characteristic, complemented
12#19133096C211yesmaximal, characteristic, complemented
13#19133083C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1514C211yesmaximal, characteristic, complemented
16#14583615C411yescharacteristic, complemented
17#14583610C411yescharacteristic, complemented
18#14583601—21no—
19#14583599C411yescharacteristic, complemented
20#14583599C411yescharacteristic, complemented
21#14583569C411yescharacteristic, complemented
22#14583544C411yescharacteristic, complemented
23#14583544C411yescharacteristic, complemented
24#14583537—21no—
25#14583537—21no—
26#14583534C411yescharacteristic, complemented
27#14583533—21no—
28#14583500—21no—
29#14583483—21no—
30#14583483—21no—
31#14583433C2211yescharacteristic
32#14583409C2211yescharacteristic
33#14583409C2211yescharacteristic
34#121×D43C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583371—21no—
37C2×C4×D172C2211yescharacteristic
38#14582976—21no—
39#14582972—21no—
40#14582972—21no—
41#14582964—21no—
42#14582952C2211yescharacteristic, complemented
43#14582861C2211yescharacteristic, complemented
44#14582861C2211yescharacteristic, complemented
45C22⋊C8×D43C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic, complemented
47#14582791—21no—
48#14582782—21no—
49#14582777—21no—
50#14582773—21no—
51#14582765C2211yescharacteristic, complemented
52#14582761C2211yescharacteristic, complemented
53#14582758C2211yescharacteristic, complemented
54#14582746C2211yescharacteristic, complemented
55#95×D43C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582635C2211yescharacteristic, complemented
59#14582635C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic
61#14582634C2211yescharacteristic
62#14582633C2211yescharacteristic, complemented
63#14582633C2211yescharacteristic, complemented
64#14582633C2211yescharacteristic, complemented
65#14582633C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic
67#14582632C2211yescharacteristic
68C43×#532C2211yescharacteristic
69C43×#432C2211yescharacteristic, complemented
70C43×#383C2211yescharacteristic, complemented
71C43×#327C2211yescharacteristic, complemented
72C43×#327C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621900C2×C411yescharacteristic
76C2×#10621900C2×C411yescharacteristic, complemented
77C22×D172D411yescharacteristic
78C2×D4×D43—21no—
79C2×D4×D43—21no—
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic
82C2×D4×D43C2×C411yescharacteristic, complemented
83C22×C4×D43—21no—
84C22×C4×D43C2311yescharacteristic
85C22×C4×D43C2311yescharacteristic
86C2×#10621872—21no—
87C2×#10621872—21no—
88C2×C8×D43—21no—
89C2×C8×D43—21no—
90#13063321—21no—
91#13063319—21no—
92#13063318—21no—
93#13063318—21no—
94#13063317C2×C411yescharacteristic, complemented
95#13063316—21no—
96#13063314—21no—
97#13063314—21no—
98#13063313C2×C411yescharacteristic, complemented
99#13063309—21no—
100#13063309—21no—
101#13063308—21no—
102#13063308—21no—
103#13063308—21no—
104#13063307—21no—
105#13063307—21no—
106#13063305C2×C411yescharacteristic
107#13063305C2×C411yescharacteristic, complemented
108#13063304C2311yescharacteristic
109#13063301—21no—
110#13063301—21no—
111#13063300—21no—
