Finite Group Databasebeta

← #25062611

Subgroups — #25062611

Order 11008.

988 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2#19143223C211yesmaximal, characteristic
3#431×D43C211yesmaximal, characteristic
4#19132957C214yesmaximal
5#19132949C214yesmaximal, complemented
6#19132919C211yesmaximal, characteristic, complemented
7#19132918C211yesmaximal, characteristic, complemented
8#19132918C211yesmaximal, characteristic, complemented
9C43×#1461C211yesmaximal, characteristic, complemented
10#14583453—21no—
11#14583453—21no—
12#14583453—21no—
13#14583453—21no—
14#14583453—21no—
15#14583453—21no—
16#14583453—21no—
17#14583453—21no—
18C2×#13063324C411yescharacteristic
19C2×#13063323C411yescharacteristic
20C2×#13063315C2212yes—
21C2×#13063305C411yescharacteristic
22C2×#13063303C2212yes—
23C2×#13063301C411yescharacteristic
24C2×C4×Dic86C412yes—
25C2×C4×Dic86C2211yescharacteristic
26C2×#13063282C412yes—
27C2×C42×D43C2211yescharacteristic
28#14582955—21no—
29#14582953C2212yes—
30#14582952C2211yescharacteristic
31#14582952C2211yescharacteristic
32#14582951—21no—
33#14582950—21no—
34#14582950—21no—
35#14582949C2212yes—
36#14582921—21no—
37C4⋊C8×D43—21no—
38#14582861C2212yes—
39C22⋊C8×D43C2212yes—
40C4×#10621872—21no—
41C4×C8×D43—21no—
42#14582625C2214yes—
43#14582624C2214yes—
44#14582624C2214yes—
45C2×C4×Q8×C43C2211yescharacteristic
46C43×#431C2211yescharacteristic
47C43×#431C2211yescharacteristic
48C43×#324C2214yes—
49C22×Dic86C2×C411yescharacteristic
50C22×Dic86C2×C412yes—
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C2×#10621872—22no—
55C2×C8×D43—22no—
56#13063324—21no—
57#13063324—21no—
58#13063324—21no—
59#13063324—21no—
60#13063323—21no—
61#13063323—21no—
62#13063323—21no—
63#13063323—21no—
64#13063315—22no—
65#13063315—22no—
66#13063315—22no—
67#13063315—22no—
68#13063305—21no—
69#13063305—21no—
70#13063305—21no—
71#13063305—21no—
72#13063303—22no—
73#13063303—22no—
74#13063303—22no—
75#13063303—22no—
76#13063301—21no—
77#13063301—21no—
78#13063301—21no—
79#13063301—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×Dic86—22no—
85C4×Dic86—22no—
86C4×Dic86—22no—
87C4×Dic86—22no—
88#13063282—22no—
89#13063282—22no—
90#13063282—22no—
91#13063282—22no—
92C2×C4⋊Dic43C2×C412yes—
93C2×C4⋊Dic43C2×C411yescharacteristic
94C2×Dic43⋊C4C2×C412yes—
95C2×Dic43⋊C4C2×C412yes—
96C2×Dic43⋊C4C2×C412yes—
97C2×Dic43⋊C4C2×C412yes—
98C2×Dic43⋊C4C2312yes—
99C2×(C2×D43)⋊C4C2×C412yes—
100C2×(C2×D43)⋊C4C2×C412yes—
101C2×C4×Dic43C2×C412yes—
102C2×C4×Dic43C2×C411yescharacteristic
103C2×C4×Dic43C2×C411yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105C42×D43D411yescharacteristic
106C42×D43D411yescharacteristic
107C42×D43D411yescharacteristic
108C42×D43D411yescharacteristic
109C42×D43D411yescharacteristic
110C42×D43D411yescharacteristic
111C42×D43D411yescharacteristic
112C42×D43D411yescharacteristic
113C4⋊(C43⋊C8)—21no—
114C4⋊(C43⋊C8)—21no—
115Dic43⋊C8—22no—
116Dic43⋊C8—22no—
117C22⋊(C43⋊C8)C2312yes—
118C22⋊(C43⋊C8)C2312yes—
119(C2×D43)⋊C8—22no—
120(C2×D43)⋊C8—22no—
121#13063235—22no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8—21no—
124C8×Dic43—22no—
125C22×Q8×C43C2×C411yescharacteristic
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C2×C4⋊C4×C43C2×C411yescharacteristic
131C2×C4⋊C4×C43C2312yes—
132C2×C42×C43C2×C412yes—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43—21no—
136C22⋊C8×C43C2312yes—
