Finite Group Databasebeta

← #24992196

Subgroups — #24992196

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582851C211yesmaximal, characteristic, complemented
2#19142897C211yesmaximal, characteristic
3#19134358C211yesmaximal, characteristic, complemented
4C2×#14582638C211yesmaximal, characteristic, complemented
5C2×#14582638C211yesmaximal, characteristic, complemented
6#19132476C211yesmaximal, characteristic, complemented
7C43×#1295C211yesmaximal, characteristic, complemented
8C22×#10621872—21no—
9C2×#13063313C2211yescharacteristic
10C2×#13063305C411yescharacteristic
11C2×#13063300C411yescharacteristic
12C2×C42×D43C2211yescharacteristic
13C2×(C2×D43)⋊C8—21no—
14#14582851—22no—
15#14582851—22no—
16C2×#13063236C2211yescharacteristic
17C2×#13063236C2211yescharacteristic
18C2×C8×Dic43—21no—
19#14582804C411yescharacteristic
20#14582800C411yescharacteristic
21#14582791—21no—
22#14582791—21no—
23#14582777—21no—
24#14582777—21no—
25#14582653—21no—
26#14582638—22no—
27#14582638—22no—
28C2×#97×C43C2211yescharacteristic
29C2×#97×C43C2211yescharacteristic
30C43×#382C2211yescharacteristic
31C22×Dic86C2×C411yescharacteristic
32C22×D172—21no—
33C22×D172C2×C411yescharacteristic
34C22×C4×D43C2×C411yescharacteristic
35C22×C4×D43D411yescharacteristic
36C22×C4×D43D411yescharacteristic
37C2×#10621872—24no—
38C2×#10621872—24no—
39C2×#10621872—24no—
40C22×C43⋊C8—21no—
41C22×C43⋊C8—21no—
42#13063313—21no—
43#13063313—21no—
44#13063313—21no—
45#13063313—21no—
46#13063305—42no—
47#13063300—42no—
48C2×C4⋊Dic43—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4—21no—
53C2×(C2×D43)⋊C4—21no—
54C2×(C2×D43)⋊C4—21no—
55C2×C4×Dic43C2×C411yescharacteristic
56C2×C4×Dic43D411yescharacteristic
57C2×C4×Dic43D411yescharacteristic
58C42×D43—21no—
59C42×D43—21no—
60C42×D43—21no—
61C42×D43—21no—
62(C2×D43)⋊C8—24no—
63#13063236—21no—
64#13063236—21no—
65#13063236—21no—
66#13063236D412yescomplemented
67C8×Dic43—24no—
68C43⋊#95—21no—
69C43⋊#95—21no—
70C22×C8×C43—21no—
71C22×C8×C43—21no—
72C2×C4⋊C4×C43C2×C411yescharacteristic
73C2×C4⋊C4×C43C2×C411yescharacteristic
74C2×C42×C43C2311yescharacteristic
75#97×C43—21no—
76#97×C43—21no—
77#97×C43—21no—
78#97×C43D412yescomplemented
79#95×C43—21no—
80#95×C43—21no—
81C23×D43—21no—
82C23×D43C22⋊C411yescharacteristic
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43C22×C411yescharacteristic
86C22×C4×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×Dic43—21no—
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C22×Dic43C22⋊C411yescharacteristic
92C2×D172—21no—
93C2×D172—21no—
94C2×D172—42no—
95C2×D172—42no—
96C2×D172—42no—
97C2×D172—41no—
98C2×D172—41no—
99C2×C4×D43—21no—
100C2×C4×D43—21no—
101C2×C4×D43—22no—
102C2×C4×D43—21no—
103C2×C4×D43—21no—
104C2×C4×D43—21no—
105C2×C4×D43—21no—
106C2×C4×D43—22no—
107C2×C4×D43—22no—
108C2×C4×D43—22no—
109C2×C4×D43—41no—
110C2×C4×D43—41no—
111C2×Dic86—21no—
112C2×Dic86—21no—
113C2×Dic86—41no—
114C2×Dic86—41no—
115C2×C8×C43—22no—
116C2×C8×C43—22no—
117C2×C8×C43—22no—
118C2×C8×C43—22no—
119C2×C8×C43—41no—
120C2×C8×C43—41no—
121C4⋊C4×C43—41no—
122C4⋊C4×C43—41no—
123C42×C43C2×D411yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43#4111yescharacteristic
126C42×C43#4111yescharacteristic
127(C2×D43)⋊C4—42no—
128(C2×D43)⋊C4—41no—
129(C2×D43)⋊C4—41no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—41no—
132(C2×D43)⋊C4—42no—
133(C2×D43)⋊C4—42no—
134(C2×D43)⋊C4—42no—
135C4⋊Dic43—42no—
136C4×Dic43—21no—
137C4×Dic43—21no—
138C4×Dic43—21no—
139C4×Dic43—21no—
140C4×Dic43—21no—
141C4×Dic43—21no—
142C2×C43⋊C8—22no—