112#13063300C2×C411yescharacteristic
113#13063300C2×C411yescharacteristic, complemented
114#13063299—21no—
115#13063299—21no—
116#13063299C2311yescharacteristic
117#13063298—21no—
118#13063298—21no—
119#13063298—21no—
120#13063298—21no—
121#13063297—21no—
122#13063297—21no—
123#13063297—21no—
124#13063297—21no—
125#13063296—21no—
126#13063296C2×C411yescharacteristic
127#13063296C2×C411yescharacteristic
128#13063296C2×C411yescharacteristic, complemented
129#13063296C2×C411yescharacteristic, complemented
130#13063295—21no—
131#13063295—21no—
132#13063293—21no—
133#13063293—21no—
134#13063293—21no—
135#13063293—21no—
136C4×Dic86C2×C411yescharacteristic, complemented
137C4×D172C2×C411yescharacteristic
138C4×D172C2×C411yescharacteristic
139C4×D172C2×C411yescharacteristic
140C4×D172C2×C411yescharacteristic
141C4×D172C2×C411yescharacteristic, complemented
142C4×D172D411yescharacteristic
143C4×D172D411yescharacteristic
144C4×D172D411yescharacteristic
145C4×D172D411yescharacteristic
146D4×Dic43—21no—
147D4×Dic43—21no—
148D4×Dic43—21no—
149#13063287—21no—
150C4×C22⋊D43—21no—
151C4×C22⋊D43—21no—
152C4×C22⋊D43—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155#13063283—21no—
156#13063283C2×C411yescharacteristic
157#13063283C2×C411yescharacteristic, complemented
158#13063282—21no—
159C2×C4⋊Dic43—21no—
160C2×C4⋊Dic43D411yescharacteristic
161C2×Dic43⋊C4—21no—
162C4⋊C4×D43C2×C411yescharacteristic
163C4⋊C4×D43C2×C411yescharacteristic, complemented
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C2×(C2×D43)⋊C4D411yescharacteristic
170C2×(C2×D43)⋊C4D411yescharacteristic
171C22⋊C4×D43—21no—
172C22⋊C4×D43—21no—
173C2×C4×Dic43—21no—
174C4⋊(C43⋊C8)—21no—
175C22⋊(C43⋊C8)C2311yescharacteristic
176C22⋊(C43⋊C8)C2311yescharacteristic
177(C2×D43)⋊C8—21no—
178(C2×D43)⋊C8—21no—
179(C2×D43)⋊C8—21no—
180(C2×D43)⋊C8—21no—
181C4×C43⋊C8—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C2×#41×C43—21no—
188C4⋊Q8×C43C2×C411yescharacteristic, complemented
189#127×C43C2×C411yescharacteristic, complemented
190#124×C43—21no—
191#121×C43—21no—
192#121×C43C2311yescharacteristic
193#121×C43C2311yescharacteristic
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic, complemented
196C4×D4×C43C2×C411yescharacteristic, complemented
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201#97×C43—21no—
202#95×C43—21no—
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C23×D43—21no—
207C23×D43—21no—
208C23×D43C2×D411yescharacteristic
209C23×D43C2×D411yescharacteristic
210#41×C43—81no—
211#41×C43—81no—
212C2×Q8×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—21no—
216C2×D4×C43—21no—
217C2×D4×C43C22×C411yescharacteristic
218C2×D4×C43C22×C411yescharacteristic
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2411yescharacteristic
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—
235C22×Dic43—21no—
236C22×Dic43—21no—
237C22×Dic43—21no—
238C22×Dic43—21no—
239C22×Dic43C2×D411yescharacteristic
240C22×Dic43C2×D411yescharacteristic
241#10621900—81no—
242#10621900—81no—
243D4×D43—44no—
244D4×D43—81no—
245D4×D43—81no—
246D4×D43—81no—
247D4×D43—81no—
248D4×D43—81no—
249D4×D43—81no—
250C2×D172—21no—
251C2×D172—21no—