137C22⋊C8×C43C2312yes—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C23×D43C22×C411yescharacteristic
141C2×Q8×C43—21no—
142C2×Q8×C43—21no—
143C2×Q8×C43—22no—
144C2×Q8×C43—22no—
145C22×C4×C43C22×C412yes—
146C22×C4×C43C22×C411yescharacteristic
147C22×C4×C43C22×C412yes—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C22×Dic43C22×C412yes—
151C22×Dic43C22×C411yescharacteristic
152C22×Dic43C22×C411yescharacteristic
153C22×Dic43C22×C411yescharacteristic
154C22×Dic43C22×C412yes—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—24no—
158C2×C4×D43—42no—
159C2×C4×D43C22⋊C411yescharacteristic
160C2×C4×D43C22⋊C411yescharacteristic
161C2×C4×D43C22⋊C411yescharacteristic
162C2×C4×D43C22⋊C411yescharacteristic
163C2×C4×D43C22⋊C411yescharacteristic
164C2×C4×D43C22⋊C411yescharacteristic
165C2×C4×D43C22⋊C411yescharacteristic
166C2×C4×D43C22⋊C411yescharacteristic
167C2×C4×D43C2×D411yescharacteristic
168C2×C4×D43C2×D411yescharacteristic
169C2×C4×D43C2×D411yescharacteristic
170C2×C4×D43C2×D411yescharacteristic
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—22no—
174C2×Dic86—22no—
175C2×Dic86—22no—
176C2×Dic86—22no—
177C2×Dic86—44no—
178C2×C8×C43—22no—
179C2×C8×C43—22no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—22no—
183C4⋊C4×C43—22no—
184C42×C43—22no—
185C42×C43—22no—
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190(C2×D43)⋊C4—22no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—22no—
193(C2×D43)⋊C4—22no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—22no—
197C4⋊Dic43—22no—
198Dic43⋊C4—22no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4—22no—
205Dic43⋊C4—22no—
206Dic43⋊C4—22no—
207Dic43⋊C4—22no—
208C4×Dic43—22no—
209C4×Dic43—22no—
210C4×Dic43C22⋊C411yescharacteristic
211C4×Dic43C22⋊C411yescharacteristic
212C4×Dic43C22⋊C411yescharacteristic
213C4×Dic43C22⋊C411yescharacteristic
214C4×Dic43C22⋊C411yescharacteristic
215C4×Dic43C22⋊C411yescharacteristic
216C4×Dic43C22⋊C411yescharacteristic
217C4×Dic43C22⋊C411yescharacteristic
218C4×Dic43C2×D411yescharacteristic
219C4×Dic43C2×D411yescharacteristic
220C4×Dic43C2×D411yescharacteristic
221C4×Dic43C2×D411yescharacteristic
222C2×C43⋊C8—22no—
223C2×C43⋊C8—22no—
224#10621872—44no—
225C8×D43—44no—
226C23×C43C23×C411yescharacteristic
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—22no—
230C22×D43—41no—
231C22×D43C2×C22⋊C411yescharacteristic
232C22×D43C2×C22⋊C411yescharacteristic
233Q8×C43—42no—
234Q8×C43—42no—
235C2×C4×C43—22no—
236C2×C4×C43—22no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—41no—
241C2×C4×C43—42no—
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43C2×C22⋊C411yescharacteristic
244C2×C4×C43C2×C22⋊C411yescharacteristic
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43#13112yes—
247C2×C4×C43#13112yes—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—42no—
259C2×Dic43C2×C22⋊C411yescharacteristic
260C2×Dic43C2×C22⋊C411yescharacteristic
261C2×Dic43C2×C22⋊C411yescharacteristic
262C2×Dic43C2×C22⋊C411yescharacteristic
263C2×Dic43C2×C22⋊C411yescharacteristic
264C2×Dic43C2×C22⋊C411yescharacteristic
265C4×D43—22no—
266C4×D43—22no—
267C4×D43—22no—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—22no—
271C4×D43—22no—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—41no—
275C4×D43—41no—
276C4×D43#10114yes—
277Dic86—44no—
278Dic86—42no—
279Dic86—42no—
280Dic86—44no—
281C8×C43—42no—
282C8×C43—42no—
283C43⋊C8—42no—
284C43⋊C8—42no—
