Finite Group Databasebeta

← #25064125

Subgroups — #25064125

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#19148629C211yesmaximal, characteristic
2#19143629C211yesmaximal, characteristic, complemented
3#19137226C211yesmaximal, characteristic, complemented
4#19133161C211yesmaximal, characteristic, complemented
5#19133156C211yesmaximal, characteristic, complemented
6#19133150C211yesmaximal, characteristic, complemented
7#19133141C211yesmaximal, characteristic, complemented
8#19133137C211yesmaximal, characteristic, complemented
9#19133133C211yesmaximal, characteristic, complemented
10#19133122C211yesmaximal, characteristic, complemented
11#19133109C211yesmaximal, characteristic, complemented
12#19133098C211yesmaximal, characteristic, complemented
13#19133085C211yesmaximal, characteristic, complemented
14#327×D43C211yesmaximal, characteristic, complemented
15C43×#1521C211yesmaximal, characteristic, complemented
16#14583614C411yescharacteristic, complemented
17#14583609C411yescharacteristic, complemented
18#14583602C411yescharacteristic, complemented
19#14583602C411yescharacteristic, complemented
20#14583595—21no—
21#14583571C411yescharacteristic, complemented
22#14583542C411yescharacteristic, complemented
23#14583542C411yescharacteristic, complemented
24#14583541—21no—
25#14583541—21no—
26D4×D172—21no—
27D4×D172C411yescharacteristic, complemented
28#14583504—21no—
29#14583488—21no—
30#14583488—21no—
31#14583449C2211yescharacteristic
32#14583412C2211yescharacteristic
33#14583412C2211yescharacteristic
34#121×D43C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583373—21no—
37C2×C4×D172C2211yescharacteristic
38#14582978—21no—
39#14582969—21no—
40#14582969—21no—
41C8×D172—21no—
42#14582956C2211yescharacteristic, 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#14582636C2211yescharacteristic, complemented
57#14582636C2211yescharacteristic, complemented
58#14582634C2211yescharacteristic, complemented
59#14582634C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582632C2211yescharacteristic, complemented
65#14582632C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C43×#529C2211yescharacteristic
69C43×#431C2211yescharacteristic, complemented
70C43×#383C2211yescharacteristic, complemented
71C43×#328C2211yescharacteristic, complemented
72C43×#328C2211yescharacteristic, complemented
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621902C2×C411yescharacteristic
76C2×#10621902C2×C411yescharacteristic, complemented
77C2×#10621898—21no—
78C22×D172—21no—
79C22×D172D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43—21no—
82C2×D4×D43C2×C411yescharacteristic
83C2×D4×D43C2×C411yescharacteristic, complemented
84C22×C4×D43—21no—
85C22×C4×D43C2311yescharacteristic
86C22×C4×D43C2311yescharacteristic
87C2×#10621872—21no—
88C2×#10621872—21no—
89C2×C8×D43—21no—
90C2×C8×D43—21no—
91#13063325C2×C411yescharacteristic, complemented
92#13063322—21no—
93#13063322C2×C411yescharacteristic, complemented
94#13063320—21no—
95#13063320—21no—
96#13063317—21no—
97#13063313—21no—
98#13063311—21no—
99#13063311—21no—
100#13063310—21no—
101#13063310—21no—
102#13063310—21no—
103#13063310—21no—
104#13063307—21no—
105#13063307—21no—
106#13063303—21no—
107#13063303—21no—
108#13063301C2×C411yescharacteristic
109#13063301C2×C411yescharacteristic, complemented
110#13063300—21no—
111#13063300—21no—
112#13063300—21no—
113#13063300—21no—
114#13063300C2×C411yescharacteristic
115#13063300C2×C411yescharacteristic