252C2×D172—42no—
253C2×D172C22⋊C411yescharacteristic
254C2×D172C22⋊C411yescharacteristic
255C2×D172C22⋊C411yescharacteristic
256C2×D172C22⋊C411yescharacteristic
257C2×D172C22×C411yescharacteristic
258C2×C4×D43—21no—
259C2×C4×D43—21no—
260C2×C4×D43—21no—
261C2×C4×D43—42no—
262C2×C4×D43—81no—
263C2×C4×D43—81no—
264C2×C4×D43—81no—
265C2×C4×D43—81no—
266C2×C4×D43C22×C411yescharacteristic
267C2×C4×D43C22×C411yescharacteristic
268C2×C4×D43C22×C411yescharacteristic
269C2×C4×D43C22×C411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×C4×D43C2×D411yescharacteristic
272C2×C4×D43C2×D411yescharacteristic
273C2×C4×D43C2×D411yescharacteristic
274C2×Dic86C22×C411yescharacteristic
275C2×C8×C43—21no—
276C2×C8×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43C22×C411yescharacteristic
279C4⋊C4×C43C22×C411yescharacteristic
280C22⋊C4×C43—21no—
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C42×C43C22×C411yescharacteristic
285C42×C43C22×C411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—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)⋊C4—21no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—21no—
302(C2×D43)⋊C4—21no—
303(C2×D43)⋊C4—42no—
304(C2×D43)⋊C4—81no—
305(C2×D43)⋊C4—81no—
306(C2×D43)⋊C4C22⋊C411yescharacteristic
307(C2×D43)⋊C4C22⋊C411yescharacteristic
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314C4⋊Dic43—21no—
315C4⋊Dic43—21no—
316C4⋊Dic43—81no—
317C4⋊Dic43C22⋊C411yescharacteristic
318C4⋊Dic43C22⋊C411yescharacteristic
319C4⋊Dic43C22⋊C411yescharacteristic
320C4⋊Dic43C22⋊C411yescharacteristic
321C4⋊Dic43C22×C411yescharacteristic
322C4⋊Dic43C22×C411yescharacteristic
323Dic43⋊C4—21no—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—21no—
327Dic43⋊C4—21no—
328Dic43⋊C4—21no—
329Dic43⋊C4—81no—
330C4×Dic43—21no—
331C4×Dic43—21no—
332C4×Dic43—21no—
333C4×Dic43—81no—
334C2×C43⋊C8—21no—
335C2×C43⋊C8—21no—
336#10621872—81no—
337#10621872—81no—
338C8×D43—81no—
339C8×D43—81no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43C22×D411yescharacteristic
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—21no—
347C22×D43—22no—
348C22×D43—21no—
349C22×D43—41no—
350C22×D43—41no—
351C22×D43—41no—
352C22×D43—42no—
353C22×D43—42no—
354C22×D43—81no—
355C22×D43—81no—
356C22×D43—81no—
357C22×D43—81no—
358C22×D43C2×C22⋊C411yescharacteristic
359C22×D43C2×C22⋊C411yescharacteristic
360C22×D43C2×C22⋊C411yescharacteristic
361C22×D43C2×C22⋊C411yescharacteristic
362Q8×C43—81no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—42no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—41no—
369D4×C43—41no—
370D4×C43—81no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—21no—
374C2×C4×C43—21no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—81no—
384C2×C4×C43—81no—
385C2×C4×C43C2×C22⋊C411yescharacteristic
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C2×C22⋊C411yescharacteristic
388C2×C4×C43C2×C22⋊C411yescharacteristic
389C2×C4×C43C23×C411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C22⋊D43—42no—
392C22⋊D43—41no—
393C22⋊D43—41no—
394C22⋊D43—42no—
395C22⋊D43—81no—
396C22⋊D43—81no—
397C22⋊D43—81no—
398C22⋊D43—81no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C2×Dic43—21no—
