Finite Group Databasebeta

← #24985407

Subgroups — #24985407

Order 11008.

536 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 87 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#19140966C211yesmaximal, characteristic
2#19135925C211yesmaximal, characteristic, complemented
3#19135678C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2058C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063305—21no—
10C2×#13063303—21no—
11C2×#13063256—21no—
12C2×#13063249—21no—
13#14582821—21no—
14#14582821—21no—
15#14582820—21no—
16#14582801C2211yescharacteristic
17#14582797C2211yescharacteristic
18#14582777—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#106×C43—21no—
24C43×#389C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C2×#10621884—42no—
31C2×#10621884—42no—
32C2×#10621884—42no—
33C22×C43⋊C8—21no—
34C22×C43⋊C8—21no—
35#13063305—42no—
36#13063305—42no—
37#13063303—42no—
38#13063303—42no—
39C2×C4⋊Dic43—21no—
40C2×C4⋊Dic43D411yescharacteristic
41C2×C4⋊Dic43D411yescharacteristic
42C2×C4⋊Dic43D411yescharacteristic
43C2×Dic43⋊C4—21no—
44C2×Dic43⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50#13063256—42no—
51#13063249—42no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×Q8×C43—21no—
55C22×C8×C43—21no—
56C4⋊Q8×C43—42no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C4⋊C4×C43D411yescharacteristic
62C2×C42×C43C2311yescharacteristic
63#106×C43—42no—
64#95×C43—21no—
65C23×D43—21no—
66C2×Q8×C43—22no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43—41no—
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×Dic43—21no—
79C22×Dic43—21no—
80C22×Dic43—21no—
81C2×D172—21no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172SD1612yes—
85C2×C4×D43—42no—
86C2×C4×D43—42no—
87C2×C4×D43—81no—
88C2×Dic86—42no—
89C2×Dic86—42no—
90C2×Dic86—81no—
91C2×C8×C43—22no—
92C2×C8×C43—41no—
93C2×C8×C43—41no—
94C4⋊C4×C43—21no—
95C4⋊C4×C43—22no—
96C4⋊C4×C43—22no—
97C4⋊C4×C43—41no—
98C4⋊C4×C43—41no—
99C4⋊C4×C43—41no—
100C4⋊C4×C43—41no—
101C4⋊C4×C43—41no—
102C4⋊C4×C43SD1612yescomplemented
103C42×C43—41no—
104#10621884—48no—
105(C2×D43)⋊C4—42no—
106(C2×D43)⋊C4—42no—
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—81no—
112C4⋊Dic43—21no—
113C4⋊Dic43—42no—
114C4⋊Dic43—41no—
115C4⋊Dic43—41no—
116C4⋊Dic43SD1612yescomplemented
117Dic43⋊C4—42no—
118Dic43⋊C4—41no—
119Dic43⋊C4—41no—
120C2×C43⋊C8—22no—
121C2×C43⋊C8—22no—
122C2×C43⋊C8—41no—
123C2×C43⋊C8—41no—
124C2×C43⋊C8—41no—
125C2×C43⋊C8—41no—
126C23×C43#12011yescharacteristic
127C22×D43—22no—
128C22×D43—41no—
129C22×D43—41no—
130C22×D43—41no—
131C22×D43—41no—
132C22×D43—41no—
133C22×D43—41no—
134Q8×C43—42no—
135Q8×C43—42no—
136Q8×C43—81no—
137Q8×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—22no—
145C2×C4×C43—41no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—81no—
152C2×C4×C43—81no—
153C2×C4×C43C2×SD1611yescharacteristic
154C2×C4×C43C2×SD1611yescharacteristic
155C2×C4×C43C2×SD1611yescharacteristic
156C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C43#13711yescharacteristic
159C2×Dic43—22no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—41no—
167C2×Dic43—41no—
168D172—42no—
169D172—81no—
170C4×D43—84no—
171Dic86—84no—
172C8×C43—42no—
173C43⋊C8—42no—
174C43⋊C8—42no—
175#7754—431nomaximal, Sylow
176C22×C43#44811yescharacteristic
177C22×C43#45011yescharacteristic
178C22×C43#45011yescharacteristic
179C22×C43#45311yescharacteristic
180C22×C43#45611yescharacteristic
181C22×C43#45611yescharacteristic
182C22×C43B(4,𝔽2)11yescharacteristic
183C2×D43—42no—
184C2×D43—42no—
185C2×D43—42no—
186C2×D43—81no—
187C2×D43—81no—
188C2×D43—81no—
189C2×D43—81no—
190C4×C43—21no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43—21no—
196C4×C43—42no—
197C4×C43—82no—
198C4×C43—81no—
199Dic43—42no—
200Dic43—81no—
201Dic43—81no—
202#2683—431no—
203#2058—431no—
204#2058D4311yescharacteristic, complemented
205#2013—431no—
206#1271—431no—
207#1271—431no—
208#1270—431no—
209C2×C43#159611yescharacteristic
210C2×C43#160411yescharacteristic
211C2×C43#160411yescharacteristic
212C2×C43#162911yescharacteristic
213C2×C43#165111yescharacteristic
214C2×C43#165111yescharacteristic
215C2×C43#166011yescharacteristic
