Finite Group Databasebeta

← #25119072

Subgroups — #25119072

Order 11008.

954 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×#14583119C211yesmaximal, characteristic
2C2×#14583004C211yesmaximal, characteristic, complemented
3C2×SD16×Dic43C211yesmaximal, characteristic
4#19137665C211yesmaximal, characteristic
5Q8×Dic43⋊C4C211yesmaximal, characteristic, complemented
6#19135410C211yesmaximal, characteristic
7#19135357C211yesmaximal, characteristic, complemented
8#19135295C211yesmaximal, characteristic
9#19135269C211yesmaximal, characteristic, complemented
10#19134934C211yesmaximal, characteristic, complemented
11#19134866C211yesmaximal, characteristic, complemented
12#19134854C211yesmaximal, characteristic
13#19134468C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C2×#13063312C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×C4×Dic86C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22#14583119C418yescomplemented
23#14583004—24no—
24SD16×Dic43—24no—
25C2×#13063257C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582797—21no—
39#14582797C2211yescharacteristic
40#14582795—21no—
41#14582795C2211yescharacteristic
42#14582793—21no—
43#14582787—21no—
44#14582771—21no—
45#14582768—21no—
46#14582768C2211yescharacteristic
47C4⋊C4×Dic43C2211yescharacteristic
48C4×Dic43⋊C4—21no—
49C4×Dic43⋊C4C2211yescharacteristic
50C22⋊C4×Dic43—21no—
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C23×Dic43—21no—
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885C2×C414yescomplemented
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063312—22no—
70#13063312C2×C414yes—
71Q8×Dic43—22no—
72Q8×Dic43—22no—
73Q8×Dic43—41no—
74Q8×Dic43C2×C414yescomplemented
75C4×Dic86—22no—
76C4×Dic86—41no—
77D4×Dic43—22no—
78D4×Dic43—41no—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×Dic43⋊C4—21no—
85C2×Dic43⋊C4—21no—
86C2×Dic43⋊C4—21no—
87C2×Dic43⋊C4—21no—
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4D411yescharacteristic
90C2×Dic43⋊C4D411yescharacteristic
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43—21no—
97C2×C4×Dic43—21no—
98C2×C4×Dic43C2311yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100#13063257—22no—
101#13063256—22no—
102Dic43⋊C8C2×C414yescomplemented
103#13063250—41no—
104#13063250C2×C414yescomplemented
105#13063249D414yes—
106#13063248—22no—
107#13063246—22no—
108#13063246C2×C414yes—
109#13063236—22no—
110#13063235—22no—
111C8×Dic43—22no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95D411yescharacteristic
118C43⋊#95D411yescharacteristic
119C22×Q8×C43C2311yescharacteristic
120C22×D4×C43C2311yescharacteristic
121C2×SD16×C43—22no—
122C2×SD16×C43—22no—
123C2×SD16×C43C2×C414yes—
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C4×Q8×C43—22no—
127C4×Q8×C43—41no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132C2×C22⋊C4×C43—21no—
133C2×C42×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#103×C43—22no—
136#102×C43—41no—
137C24×C43—21no—
138C2×Q8×C43—21no—
139C2×Q8×C43—21no—
140C2×Q8×C43—21no—
141C2×Q8×C43C22×C412yes—
142C2×Q8×C43C2×D412yes—
143C2×Q8×C43#4112yes—
144C2×D4×C43—21no—
