Finite Group Databasebeta

← #24988266

Subgroups — #24988266

Order 11008.

1034 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583553C211yesmaximal, characteristic
2#19134679C212yesmaximal, complemented
3#19133162C212yesmaximal, complemented
4#19132913C211yesmaximal, characteristic, complemented
5C43×#1799C211yesmaximal, characteristic, complemented
6C22×#10621900—21no—
7#14583553—24no—
8#14583553—24no—
9C2×#13063325C411yescharacteristic, complemented
10C2×#13063309—21no—
11C2×#13063309—21no—
12C2×#13063305—21no—
13C2×#13063299C411yescharacteristic, complemented
14C2×#13063299C2211yescharacteristic
15C2×C4×D172C411yescharacteristic, complemented
16C22×C4⋊Dic43C411yescharacteristic, complemented
17C22×C4⋊Dic43C2211yescharacteristic
18C2×C22⋊(C43⋊C8)C2212yes—
19#14582661—24no—
20#14582632—24no—
21#14582625—21no—
22#14582623—21no—
23C2×C4×D4×C43C2211yescharacteristic
24C2×#99×C43—21no—
25C43×#380C2212yes—
26C43×#342—21no—
27C2×#10621900—28no—
28C2×#10621900—44no—
29C2×#10621900—42no—
30C2×#10621900—42no—
31C22×Dic86—21no—
32C22×D172C2×C411yescharacteristic
33C22×C22⋊D43—21no—
34C22×C22⋊D43—21no—
35C23×Dic43—21no—
36C23×Dic43—21no—
37C22×C4×D43—21no—
38C22×C43⋊C8—22no—
39#13063325—22no—
40#13063325—22no—
41#13063309—28no—
42#13063309—28no—
43#13063305—28no—
44#13063299—22no—
45#13063299—22no—
46#13063299—22no—
47#13063299D414yes—
48C4×D172—22no—
49C4×D172—22no—
50C2×C4⋊Dic43—21no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—22no—
55C2×C4⋊Dic43—22no—
56C2×C4⋊Dic43C2×C411yescharacteristic
57C2×C4⋊Dic43C2×C411yescharacteristic
58C2×C4⋊Dic43C2×C411yescharacteristic
59C2×C4⋊Dic43D414yes—
60C2×(C2×D43)⋊C4—21no—
61C2×(C2×D43)⋊C4—21no—
62C2×(C2×D43)⋊C4—21no—
63C22⋊(C43⋊C8)—22no—
64C22⋊(C43⋊C8)—22no—
65C22×D4×C43D411yescharacteristic
66C23×C4×C43C2×C411yescharacteristic
67C23×C4×C43C2311yescharacteristic
68C4×D4×C43—22no—
69C4×D4×C43—22no—
70C2×C4⋊C4×C43—22no—
71C2×C4⋊C4×C43D411yescharacteristic
72C2×C22⋊C4×C43—22no—
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43D411yescharacteristic
75C2×C42×C43C2×C411yescharacteristic
76#99×C43—42no—
77#95×C43—22no—
78C24×C43C22⋊C411yescharacteristic
79C24×C43C2×D411yescharacteristic
80C23×D43—21no—
81C2×D4×C43—22no—
82C2×D4×C43—22no—
83C2×D4×C43D812yes—
84C2×D4×C43SD1612yes—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—42no—
88C22×C4×C43—42no—
89C22×C4×C43—42no—
90C22×C4×C43C22⋊C411yescharacteristic
91C22×C4×C43C22⋊C411yescharacteristic
92C22×C4×C43C22⋊C411yescharacteristic
93C22×C4×C43C22×C411yescharacteristic
94C22×C4×C43C2×D411yescharacteristic
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C2×C22⋊D43—24no—
98C2×C22⋊D43—24no—
99C2×C22⋊D43—42no—
100C2×C22⋊D43—42no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—42no—
104C22×Dic43—24no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—24no—
109C22×Dic43—42no—
110C22×Dic43—42no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—42no—
114#10621900—416no—
115#10621900—416no—
116C2×D172—21no—
117C2×D172—42no—
118C2×D172C22⋊C412yes—
119C2×C4×D43—24no—
120C2×C4×D43—42no—
121C2×C4×D43—42no—
122C2×Dic86—24no—
123C2×Dic86—42no—
124C2×Dic86—42no—
125C4⋊C4×C43—22no—
126C4⋊C4×C43—44no—
127C22⋊C4×C43—22no—
128C22⋊C4×C43—22no—
129C22⋊C4×C43—42no—
130C22⋊C4×C43—42no—
131C42×C43—21no—
132C42×C43—21no—
133(C2×D43)⋊C4—24no—
134(C2×D43)⋊C4—24no—
135(C2×D43)⋊C4—24no—
136C4⋊Dic43—24no—
137C4⋊Dic43—24no—
138C4⋊Dic43—21no—
139C4⋊Dic43—21no—
140C4⋊Dic43—21no—
141C4⋊Dic43—24no—
142C4⋊Dic43C22⋊C412yes—
143C4⋊Dic43C22⋊C412yes—
144C4⋊Dic43C22⋊C412yes—
145C2×C43⋊C8—44no—