143C2×C43⋊C8—22no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—41no—
148#10621872—216no—
149C23×C43C2×C22⋊C411yescharacteristic
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—41no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—41no—
160C22×D43—41no—
161C22×D43—41no—
162C22×D43—41no—
163C22×D43#10412yes—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—41no—
171C2×C4×C43—41no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43C4×D411yescharacteristic
177C2×C4×C43C4×D411yescharacteristic
178C2×C4×C43#12011yescharacteristic
179C2×C4×C43#12111yescharacteristic
180C2×C4×C43#12111yescharacteristic
181C2×C4×C43#12311yescharacteristic
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—41no—
189C2×Dic43—41no—
190C2×Dic43—41no—
191C2×Dic43#10012yes—
192C2×Dic43#10412yes—
193C2×Dic43#10412yes—
194D172—81no—
195D172—81no—
196D172—84no—
197C4×D43—24no—
198C4×D43—24no—
199C4×D43—42no—
200C4×D43—42no—
201C4×D43—42no—
202C4×D43—42no—
203Dic86—81no—
204Dic86—81no—
205C8×C43—24no—
206C8×C43—42no—
207C43⋊C8—24no—
208C43⋊C8—42no—
209#9120—431nomaximal, Sylow
210C22×C43#38611yescharacteristic
211C22×C43C2×#10011yescharacteristic
212C22×C43#41311yescharacteristic
213C22×C43C2×#10411yescharacteristic
214C22×C43C2×#10411yescharacteristic
215C22×C43C2×#10411yescharacteristic
216C22×C43#42111yescharacteristic
217C2×D43—22no—
218C2×D43—22no—
219C2×D43—22no—
220C2×D43—41no—
221C2×D43—41no—
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—81no—
225C2×D43—81no—
226C2×D43—81no—
227C2×D43—81no—
228C2×D43—81no—
229C2×D43—81no—
230C2×D43—81no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—81no—
238C4×C43—81no—
239Dic43—22no—
240Dic43—22no—
241Dic43—22no—
242Dic43—81no—
243C2×C4×M16—431no—
244#2850—431no—
245#1749—431no—
246C2×#329—431no—
247C2×#329—431no—
248#1295—431no—
249#1295D4311yescharacteristic, complemented
250C2×C43#152411yescharacteristic
251C2×C43#152511yescharacteristic
252C2×C43#152711yescharacteristic
253C2×C43#152911yescharacteristic
254C2×C43#187111yescharacteristic
255C2×C43#189611yescharacteristic
256C2×C43#190011yescharacteristic
257D43—42no—
258D43—161no—
259C22×M16—861no—
260C2×#124—431no—
261C2×C22⋊Q8—431no—
262C2×#121—431no—
263C22×C42—431no—
264C2×C22⋊C8—861no—
265C4×M16—862no—
266C4×M16—862no—
267C2×#97—431no—
268C2×#97—431no—
269C2×#97C2×D4311yescharacteristic
270C2×#97C2×D4311yescharacteristic
271C2×C4×C8—861no—
272#391—431no—
273#390—431no—
274#388—861no—
275#388—861no—
276#386—861no—
277#386—861no—
278#382C2×D4311yescharacteristic
279#336—861no—
280#329—862no—
281#329—862no—
282C43#912011yescharacteristic, complemented, Sylow
283C22×Q8—431no—
284C22×D4—431no—
285C22×D4—861no—
286C23×C4—431no—
287C23×C4—431no—
288C23×C4—431no—
289C2×M16—864no—
290C2×M16—864no—
291C2×M16—864no—
292C22×C8—21no—
293C22×C8—21no—
294C22×C8—861no—
295C22×C8—861no—
296#124—861no—
297#124—861no—
298#124—861no—
299#124—861no—
300C22⋊Q8—1722no—
301#121—1722no—
302C2×C4⋊C4—861no—
303C2×C4⋊C4C4×D4311yescharacteristic
304C2×C4⋊C4C4×D4311yescharacteristic
305C2×C22⋊C4—861no—
306C2×C22⋊C4—861no—
307C2×C22⋊C4—861no—
308C2×C22⋊C4—861no—
309C2×C22⋊C4—861no—
310C2×C22⋊C4—861no—
311C2×C42—431no—
312C2×C42—431no—
313C2×C42—431no—
314C2×C42—861no—
315C2×C42—861no—
316C2×C42—861no—
317C2×C42—861no—
318C2×C42C22×D4311yescharacteristic
319C22⋊C8—864no—
320#97—21no—
321#97—21no—
322#97—21no—
323#97—432no—
324#97—861no—
325#97—861no—
326#97—861no—
327#97D17212yescomplemented
328C4×C8—864no—
329#95—21no—
330#95—21no—
331#95—861no—
332#95—861no—
333C24—431no—
