Finite Group Databasebeta

← #25113188

Subgroups — #25113188

Order 11008.

1086 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×#14583608C211yesmaximal, characteristic
2C2×#14583023C211yesmaximal, characteristic, complemented
3#19137547C211yesmaximal, characteristic, complemented
4#19135559C211yesmaximal, characteristic, complemented
5#19135558C211yesmaximal, characteristic, complemented
6#19135554C211yesmaximal, characteristic, complemented
7#19135550C211yesmaximal, characteristic, complemented
8#19135549C211yesmaximal, characteristic, complemented
9#19135541C211yesmaximal, characteristic, complemented
10#19134603C211yesmaximal, characteristic
11#19134593C211yesmaximal, characteristic
12#102×Dic43C211yesmaximal, characteristic
13#102×Dic43C211yesmaximal, characteristic
14C4×#13063246C211yesmaximal, characteristic
15C43×#1804C211yesmaximal, characteristic
16#14583608—24no—
17#14583608C418yescomplemented
18C2×#13063324C2211yescharacteristic
19C2×#13063317C2211yescharacteristic
20C2×#13063316C2211yescharacteristic
21C2×#13063304—21no—
22C2×#13063302—21no—
23C2×#13063302—21no—
24C2×C4×Dic86C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C22×Dic43⋊C4—21no—
28#14583023—24no—
29C2×Dic43⋊C8C2211yescharacteristic
30C2×Dic43⋊C8C2211yescharacteristic
31C2×#13063246C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×C4×C43⋊C8C2211yescharacteristic
34C2×C8×Dic43C2211yescharacteristic
35C2×C8×Dic43C2211yescharacteristic
36#14582803—21no—
37#14582784—21no—
38#14582781—21no—
39#14582768C2211yescharacteristic
40#14582764C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582750—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×C4×D4×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#382C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—21no—
63C22×Dic86D411yescharacteristic
64C23×Dic43—21no—
65C23×Dic43—21no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—22no—
69#13063324C2×C414yes—
70#13063317—22no—
71#13063317C2×C414yes—
72#13063316—22no—
73#13063316C2×C414yes—
74#13063304—28no—
75#13063302—28no—
76#13063302—28no—
77C4×Dic86C2×C414yes—
78C4×Dic86D414yes—
79D4×Dic43—22no—
80D4×Dic43—22no—
81D4×Dic43C2×C414yes—
82D4×Dic43C2×C414yes—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43D411yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×C4⋊Dic43C2311yescharacteristic
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4—28no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4D411yescharacteristic
97C2×Dic43⋊C4D411yescharacteristic
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43C2311yescharacteristic
104C2×C4×Dic43C2311yescharacteristic
105Dic43⋊C8—22no—
106Dic43⋊C8—22no—
107#13063246—22no—
108#13063246Q814yescomplemented
109C4×C43⋊C8—22no—
110C8×Dic43—22no—
111C8×Dic43—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C22×D4×C43C2311yescharacteristic
118C23×C4×C43—21no—
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C4×D4×C43—22no—
122C4×D4×C43C2×C414yes—
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C4⋊C4×C43C2311yescharacteristic
126C2×C22⋊C4×C43—21no—
127C2×C42×C43C2311yescharacteristic
128C4⋊C8×C43—22no—
129#102×C43—22no—
130#102×C43—22no—
131#95×C43—21no—
132#95×C43—21no—
133C24×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43C22×C412yes—
138C2×D4×C43C2×Q812yes—
139C2×D4×C43#4112yes—
140C22×C4×C43—24no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C22×Dic43—24no—
150C22×Dic43—24no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43—81no—
158C22×Dic43—81no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×Dic86—22no—
164C2×Dic86—22no—
165C2×Dic86—24no—
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×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43C22×C412yes—
181C22⋊C4×C43—24no—
182C42×C43C22×C412yes—
