Finite Group Databasebeta

← #25064209

Subgroups — #25064209

Order 11008.

1004 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148324C211yesmaximal, characteristic
2#19143255C211yesmaximal, characteristic, complemented
3#19137457C211yesmaximal, characteristic, complemented
4#19133169C211yesmaximal, characteristic, complemented
5#19133153C211yesmaximal, characteristic, complemented
6#19133149C211yesmaximal, characteristic, complemented
7#19133140C211yesmaximal, characteristic, complemented
8#19133130C211yesmaximal, characteristic, complemented
9#19133117C211yesmaximal, characteristic, complemented
10#19133101C211yesmaximal, characteristic, complemented
11#19133100C211yesmaximal, characteristic, complemented
12#19133088C211yesmaximal, characteristic, complemented
13#19133078C211yesmaximal, characteristic, complemented
14C2×#14582633C211yesmaximal, characteristic, complemented
15C43×#1510C211yesmaximal, characteristic, complemented
16#14583613—21no—
17#14583601—21no—
18#14583596—21no—
19#14583575—21no—
20#14583575—21no—
21#14583549—21no—
22#14583543—21no—
23#14583543—21no—
24#14583530C411yescharacteristic, complemented
25#14583516C411yescharacteristic, complemented
26#14583516C411yescharacteristic, complemented
27#14583502C411yescharacteristic, complemented
28#14583502C411yescharacteristic, complemented
29#14583466C411yescharacteristic, complemented
30#14583444C2211yescharacteristic
31#14583444C2211yescharacteristic
32#14583430C2211yescharacteristic
33#14583430C2211yescharacteristic
34#14583410C2211yescharacteristic
35#14583380C411yescharacteristic, complemented
36#14583374C411yescharacteristic, complemented
37C2×#13063284C2211yescharacteristic
38#14582957—21no—
39#14582957—21no—
40#14582953C2211yescharacteristic, complemented
41#14582953C2211yescharacteristic, complemented
42#14582949C2211yescharacteristic, complemented
43#14582949C2211yescharacteristic, complemented
44#14582927—21no—
45C2×C22⋊(C43⋊C8)C2211yescharacteristic
46#14582857—21no—
47#14582784—21no—
48#14582782—21no—
49#14582771—21no—
50#14582766C2211yescharacteristic, complemented
51#14582763C2211yescharacteristic, complemented
52#14582750C2211yescharacteristic, complemented
53C22⋊C4×Dic43—21no—
54#14582744C2211yescharacteristic, complemented
55C2×C43⋊#95C2211yescharacteristic
56#14582637C2211yescharacteristic, complemented
57#14582637C2211yescharacteristic, complemented
58#14582635C2211yescharacteristic, complemented
59#14582635C2211yescharacteristic, complemented
60#14582634C2211yescharacteristic, complemented
61#14582634C2211yescharacteristic, complemented
62#14582633C2211yescharacteristic
63#14582633C2211yescharacteristic
64#14582633C2211yescharacteristic
65#14582633C2211yescharacteristic
66#14582632C2211yescharacteristic, complemented
67#14582632C2211yescharacteristic, complemented
68C2×#121×C43C2211yescharacteristic
69C43×#407C2211yescharacteristic
70C43×#381C2211yescharacteristic
71C43×#327C2211yescharacteristic
72C43×#327C2211yescharacteristic
73C43×#327C2211yescharacteristic
74C43×#327C2211yescharacteristic
75C2×#10621898C2×C411yescharacteristic
76C2×#10621900—21no—
77C2×#10621900—21no—