402C2×Dic43—21no—
403C2×Dic43—21no—
404C2×Dic43—41no—
405C2×Dic43—41no—
406C2×Dic43—41no—
407C2×Dic43—41no—
408C2×Dic43—41no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—41no—
412C2×Dic43—81no—
413C2×Dic43—81no—
414C2×Dic43C2×C22⋊C411yescharacteristic
415C2×Dic43C2×C22⋊C411yescharacteristic
416C2×Dic43C2×C22⋊C411yescharacteristic
417C2×Dic43C2×C22⋊C411yescharacteristic
418D172—22no—
419D172—22no—
420D172—41no—
421D172—41no—
422D172—41no—
423D172—81no—
424D172—81no—
425C4×D43—41no—
426C4×D43—41no—
427C4×D43—41no—
428C4×D43—41no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—41no—
433C4×D43—42no—
434C4×D43—81no—
435C4×D43—81no—
436C4×D43—84no—
437Dic86—41no—
438C8×C43—41no—
439C8×C43—41no—
440C43⋊C8—41no—
441C43⋊C8—41no—
442#17597—431nomaximal, Sylow
443C22×C43—21no—
444C22×C43—21no—
445C22×C43—41no—
446C22×C43—41no—
447C22×C43—41no—
448C22×C43—41no—
449C22×C43—41no—
450C22×C43—41no—
451C22×C43C22×C22⋊C411yescharacteristic
452C22×C43#57611yescharacteristic
453C22×C43#57711yescharacteristic
454C2×D43—21no—
455C2×D43—21no—
456C2×D43—21no—
457C2×D43—21no—
458C2×D43—21no—
459C2×D43—21no—
460C2×D43—21no—
461C2×D43—21no—
462C2×D43—21no—
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—42no—
466C2×D43—42no—
467C2×D43—41no—
468C2×D43—41no—
469C2×D43—41no—
470C2×D43—81no—
471C2×D43—81no—
472C2×D43—162no—
473C2×D43—162no—
474C2×D43#42112yes—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—21no—
480C4×C43—21no—
481C4×C43—41no—
482C4×C43—41no—
483C4×C43—81no—
484C4×C43—81no—
485Dic43—21no—
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—41no—
490Dic43—41no—
491Dic43—41no—
492Dic43—81no—
493Dic43—81no—
494#3519—431no—
495#2974—431no—
496#2318—431no—
497#1521—431no—
498#1519—431no—
499#1517—431no—
500#1516—431no—
501#1514D4311yescharacteristic, complemented
502#1513—431no—
503#1512—431no—
504#1510—431no—
505#1507—431no—
506#1504—431no—
507#1501—431no—
508C2×#327—431no—
509C2×C43—21no—
510C2×C43—21no—
511C2×C43—81no—
512C2×C43—81no—
513C2×C43#288311yescharacteristic
514C2×C43#289711yescharacteristic
515C2×C43C2×#42111yescharacteristic
516D43—22no—
517D43—41no—
518D43—41no—
519D43—41no—
520D43—81no—
521#555—431no—
522#554—431no—
523#553—431no—
524#553—431no—
525#553—861no—
526#550—431no—
527#546—431no—
528#546—431no—
529#546—861no—
530#546—861no—
531D42—431no—
532D42—861no—
533#540—861no—
534#538—861no—
535#538—861no—
536#532C2×D4311yescharacteristic
537#529—431no—
538#525—431no—
539#525—431no—
540C2×#121—431no—
541C2×#121—431no—
542#518—861no—
543C2×C4×D4—431no—
544#436—861no—
545#435—861no—
546#435—861no—
547C8×D4—861no—
548#432C2×D4311yescharacteristic, complemented
549#431—431no—
550#407—431no—
551#407—431no—
552C2×C22⋊C8—431no—
553C2×C22⋊C8—431no—
554#388—861no—
555#387—861no—
556#386—861no—
557#385—861no—
558#383C2×D4311yescharacteristic, complemented
559#382—431no—
560#381—431no—
561#380—431no—
562C4×C22⋊C4—431no—
563C2×#95—431no—
564#328—431no—
565#328—431no—
566#328—431no—
567#328—431no—
568#327—431no—
569#327—431no—
570#327—431no—
571#327—431no—
572#327—431no—
573#327—431no—
574#327—431no—
575#327—431no—