183C42×C43C2×D412yes—
184C22⋊Dic43—24no—
185C22⋊Dic43—24no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—24no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43C22⋊C414yes—
193C4⋊Dic43C22×C412yes—
194C4⋊Dic43C22×C412yes—
195C4⋊Dic43C2×Q812yes—
196Dic43⋊C4—24no—
197Dic43⋊C4—24no—
198Dic43⋊C4—24no—
199Dic43⋊C4—24no—
200Dic43⋊C4—42no—
201Dic43⋊C4—81no—
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⋊C8C2×Q812yes—
217C23×C43—22no—
218C23×C43—22no—
219C23×C43—22no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43C22×D411yescharacteristic
225D4×C43—22no—
226D4×C43—22no—
227D4×C43—22no—
228D4×C43C4×Q814yes—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—22no—
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×C43—41no—
242C2×C4×C43—84no—
243C2×C4×C43C2×C22⋊C412yes—
244C2×C4×C43C2×C22⋊C412yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C22×D411yescharacteristic
247C2×C4×C43C22×Q811yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C2×C4×C432−1+411yescharacteristic
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—22no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—48no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—84no—
271C2×Dic43C2×C22⋊C412yes—
272C2×Dic43C2×C22⋊C412yes—
273C2×Dic43C2×C22⋊C412yes—
274C2×Dic43C2×C22⋊C412yes—
275C2×Dic43#13512yes—
276C2×Dic43#13512yes—
277Dic86—28no—
278Dic86—84no—
279C8×C43—41no—
280C8×C43—41no—
281C43⋊C8—22no—
282C43⋊C8—41no—
283#22519—431nomaximal, Sylow
284C22×C43—24no—
285C22×C43—42no—
286C22×C43—42no—
287C22×C43—42no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—42no—
291C22×C43C22×C22⋊C411yescharacteristic
292C22×C43#54811yescharacteristic
293C22×C43D4×Q811yescharacteristic
294C22×C43C2×#13511yescharacteristic
295C22×C43C2×#13511yescharacteristic
296C22×C43#57611yescharacteristic
297C22×C43#57711yescharacteristic
298C4×C43—22no—
299C4×C43—22no—
300C4×C43—42no—
301C4×C43—81no—
302C4×C43—81no—
303C4×C43C2×C4×Q811yescharacteristic
304C4×C43#51911yescharacteristic
305C4×C43#54811yescharacteristic
306C4×C43D4×Q811yescharacteristic
307Dic43—22no—
308Dic43—22no—
309Dic43—22no—
310Dic43—42no—
311Dic43—42no—
312Dic43—42no—
313Dic43—81no—
314Dic43#41614yes—
315C2×#554—431no—
316C2×C8×Q8—431no—
317#2355—431no—
318#1991—431no—
319#1991—431no—
320#1990—431no—
321#1989—431no—
322#1989—431no—
323#1987—431no—
324#1804—431no—
325#1804D4311yescharacteristic
326#1802—431no—
327C4×#102—431no—
328C4×#102—431no—
329C4×#102—431no—
330C2×C43—44no—
331C2×C43Q8×C22⋊C411yescharacteristic
332C2×C43C2×#41611yescharacteristic
333C2×C43#289711yescharacteristic
334C2×C43#336011yescharacteristic
335C2×C43#336111yescharacteristic
336C2×C43#338011yescharacteristic
337C2×C43#338111yescharacteristic
338#554—438no—
339#554—864no—
340C2×C4⋊Q8—431no—
341C2×#125—431no—
342C2×#125—431no—
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×D4C2×D4311yescharacteristic
350C22×C4⋊C4—861no—
351C8×Q8—864no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8—431no—
354C2×C4⋊C8C2×D4311yescharacteristic
355C2×#102—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#102C2×D4311yescharacteristic
359C2×C4×C8—431no—
360C2×C4×C8—431no—
361C2×C4×C8—431no—
362#391—861no—
363#387—861no—
364#387—861no—
365#384—431no—
366#382—431no—
367#382C2×D4311yescharacteristic
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#340—431no—
381#340—431no—
382#340C2×D4311yescharacteristic
383#340C2×D4311yescharacteristic
384C43#2251911yescharacteristic, complemented, Sylow
385C22×Q8—431no—
386C22×Q8—861no—
387C22×D4C22×D4311yescharacteristic
388C23×C4—21no—
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—434no—
398#125—434no—
399#125—862no—
400#125—862no—
401C22⋊Q8—868no—
402C22⋊Q8—868no—
403C22⋊Q8—868no—
404C4×Q8—434no—
405C4×Q8—434no—
406C4×D4—22no—