146C2×C43⋊C8—42no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43#10212yes—
154C23×C43C2×C22⋊C411yescharacteristic
155C23×C43#12012yes—
156C23×C43C2×D811yescharacteristic
157C23×C43C2×SD1611yescharacteristic
158C23×C43AGL(1,ℤ/8)12yes—
159C22×D43—22no—
160C22×D43—42no—
161C22×D43—42no—
162C22×D43—41no—
163C22×D43—41no—
164D4×C43—24no—
165D4×C43—24no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—24no—
169C2×C4×C43—22no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—41no—
173C2×C4×C43—42no—
174C2×C4×C43—42no—
175C2×C4×C43—42no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—82no—
179C2×C4×C43—82no—
180C2×C4×C43—82no—
181C2×C4×C43#10212yes—
182C2×C4×C43C2×C22⋊C411yescharacteristic
183C2×C4×C43C2×C22⋊C411yescharacteristic
184C2×C4×C43#12012yes—
185C22⋊D43—48no—
186C22⋊D43—44no—
187C22⋊D43—44no—
188C2×Dic43—22no—
189C2×Dic43—22no—
190C2×Dic43—22no—
191C2×Dic43—48no—
192C2×Dic43—41no—
193C2×Dic43—41no—
194C2×Dic43—41no—
195C2×Dic43—41no—
196C2×Dic43—41no—
197C2×Dic43—41no—
198C2×Dic43—44no—
199C2×Dic43—44no—
200D172—42no—
201D172—42no—
202C4×D43—48no—
203Dic86—48no—
204C43⋊C8—82no—
205#8376—431nomaximal, Sylow
206C22×C43—21no—
207C22×C43—22no—
208C22×C43—21no—
209C22×C43—22no—
210C22×C43—22no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—42no—
214C22×C43—42no—
215C22×C43—42no—
216C22×C43—41no—
217C22×C43—41no—
218C22×C43#37911yescharacteristic
219C22×C43C2×#10211yescharacteristic
220C22×C43#41811yescharacteristic
221C22×C43#44712yes—
222C22×C43#45012yes—
223C2×D43—42no—
224C2×D43—42no—
225C2×D43—42no—
226C2×D43—82no—
227C2×D43—82no—
228C4×C43—22no—
229C4×C43—21no—
230C4×C43—22no—
231C4×C43—41no—
232C4×C43—41no—
233C4×C43—162no—
234C4×C43#41012yes—
235Dic43—42no—
236Dic43—42no—
237Dic43—42no—
238C2×#547—431no—
239#1823—432no—
240#1799D4311yescharacteristic, complemented
241#1519—432no—
242#1459—431no—
243C2×C43—22no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43—22no—
247C2×C43—42no—
248C2×C43#178211yescharacteristic
249C2×C43#178611yescharacteristic
250C2×C43#179611yescharacteristic
251D43—82no—
252C22×#41—861no—
253#547—864no—
254#547—864no—
255C2×C4⋊Q8—431no—
256C2×#123—861no—
257C2×#123—861no—
258C2×C22⋊Q8—861no—
259C2×#121—431no—
260C2×#121—431no—
261C2×C4×D4—431no—
262C2×C4×D4C2×D4311yescharacteristic
263C22×C4⋊C4—431no—
264C22×C4⋊C4—431no—
265C2×#99—21no—
266C2×C22⋊C8—432no—
267#380C2×D4312yes—
268#342—21no—
269#340—864no—
270#327—864no—
271#324—861no—
272#323—861no—
273C43#837611yescharacteristic, complemented, Sylow
274C2×#41—868no—
275C2×#41—1724no—
276C2×#41—1722no—
277C2×#41—1722no—
278C22×Q8—861no—
279C22×D4—431no—
280C22×D4—861no—
281C22×D4—861no—
282C22×D4C22⋊D4311yescharacteristic
283C23×C4—861no—
284C23×C4—861no—
285C23×C4—861no—
286C23×C4C4×D4311yescharacteristic
287C23×C4C22×D4311yescharacteristic
288C22×C8—862no—
289C4⋊Q8—862no—
290C4⋊Q8—862no—
291#123—868no—
292#123—868no—
293C22⋊Q8—868no—
294#121—434no—
295#121—862no—
296#121—862no—
297#121—862no—
298C4×D4—22no—
299C4×D4—22no—
300C4×D4—862no—
301C4×D4—862no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—431no—
304C2×C4⋊C4—431no—
305C2×C4⋊C4—431no—
306C2×C4⋊C4—434no—
307C2×C4⋊C4—862no—
308C2×C4⋊C4—862no—
309C2×C4⋊C4—861no—
310C2×C4⋊C4—861no—
311C2×C4⋊C4—861no—
312C2×C4⋊C4—862no—
313C2×C4⋊C4D17211yescharacteristic
314C2×C22⋊C4—22no—
315C2×C22⋊C4—861no—
316C2×C22⋊C4—861no—
317C2×C22⋊C4—861no—
318C2×C22⋊C4D17211yescharacteristic
319C2×C22⋊C4C22⋊D4311yescharacteristic
320C2×C42C4×D4311yescharacteristic
321#99—42no—
322C22⋊C8—862no—
323C22⋊C8—862no—
324#95—22no—
325C24—861no—