78C23×Dic43—21no—
79C22×C43⋊C8—21no—
80#13063324—21no—
81#13063324C2×C411yescharacteristic, complemented
82#13063324C2×C411yescharacteristic, complemented
83#13063321C2×C411yescharacteristic, complemented
84#13063321C2×C411yescharacteristic, complemented
85#13063318—21no—
86#13063318—21no—
87#13063318—21no—
88#13063318—21no—
89#13063316—21no—
90#13063316C2×C411yescharacteristic, complemented
91#13063316C2×C411yescharacteristic, complemented
92#13063312—21no—
93#13063312—21no—
94#13063312C2×C411yescharacteristic, complemented
95#13063312C2×C411yescharacteristic, complemented
96#13063311—21no—
97#13063311—21no—
98#13063309—21no—
99#13063309—21no—
100#13063308—21no—
101#13063307—21no—
102#13063307—21no—
103#13063306—21no—
104#13063306—21no—
105#13063306—21no—
106#13063306—21no—
107#13063304—21no—
108#13063304—21no—
109#13063304C2×C411yescharacteristic
110#13063304C2311yescharacteristic
111#13063302—21no—
112#13063302—21no—
113#13063299C2×C411yescharacteristic
114#13063299C2311yescharacteristic
115#13063297—21no—
116#13063297—21no—
117#13063297—21no—
118#13063297—21no—
119#13063296—21no—
120#13063296—21no—
121#13063296—21no—
122#13063296—21no—
123#13063294—21no—
124#13063294—21no—
125#13063294—21no—
126#13063290C2×C411yescharacteristic, complemented
127#13063290C2×C411yescharacteristic, complemented
128D4×Dic43—21no—
129D4×Dic43—21no—
130D4×Dic43—21no—
131D4×Dic43—21no—
132D4×Dic43C2×C411yescharacteristic, complemented
133D4×Dic43C2×C411yescharacteristic, complemented
134D4×Dic43C2×C411yescharacteristic, complemented
135D4×Dic43C2×C411yescharacteristic, complemented
136#13063287C2×C411yescharacteristic, complemented
137#13063287C2×C411yescharacteristic, complemented
138C4×C22⋊D43—21no—
139C4×C22⋊D43—21no—
140C4×C22⋊D43—21no—
141C4×C22⋊D43—21no—
142(C22⋊D43)⋊C4—21no—
143(C22⋊D43)⋊C4—21no—
144#13063284C2×C411yescharacteristic
145#13063284C2×C411yescharacteristic
146#13063284C2×C411yescharacteristic
147#13063284C2×C411yescharacteristic
148#13063284C2×C411yescharacteristic
149#13063284D411yescharacteristic
150#13063284D411yescharacteristic
151#13063284D411yescharacteristic
152#13063284D411yescharacteristic
153#13063283—21no—
154#13063281—21no—
155#13063281—21no—
156C2×C4⋊Dic43D411yescharacteristic
157C2×C4⋊Dic43D411yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C4⋊C4×D43—21no—
161C2×C22⋊Dic43—21no—
162C2×C22⋊Dic43—21no—
163C2×C22⋊Dic43D411yescharacteristic
164C2×C22⋊Dic43D411yescharacteristic
165C2×C4×Dic43—21no—
166C2×C4×Dic43—21no—
167C2×C4×Dic43C2311yescharacteristic
168C2×C4×Dic43C2311yescharacteristic
169Dic43⋊C8—21no—
170Dic43⋊C8—21no—
171Dic43⋊C8—21no—
172Dic43⋊C8—21no—
173C22⋊(C43⋊C8)—21no—
174C22⋊(C43⋊C8)C2311yescharacteristic
175C22⋊(C43⋊C8)C2311yescharacteristic
176#13063235—21no—
177#13063235—21no—
178C8×Dic43—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—
200C22⋊C8×C43—21no—
201C22⋊C8×C43C2311yescharacteristic
202C22⋊C8×C43C2311yescharacteristic
203#95×C43—21no—
204#95×C43C2311yescharacteristic
205#95×C43C2311yescharacteristic
206C24×C43—21no—
207C24×C43C2×D411yescharacteristic
208C2×D4×C43—21no—
209C2×D4×C43—21no—
