Finite Group Databasebeta

← #25153562

Subgroups — #25153562

Order 11008.

1022 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583625C211yesmaximal, characteristic, complemented
2C2×#14583260C211yesmaximal, characteristic
3C2×#14583123C211yesmaximal, characteristic
4#19140082C211yesmaximal, characteristic
5#19135746C211yesmaximal, characteristic, complemented
6#19135744C211yesmaximal, characteristic, complemented
7#19135742C211yesmaximal, characteristic
8#19135740C211yesmaximal, characteristic
9#19135541C211yesmaximal, characteristic, complemented
10#19135533C211yesmaximal, characteristic, complemented
11#19134950C211yesmaximal, characteristic
12#19134948C211yesmaximal, characteristic
13#19134938C211yesmaximal, characteristic, complemented
14#19134427C211yesmaximal, characteristic, complemented
15C43×#1878C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17#14583625—24no—
18#14583625—24no—
19C2×#13063324—21no—
20C2×#13063324C2211yescharacteristic
21C2×#13063317—21no—
22C2×#13063317C2211yescharacteristic
23C2×#13063316—21no—
24C2×#13063316C2211yescharacteristic
25C2×#13063314C2211yescharacteristic
26C2×Q8×Dic43C2211yescharacteristic
27C2×Q8×Dic43C2211yescharacteristic
28C2×C4×Dic86—21no—
29C2×C4×Dic86C2211yescharacteristic
30#14583260—24no—
31#14583123—24no—
32C2×Dic43⋊C8C2211yescharacteristic
33C2×#13063249C2211yescharacteristic
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063235C2211yescharacteristic
40#14582828—21no—
41#14582812—21no—
42#14582806C2211yescharacteristic
43#14582801C2211yescharacteristic
44#14582800C2211yescharacteristic
45#14582791—21no—
46#14582788—21no—
47C4⋊C4×Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582654C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×Q16×C43C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C43×#391C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86—21no—
64C22×Dic86D411yescharacteristic
65C22×D172C2311yescharacteristic
66C2×#10621884—22no—
67C2×#10621884—22no—
68C2×#10621884—22no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063324—28no—
72#13063324—22no—
73#13063324D414yes—
74#13063317—28no—
75#13063317—22no—
76#13063317—22no—
77#13063316—28no—
78#13063316—22no—
79#13063316—22no—
80#13063314—22no—
81#13063314—22no—
82Q8×Dic43—22no—
83Q8×Dic43—22no—
84Q8×Dic43—22no—
85Q8×Dic43D414yes—
86C4×Dic86—28no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92C2×C4⋊Dic43D411yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×C4⋊Dic43C2311yescharacteristic
95C2×C4⋊Dic43C2311yescharacteristic
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×Dic43⋊C4—21no—
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4D411yescharacteristic
101C2×Dic43⋊C4D411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4—21no—
106C2×(C2×D43)⋊C4—21no—
107C2×(C2×D43)⋊C4—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43—21no—
110C2×C4×Dic43—21no—
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2311yescharacteristic
113Dic43⋊C8—22no—
114#13063249—22no—
115#13063249—22no—
116#13063249—22no—
117#13063247—22no—
118#13063247—22no—
119#13063245—22no—
120#13063235—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C22×Q8×C43C2311yescharacteristic
125C22×Q8×C43C2311yescharacteristic
126C2×Q16×C43—22no—
