Finite Group Databasebeta

← #25113263

Subgroups — #25113263

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583605C211yesmaximal, characteristic
2C2×#14583027C211yesmaximal, characteristic, complemented
3#19137554C211yesmaximal, characteristic, complemented
4#19135566C211yesmaximal, characteristic, complemented
5#19135558C211yesmaximal, characteristic, complemented
6#19135553C211yesmaximal, characteristic, complemented
7#19135551C211yesmaximal, characteristic, complemented
8#19135545C211yesmaximal, characteristic, complemented
9#19134604C211yesmaximal, characteristic
10#19134604C211yesmaximal, characteristic
11#19134592C211yesmaximal, characteristic
12#19134421C211yesmaximal, characteristic
13#19134419C211yesmaximal, characteristic
14#19134409C211yesmaximal, characteristic
15C43×#1992C211yesmaximal, characteristic, complemented
16#14583605—24no—
17#14583605C418yescomplemented
18C2×#13063324C2211yescharacteristic
19C2×#13063316C2211yescharacteristic
20C2×#13063305—21no—
21C2×#13063303—21no—
22C2×#13063303—21no—
23C2×C4×Dic86C2211yescharacteristic
24C2×C4×D172C2211yescharacteristic
25C2×#13063287C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×C4⋊C4×D43—21no—
28#14583027—24no—
29C2×C4⋊(C43⋊C8)C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×Dic43⋊C8C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063247C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×#13063245C2211yescharacteristic
36C2×#13063235C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582804—21no—
39#14582780—21no—
40#14582780—21no—
41#14582764C2211yescharacteristic
42#14582764C2211yescharacteristic
43C4⋊C4×Dic43—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#125×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C43×#384C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86D411yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70#13063324—22no—
71#13063324C2×C414yes—
72#13063316—22no—
73#13063316C2×C414yes—
74#13063305—28no—
75#13063303—28no—
76#13063303—28no—
77C4×Dic86C2×C414yes—
78C4×Dic86D414yes—
79C4×D172—22no—
80C4×D172C2×C414yes—
81#13063287—22no—
82#13063287—22no—
83#13063287C2×C414yes—
84#13063287C2×C414yes—
85C2×C4⋊Dic43—21no—
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4D411yescharacteristic
93C2×Dic43⋊C4D411yescharacteristic
94C4⋊C4×D43—28no—
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×C4×Dic43—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43C2311yescharacteristic
102C2×C4×Dic43C2311yescharacteristic
103C4⋊(C43⋊C8)—22no—
104Dic43⋊C8—22no—
105Dic43⋊C8—22no—
106#13063247—22no—
107#13063247Q814yescomplemented
108#13063245—22no—
109#13063245—22no—
110#13063235—22no—
111C8×Dic43—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121#125×C43—22no—
122#125×C43C2×C414yes—
123C2×C4⋊C4×C43—21no—
124C2×C4⋊C4×C43—21no—
125C2×C4⋊C4×C43—21no—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132#97×C43—22no—
133C23×D43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C22×Dic43C2×D411yescharacteristic
148C2×D172—21no—
149C2×D172—21no—
150C2×D172—21no—
151C2×D172C22×C412yes—
152C2×D172C2×Q812yes—
153C2×D172#4112yes—
154C2×C4×D43—24no—
155C2×C4×D43—24no—
156C2×C4×D43—24no—
157C2×C4×D43—42no—
158C2×C4×D43—42no—
159C2×C4×D43—81no—
160C2×C4×D43—81no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×Dic86—24no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C2×Dic86—81no—
167C2×Dic86—81no—
168C2×Dic86C22⋊C414yes—
169C2×C8×C43—21no—
170C2×C8×C43—21no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43C2×Q812yes—
175C4⋊C4×C43—24no—
176C4⋊C4×C43—24no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—42no—
184C4⋊C4×C43—81no—
185C4⋊C4×C43C22×C412yes—
186C4⋊C4×C43C22×C412yes—
187C42×C43C22×C412yes—