210C2×D4×C43—21no—
211C2×D4×C43—21no—
212C2×D4×C43—21no—
213C2×D4×C43—42no—
214C2×D4×C43—81no—
215C2×D4×C43—81no—
216C2×D4×C43C22×C411yescharacteristic
217C2×D4×C43C22×C411yescharacteristic
218C22×C4×C43—21no—
219C22×C4×C43—21no—
220C22×C4×C43—21no—
221C22×C4×C43—42no—
222C22×C4×C43C22×C411yescharacteristic
223C22×C4×C43C22×C411yescharacteristic
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2411yescharacteristic
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×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—42no—
242C22×Dic43—42no—
243C22×Dic43—81no—
244C22×Dic43C2×D411yescharacteristic
245C22×Dic43C2×D411yescharacteristic
246C22×Dic43C2×D411yescharacteristic
247C22×Dic43C2×D411yescharacteristic
248#10621900—81no—
249#10621900—81no—
250#10621900—81no—
251#10621900—81no—
252#10621898—42no—
253C2×D172C22×C411yescharacteristic
254C2×C4×D43—21no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×Dic86—21no—
258C2×Dic86—21no—
259C2×Dic86C22×C411yescharacteristic
260M16×C43—42no—
261C2×C8×C43—21no—
262C2×C8×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C22×C411yescharacteristic
265C4⋊C4×C43C22×C411yescharacteristic
266C22⋊C4×C43—21no—
267C22⋊C4×C43—21no—
268C22⋊C4×C43—21no—
269C22⋊C4×C43—21no—
270C22⋊C4×C43—42no—
271C22⋊Dic43—21no—
272C22⋊Dic43—21no—
273C22⋊Dic43—21no—
274C22⋊Dic43—21no—
275C22⋊Dic43—21no—
276C22⋊Dic43—21no—
277C22⋊Dic43—21no—
278C22⋊Dic43—21no—
279C22⋊Dic43—21no—
280C22⋊Dic43—21no—
281C22⋊Dic43—21no—
282C22⋊Dic43C22⋊C411yescharacteristic
283C22⋊Dic43C22⋊C411yescharacteristic
284C22⋊Dic43C22⋊C411yescharacteristic
285C22⋊Dic43C22⋊C411yescharacteristic
286C22⋊Dic43C22⋊C411yescharacteristic
287C22⋊Dic43C22⋊C411yescharacteristic
288C22⋊Dic43C22⋊C411yescharacteristic
289C22⋊Dic43C22⋊C411yescharacteristic
290(C2×D43)⋊C4—21no—
291(C2×D43)⋊C4—21no—
292(C2×D43)⋊C4—21no—
293(C2×D43)⋊C4—21no—
294C4⋊Dic43—21no—
295C4⋊Dic43—21no—
296C4⋊Dic43C22⋊C411yescharacteristic
297C4⋊Dic43C22⋊C411yescharacteristic
298C4⋊Dic43C22⋊C411yescharacteristic
299C4⋊Dic43C22⋊C411yescharacteristic
300C4⋊Dic43C22⋊C411yescharacteristic
301C4⋊Dic43C22⋊C411yescharacteristic
302C4⋊Dic43C22⋊C411yescharacteristic
303C4⋊Dic43C22⋊C411yescharacteristic
304C4⋊Dic43C22×C411yescharacteristic
305C4⋊Dic43C22×C411yescharacteristic
306Dic43⋊C4—21no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309Dic43⋊C4—21no—
310Dic43⋊C4—21no—
311Dic43⋊C4—21no—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—42no—
315Dic43⋊C4—81no—
316C4×Dic43—21no—
317C4×Dic43—21no—
318C4×Dic43—21no—
319C4×Dic43—42no—
320C4×Dic43—81no—
321C4×Dic43C22×C411yescharacteristic
322C4×Dic43C22×C411yescharacteristic
323C4×Dic43C22×C411yescharacteristic
324C4×Dic43C22×C411yescharacteristic
325C4×Dic43C2×D411yescharacteristic
326C4×Dic43C2×D411yescharacteristic
327C4×Dic43C2×D411yescharacteristic
328C4×Dic43C2×D411yescharacteristic
329C2×C43⋊C8—21no—
330C2×C43⋊C8—21no—
331C2×C43⋊C8—42no—
332C23×C43—21no—
333C23×C43—21no—
334C23×C43—22no—
335C23×C43—21no—
336C23×C43—21no—
337C23×C43—41no—
338C23×C43—42no—
339C23×C43—81no—
340C23×C43—81no—
341C23×C43C2×C22⋊C411yescharacteristic
342C23×C43C2×C22⋊C411yescharacteristic