116#13063300C2×C411yescharacteristic, complemented
117#13063300C2×C411yescharacteristic, complemented
118#13063299—21no—
119#13063299—21no—
120#13063299—21no—
121#13063299C2311yescharacteristic
122#13063299C2311yescharacteristic
123#13063298—21no—
124#13063298—21no—
125#13063298—21no—
126#13063298—21no—
127#13063297—21no—
128#13063297—21no—
129#13063296C2×C411yescharacteristic
130#13063296C2×C411yescharacteristic, complemented
131#13063295—21no—
132#13063295—21no—
133#13063295—21no—
134#13063295—21no—
135#13063295—21no—
136#13063295—21no—
137C4×D172—21no—
138C4×D172—21no—
139C4×D172—21no—
140C4×D172C2×C411yescharacteristic
141C4×D172C2×C411yescharacteristic
142C4×D172C2×C411yescharacteristic
143C4×D172C2×C411yescharacteristic
144C4×D172C2×C411yescharacteristic, complemented
145C4×D172C2×C411yescharacteristic, complemented
146C4×D172D411yescharacteristic
147C4×D172D411yescharacteristic
148C4×D172D411yescharacteristic
149C4×D172D411yescharacteristic
150#13063287—21no—
151#13063287—21no—
152#13063287—21no—
153#13063287—21no—
154(C22⋊D43)⋊C4—21no—
155(C22⋊D43)⋊C4—21no—
156#13063284—21no—
157#13063283C2×C411yescharacteristic
158#13063283C2×C411yescharacteristic, complemented
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)⋊C4D411yescharacteristic
168C2×(C2×D43)⋊C4D411yescharacteristic
169C22⋊C4×D43—21no—
170C22⋊C4×D43—21no—
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—
181#13063236—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187#126×C43—21no—
188#125×C43C2×C411yescharacteristic, complemented
189#124×C43C2×C411yescharacteristic, complemented
190#123×C43—21no—
191C22⋊Q8×C43C2311yescharacteristic
192#121×C43C2311yescharacteristic
193C4×Q8×C43C2×C411yescharacteristic, complemented
194C4×D4×C43—21no—
195C4×D4×C43C2×C411yescharacteristic, complemented
196#117×C43—21no—
197C2×C42×C43C2311yescharacteristic
198C4⋊C8×C43—21no—
199C22⋊C8×C43C2311yescharacteristic
200C22⋊C8×C43C2311yescharacteristic
201C4×C8×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
210C2×Q8×C43C22×C411yescharacteristic
211C2×D4×C43—21no—
212C2×D4×C43C22×C411yescharacteristic
213C22×C4×C43—21no—
214C22×C4×C43—21no—
215C22×C4×C43—21no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—21no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—21no—
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229#10621902—81no—
230#10621902—81no—
231D4×D43—81no—
232D4×D43—81no—
233D4×D43—81no—
234D4×D43—81no—
235D4×D43—81no—
236D4×D43—81no—
237#10621898—81no—
238#10621898—81no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172—21no—
243C2×D172—21no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172—21no—
247C2×D172—42no—
248C2×D172—44no—
249C2×D172C22⋊C411yescharacteristic
250C2×D172C22⋊C411yescharacteristic
251C2×D172C22⋊C411yescharacteristic
252C2×D172C22⋊C411yescharacteristic
253C2×D172C22×C411yescharacteristic
254C2×D172C22×C411yescharacteristic
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—21no—
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×Dic86—21no—
275C2×C8×C43—21no—
276C2×C8×C43—21no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43C22×C411yescharacteristic
282C4⋊C4×C43C22×C411yescharacteristic
283C22⋊C4×C43—21no—
284C22⋊C4×C43—21no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—21no—
287C22⋊C4×C43—21no—
288C42×C43—21no—
289C42×C43C22×C411yescharacteristic
290C42×C43C22×C411yescharacteristic
291C42×C43C2×D411yescharacteristic
292C42×C43C2×D411yescharacteristic
293C22⋊Dic43—21no—