145C2×D4×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43C22×C412yes—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—42no—
161C22×Dic43—42no—
162C22×Dic43—81no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86C22×C412yes—
173SD16×C43—28no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43C22×C412yes—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—42no—
185C22⋊C4×C43—42no—
186C22⋊C4×C43—81no—
187C42×C43—21no—
188C42×C43—21no—
189C42×C43—42no—
190C22⋊Dic43—24no—
191C22⋊Dic43—24no—
192C22⋊Dic43—42no—
193#10621885—28no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—24no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—42no—
200C4⋊Dic43C22×C412yes—
201C4⋊Dic43C2×D412yes—
202Dic43⋊C4—22no—
203Dic43⋊C4—41no—
204Dic43⋊C4—42no—
205Dic43⋊C4—42no—
206Dic43⋊C4—81no—
207Dic43⋊C4—81no—
208Dic43⋊C4—81no—
209C4×Dic43—21no—
210C4×Dic43—21no—
211C4×Dic43—24no—
212C4×Dic43—42no—
213C4×Dic43—42no—
214C4×Dic43—81no—
215C4×Dic43C22×C412yes—
216C4×Dic43#4112yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8C22×C412yes—
222C2×C43⋊C8C2×D412yes—
223C23×C43—22no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43C22×D411yescharacteristic
231Q8×C43—22no—
232Q8×C43—22no—
233Q8×C43—22no—
234Q8×C43C4×D414yes—
235D4×C43—22no—
236D4×C43—22no—
237D4×C43—41no—
238D4×C43—41no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—22no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C22×D411yescharacteristic
256C2×C4×C43C2×#4111yescharacteristic
257C2×C4×C43C2×#4111yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C432−1+411yescharacteristic
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—22no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—84no—
282C2×Dic43C4×D412yes—
283C2×Dic43C4×D412yes—
284C2×Dic43#13712yes—
285Dic86—22no—
286Dic86—22no—
287Dic86—41no—
288Dic86—41no—
289C8×C43—22no—
290C8×C43—41no—
291C43⋊C8—22no—
292C43⋊C8—22no—
293#23013—431nomaximal, Sylow
294C22×C43—42no—
295C22×C43—42no—
296C22×C43—42no—
297C22×C43—81no—
298C22×C43—81no—
299C22×C43—81no—
300C22×C43—81no—
301C22×C43C2×C4×D411yescharacteristic
302C22×C43D4211yescharacteristic
303C22×C43#54811yescharacteristic
304C22×C43C2×#13711yescharacteristic
305C22×C43#57511yescharacteristic
306C22×C43#57711yescharacteristic
307C22×C43#57711yescharacteristic
308C4×C43—24no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—81no—
312C4×C43—81no—
313C4×C43C2×C4×D411yescharacteristic
314C4×C43#52011yescharacteristic
315C4×C43#54711yescharacteristic
316C4×C43#55311yescharacteristic
317Dic43—22no—
318Dic43—22no—
319Dic43—22no—
320Dic43—42no—
321Dic43—42no—
322Dic43—42no—
323Dic43—41no—
324Dic43—81no—
325C2×#464—431no—
326C2×#441—431no—
327C2×C4×SD16—431no—
328#2367—431no—
329Q8×C4⋊C4—431no—
330#1959—431no—
331#1948—431no—
332#1936—431no—
333#1933—431no—
334#1880D4311yescharacteristic
335#1878—431no—
336#1865—431no—
337#1864—431no—
338#1771—431no—
339#1763—431no—
340C2×C43—82no—
341C2×C43#236111yescharacteristic
342C2×C43C4×#13711yescharacteristic
343C2×C43#295211yescharacteristic
344C2×C43#326611yescharacteristic
345C2×C43#327111yescharacteristic
346C2×C43#336911yescharacteristic
347C2×C43#337111yescharacteristic
348C22×Q16—431no—
