Finite Group Databasebeta

← #25106344

Subgroups — #25106344

Order 11008.

1118 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583434C211yesmaximal, characteristic
2C2×#14582954C211yesmaximal, characteristic, complemented
3#19137000C211yesmaximal, characteristic, complemented
4#19135565C211yesmaximal, characteristic, complemented
5#19135411C211yesmaximal, characteristic, complemented
6#19135409C211yesmaximal, characteristic, complemented
7#19134916C212yesmaximal
8#19134906C212yesmaximal, complemented
9#19134609C212yesmaximal, complemented
10#19134604C212yesmaximal, complemented
11C43×#1992C211yesmaximal, characteristic, complemented
12#14583434—24no—
13#14583434C418yescomplemented
14C2×#13063320—21no—
15C2×#13063313C2211yescharacteristic
16C2×#13063310—21no—
17C2×#13063305C2211yescharacteristic
18C2×#13063300C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063287—21no—
21C2×#13063287C2211yescharacteristic
22C2×#13063283—21no—
23C2×#13063283C2212yes—
24C2×C42×D43C2211yescharacteristic
25#14582954—24no—
26C2×Dic43⋊C8C2212yes—
27C2×#13063250C2212yes—
28C2×#13063248C2212yes—
29C2×#13063247C2212yes—
30C2×#13063245C2212yes—
31C2×(C2×D43)⋊C8C2212yes—
32C2×#13063236C2211yescharacteristic
33#14582769C2211yescharacteristic
34#14582764C2212yes—
35#14582756—21no—
36#14582756—21no—
37C4⋊C4×Dic43—21no—
38C4⋊C4×Dic43—21no—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×#125×C43C2211yescharacteristic
42C2×#97×C43C2211yescharacteristic
43C43×#384C2211yescharacteristic
44C43×#340C2212yes—
45C43×#340C2212yes—
46C22×Dic86C2311yescharacteristic
47C22×D172—21no—
48C22×D172C2311yescharacteristic
49C22×C4×D43—21no—
50C22×C4×D43D411yescharacteristic
51C22×C4×D43D411yescharacteristic
52C22×C4×D43C2311yescharacteristic
53C22×C43⋊C8C2312yes—
54#13063320—28no—
55#13063313—22no—
56#13063313C2×C414yes—
57#13063310—28no—
58#13063305—22no—
59#13063305C2×C414yes—
60#13063300—22no—
61#13063300C2×C414yes—
62#13063290—22no—
63#13063290C2×C414yes—
64#13063287—28no—
65#13063287—22no—
66#13063287C2×C414yes—
67#13063283—28no—
68#13063283—42no—
69#13063283—42no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2312yes—
74C2×Dic43⋊C4—21no—
75C2×(C2×D43)⋊C4—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—22no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43C2×C414yes—
87C42×D43D414yes—
88Dic43⋊C8—24no—
89#13063250—42no—
90#13063248—42no—
91#13063247—42no—
92#13063245—42no—
93(C2×D43)⋊C8—24no—
94#13063236—22no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C22×C8×C43C2312yes—
98#125×C43—22no—
99#125×C43C2×C414yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C4⋊C4×C43C2311yescharacteristic
107C2×C42×C43C2311yescharacteristic
108#97×C43—22no—
109C23×D43—21no—
110C23×D43C2×D411yescharacteristic
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2411yescharacteristic
117C22×Dic43—21no—
118C22×Dic43—22no—
119C22×Dic43C2×D411yescharacteristic
120C22×Dic43C2×D411yescharacteristic
121C22×Dic43C2×D411yescharacteristic
122C2×D172—21no—
123C2×D172—24no—
124C2×D172—22no—
125C2×D172—22no—
126C2×D172—42no—
127C2×D172—42no—
128C2×D172C22×C412yes—
129C2×C4×D43—22no—
130C2×C4×D43—22no—
131C2×C4×D43—24no—
132C2×C4×D43—41no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43—42no—
137C2×C4×D43—42no—
138C2×C4×D43C22⋊C414yes—
139C2×C4×D43C22⋊C414yes—
140C2×C4×D43C22×C412yes—
141C2×C4×D43C2×D412yes—
142C2×Dic86—22no—
143C2×Dic86—22no—
144C2×Dic86—21no—
145C2×Dic86C22×C412yes—
146C2×C8×C43—22no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C4⋊C4×C43—24no—
150C4⋊C4×C43—24no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—42no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43C22×C412yes—
158C4⋊C4×C43C22×C412yes—
159C42×C43C22×C412yes—
160C42×C43C2×D412yes—
161(C2×D43)⋊C4—24no—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—44no—
167C4⋊Dic43—24no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43—42no—
