Finite Group Databasebeta

← #25118694

Subgroups — #25118694

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144377C211yesmaximal, characteristic
2#19143544C211yesmaximal, characteristic, complemented
3#19143164C211yesmaximal, characteristic
4#19135368C211yesmaximal, characteristic, complemented
5#19135347C211yesmaximal, characteristic, complemented
6#19135342C211yesmaximal, characteristic, complemented
7#19135192C211yesmaximal, characteristic, complemented
8#19135192C211yesmaximal, characteristic, complemented
9#19134871C211yesmaximal, characteristic
10#19134871C211yesmaximal, characteristic
11#19134452C211yesmaximal, characteristic, complemented
12#19134436C211yesmaximal, characteristic
13#19134429C211yesmaximal, characteristic
14#19134406C211yesmaximal, characteristic
15C43×#1995C211yesmaximal, characteristic, complemented
16C2×#13063333C2211yescharacteristic
17C2×#13063333C2211yescharacteristic
18C4×#10621898C2211yescharacteristic
19#14583203C411yescharacteristic, complemented
20#14583203C411yescharacteristic, complemented
21#14583196C411yescharacteristic, complemented
22#14583196C411yescharacteristic, complemented
23#14583191C411yescharacteristic, complemented
24#14583186C411yescharacteristic, complemented
25#14583181C411yescharacteristic, complemented
26#14583176C411yescharacteristic, complemented
27#14583030—21no—
28#14583030—21no—
29#14583030—21no—
30Q8×C43⋊C8—21no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582935C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582927C2211yescharacteristic
36#14582927C2211yescharacteristic
37#14582926C2211yescharacteristic
38#14582926C2211yescharacteristic
39#14582924—21no—
40#14582924—21no—
41#14582921—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44C4⋊C8×D43—21no—
45C2×#13063253C2211yescharacteristic
46C2×#13063253C2211yescharacteristic
47#14582893C2211yescharacteristic
48#14582893C2211yescharacteristic
49#14582855C2211yescharacteristic
50#14582855C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52C2×#13063236C2211yescharacteristic
53C2×C4×C43⋊C8C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56#14582659C2211yescharacteristic
57#14582659C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582654C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C43×#376C2211yescharacteristic
63C43×#339C2211yescharacteristic
64C43×#339C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68#13063333—22no—
69#13063333—22no—
70#13063333—41no—
71#13063333—41no—
72C2×#10621877C2311yescharacteristic
73C2×#10621877C2311yescharacteristic
74C2×#10621872—21no—
75C2×#10621872—21no—
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C2×C8×D43—21no—
81C2×C8×D43—21no—
82C4×Dic86C2×C411yescharacteristic
83C4×Dic86C2×C411yescharacteristic
84C4×D172C2×C411yescharacteristic
85C4×D172C2×C411yescharacteristic
86C4×C22⋊D43—21no—
87C4×C22⋊D43—21no—
88#13063284C2311yescharacteristic
89#13063282—21no—
90C42×D43—21no—
91#13063260—41no—
92#13063260—41no—
93#13063258C2×C411yescharacteristic
94#13063258C2×C411yescharacteristic
95#13063258C2×C411yescharacteristic
96#13063258C2×C411yescharacteristic
97#13063256C2×C411yescharacteristic
98#13063256C2×C411yescharacteristic
99#13063256C2×C411yescharacteristic
100#13063256C2×C411yescharacteristic
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103C4⋊(C43⋊C8)—21no—
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2×C411yescharacteristic
106C4⋊(C43⋊C8)C2×C411yescharacteristic
107C4⋊(C43⋊C8)C2×C411yescharacteristic
108C4⋊(C43⋊C8)C2×C411yescharacteristic
109C4⋊(C43⋊C8)D411yescharacteristic
110C4⋊(C43⋊C8)D411yescharacteristic
111C4⋊(C43⋊C8)D411yescharacteristic
