Finite Group Databasebeta

← #25064124

Subgroups — #25064124

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#19148621C211yesmaximal, characteristic
2#19143631C211yesmaximal, characteristic, complemented
3#19137222C211yesmaximal, characteristic, complemented
4#19133169C211yesmaximal, characteristic, complemented
5#19133161C211yesmaximal, characteristic, complemented
6#19133153C211yesmaximal, characteristic, complemented
7#19133148C211yesmaximal, characteristic, complemented
8#19133140C211yesmaximal, characteristic, complemented
9#19133135C211yesmaximal, characteristic, complemented
10#19133130C211yesmaximal, characteristic, complemented
11#19133122C211yesmaximal, characteristic, complemented
12#19133100C211yesmaximal, characteristic, complemented
13#19133084C211yesmaximal, characteristic, complemented
14C2×#14582633C211yesmaximal, characteristic, complemented
15C43×#1507C211yesmaximal, characteristic, complemented
16#14583613C411yescharacteristic, complemented
17#14583604C411yescharacteristic, complemented
18#14583597C411yescharacteristic, complemented
19#14583596C411yescharacteristic, complemented
20#14583592—21no—
21#14583567C411yescharacteristic, complemented
22#14583546C411yescharacteristic, complemented
23#14583543—21no—
24#14583543C411yescharacteristic, complemented
25#14583538—21no—
26D4×C22⋊D43—21no—
27D4×C22⋊D43C411yescharacteristic, complemented
28#14583499—21no—
29#14583487—21no—
30#14583481—21no—
31#14583444C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583410C2211yescharacteristic
34#14583409C2211yescharacteristic
35#121×D43C2211yescharacteristic
36#14583372—21no—
37C2×C4×C22⋊D43C2211yescharacteristic
38#14582975—21no—
39#14582968—21no—
40#14582967—21no—
41(C22⋊D43)⋊C8—21no—
42#14582953C2211yescharacteristic, complemented
43#14582949C2211yescharacteristic, complemented
44#14582861C2211yescharacteristic, complemented
45C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
46C22⋊C8×D43C2211yescharacteristic, complemented
47#14582790—21no—
48#14582783—21no—
49#14582776—21no—
50#14582771—21no—
51#14582766C2211yescharacteristic, complemented
52#14582763C2211yescharacteristic, complemented
53#14582761C2211yescharacteristic, complemented
54#14582758C2211yescharacteristic, complemented
55C2×C43⋊#95C2211yescharacteristic, complemented
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582635C2211yescharacteristic, complemented
59#14582635C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582633C2211yescharacteristic, complemented
65#14582633C2211yescharacteristic, complemented
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C2×#121×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic, complemented
70C4×C22⋊C4×C43C2211yescharacteristic, complemented
71C43×#327C2211yescharacteristic
72C43×#327C2211yescharacteristic
73C43×#327C2211yescharacteristic, complemented
74C43×#327C2211yescharacteristic, complemented
75C2×#10621898C2×C411yescharacteristic
76C2×#10621900—21no—
77C2×#10621900C2×C411yescharacteristic, complemented