576#327C2×D4311yescharacteristic, complemented
577#327C2×D4311yescharacteristic, complemented
578#327C2×D4311yescharacteristic, complemented
579#327C2×D4311yescharacteristic, complemented
580C43#1759711yescharacteristic, complemented, Sylow
581C2×#41—21no—
582C2×#41—431no—
583C2×#41—431no—
584C22×D4—431no—
585C22×D4—431no—
586C22×D4—431no—
587C22×D4—861no—
588C22×D4—861no—
589C22×D4—861no—
590C23×C4—431no—
591C23×C4—431no—
592C23×C4—861no—
593C2×M16—861no—
594C2×M16—861no—
595C22×C8—861no—
596C22×C8—861no—
597C4⋊Q8C4×D4311yescharacteristic, complemented
598#127—861no—
599#127C4×D4311yescharacteristic, complemented
600#126—861no—
601#126—861no—
602#126—861no—
603#125—431no—
604#125—861no—
605#124—21no—
606#124—431no—
607#124—861no—
608#124—861no—
609#123—861no—
610#123—861no—
611#123—861no—
612#123—861no—
613#123—861no—
614#123—861no—
615#123—861no—
616C22⋊Q8—431no—
617C22⋊Q8—431no—
618C22⋊Q8—431no—
619C22⋊Q8—861no—
620C22⋊Q8—861no—
621#121—21no—
622#121—431no—
623#121—431no—
624#121—431no—
625#121—431no—
626#121—431no—
627#121—431no—
628#121—431no—
629#121—861no—
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#121—861no—
639#121—861no—
640#121—861no—
641#121C22×D4311yescharacteristic
642#121C22×D4311yescharacteristic
643#120—861no—
644#120—861no—
645#120—861no—
646#120—861no—
647#120—861no—
648#120—861no—
649C4×Q8—431no—
650C4×D4—21no—
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—861no—
661C4×D4—861no—
662C4×D4—861no—
663C4×D4—861no—
664C4×D4—861no—
665C4×D4—861no—
666C4×D4—861no—
667C4×D4—861no—
668C4×D4—861no—
669C4×D4C4×D4311yescharacteristic, complemented
670C4×D4C4×D4311yescharacteristic, complemented
671#117—431no—
672#117—431no—
673#117—861no—
674#117—861no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—431no—
677C2×C4⋊C4—431no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4—861no—
680C2×C22⋊C4—431no—
681C2×C22⋊C4—431no—
682C2×C22⋊C4—861no—
683C2×C22⋊C4—861no—
684C2×C22⋊C4—861no—
685C2×C22⋊C4—861no—
686C2×C22⋊C4—861no—
687C2×C22⋊C4—861no—
688C2×C22⋊C4—861no—
689C2×C42—861no—
690C2×C42C22×D4311yescharacteristic
691C4⋊C8—21no—
692C4⋊C8—861no—
693C22⋊C8—431no—
694C22⋊C8—431no—
695C22⋊C8—861no—
696C22⋊C8—861no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8C22×D4311yescharacteristic
700C22⋊C8C22×D4311yescharacteristic
701#97—21no—
702C4×C8—861no—
703#95—21no—
704#95—21no—
705#95—431no—
706#95—431no—
707#95—861no—
708#95—861no—
709#95—861no—
710#95C22×D4311yescharacteristic
711#95C22×D4311yescharacteristic
712C24—431no—
713C24—431no—
714C24—861no—
715C24—861no—
716#41—81no—
717#41—81no—
718#41—3441no—
719#41—3441no—
720C2×Q8—21no—
721C2×Q8—431no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—431no—
727C2×D4—431no—
728C2×D4—431no—
729C2×D4—431no—
730C2×D4—431no—
731C2×D4—861no—
732C2×D4—861no—
733C2×D4—861no—
734C2×D4—861no—
735C2×D4—861no—
736C2×D4—861no—
737C2×D4—861no—
738C2×D4—861no—
739C2×D4—861no—
740C2×D4—861no—
741C2×D4—861no—
742C2×D4—3441no—
743C2×D4—3441no—
744C2×D4—3441no—
745C2×D4—3441no—
746C2×D4—3441no—
747C2×D4—3441no—
748C2×D4—1722no—
749C2×D4—1724no—
750C2×D4C2×C4×D4311yescharacteristic
751C2×D4C2×C4×D4311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—431no—