285#17385—431nomaximal, Sylow
286C22×C43—21no—
287C22×C43—21no—
288C22×C43C22×C22⋊C411yescharacteristic
289C22×C43C2×#13111yescharacteristic
290C22×C43C2×#13111yescharacteristic
291C2×D43—21no—
292C2×D43—21no—
293C2×D43—21no—
294C2×D43—21no—
295C2×D43—21no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43C2×#10112yes—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—42no—
303C4×C43—42no—
304C4×C43#40812yes—
305C4×C43#40812yes—
306C4×C43C2×#10112yes—
307Dic43—21no—
308Dic43—21no—
309Dic43—21no—
310Dic43—21no—
311Dic43—42no—
312Dic43—42no—
313Dic43#41012yes—
314Dic43C2×#10112yes—
315C2×#533—431no—
316#2920—431no—
317C2×#431—431no—
318#1472—434no—
319#1470—434no—
320#1461—431no—
321#1461—431no—
322#1461—431no—
323#1461D4311yescharacteristic, complemented
324C2×C43—21no—
325C2×C43—21no—
326C2×C43C2×#40811yescharacteristic
327C2×C43C2×#41011yescharacteristic
328C2×C43C22×#10111yescharacteristic
329D43—22no—
330D43—41no—
331#533—861no—
332#533—861no—
333#533—861no—
334#533—861no—
335#533—861no—
336#533—861no—
337#533—861no—
338#533—861no—
339C2×C4⋊Q8—431no—
340C2×C4⋊Q8—431no—
341C2×#125—432no—
342C2×C22⋊Q8—431no—
343C2×C22⋊Q8—432no—
344C2×C22⋊Q8—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8—432no—
347C2×C4×Q8C2×D4311yescharacteristic
348C2×#117—432no—
349C22×C42—431no—
350#432—432no—
351#432—861no—
352#431—431no—
353#431—431no—
354#431—432no—
355#431—861no—
356#431—861no—
357#431—861no—
358#431C2×D4311yescharacteristic
359#431C2×D4311yescharacteristic
360#423—861no—
361C2×C4⋊C8—861no—
362#407—432no—
363C2×C22⋊C8—432no—
364C4×M16—861no—
365C2×C4×C8—861no—
366#324—434no—
367#324—434no—
368#324—434no—
369#324C2×D4314yes—
370C43#1738511yescharacteristic, complemented, Sylow
371C22×Q8—431no—
372C22×Q8—432no—
373C22×Q8C4×D4311yescharacteristic
374C23×C4—431no—
375C23×C4—431no—
376C23×C4—431no—
377C2×M16—862no—
378C22×C8—862no—
379C4⋊Q8—861no—
380C4⋊Q8—861no—
381C4⋊Q8—861no—
382C4⋊Q8—861no—
383C4⋊Q8—861no—
384C4⋊Q8—861no—
385C4⋊Q8—861no—
386C4⋊Q8—861no—
387#125—862no—
388#125—862no—
389#125—862no—
390#125—862no—
391C22⋊Q8—862no—
392C22⋊Q8—862no—
393C22⋊Q8—862no—
394C22⋊Q8—862no—
395C22⋊Q8—861no—
396C22⋊Q8—861no—
397C22⋊Q8—861no—
398C22⋊Q8—861no—
399C22⋊Q8—861no—
400C22⋊Q8—861no—
401C22⋊Q8—861no—
402C22⋊Q8—861no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—862no—
408C4×Q8—862no—
409C4×Q8—862no—
410C4×Q8—862no—
411C4×Q8—861no—
412C4×Q8—861no—
413C4×Q8—861no—
414C4×Q8—861no—
415#117—862no—
416#117—862no—
417#117—862no—
418#117—862no—
419C2×C4⋊C4—432no—
420C2×C4⋊C4—432no—
421C2×C4⋊C4—432no—
422C2×C4⋊C4—432no—
423C2×C4⋊C4—432no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—432no—
426C2×C4⋊C4C4×D4311yescharacteristic
427C2×C4⋊C4C22×D4312yes—
428C2×C22⋊C4—432no—
429C2×C22⋊C4—432no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—431no—
433C2×C42—431no—
434C2×C42—431no—
435C2×C42—431no—
436C2×C42—431no—
437C2×C42—431no—
438C2×C42—431no—
439C2×C42—431no—
440C2×C42—431no—
441C2×C42—432no—
442C2×C42C4×D4312yes—
443C2×C42C22×D4311yescharacteristic
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—862no—
447C4⋊C8—862no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C22⋊C8—432no—
451C22⋊C8—432no—
452C22⋊C8—862no—
453C22⋊C8—862no—
454C22⋊C8C22×D4312yes—
455C22⋊C8C22×D4312yes—
456#97—862no—
457C4×C8—21no—
458C4×C8—21no—
459C4×C8—862no—
460C4×C8—861no—
461C4×C8—861no—
462C24—431no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—862no—