343C23×C43C22×D411yescharacteristic
344C22×D43—21no—
345D4×C43—41no—
346D4×C43—41no—
347D4×C43—42no—
348D4×C43—41no—
349D4×C43—41no—
350D4×C43—41no—
351D4×C43—41no—
352D4×C43—81no—
353D4×C43—81no—
354C2×C4×C43—22no—
355C2×C4×C43—22no—
356C2×C4×C43—21no—
357C2×C4×C43—21no—
358C2×C4×C43—41no—
359C2×C4×C43—41no—
360C2×C4×C43—41no—
361C2×C4×C43—41no—
362C2×C4×C43—41no—
363C2×C4×C43—41no—
364C2×C4×C43—41no—
365C2×C4×C43—41no—
366C2×C4×C43—41no—
367C2×C4×C43—41no—
368C2×C4×C43—81no—
369C2×C4×C43C2×C22⋊C411yescharacteristic
370C2×C4×C43C2×C22⋊C411yescharacteristic
371C2×C4×C43C23×C411yescharacteristic
372C2×C4×C43C22×D411yescharacteristic
373C22⋊D43—41no—
374C22⋊D43—41no—
375C22⋊D43—42no—
376C22⋊D43—81no—
377C22⋊D43—81no—
378C22⋊D43—81no—
379C22⋊D43—81no—
380C22⋊D43—81no—
381C2×Dic43—21no—
382C2×Dic43—21no—
383C2×Dic43—21no—
384C2×Dic43—21no—
385C2×Dic43—22no—
386C2×Dic43—21no—
387C2×Dic43—21no—
388C2×Dic43—21no—
389C2×Dic43—41no—
390C2×Dic43—41no—
391C2×Dic43—41no—
392C2×Dic43—41no—
393C2×Dic43—41no—
394C2×Dic43—41no—
395C2×Dic43—41no—
396C2×Dic43—81no—
397C2×Dic43—81no—
398C2×Dic43—81no—
399C2×Dic43—81no—
400C2×Dic43—84no—
401C2×Dic43C2×C22⋊C411yescharacteristic
402C2×Dic43C2×C22⋊C411yescharacteristic
403C2×Dic43C2×C22⋊C411yescharacteristic
404C2×Dic43C2×C22⋊C411yescharacteristic
405C2×Dic43C2×C22⋊C411yescharacteristic
406C2×Dic43C2×C22⋊C411yescharacteristic
407C2×Dic43C2×C22⋊C411yescharacteristic
408C2×Dic43C2×C22⋊C411yescharacteristic
409D172—41no—
410C4×D43—42no—
411C4×D43—81no—
412C4×D43—81no—
413Dic86—41no—
414Dic86—81no—
415Dic86—81no—
416C8×C43—41no—
417C8×C43—41no—
418C43⋊C8—41no—
419C43⋊C8—41no—
420#17604—431nomaximal, Sylow
421C22×C43—21no—
422C22×C43—21no—
423C22×C43—21no—
424C22×C43—21no—
425C22×C43—21no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—42no—
429C22×C43—42no—
430C22×C43—41no—
431C22×C43—41no—
432C22×C43—41no—
433C22×C43—41no—
434C22×C43—41no—
435C22×C43—41no—
436C22×C43—162no—
437C22×C43#41012yes—
438C22×C43C22×C22⋊C411yescharacteristic
439C22×C43#57611yescharacteristic
440C22×C43#57711yescharacteristic
441C2×D43—41no—
442C2×D43—41no—
443C2×D43—41no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—41no—
449C4×C43—41no—
450C4×C43—81no—
451C4×C43—81no—
452Dic43—21no—
453Dic43—21no—
454Dic43—21no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—21no—
459Dic43—21no—
460Dic43—42no—
461Dic43—41no—
462Dic43—41no—
463Dic43—41no—
464Dic43—81no—
465#3494—431no—
466#2924—431no—
467#2343—431no—
468#1521—431no—
469#1517—431no—
470#1516—431no—
471#1514—431no—
472#1512—431no—
473#1510D4311yescharacteristic, complemented
474#1509—431no—
475#1505—431no—
476#1504—431no—
477#1502—431no—
478#1500—431no—
479C2×#327—431no—
480C2×C43—21no—
481C2×C43—21no—
482C2×C43—22no—
483C2×C43—41no—
484C2×C43—81no—
485C2×C43—81no—
486C2×C43C2×#41011yescharacteristic
487C2×C43#289711yescharacteristic
488C2×C43#290111yescharacteristic
489D43—81no—
490#555—861no—
491#553—861no—
492#553—861no—
493#551—861no—
494#551—861no—
495#547—861no—
496#546—861no—
497#546—861no—
498#544—431no—
499#542—431no—
500#542—431no—
501#540—431no—
502#540—431no—
503#535—431no—
