Finite Group Databasebeta

← #25000137

Subgroups — #25000137

Order 11008.

530 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139513C211yesmaximal, characteristic
2#19134722C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic
4C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic
6#19132479C211yesmaximal, characteristic, complemented
7C43×#1803C211yesmaximal, characteristic, complemented
8C2×#13063301—21no—
9C2×C4×D172C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063245—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582821—22no—
14#14582801—21no—
15#14582797—21no—
16#14582769C2211yescharacteristic
17#14582756—21no—
18#14582661—22no—
19#14582661—21no—
20Q8⋊(C43⋊C8)—22no—
21#14582626—22no—
22C2×C4×Q8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#103×C43—21no—
25C43×#384C2211yescharacteristic
26C43×#340—21no—
27C22×D172D411yescharacteristic
28C22×C4×D43—21no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—21no—
31#13063301—42no—
32#13063301—42no—
33C4×D172—21no—
34C4×D172—21no—
35C4×D172—21no—
36C4×D172—21no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43—21no—
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D412yes—
41C2×Dic43⋊C4—22no—
42C2×(C2×D43)⋊C4—22no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—22no—
45C4⋊(C43⋊C8)—21no—
46C4⋊(C43⋊C8)—21no—
47#13063245—42no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8D412yes—
50C43⋊#95—22no—
51C22×Q8×C43D411yescharacteristic
52C22×C8×C43—21no—
53C4×Q8×C43—21no—
54C4×Q8×C43—21no—
55C4×Q8×C43—21no—
56C4×Q8×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43D411yescharacteristic
62C2×C42×C43—21no—
63C2×C42×C43C2311yescharacteristic
64C4⋊C8×C43—21no—
65C4⋊C8×C43—21no—
66#103×C43—42no—
67C23×D43—21no—
68C2×Q8×C43—21no—
69C2×Q8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C2×Q8×C43—21no—
73C2×Q8×C43SD1612yes—
74C22×C4×C43—21no—
75C22×C4×C43—21no—
76C22×C4×C43—41no—
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×D411yescharacteristic
79C22×C4×C43C2×D411yescharacteristic
80C22×Dic43—21no—
81C22×Dic43—22no—
82C2×D172—21no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—21no—
86C2×D172—21no—
87C2×D172Q1612yes—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C8×C43—41no—
95C2×C8×C43—41no—
96C2×C8×C43—41no—
97C4⋊C4×C43—21no—
98C4⋊C4×C43—21no—
99C4⋊C4×C43—42no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43—41no—
103C4⋊C4×C43—41no—
104C4⋊C4×C43—41no—
105C4⋊C4×C43—41no—
106C42×C43—41no—
107C42×C43—41no—
108C42×C43C2×D411yescharacteristic
109C42×C43#4111yescharacteristic
110C42×C43#4111yescharacteristic
111C42×C43#4111yescharacteristic
112(C2×D43)⋊C4—44no—
113(C2×D43)⋊C4—41no—
114(C2×D43)⋊C4—41no—
115(C2×D43)⋊C4—82no—
116C4⋊Dic43—21no—
117C4⋊Dic43—21no—
118C4⋊Dic43—41no—
119C4⋊Dic43—41no—
120C4⋊Dic43—41no—
121C4⋊Dic43—41no—
122C4⋊Dic43—42no—
123Dic43⋊C4—44no—
124C2×C43⋊C8—22no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C23×C43#12011yescharacteristic
131C22×D43—22no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136C22×D43—41no—
137C22×D43—41no—
138Q8×C43—22no—
139Q8×C43—22no—
140Q8×C43—41no—
141Q8×C43—41no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—81no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43#12111yescharacteristic
154C2×C4×C43#12111yescharacteristic
