Finite Group Databasebeta

← #25065937

Subgroups — #25065937

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143722C211yesmaximal, characteristic
2#19143721C211yesmaximal, characteristic
3#19143557C211yesmaximal, characteristic
4#19133379C211yesmaximal, characteristic, complemented
5#19133377C211yesmaximal, characteristic, complemented
6#19133376C211yesmaximal, characteristic, complemented
7#19133372C211yesmaximal, characteristic, complemented
8#19133371C211yesmaximal, characteristic, complemented
9#19133368C211yesmaximal, characteristic, complemented
10#19133361C211yesmaximal, characteristic, complemented
11#19133355C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133344C211yesmaximal, characteristic, complemented
14#335×D43C211yesmaximal, characteristic, complemented
15C43×#1569C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583027—21no—
18#14583027C411yescharacteristic
19#14583027C411yescharacteristic
20#14583026—21no—
21#14582975C411yescharacteristic
22#14582975C411yescharacteristic
23#14582972—21no—
24#14582972C411yescharacteristic
25#14582972C411yescharacteristic
26#14582968—21no—
27#14582968—21no—
28#14582968C411yescharacteristic
29#14582968C411yescharacteristic
30#14582967—21no—
31#14582964—21no—
32(C22⋊D43)⋊C8—21no—
33#14582955C2211yescharacteristic
34#14582955C2211yescharacteristic
35#14582955C2211yescharacteristic
36#14582952C2211yescharacteristic
37#14582952C2211yescharacteristic
38#14582951C2211yescharacteristic
39#14582950C2211yescharacteristic
40#14582950C2211yescharacteristic
41#14582921C2211yescharacteristic
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C4⋊C8×D43C2211yescharacteristic
44C4⋊C8×D43C2211yescharacteristic
45C4⋊C8×D43C2211yescharacteristic
46C4×#10621872C2211yescharacteristic
47C4×C8×D43C2211yescharacteristic
48#14582652C2211yescharacteristic
49#14582652C2211yescharacteristic
50#14582651C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582651C2211yescharacteristic
55#14582651C2211yescharacteristic
56#14582650C2211yescharacteristic
57#14582650C2211yescharacteristic
58#14582649C2211yescharacteristic
59#14582649C2211yescharacteristic
60C43×#432C2211yescharacteristic
61C43×#423C2211yescharacteristic
62C4×M16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#334C2211yescharacteristic
66C43×#334C2211yescharacteristic
67C2×#10621898Q811yescharacteristic
68C2×#10621872—21no—
69C2×#10621872C2×C411yescharacteristic
70C2×#10621872C2×C411yescharacteristic
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C2×C8×D43C2×C411yescharacteristic
76C2×C8×D43C2×C411yescharacteristic
77C4×Dic86C2×C411yescharacteristic
78C4×Dic86D411yescharacteristic
79C4×D172C2×C411yescharacteristic
80C4×D172D411yescharacteristic
81C4×C22⋊D43C2×C411yescharacteristic
82C4×C22⋊D43C2×C411yescharacteristic
83C4×C22⋊D43D411yescharacteristic
84C4×C22⋊D43D411yescharacteristic
85#13063284Q811yescharacteristic
86#13063282Q811yescharacteristic
87#13063282Q811yescharacteristic
88C42×D43C2311yescharacteristic
89C42×D43C2311yescharacteristic
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2×C411yescharacteristic
92C4⋊(C43⋊C8)C2×C411yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99Dic43⋊C8—21no—
100Dic43⋊C8—21no—
101Dic43⋊C8C2×C411yescharacteristic
102Dic43⋊C8C2×C411yescharacteristic
103Dic43⋊C8C2×C411yescharacteristic