764C22×C4—431no—
765C22×C4—431no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—861no—
772C22×C4—861no—
773C22×C4—3441no—
774C22×C4—3441no—
775C22×C4—3441no—
776C22×C4—3441no—
777C22×C4—1722no—
778C22×C4D4×D4311yescharacteristic
779C22×C4D4×D4311yescharacteristic
780C22×C4C23×D4311yescharacteristic
781M16—3441no—
782M16—3441no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—861no—
786C2×C8—861no—
787C2×C8—3441no—
788C2×C8—3441no—
789C4⋊C4—21no—
790C4⋊C4—431no—
791C4⋊C4—431no—
792C4⋊C4—431no—
793C4⋊C4—431no—
794C4⋊C4—431no—
795C4⋊C4—431no—
796C4⋊C4—861no—
797C4⋊C4—861no—
798C4⋊C4—861no—
799C4⋊C4—861no—
800C4⋊C4—861no—
801C4⋊C4—861no—
802C4⋊C4—861no—
803C4⋊C4—861no—
804C4⋊C4—3441no—
805C4⋊C4—3441no—
806C4⋊C4C2×C4×D4311yescharacteristic
807C4⋊C4C2×C4×D4311yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—431no—
813C22⋊C4—431no—
814C22⋊C4—431no—
815C22⋊C4—431no—
816C22⋊C4—431no—
817C22⋊C4—431no—
818C22⋊C4—431no—
819C22⋊C4—431no—
820C22⋊C4—861no—
821C22⋊C4—861no—
822C22⋊C4—861no—
823C22⋊C4—861no—
824C22⋊C4—861no—
825C22⋊C4—861no—
826C22⋊C4—861no—
827C22⋊C4—861no—
828C22⋊C4—861no—
829C22⋊C4—861no—
830C22⋊C4—861no—
831C22⋊C4—861no—
832C22⋊C4—861no—
833C22⋊C4—861no—
834C22⋊C4—861no—
835C22⋊C4—3441no—
836C22⋊C4—3441no—
837C22⋊C4—1722no—
838C42—861no—
839C42—861no—
840C42—861no—
841C42—3441no—
842C42C2×C4×D4311yescharacteristic
843C42C2×C4×D4311yescharacteristic
844C42D4×D4311yescharacteristic
845C42D4×D4311yescharacteristic
846C23—21no—
847C23—21no—
848C23—431no—
849C23—431no—
850C23—431no—
851C23—431no—
852C23—862no—
853C23—861no—
854C23—861no—
855C23—861no—
856C23—861no—
857C23—861no—
858C23—3441no—
859C23—3441no—
860C23—3441no—
861C23—3441no—
862C23—1721no—
863C23—1721no—
864C23—1721no—
865C23—1722no—
866C23—1722no—
867C23C2×D4×D4311yescharacteristic
868Q8—81no—
869Q8—1721no—
870D4—41no—
871D4—41no—
872D4—42no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—81no—
878D4—862no—
879D4—862no—
880D4—3441no—
881D4—3441no—
882D4—3441no—
883D4—3441no—
884D4—3441no—
885D4—3441no—
886D4—3441no—
887D4—3441no—
888D4—1721no—
889D4—1721no—
890D4—1721no—
891D4—1722no—
892D4—1722no—
893D4—1721no—
894D4—1721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—81no—
908C2×C4—81no—
909C2×C4—431no—
910C2×C4—431no—
911C2×C4—431no—
912C2×C4—431no—
913C2×C4—861no—
914C2×C4—861no—
915C2×C4—861no—
916C2×C4—3441no—
917C2×C4—3441no—
918C2×C4—3444no—
919C2×C4—3441no—
920C2×C4—3441no—
921C2×C4—1721no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1722no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1721no—
934C2×C4—1721no—
935C2×C4—1721no—
936C2×C4—1721no—
937C2×C4—1721no—
938C2×C4C22⋊C4×D4311yescharacteristic
939C2×C4C22⋊C4×D4311yescharacteristic
940C2×C4C22⋊C4×D4311yescharacteristic
941C2×C4C22⋊C4×D4311yescharacteristic
942C2×C4C22×C4×D4311yescharacteristic
943C2×C4C2×D4×D4311yescharacteristic
944C8—41no—
945C8—41no—
946C8—1721no—
947C8—1721no—
948C22—21no—
949C22—21no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—41no—
956C22—432no—
957C22—861no—
958C22—861no—
959C22—861no—
960C22—861no—
961C22—861no—
962C22—861no—