112C4⋊(C43⋊C8)D411yescharacteristic
113Dic43⋊C8—21no—
114Dic43⋊C8—21no—
115Dic43⋊C8—21no—
116Dic43⋊C8—21no—
117#13063253—22no—
118#13063253Q814yescomplemented
119#13063248C2×C411yescharacteristic
120#13063248C2×C411yescharacteristic
121#13063248C2×C411yescharacteristic
122#13063248C2×C411yescharacteristic
123#13063245C2×C411yescharacteristic
124#13063245C2×C411yescharacteristic
125#13063245C2×C411yescharacteristic
126#13063245C2×C411yescharacteristic
127#13063236—21no—
128#13063236—21no—
129#13063236—21no—
130#13063236—41no—
131C4×C43⋊C8—21no—
132C4×C43⋊C8—21no—
133C4×C43⋊C8—21no—
134C4×C43⋊C8—41no—
135C2×M16×C43C2311yescharacteristic
136C2×M16×C43C2311yescharacteristic
137C4⋊Q8×C43C2×C411yescharacteristic
138C4⋊Q8×C43C2×C411yescharacteristic
139#125×C43C2×C411yescharacteristic
140#125×C43C2×C411yescharacteristic
141C22⋊Q8×C43—21no—
142C22⋊Q8×C43—21no—
143C4×Q8×C43—21no—
144C4×Q8×C43—21no—
145#117×C43C2311yescharacteristic
146#117×C43C2311yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152#95×C43—21no—
153#95×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43#4111yescharacteristic
159C22×C4×C43#4111yescharacteristic
160C22×C4×C43C2411yescharacteristic
161C2×C22⋊D43—21no—
162#10621898—21no—
163#10621898—21no—
164#10621898C2×Q812yes—
165#10621898#4112yes—
166C2×D172C22×C411yescharacteristic
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×Dic86C22×C411yescharacteristic
171M16×C43—21no—
172M16×C43—21no—
173M16×C43—21no—
174M16×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—21no—
183C4⋊C4×C43C22×C411yescharacteristic
184C4⋊C4×C43C22×C411yescharacteristic
185C4⋊C4×C43C22×C411yescharacteristic
186C4⋊C4×C43C22×C411yescharacteristic
187C22⋊C4×C43—21no—
188C22⋊C4×C43—21no—
189C42×C43—21no—
190C42×C43—21no—
191C42×C43—21no—
192C42×C43—21no—
193C42×C43—21no—
194C42×C43C22×C411yescharacteristic
195C42×C43C22×C411yescharacteristic
196C42×C43C2×D411yescharacteristic
197C42×C43C2×D411yescharacteristic
198C42×C43C2×Q812yes—
199C22⋊Dic43—21no—
200(C2×D43)⋊C4—21no—
201(C2×D43)⋊C4—21no—
202C4⋊Dic43C22×C411yescharacteristic
203C4⋊Dic43C22×C411yescharacteristic
204Dic43⋊C4—21no—
205Dic43⋊C4—21no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209#10621877—21no—
210#10621877—21no—
211#10621877—21no—
212#10621877C2×Q812yes—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8C22×C411yescharacteristic
224C2×C43⋊C8C22×C411yescharacteristic
225C2×C43⋊C8C22×C411yescharacteristic
226C2×C43⋊C8C22×C411yescharacteristic
227C2×C43⋊C8C2×D411yescharacteristic
228C2×C43⋊C8C2×D411yescharacteristic
229C2×C43⋊C8C2×D411yescharacteristic
230C2×C43⋊C8C2×D411yescharacteristic
231#10621872—42no—
232#10621872—42no—
233C8×D43—42no—
234C8×D43—42no—
235C23×C43C2×#4111yescharacteristic
236C22×D43—21no—
237Q8×C43—42no—
238Q8×C43—81no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—22no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43C4×D411yescharacteristic
252C2×C4×C43C4×D411yescharacteristic
253C2×C4×C43C4×D411yescharacteristic
254C2×C4×C43C4×D411yescharacteristic
255C2×C4×C43C23×C411yescharacteristic
256C2×C4×C43C22×D411yescharacteristic
257C2×C4×C43C22×Q811yescharacteristic
258C2×C4×C43C2×#4111yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×C4×C432−1+411yescharacteristic
261C22⋊D43—22no—
262C22⋊D43—22no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266D172—21no—
267D172C4×Q812yes—
268C4×D43—22no—
269C4×D43—22no—
270C4×D43—42no—
271C4×D43—81no—
272Dic86—21no—
273Dic86C4×Q812yes—
274C8×C43—41no—
275C8×C43—41no—
276C43⋊C8—21no—
277C43⋊C8—21no—
278C43⋊C8—21no—
279C43⋊C8—21no—
280C43⋊C8—21no—
281C43⋊C8—21no—
282C43⋊C8—21no—
283C43⋊C8—21no—