349C22×SD16C2×D4311yescharacteristic
350C2×#124—431no—
351C2×C4×Q8—431no—
352C2×C4×Q8—431no—
353C2×C4×Q8—431no—
354C2×C4×Q8C2×D4311yescharacteristic
355C2×C4×D4—431no—
356#464—438no—
357#441—864no—
358C4×SD16—864no—
359C2×#106—431no—
360C2×#106—431no—
361C2×C4⋊C8—431no—
362C2×#103—431no—
363C2×#103—431no—
364C2×#103—431no—
365C2×#103—431no—
366C2×#103C2×D4311yescharacteristic
367C2×#102—431no—
368C2×#102—431no—
369C2×#102C2×D4311yescharacteristic
370C2×#97—431no—
371C2×#97—431no—
372C2×C4×C8—431no—
373#391—431no—
374#390C2×D4311yescharacteristic
375#389—431no—
376#389—431no—
377#389—861no—
378#389—861no—
379#388—861no—
380#388—861no—
381#385—861no—
382#384—431no—
383#384—861no—
384C4×C4⋊C4—431no—
385C4×C4⋊C4—431no—
386C4×C4⋊C4—861no—
387C4×C22⋊C4—861no—
388#340—431no—
389#340—431no—
390#340—431no—
391#340C2×D4311yescharacteristic
392#336—431no—
393#336C2×D4311yescharacteristic
394C43#2301311yescharacteristic, complemented, Sylow
395C22×Q8—431no—
396C22×Q8C22×D4311yescharacteristic
397C22×D4C22×D4311yescharacteristic
398C23×C4—861no—
399C2×Q16—434no—
400C2×Q16—862no—
401C2×Q16—862no—
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16C4×D4314yes—
405C22×C8—431no—
406C22×C8—431no—
407C22×C8C22×D4311yescharacteristic
408C22×C8C22×D4311yescharacteristic
409#124—434no—
410#124—862no—
411C4×Q8—22no—
412C4×Q8—41no—
413C4×Q8—434no—
414C4×Q8—862no—
415C4×Q8—862no—
416C4×Q8—862no—
417C4×Q8—1721no—
418C4×Q8—1721no—
419C4×D4—862no—
420C4×D4—1721no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—431no—
423C2×C4⋊C4—431no—
424C2×C4⋊C4—431no—
425C2×C4⋊C4—431no—
426C2×C4⋊C4—431no—
427C2×C4⋊C4—861no—
428C2×C4⋊C4—861no—
429C2×C4⋊C4—861no—
430C2×C4⋊C4—861no—
431C2×C4⋊C4—861no—
432C2×C4⋊C4—861no—
433C2×C4⋊C4—861no—
434C2×C4⋊C4C22×D4311yescharacteristic
435C2×C4⋊C4C22×D4311yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—861no—
439C2×C22⋊C4—861no—
440C2×C22⋊C4—861no—
441C2×C42—21no—
442C2×C42—431no—
443C2×C42—431no—
444C2×C42—861no—
445C2×C42—861no—
446C2×C42—861no—
447C2×C42—861no—
448C2×C42C22×D4311yescharacteristic
449#106—862no—
450#106—862no—
451C4⋊C8—434no—
452#103—22no—
453#103—434no—
454#103—434no—
455#103—862no—
456#103—1721no—
457#102—41no—
458#102—434no—
459#102—862no—
460#97—862no—
461#97—862no—
462C4×C8—862no—
463#95—431no—
464#95—431no—
465#95—861no—
466#95—861no—
467#95—861no—
468#95—861no—
469#95—861no—
470C24—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—432no—
475C2×Q8—861no—
476C2×Q8—861no—
477C2×Q8—861no—
478C2×Q8—861no—
479C2×Q8—861no—
480C2×Q8C2×C4×D4312yes—
481C2×Q8D4×D4312yes—
482C2×Q8#1062190012yes—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4C2×C4×D4312yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—431no—
493C22×C4—431no—
494C22×C4—431no—
495C22×C4—431no—
496C22×C4—861no—
497C22×C4—861no—
498C22×C4—861no—
499C22×C4—861no—
500C22×C4—3441no—
501C22×C4—1722no—
502C22×C4—1722no—
503C22×C4D4×D4311yescharacteristic
504C22×C4D4×D4311yescharacteristic
505C22×C4C23×D4311yescharacteristic
506Q16—868no—
507SD16—28no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—432no—
514C2×C8—432no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8C2×C4×D4312yes—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—432no—
