Finite Group Databasebeta

← #25103218

Subgroups — #25103218

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583127C211yesmaximal, characteristic
2C2×#14582996C211yesmaximal, characteristic, complemented
3C2×#14582853C211yesmaximal, characteristic, complemented
4#19137291C211yesmaximal, characteristic
5#19137275C211yesmaximal, characteristic, complemented
6#19135475C211yesmaximal, characteristic, complemented
7#19135335C211yesmaximal, characteristic, complemented
8#19135271C211yesmaximal, characteristic, complemented
9#19135030C211yesmaximal, characteristic
10#19135027C211yesmaximal, characteristic, complemented
11#19134623C211yesmaximal, characteristic, complemented
12#19134491C211yesmaximal, characteristic, complemented
13#19134414C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#1934C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063305C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×D4×Dic43C2211yescharacteristic
23C2×#13063282C2211yescharacteristic
24#14583127C418yescomplemented
25#14582996—24no—
26C2×#13063258C2211yescharacteristic
27C2×#13063258C2211yescharacteristic
28C2×#13063256C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063250C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063246C2211yescharacteristic
33#14582853—24no—
34C2×#13063236C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582805C2211yescharacteristic
38#14582799—21no—
39#14582797C2211yescharacteristic
40#14582795—21no—
41#14582789—21no—
42#14582788—21no—
43#14582787—21no—
44#14582782—21no—
45#14582776—21no—
46#14582771—21no—
47#14582756C2211yescharacteristic
48#14582756C2211yescharacteristic
49C4⋊C4×Dic43C2211yescharacteristic
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×C4×C8×C43C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C43×#389C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86C2311yescharacteristic
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C22×C4×D43C2311yescharacteristic
66C2×#10621883—22no—
67C2×#10621883—22no—
68C2×#10621883C2×C414yes—
69C2×#10621872—22no—
70C2×#10621872—22no—
71C2×#10621872—22no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C2×C8×D43—22no—
75C2×C8×D43—22no—
76C2×C8×D43C2×C414yescomplemented
77#13063305—22no—
78#13063305C2×C414yescomplemented
79#13063296—22no—
80#13063296C2×C414yes—
81#13063290—22no—
82#13063290—22no—
83D4×Dic43—22no—
84D4×Dic43—22no—
85#13063282—22no—
86#13063282—22no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43C2311yescharacteristic
89C2×C4⋊Dic43C2311yescharacteristic
90C2×C4⋊Dic43C2311yescharacteristic
91C2×Dic43⋊C4—21no—
92C2×Dic43⋊C4—21no—
93C2×Dic43⋊C4D411yescharacteristic
94C2×Dic43⋊C4D411yescharacteristic
95C2×C22⋊Dic43—21no—
96C2×C22⋊Dic43—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×(C2×D43)⋊C4—21no—
100C2×(C2×D43)⋊C4D411yescharacteristic
101C2×(C2×D43)⋊C4D411yescharacteristic
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106#13063258—22no—
107#13063258—22no—
108#13063256C2×C414yescomplemented
109#13063250—22no—
110#13063250C2×C414yescomplemented
111#13063248—22no—
112#13063246—22no—
113#13063236—22no—
114#13063235D414yescomplemented
115C8×Dic43—22no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C22×D4×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43C2311yescharacteristic
133#102×C43—22no—
134#102×C43C2×C414yes—
135C4×C8×C43—22no—
136#95×C43—21no—
137C24×C43—21no—
138C23×D43C2×D411yescharacteristic
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—21no—
144C2×D4×C43C22×C412yes—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2411yescharacteristic
151C2×C22⋊D43—24no—
152C2×C22⋊D43—81no—
153C2×C22⋊D43—81no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—42no—
159C22×Dic43—81no—
160C22×Dic43—81no—
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43C22×C412yes—
169C2×C4×D43#4112yes—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86C22×C412yes—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C2×C8×C43—21no—
179C2×C8×C43—21no—
180C2×C8×C43C22×C412yes—
181C2×C8×C43C2×D412yes—
182C4⋊C4×C43—21no—
183C4⋊C4×C43—21no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43—21no—
186C4⋊C4×C43—21no—
187C4⋊C4×C43—81no—
188C4⋊C4×C43C22×C412yes—
189C22⋊C4×C43—81no—
190C22⋊C4×C43—81no—
191C42×C43—21no—
192C42×C43—21no—
193C22⋊Dic43—24no—
194C22⋊Dic43—42no—
195#10621883—28no—
196(C2×D43)⋊C4—22no—
197(C2×D43)⋊C4—22no—
198(C2×D43)⋊C4—24no—
199(C2×D43)⋊C4—81no—
200(C2×D43)⋊C4—81no—
201C4⋊Dic43—21no—
