Finite Group Databasebeta

← #24988444

Subgroups — #24988444

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134579C211yesmaximal, characteristic, complemented
2#19133252C211yesmaximal, characteristic, complemented
3#19133244C211yesmaximal, characteristic, complemented
4#19132998C211yesmaximal, characteristic, complemented
5#19132994C211yesmaximal, characteristic, complemented
6#19132909C211yesmaximal, characteristic, complemented
7C43×#3455C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9#14582952C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×C22⋊(C43⋊C8)—21no—
13#14582654—21no—
14#14582648—21no—
15#14582645—21no—
16#14582645—21no—
17#14582643—21no—
18Q8⋊(C43⋊C8)—22no—
19D4⋊(C43⋊C8)—22no—
20#14582625—21no—
21#14582623—21no—
22C43×#542—21no—
23C43×#542—21no—
24C43×#541—21no—
25C43×#540—21no—
26C43×#539—21no—
27C43×#539C412yes—
28C43×#538—21no—
29C43×#538C412yes—
30C43×#533C2211yescharacteristic
31C43×#532C2211yescharacteristic
32C43×#529—22no—
33C43×#529—22no—
34C43×#525—21no—
35C4×#41×C43—21no—
36C2×#117×C43C2211yescharacteristic
37C22×C43⋊C8—21no—
38C22×C43⋊C8—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—42no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C2×#41×C43—21no—
51C23×C4×C43D411yescharacteristic
52C4⋊Q8×C43D411yescharacteristic
53C4⋊Q8×C43D411yescharacteristic
54C4⋊Q8×C43D411yescharacteristic
55#127×C43D411yescharacteristic
56#126×C43—22no—
57#126×C43—22no—
58#126×C43—22no—
59#126×C43—22no—
60#125×C43—22no—
61#125×C43—22no—
62#125×C43—21no—
63#124×C43—22no—
64#124×C43—22no—
65#124×C43—21no—
66#123×C43—22no—
67#123×C43—22no—
68#123×C43—22no—
69#123×C43—22no—
70#123×C43—22no—
71C22⋊Q8×C43—21no—
72C22⋊Q8×C43—21no—
73C22⋊Q8×C43—22no—
74C22⋊Q8×C43—22no—
75C22⋊Q8×C43—21no—
76C22⋊Q8×C43C2×C412yes—
77#121×C43—21no—
78#121×C43—21no—
79#121×C43—22no—
80#121×C43—22no—
81#121×C43—21no—
82#121×C43C2×C412yes—
83#120×C43—22no—
84C4×Q8×C43—21no—
85C4×Q8×C43—21no—
86C4×Q8×C43—21no—
87C4×Q8×C43D412yes—
88C4×D4×C43—21no—
89C4×D4×C43—21no—
90C4×D4×C43—22no—
91C4×D4×C43—22no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—21no—
95C4×D4×C43D412yes—
96#117×C43—22no—
97#117×C43—21no—
98#117×C43—21no—
99#117×C43—21no—
100#117×C43—21no—
101#117×C43—21no—
102C2×C4⋊C4×C43C2×C411yescharacteristic
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43C2×C411yescharacteristic
105C2×C22⋊C4×C43D411yescharacteristic
106C2×C42×C43—22no—
107C2×C42×C43D411yescharacteristic
108C2×C42×C43C2311yescharacteristic
109C24×C43C22⋊C411yescharacteristic
110#41×C43—41no—
111#41×C43—41no—
112#41×C43—41no—
113#41×C43—41no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43C22⋊C412yes—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—22no—
122C2×D4×C43C22⋊C412yes—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C22⋊C411yescharacteristic
133C22×C4×C43C22⋊C411yescharacteristic
134C22×C4×C43C22⋊C411yescharacteristic
135C22×C4×C43C22×C411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43C22⋊C412yes—
153C4⋊C4×C43C22⋊C412yes—
154C22⋊C4×C43—22no—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—21no—
161C22⋊C4×C43—21no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—21no—
164C22⋊C4×C43—21no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C42×C43—22no—
168C42×C43—22no—
169C42×C43—21no—
170C42×C43—22no—
171C42×C43—21no—
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C2×C43⋊C8—41no—
177C2×C43⋊C8—41no—
178C2×C43⋊C8—41no—
179C2×C43⋊C8—41no—
180C2×C43⋊C8—41no—
181C2×C43⋊C8—41no—
182C2×C43⋊C8—41no—