284C43⋊C8—22no—
285C43⋊C8—41no—
286#22984—431nomaximal, Sylow
287C22×C43—21no—
288C22×C43—21no—
289C22×C43C2×C4×D411yescharacteristic
290C22×C43#55211yescharacteristic
291C22×C43#55411yescharacteristic
292C2×D43—22no—
293C2×D43—41no—
294C2×D43—41no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—21no—
298C4×C43—21no—
299C4×C43—42no—
300C4×C43—41no—
301C4×C43—41no—
302C4×C43—41no—
303C4×C43—41no—
304C4×C43—81no—
305C4×C43C2×C4×Q811yescharacteristic
306C4×C43#52011yescharacteristic
307C4×C43#54611yescharacteristic
308C4×C43D4×Q811yescharacteristic
309Dic43—22no—
310Dic43—41no—
311Dic43—41no—
312#3076—431no—
313#2962—431no—
314#2906—431no—
315#1995D4311yescharacteristic, complemented
316#1950—431no—
317#1946—431no—
318#1945—431no—
319#1922—431no—
320#1922—431no—
321#1866—431no—
322#1866—431no—
323#1768—431no—
324#1765—431no—
325#1764—431no—
326#1759—431no—
327C2×C43—21no—
328C2×C43—21no—
329C2×C43#236011yescharacteristic
330C2×C43#295511yescharacteristic
331C2×C43#295711yescharacteristic
332D43—42no—
333C2×#131—431no—
334C2×#131—431no—
335#533C2×D4311yescharacteristic
336C4×#41—431no—
337#479—431no—
338#479—431no—
339#478—431no—
340#478—431no—
341#477—431no—
342#476—431no—
343#475—431no—
344#474—431no—
345#446—861no—
346#446—861no—
347#446—861no—
348C8×Q8—861no—
349C2×#108—431no—
350C2×#108—431no—
351#427—431no—
352#427—431no—
353#424—431no—
354#424—431no—
355#424—431no—
356#424—431no—
357#424—861no—
358#424—861no—
359#423—861no—
360#423C2×D4311yescharacteristic
361C2×C4⋊C8—431no—
362C2×C4⋊C8—431no—
363C2×C4⋊C8—861no—
364C2×#104—431no—
365C2×#104—431no—
366#416—431no—
367#416—431no—
368#405—431no—
369#405—431no—
370C4×M16—431no—
371C2×#97—431no—
372C2×C4×C8—431no—
373#376C2×D4311yescharacteristic
374#341—431no—
375#341—431no—
376#339—431no—
377#339—431no—
378#339C2×D4311yescharacteristic
379#339C2×D4311yescharacteristic
380#339C2×D4311yescharacteristic
381#339C2×D4311yescharacteristic
382#336—431no—
383#336—431no—
384C43#2298411yescharacteristic, complemented, Sylow
385C2×#41—431no—
386#131—862no—
387#131—862no—
388#131—1721no—
389#131—1721no—
390C2×M16—431no—
391C2×M16—431no—
392C2×M16—861no—
393C2×M16—861no—
394C2×M16C22×D4311yescharacteristic
395C2×M16C22×D4311yescharacteristic
396C22×C8—431no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—861no—
401C22×C8—861no—
402C4⋊Q8C4×D4311yescharacteristic
403C4⋊Q8C4×D4311yescharacteristic
404#125C4×D4311yescharacteristic
405#125C4×D4311yescharacteristic
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—431no—
411C4×Q8—431no—
412C4×D4—431no—
413C4×D4—431no—
414C4×D4—861no—
415C4×D4—861no—
416#117—431no—
417#117—861no—
418#117C22×D4311yescharacteristic
419#117C22×D4311yescharacteristic
420C2×C42—861no—
421C2×C42C22×D4311yescharacteristic
422C2×C42C22×D4311yescharacteristic
423C2×C42C22×D4311yescharacteristic
424#108—1721no—
425#108—1721no—
426#107—431no—
427#107—431no—
428#107—431no—
429#107—431no—
430#106—431no—
431#106—431no—
432#106—431no—
433#106—431no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—431no—
437C4⋊C8—431no—
438C4⋊C8—431no—
439C4⋊C8—431no—
440C4⋊C8—431no—
441C4⋊C8—431no—
442C4⋊C8—431no—
443C4⋊C8—431no—
444C4⋊C8—861no—
445C4⋊C8—861no—
446C4⋊C8—861no—
447C4⋊C8—861no—
448C4⋊C8—861no—
449C4⋊C8—861no—
450C4⋊C8—861no—
451C4⋊C8—861no—
452#104—434no—
453#104—862no—
454#103—431no—
455#103—431no—
456#103—431no—
457#103—431no—
458#102—431no—
459#102—431no—
460#102—431no—
461#102—431no—
462#97—861no—
463#97—861no—
464#97—861no—
465#97—1721no—
466C4×C8—861no—
467C4×C8—861no—
468C4×C8—861no—
469C4×C8—1721no—
470#95—21no—
471#95—21no—
472#41—432no—
473#41—432no—
474#41—861no—