326C24(C2×D43)⋊C411yescharacteristic
327C24C2×C22⋊D4311yescharacteristic
328#41—17216no—
329#41—17216no—
330C2×Q8—864no—
331C2×Q8—1722no—
332C2×Q8—1722no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—432no—
336C2×D4—864no—
337C2×D4—864no—
338C2×D4—861no—
339C2×D4—1722no—
340C2×D4—1722no—
341C2×D4—1722no—
342C2×D4—1721no—
343C2×D4—1721no—
344C2×D4—1722no—
345C2×D4#1062188212yes—
346C2×D4#1062188412yes—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—864no—
353C22×C4—864no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—864no—
358C22×C4—1722no—
359C22×C4—1722no—
360C22×C4—1722no—
361C22×C4—1721no—
362C22×C4—1721no—
363C22×C4—1722no—
364C22×C4—1722no—
365C22×C4(C2×D43)⋊C411yescharacteristic
366C22×C4(C2×D43)⋊C411yescharacteristic
367C22×C4(C2×D43)⋊C411yescharacteristic
368C22×C4C2×C4×D4311yescharacteristic
369C22×C4C2×D17211yescharacteristic
370C22×C4D4×D4312yes—
371C22×C4D4×D4312yes—
372C2×C8—1724no—
373C2×C8—1722no—
374C4⋊C4—22no—
375C4⋊C4—44no—
376C4⋊C4—432no—
377C4⋊C4—432no—
378C4⋊C4—432no—
379C4⋊C4—864no—
380C4⋊C4—864no—
381C4⋊C4—861no—
382C4⋊C4—861no—
383C4⋊C4—861no—
384C4⋊C4—864no—
385C22⋊C4—22no—
386C22⋊C4—22no—
387C22⋊C4—42no—
388C22⋊C4—42no—
389C22⋊C4—864no—
390C22⋊C4—864no—
391C22⋊C4—864no—
392C42—21no—
393C42—21no—
394C23—21no—
395C23—21no—
396C23—41no—
397C23—41no—
398C23—41no—
399C23—41no—
400C23—862no—
401C23—1722no—
402C23—1722no—
403C23—1721no—
404C23—1721no—
405C23#1306324512yes—
406C23C2×(C2×D43)⋊C411yescharacteristic
407C23#1306329312yes—
408C23C2×#1062188211yescharacteristic
409C23C2×#1062188411yescharacteristic
410C23#1306335012yes—
411Q8—1728no—
412D4—24no—
413D4—24no—
414D4—1722no—
415D4—1728no—
416D4—1724no—
417D4—1724no—
418D4—1722no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—24no—
422C2×C4—22no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—82no—
432C2×C4—82no—
433C2×C4—82no—
434C2×C4—862no—
435C2×C4—862no—
436C2×C4—862no—
437C2×C4—1728no—
438C2×C4—1728no—
439C2×C4—1724no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4—1721no—
445C2×C4—1721no—
446C2×C4—1724no—
447C2×C4#1306324512yes—
448C2×C4C22⋊C4×D4311yescharacteristic
449C2×C4C22⋊C4×D4311yescharacteristic
450C2×C4#1306329512yes—
451C8—3442no—
452C22—21no—
453C22—22no—
454C22—21no—
455C22—22no—
456C22—22no—
457C22—41no—
458C22—41no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—41no—
463C22—41no—
464C22—3442no—
465C22—3442no—
466C22—1722no—
467C22—1722no—
468C22—1722no—
469C22#1458275411yescharacteristic
470C22C2×#1306324511yescharacteristic
471C22#1458290311yescharacteristic
472C22#1458303212yes—
473C22#1458304912yes—
474C4—22no—
475C4—21no—
476C4—22no—
477C4—41no—
478C4—41no—
479C4—162no—
480C4—1722no—
481C4—1722no—
482C4—1722no—
483C4#1458287112yes—
484C2—22no—
485C2—21no—
486C2—21no—
487C2—22no—
488C2—42no—
489C2—3442no—
490C2#1913451111yescharacteristic
491C2#1913452511yescharacteristic
492C2#1913456811yescharacteristic
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1799C2
socleC22×C43#379
prime radicalC2×#14583553C2
cosocleC23×C4×C43C23
hypercenter#1799D43
hypocenterC43#8376
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
2. #19134679C2semidirect
3. #19133162C2semidirect
4. #19132913C2semidirect
5. C43×#1799C2semidirect
9. C2×#13063325C4semidirect
13. C2×#13063299C4semidirect
15. C2×C4×D172C4semidirect
16. C22×C4⋊Dic43C4semidirect
240. #1799D43semidirect
273. C43#8376semidirect

Maximal subgroups

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

subgroupindex
C2×#145835532
#191346792
#191331622
#191329132
C43×#17992
#837643