188C42×C43C2×D412yes—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—24no—
191(C2×D43)⋊C4—24no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—24no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43C22⋊C414yes—
198C4⋊Dic43C22×C412yes—
199C4⋊Dic43C2×Q812yes—
200Dic43⋊C4—24no—
201Dic43⋊C4—24no—
202Dic43⋊C4C22⋊C414yes—
203Dic43⋊C4C22⋊C414yes—
204C4×Dic43—42no—
205C4×Dic43—81no—
206C4×Dic43—81no—
207C4×Dic43C22×C412yes—
208C4×Dic43C22×C412yes—
209C4×Dic43C2×D412yes—
210C4×Dic43C2×D412yes—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—22no—
220C22×D43—22no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43C2×C22⋊C412yes—
242C2×C4×C43C2×C22⋊C412yes—
243C2×C4×C43C23×C411yescharacteristic
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C22×Q811yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—22no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43C2×C22⋊C412yes—
267C2×Dic43C2×C22⋊C412yes—
268C2×Dic43C2×C22⋊C412yes—
269C2×Dic43C2×C22⋊C412yes—
270D172—22no—
271D172—22no—
272D172—22no—
273D172C4×Q814yes—
274C4×D43—48no—
275C4×D43—84no—
276C4×D43—84no—
277Dic86—44no—
278Dic86—84no—
279C8×C43—22no—
280C8×C43—41no—
281C43⋊C8—41no—
282C43⋊C8—41no—
283#22526—431nomaximal, Sylow
284C22×C43C22×C22⋊C411yescharacteristic
285C22×C43#54811yescharacteristic
286C22×C43D4×Q811yescharacteristic
287C22×C43#57511yescharacteristic
288C22×C43#57511yescharacteristic
289C22×C43#57611yescharacteristic
290C22×C43#57711yescharacteristic
291C2×D43—24no—
292C2×D43—42no—
293C2×D43—42no—
294C2×D43—42no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—42no—
301C4×C43—42no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43C2×C4×Q811yescharacteristic
305C4×C43#51911yescharacteristic
306C4×C43#54811yescharacteristic
307C4×C43D4×Q811yescharacteristic
308Dic43—22no—
309Dic43—22no—
310Dic43—22no—
311Dic43—22no—
312Dic43—42no—
313Dic43—42no—
314Dic43—81no—
315C2×#554—431no—
316C2×#446—431no—
317#2355—431no—
318#1993—431no—
319#1992D4311yescharacteristic, complemented
320#1991—431no—
321#1989—431no—
322#1989—431no—
323#1988—431no—
324#1804—431no—
325#1804—431no—
326#1802—431no—
327#1762—431no—
328#1762—431no—
329C4×#102—431no—
330C2×C43Q8×C22⋊C411yescharacteristic
331C2×C43#289611yescharacteristic
332C2×C43#289711yescharacteristic
333C2×C43#337011yescharacteristic
334C2×C43#337611yescharacteristic
335C2×C43#338811yescharacteristic
336C2×C43#338911yescharacteristic
337D43—44no—
338#554—438no—
339#554—864no—
340C2×C4⋊Q8—431no—
341C2×#125—431no—
342C2×#125C2×D4311yescharacteristic
343C2×C22⋊Q8—861no—
344C2×C22⋊Q8—861no—
345C2×C22⋊Q8—861no—
346C2×C4×Q8—431no—
347C2×C4×D4—431no—
348C2×C4×D4—431no—
349C2×C4×D4—431no—
350C22×C4⋊C4—861no—
351#446—864no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#97—431no—
360C2×#97C2×D4311yescharacteristic
361C2×C4×C8—431no—
362#391—861no—
363#387—861no—
364#387—861no—
365#384C2×D4311yescharacteristic
366#382—431no—
367#382—431no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—861no—
372#340—431no—
373#340—431no—
374#340—431no—
375#340—431no—
376#340—431no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340C2×D4311yescharacteristic
381#340C2×D4311yescharacteristic
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384C43#2252611yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8—861no—
387C22×D4—431no—
388C23×C4—861no—
389C23×C4—861no—
390C23×C4—861no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395C4⋊Q8—434no—
396C4⋊Q8—862no—
397#125—22no—
398#125—434no—
399#125—862no—
400#125C4×D4314yes—
401C22⋊Q8—868no—
402C22⋊Q8—868no—
403C22⋊Q8—868no—
404C4×Q8—434no—
405C4×Q8—434no—
406C4×D4—434no—
407C4×D4—434no—
408C4×D4—434no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4—862no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—431no—
420C2×C4⋊C4—431no—