963C22—861no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—861no—
968C22—3441no—
969C22—3441no—
970C22—1722no—
971C22—1722no—
972C22—1721no—
973C22—1721no—
974C22—1721no—
975C22—6882no—
976C22—6882no—
977C22C2×C22⋊C4×D4311yescharacteristic
978C22#1458370311yescharacteristic
979C22#1458370911yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—81no—
989C4—81no—
990C4—861no—
991C4—861no—
992C4—861no—
993C4—861no—
994C4—3441no—
995C4—3441no—
996C4—1721no—
997C4—1721no—
998C4—1721no—
999C2—21no—
1000C2—21no—
1001C2—81no—
1002C2—81no—
1003C2—862no—
1004C2—3441no—
1005C2—1721no—
1006C2—1721no—
1007C2—1721no—
1008C2#1914305411yescharacteristic
1009C2#1914312011yescharacteristic
1010C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1514C2
socleC22×C43C22×C22⋊C4
prime radical#19148622C2
cosocleC22×C4×C43C24
hypercenter#1514D43
hypocenterC43#17597
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1514

Complements

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

NH ≅ G/Ntype
2. #19143632C2semidirect
3. #19137226C2semidirect
4. #19133170C2semidirect
5. #19133161C2semidirect
6. #19133155C2semidirect
7. #19133148C2semidirect
8. #19133135C2semidirect
9. #19133134C2semidirect
10. #19133122C2semidirect
11. #19133109C2semidirect
12. #19133096C2semidirect
13. #19133083C2semidirect
14. #327×D43C2semidirect
15. C43×#1514C2semidirect
16. #14583615C4semidirect
17. #14583610C4semidirect
19. #14583599C4semidirect
20. #14583599C4semidirect
21. #14583569C4semidirect
22. #14583544C4semidirect
23. #14583544C4semidirect
26. #14583534C4semidirect
42. #14582952C22semidirect
43. #14582861C22semidirect
44. #14582861C22semidirect
45. C22⋊C8×D43C22semidirect
46. C22⋊C8×D43C22semidirect
51. #14582765C22semidirect
52. #14582761C22semidirect
53. #14582758C22semidirect
54. #14582746C22semidirect
55. #95×D43C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582635C22semidirect
59. #14582635C22semidirect
62. #14582633C22semidirect
63. #14582633C22semidirect
64. #14582633C22semidirect
65. #14582633C22semidirect
69. C43×#432C22semidirect
70. C43×#383C22semidirect
71. C43×#327C22semidirect
72. C43×#327C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
76. C2×#10621900C2×C4semidirect
82. C2×D4×D43C2×C4semidirect
94. #13063317C2×C4semidirect
98. #13063313C2×C4semidirect
107. #13063305C2×C4semidirect
113. #13063300C2×C4semidirect
128. #13063296C2×C4semidirect
129. #13063296C2×C4semidirect
136. C4×Dic86C2×C4semidirect
141. C4×D172C2×C4semidirect
157. #13063283C2×C4semidirect
163. C4⋊C4×D43C2×C4semidirect
188. C4⋊Q8×C43C2×C4semidirect
189. #127×C43C2×C4semidirect
195. C4×D4×C43C2×C4semidirect
196. C4×D4×C43C2×C4semidirect
501. #1514D43semidirect
548. #432C2×D43semidirect
558. #383C2×D43semidirect
576. #327C2×D43semidirect
577. #327C2×D43semidirect
578. #327C2×D43semidirect
579. #327C2×D43semidirect
580. C43#17597semidirect
597. C4⋊Q8C4×D43semidirect
599. #127C4×D43semidirect
669. C4×D4C4×D43semidirect
670. C4×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191486222
#191436322
#191372262
#191331702
#191331612
#191331552
#191331482
#191331352
#191331342
#191331222
#191331092
#191330962
#191330832
#327×D432
C43×#15142
#1759743