Finite Group Databasebeta

← #25102998

Subgroups — #25102998

Order 11008.

1008 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583105C211yesmaximal, characteristic
2C2×#14583001C211yesmaximal, characteristic
3C2×C4×#10621873C211yesmaximal, characteristic
4#19137314C211yesmaximal, characteristic, complemented
5#19136957C211yesmaximal, characteristic
6#19135517C211yesmaximal, characteristic, complemented
7#19135365C211yesmaximal, characteristic, complemented
8#19135237C211yesmaximal, characteristic, complemented
9#19135230C211yesmaximal, characteristic, complemented
10#19134928C211yesmaximal, characteristic
11#19134928C211yesmaximal, characteristic
12#19134606C211yesmaximal, characteristic
13#19134426C211yesmaximal, characteristic, complemented
14C4×#13063250C211yesmaximal, characteristic, complemented
15C43×#1768C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063325C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4×D172C2211yescharacteristic
24#14583105C418yescomplemented
25#14583001—24no—
26C4×#10621873—24no—
27C2×#13063259C2211yescharacteristic
28C2×#13063257C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063250C2211yescharacteristic
32C2×#13063250C2211yescharacteristic
33C2×#13063250C2211yescharacteristic
34C2×#13063250C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582805C2211yescharacteristic
39#14582784—21no—
40#14582784—21no—
41#14582784—21no—
42#14582784—21no—
43#14582765C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×C4⋊Dic43C2211yescharacteristic
46C4×C4⋊Dic43C2211yescharacteristic
47#14582746—21no—
48#14582746—21no—
49#14582746—21no—
50#95×D43—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582662C2211yescharacteristic
54#14582662C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×C4⋊C8×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C2×C4×C8×C43C2211yescharacteristic
59C43×#376C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×D172C2311yescharacteristic
65C22×C4×D43—21no—
66C22×C4×D43—21no—
67C22×C4×D43—21no—
68C2×#10621873—22no—
69C2×#10621873—22no—
70C2×#10621873—22no—
71C2×#10621873—22no—
72C2×#10621873C2×C414yes—
73C2×#10621873C2×C414yes—
74#13063325—22no—
75#13063325C2×C414yescomplemented
76C4×Dic86—22no—
77C4×Dic86—22no—
78C4×Dic86—22no—
79C4×Dic86—22no—
80C4×D172—22no—
81C4×D172—22no—
82C4×D172—22no—
83C4×D172—22no—
84C4×D172C2×C414yes—
85C4×D172D414yes—
86C2×C4⋊Dic43—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
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×Dic43—21no—
102C2×C4×Dic43—21no—
103#13063259—22no—
104#13063257—22no—
105#13063250—22no—
106#13063250—22no—
107#13063250—22no—
108#13063250—22no—
109#13063250C2×C414yescomplemented
110#13063250C2×C414yescomplemented
111#13063247—22no—
112#13063247—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C42×C43C2311yescharacteristic
127C2×C42×C43C2311yescharacteristic
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—22no—
130C4⋊C8×C43C2×C414yescomplemented
131#97×C43—22no—
132C4×C8×C43—22no—
133#95×C43D411yescharacteristic
134#95×C43D411yescharacteristic
135#95×C43D411yescharacteristic
136#95×C43D411yescharacteristic
137C23×D43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172C22×C412yes—
156C2×D172C2×D412yes—
157C2×D172#4112yes—
158C2×C4×D43—24no—
159C2×C4×D43—24no—
160C2×C4×D43—24no—
161C2×C4×D43—81no—
162C2×C4×D43—81no—
163C2×C4×D43—81no—
164C2×C4×D43—81no—
165C2×C4×D43—81no—
166C2×C4×D43—81no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86C22×C412yes—
178C2×Dic86C22×C412yes—
179C2×C8×C43—21no—
180C2×C8×C43—21no—
181C2×C8×C43—21no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C22×C412yes—
190C2×C8×C43C22×C412yes—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43C22×C412yes—
194C42×C43C2×D412yes—
195C42×C43#4112yes—
196C42×C43#4112yes—
197(C2×D43)⋊C4—24no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—24no—
200C4⋊Dic43—24no—
201C4⋊Dic43—24no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—21no—
208C4⋊Dic43—21no—
209C4⋊Dic43C22×C412yes—
210C4⋊Dic43C2×D412yes—
211C4⋊Dic43#4112yes—
212Dic43⋊C4—42no—
213Dic43⋊C4—42no—
214C4×Dic43—42no—
215C4×Dic43—42no—
216C4×Dic43—81no—
217C4×Dic43—81no—
218C4×Dic43—81no—