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12311yescharacteristic
157C2×C4×C43#12311yescharacteristic
158C2×C4×C43#12411yescharacteristic
159C2×C4×C43C2×SD1611yescharacteristic
160C2×C4×C43C2×Q1611yescharacteristic
161C2×C4×C43#13511yescharacteristic
162C2×C4×C43#13511yescharacteristic
163C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C43#13711yescharacteristic
167C2×Dic43—41no—
168C2×Dic43—42no—
169C2×Dic43—41no—
170C2×Dic43—41no—
171C2×Dic43—42no—
172C2×Dic43—42no—
173D172—22no—
174D172—22no—
175D172—41no—
176D172—41no—
177C4×D43—81no—
178C4×D43—81no—
179C4×D43—81no—
180C4×D43—81no—
181C8×C43—81no—
182C43⋊C8—42no—
183C43⋊C8—81no—
184#10436—431nomaximal, Sylow
185C22×C43#39411yescharacteristic
186C22×C43#44911yescharacteristic
187C22×C43#44911yescharacteristic
188C22×C43#45011yescharacteristic
189C22×C43#45111yescharacteristic
190C22×C43#45411yescharacteristic
191C22×C43#45511yescharacteristic
192C2×D43—42no—
193C2×D43—42no—
194C2×D43—42no—
195C2×D43—81no—
196C2×D43—81no—
197C2×D43—81no—
198C2×D43—81no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—42no—
202C4×C43—81no—
203C4×C43—161no—
204C4×C43#46511yescharacteristic
205C4×C43#46711yescharacteristic
206C4×C43#46811yescharacteristic
207C4×C43#46911yescharacteristic
208C4×C43#48111yescharacteristic
209C4×C43#48211yescharacteristic
210C4×C43#48411yescharacteristic
211C4×C43#48511yescharacteristic
212Dic43—82no—
213Dic43—81no—
214#2538—431no—
215#1834—431no—
216#1803D4311yescharacteristic, complemented
217#1802—431no—
218C2×Q8⋊C8—431no—
219C2×D4⋊C8—431no—
220#1296—431no—
221C2×C43#162811yescharacteristic
222C2×C43#163711yescharacteristic
223C2×C43#164211yescharacteristic
224C2×C43#164411yescharacteristic
225C2×C43#203411yescharacteristic
226C2×C43#203611yescharacteristic
227C2×C43#204011yescharacteristic
228D43—82no—
229C2×C22⋊Q8—861no—
230C2×C4×Q8C2×D4311yescharacteristic
231C2×C4×D4—431no—
232C2×C4⋊C8—431no—
233C2×C4⋊C8C2×D4311yescharacteristic
234C2×#103—21no—
235C2×#102—861no—
236C2×C4×C8—431no—
237#396—862no—
238#390—861no—
239#389—861no—
240#384—431no—
241#384C2×D4311yescharacteristic
242#380—861no—
243#340—21no—
244#340—861no—
245#340—862no—
246Q8⋊C8—862no—
247D4⋊C8—862no—
248C43#1043611yescharacteristic, complemented, Sylow
249C22×Q8C22⋊D4311yescharacteristic
250C22×D4—431no—
251C23×C4—861no—
252C22×C8—21no—
253C22×C8—861no—
254C22×C8—861no—
255C22⋊Q8—1722no—
256C22⋊Q8—1722no—
257C4×Q8—21no—
258C4×Q8—21no—
259C4×Q8—21no—
260C4×Q8—21no—
261C4×D4—861no—
262C4×D4—861no—
263C4×D4—861no—
264C4×D4—861no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—432no—
271C2×C4⋊C4—862no—
272C2×C4⋊C4—861no—
273C2×C4⋊C4—861no—
274C2×C4⋊C4C22⋊D4311yescharacteristic
275C2×C22⋊C4—862no—
276C2×C22⋊C4—862no—
277C2×C22⋊C4—861no—
278C2×C42—21no—
279C2×C42C22×D4311yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—21no—
282C4⋊C8—861no—
283C4⋊C8—861no—
284#103—42no—
285#102—1722no—
286C4×C8—432no—
287C4×C8—861no—
288#95—862no—
289C24—861no—
290C2×Q8—21no—
291C2×Q8—21no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×Q8#1062188412yes—
296C2×D4—432no—
297C2×D4—861no—
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—861no—
301C2×D4—861no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—41no—
305C22×C4—861no—
306C22×C4—862no—
307C22×C4—1721no—
308C22×C4—1721no—
309C22×C4—1721no—