78C22×C22⋊D43—21no—
79C22×C22⋊D43D411yescharacteristic
80C2×D4×D43—21no—
81C2×D4×D43C2×C411yescharacteristic, complemented
82C23×Dic43—21no—
83C22×C4×D43C2311yescharacteristic
84C2×#10621872—21no—
85C22×C43⋊C8—21no—
86C2×C8×D43—21no—
87#13063324C2×C411yescharacteristic, complemented
88#13063321—21no—
89#13063321C2×C411yescharacteristic, complemented
90#13063320—21no—
91#13063318—21no—
92#13063318—21no—
93#13063316C2×C411yescharacteristic, complemented
94#13063315—21no—
95#13063312—21no—
96#13063312C2×C411yescharacteristic, complemented
97#13063311—21no—
98#13063311—21no—
99#13063310—21no—
100#13063308—21no—
101#13063307—21no—
102#13063307—21no—
103#13063306—21no—
104#13063306—21no—
105#13063306—21no—
106#13063305C2×C411yescharacteristic, complemented
107#13063304—21no—
108#13063304C2×C411yescharacteristic
109#13063304C2311yescharacteristic
110#13063303—21no—
111#13063300C2×C411yescharacteristic, complemented
112#13063299—21no—
113#13063299C2×C411yescharacteristic
114#13063299C2311yescharacteristic
115#13063298—21no—
116#13063298—21no—
117#13063297—21no—
118#13063297—21no—
119#13063297—21no—
120#13063297—21no—
121#13063297—21no—
122#13063297—21no—
123#13063296—21no—
124#13063296—21no—
125#13063296C2×C411yescharacteristic, complemented
126#13063296C2×C411yescharacteristic, complemented
127#13063294—21no—
128#13063294—21no—
129#13063294—21no—
130#13063293—21no—
131#13063293—21no—
132#13063293—21no—
133#13063290C2×C411yescharacteristic, complemented
134D4×Dic43—21no—
135D4×Dic43—21no—
136D4×Dic43C2×C411yescharacteristic, complemented
137D4×Dic43C2×C411yescharacteristic, complemented
138#13063287C2×C411yescharacteristic, complemented
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142C4×C22⋊D43—21no—
143C4×C22⋊D43C2×C411yescharacteristic
144C4×C22⋊D43C2×C411yescharacteristic
145C4×C22⋊D43C2×C411yescharacteristic
146C4×C22⋊D43C2×C411yescharacteristic
147C4×C22⋊D43D411yescharacteristic
148C4×C22⋊D43D411yescharacteristic
149C4×C22⋊D43D411yescharacteristic
150C4×C22⋊D43D411yescharacteristic
151(C22⋊D43)⋊C4—21no—
152(C22⋊D43)⋊C4—21no—
153(C22⋊D43)⋊C4—21no—
154(C22⋊D43)⋊C4—21no—
155#13063284C2×C411yescharacteristic
156#13063283C2×C411yescharacteristic, complemented
157#13063281—21no—
158#13063281—21no—
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C4⋊C4×D43C2×C411yescharacteristic, complemented
163C2×C22⋊Dic43—21no—
164C2×C22⋊Dic43D411yescharacteristic
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—21no—
169C22⋊C4×D43—21no—
170C2×C4×Dic43C2311yescharacteristic
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176(C2×D43)⋊C8—21no—
177(C2×D43)⋊C8—21no—
178#13063235—21no—
179C8×Dic43—21no—
180C43⋊#95—21no—
181C43⋊#95—21no—
182C43⋊#95—21no—
183C43⋊#95—21no—
184C43⋊#95—21no—
185C43⋊#95C2311yescharacteristic
186C43⋊#95C2311yescharacteristic
187C22×D4×C43—21no—
188C22×D4×C43C2×C411yescharacteristic
189C23×C4×C43C2311yescharacteristic
190C2×M16×C43—21no—
191#121×C43—21no—
192#121×C43—21no—