421C2×C4⋊C4—431no—
422C2×C4⋊C4—868no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42C22×D4311yescharacteristic
439C4⋊C8—862no—
440C4⋊C8—862no—
441C4⋊C8—862no—
442#102—434no—
443#102—862no—
444#102—862no—
445#102—862no—
446#97—22no—
447#97—862no—
448C4×C8—862no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—861no—
457C2×Q8—434no—
458C2×Q8—864no—
459C2×Q8—3441no—
460C2×Q8—3441no—
461C2×Q8—1721no—
462C2×Q8—1721no—
463C2×D4—432no—
464C2×D4—432no—
465C2×D4—432no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—864no—
482C22×C4—861no—
483C22×C4—3441no—
484C22×C4—3441no—
485C22×C4—3441no—
486C22×C4—3441no—
487C22×C4—1722no—
488C22×C4—1722no—
489C22×C4D4×D4311yescharacteristic
490C22×C4D4×D4311yescharacteristic
491C22×C4C23×D4311yescharacteristic
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8Q8×D4312yes—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—42no—
513C4⋊C4—81no—
514C4⋊C4—434no—
515C4⋊C4—434no—
516C4⋊C4—434no—
517C4⋊C4—432no—
518C4⋊C4—432no—
519C4⋊C4—864no—
520C4⋊C4—864no—
521C4⋊C4—864no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4C2×C4×D4312yes—
527C4⋊C4C2×C4×D4312yes—
528C22⋊C4—864no—
529C22⋊C4—864no—
530C22⋊C4—864no—
531C42—432no—
532C42—432no—
533C42—432no—
534C42—432no—
535C42—3441no—
536C42—3441no—
537C42—1722no—
538C42C2×C4×D4312yes—
539C42D4×D4312yes—
540C23—862no—
541C23—862no—
542C23—862no—
543C23—1721no—
544C23—1721no—
545C23—1721no—
546C23—1721no—
547C23C2×D4×D4311yescharacteristic
548Q8—3444no—
549Q8—1724no—
550D4—434no—
551D4—862no—
552D4—862no—
553D4—862no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—432no—
571C2×C4—432no—
572C2×C4—432no—
573C2×C4—432no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—3444no—
585C2×C4—3444no—
586C2×C4—1728no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4C22⋊C4×D4312yes—
595C2×C4C22⋊C4×D4312yes—
596C2×C4C22×C4×D4311yescharacteristic
597C2×C4C2×D4×D4311yescharacteristic
598C2×C4C2×Q8×D4311yescharacteristic
599C2×C4#41×D4311yescharacteristic
600C2×C4#1306337211yescharacteristic
601C2×C4#1306337311yescharacteristic
602C8—22no—
603C8—41no—
604C8—1721no—
605C8—1721no—
606C22—864no—
607C22—1722no—
608C22—1722no—
609C22—1722no—
610C22—1722no—
611C22—1722no—
612C22—1722no—
613C22C2×C22⋊C4×D4311yescharacteristic
614C22#1458355711yescharacteristic
615C22#1458356411yescharacteristic
616C22#1458369511yescharacteristic
617C22#1458369811yescharacteristic
618C22#1458370311yescharacteristic
619C22#1458370811yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—42no—
624C4—81no—
625C4—81no—
626C4—862no—
627C4—862no—
628C4—862no—
629C4—862no—
630C4—3441no—
631C4—1722no—
632C4—1722no—
633C4C4×Q8×D4311yescharacteristic
634C4#1458337511yescharacteristic
635C4#1458355911yescharacteristic
636C4#1458356211yescharacteristic
637C2—1724no—
638C2#1913742911yescharacteristic
639C2#1914311111yescharacteristic
640C2#1914311911yescharacteristic
641C2#1914734311yescharacteristic
642C2#1914741711yescharacteristic
643C2#1914753511yescharacteristic
644C2#1914755011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1992C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1992D43
hypocenterC43#22526
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. C2×#14583027C2semidirect
3. #19137554C2semidirect
4. #19135566C2semidirect
5. #19135558C2semidirect
6. #19135553C2semidirect
7. #19135551C2semidirect
8. #19135545C2semidirect
15. C43×#1992C2semidirect
17. #14583605C4semidirect
107. #13063247Q8semidirect
319. #1992D43semidirect
384. C43#22526semidirect

Maximal subgroups

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

subgroupindex
C2×#145836052
C2×#145830272
#191375542
#191355662
#191355582
#191355532
#191355512
#191355452
#191346042
#191345922
#191344212
#191344192
#191344092
C43×#19922
#2252643