334C24—861no—
335C2×Q8—861no—
336C2×Q8—861no—
337C2×Q8—1721no—
338C2×Q8—1721no—
339C2×D4—861no—
340C2×D4—861no—
341C2×D4—1721no—
342C2×D4—1721no—
343C2×D4—1722no—
344C2×D4—1722no—
345C2×D4—1722no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—431no—
349C22×C4—431no—
350C22×C4—431no—
351C22×C4—862no—
352C22×C4—862no—
353C22×C4—862no—
354C22×C4—862no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—861no—
358C22×C4—861no—
359C22×C4—861no—
360C22×C4—861no—
361C22×C4—861no—
362C22×C4—1721no—
363C22×C4—1721no—
364C22×C4C2×C4×D4311yescharacteristic
365C22×C4D4×D4311yescharacteristic
366C22×C4D4×D4311yescharacteristic
367M16—8616no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—862no—
375C2×C8—862no—
376C2×C8—862no—
377C2×C8—862no—
378C2×C8—1721no—
379C2×C8—1721no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—1722no—
383C22⋊C4—1722no—
384C22⋊C4—1722no—
385C22⋊C4—1722no—
386C22⋊C4—1722no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4—1721no—
391C42—861no—
392C42—861no—
393C42—861no—
394C42—861no—
395C42—861no—
396C42—861no—
397C42C2×D17211yescharacteristic
398C42#1062189811yescharacteristic
399C42D4×D4311yescharacteristic
400C42#1062190211yescharacteristic
401C23—432no—
402C23—861no—
403C23—861no—
404C23—861no—
405C23—861no—
406C23—861no—
407C23—861no—
408C23—1721no—
409C23—1721no—
410C23—1721no—
411C23—1721no—
412C23—1721no—
413C23—1721no—
414C23—1721no—
415C23C22⋊C4×D4311yescharacteristic
416Q8—3441no—
417Q8—3441no—
418D4—3441no—
419D4—3441no—
420D4—3444no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—432no—
434C2×C4—432no—
435C2×C4—432no—
436C2×C4—864no—
437C2×C4—864no—
438C2×C4—861no—
439C2×C4—861no—
440C2×C4—861no—
441C2×C4—861no—
442C2×C4—861no—
443C2×C4—861no—
444C2×C4—1722no—
445C2×C4—1722no—
446C2×C4—1722no—
447C2×C4—1722no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1721no—
451C2×C4#1306328711yescharacteristic
452C2×C4C4×D17211yescharacteristic
453C2×C4#1306329511yescharacteristic
454C2×C4#1306329811yescharacteristic
455C2×C4#1306330011yescharacteristic
456C2×C4#1306331011yescharacteristic
457C8—24no—
458C8—42no—
459C8—864no—
460C8—1722no—
461C22—862no—
462C22—862no—
463C22—862no—
464C22—3441no—
465C22—3441no—
466C22—3441no—
467C22—3441no—
468C22—3441no—
469C22—3441no—
470C22—3441no—
471C22—1721no—
472C22—1721no—
473C22—1721no—
474C22—1721no—
475C22#1458277711yescharacteristic
476C22#100×D4311yescharacteristic
477C22#1458288211yescharacteristic
478C22#104×D4311yescharacteristic
479C22#104×D4311yescharacteristic
480C22#104×D4311yescharacteristic
481C22#1458291411yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—21no—
487C4—21no—
488C4—81no—
489C4—81no—
490C4—862no—
491C4—862no—
492C4—862no—
493C4—3441no—
494C2—1722no—
495C2—6881no—
496C2#1913318211yescharacteristic
497C2#1913318511yescharacteristic
498C2#1913319111yescharacteristic
499C2#1913320111yescharacteristic
500C2#1913489611yescharacteristic
501C2#1913503711yescharacteristic
502C2#1913505711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063300C4
cosocleC2×C42×C43C23
hypercenter#1295D43
hypocenterC43#9120
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. C2×#14582851C2semidirect
3. #19134358C2semidirect
4. C2×#14582638C2semidirect
5. C2×#14582638C2semidirect
6. #19132476C2semidirect
7. C43×#1295C2semidirect
66. #13063236D4semidirect
78. #97×C43D4semidirect
249. #1295D43semidirect
282. C43#9120semidirect
327. #97D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145828512
#191428972
#191343582
C2×#145826382
#191324762
C43×#12952
#912043