202C4⋊Dic43—24no—
203C4⋊Dic43—21no—
204C4⋊Dic43—21no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43C22×C412yes—
208Dic43⋊C4—22no—
209Dic43⋊C4—22no—
210Dic43⋊C4—42no—
211Dic43⋊C4—81no—
212C4×Dic43—42no—
213C4×Dic43—81no—
214C4×Dic43—81no—
215C4×Dic43C2×D412yes—
216C4×Dic43#4112yes—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8C22×C412yes—
220C2×C43⋊C8C2×D412yes—
221C2×C43⋊C8#4112yes—
222C2×C43⋊C8#4112yes—
223#10621872—28no—
224C8×D43—28no—
225C23×C43—22no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43C22×D411yescharacteristic
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43C4×D412yes—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43C23×C411yescharacteristic
260C2×C4×C43C22×D411yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C22⋊D43—84no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—22no—
273C2×Dic43—22no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—84no—
285C2×Dic43C4×D412yes—
286C2×Dic43#12112yes—
287C2×Dic43#12112yes—
288C4×D43—22no—
289C4×D43—22no—
290C4×D43—22no—
291C4×D43—22no—
292Dic86—22no—
293Dic86—22no—
294Dic86—41no—
295Dic86—41no—
296C8×C43—22no—
297C8×C43—22no—
298C43⋊C8—22no—
299C43⋊C8C4×D414yes—
300#21531—431nomaximal, Sylow
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43C2×C4×D411yescharacteristic
309C22×C43C2×#12111yescharacteristic
310C22×C43#53211yescharacteristic
311C22×C43#57611yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57711yescharacteristic
314C22×C43#57811yescharacteristic
315C2×D43—22no—
316C2×D43—22no—
317C2×D43—22no—
318C2×D43—41no—
319C2×D43—41no—
320C2×D43—41no—
321C2×D43—41no—
322C4×C43—42no—
323C4×C43—41no—
324C4×C43—41no—
325C4×C43—81no—
326C4×C43—81no—
327C4×C43C2×C4×D411yescharacteristic
328C4×C43C4×#4111yescharacteristic
329C4×C43#52511yescharacteristic
330C4×C43#52911yescharacteristic
331Dic43—22no—
332Dic43—22no—
333Dic43—22no—
334Dic43—42no—
335Dic43—42no—
336Dic43—81no—
337Dic43—81no—
338C2×#465—431no—
339C2×#440—431no—
340C2×#405—431no—
341#2324—431no—
342#2323—431no—
343#1973—431no—
344#1944—431no—
345#1934D4311yescharacteristic, complemented
346#1933—431no—
347#1895—431no—
348#1894—431no—
349#1808—431no—
350#1776—431no—
351C4×#103—431no—
352C4×#102—431no—
353C2×C43—82no—
354C2×C43C4×#12111yescharacteristic
355C2×C43#294911yescharacteristic
356C2×C43#295111yescharacteristic
357C2×C43#306211yescharacteristic
358C2×C43#306311yescharacteristic
359C2×C43#317811yescharacteristic
360C2×C43#317911yescharacteristic
361D43—42no—
362C22×SD16—431no—
363C22×M16—431no—
364C23×C8—431no—
365C2×C22⋊Q8—431no—
366C2×#121—431no—
367C2×C4×Q8—431no—
368C2×C4×D4—431no—
369C2×#117—431no—
370#465—438no—
371#440—864no—
372C2×#107—431no—
373C2×#107—431no—
374C2×#106—431no—
375C2×#103—431no—
376C2×#103—431no—
377C2×#103—431no—
378C2×#102—431no—
379C2×#102C2×D4311yescharacteristic
380C2×#102C2×D4311yescharacteristic
381#405—864no—
382C2×#97—431no—
383C2×#97—431no—
384C2×C4×C8—431no—
385C2×C4×C8C2×D4311yescharacteristic
386#391—431no—
387#390—861no—
388#390C2×D4311yescharacteristic
389#389—431no—
390#389—861no—
391#389C2×D4311yescharacteristic
392#388—861no—
393#388—861no—
394#388—861no—
395#387—861no—
396#386—861no—
397#385—861no—
398#380—431no—
399#380—431no—
400C4×C4⋊C4—431no—
401C4×C4⋊C4—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340—431no—
406#340C2×D4311yescharacteristic
407#340C2×D4311yescharacteristic
408C43#2153111yescharacteristic, complemented, Sylow
409C22×Q8—431no—
410C22×D4—861no—
411C22×D4C22×D4311yescharacteristic
412C23×C4—431no—
413C23×C4—861no—
414C2×SD16—434no—
415C2×SD16—862no—
416C2×SD16—862no—
417C2×M16—862no—
418C2×M16—862no—
419C2×M16—862no—
420C22×C8—431no—
421C22×C8—431no—
422C22×C8—434no—
423C22×C8—862no—
424C22×C8—862no—
425C22×C8C22×D4311yescharacteristic
426C22×C8C22×D4311yescharacteristic
427C22⋊Q8—434no—
428C22⋊Q8—862no—
429#121—434no—
430#121—862no—
431C4×Q8—862no—
432C4×Q8—862no—
433C4×D4—862no—
434C4×D4—862no—
435#117—862no—
436#117—862no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—861no—
444C2×C4⋊C4—861no—
445C2×C4⋊C4—861no—
446C2×C4⋊C4C22×D4311yescharacteristic
447C2×C4⋊C4C22×D4311yescharacteristic
448C2×C4⋊C4C22×D4311yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—431no—
452C2×C22⋊C4—431no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C42—431no—
459C2×C42—861no—
460C2×C42—861no—
461C2×C42—861no—
462C2×C42C22×D4311yescharacteristic
463#107—862no—
464#107—862no—
465#106—434no—