183C2×C43⋊C8—41no—
184C23×C43—21no—
185C23×C43—22no—
186C23×C43—21no—
187C23×C43—21no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43C2×C22⋊C411yescharacteristic
191Q8×C43—42no—
192Q8×C43—41no—
193Q8×C43—41no—
194Q8×C43—81no—
195D4×C43—42no—
196D4×C43—42no—
197D4×C43—42no—
198D4×C43—41no—
199D4×C43—41no—
200D4×C43—81no—
201D4×C43—82no—
202D4×C43—82no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—82no—
222C2×C4×C43—82no—
223C2×C4×C43C2×C22⋊C411yescharacteristic
224C2×C4×C43C2×C22⋊C411yescharacteristic
225C2×C4×C43#12011yescharacteristic
226C2×C4×C43#12011yescharacteristic
227C2×C4×C43#12011yescharacteristic
228C2×C4×C43#12011yescharacteristic
229C2×C4×C43#13511yescharacteristic
230C2×C4×C43#13511yescharacteristic
231C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
232C2×C4×C43#13711yescharacteristic
233C43⋊C8—81no—
234C43⋊C8—81no—
235C43⋊C8—81no—
236C43⋊C8—81no—
237#8411—431nomaximal, Sylow
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—42no—
241C22×C43—41no—
242C22×C43—42no—
243C22×C43—41no—
244C22×C43—42no—
245C22×C43—41no—
246C22×C43—42no—
247C22×C43—81no—
248C22×C43#37911yescharacteristic
249C22×C43#41611yescharacteristic
250C22×C43#41711yescharacteristic
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—41no—
256C4×C43—42no—
257C4×C43—41no—
258C4×C43—42no—
259C4×C43—41no—
260C4×C43—42no—
261C4×C43#44911yescharacteristic
262C4×C43#44911yescharacteristic
263C4×C43#45211yescharacteristic
264C4×C43#45211yescharacteristic
265#3455D4311yescharacteristic
266#1798—431no—
267#1542—431no—
268#1540—431no—
269#1481—431no—
270#1480—431no—
271#1458—431no—
272C2×C43—21no—
273C2×C43—21no—
274C2×C43—82no—
275C2×C43—81no—
276C2×C43#178811yescharacteristic
277C2×C43#179111yescharacteristic
278C2×C43#179411yescharacteristic
279#542—21no—
280#542—21no—
281#541—21no—
282#540—21no—
283#539—21no—
284#539Dic4312yes—
285#538—21no—
286#538Dic4312yes—
287#533C2×D4311yescharacteristic
288#532C2×D4311yescharacteristic
289#529—22no—
290#529—22no—
291#525—21no—
292C4×#41—21no—
293C2×#117C2×D4311yescharacteristic
294#431—431no—
295#431—431no—
296C2×C4⋊C8—431no—
297C2×C4⋊C8—431no—
298C2×C22⋊C8—861no—
299#336—861no—
300#333—861no—
301#332—861no—
302#332—861no—
303#331—861no—
304Q8⋊C8—862no—
305D4⋊C8—862no—
306#324—861no—
307#323—861no—
308C43#841111yescharacteristic, complemented, Sylow
309C2×#41—21no—
310C23×C4C22⋊D4311yescharacteristic
311C22×C8—861no—
312C22×C8—861no—
313C4⋊Q8C22⋊D4311yescharacteristic
314C4⋊Q8C22⋊D4311yescharacteristic
315C4⋊Q8C22⋊D4311yescharacteristic
316#127C22⋊D4311yescharacteristic
317#126—22no—
318#126—22no—
319#126—22no—
320#126—22no—
321#125—22no—
322#125—22no—
323#125—21no—
324#124—22no—
325#124—22no—
326#124—21no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331#123—22no—
332C22⋊Q8—21no—
333C22⋊Q8—21no—
334C22⋊Q8—22no—
335C22⋊Q8—22no—
336C22⋊Q8—21no—
337C22⋊Q8C2×Dic4312yes—
338#121—21no—
339#121—21no—
340#121—22no—
341#121—22no—
342#121—21no—
343#121C2×Dic4312yes—
344#120—22no—
345C4×Q8—21no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8C22⋊D4312yes—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355C4×D4—21no—
356C4×D4C22⋊D4312yes—
357#117—22no—
358#117—21no—
359#117—21no—
360#117—21no—
361#117—21no—
362#117—21no—
363C2×C4⋊C4C2×Dic4311yescharacteristic
364C2×C4⋊C4C22⋊D4311yescharacteristic
365C2×C22⋊C4C2×Dic4311yescharacteristic
366C2×C22⋊C4C22⋊D4311yescharacteristic
367C2×C42—22no—
368C2×C42C22⋊D4311yescharacteristic
369C2×C42C22×D4311yescharacteristic
