Finite Group Databasebeta

← #24999969

Subgroups — #24999969

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139594C211yesmaximal, characteristic
2#19135400C211yesmaximal, characteristic
3#19135356C211yesmaximal, characteristic, complemented
4C2×#14582642C211yesmaximal, characteristic
5C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#19132434C211yesmaximal, characteristic, complemented
7C43×#1803C211yesmaximal, characteristic, complemented
8C2×#13063322C2211yescharacteristic
9C2×#13063314—21no—
10C2×#13063256—21no—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063245—22no—
13C2×C4×C43⋊C8C2211yescharacteristic
14#14582816—22no—
15#14582801—21no—
16#14582801—21no—
17#14582800—21no—
18C4×C4⋊Dic43C2211yescharacteristic
19#14582661—21no—
20#14582642—22no—
21Q8⋊(C43⋊C8)—22no—
22C2×C4×Q8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#103×C43—21no—
25C43×#384C2211yescharacteristic
26C43×#340—21no—
27C22×D172—21no—
28C22×D172—21no—
29C22×D172D412yes—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063322—21no—
33#13063322—21no—
34#13063322—21no—
35#13063322—21no—
36#13063314—42no—
37#13063314—42no—
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×(C2×D43)⋊C4—22no—
41C2×(C2×D43)⋊C4—22no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—22no—
44C2×C4×Dic43—21no—
45#13063256—42no—
46C4⋊(C43⋊C8)—21no—
47C4⋊(C43⋊C8)D412yes—
48#13063245—44no—
49C4×C43⋊C8—21no—
50C4×C43⋊C8—21no—
51C43⋊#95—21no—
52C22×Q8×C43D411yescharacteristic
53C22×C8×C43—21no—
54C4×Q8×C43—21no—
55C4×Q8×C43—21no—
56C4×Q8×C43—21no—
57C4×Q8×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C42×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C4⋊C8×C43—21no—
67#103×C43—42no—
68C23×D43—22no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43—21no—
74C2×Q8×C43SD1612yes—
75C22×C4×C43—21no—
76C22×C4×C43—21no—
77C22×C4×C43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×Dic43—21no—
82C22×Dic43—21no—
83C2×D172—22no—
84C2×D172—22no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—42no—
98C2×D172—42no—
99C2×C8×C43—41no—
100C2×C8×C43—41no—
101C2×C8×C43—41no—
102C4⋊C4×C43—21no—
103C4⋊C4×C43—21no—
104C4⋊C4×C43—42no—
105C4⋊C4×C43—41no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—41no—
109C4⋊C4×C43—41no—
110C4⋊C4×C43—41no—
111C42×C43—41no—
112C42×C43—41no—
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C42×C43#4111yescharacteristic
116C42×C43#4111yescharacteristic
117(C2×D43)⋊C4—44no—
118(C2×D43)⋊C4—44no—
119(C2×D43)⋊C4—82no—
120(C2×D43)⋊C4—82no—
121C4⋊Dic43—21no—
122C4⋊Dic43—21no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125C4×Dic43—41no—
126C4×Dic43—41no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133C23×C43#12011yescharacteristic
134C22×D43—42no—
135C22×D43—42no—
136C22×D43—42no—
137C22×D43—42no—
138C22×D43—42no—
139C22×D43—42no—
140C22×D43—42no—
141Q8×C43—22no—
142Q8×C43—22no—
143Q8×C43—41no—
144Q8×C43—41no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—22no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#12111yescharacteristic
159C2×C4×C43#12311yescharacteristic
160C2×C4×C43#12311yescharacteristic
161C2×C4×C43#12411yescharacteristic