468C2×Q8—862no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—862no—
472C2×Q8—862no—
473C2×Q8—1724no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—431no—
481C22×C4—431no—
482C22×C4—431no—
483C22×C4—431no—
484C22×C4—431no—
485C22×C4—431no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—431no—
489C22×C4—432no—
490C22×C4—432no—
491C22×C4—864no—
492C22×C4—862no—
493C22×C4—862no—
494C22×C4—1722no—
495C22×C4C2×C4×D4312yes—
496C22×C4C2×C4×D4311yescharacteristic
497C22×C4C2×C4×D4312yes—
498C22×C4C2×C4×D4311yescharacteristic
499C22×C4C23×D4311yescharacteristic
500M16—1724no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—862no—
504C2×C8—862no—
505C2×C8—1724no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—862no—
511C4⋊C4—862no—
512C4⋊C4—862no—
513C4⋊C4—862no—
514C4⋊C4—862no—
515C4⋊C4—862no—
516C4⋊C4—862no—
517C4⋊C4—862no—
518C4⋊C4—862no—
519C4⋊C4—862no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—862no—
523C4⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—862no—
526C22⋊C4—862no—
527C22⋊C4—862no—
528C42—22no—
529C42—22no—
530C42—431no—
531C42—431no—
532C42—431no—
533C42—431no—
534C42—431no—
535C42—431no—
536C42—431no—
537C42—431no—
538C42—431no—
539C42—431no—
540C42—431no—
541C42—431no—
542C42—862no—
543C42—862no—
544C42D4×D4311yescharacteristic
545C42D4×D4311yescharacteristic
546C42D4×D4311yescharacteristic
547C42D4×D4311yescharacteristic
548C23—431no—
549C23—431no—
550C23—862no—
551C23—861no—
552C23—861no—
553C23—1721no—
554C23C22×C4×D4311yescharacteristic
555Q8—42no—
556Q8—42no—
557Q8—1724no—
558Q8—1724no—
559Q8—1722no—
560Q8—1722no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—431no—
569C2×C4—431no—
570C2×C4—434no—
571C2×C4—431no—
572C2×C4—431no—
573C2×C4—431no—
574C2×C4—431no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1722no—
595C2×C4C22⋊C4×D4311yescharacteristic
596C2×C4C22⋊C4×D4311yescharacteristic
597C2×C4C22⋊C4×D4311yescharacteristic
598C2×C4C22⋊C4×D4311yescharacteristic
599C2×C4#1306333112yes—
600C2×C4#1306333312yes—
601C2×C4C2×D4×D4311yescharacteristic
602C2×C4C2×D4×D4311yescharacteristic
603C8—42no—
604C8—42no—
605C8—1722no—
606C8—1722no—
607C22—21no—
608C22—21no—
609C22—432no—
610C22—861no—
611C22—861no—
612C22—861no—
613C22—861no—
614C22—861no—
615C22—1722no—
616C22—1722no—
617C22C2×C22⋊C4×D4311yescharacteristic
618C22C2×#1306333111yescharacteristic
619C22C2×#1306333311yescharacteristic
620C4—21no—
621C4—21no—
622C4—21no—
623C4—42no—
624C4—42no—
625C4—432no—
626C4—432no—
627C4—861no—
628C4—861no—
629C4—861no—
630C4—861no—
631C4—1722no—
632C4—1722no—
633C4#1458286412yes—
634C4#1458286412yes—
635C4#101×D4312yes—
636C2—21no—
637C2—21no—
638C2—862no—
639C2—1721no—
640C2C2×#1458286411yescharacteristic
641C2#410×D4311yescharacteristic
642C2C2×#101×D4311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1461C2
socleC22×C43C22×C22⋊C4
prime radicalC23×D43C22×C4
cosocleC22×C4×C43C24
hypercenter#1461D43
hypocenterC43#17385
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1461

Complements

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

NH ≅ G/Ntype
5. #19132949C2semidirect
6. #19132919C2semidirect
7. #19132918C2semidirect
8. #19132918C2semidirect
9. C43×#1461C2semidirect
323. #1461D43semidirect
370. C43#17385semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
#191432232
#431×D432
#191329572
#191329492
#191329192
#191329182
C43×#14612
#1738543