Finite Group Databasebeta

← #25113877

Subgroups — #25113877

Order 11008.

934 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582906C211yesmaximal, characteristic
2#19137487C211yesmaximal, characteristic
3Q8×(C2×D43)⋊C4C211yesmaximal, characteristic
4#19135286C211yesmaximal, characteristic, complemented
5#19135270C211yesmaximal, characteristic, complemented
6#19135237C211yesmaximal, characteristic, complemented
7#19135228C211yesmaximal, characteristic, complemented
8#19134851C211yesmaximal, characteristic, complemented
9#19134689C211yesmaximal, characteristic
10#19134625C211yesmaximal, characteristic
11#19134528C211yesmaximal, characteristic
12#19134427C211yesmaximal, characteristic, complemented
13C4×#13063249C211yesmaximal, characteristic, complemented
14#19134375C211yesmaximal, characteristic
15C43×#1865C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21#14582906C418yescomplemented
22C2×#13063250C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582805—21no—
32#14582805C2211yescharacteristic
33#14582804—21no—
34#14582804C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582791—21no—
37#14582789—21no—
38#14582766—21no—
39#14582756—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43—21no—
43C4⋊C4×Dic43C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45C4×(C2×D43)⋊C4—21no—
46C4×(C2×D43)⋊C4C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×Q8×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×#103×C43C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86C2311yescharacteristic
62C2×Q8×D43—22no—
63C2×Q8×D43—22no—
64C2×Q8×D43—22no—
65C2×Q8×D43—41no—
66C2×Q8×D43—41no—
67C2×Q8×D43C2×C414yes—
68C22×C4×D43—21no—
69C22×C4×D43C2311yescharacteristic
70C2×#10621872—41no—
71C2×#10621872—41no—
72C2×#10621872C2×C414yes—
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75Q8×Dic43—22no—
76Q8×Dic43—41no—
77#13063283—22no—
78#13063283C2×C414yes—
79C2×C4⋊Dic43—21no—
80C2×C4⋊Dic43—21no—
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×C4⋊Dic43C2311yescharacteristic
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94#13063259—41no—
95#13063250—41no—
96#13063250C2×C414yes—
97#13063249—22no—
98#13063249C2×C414yes—
99#13063248—41no—
100#13063248C2×C414yes—
101(C2×D43)⋊C8—22no—
102#13063235—41no—
103C4×C43⋊C8—41no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95D411yescharacteristic
114C43⋊#95D411yescharacteristic
115C22×Q8×C43C2311yescharacteristic
116C22×C8×C43C2311yescharacteristic
117C22×C8×C43C2311yescharacteristic
118C4×Q8×C43—22no—
119C4×Q8×C43—41no—
120C2×C4⋊C4×C43—21no—
121C2×C4⋊C4×C43—21no—
122C2×C4⋊C4×C43C2311yescharacteristic
123C2×C4⋊C4×C43C2311yescharacteristic
124C2×C4⋊C4×C43C2311yescharacteristic
125C2×C42×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#106×C43—41no—
128#103×C43—22no—
129#103×C43C2×C414yes—
130#95×C43—21no—
131C23×D43C2×D411yescharacteristic
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43C22×C412yes—
136C2×Q8×C43#4112yes—
137C2×Q8×C43#4112yes—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152Q8×D43—28no—
153Q8×D43—44no—
154Q8×D43—44no—
155Q8×D43—44no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—24no—
161C2×C4×D43—42no—
162C2×C4×D43—42no—
163C2×C4×D43C22×C412yes—
164C2×C4×D43#4112yes—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—24no—
171C2×Dic86—42no—
172C2×Dic86—42no—
173C2×Dic86C22×C412yes—
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—21no—
185C4⋊C4×C43—42no—
186C4⋊C4×C43—42no—
187C4⋊C4×C43C22×C412yes—
188C42×C43—21no—
189C42×C43—21no—
190C42×C43—42no—
191(C2×D43)⋊C4—22no—
192(C2×D43)⋊C4—24no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—42no—
202C4⋊Dic43—42no—
203C4⋊Dic43C22×C412yes—
204C4×Dic43—21no—
205C4×Dic43—21no—
206C4×Dic43—24no—
207C4×Dic43—42no—
208C4×Dic43—81no—
209C4×Dic43—81no—