162C2×C4×C43C2×SD1611yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43#13511yescharacteristic
165C2×C4×C43#13511yescharacteristic
166C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
169C2×C4×C43#13711yescharacteristic
170C2×Dic43—41no—
171C2×Dic43—41no—
172C2×Dic43—41no—
173C2×Dic43—41no—
174C2×Dic43—41no—
175C2×Dic43—41no—
176D172—44no—
177D172—82no—
178D172—81no—
179D172—81no—
180D172—81no—
181D172—81no—
182D172—81no—
183D172—81no—
184D172—81no—
185D172—81no—
186C8×C43—81no—
187C43⋊C8—42no—
188C43⋊C8—42no—
189#10410—431nomaximal, Sylow
190C22×C43#39411yescharacteristic
191C22×C43#44911yescharacteristic
192C22×C43#44911yescharacteristic
193C22×C43#45011yescharacteristic
194C22×C43#45211yescharacteristic
195C22×C43#45311yescharacteristic
196C22×C43#45511yescharacteristic
197C2×D43—82no—
198C2×D43—82no—
199C2×D43—82no—
200C2×D43—82no—
201C2×D43—82no—
202C2×D43—82no—
203C2×D43—82no—
204C4×C43—21no—
205C4×C43—21no—
206C4×C43—42no—
207C4×C43—81no—
208C4×C43—161no—
209C4×C43#46311yescharacteristic
210C4×C43#46411yescharacteristic
211C4×C43#46511yescharacteristic
212C4×C43#46911yescharacteristic
213C4×C43#48111yescharacteristic
214C4×C43#48211yescharacteristic
215C4×C43#48811yescharacteristic
216C4×C43#48911yescharacteristic
217Dic43—81no—
218Dic43—81no—
219#2548—431no—
220#1957—431no—
221#1948—431no—
222#1803D4311yescharacteristic, complemented
223C2×#331—431no—
224C2×Q8⋊C8—431no—
225#1279—431no—
226C2×C43#162011yescharacteristic
227C2×C43#163111yescharacteristic
228C2×C43#164011yescharacteristic
229C2×C43#164211yescharacteristic
230C2×C43#203411yescharacteristic
231C2×C43#203711yescharacteristic
232C2×C43#204211yescharacteristic
233D43—162no—
234C2×#127—431no—
235C2×#124—861no—
236C2×C4×Q8C2×D4311yescharacteristic
237C2×#106—861no—
238C2×C4⋊C8—431no—
239C2×C4⋊C8C2×D4311yescharacteristic
240C2×#103—21no—
241C2×#102—862no—
242C2×C4×C8—431no—
243#394—862no—
244#390—861no—
245#390—861no—
246#390—861no—
247#384C2×D4311yescharacteristic
248C4×C4⋊C4—431no—
249#340—21no—
250#340—861no—
251#331—862no—
252Q8⋊C8—862no—
253C43#1041011yescharacteristic, complemented, Sylow
254C22×Q8C22⋊D4311yescharacteristic
255C22×D4—432no—
256C22×D4—861no—
257C22×D4—861no—
258C22×C8—21no—
259C22×C8—861no—
260C22×C8—861no—
261#127—861no—
262#127—861no—
263#127—861no—
264#127—861no—
265#124—1722no—
266#124—1722no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4C22⋊D4311yescharacteristic
278C2×C22⋊C4—862no—
279C2×C22⋊C4—862no—
280C2×C22⋊C4—862no—
281C2×C22⋊C4—862no—
282C2×C42—21no—
283C2×C42—861no—
284C2×C42C22×D4311yescharacteristic
285#106—1722no—
286C4⋊C8—21no—
287C4⋊C8—21no—
288C4⋊C8—432no—
289C4⋊C8—861no—
290#103—42no—
291#102—1724no—
292C4×C8—861no—
293C4×C8—861no—
294#95—861no—
295C24—862no—
296C2×Q8—21no—
297C2×Q8—21no—
298C2×Q8—21no—
299C2×Q8—21no—
300C2×Q8—21no—
301C2×Q8#1062188412yes—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—1722no—
305C2×D4—1722no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C2×D4—1721no—
316C2×D4—1721no—
317C2×D4—1721no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—861no—
322C22×C4—861no—
323C22×C4D4×D4311yescharacteristic
324C22×C4D4×D4311yescharacteristic