193#121×C43C2×C411yescharacteristic
194#121×C43C2×C411yescharacteristic
195#121×C43C2311yescharacteristic
196#121×C43C2311yescharacteristic
197C2×C4⋊C4×C43C2×C411yescharacteristic
198C2×C22⋊C4×C43—21no—
199C2×C22⋊C4×C43—21no—
200C2×C42×C43—21no—
201C22⋊C8×C43—21no—
202C22⋊C8×C43C2311yescharacteristic
203C22⋊C8×C43C2311yescharacteristic
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208C23×D43—21no—
209C23×D43C2×D411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—21no—
214C2×D4×C43—21no—
215C2×D4×C43—81no—
216C2×D4×C43—81no—
217C2×D4×C43—81no—
218C2×D4×C43C22×C411yescharacteristic
219C2×D4×C43C22×C411yescharacteristic
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43—21no—
223C22×C4×C43—81no—
224C22×C4×C43C22×C411yescharacteristic
225C22×C4×C43C22×C411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
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—21no—
237C2×C22⋊D43—21no—
238C2×C22⋊D43—21no—
239C2×C22⋊D43—42no—
240C2×C22⋊D43—44no—
241C2×C22⋊D43C22⋊C411yescharacteristic
242C2×C22⋊D43C22⋊C411yescharacteristic
243C2×C22⋊D43C22⋊C411yescharacteristic
244C2×C22⋊D43C22⋊C411yescharacteristic
245C22×Dic43—21no—
246C22×Dic43—21no—
247C22×Dic43—21no—
248C22×Dic43—21no—
249C22×Dic43—21no—
250C22×Dic43—42no—
251C22×Dic43—81no—
252C22×Dic43—81no—
253C22×Dic43C2×D411yescharacteristic
254C22×Dic43C2×D411yescharacteristic
255C22×Dic43C2×D411yescharacteristic
256#10621900—81no—
257#10621900—81no—
258#10621900—81no—
259D4×D43—81no—
260D4×D43—81no—
261D4×D43—81no—
262#10621898—81no—
263C2×D172—21no—
264C2×D172C22×C411yescharacteristic
265C2×C4×D43—21no—
266C2×C4×D43—21no—
267C2×C4×D43—21no—
268C2×C4×D43—81no—
269C2×C4×D43C22×C411yescharacteristic
270C2×C4×D43C22×C411yescharacteristic
271C2×C4×D43C2×D411yescharacteristic
272C2×C4×D43C2×D411yescharacteristic
273C2×Dic86—21no—
274C2×Dic86C22×C411yescharacteristic
275M16×C43—81no—
276C2×C8×C43—21no—
277C2×C8×C43—21no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43C22×C411yescharacteristic
280C4⋊C4×C43C22×C411yescharacteristic
281C22⋊C4×C43—21no—
282C22⋊C4×C43—21no—
283C22⋊C4×C43—21no—
284C22⋊C4×C43—21no—
285C22⋊C4×C43—42no—
286C42×C43—81no—
287C22⋊Dic43—21no—
288C22⋊Dic43—21no—
289C22⋊Dic43—21no—
290C22⋊Dic43—21no—
291C22⋊Dic43—21no—
292C22⋊Dic43—21no—
293C22⋊Dic43—21no—
294C22⋊Dic43—21no—
295C22⋊Dic43—21no—
296C22⋊Dic43C22⋊C411yescharacteristic
297C22⋊Dic43C22⋊C411yescharacteristic
298C22⋊Dic43C22⋊C411yescharacteristic
299C22⋊Dic43C22⋊C411yescharacteristic
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—81no—
307(C2×D43)⋊C4—81no—
308(C2×D43)⋊C4C22⋊C411yescharacteristic
309(C2×D43)⋊C4C22⋊C411yescharacteristic
310(C2×D43)⋊C4C22⋊C411yescharacteristic
311(C2×D43)⋊C4C22⋊C411yescharacteristic
312C4⋊Dic43—21no—
313C4⋊Dic43—21no—
314C4⋊Dic43C22×C411yescharacteristic
315C4⋊Dic43C22×C411yescharacteristic
316Dic43⋊C4—21no—
317Dic43⋊C4—21no—
318Dic43⋊C4—21no—
319Dic43⋊C4—21no—
320Dic43⋊C4—21no—
321Dic43⋊C4—21no—
322Dic43⋊C4—81no—
323Dic43⋊C4—81no—
324Dic43⋊C4C22⋊C411yescharacteristic