504#532—431no—
505#532—431no—
506#529—431no—
507#529—431no—
508#525—431no—
509C2×#121C2×D4311yescharacteristic
510#520—431no—
511#518—431no—
512C2×#117—431no—
513#433—861no—
514#433—861no—
515#432—431no—
516#432—431no—
517#431—431no—
518#431—431no—
519#424—861no—
520#407C2×D4311yescharacteristic
521C2×C22⋊C8—431no—
522#405—861no—
523#387—861no—
524#387—861no—
525#385—861no—
526#383—431no—
527#382—431no—
528#381C2×D4311yescharacteristic
529C4×C4⋊C4—431no—
530C4×C22⋊C4—861no—
531#376—431no—
532C2×#95—431no—
533#328—431no—
534#328—431no—
535#328—431no—
536#328—431no—
537#327—431no—
538#327—431no—
539#327—431no—
540#327—431no—
541#327—431no—
542#327—431no—
543#327—431no—
544#327—431no—
545#327C2×D4311yescharacteristic
546#327C2×D4311yescharacteristic
547#327C2×D4311yescharacteristic
548#327C2×D4311yescharacteristic
549C43#1760411yescharacteristic, complemented, Sylow
550C2×#41—431no—
551C2×#41—861no—
552C2×#41—861no—
553C22×D4—21no—
554C22×D4C4×D4311yescharacteristic
555C23×C4—861no—
556C23×C4C22×D4311yescharacteristic
557C2×M16—21no—
558C22×C8—861no—
559C4⋊Q8—431no—
560C4⋊Q8—431no—
561C4⋊Q8—861no—
562#127—431no—
563#127—431no—
564#126—861no—
565#126—861no—
566#126—861no—
567#126—861no—
568#125—431no—
569#125—431no—
570#125—861no—
571#124—431no—
572#124—431no—
573#124—861no—
574#124—861no—
575#124—861no—
576#124—861no—
577#123—861no—
578#123—861no—
579#123—861no—
580#123—861no—
581#123—861no—
582#123—861no—
583#123—861no—
584#123—861no—
585#123—861no—
586C22⋊Q8—431no—
587C22⋊Q8—431no—
588C22⋊Q8—861no—
589C22⋊Q8—861no—
590C22⋊Q8—861no—
591C22⋊Q8—861no—
592#121—21no—
593#121—21no—
594#121—431no—
595#121—431no—
596#121—861no—
597#121—861no—
598#121—861no—
599#121—861no—
600#121—861no—
601#121—861no—
602#121—861no—
603#121—861no—
604#121C4×D4311yescharacteristic
605#121C4×D4311yescharacteristic
606#121C22×D4311yescharacteristic
607#121C22×D4311yescharacteristic
608#120—861no—
609#120—861no—
610#120—861no—
611C4×Q8—431no—
612C4×Q8—431no—
613C4×D4—431no—
614C4×D4—431no—
615C4×D4—431no—
616C4×D4—431no—
617C4×D4—431no—
618C4×D4—431no—
619C4×D4—861no—
620C4×D4—861no—
621C4×D4—861no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627C4×D4—861no—
628C4×D4—861no—
629#117—431no—
630#117—431no—
631#117—431no—
632#117—431no—
633#117—431no—
634#117—431no—
635#117—431no—
636#117—431no—
637#117—431no—
638#117—861no—
639#117—861no—
640#117—861no—
641C2×C4⋊C4—431no—
642C2×C4⋊C4—431no—
643C2×C4⋊C4—861no—
644C2×C4⋊C4—861no—
645C2×C4⋊C4—861no—
646C2×C4⋊C4C4×D4311yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—431no—
650C2×C22⋊C4—431no—
651C2×C22⋊C4—861no—
652C2×C22⋊C4—861no—
653C2×C42—431no—
654C2×C42—431no—
655C2×C42—861no—
656C2×C42—861no—
657C4⋊C8—861no—
658C4⋊C8—861no—
659C4⋊C8—861no—
660C4⋊C8—861no—
661C22⋊C8—21no—
662C22⋊C8—431no—
663C22⋊C8—431no—
664C22⋊C8—861no—
665C22⋊C8C22×D4311yescharacteristic
666C22⋊C8C22×D4311yescharacteristic
667#97—861no—
668#97—861no—
669C4×C8—861no—
670C4×C8—861no—
671#95—21no—
672#95—431no—
673#95—431no—
674#95—861no—
675#95—861no—
676#95—861no—
677#95—861no—
678#95—861no—
679#95C22×D4311yescharacteristic
680#95C22×D4311yescharacteristic