294C22⋊Dic43—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—21no—
304(C2×D43)⋊C4—21no—
305(C2×D43)⋊C4—21no—
306(C2×D43)⋊C4—21no—
307(C2×D43)⋊C4—42no—
308(C2×D43)⋊C4—81no—
309(C2×D43)⋊C4—81no—
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312(C2×D43)⋊C4C22⋊C411yescharacteristic
313(C2×D43)⋊C4C22⋊C411yescharacteristic
314(C2×D43)⋊C4C22⋊C411yescharacteristic
315(C2×D43)⋊C4C22⋊C411yescharacteristic
316(C2×D43)⋊C4C22⋊C411yescharacteristic
317(C2×D43)⋊C4C22⋊C411yescharacteristic
318C4⋊Dic43—21no—
319C4⋊Dic43—81no—
320C4⋊Dic43C22⋊C411yescharacteristic
321C4⋊Dic43C22⋊C411yescharacteristic
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⋊C4—81no—
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×C43C22×D411yescharacteristic
342C22×D43—21no—
343C22×D43—21no—
344C22×D43—21no—
345C22×D43—21no—
346C22×D43—22no—
347C22×D43—21no—
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—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366C2×C4×C43—21no—
367C2×C4×C43—21no—
368C2×C4×C43—21no—
369C2×C4×C43—21no—
370C2×C4×C43—21no—
371C2×C4×C43—41no—
372C2×C4×C43—41no—
373C2×C4×C43—42no—
374C2×C4×C43—41no—
375C2×C4×C43—41no—
376C2×C4×C43—41no—
377C2×C4×C43—41no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43C2×C22⋊C411yescharacteristic
381C2×C4×C43C2×C22⋊C411yescharacteristic
382C2×C4×C43C2×C22⋊C411yescharacteristic
383C2×C4×C43C2×C22⋊C411yescharacteristic
384C2×C4×C43C23×C411yescharacteristic
385C2×C4×C43C22×D411yescharacteristic
386C22⋊D43—41no—
387C22⋊D43—41no—
388C22⋊D43—41no—
389C22⋊D43—41no—
390C22⋊D43—81no—
391C22⋊D43—81no—
392C22⋊D43—81no—
393C22⋊D43—81no—
394C2×Dic43—21no—
395C2×Dic43—21no—
396C2×Dic43—41no—
397C2×Dic43—41no—
398C2×Dic43—41no—
399C2×Dic43—41no—
400C2×Dic43—41no—
401C2×Dic43—41no—
402C2×Dic43—41no—
403C2×Dic43—41no—
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C2×Dic43C2×C22⋊C411yescharacteristic
408D172—22no—
409D172—22no—
410D172—41no—
411D172—41no—
412D172—41no—
413D172—41no—
414D172—42no—
415D172—42no—
416D172—42no—
417D172—81no—
418D172—81no—
419D172—81no—
420D172—81no—
421D172—81no—
422C4×D43—41no—
423C4×D43—41no—
424C4×D43—41no—
425C4×D43—41no—
426C4×D43—41no—
427C4×D43—41no—
428C4×D43—41no—
429C4×D43—41no—
430C4×D43—81no—
431C4×D43—81no—
432C4×D43—81no—
433C4×D43—81no—
434C4×D43—81no—
435C4×D43—81no—
436C4×D43—84no—
437Dic86—81no—
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×C43C22×C22⋊C411yescharacteristic
449C22×C43#57611yescharacteristic
450C22×C43#57711yescharacteristic
451C2×D43—21no—
452C2×D43—21no—
453C2×D43—21no—
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—42no—
463C2×D43—42no—
464C2×D43—41no—
465C2×D43—41no—
466C2×D43—41no—
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—41no—
484C4×C43—81no—
485C4×C43—81no—
486Dic43—21no—
487Dic43—21no—
488Dic43—21no—
489Dic43—21no—
490Dic43—41no—
491Dic43—41no—
492Dic43—81no—
493Dic43—81no—
494#3519—431no—
495#2974—431no—
496#2318—431no—
497#1521D4311yescharacteristic, complemented
498#1519—431no—
499#1517—431no—
500#1516—431no—
501#1514—431no—
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#288311yescharacteristic
513C2×C43#289711yescharacteristic
514C2×C43C2×#42111yescharacteristic
515D43—22no—
516D43—41no—
517D43—41no—
518D43—41no—
519D43—81no—
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#532—431no—
537#529C2×D4311yescharacteristic
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#432—431no—
549#431C2×D4311yescharacteristic, complemented