325Dic43⋊C4C22⋊C411yescharacteristic
326Dic43⋊C4C22⋊C411yescharacteristic
327Dic43⋊C4C22⋊C411yescharacteristic
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43—21no—
331C4×Dic43C22×C411yescharacteristic
332C4×Dic43C22×C411yescharacteristic
333C4×Dic43C2×D411yescharacteristic
334C4×Dic43C2×D411yescharacteristic
335C2×C43⋊C8—21no—
336C2×C43⋊C8—21no—
337C2×C43⋊C8—81no—
338#10621872—81no—
339C8×D43—81no—
340C23×C43—21no—
341C23×C43—21no—
342C23×C43—22no—
343C23×C43—21no—
344C23×C43—21no—
345C23×C43—41no—
346C23×C43—42no—
347C23×C43—81no—
348C23×C43—81no—
349C23×C43C2×C22⋊C411yescharacteristic
350C23×C43C2×C22⋊C411yescharacteristic
351C23×C43C22×D411yescharacteristic
352C22×D43—21no—
353C22×D43—21no—
354C22×D43—21no—
355C22×D43—41no—
356C22×D43—41no—
357C22×D43—42no—
358C22×D43—81no—
359C22×D43—81no—
360C22×D43C2×C22⋊C411yescharacteristic
361C22×D43C2×C22⋊C411yescharacteristic
362D4×C43—41no—
363D4×C43—41no—
364D4×C43—41no—
365D4×C43—41no—
366D4×C43—41no—
367D4×C43—41no—
368D4×C43—81no—
369D4×C43—81no—
370D4×C43—81no—
371C2×C4×C43—21no—
372C2×C4×C43—21no—
373C2×C4×C43—41no—
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×C43—41no—
381C2×C4×C43—41no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—41no—
385C2×C4×C43—81no—
386C2×C4×C43C2×C22⋊C411yescharacteristic
387C2×C4×C43C2×C22⋊C411yescharacteristic
388C2×C4×C43C23×C411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C22⋊D43—22no—
391C22⋊D43—22no—
392C22⋊D43—41no—
393C22⋊D43—41no—
394C22⋊D43—42no—
395C22⋊D43—42no—
396C22⋊D43—41no—
397C22⋊D43—41no—
398C22⋊D43—42no—
399C22⋊D43—81no—
400C22⋊D43—81no—
401C22⋊D43—81no—
402C22⋊D43—81no—
403C22⋊D43—81no—
404C2×Dic43—21no—
405C2×Dic43—21no—
406C2×Dic43—21no—
407C2×Dic43—21no—
408C2×Dic43—21no—
409C2×Dic43—41no—
410C2×Dic43—41no—
411C2×Dic43—42no—
412C2×Dic43—41no—
413C2×Dic43—41no—
414C2×Dic43—41no—
415C2×Dic43—41no—
416C2×Dic43—41no—
417C2×Dic43—41no—
418C2×Dic43—81no—
419C2×Dic43—81no—
420C2×Dic43—84no—
421C2×Dic43C2×C22⋊C411yescharacteristic
422C2×Dic43C2×C22⋊C411yescharacteristic
423C2×Dic43C2×C22⋊C411yescharacteristic
424C2×Dic43C2×C22⋊C411yescharacteristic
425C2×Dic43C2×C22⋊C411yescharacteristic
426C2×Dic43C2×C22⋊C411yescharacteristic
427D172—41no—
428D172—81no—
429C4×D43—41no—
430C4×D43—41no—
431C4×D43—41no—
432C4×D43—41no—
433C4×D43—81no—
434C4×D43—81no—
435C4×D43—81no—
436Dic86—41no—
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—21no—
446C22×C43—21no—
447C22×C43—21no—
448C22×C43—21no—
449C22×C43—21no—
450C22×C43—42no—
451C22×C43—42no—
452C22×C43—41no—
453C22×C43—41no—
454C22×C43—41no—
455C22×C43—41no—
456C22×C43—41no—
457C22×C43—41no—
458C22×C43—162no—
459C22×C43#42112yes—
460C22×C43C22×C22⋊C411yescharacteristic
461C22×C43#57611yescharacteristic
462C22×C43#57711yescharacteristic
463C2×D43—21no—
464C2×D43—21no—
465C2×D43—21no—
466C2×D43—21no—
467C2×D43—21no—
468C2×D43—21no—
469C2×D43—41no—
470C2×D43—41no—
471C2×D43—41no—
472C2×D43—81no—
473C2×D43—81no—
474C2×D43—162no—
475C4×C43—21no—
476C4×C43—21no—