127C2×Q16×C43—22no—
128C2×Q16×C43—22no—
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4×Q8×C43—22no—
132C4×Q8×C43—22no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C42×C43—21no—
137C2×C42×C43C2311yescharacteristic
138#103×C43—22no—
139#103×C43—22no—
140#95×C43—21no—
141#95×C43—21no—
142C23×D43—21no—
143C2×Q8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43C2×D412yes—
153C2×Q8×C43#4112yes—
154C2×Q8×C43#4112yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43C2411yescharacteristic
162C22×Dic43—21no—
163C22×Dic43—21no—
164C22×Dic43—21no—
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×Dic86—22no—
176C2×Dic86—24no—
177C2×Dic86—41no—
178C2×Dic86—41no—
179C2×Dic86—42no—
180C2×Dic86—42no—
181Q16×C43—44no—
182C2×C8×C43—21no—
183C2×C8×C43—21no—
184C2×C8×C43—21no—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C4⋊C4×C43—24no—
189C4⋊C4×C43—21no—
190C4⋊C4×C43—21no—
191C4⋊C4×C43—21no—
192C4⋊C4×C43C2×D412yes—
193C42×C43—24no—
194C42×C43—21no—
195C42×C43—21no—
196#10621884—44no—
197(C2×D43)⋊C4—42no—
198(C2×D43)⋊C4—42no—
199(C2×D43)⋊C4—42no—
200(C2×D43)⋊C4—42no—
201(C2×D43)⋊C4—81no—
202(C2×D43)⋊C4—81no—
203C4⋊Dic43—24no—
204C4⋊Dic43—24no—
205C4⋊Dic43—21no—
206C4⋊Dic43—21no—
207C4⋊Dic43—24no—
208C4⋊Dic43—22no—
209C4⋊Dic43—21no—
210C4⋊Dic43—21no—
211C4⋊Dic43C2×D412yes—
212C4⋊Dic43C2×D412yes—
213Dic43⋊C4—24no—
214Dic43⋊C4—24no—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—22no—
218Dic43⋊C4—22no—
219C4×Dic43—24no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—24no—
223C4×Dic43—81no—
224C4×Dic43C2×D412yes—
225C4×Dic43C2×D412yes—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C23×C43C22×D411yescharacteristic
233C22×D43—41no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240Q8×C43—22no—
241Q8×C43—22no—
242Q8×C43—22no—
243Q8×C43—41no—
244Q8×C43—41no—
245Q8×C43—41no—
246Q8×C43—41no—
247Q8×C43#12414yes—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—22no—
254C2×C4×C43—21no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C22×D411yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43C2×#4111yescharacteristic
270C2×C4×C432−1+411yescharacteristic
271C2×C4×C432−1+411yescharacteristic
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—22no—
278C2×Dic43—21no—
279C2×Dic43—22no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43#12012yes—
292C2×Dic43#12012yes—
293D172—41no—
294D172—41no—
295D172—41no—
296D172—41no—
297Dic86—44no—
298Dic86—48no—
299C8×C43—41no—
300C8×C43—41no—
301C43⋊C8—41no—
302C43⋊C8—41no—
303#25941—431nomaximal, Sylow
304C22×C43C2×#12011yescharacteristic
305C22×C43#54811yescharacteristic
306C22×C43#54811yescharacteristic
307C22×C43#57511yescharacteristic
308C22×C43#57511yescharacteristic
309C22×C43#57711yescharacteristic
310C22×C43#57811yescharacteristic
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—81no—
315C2×D43—81no—
316C2×D43—81no—
317C2×D43—81no—
318C4×C43—24no—
319C4×C43—41no—
320C4×C43—42no—
321C4×C43—41no—
322C4×C43—81no—
323C4×C43—81no—
324C4×C43C2×#12411yescharacteristic
325C4×C43#53611yescharacteristic
326C4×C43#54811yescharacteristic
327C4×C43#54811yescharacteristic
328Dic43—22no—
329Dic43—22no—
330Dic43—41no—
331Dic43—42no—
332Dic43—41no—
333Dic43—42no—
334Dic43—81no—
335C2×#557—431no—