681C24—21no—
682C24D4×D4311yescharacteristic
683#41—3441no—
684#41—3441no—
685#41—3441no—
686#41—3441no—
687#41—1722no—
688C2×Q8—431no—
689C2×Q8—861no—
690C2×Q8—861no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—42no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—431no—
700C2×D4—861no—
701C2×D4—861no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—861no—
705C2×D4—861no—
706C2×D4—861no—
707C2×D4C2×C4×D4311yescharacteristic
708C2×D4C2×C4×D4311yescharacteristic
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—42no—
713C22×C4—431no—
714C22×C4—431no—
715C22×C4—431no—
716C22×C4—431no—
717C22×C4—861no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—861no—
723C22×C4—861no—
724C22×C4—861no—
725C22×C4—861no—
726C22×C4—3441no—
727C22×C4—1722no—
728C22×C4—1722no—
729C22×C4C2×C4×D4311yescharacteristic
730C22×C4C2×C4×D4311yescharacteristic
731C22×C4D4×D4311yescharacteristic
732C22×C4D4×D4311yescharacteristic
733C22×C4D4×D4311yescharacteristic
734C22×C4C23×D4311yescharacteristic
735M16—42no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—861no—
739C2×C8—861no—
740C2×C8—1722no—
741C4⋊C4—21no—
742C4⋊C4—431no—
743C4⋊C4—431no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—431no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—431no—
751C4⋊C4—431no—
752C4⋊C4—861no—
753C4⋊C4—861no—
754C4⋊C4—861no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4—861no—
759C4⋊C4—861no—
760C4⋊C4—861no—
761C4⋊C4—861no—
762C4⋊C4—3441no—
763C4⋊C4—1722no—
764C4⋊C4C2×C4×D4311yescharacteristic
765C4⋊C4C2×C4×D4311yescharacteristic
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—42no—
771C22⋊C4—431no—
772C22⋊C4—431no—
773C22⋊C4—431no—
774C22⋊C4—431no—
775C22⋊C4—431no—
776C22⋊C4—431no—
777C22⋊C4—431no—
778C22⋊C4—431no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C22⋊C4—861no—
782C22⋊C4—861no—
783C22⋊C4—861no—
784C22⋊C4—861no—
785C22⋊C4—861no—
786C22⋊C4—861no—
787C22⋊C4—861no—
788C22⋊C4—861no—
789C22⋊C4—861no—
790C22⋊C4—861no—
791C22⋊C4—861no—
792C22⋊C4—861no—
793C22⋊C4—861no—
794C42—431no—
795C42—431no—
796C42—431no—
797C42—431no—
798C42—431no—
799C42—431no—
800C42—431no—
801C42—431no—
802C42—861no—
803C42—861no—
804C42—861no—
805C42—3441no—
806C42—1722no—
807C23—22no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—41no—
813C23—42no—
814C23—81no—
815C23—81no—
816C23—861no—
817C23C22⋊C4×D4311yescharacteristic
818C23C22⋊C4×D4311yescharacteristic
819C23C2×D4×D4311yescharacteristic
820Q8—3441no—
821Q8—3441no—
822Q8—1721no—
823D4—41no—
824D4—41no—
825D4—42no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—81no—
831D4—81no—
832D4—3441no—
833D4—3441no—
834D4—3441no—
835D4—3441no—
836D4—3441no—
837D4—1721no—
838D4—1722no—
839D4—1721no—
840D4—1721no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—81no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—431no—
860C2×C4—431no—
861C2×C4—431no—
862C2×C4—431no—
863C2×C4—431no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—861no—
868C2×C4—862no—
869C2×C4—861no—
870C2×C4—861no—
871C2×C4—861no—
872C2×C4—3441no—
873C2×C4—3441no—
874C2×C4—3441no—
875C2×C4—3441no—
876C2×C4—3441no—