104Dic43⋊C8C2×C411yescharacteristic
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)C2×C411yescharacteristic
107C22⋊(C43⋊C8)C2×C411yescharacteristic
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110(C2×D43)⋊C8—21no—
111(C2×D43)⋊C8—21no—
112(C2×D43)⋊C8C2×C411yescharacteristic
113(C2×D43)⋊C8C2×C411yescharacteristic
114(C2×D43)⋊C8C2×C411yescharacteristic
115(C2×D43)⋊C8C2×C411yescharacteristic
116#13063235—21no—
117#13063235—21no—
118#13063235—21no—
119#13063235C2×C411yescharacteristic
120#13063235C2×C411yescharacteristic
121C4×C43⋊C8—21no—
122C4×C43⋊C8C2311yescharacteristic
123C4×C43⋊C8C2311yescharacteristic
124C8×Dic43—21no—
125C8×Dic43C2×C411yescharacteristic
126C8×Dic43C2×C411yescharacteristic
127C2×M16×C43—21no—
128C2×M16×C43C2×C411yescharacteristic
129C2×M16×C43C2×C411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43C2×C411yescharacteristic
139#97×C43C2×C411yescharacteristic
140C4×C8×C43C2311yescharacteristic
141C4×C8×C43C2311yescharacteristic
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×Q811yescharacteristic
145C2×C22⋊D43C4⋊C411yescharacteristic
146C2×C22⋊D43C4⋊C411yescharacteristic
147#10621898—42no—
148C2×D172C4⋊C411yescharacteristic
149C2×C4×D43C22×C411yescharacteristic
150C2×C4×D43C22×C411yescharacteristic
151C2×C4×D43C2×D411yescharacteristic
152C2×C4×D43C2×D411yescharacteristic
153C2×C4×D43C2×Q811yescharacteristic
154C2×C4×D43C2×Q811yescharacteristic
155C2×Dic86C4⋊C411yescharacteristic
156M16×C43—22no—
157M16×C43—41no—
158M16×C43—81no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43C22×C411yescharacteristic
164C2×C8×C43C22×C411yescharacteristic
165C2×C8×C43C22×C411yescharacteristic
166C2×C8×C43C22×C411yescharacteristic
167C42×C43C22×C411yescharacteristic
168C42×C43C2×D411yescharacteristic
169C42×C43C2×Q811yescharacteristic
170C42×C43C2411yescharacteristic
171C22⋊Dic43C4⋊C411yescharacteristic
172C22⋊Dic43C4⋊C411yescharacteristic
173(C2×D43)⋊C4C4⋊C411yescharacteristic
174(C2×D43)⋊C4C4⋊C411yescharacteristic
175(C2×D43)⋊C4C4⋊C411yescharacteristic
176(C2×D43)⋊C4C4⋊C411yescharacteristic
177C4⋊Dic43C4⋊C411yescharacteristic
178C4⋊Dic43C4⋊C411yescharacteristic
179Dic43⋊C4C4⋊C411yescharacteristic
180Dic43⋊C4C4⋊C411yescharacteristic
181Dic43⋊C4C4⋊C411yescharacteristic
182Dic43⋊C4C4⋊C411yescharacteristic
183C4×Dic43C22×C411yescharacteristic
184C4×Dic43C22×C411yescharacteristic
185C4×Dic43C2×D411yescharacteristic
186C4×Dic43C2×D411yescharacteristic
187C4×Dic43C2×Q811yescharacteristic
188C4×Dic43C2×Q811yescharacteristic
189C2×C43⋊C8—21no—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—81no—
194C2×C43⋊C8C22×C411yescharacteristic
195C2×C43⋊C8C22×C411yescharacteristic
196C2×C43⋊C8C22×C411yescharacteristic
197C2×C43⋊C8C22×C411yescharacteristic
198#10621872—22no—
199#10621872—41no—
200#10621872—81no—
201C8×D43—22no—
202C8×D43—41no—
203C8×D43—81no—
204C8×D43—81no—
205C8×D43—81no—
206C23×C43C2×C4⋊C411yescharacteristic
207C22×D43C2×C4⋊C411yescharacteristic
208C22×D43C2×C4⋊C411yescharacteristic
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—41no—
214C2×C4×C43C2×C4⋊C411yescharacteristic
215C2×C4×C43C2×C4⋊C411yescharacteristic
216C2×C4×C43C2×C4⋊C411yescharacteristic
217C2×C4×C43C23×C411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×Q811yescharacteristic
220C22⋊D43—22no—
221C22⋊D43—41no—