336C2×#489—431no—
337C2×#464—431no—
338#2592—431no—
339#2026—431no—
340#2026—431no—
341#2025—431no—
342#2025—431no—
343#1987—431no—
344#1985—431no—
345#1880—431no—
346#1880—431no—
347#1878—431no—
348#1878D4311yescharacteristic, complemented
349#1763—431no—
350C2×C43#243611yescharacteristic
351C2×C43#300511yescharacteristic
352C2×C43#301311yescharacteristic
353C2×C43#337111yescharacteristic
354C2×C43#337111yescharacteristic
355C2×C43#337711yescharacteristic
356C2×C43#337711yescharacteristic
357D43—161no—
358C22×Q16C2×D4311yescharacteristic
359C22×SD16—431no—
360#557—864no—
361#557—864no—
362C2×C4⋊Q8—431no—
363C2×C4⋊Q8—861no—
364C2×#125—431no—
365C2×#125—431no—
366C2×#125—861no—
367C2×#125—861no—
368C2×#124—431no—
369C2×C4×Q8—431no—
370C2×C4×Q8—431no—
371C2×C4×Q8—431no—
372C2×C4×Q8—861no—
373C2×C4×Q8C2×D4311yescharacteristic
374#489—864no—
375#464—864no—
376C2×C4⋊C8—431no—
377C2×#103—431no—
378C2×#103—431no—
379C2×#103—431no—
380C2×#103C2×D4311yescharacteristic
381C2×#103C2×D4311yescharacteristic
382C2×#102—431no—
383C2×#102—431no—
384C2×#102—431no—
385C2×#97—431no—
386#397—861no—
387#393—861no—
388#391—431no—
389#391C2×D4311yescharacteristic
390#390—431no—
391#390—431no—
392#388—861no—
393#388—861no—
394C4×C4⋊C4—431no—
395#340—431no—
396#340—431no—
397#340—431no—
398#340—431no—
399#340—431no—
400#340C2×D4311yescharacteristic
401#336—431no—
402#336—431no—
403#336—431no—
404#336C2×D4311yescharacteristic
405C43#2594111yescharacteristic, complemented, Sylow
406C22×Q8—431no—
407C22×Q8—861no—
408C22×Q8C22×D4311yescharacteristic
409C22×Q8C22×D4311yescharacteristic
410C22×D4—431no—
411C2×Q16—22no—
412C2×Q16—22no—
413C2×Q16—22no—
414C2×SD16—862no—
415C2×SD16—862no—
416C2×SD16—862no—
417C22×C8—431no—
418C22×C8—431no—
419C22×C8C22×D4311yescharacteristic
420C22×C8C22×D4311yescharacteristic
421C4⋊Q8—434no—
422C4⋊Q8—862no—
423C4⋊Q8—868no—
424#125—862no—
425#125—862no—
426#125—868no—
427#125—862no—
428#125—868no—
429#125—862no—
430#124—862no—
431#124—862no—
432C4×Q8—22no—
433C4×Q8—22no—
434C4×Q8—434no—
435C4×Q8—862no—
436C4×Q8—862no—
437C4×Q8—868no—
438C4×Q8—862no—
439C4×Q8—862no—
440C4×Q8—862no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—431no—
443C2×C4⋊C4—431no—
444C2×C4⋊C4—431no—
445C2×C4⋊C4—431no—
446C2×C4⋊C4—431no—
447C2×C4⋊C4—431no—
448C2×C4⋊C4—861no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4—861no—
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C4⋊C4C22×D4311yescharacteristic
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C22⋊C4—861no—
460C2×C22⋊C4—861no—
461C2×C22⋊C4—861no—
462C2×C22⋊C4—861no—
463C2×C42—21no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—861no—
467C2×C42—861no—
468C2×C42—861no—
469C2×C42C22×D4311yescharacteristic
470C4⋊C8—862no—
471#103—22no—
472#103—22no—
473#103—862no—
474#103—862no—
475#103—862no—
476#102—862no—
477#102—862no—
478#102—862no—
479#97—862no—
480#95—21no—
481#95—21no—
482#95—861no—
483#95—861no—
484#95—861no—
485C24—861no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—864no—
496C2×Q8—862no—
497C2×Q8—1721no—
498C2×Q8—1721no—
499C2×Q8—1722no—
500C2×Q8—1722no—
501C2×Q8#1062189812yes—
502C2×Q8D4×D4312yes—
503C2×Q8#1062190012yes—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—861no—
508C2×D4—861no—