219#10621873—28no—
220#10621873—28no—
221C23×C43C22×D411yescharacteristic
222C22×D43—22no—
223C22×D43—22no—
224C22×D43—22no—
225C22×D43—41no—
226C22×D43—41no—
227C22×D43—41no—
228C22×D43—41no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43C4×D412yes—
244C2×C4×C43C4×D412yes—
245C2×C4×C43#12112yes—
246C2×C4×C43#12112yes—
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43C2×#4111yescharacteristic
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274D172—22no—
275D172—22no—
276D172—22no—
277D172C4×D414yes—
278C4×D43—84no—
279C4×D43—84no—
280C4×D43—84no—
281Dic86—22no—
282Dic86—22no—
283Dic86—22no—
284Dic86—22no—
285Dic86—41no—
286Dic86—41no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—22no—
290C8×C43—22no—
291C8×C43—41no—
292C8×C43—41no—
293#21514—431nomaximal, Sylow
294C22×C43C2×C4×D411yescharacteristic
295C22×C43C2×#12111yescharacteristic
296C22×C43#52511yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57711yescharacteristic
299C22×C43#57711yescharacteristic
300C22×C43#57811yescharacteristic
301C2×D43—24no—
302C2×D43—42no—
303C2×D43—42no—
304C2×D43—42no—
305C2×D43—42no—
306C2×D43—42no—
307C2×D43—42no—
308C4×C43—22no—
309C4×C43—22no—
310C4×C43—22no—
311C4×C43—22no—
312C4×C43—41no—
313C4×C43—41no—
314C4×C43C2×C4×D411yescharacteristic
315C4×C43C4×#4111yescharacteristic
316C4×C43#52911yescharacteristic
317C4×C43#53211yescharacteristic
318Dic43—42no—
319Dic43—42no—
320Dic43—42no—
321Dic43—42no—
322Dic43—42no—
323Dic43—81no—
324Dic43—81no—
325C2×#461—431no—
326C2×#440—431no—
327C2×C4×SD16—431no—
328#2327—431no—
329#2275—431no—
330#1981—431no—
331#1949—431no—
332#1928—431no—
333#1927—431no—
334#1877—431no—
335#1877—431no—
336#1804—431no—
337#1768D4311yescharacteristic, complemented
338#1763—431no—
339C4×#103—431no—
340C2×C43C4×#12111yescharacteristic
341C2×C43#294711yescharacteristic
342C2×C43#294911yescharacteristic
343C2×C43#304211yescharacteristic
344C2×C43#304611yescharacteristic
345C2×C43#312011yescharacteristic
346C2×C43#312311yescharacteristic
347D43—44no—
348C22×SD16—431no—
349C22×SD16—431no—
350C2×C4⋊Q8—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×D4—431no—
354C2×C4×D4—431no—
355C2×C4×D4—431no—
356#461—438no—
357#440—864no—
358C4×SD16—864no—
359C2×#107—431no—
360C2×#106—431no—
361C2×C4⋊C8C2×D4311yescharacteristic
362C2×C4⋊C8C2×D4311yescharacteristic
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103—431no—
367C2×#103—431no—
368C2×#103—431no—
369C2×#102—431no—
370C2×#102—431no—
371C2×#97C2×D4311yescharacteristic
372C2×C4×C8C2×D4311yescharacteristic
373#391—431no—
374#391—431no—
375#387—861no—
376#387—861no—
377#387—861no—
378#387—861no—
379#382—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4—431no—
382C4×C4⋊C4—431no—
383C4×C22⋊C4—861no—
384C4×C22⋊C4—861no—
385C4×C22⋊C4—861no—
386#376C2×D4311yescharacteristic
387C2×#95—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340—431no—
392#336C2×D4311yescharacteristic
393#336C2×D4311yescharacteristic
394C43#2151411yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×Q8—431no—
397C22×D4—431no—
398C23×C4—861no—
399C23×C4—861no—
400C23×C4—861no—
401C2×SD16—434no—
402C2×SD16—434no—
403C2×SD16—862no—
404C2×SD16—862no—
405C2×SD16—862no—
406C2×SD16—862no—
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409C22×C8C22×D4311yescharacteristic
410C22×C8C22×D4311yescharacteristic
411C4⋊Q8—434no—
412C4⋊Q8—862no—
413C4×Q8—862no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×D4—434no—
418C4×D4—434no—
419C4×D4—862no—
420C4×D4—862no—
421C4×D4—862no—
422C4×D4—862no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—431no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—861no—
436C2×C42—861no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42—861no—
440C2×C42C22×D4311yescharacteristic
441C2×C42C22×D4311yescharacteristic
442C2×C42C22×D4311yescharacteristic
443#107—862no—
444#106—862no—
445C4⋊C8—22no—
446C4⋊C8C4×D4314yescomplemented
447#103—434no—
448#103—434no—
449#103—862no—
450#103—862no—
451#103—862no—
452#103—862no—
453#102—862no—
454#102—862no—
455#97—22no—
456C4×C8—22no—
457#95—861no—
458#95—861no—
459#95—861no—
460#95—861no—
461#95—861no—
462#95—861no—
463#95—861no—