222C2×Dic43C2×C4⋊C411yescharacteristic
223C2×Dic43C2×C4⋊C411yescharacteristic
224C2×Dic43C2×C4⋊C411yescharacteristic
225C2×Dic43C2×C4⋊C411yescharacteristic
226C2×Dic43C2×C4⋊C411yescharacteristic
227C2×Dic43C2×C4⋊C411yescharacteristic
228D172—22no—
229C4×D43—22no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—21no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—41no—
239Dic86—41no—
240C8×C43—21no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43#13112yes—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256#17840—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43C22×C4⋊C411yescharacteristic
261C2×D43—21no—
262C2×D43—21no—
263C2×D43—21no—
264C2×D43—21no—
265C2×D43—21no—
266C2×D43#43012yes—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43C2×#13111yescharacteristic
272C4×C43#56811yescharacteristic
273C4×C43#57611yescharacteristic
274C4×C43#57811yescharacteristic
275Dic43—21no—
276Dic43—21no—
277Dic43—21no—
278Dic43—21no—
279Dic43—21no—
280Dic43—21no—
281#2990—431no—
282#2990—431no—
283#2965—431no—
284#1573—431no—
285#1573—431no—
286#1572—431no—
287#1572—431no—
288#1571—431no—
289#1571—431no—
290#1569—431no—
291#1569D4311yescharacteristic, complemented
292#1568—431no—
293#1565—431no—
294#1565—431no—
295C2×#335—431no—
296C2×C43—41no—
297C2×C43#290611yescharacteristic
298C2×C43#291311yescharacteristic
299C2×C43C2×#43011yescharacteristic
300D43—22no—
301D43—41no—
302C4×#41—431no—
303#446—431no—
304#446—431no—
305#446—861no—
306#446—861no—
307#436—431no—
308#436—431no—
309#435—431no—
310#435—431no—
311#435—431no—
312#435—431no—
313#435—861no—
314#435—861no—
315#435—861no—
316#435—861no—
317C8×D4—861no—
318C8×D4—861no—
319#432—431no—
320#432—431no—
321#432—431no—
322#432C2×D4311yescharacteristic
323#431—431no—
324#431—431no—
325#431—431no—
326#431—431no—
327#431—431no—
328#423—431no—
329#423C2×D4311yescharacteristic
330C2×C4⋊C8—431no—
331C2×C4⋊C8—431no—
332C2×C4⋊C8—431no—
333C2×C4⋊C8—431no—
334C4×M16—431no—
335C4×M16C2×D4311yescharacteristic
336C2×C4×C8—431no—
337#335—431no—
338#335—431no—
339#335—431no—
340#335—431no—
341#335—431no—
342#335—431no—
343#335—431no—
344#335—431no—
345#335C2×D4311yescharacteristic
346#335C2×D4311yescharacteristic
347#334—431no—
348#334—431no—
349#334—431no—
350#334—431no—
351#334C2×D4311yescharacteristic
352#334C2×D4311yescharacteristic
353C43#1784011yescharacteristic, complemented, Sylow
354C2×#41—431no—
355C2×M16—21no—
356C2×M16—431no—
357C2×M16—431no—
358C2×M16—861no—
359C2×M16C4×D4311yescharacteristic
360C2×M16C4×D4311yescharacteristic
361C22×C8—431no—
362C22×C8—431no—
363C22×C8—861no—
364C22×C8—861no—
365C22×C8—861no—
366C22×C8—861no—
367C4×Q8—431no—
368C4×Q8—431no—
369C4×D4—431no—
370C4×D4—431no—
371C4×D4—431no—
372C4×D4—431no—
373C4×D4—431no—
374C4×D4—431no—
375#117—431no—
376#117—431no—
377#117—431no—
378C2×C42—431no—
379C2×C42—431no—
380C2×C42C22×D4311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8—861no—
396C4⋊C8—861no—
397C4⋊C8C22×D4311yescharacteristic
398C4⋊C8C22×D4311yescharacteristic
399C4⋊C8C22×D4311yescharacteristic
400C4⋊C8C22×D4311yescharacteristic
401C22⋊C8—21no—
402C22⋊C8—431no—
403C22⋊C8—431no—
404C22⋊C8—431no—
405C22⋊C8—431no—
406C22⋊C8—431no—
407C22⋊C8—431no—
408C22⋊C8—861no—
409C22⋊C8—861no—
410C22⋊C8—861no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413#97—21no—