477C4×C43—21no—
478C4×C43—21no—
479C4×C43—41no—
480C4×C43—41no—
481C4×C43—81no—
482C4×C43—81no—
483Dic43—21no—
484Dic43—21no—
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#1514—431no—
502#1513—431no—
503#1512—431no—
504#1510—431no—
505#1507D4311yescharacteristic, complemented
506#1504—431no—
507#1501—431no—
508C2×#327—431no—
509C2×C43—21no—
510C2×C43—21no—
511C2×C43—22no—
512C2×C43—41no—
513C2×C43—81no—
514C2×C43—81no—
515C2×C43#288311yescharacteristic
516C2×C43#289711yescharacteristic
517C2×C43C2×#42111yescharacteristic
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#532—431no—
537#529—431no—
538#525—431no—
539#525—431no—
540C2×#121—431no—
541C2×#121C2×D4311yescharacteristic
542#518—861no—
543C2×C4×D4—431no—
544#436—861no—
545#435—861no—
546#435—861no—
547C8×D4—861no—
548#432—431no—
549#431—431no—
550#407—431no—
551#407C2×D4311yescharacteristic, complemented
552C2×C22⋊C8—431no—
553C2×C22⋊C8—431no—
554#388—861no—
555#387—861no—
556#386—861no—
557#385—861no—
558#383—431no—
559#382—431no—
560#381—431no—
561#380—431no—
562C4×C22⋊C4C2×D4311yescharacteristic, complemented
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
577#327C2×D4311yescharacteristic
578#327C2×D4311yescharacteristic, complemented
579#327C2×D4311yescharacteristic, complemented
580C43#1759711yescharacteristic, complemented, Sylow
581C2×#41—431no—
582C2×#41—431no—
583C2×#41—861no—
584C22×D4—21no—
585C22×D4—431no—
586C22×D4—431no—
587C22×D4—861no—
588C22×D4—861no—
589C22×D4C4×D4311yescharacteristic
590C23×C4—431no—
591C23×C4—861no—
592C23×C4C22×D4311yescharacteristic
593C2×M16—21no—
594C2×M16—861no—
595C22×C8—861no—
596C22×C8—861no—
597C4⋊Q8—431no—
598#127—431no—
599#127—861no—
600#126—861no—
601#126—861no—
602#126—861no—
603#125—431no—
604#125—861no—
605#124—431no—
606#124—861no—
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—21no—
623#121—431no—
624#121—431no—
625#121—431no—
626#121—431no—
627#121—431no—
628#121—861no—
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#121C4×D4311yescharacteristic
640#121C4×D4311yescharacteristic
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—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—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×D4—861no—
671#117—431no—
672#117—431no—
673#117—861no—
674#117—861no—
675C2×C4⋊C4—431no—
676C2×C4⋊C4—431no—
677C2×C4⋊C4—861no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4C4×D4311yescharacteristic
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—431no—
683C2×C22⋊C4—431no—
684C2×C22⋊C4—861no—
685C2×C22⋊C4—861no—
686C2×C22⋊C4—861no—
687C2×C22⋊C4—861no—
688C2×C22⋊C4—861no—
689C2×C42—21no—
690C2×C42—431no—
691C4⋊C8—861no—
692C4⋊C8—861no—
693C22⋊C8—21no—
694C22⋊C8—431no—
695C22⋊C8—431no—
696C22⋊C8—861no—
697C22⋊C8—861no—
698C22⋊C8—861no—
699C22⋊C8C22×D4311yescharacteristic
700C22⋊C8C22×D4311yescharacteristic
701#97—861no—
702C4×C8—861no—
703#95—431no—
704#95—431no—
705#95—861no—
706#95—861no—
707#95—861no—
708#95—861no—
709#95—861no—