370C4⋊C8—861no—
371C4⋊C8—861no—
372C4⋊C8—861no—
373C4⋊C8—861no—
374C4⋊C8—861no—
375C4⋊C8—861no—
376C22⋊C8—861no—
377C22⋊C8—861no—
378C22⋊C8—1722no—
379C4×C8—861no—
380C4×C8—861no—
381C24C22⋊Dic4311yescharacteristic
382#41—41no—
383#41—41no—
384#41—41no—
385#41—41no—
386C2×Q8—21no—
387C2×Q8—21no—
388C2×Q8C22⋊Dic4312yes—
389C2×D4—22no—
390C2×D4—22no—
391C2×D4—22no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4C22⋊Dic4312yes—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4C22⋊Dic4311yescharacteristic
405C22×C4C22⋊Dic4311yescharacteristic
406C22×C4C22⋊Dic4311yescharacteristic
407C22×C4C22×Dic4311yescharacteristic
408C22×C4C2×C22⋊D4311yescharacteristic
409C22×C4C2×C22⋊D4311yescharacteristic
410C2×C8—1721no—
411C2×C8—1721no—
412C2×C8—1721no—
413C2×C8—1721no—
414C2×C8—1721no—
415C2×C8—1721no—
416C2×C8—1721no—
417C2×C8—1721no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—22no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4C22⋊Dic4312yes—
433C4⋊C4C22⋊Dic4312yes—
434C22⋊C4—22no—
435C22⋊C4—22no—
436C22⋊C4—22no—
437C22⋊C4—22no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—21no—
442C22⋊C4—21no—
443C22⋊C4—22no—
444C22⋊C4—21no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—22no—
452C42C2×C22⋊D4311yescharacteristic
453C42C2×C22⋊D4311yescharacteristic
454C42C2×C22⋊D4311yescharacteristic
455C42C2×C22⋊D4311yescharacteristic
456C23—21no—
457C23—21no—
458C23—22no—
459C23—21no—
460C23—41no—
461C23—41no—
462C23C2×C22⋊Dic4311yescharacteristic
463Q8—42no—
464Q8—41no—
465Q8—41no—
466Q8—81no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—41no—
471D4—41no—
472D4—81no—
473D4—82no—
474D4—82no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—42no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4C2×C22⋊Dic4311yescharacteristic
496C2×C4C2×C22⋊Dic4311yescharacteristic
497C2×C4#1306329411yescharacteristic
498C2×C4#1306329411yescharacteristic
499C2×C4#1306329411yescharacteristic
500C2×C4#1306329411yescharacteristic
501C2×C4#1306334511yescharacteristic
502C2×C4#1306334511yescharacteristic
503C2×C4#1306335011yescharacteristic
504C2×C4#1306335511yescharacteristic
505C8—3441no—
506C8—3441no—
507C8—3441no—
508C8—3441no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—41no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22—42no—
517C22—41no—
518C22—81no—
519C22#1458275511yescharacteristic
520C22#1458289511yescharacteristic
521C22#1458290011yescharacteristic
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—41no—
527C4—42no—
528C4—41no—
529C4—42no—
530C4—41no—
531C4—42no—
532C4#1458304411yescharacteristic
533C4#1458304411yescharacteristic
534C4#1458306111yescharacteristic
535C4#1458306111yescharacteristic
536C2—21no—
537C2—21no—
538C2—81no—
539C2—82no—
540C2#1913453511yescharacteristic
541C2#1913454611yescharacteristic
542C2#1913455911yescharacteristic
subgroupG/H
centerC2×C4#13063294
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3455C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3455D43
hypocenterC43#8411
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3455

Complements

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

NH ≅ G/Ntype
1. #19134579C2semidirect
2. #19133252C2semidirect
3. #19133244C2semidirect
4. #19132998C2semidirect
5. #19132994C2semidirect
6. #19132909C2semidirect
308. C43#8411semidirect

Maximal subgroups

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

subgroupindex
#191345792
#191332522
#191332442
#191329982
#191329942
#191329092
C43×#34552
#841143