210C2×C43⋊C8—21no—
211C2×C43⋊C8—21no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8C22×C412yes—
216#10621872—44no—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43C4×D412yes—
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—22no—
228Q8×C43#11714yes—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—22no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43#13712yes—
247C2×C4×C43C23×C411yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
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×Dic43C4×D412yes—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—48no—
279Dic86—22no—
280Dic86—22no—
281Dic86—48no—
282Dic86—41no—
283Dic86—41no—
284C8×C43—22no—
285C8×C43—41no—
286C43⋊C8—22no—
287C43⋊C8—41no—
288#22581—431nomaximal, Sylow
289C22×C43C2×C4×D411yescharacteristic
290C22×C43#54611yescharacteristic
291C22×C43#54611yescharacteristic
292C22×C43C2×#13711yescharacteristic
293C22×C43#57511yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57811yescharacteristic
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C4×C43—24no—
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—41no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C2×#11711yescharacteristic
310C4×C43#51811yescharacteristic
311C4×C43#55111yescharacteristic
312C4×C43#55111yescharacteristic
313Dic43—22no—
314Dic43—41no—
315Dic43—42no—
316Dic43—42no—
317Dic43—41no—
318Dic43—81no—
319Dic43—81no—
320C2×#419—431no—
321#2347—431no—
322Q8×C22⋊C4—431no—
323#1935—431no—
324#1933—431no—
325#1928—431no—
326#1927—431no—
327#1865D4311yescharacteristic, complemented
328#1863—431no—
329#1825—431no—
330#1809—431no—
331#1787—431no—
332#1763—431no—
333C4×#103—431no—
334#1753—431no—
335C2×C43#234211yescharacteristic
336C2×C43C4×#13711yescharacteristic
337C2×C43#294711yescharacteristic
338C2×C43#331311yescharacteristic
339C2×C43#332011yescharacteristic
340C2×C43#332611yescharacteristic
341C2×C43#332811yescharacteristic
342D43—42no—
343C23×Q8—431no—
344C22×M16—431no—
345C2×C4×Q8—431no—
346C2×C4×Q8C2×D4311yescharacteristic
347C2×#117—431no—
348C2×#107—431no—
349C2×#106C2×D4311yescharacteristic
350#419—438no—
351C2×#103—431no—
352C2×#103—431no—
353C2×#103—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#103C2×D4311yescharacteristic
358C2×#103C2×D4311yescharacteristic
359C2×C22⋊C8—431no—
360C2×#97—431no—
361C2×C4×C8—431no—
362#391—431no—
363#391—431no—
364#391—861no—
365#391—861no—
366#389—431no—
367#389C2×D4311yescharacteristic
368#388—861no—
369#388—861no—
370#383—861no—
371#380—431no—
372#380—431no—
373#380—861no—
374C4×C4⋊C4—431no—
375C4×C4⋊C4—431no—
376C4×C4⋊C4—861no—
377C4×C22⋊C4—431no—
378C4×C22⋊C4—861no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340C2×D4311yescharacteristic
385#336—431no—
386#336C2×D4311yescharacteristic
387C43#2258111yescharacteristic, complemented, Sylow
388C22×Q8—434no—
389C22×Q8—431no—
390C22×Q8—861no—
391C22×Q8—862no—
392C22×Q8—862no—
393C22×Q8—862no—
394C22×Q8—1721no—
395C22×Q8—1721no—
396C22×Q8C22×D4311yescharacteristic
397C23×C4—431no—
398C23×C4—861no—
399C2×M16—434no—
400C2×M16—1721no—
401C2×M16—1721no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4×Q8—22no—
407C4×Q8—41no—
408C4×Q8—862no—
409C4×Q8—1721no—
410#117—434no—
411#117—862no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—431no—
423C2×C22⋊C4—431no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—21no—
428C2×C42—431no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434#107—1721no—
435#106—41no—
436#103—22no—
437#103—434no—
438#103—434no—
439#103—434no—
440#103—862no—
441#103—1721no—
442#103—1721no—
443#103C4×D4314yes—
444C22⋊C8—862no—
445#97—1721no—
446C4×C8—1721no—
447#95—21no—
448#95—431no—
449#95—431no—
450#95—861no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459C24—431no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—432no—