526C4⋊C4—432no—
527C4⋊C4—862no—
528C4⋊C4—864no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4—861no—
532C4⋊C4—861no—
533C4⋊C4—3441no—
534C4⋊C4—3441no—
535C4⋊C4—3441no—
536C4⋊C4—1721no—
537C4⋊C4—1722no—
538C4⋊C4—1722no—
539C4⋊C4—1722no—
540C22⋊C4—42no—
541C22⋊C4—81no—
542C22⋊C4—864no—
543C22⋊C4—864no—
544C22⋊C4—1722no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—432no—
549C42—432no—
550C42—864no—
551C42—861no—
552C42—861no—
553C42—3441no—
554C42—1722no—
555C42—1722no—
556C23—22no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C2×D4×D4311yescharacteristic
564Q8—22no—
565Q8—22no—
566Q8—22no—
567Q8—862no—
568Q8—862no—
569Q8—1721no—
570Q8—1721no—
571Q8(C22⋊D43)⋊C414yes—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—432no—
592C2×C4—432no—
593C2×C4—432no—
594C2×C4—861no—
595C2×C4—861no—
596C2×C4—861no—
597C2×C4—861no—
598C2×C4—861no—
599C2×C4—861no—
600C2×C4—862no—
601C2×C4—862no—
602C2×C4—861no—
603C2×C4—861no—
604C2×C4—861no—
605C2×C4—862no—
606C2×C4—3444no—
607C2×C4—1721no—
608C2×C4—1721no—
609C2×C4—1721no—
610C2×C4—1721no—
611C2×C4—1721no—
612C2×C4—1721no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4C22×C4×D4311yescharacteristic
617C2×C4C2×D4×D4311yescharacteristic
618C2×C4#41×D4311yescharacteristic
619C2×C4C2×#1062190011yescharacteristic
620C2×C4#1306337011yescharacteristic
621C2×C4#1306337211yescharacteristic
622C8—22no—
623C8—41no—
624C8—862no—
625C8—862no—
626C22—42no—
627C22—42no—
628C22—42no—
629C22—81no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22C4×D4×D4311yescharacteristic
634C22#1458353111yescharacteristic
635C22#1458355511yescharacteristic
636C22#137×D4311yescharacteristic
637C22#1458369511yescharacteristic
638C22#1458370511yescharacteristic
639C22#1458370611yescharacteristic
640C4—24no—
641C4—41no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—862no—
646C4—862no—
647C4—862no—
648C4—3441no—
649C4—1722no—
650C4—1722no—
651C4—1722no—
652C4—1721no—
653C4C2×(C22⋊D43)⋊C411yescharacteristic
654C4#1458337811yescharacteristic
655C4#1458354711yescharacteristic
656C4#1458359211yescharacteristic
657C2—82no—
658C2#1913760611yescharacteristic
659C2#1914341711yescharacteristic
660C2#1914347311yescharacteristic
661C2#1914610811yescharacteristic
662C2#1914617811yescharacteristic
663C2#1914733011yescharacteristic
664C2#1914735611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#23013
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×#14583004C2semidirect
5. Q8×Dic43⋊C4C2semidirect
7. #19135357C2semidirect
9. #19135269C2semidirect
10. #19134934C2semidirect
11. #19134866C2semidirect
13. #19134468C2semidirect
14. #19134427C2semidirect
22. #14583119C4semidirect
66. C2×#10621885C2×C4semidirect
74. Q8×Dic43C2×C4semidirect
102. Dic43⋊C8C2×C4semidirect
104. #13063250C2×C4semidirect
394. C43#23013semidirect

Maximal subgroups

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

subgroupindex
C2×#145831192
C2×#145830042
C2×SD16×Dic432
#191376652
Q8×Dic43⋊C42
#191354102
#191353572
#191352952
#191352692
#191349342
#191348662
#191348542
#191344682
#191344272
C43×#18802
#2301343