877C2×C4—3441no—
878C2×C4—3444no—
879C2×C4—1722no—
880C2×C4—1721no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1721no—
884C2×C4—1721no—
885C2×C4—1721no—
886C2×C4—1721no—
887C2×C4C22⋊C4×D4311yescharacteristic
888C2×C4C22⋊C4×D4311yescharacteristic
889C2×C4C22×C4×D4311yescharacteristic
890C2×C4C2×D4×D4311yescharacteristic
891C8—41no—
892C8—41no—
893C8—1721no—
894C8—1721no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—42no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—162no—
911C22—1721no—
912C22—1721no—
913C22—1721no—
914C22#1458287112yes—
915C22C2×C22⋊C4×D4311yescharacteristic
916C22#1458370311yescharacteristic
917C22#1458370911yescharacteristic
918C4—21no—
919C4—21no—
920C4—21no—
921C4—21no—
922C4—41no—
923C4—41no—
924C4—81no—
925C4—81no—
926C4—861no—
927C4—861no—
928C4—861no—
929C4—861no—
930C4—861no—
931C4—861no—
932C4—861no—
933C4—861no—
934C4—3441no—
935C4—1722no—
936C4—1721no—
937C4—1721no—
938C4—1721no—
939C2—21no—
940C2—21no—
941C2—22no—
942C2—41no—
943C2—81no—
944C2—81no—
945C2—3441no—
946C2C2×#1458287111yescharacteristic
947C2#1914312011yescharacteristic
948C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1510C2
socleC22×C43C22×C22⋊C4
prime radical#19148324C2
cosocleC22×C4×C43C24
hypercenter#1510D43
hypocenterC43#17604
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
2. #19143255C2semidirect
3. #19137457C2semidirect
4. #19133169C2semidirect
5. #19133153C2semidirect
6. #19133149C2semidirect
7. #19133140C2semidirect
8. #19133130C2semidirect
9. #19133117C2semidirect
10. #19133101C2semidirect
11. #19133100C2semidirect
12. #19133088C2semidirect
13. #19133078C2semidirect
14. C2×#14582633C2semidirect
15. C43×#1510C2semidirect
24. #14583530C4semidirect
25. #14583516C4semidirect
26. #14583516C4semidirect
27. #14583502C4semidirect
28. #14583502C4semidirect
29. #14583466C4semidirect
35. #14583380C4semidirect
36. #14583374C4semidirect
40. #14582953C22semidirect
41. #14582953C22semidirect
42. #14582949C22semidirect
43. #14582949C22semidirect
50. #14582766C22semidirect
51. #14582763C22semidirect
52. #14582750C22semidirect
54. #14582744C22semidirect
56. #14582637C22semidirect
57. #14582637C22semidirect
58. #14582635C22semidirect
59. #14582635C22semidirect
60. #14582634C22semidirect
61. #14582634C22semidirect
66. #14582632C22semidirect
67. #14582632C22semidirect
81. #13063324C2×C4semidirect
82. #13063324C2×C4semidirect
83. #13063321C2×C4semidirect
84. #13063321C2×C4semidirect
90. #13063316C2×C4semidirect
91. #13063316C2×C4semidirect
94. #13063312C2×C4semidirect
95. #13063312C2×C4semidirect
126. #13063290C2×C4semidirect
127. #13063290C2×C4semidirect
132. D4×Dic43C2×C4semidirect
133. D4×Dic43C2×C4semidirect
134. D4×Dic43C2×C4semidirect
135. D4×Dic43C2×C4semidirect
136. #13063287C2×C4semidirect
137. #13063287C2×C4semidirect
473. #1510D43semidirect
549. C43#17604semidirect

Maximal subgroups

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

subgroupindex
#191483242
#191432552
#191374572
#191331692
#191331532
#191331492
#191331402
#191331302
#191331172
#191331012
#191331002
#191330882
#191330782
C2×#145826332
C43×#15102
#1760443