325C22×C4C2×C22⋊D4311yescharacteristic
326C2×C8—41no—
327C2×C8—41no—
328C2×C8—41no—
329C2×C8—862no—
330C2×C8—862no—
331C2×C8—1721no—
332C2×C8—1721no—
333C2×C8—1721no—
334C2×C8—1721no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—42no—
338C4⋊C4—41no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4—861no—
345C4⋊C4—861no—
346C4⋊C4—861no—
347C4⋊C4—861no—
348C22⋊C4—3442no—
349C22⋊C4—3442no—
350C22⋊C4—1724no—
351C22⋊C4—1724no—
352C42—41no—
353C42—41no—
354C42—1721no—
355C42—1721no—
356C42#1062189811yescharacteristic
357C42#1062189811yescharacteristic
358C42D4×D4311yescharacteristic
359C42#1062190011yescharacteristic
360C23—1722no—
361C23—1722no—
362C23—1722no—
363C23—1722no—
364C23—1722no—
365C23—1722no—
366C23—1722no—
367C23#1306329311yescharacteristic
368Q8—22no—
369Q8—22no—
370Q8—41no—
371Q8—41no—
372D4—3442no—
373D4—3441no—
374D4—3441no—
375D4—3441no—
376D4—3441no—
377D4—3441no—
378D4—3441no—
379D4—3441no—
380D4—3441no—
381D4—1724no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—1721no—
394C2×C4—1721no—
395C2×C4—1721no—
396C2×C4—1721no—
397C2×C4—1721no—
398C2×C4—1721no—
399C2×C4#1306329711yescharacteristic
400C2×C4#1306329811yescharacteristic
401C2×C4#1306329811yescharacteristic
402C2×C4#1306330711yescharacteristic
403C2×C4#1306330811yescharacteristic
404C2×C4#1306331111yescharacteristic
405C2×C4C2×#1062188411yescharacteristic
406C2×C4#1306334511yescharacteristic
407C2×C4#1306334611yescharacteristic
408C2×C4#1306334811yescharacteristic
409C2×C4#1306335011yescharacteristic
410C2×C4#1306335111yescharacteristic
411C2×C4#1306335211yescharacteristic
412C2×C4#1306335711yescharacteristic
413C8—81no—
414C8—1722no—
415C8—1722no—
416C22—3442no—
417C22—3442no—
418C22—3442no—
419C22—3442no—
420C22—3442no—
421C22—3442no—
422C22—3442no—
423C22#1458281411yescharacteristic
424C22#1458304211yescharacteristic
425C22#1458304311yescharacteristic
426C22#1458304911yescharacteristic
427C22#1458306011yescharacteristic
428C22#1458306511yescharacteristic
429C22#1458307511yescharacteristic
430C4—21no—
431C4—21no—
432C4—42no—
433C4—81no—
434C4—161no—
435C4—3441no—
436C4—3441no—
437C4#1458311711yescharacteristic
438C4#1458312411yescharacteristic
439C4#1458313011yescharacteristic
440C4#1458315011yescharacteristic
441C4#1458321711yescharacteristic
442C4#1458322311yescharacteristic
443C4#1458325511yescharacteristic
444C4#1458326011yescharacteristic
445C2—6882no—
446C2#1913365311yescharacteristic
447C2#1913372011yescharacteristic
448C2#1913377911yescharacteristic
449C2#1913379411yescharacteristic
450C2#1913578411yescharacteristic
451C2#1913580311yescharacteristic
452C2#1913583211yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1803C2
socleC23×C43#120
prime radicalC2×#13063322C22
hypercenter#1803D43
hypocenterC43#10410
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
3. #19135356C2semidirect
5. C2×Q8⋊(C43⋊C8)C2semidirect
6. #19132434C2semidirect
7. C43×#1803C2semidirect
222. #1803D43semidirect
253. C43#10410semidirect

Maximal subgroups

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

subgroupindex
#191395942
#191354002
#191353562
C2×#145826422
C2×Q8⋊(C43⋊C8)2
#191324342
C43×#18032
#1041043