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#328C2×D4311yescharacteristic, complemented
567#328C2×D4311yescharacteristic, complemented
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#327—431no—
577#327—431no—
578#327C2×D4311yescharacteristic
579#327C2×D4311yescharacteristic
580C43#1759711yescharacteristic, complemented, Sylow
581C2×#41—431no—
582C2×#41—431no—
583C2×#41—861no—
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⋊Q8—431no—
598#127—431no—
599#127—861no—
600#126—21no—
601#126—861no—
602#126—861no—
603#125—861no—
604#125C4×D4311yescharacteristic, complemented
605#124—861no—
606#124—861no—
607#124—861no—
608#124C4×D4311yescharacteristic, complemented
609#123—21no—
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—861no—
619C22⋊Q8—861no—
620C22⋊Q8C22×D4311yescharacteristic
621#121—431no—
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#121—861no—
642#121C22×D4311yescharacteristic
643#120—861no—
644#120—861no—
645#120—861no—
646#120—861no—
647#120—861no—
648#120—861no—
649C4×Q8C4×D4311yescharacteristic, complemented
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—431no—
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×D4—861no—
670C4×D4C4×D4311yescharacteristic, complemented
671#117—21no—
672#117—431no—
673#117—431no—
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—861no—
702C4×C8—21no—
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—3441no—
717#41—3441no—
718#41—3441no—
719#41—3441no—
720C2×Q8—861no—
721C2×Q8C2×C4×D4311yescharacteristic
722C2×D4—21no—
723C2×D4—431no—
724C2×D4—431no—
725C2×D4—431no—
726C2×D4—431no—
727C2×D4—431no—
728C2×D4—431no—
729C2×D4—861no—
730C2×D4—861no—
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—861no—
743C2×D4—3441no—
744C2×D4—3441no—
745C2×D4—3441no—
746C2×D4—3441no—
747C2×D4—3441no—
748C2×D4—3441no—
749C2×D4—1722no—
750C2×D4—1724no—
751C2×D4C2×C4×D4311yescharacteristic
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—431no—
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—861no—
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—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—431no—
794C4⋊C4—431no—
795C4⋊C4—431no—
796C4⋊C4—431no—
797C4⋊C4—431no—
798C4⋊C4—431no—
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—21no—
813C22⋊C4—431no—
814C22⋊C4—431no—
815C22⋊C4—431no—
816C22⋊C4—431no—
817C22⋊C4—431no—
818C22⋊C4—431no—
819C22⋊C4—431no—
820C22⋊C4—431no—
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—21no—
839C42—861no—
840C42—861no—
841C42—3441no—
842C42C2×C4×D4311yescharacteristic
843C42C2×C4×D4311yescharacteristic
844C42D4×D4311yescharacteristic
845C42D4×D4311yescharacteristic
846C23—21no—
847C23—431no—
848C23—431no—
849C23—431no—
850C23—431no—
851C23—862no—
852C23—861no—
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—41no—
869Q8—3441no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—862no—
874D4—862no—
875D4—3441no—
876D4—3441no—
877D4—3441no—
878D4—3441no—
879D4—3441no—
880D4—3441no—
881D4—3441no—
882D4—3441no—
883D4—3441no—
884D4—1721no—
885D4—1721no—
886D4—1721no—
887D4—1721no—
888D4—1722no—
889D4—1722no—
890D4—1722no—
891D4—1721no—
892D4—1721no—
893D4—1721no—
894D4—1721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—42no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—431no—
910C2×C4—431no—
911C2×C4—431no—
912C2×C4—431no—
913C2×C4—861no—
914C2×C4—861no—
915C2×C4—3441no—
916C2×C4—3441no—
917C2×C4—3441no—
918C2×C4—3441no—
919C2×C4—3441no—
920C2×C4—3441no—
