Finite Group Databasebeta

← #24985679

Subgroups — #24985679

Order 11008.

500 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140959C211yesmaximal, characteristic
2#19136152C211yesmaximal, characteristic, complemented
3#19135999C211yesmaximal, characteristic, complemented
4#19132419C211yesmaximal, characteristic, complemented
5#19132416C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic, complemented
7C43×#2071C211yesmaximal, characteristic, complemented
8C2×#13063309—21no—
9C2×#13063297—21no—
10C2×#13063245—21no—
11#14582821—21no—
12#14582815—21no—
13#14582808—21no—
14#14582801C2211yescharacteristic
15#14582797C2211yescharacteristic
16#14582774—21no—
17#14582661—21no—
18#14582661—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×#102×C43—21no—
23C43×#390C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×D172D411yescharacteristic
28C22×C22⋊D43—21no—
29C22×C22⋊D43—21no—
30C23×Dic43—21no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33#13063309—42no—
34#13063309—42no—
35#13063297—42no—
36#13063297—42no—
37C2×C4⋊Dic43—21no—
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×C4⋊Dic43D411yescharacteristic
41C2×Dic43⋊C4—21no—
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47#13063245—42no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×D4×C43D411yescharacteristic
51C22×C8×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C22⋊C4×C43—21no—
57C2×C22⋊C4×C43—21no—
58C2×C42×C43C2311yescharacteristic
59#102×C43—42no—
60C24×C43—21no—
61C23×D43—21no—
62C2×D4×C43—21no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C2×D4×C43D812yes—
66C22×C4×C43—21no—
67C22×C4×C43—41no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C2×C22⋊D43—42no—
72C2×C22⋊D43—42no—
73C2×C22⋊D43—42no—
74C2×C22⋊D43—81no—
75C2×C22⋊D43—81no—
76C2×C22⋊D43—81no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—42no—
81C22×Dic43—42no—
82C22×Dic43—81no—
83C2×D172—21no—
84C2×D172—21no—
85C2×D172—41no—
86C2×D172—41no—
87C2×C8×C43—41no—
88C2×C8×C43—41no—
89C2×C8×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—42no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C4⋊C4×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C42×C43—41no—
101C22⋊Dic43—42no—
102(C2×D43)⋊C4—42no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—81no—
108C4⋊Dic43—21no—
109C4⋊Dic43—42no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112C4⋊Dic43SD1612yes—
113Dic43⋊C4—41no—
114Dic43⋊C4—41no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C2×C43⋊C8—41no—
119C2×C43⋊C8—41no—
120C2×C43⋊C8—41no—
121C23×C43—22no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43—41no—
128C23×C43#12011yescharacteristic
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134C22×D43—41no—
135C22×D43—41no—
136D4×C43—42no—
137D4×C43—81no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—41no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—81no—
148C2×C4×C43—81no—
149C2×C4×C43—81no—
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43C2×SD1611yescharacteristic
152C2×C4×C43#13511yescharacteristic
153C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
156C22⋊D43—84no—
157C22⋊D43—84no—
158C2×Dic43—22no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—84no—
168D172—42no—
169D172—81no—
170C8×C43—81no—
171C43⋊C8—81no—
172C43⋊C8—81no—
173#7795—431nomaximal, Sylow
174C22×C43—42no—
175C22×C43—42no—
176C22×C43—42no—
177C22×C43—81no—
178C22×C43—81no—
179C22×C43—81no—
180C22×C43—81no—
181C22×C43#44711yescharacteristic
182C22×C43#44911yescharacteristic
183C22×C43#45011yescharacteristic
184C22×C43#45411yescharacteristic
185C22×C43#45511yescharacteristic
186C22×C43#45511yescharacteristic
187C22×C43#45811yescharacteristic
188C2×D43—81no—
189C2×D43—81no—
190C2×D43—81no—
191C2×D43—81no—
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—81no—
202C4×C43—161no—
203Dic43—42no—
204Dic43—81no—
205Dic43—81no—
206#2682—431no—
207#2099—431no—
208#2071—431no—
209#2071D4311yescharacteristic, complemented
210#1271—431no—
211#1270—431no—
212#1270—431no—
213C2×C43—82no—
214C2×C43#160711yescharacteristic
215C2×C43#161211yescharacteristic
216C2×C43#161611yescharacteristic
217C2×C43#162511yescharacteristic
218C2×C43#163911yescharacteristic