407C4×D4—434no—
408C4×D4—434no—
409C4×D4—862no—
410C4×D4—862no—
411C4×D4C4×D4314yes—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—431no—
418C2×C4⋊C4—431no—
419C2×C4⋊C4—868no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—861no—
422C2×C4⋊C4—861no—
423C2×C4⋊C4—861no—
424C2×C4⋊C4—861no—
425C2×C4⋊C4—861no—
426C2×C4⋊C4—861no—
427C2×C4⋊C4C22×D4311yescharacteristic
428C2×C4⋊C4C22×D4311yescharacteristic
429C2×C4⋊C4C22×D4311yescharacteristic
430C2×C22⋊C4—21no—
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—22no—
440C4⋊C8—862no—
441C4⋊C8—862no—
442#102—22no—
443#102—22no—
444#102—434no—
445#102—862no—
446C4×C8—862no—
447C4×C8—862no—
448C4×C8—862no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—21no—
457C2×Q8—434no—
458C2×Q8—862no—
459C2×Q8—862no—
460C2×Q8—864no—
461C2×Q8—3441no—
462C2×Q8—3441no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4C2×C4×D4312yes—
467C2×D4#1062190012yes—
468C2×D4Q8×D4312yes—
469C22×C4—21no—
470C22×C4—24no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—864no—
480C22×C4—864no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
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—21no—
498C2×C8—432no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—434no—
510C4⋊C4—434no—
511C4⋊C4—434no—
512C4⋊C4—432no—
513C4⋊C4—432no—
514C4⋊C4—432no—
515C4⋊C4—864no—
516C4⋊C4—864no—
517C4⋊C4—864no—
518C4⋊C4—864no—
519C4⋊C4—864no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—3441no—
526C4⋊C4—1722no—
527C4⋊C4C2×C4×D4312yes—
528C22⋊C4—24no—
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—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C2×D4×D4311yescharacteristic
548Q8—868no—
549Q8—3444no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4#1306329014yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—432no—
569C2×C4—432no—
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—862no—
581C2×C4—862no—
582C2×C4—862no—
583C2×C4—3444no—
584C2×C4—1728no—
585C2×C4—1721no—
586C2×C4—1721no—
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×C4C2×#1062190011yescharacteristic
600C2×C4#1306337211yescharacteristic
601C2×C4#1306337211yescharacteristic
602C8—41no—
603C8—41no—
604C8—862no—
605C8—1721no—
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22C2×C22⋊C4×D4311yescharacteristic
614C22#1458355511yescharacteristic
615C22#1458356211yescharacteristic
616C22#135×D4311yescharacteristic
617C22#135×D4311yescharacteristic
618C22#1458370311yescharacteristic
619C22#1458370911yescharacteristic
620C4—22no—
621C4—22no—
622C4—42no—
623C4—81no—
624C4—81no—
625C4—434no—
626C4—862no—
627C4—862no—
628C4—862no—
629C4—3441no—
630C4—1722no—
631C4—1722no—
632C4—1722no—
633C4C2×#1306329011yescharacteristic
634C4#1458337611yescharacteristic
635C4#1458355511yescharacteristic
636C4#1458356211yescharacteristic
637C2—44no—
638C2#1913742711yescharacteristic
639C2#416×D4311yescharacteristic
640C2#1914312011yescharacteristic
641C2#1914723911yescharacteristic
642C2#1914725011yescharacteristic
643C2#1914745711yescharacteristic
644C2#1914746511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1804C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1804D43
hypocenterC43#22519
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#14583023C2semidirect
3. #19137547C2semidirect
4. #19135559C2semidirect
5. #19135558C2semidirect
6. #19135554C2semidirect
7. #19135550C2semidirect
8. #19135549C2semidirect
9. #19135541C2semidirect
17. #14583608C4semidirect
108. #13063246Q8semidirect
384. C43#22519semidirect

Maximal subgroups

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

subgroupindex
C2×#145836082
C2×#145830232
#191375472
#191355592
#191355582
#191355542
#191355502
#191355492
#191355412
#191346032
#191345932
#102×Dic432
C4×#130632462
C43×#18042
#2251943