475#41—861no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—431no—
479C2×D4—431no—
480C2×D4—861no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4#1062190011yescharacteristic
487C22×C4#1062190011yescharacteristic
488C22×C4C23×D4311yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—432no—
494M16—861no—
495M16—861no—
496M16—861no—
497M16—1722no—
498M16—1722no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—431no—
502C2×C8—431no—
503C2×C8—431no—
504C2×C8—431no—
505C2×C8—431no—
506C2×C8—431no—
507C2×C8—431no—
508C2×C8—431no—
509C2×C8—861no—
510C2×C8—861no—
511C2×C8—861no—
512C2×C8—861no—
513C2×C8—861no—
514C2×C8—861no—
515C2×C8—861no—
516C2×C8—861no—
517C2×C8—861no—
518C2×C8—861no—
519C2×C8—1722no—
520C2×C8—1722no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—431no—
528C4⋊C4—431no—
529C4⋊C4—861no—
530C4⋊C4—861no—
531C4⋊C4C2×C4×D4311yescharacteristic
532C4⋊C4C2×C4×D4311yescharacteristic
533C4⋊C4C2×C4×D4311yescharacteristic
534C4⋊C4C2×C4×D4311yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—861no—
538C22⋊C4—861no—
539C22⋊C4—861no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—861no—
546C42—861no—
547C42—861no—
548C42C2×C4×D4311yescharacteristic
549C42C2×C4×D4311yescharacteristic
550C42D4×D4311yescharacteristic
551C42D4×D4311yescharacteristic
552C42Q8×D4312yes—
553C23—861no—
554C23C2×#1062190011yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—432no—
558Q8—861no—
559D4—432no—
560D4—862no—
561D4—862no—
562D4—861no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—861no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—3441no—
581C2×C4—1722no—
582C2×C4(C22⋊D43)⋊C411yescharacteristic
583C2×C4(C22⋊D43)⋊C411yescharacteristic
584C2×C4(C22⋊D43)⋊C411yescharacteristic
585C2×C4(C22⋊D43)⋊C411yescharacteristic
586C2×C4C22×C4×D4311yescharacteristic
587C2×C4C2×D4×D4311yescharacteristic
588C2×C4C2×Q8×D4311yescharacteristic
589C2×C4#41×D4311yescharacteristic
590C2×C4#1306337111yescharacteristic
591C2×C4#1306337311yescharacteristic
592C8—41no—
593C8—41no—
594C8—862no—
595C8—861no—
596C8—861no—
597C8—861no—
598C8—861no—
599C8—861no—
600C8—861no—
601C8—861no—
602C8—861no—
603C8—1721no—
604C22—21no—
605C22—21no—
606C22—862no—
607C22—1721no—
608C22—1721no—
609C22C2×(C22⋊D43)⋊C411yescharacteristic
610C22#1458358311yescharacteristic
611C22#1458360711yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—862no—
623C4—1721no—
624C4—1721no—
625C4C4×Q8×D4311yescharacteristic
626C4#1458338111yescharacteristic
627C4#1458354211yescharacteristic
628C4#1458356411yescharacteristic
629C2—21no—
630C2—21no—
631C2—1722no—
632C2#1913760511yescharacteristic
633C2#1914349411yescharacteristic
634C2#1914350811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1995C2
socleC22×C43C2×C4×D4
prime radicalC2×#10621898C23
cosocleC22×C4×C43C24
hypercenter#1995D43
hypocenterC43#22984
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
2. #19143544C2semidirect
4. #19135368C2semidirect
5. #19135347C2semidirect
6. #19135342C2semidirect
7. #19135192C2semidirect
8. #19135192C2semidirect
11. #19134452C2semidirect
15. C43×#1995C2semidirect
19. #14583203C4semidirect
20. #14583203C4semidirect
21. #14583196C4semidirect
22. #14583196C4semidirect
23. #14583191C4semidirect
24. #14583186C4semidirect
25. #14583181C4semidirect
26. #14583176C4semidirect
118. #13063253Q8semidirect
315. #1995D43semidirect
384. C43#22984semidirect

Maximal subgroups

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

subgroupindex
#191443772
#191435442
#191431642
#191353682
#191353472
#191353422
#191351922
#191348712
#191344522
#191344362
#191344292
#191344062
C43×#19952
#2298443