710#95C22×D4311yescharacteristic
711#95C22×D4311yescharacteristic
712C24—21no—
713C24—431no—
714C24—861no—
715C24D4×D4311yescharacteristic
716#41—3441no—
717#41—3441no—
718#41—3441no—
719#41—3441no—
720C2×Q8—431no—
721C2×Q8—861no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—81no—
728C2×D4—81no—
729C2×D4—81no—
730C2×D4—431no—
731C2×D4—431no—
732C2×D4—431no—
733C2×D4—431no—
734C2×D4—431no—
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—861no—
744C2×D4—861no—
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—81no—
756C22×C4—431no—
757C22×C4—431no—
758C22×C4—431no—
759C22×C4—431no—
760C22×C4—431no—
761C22×C4—431no—
762C22×C4—431no—
763C22×C4—861no—
764C22×C4—861no—
765C22×C4—861no—
766C22×C4—861no—
767C22×C4—861no—
768C22×C4—861no—
769C22×C4—861no—
770C22×C4—861no—
771C22×C4—3441no—
772C22×C4—3441no—
773C22×C4—3441no—
774C22×C4—1722no—
775C22×C4C2×C4×D4311yescharacteristic
776C22×C4C2×C4×D4311yescharacteristic
777C22×C4D4×D4311yescharacteristic
778C22×C4D4×D4311yescharacteristic
779C22×C4D4×D4311yescharacteristic
780C22×C4C23×D4311yescharacteristic
781M16—81no—
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—42no—
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—861no—
836C22⋊C4—3441no—
837C22⋊C4—3441no—
838C42—81no—
839C42—431no—
840C42—431no—
841C42—431no—
842C42—431no—
843C42—861no—
844C42—861no—
845C42—861no—
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—41no—
852C23—42no—
853C23—81no—
854C23—81no—
855C23—431no—
856C23—431no—
857C23—861no—
858C23—861no—
859C23—861no—
860C23—3441no—
861C23—3441no—
862C23—1721no—
863C23—1721no—
864C23—1722no—
865C23C22⋊C4×D4311yescharacteristic
866C23C22⋊C4×D4311yescharacteristic
867C23C2×D4×D4311yescharacteristic
868Q8—3441no—
869Q8—1721no—
870D4—41no—
871D4—41no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—81no—
877D4—81no—
878D4—81no—
879D4—862no—
880D4—862no—
881D4—3441no—
882D4—3441no—
883D4—3441no—
884D4—3441no—
885D4—3441no—
886D4—3441no—
887D4—1721no—
888D4—1721no—
889D4—1721no—
890D4—1722no—
891D4—1722no—
892D4—1722no—
893D4—1721no—
894D4—1721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—41no—
898C2×C4—41no—
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—41no—
908C2×C4—41no—
909C2×C4—81no—
910C2×C4—431no—
911C2×C4—431no—
912C2×C4—431no—
913C2×C4—431no—
914C2×C4—431no—
915C2×C4—431no—
916C2×C4—861no—
917C2×C4—861no—
918C2×C4—861no—
919C2×C4—861no—
920C2×C4—861no—
921C2×C4—3441no—
922C2×C4—3441no—
923C2×C4—3441no—
924C2×C4—3441no—
925C2×C4—3441no—
926C2×C4—3444no—
927C2×C4—1721no—
928C2×C4—1721no—
929C2×C4—1721no—
930C2×C4—1721no—
931C2×C4—1721no—
932C2×C4—1721no—
933C2×C4—1722no—
934C2×C4—1721no—
935C2×C4—1721no—
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×C4C2×D4×D4311yescharacteristic
944C8—41no—
945C8—41no—
946C8—1721no—
947C8—1721no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—42no—
956C22—42no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—162no—
964C22—861no—
965C22—861no—
966C22—861no—
967C22—861no—