171C4⋊Dic43—42no—
172Dic43⋊C4—24no—
173C4×Dic43—24no—
174C4×Dic43—44no—
175C4×Dic43C22⋊C414yes—
176C4×Dic43C22⋊C414yes—
177C4×Dic43C22×C412yes—
178C4×Dic43C2×D412yes—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C23×C43C22×D411yescharacteristic
183C22×D43—21no—
184C22×D43—21no—
185C22×D43—21no—
186C22×D43—21no—
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—22no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—41no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43C2×C22⋊C412yes—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—22no—
202C2×C4×C43—22no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43C2×C22⋊C412yes—
211C2×C4×C43C2×C22⋊C412yes—
212C2×C4×C43C23×C411yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43H(5,𝔽2)12yes—
215C2×C4×C432−1+412yes—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—22no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—42no—
226C2×Dic43—42no—
227C2×Dic43—42no—
228C2×Dic43C2×C22⋊C412yes—
229C2×Dic43C2×C22⋊C412yes—
230C2×Dic43C2×C22⋊C412yes—
231D172—24no—
232D172—48no—
233D172—42no—
234C4×D43—24no—
235C4×D43—24no—
236C4×D43—44no—
237C4×D43—44no—
238C4×D43—48no—
239Dic86—24no—
240Dic86—42no—
241C8×C43—42no—
242C43⋊C8—42no—
243#21868—431nomaximal, Sylow
244C22×C43C22×C22⋊C411yescharacteristic
245C22×C43#53511yescharacteristic
246C22×C43#53611yescharacteristic
247C22×C43#57511yescharacteristic
248C22×C43#57511yescharacteristic
249C22×C43#57511yescharacteristic
250C22×C43#57511yescharacteristic
251C2×D43—22no—
252C2×D43—22no—
253C2×D43—22no—
254C2×D43—41no—
255C2×D43—41no—
256C2×D43—41no—
257C2×D43—41no—
258C2×D43—42no—
259C2×D43—42no—
260C2×D43—42no—
261C2×D43—81no—
262C2×D43—81no—
263C2×D43—81no—
264C2×D43—81no—
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—82no—
270C4×C43#52012yes—
271C4×C43#53712yes—
272Dic43—22no—
273Dic43—22no—
274Dic43—22no—
275Dic43—42no—
276Dic43—82no—
277C2×#529—431no—
278C2×#432—431no—
279#2285—431no—
280#1992—431no—
281#1992D4311yescharacteristic, complemented
282#1959—431no—
283#1959—431no—
284#1875—432no—
285#1873—432no—
286#1805—432no—
287#1804—432no—
288C2×C43#231111yescharacteristic
289C2×C43#289611yescharacteristic
290C2×C43#289611yescharacteristic
291C2×C43#321911yescharacteristic
292C2×C43#321911yescharacteristic
293C2×C43#324011yescharacteristic
294C2×C43#324011yescharacteristic
295D43—42no—
296D43—82no—
297#529—438no—
298#529—864no—
299C2×#126—861no—
300C2×#125C2×D4311yescharacteristic
301C2×#124—431no—
302C2×#123—861no—
303C2×C22⋊Q8—431no—
304C2×#121—431no—
305C2×C4×Q8—431no—
306C2×C4×D4—431no—
307C2×C4×D4—861no—
308C2×#117—432no—
309C2×#117—861no—
310C22×C42—431no—
311#432—864no—
312C2×C4⋊C8—432no—
313C2×#103—432no—
314C2×#103—432no—
315C2×#102—432no—
316C2×#102—432no—
317C2×C22⋊C8—432no—
318C2×#97—431no—
319C2×#97C2×D4311yescharacteristic
320#384—431no—
321#384C2×D4311yescharacteristic
322#382—432no—
323#380—861no—
324#380—861no—
325C4×C4⋊C4—861no—
326C4×C4⋊C4—861no—
327#340—432no—
328#340—432no—
329#340C2×D4312yes—
330#340C2×D4312yes—
331C43#2186811yescharacteristic, complemented, Sylow
332C22×Q8—431no—
333C22×D4—431no—
334C22×D4—861no—
335C23×C4—431no—
336C23×C4—431no—
337C23×C4—431no—
338C23×C4—861no—
339C22×C8—432no—
340C22×C8C22×D4312yes—
341#126—868no—
342#125—22no—
343#125C4×D4314yes—
344#124—434no—
345#124—862no—
346#123—868no—
347C22⋊Q8—434no—
348C22⋊Q8—862no—
349#121—434no—
350#121—862no—
351C4×Q8—434no—
352C4×Q8—862no—
353C4×D4—434no—
354C4×D4—862no—
355C4×D4—868no—
356#117—868no—
357#117—1722no—
358#117—1722no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—432no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4C22×D4312yes—
369C2×C4⋊C4C22×D4311yescharacteristic
370C2×C4⋊C4C22×D4311yescharacteristic
371C2×C22⋊C4—861no—
372C2×C22⋊C4—861no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—862no—