509C2×D4—861no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4D4×D4311yescharacteristic
522C22×C4D4×D4311yescharacteristic
523C22×C4C23×D4311yescharacteristic
524Q16—44no—
525SD16—1724no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C4⋊C4—24no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—432no—
543C4⋊C4—432no—
544C4⋊C4—862no—
545C4⋊C4—862no—
546C4⋊C4—862no—
547C4⋊C4—864no—
548C4⋊C4—864no—
549C4⋊C4—864no—
550C4⋊C4—864no—
551C4⋊C4—864no—
552C4⋊C4—864no—
553C4⋊C4—864no—
554C4⋊C4—861no—
555C4⋊C4—861no—
556C4⋊C4—861no—
557C4⋊C4—861no—
558C4⋊C4D4×D4312yes—
559C22⋊C4—3441no—
560C22⋊C4—3441no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C42—24no—
566C42—21no—
567C42—21no—
568C42—432no—
569C42—432no—
570C42—864no—
571C42—864no—
572C42—861no—
573C42—861no—
574C42—3441no—
575C23—1721no—
576C23—1721no—
577C23—1721no—
578C23—1721no—
579C23—1721no—
580C23—1721no—
581C23—1721no—
582C23C2×D4×D4311yescharacteristic
583Q8—22no—
584Q8—22no—
585Q8—22no—
586Q8—41no—
587Q8—41no—
588Q8—41no—
589Q8—41no—
590Q8—1724no—
591Q8—1728no—
592Q8#1306331114yes—
593D4—1721no—
594D4—1721no—
595D4—1721no—
596D4—1721no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—432no—
616C2×C4—432no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—862no—
623C2×C4—862no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4C2×D4×D4311yescharacteristic
637C2×C4C2×D4×D4311yescharacteristic
638C2×C4C2×#1062190011yescharacteristic
639C2×C4C2×#1062189811yescharacteristic
640C2×C4#1306337211yescharacteristic
641C2×C4#1306337211yescharacteristic
642C8—41no—
643C8—41no—
644C8—1721no—
645C8—1721no—
646C22—3441no—
647C22—3441no—
648C22—3441no—
649C22—3441no—
650C22—3441no—
651C22—3441no—
652C22—3441no—
653C22#120×D4311yescharacteristic
654C22#1458355511yescharacteristic
655C22#1458355811yescharacteristic
656C22#1458369611yescharacteristic
657C22#1458369811yescharacteristic
658C22#1458370811yescharacteristic
659C22#1458371211yescharacteristic
660C4—24no—
661C4—41no—
662C4—42no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—862no—
667C4—862no—
668C4—3441no—
669C4—1721no—
670C4—1722no—
671C4—1721no—
672C4—1722no—
673C4C2×#1306331111yescharacteristic
674C4#1458347111yescharacteristic
675C4#1458355511yescharacteristic
676C4#1458355811yescharacteristic
677C2—6881no—
678C2#1913825111yescharacteristic
679C2#1914383811yescharacteristic
680C2#1914391111yescharacteristic
681C2#1914736411yescharacteristic
682C2#1914736711yescharacteristic
683C2#1914743011yescharacteristic
684C2#1914743311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1878C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1878D43
hypocenterC43#25941
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
1. C2×#14583625C2semidirect
5. #19135746C2semidirect
6. #19135744C2semidirect
9. #19135541C2semidirect
10. #19135533C2semidirect
13. #19134938C2semidirect
14. #19134427C2semidirect
15. C43×#1878C2semidirect
348. #1878D43semidirect
405. C43#25941semidirect

Maximal subgroups

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

subgroupindex
C2×#145836252
C2×#145832602
C2×#145831232
#191400822
#191357462
#191357442
#191357422
#191357402
#191355412
#191355332
#191349502
#191349482
#191349382
#191344272
C43×#18782
#2594143