310C22×C4—1721no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4D4×D4311yescharacteristic
314C22×C4D4×D4311yescharacteristic
315C22×C4C2×C22⋊D4311yescharacteristic
316C2×C8—41no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—862no—
320C2×C8—1721no—
321C2×C8—1721no—
322C2×C8—1721no—
323C2×C8—1721no—
324C2×C8—1721no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C4⋊C4—861no—
335C4⋊C4—861no—
336C4⋊C4—1722no—
337C4⋊C4—1724no—
338C4⋊C4—1721no—
339C4⋊C4—1721no—
340C4⋊C4—1721no—
341C4⋊C4—1721no—
342C22⋊C4—3442no—
343C22⋊C4—1724no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C42—41no—
347C42—41no—
348C42#1062189811yescharacteristic
349C42#1062189811yescharacteristic
350C42D4×D4311yescharacteristic
351C42#1062190011yescharacteristic
352C23—862no—
353C23—1721no—
354C23—1721no—
355C23—1721no—
356C23—1721no—
357C23—1721no—
358C23—1721no—
359C23#1306329311yescharacteristic
360Q8—22no—
361Q8—22no—
362Q8—41no—
363Q8—41no—
364D4—862no—
365D4—862no—
366D4—1721no—
367D4—1721no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—22no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—3441no—
380C2×C4—3441no—
381C2×C4—3441no—
382C2×C4—3441no—
383C2×C4—1721no—
384C2×C4—1722no—
385C2×C4—1722no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1722no—
389C2×C4#1306329711yescharacteristic
390C2×C4#1306329811yescharacteristic
391C2×C4#1306329811yescharacteristic
392C2×C4#1306330711yescharacteristic
393C2×C4#1306330811yescharacteristic
394C2×C4#1306331111yescharacteristic
395C2×C4C2×#1062188411yescharacteristic
396C2×C4Q16×D4311yescharacteristic
397C2×C4#1306334511yescharacteristic
398C2×C4#1306334611yescharacteristic
399C2×C4#1306335011yescharacteristic
400C2×C4#1306335111yescharacteristic
401C2×C4#1306335211yescharacteristic
402C2×C4#1306335711yescharacteristic
403C8—81no—
404C8—3441no—
405C8—1722no—
406C22—3441no—
407C22—3441no—
408C22—3441no—
409C22—3441no—
410C22—1722no—
411C22—1722no—
412C22—1722no—
413C22#1458281411yescharacteristic
414C22#1458304211yescharacteristic
415C22#1458304311yescharacteristic
416C22#1458304911yescharacteristic
417C22#1458305311yescharacteristic
418C22#1458307011yescharacteristic
419C22#1458307511yescharacteristic
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4—161no—
425C4—3441no—
426C4—3442no—
427C4#1458313011yescharacteristic
428C4#1458313911yescharacteristic
429C4#1458314811yescharacteristic
430C4#1458315011yescharacteristic
431C4#1458321711yescharacteristic
432C4#1458322311yescharacteristic
433C4#1458323311yescharacteristic
434C4#1458323811yescharacteristic
435C2—3442no—
436C2#1913370411yescharacteristic
437C2#1913375811yescharacteristic
438C2#1913379411yescharacteristic
439C2#1913380711yescharacteristic
440C2#1913578411yescharacteristic
441C2#1913579611yescharacteristic
442C2#1913582211yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1803C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#1803D43
hypocenterC43#10436
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
2. #19134722C2semidirect
4. C2×Q8⋊(C43⋊C8)C2semidirect
6. #19132479C2semidirect
7. C43×#1803C2semidirect
216. #1803D43semidirect
248. C43#10436semidirect

Maximal subgroups

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

subgroupindex
#191395132
#191347222
#191345922
C2×Q8⋊(C43⋊C8)2
C2×#145826262
#191324792
C43×#18032
#1043643