377C2×C42—431no—
378C2×C42—431no—
379C2×C42—431no—
380C2×C42—434no—
381C2×C42—434no—
382C2×C42—861no—
383C2×C42—862no—
384C2×C42C22×D4311yescharacteristic
385C4⋊C8—864no—
386#103—1722no—
387#103—1722no—
388#102—1722no—
389#102—1722no—
390C22⋊C8—864no—
391#97—22no—
392#97—862no—
393#95—862no—
394#95—862no—
395C24—431no—
396C24—861no—
397C2×Q8—432no—
398C2×Q8—861no—
399C2×Q8—862no—
400C2×Q8—862no—
401C2×D4—432no—
402C2×D4—864no—
403C2×D4—861no—
404C2×D4—862no—
405C2×D4—862no—
406C2×D4—1722no—
407C2×D4—1722no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—431no—
412C22×C4—431no—
413C22×C4—431no—
414C22×C4—432no—
415C22×C4—432no—
416C22×C4—434no—
417C22×C4—434no—
418C22×C4—864no—
419C22×C4—862no—
420C22×C4—862no—
421C22×C4—861no—
422C22×C4—862no—
423C22×C4—1721no—
424C22×C4—1721no—
425C22×C4—1721no—
426C22×C4—1721no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—862no—
436C2×C8—862no—
437C2×C8—862no—
438C4⋊C4—24no—
439C4⋊C4—24no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—42no—
445C4⋊C4—42no—
446C4⋊C4—864no—
447C4⋊C4—864no—
448C4⋊C4—862no—
449C4⋊C4—862no—
450C4⋊C4—1722no—
451C4⋊C4—1722no—
452C4⋊C4C2×C4×D4312yes—
453C4⋊C4C2×C4×D4312yes—
454C22⋊C4—864no—
455C22⋊C4—864no—
456C22⋊C4—864no—
457C22⋊C4—864no—
458C22⋊C4—864no—
459C22⋊C4—1724no—
460C42—434no—
461C42—434no—
462C42—432no—
463C42—432no—
464C42—864no—
465C42—1724no—
466C42C2×C4×D4312yes—
467C42D4×D4312yes—
468C23—432no—
469C23—861no—
470C23—861no—
471C23—861no—
472C23—861no—
473C23—861no—
474C23—861no—
475C23—862no—
476C23—1721no—
477C23—1721no—
478C23—1721no—
479C23—1721no—
480C23—1721no—
481C23—1721no—
482C23C2×D4×D4311yescharacteristic
483Q8—864no—
484Q8—1722no—
485D4—864no—
486D4—1728no—
487D4—1722no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—432no—
502C2×C4—432no—
503C2×C4—432no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—864no—
511C2×C4—864no—
512C2×C4—862no—
513C2×C4—1724no—
514C2×C4—1724no—
515C2×C4—1728no—
516C2×C4—1722no—
517C2×C4—1722no—
518C2×C4—1722no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4C22⋊C4×D4312yes—
522C2×C4C22⋊C4×D4312yes—
523C2×C4C22×C4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4#1306337112yes—
526C2×C4#1306337312yes—
527C8—42no—
528C8—1722no—
529C22—862no—
530C22—862no—
531C22—862no—
532C22—3441no—
533C22—3441no—
534C22—3441no—
535C22—3441no—
536C22—1722no—
537C22—1722no—
538C22—1722no—
539C22—1721no—
540C22—1721no—
541C22—1721no—
542C22—1721no—
543C22C2×C22⋊C4×D4311yescharacteristic
544C22#1458346711yescharacteristic
545C22#1458347411yescharacteristic
546C22#1458369511yescharacteristic
547C22#1458369511yescharacteristic
548C22#1458369811yescharacteristic
549C22#1458369811yescharacteristic
550C4—22no—
551C4—22no—
552C4—42no—
553C4—42no—
554C4—82no—
555C4—862no—
556C4—862no—
557C4—862no—
558C4—3442no—
559C4—1722no—
560C4#1458338112yes—
561C4#1458347912yes—
562C2—3442no—
563C2—1722no—
564C2#1913718611yescharacteristic
565C2#1914311111yescharacteristic
566C2#1914311111yescharacteristic
567C2#1914563311yescharacteristic
568C2#1914563511yescharacteristic
569C2#1914583611yescharacteristic
570C2#1914583811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1992C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
cosocleC22×C4×C43C24
hypercenter#1992D43
hypocenterC43#21868
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
2. C2×#14582954C2semidirect
3. #19137000C2semidirect
4. #19135565C2semidirect
5. #19135411C2semidirect
6. #19135409C2semidirect
8. #19134906C2semidirect
9. #19134609C2semidirect
10. #19134604C2semidirect
11. C43×#1992C2semidirect
13. #14583434C4semidirect
281. #1992D43semidirect
331. C43#21868semidirect

Maximal subgroups

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

subgroupindex
C2×#145834342
C2×#145829542
#191370002
#191355652
#191354112
#191354092
#191349162
#191349062
#191346092
#191346042
C43×#19922
#2186843