464C2×Q8—864no—
465C2×Q8—861no—
466C2×Q8—868no—
467C2×Q8—861no—
468C2×Q8—861no—
469C2×Q8—861no—
470C2×Q8—861no—
471C2×Q8—1722no—
472C2×Q8—1722no—
473C2×Q8—1724no—
474C2×Q8—1724no—
475C2×Q8—1724no—
476C2×Q8C2×C4×D4312yes—
477C2×Q8#1062190012yes—
478C2×Q8#1062190212yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—431no—
484C22×C4—432no—
485C22×C4—432no—
486C22×C4—431no—
487C22×C4—431no—
488C22×C4—864no—
489C22×C4—861no—
490C22×C4—861no—
491C22×C4—861no—
492C22×C4—861no—
493C22×C4—861no—
494C22×C4—861no—
495C22×C4—861no—
496C22×C4—861no—
497C22×C4—1722no—
498C22×C4—1722no—
499C22×C4D4×D4311yescharacteristic
500C22×C4D4×D4311yescharacteristic
501C22×C4C23×D4311yescharacteristic
502M16—1724no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—432no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8C2×C4×D4312yes—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—432no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—861no—
527C4⋊C4—861no—
528C4⋊C4—1722no—
529C4⋊C4—1722no—
530C4⋊C4C2×C4×D4312yes—
531C22⋊C4—864no—
532C22⋊C4—862no—
533C22⋊C4—3441no—
534C22⋊C4—1721no—
535C22⋊C4—1722no—
536C42—21no—
537C42—21no—
538C42—42no—
539C42—864no—
540C42—861no—
541C42—861no—
542C42—3441no—
543C42—3441no—
544C42—1722no—
545C23—432no—
546C23—861no—
547C23—861no—
548C23—861no—
549C23—861no—
550C23—861no—
551C23—861no—
552C23C2×D4×D4311yescharacteristic
553Q8—22no—
554Q8—22no—
555Q8—22no—
556Q8—862no—
557Q8—862no—
558Q8—1728no—
559Q8—1721no—
560Q8—1721no—
561Q8#1306328314yes—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—432no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—862no—
584C2×C4—862no—
585C2×C4—862no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—861no—
591C2×C4—861no—
592C2×C4—861no—
593C2×C4—861no—
594C2×C4—1728no—
595C2×C4—1721no—
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#1306335412yes—
606C2×C4C22×C4×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4C2×#1062190011yescharacteristic
609C2×C4C2×#1062190211yescharacteristic
610C2×C4#1306337011yescharacteristic
611C2×C4#1306337111yescharacteristic
612C8—22no—
613C8—41no—
614C8—862no—
615C8—1721no—
616C22—862no—
617C22—862no—
618C22—862no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22—1721no—
623C22C4×D4×D4311yescharacteristic
624C22#1458353611yescharacteristic
625C22#1458354011yescharacteristic
626C22C2×#1306335411yescharacteristic
627C22#1458369611yescharacteristic
628C22#1458370811yescharacteristic
629C22#1458371511yescharacteristic
630C4—22no—
631C4—24no—
632C4—41no—
633C4—42no—
634C4—81no—
635C4—81no—
636C4—862no—
637C4—3441no—
638C4—3441no—
639C4—1722no—
640C4—1721no—
641C4—1721no—
642C4—1722no—
643C4C2×#1306328311yescharacteristic
644C4#1458337111yescharacteristic
645C4#1458357211yescharacteristic
646C4#1458357611yescharacteristic
647C2—1722no—
648C2#1913744211yescharacteristic
649C2C4×#1306335411yescharacteristic
650C2#1914343711yescharacteristic
651C2#1914666511yescharacteristic
652C2#1914677011yescharacteristic
653C2#1914684511yescharacteristic
654C2#1914687511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1865C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1865D43
hypocenterC43#22581
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
4. #19135286C2semidirect
5. #19135270C2semidirect
6. #19135237C2semidirect
7. #19135228C2semidirect
8. #19134851C2semidirect
12. #19134427C2semidirect
13. C4×#13063249C2semidirect
15. C43×#1865C2semidirect
21. #14582906C4semidirect
327. #1865D43semidirect
387. C43#22581semidirect

Maximal subgroups

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

subgroupindex
C2×#145829062
#191374872
Q8×(C2×D43)⋊C42
#191352862
#191352702
#191352372
#191352282
#191348512
#191346892
#191346252
#191345282
#191344272
C4×#130632492
#191343752
C43×#18652
#2258143