968C22—861no—
969C22—861no—
970C22—3441no—
971C22—3441no—
972C22—1721no—
973C22—1721no—
974C22—1721no—
975C22—6882no—
976C22#1458291412yes—
977C22C2×C22⋊C4×D4311yescharacteristic
978C22#1458370311yescharacteristic
979C22#1458370911yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—41no—
985C4—41no—
986C4—81no—
987C4—81no—
988C4—861no—
989C4—861no—
990C4—861no—
991C4—861no—
992C4—861no—
993C4—861no—
994C4—3441no—
995C4—3441no—
996C4—1721no—
997C4—1721no—
998C4—1721no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—81no—
1004C2—81no—
1005C2—3441no—
1006C2—1721no—
1007C2—1721no—
1008C2#1914305311yescharacteristic
1009C2#1914312011yescharacteristic
1010C2C2×#1458291411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1507C2
socleC22×C43C22×C22⋊C4
prime radical#19148621C2
cosocleC22×C4×C43C24
hypercenter#1507D43
hypocenterC43#17597
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #19143631C2semidirect
3. #19137222C2semidirect
4. #19133169C2semidirect
5. #19133161C2semidirect
6. #19133153C2semidirect
7. #19133148C2semidirect
8. #19133140C2semidirect
9. #19133135C2semidirect
10. #19133130C2semidirect
11. #19133122C2semidirect
12. #19133100C2semidirect
13. #19133084C2semidirect
14. C2×#14582633C2semidirect
15. C43×#1507C2semidirect
16. #14583613C4semidirect
17. #14583604C4semidirect
18. #14583597C4semidirect
19. #14583596C4semidirect
21. #14583567C4semidirect
22. #14583546C4semidirect
24. #14583543C4semidirect
27. D4×C22⋊D43C4semidirect
42. #14582953C22semidirect
43. #14582949C22semidirect
44. #14582861C22semidirect
45. C2×C22⋊(C43⋊C8)C22semidirect
46. C22⋊C8×D43C22semidirect
51. #14582766C22semidirect
52. #14582763C22semidirect
53. #14582761C22semidirect
54. #14582758C22semidirect
55. C2×C43⋊#95C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582635C22semidirect
59. #14582635C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
64. #14582633C22semidirect
65. #14582633C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
69. C43×#407C22semidirect
70. C4×C22⋊C4×C43C22semidirect
73. C43×#327C22semidirect
74. C43×#327C22semidirect
77. C2×#10621900C2×C4semidirect
81. C2×D4×D43C2×C4semidirect
87. #13063324C2×C4semidirect
89. #13063321C2×C4semidirect
93. #13063316C2×C4semidirect
96. #13063312C2×C4semidirect
106. #13063305C2×C4semidirect
111. #13063300C2×C4semidirect
125. #13063296C2×C4semidirect
126. #13063296C2×C4semidirect
133. #13063290C2×C4semidirect
136. D4×Dic43C2×C4semidirect
137. D4×Dic43C2×C4semidirect
138. #13063287C2×C4semidirect
156. #13063283C2×C4semidirect
162. C4⋊C4×D43C2×C4semidirect
505. #1507D43semidirect
551. #407C2×D43semidirect
562. C4×C22⋊C4C2×D43semidirect
578. #327C2×D43semidirect
579. #327C2×D43semidirect
580. C43#17597semidirect

Maximal subgroups

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

subgroupindex
#191486212
#191436312
#191372222
#191331692
#191331612
#191331532
#191331482
#191331402
#191331352
#191331302
#191331222
#191331002
#191330842
C2×#145826332
C43×#15072
#1759743