466#103—434no—
467#103—862no—
468#103—862no—
469#102—22no—
470#102—862no—
471#102C4×D4314yes—
472#97—434no—
473#97—862no—
474C4×C8—22no—
475C4×C8—862no—
476#95—21no—
477#95—861no—
478#95—861no—
479#95—861no—
480#95—861no—
481#95—861no—
482#95—861no—
483#95—861no—
484C24—21no—
485C24—431no—
486C2×Q8—432no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—864no—
498C2×D4—3441no—
499C2×D4—3441no—
500C2×D4C2×C4×D4312yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—431no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—432no—
508C22×C4—432no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—3441no—
518C22×C4—3441no—
519C22×C4—1722no—
520C22×C4D4×D4311yescharacteristic
521C22×C4D4×D4311yescharacteristic
522C22×C4C23×D4311yescharacteristic
523SD16—868no—
524M16—868no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—432no—
530C2×C8—432no—
531C2×C8—432no—
532C2×C8—432no—
533C2×C8—868no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8C2×C4×D4312yes—
537C2×C8D4×D4312yes—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—81no—
544C4⋊C4—432no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—864no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—861no—
551C4⋊C4—861no—
552C4⋊C4—861no—
553C4⋊C4—3441no—
554C4⋊C4—1722no—
555C4⋊C4C2×C4×D4312yes—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—862no—
559C22⋊C4—862no—
560C22⋊C4—864no—
561C22⋊C4—864no—
562C22⋊C4—3441no—
563C22⋊C4—3441no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—432no—
568C42—432no—
569C42—3441no—
570C42—3441no—
571C42—1722no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—432no—
580C23—861no—
581C23—861no—
582C23—861no—
583C23—861no—
584C23—861no—
585C23—861no—
586C23C2×D4×D4311yescharacteristic
587Q8—862no—
588Q8—862no—
589Q8—1721no—
590Q8—1721no—
591D4—22no—
592D4—22no—
593D4—41no—
594D4—41no—
595D4—3444no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—432no—
612C2×C4—432no—
613C2×C4—432no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—862no—
621C2×C4—862no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—3444no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4C22×C4×D4311yescharacteristic
638C2×C4C2×D4×D4311yescharacteristic
639C2×C4#41×D4311yescharacteristic
640C2×C4#41×D4311yescharacteristic
641C2×C4#41×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C8—22no—
644C8—22no—
645C8—434no—
646C8—862no—
647C22—42no—
648C22—42no—
649C22—42no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—862no—
655C22—862no—
656C22—862no—
657C22—1721no—
658C22—1721no—
659C22—1721no—
660C22—1721no—
661C22C4×D4×D4311yescharacteristic
662C22#121×D4311yescharacteristic
663C22#1458344811yescharacteristic
664C22#1458370011yescharacteristic
665C22#1458370511yescharacteristic
666C22#1458370611yescharacteristic
667C22#1458371311yescharacteristic
668C4—42no—
669C4—41no—
670C4—41no—
671C4—81no—
672C4—81no—
673C4—862no—
674C4—862no—
675C4—862no—
676C4—3441no—
677C4—3441no—
678C4—1722no—
679C4—1722no—
680C4C4×D4×D4311yescharacteristic
681C4#1458336711yescharacteristic
682C4#1458340711yescharacteristic
683C4#1458343211yescharacteristic
684C2—82no—
685C2—1722no—
686C2#1913710711yescharacteristic
687C2#1914344911yescharacteristic
688C2#1914346511yescharacteristic
689C2#1914427411yescharacteristic
690C2#1914427911yescharacteristic
691C2#1914526211yescharacteristic
692C2#1914528511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1934C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1934D43
hypocenterC43#21531
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1934

Complements

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

NH ≅ G/Ntype
2. C2×#14582996C2semidirect
3. C2×#14582853C2semidirect
5. #19137275C2semidirect
6. #19135475C2semidirect
7. #19135335C2semidirect
8. #19135271C2semidirect
10. #19135027C2semidirect
11. #19134623C2semidirect
12. #19134491C2semidirect
13. #19134414C2semidirect
14. #102×Dic43C2semidirect
15. C43×#1934C2semidirect
24. #14583127C4semidirect
76. C2×C8×D43C2×C4semidirect
78. #13063305C2×C4semidirect
108. #13063256C2×C4semidirect
110. #13063250C2×C4semidirect
114. #13063235D4semidirect
345. #1934D43semidirect
408. C43#21531semidirect

Maximal subgroups

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

subgroupindex
C2×#145831272
C2×#145829962
C2×#145828532
#191372912
#191372752
#191354752
#191353352
#191352712
#191350302
#191350272
#191346232
#191344912
#191344142
#102×Dic432
C43×#19342
#2153143