921C2×C4—3444no—
922C2×C4—1721no—
923C2×C4—1721no—
924C2×C4—1721no—
925C2×C4—1721no—
926C2×C4—1721no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
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—432no—
954C22—861no—
955C22—861no—
956C22—861no—
957C22—861no—
958C22—861no—
959C22—861no—
960C22—861no—
961C22—861no—
962C22—861no—
963C22—861no—
964C22—861no—
965C22—3441no—
966C22—3441no—
967C22—1722no—
968C22—1722no—
969C22—1721no—
970C22—1721no—
971C22—1721no—
972C22—1721no—
973C22—1721no—
974C22—1721no—
975C22—6882no—
976C22—6882no—
977C22C2×C22⋊C4×D4311yescharacteristic
978C22#1458370111yescharacteristic
979C22#1458370611yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—41no—
987C4—41no—
988C4—41no—
989C4—81no—
990C4—81no—
991C4—861no—
992C4—861no—
993C4—861no—
994C4—861no—
995C4—3441no—
996C4—3441no—
997C4—1721no—
998C4—1721no—
999C2—21no—
1000C2—21no—
1001C2—81no—
1002C2—862no—
1003C2—3441no—
1004C2—3441no—
1005C2—1721no—
1006C2—1721no—
1007C2—1721no—
1008C2#1914305411yescharacteristic
1009C2#1914311711yescharacteristic
1010C2#421×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1521C2
socleC22×C43C22×C22⋊C4
prime radical#19148629C2
cosocleC22×C4×C43C24
hypercenter#1521D43
hypocenterC43#17597
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1521

Complements

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

NH ≅ G/Ntype
2. #19143629C2semidirect
3. #19137226C2semidirect
4. #19133161C2semidirect
5. #19133156C2semidirect
6. #19133150C2semidirect
7. #19133141C2semidirect
8. #19133137C2semidirect
9. #19133133C2semidirect
10. #19133122C2semidirect
11. #19133109C2semidirect
12. #19133098C2semidirect
13. #19133085C2semidirect
14. #327×D43C2semidirect
15. C43×#1521C2semidirect
16. #14583614C4semidirect
17. #14583609C4semidirect
18. #14583602C4semidirect
19. #14583602C4semidirect
21. #14583571C4semidirect
22. #14583542C4semidirect
23. #14583542C4semidirect
27. D4×D172C4semidirect
42. #14582956C22semidirect
43. #14582861C22semidirect
44. #14582861C22semidirect
45. C22⋊C8×D43C22semidirect
46. C22⋊C8×D43C22semidirect
51. #14582765C22semidirect
52. #14582761C22semidirect
53. #14582758C22semidirect
54. #14582746C22semidirect
55. #95×D43C22semidirect
56. #14582636C22semidirect
57. #14582636C22semidirect
58. #14582634C22semidirect
59. #14582634C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
64. #14582632C22semidirect
65. #14582632C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#431C22semidirect
70. C43×#383C22semidirect
71. C43×#328C22semidirect
72. C43×#328C22semidirect
76. C2×#10621902C2×C4semidirect
83. C2×D4×D43C2×C4semidirect
91. #13063325C2×C4semidirect
93. #13063322C2×C4semidirect
109. #13063301C2×C4semidirect
116. #13063300C2×C4semidirect
117. #13063300C2×C4semidirect
130. #13063296C2×C4semidirect
144. C4×D172C2×C4semidirect
145. C4×D172C2×C4semidirect
158. #13063283C2×C4semidirect
163. C4⋊C4×D43C2×C4semidirect
188. #125×C43C2×C4semidirect
189. #124×C43C2×C4semidirect
193. C4×Q8×C43C2×C4semidirect
195. C4×D4×C43C2×C4semidirect
497. #1521D43semidirect
549. #431C2×D43semidirect
558. #383C2×D43semidirect
566. #328C2×D43semidirect
567. #328C2×D43semidirect
580. C43#17597semidirect
604. #125C4×D43semidirect
608. #124C4×D43semidirect
649. C4×Q8C4×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
#191486292
#191436292
#191372262
#191331612
#191331562
#191331502
#191331412
#191331372
#191331332
#191331222
#191331092
#191330982
#191330852
#327×D432
C43×#15212
#1759743