414#97—431no—
415#97—431no—
416#97—861no—
417#97—861no—
418#97—861no—
419#97C4×D4311yescharacteristic
420#97C4×D4311yescharacteristic
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8—861no—
427C4×C8C22×D4311yescharacteristic
428C4×C8C22×D4311yescharacteristic
429#41—1722no—
430C2×Q8—431no—
431C2×D4—431no—
432C2×D4—431no—
433C2×D4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4C2×C4×D4311yescharacteristic
441C22×C4D4×D4311yescharacteristic
442C22×C4Q8×D4311yescharacteristic
443M16—22no—
444M16—41no—
445M16—81no—
446M16—862no—
447M16—3441no—
448M16—1721no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—862no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C2×C8—3441no—
464C2×C8—3441no—
465C2×C8—3441no—
466C2×C8—1721no—
467C2×C8C2×C4×D4311yescharacteristic
468C2×C8C2×C4×D4311yescharacteristic
469C2×C8C2×C4×D4311yescharacteristic
470C2×C8C2×C4×D4311yescharacteristic
471C4⋊C4—431no—
472C4⋊C4—431no—
473C4⋊C4—431no—
474C4⋊C4—431no—
475C4⋊C4—431no—
476C4⋊C4—431no—
477C22⋊C4—431no—
478C22⋊C4—431no—
479C22⋊C4—431no—
480C22⋊C4—431no—
481C22⋊C4—431no—
482C22⋊C4—431no—
483C42—431no—
484C42—431no—
485C42—431no—
486C42—431no—
487C42—431no—
488C42—431no—
489C42C2×C4×D4311yescharacteristic
490C42D4×D4311yescharacteristic
491C42Q8×D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—431no—
494C23—431no—
495C23C4⋊C4×D4311yescharacteristic
496Q8—1721no—
497D4—862no—
498D4—862no—
499D4—1721no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—431no—
506C2×C4—431no—
507C2×C4—431no—
508C2×C4—431no—
509C2×C4—431no—
510C2×C4—431no—
511C2×C4—862no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—1721no—
521C2×C4C4⋊C4×D4311yescharacteristic
522C2×C4C4⋊C4×D4311yescharacteristic
523C2×C4C4⋊C4×D4311yescharacteristic
524C2×C4C22×C4×D4311yescharacteristic
525C2×C4C2×D4×D4311yescharacteristic
526C2×C4C2×Q8×D4311yescharacteristic
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C8#1306333312yes—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—432no—
547C22—861no—
548C22—861no—
549C22—861no—
550C22—861no—
551C22—861no—
552C22C2×C4⋊C4×D4311yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—861no—
558C4—861no—
559C4—861no—
560C4—861no—
561C4—861no—
562C4—861no—
563C4C2×#1306333311yescharacteristic
564C4#1458366511yescharacteristic
565C4#1458370311yescharacteristic
566C4#1458371511yescharacteristic
567C2—41no—
568C2—862no—
569C2—1721no—
570C2#1914316411yescharacteristic
571C2#1914319411yescharacteristic
572C2#430×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1569C2
socleC22×C43C22×C4⋊C4
prime radicalC2×#10621898Q8
cosocleC42×C43C24
hypercenter#1569D43
hypocenterC43#17840
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
4. #19133379C2semidirect
5. #19133377C2semidirect
6. #19133376C2semidirect
7. #19133372C2semidirect
8. #19133371C2semidirect
9. #19133368C2semidirect
10. #19133361C2semidirect
11. #19133355C2semidirect
12. #19133347C2semidirect
13. #19133344C2semidirect
14. #335×D43C2semidirect
15. C43×#1569C2semidirect
291. #1569D43semidirect
353. C43#17840semidirect

Maximal subgroups

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

subgroupindex
#191437222
#191437212
#191435572
#191333792
#191333772
#191333762
#191333722
#191333712
#191333682
#191333612
#191333552
#191333472
#191333442
#335×D432
C43×#15692
#1784043