216D43—82no—
217C22×SD16—861no—
218C2×C4⋊Q8C2×D4311yescharacteristic
219C2×C22⋊Q8—861no—
220C2×C22⋊Q8—861no—
221C2×#106—21no—
222C2×#106—861no—
223C2×#103—861no—
224#396—861no—
225#396—861no—
226#395—861no—
227#390—431no—
228#389—431no—
229#389C2×D4311yescharacteristic
230#386—861no—
231#340—21no—
232#340—861no—
233#336—431no—
234#336—431no—
235#336C2×D4311yescharacteristic
236C43#775411yescharacteristic, complemented, Sylow
237C22×Q8—21no—
238C22×Q8—861no—
239C22×D4—431no—
240C23×C4—861no—
241C2×SD16—1722no—
242C2×SD16—1722no—
243C2×SD16—1722no—
244C22×C8—21no—
245C22×C8—861no—
246C22×C8—861no—
247C4⋊Q8—42no—
248C22⋊Q8—1722no—
249C22⋊Q8—1722no—
250C22⋊Q8—1722no—
251C22⋊Q8—1722no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4—861no—
260C2×C4⋊C4—861no—
261C2×C4⋊C4C22⋊D4311yescharacteristic
262C2×C4⋊C4C22⋊D4311yescharacteristic
263C2×C22⋊C4—861no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C42C22×D4311yescharacteristic
269#106—42no—
270#106—1722no—
271#103—1722no—
272#95—21no—
273#95—861no—
274#95—861no—
275C24—861no—
276C2×Q8—22no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—3441no—
283C2×Q8—1722no—
284C2×Q8—1722no—
285C2×D4—432no—
286C2×D4—861no—
287C2×D4—1721no—
288C2×D4—1721no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—41no—
292C22×C4—861no—
293C22×C4—861no—
294C22×C4—861no—
295C22×C4—3441no—
296C22×C4—1722no—
297C22×C4—1722no—
298C22×C4D4×D4311yescharacteristic
299C22×C4D4×D4311yescharacteristic
300C22×C4C2×C22⋊D4311yescharacteristic
301SD16—1728no—
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—862no—
306C2×C8—862no—
307C2×C8—1721no—
308C2×C8—1721no—
309C2×C8—1721no—
310C2×C8—1721no—
311C4⋊C4—21no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—432no—
320C4⋊C4—861no—
321C4⋊C4—1721no—
322C4⋊C4—1721no—
323C4⋊C4—1722no—
324C4⋊C4—1722no—
325C4⋊C4—1721no—
326C4⋊C4—1721no—
327C4⋊C4#1062188412yescomplemented
328C22⋊C4—3441no—
329C22⋊C4—1722no—
330C22⋊C4—1722no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C42—41no—
336C23—862no—
337C23—1721no—
338C23—1721no—
339C23—1721no—
340C23—1721no—
341C23—1721no—
342C23—1721no—
343C23#1306329311yescharacteristic
344Q8—42no—
345Q8—42no—
346Q8—81no—
347Q8—81no—
348Q8—3444no—
349D4—3441no—
350D4—1722no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—42no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—862no—
367C2×C4—3444no—
368C2×C4—1721no—
369C2×C4—1721no—
370C2×C4—1721no—
371C2×C4—1721no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4SD16×D4311yescharacteristic
377C2×C4SD16×D4311yescharacteristic
378C2×C4C2×#1062188411yescharacteristic
379C2×C4#1306335011yescharacteristic
380C2×C4#1306335211yescharacteristic
381C2×C4#1306335411yescharacteristic
382C8—42no—
383C8—1722no—
384C8—1722no—
385C22—3441no—
386C22—3441no—
387C22—3441no—
388C22—3441no—
389C22—1722no—
390C22—1722no—
391C22—1722no—
392C22#1458303611yescharacteristic
393C22#1458304811yescharacteristic
394C22#1458304911yescharacteristic
395C22#1458306511yescharacteristic
396C22#1458308011yescharacteristic
397C22#1458308111yescharacteristic
398C22#1458308511yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—42no—
406C4—82no—
407C4—81no—
408C4—3441no—
409C4—3441no—
410C4—1722no—
411C2—3442no—
412C2#1913351611yescharacteristic
413C2#1913356211yescharacteristic
414C2#1913356311yescharacteristic
415C2#1913371011yescharacteristic
416C2#1913385511yescharacteristic
417C2#1913385711yescharacteristic
418C2#1913390511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2058C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2058D43
hypocenterC43#7754
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2058

Complements

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

NH ≅ G/Ntype
2. #19135925C2semidirect
4. #19132419C2semidirect
5. #19132418C2semidirect
7. C43×#2058C2semidirect
102. C4⋊C4×C43SD16semidirect
116. C4⋊Dic43SD16semidirect
204. #2058D43semidirect
236. C43#7754semidirect
327. C4⋊C4#10621884semidirect

Maximal subgroups

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

subgroupindex
#191409662
#191359252
#191356782
#191324192
#191324182
#191324152
C43×#20582
#775443