464#95—861no—
465#95—861no—
466#95D17211yescharacteristic
467#95D17211yescharacteristic
468#95D17211yescharacteristic
469#95D17211yescharacteristic
470C24—861no—
471C2×Q8—432no—
472C2×Q8—432no—
473C2×Q8—861no—
474C2×Q8—861no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8—861no—
481C2×Q8—861no—
482C2×Q8—861no—
483C2×D4—432no—
484C2×D4—432no—
485C2×D4—432no—
486C2×D4—861no—
487C2×D4—861no—
488C2×D4—861no—
489C22×C4—864no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—864no—
496C22×C4—864no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—3441no—
500C22×C4—3441no—
501C22×C4—3441no—
502C22×C4—3441no—
503C22×C4—3441no—
504C22×C4—3441no—
505C22×C4C2×D17211yescharacteristic
506C22×C4C2×D17211yescharacteristic
507C22×C4C2×D17211yescharacteristic
508C22×C4C2×D17211yescharacteristic
509C22×C4C2×D17211yescharacteristic
510C22×C4C2×D17211yescharacteristic
511C22×C4C23×D4311yescharacteristic
512SD16—868no—
513SD16—868no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C2×C4×D4312yes—
525C2×C8C2×C4×D4312yes—
526C4⋊C4—432no—
527C4⋊C4—432no—
528C4⋊C4—432no—
529C4⋊C4—864no—
530C4⋊C4—864no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—861no—
534C4⋊C4—861no—
535C4⋊C4—861no—
536C4⋊C4—861no—
537C4⋊C4—861no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C22⋊C4—864no—
541C22⋊C4—864no—
542C22⋊C4—864no—
543C42—21no—
544C42—21no—
545C42—3441no—
546C42—3441no—
547C42—3441no—
548C42—1722no—
549C42—1722no—
550C42C2×C4×D4312yes—
551C42#1062189812yes—
552C42D4×D4312yes—
553C42#1062190212yes—
554C23—862no—
555C23—862no—
556C23—862no—
557C23—1721no—
558C23—1721no—
559C23—1721no—
560C23—1721no—
561C23C22×D17211yescharacteristic
562Q8—862no—
563Q8—862no—
564Q8—862no—
565Q8—862no—
566Q8—1721no—
567Q8—1721no—
568Q8—1721no—
569Q8—1721no—
570D4—434no—
571D4—862no—
572D4—862no—
573D4—862no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—862no—
592C2×C4—862no—
593C2×C4—3444no—
594C2×C4—3444no—
595C2×C4—3444no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4—1721no—
605C2×C4—1721no—
606C2×C4—1721no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4C4×D17212yes—
613C2×C4C4×D17212yes—
614C2×C4#1306330012yes—
615C2×C4#1306330012yes—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4#41×D4311yescharacteristic
620C2×C4C2×#1062189811yescharacteristic
621C2×C4C2×#1062190211yescharacteristic
622C8—22no—
623C8—22no—
624C8—41no—
625C8—41no—
626C22—864no—
627C22—1722no—
628C22—1722no—
629C22—1722no—
630C22—1722no—
631C22—1722no—
632C22—1722no—
633C22C2×C4×D17211yescharacteristic
634C22C2×#1306330011yescharacteristic
635C22#1458341111yescharacteristic
636C22#1458371111yescharacteristic
637C22#1458371111yescharacteristic
638C22#1458371111yescharacteristic
639C22#1458371611yescharacteristic
640C4—22no—
641C4—22no—
642C4—22no—
643C4—22no—
644C4—41no—
645C4—41no—
646C4—3441no—
647C4—3441no—
648C4—1722no—
649C4—1722no—
650C4—1722no—
651C4—1722no—
652C4—1722no—
653C4C4×D4×D4311yescharacteristic
654C4C4×#1062190211yescharacteristic
655C4#1458343611yescharacteristic
656C4#1458344611yescharacteristic
657C2—1724no—
658C2C4×#1306330011yescharacteristic
659C2#1914344011yescharacteristic
660C2#1914345611yescharacteristic
661C2#1914410811yescharacteristic
662C2#1914414711yescharacteristic
663C2#1914481111yescharacteristic
664C2#1914484811yescharacteristic
subgroupG/H
centerC23C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1768C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenter#1768D43
hypocenterC43#21514
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
4. #19137314C2semidirect
6. #19135517C2semidirect
7. #19135365C2semidirect
8. #19135237C2semidirect
9. #19135230C2semidirect
13. #19134426C2semidirect
14. C4×#13063250C2semidirect
15. C43×#1768C2semidirect
24. #14583105C4semidirect
75. #13063325C2×C4semidirect
109. #13063250C2×C4semidirect
110. #13063250C2×C4semidirect
130. C4⋊C8×C43C2×C4semidirect
337. #1768D43semidirect
394. C43#21514semidirect
446. C4⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831052
C2×#145830012
C2×C4×#106218732
#191373142
#191369572
#191355172
#191353652
#191352372
#191352302
#191349282
#191346062
#191344262
C4×#130632502
C43×#17682
#2151443