219C2×C43#164211yescharacteristic
220C2×C43#166211yescharacteristic
221D43—161no—
222C2×#123—861no—
223C2×#121—861no—
224C2×#102—21no—
225C2×#102—861no—
226#396—861no—
227#394—861no—
228#392—861no—
229#390—431no—
230#390C2×D4311yescharacteristic
231#389—431no—
232#385—861no—
233#384C2×D4311yescharacteristic
234#340—21no—
235#340—861no—
236#340—861no—
237#340—861no—
238#336—431no—
239#336—431no—
240#336C2×D4311yescharacteristic
241C43#779511yescharacteristic, complemented, Sylow
242C22×D4—431no—
243C22×D4—861no—
244C22×D4—861no—
245C22×D4C22⋊D4311yescharacteristic
246C23×C4—861no—
247C22×C8—21no—
248C22×C8—861no—
249C22×C8—861no—
250#123—1722no—
251#123—1722no—
252#121—1722no—
253#121—1722no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—431no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4—861no—
262C2×C4⋊C4C22⋊D4311yescharacteristic
263C2×C22⋊C4—21no—
264C2×C22⋊C4—21no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4—861no—
270C2×C42C22×D4311yescharacteristic
271#102—42no—
272#102—1722no—
273#95—861no—
274#95—861no—
275C24—21no—
276C24—861no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—861no—
281C2×D4—861no—
282C2×D4—3441no—
283C2×D4—3441no—
284C2×D4—3441no—
285C2×D4—1721no—
286C2×D4—1721no—
287C2×D4—1722no—
288C2×D4—1722no—
289C2×D4—1722no—
290C2×D4#1062188212yes—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—861no—
296C22×C4—3441no—
297C22×C4—1722no—
298C22×C4—1722no—
299C22×C4D4×D4311yescharacteristic
300C22×C4D4×D4311yescharacteristic
301C22×C4C2×C22⋊D4311yescharacteristic
302C2×C8—41no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—1721no—
306C2×C8—1721no—
307C2×C8—1721no—
308C2×C8—1721no—
309C2×C8—1721no—
310C2×C8—1721no—
311C4⋊C4—41no—
312C4⋊C4—42no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—432no—
318C4⋊C4—861no—
319C4⋊C4—1721no—
320C4⋊C4—1721no—
321C4⋊C4—1722no—
322C4⋊C4—1721no—
323C4⋊C4—1721no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—3441no—
329C22⋊C4—1722no—
330C22⋊C4—1722no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C42—41no—
336C23—22no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—1721no—
344C23—1721no—
345C23—1721no—
346C23—1721no—
347C23—1721no—
348C23—1721no—
349C23—1721no—
350C23#1306329311yescharacteristic
351D4—42no—
352D4—81no—
353D4—3441no—
354D4—3444no—
355D4—3444no—
356D4—1722no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—862no—
370C2×C4—3444no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1721no—
377C2×C4—1721no—
378C2×C4—1721no—
379C2×C4C2×#1062188211yescharacteristic
380C2×C4SD16×D4311yescharacteristic
381C2×C4#1306334411yescharacteristic
382C2×C4#1306334911yescharacteristic
383C2×C4#1306335011yescharacteristic
384C2×C4#1306335211yescharacteristic
385C8—81no—
386C8—3441no—
387C8—3441no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—3441no—
396C22—3441no—
397C22—3441no—
398C22—3441no—
399C22—3441no—
400C22—3441no—
401C22—3441no—
402C22#1458303211yescharacteristic
403C22#1458304111yescharacteristic
404C22#1458304811yescharacteristic
405C22#1458307011yescharacteristic
406C22#1458307511yescharacteristic
407C22#1458307611yescharacteristic
408C22#1458308811yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—81no—
416C4—161no—
417C4—3441no—
418C4—3441no—
419C4—1722no—
420C2—82no—
421C2—6881no—
422C2#1913358011yescharacteristic
423C2#1913360611yescharacteristic
424C2#1913363011yescharacteristic
425C2#1913368211yescharacteristic
426C2#1913377211yescharacteristic
427C2#1913379211yescharacteristic
428C2#1913391711yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2071C2
socleC23×C43#120
prime radical#19140959C2
hypercenter#2071D43
hypocenterC43#7795
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2071

Complements

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

NH ≅ G/Ntype
2. #19136152C2semidirect
3. #19135999C2semidirect
4. #19132419C2semidirect
5. #19132416C2semidirect
6. #19132415C2semidirect
7. C43×#2071C2semidirect
209. #2071D43semidirect
241. C43#7795semidirect

Maximal subgroups

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

subgroupindex
#191409592
#191361522
#191359992
#191324192
#191324162
#191324152
C43×#20712
#779543