Finite Group Databasebeta

← #24985876

Subgroups — #24985876

Order 11008.

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

normal subgroups only

This group has 462 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#19136157C211yesmaximal, characteristic, complemented
3#19136129C211yesmaximal, characteristic
4#19132419C211yesmaximal, characteristic, complemented
5#19132418C211yesmaximal, characteristic, complemented
6#19132415C211yesmaximal, characteristic
7C43×#2100C211yesmaximal, characteristic, complemented
8C2×#13063305—21no—
9C2×#13063303—21no—
10C2×#13063256—21no—
11C2×#13063245—21no—
12#14582821—21no—
13#14582821—21no—
14#14582820—21no—
15#14582801C2211yescharacteristic
16#14582797C2211yescharacteristic
17#14582777—21no—
18#14582661—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C43×#389C2211yescharacteristic
23C43×#384C2211yescharacteristic
24C43×#340—21no—
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×D172D411yescharacteristic
29C22×C4×D43—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063305—42no—
33#13063305—42no—
34#13063303—42no—
35#13063303—42no—
36C2×C4⋊Dic43—21no—
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×C4⋊Dic43D411yescharacteristic
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×(C2×D43)⋊C4—21no—
43C2×(C2×D43)⋊C4—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47#13063256—42no—
48#13063245—42no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C22×C8×C43—21no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C42×C43C2311yescharacteristic
59#95×C43—21no—
60C23×D43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C2×D172—21no—
71C2×D172—41no—
72C2×D172—41no—
73C2×D172Q1612yes—
74C2×C4×D43—42no—
75C2×C4×D43—42no—
76C2×C4×D43—81no—
77C2×Dic86—42no—
78C2×Dic86—42no—
79C2×Dic86—81no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C2×C8×C43—41no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—42no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43SD1612yes—
92C42×C43—41no—
93(C2×D43)⋊C4—42no—
94(C2×D43)⋊C4—42no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—81no—
100C4⋊Dic43—21no—
101C4⋊Dic43—42no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43SD1612yes—
105Dic43⋊C4—42no—
106Dic43⋊C4—41no—
107Dic43⋊C4—41no—
108C2×C43⋊C8—22no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C2×C43⋊C8—41no—
112C2×C43⋊C8—41no—
113C2×C43⋊C8—41no—
114C23×C43#12011yescharacteristic
115C22×D43—22no—
116C22×D43—41no—
117C22×D43—41no—
118C22×D43—41no—
119C22×D43—41no—
120C22×D43—41no—
121C22×D43—41no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—41no—
133C2×C4×C43—41no—
134C2×C4×C43—81no—
135C2×C4×C43—81no—
136C2×C4×C43—81no—
137C2×C4×C43C2×SD1611yescharacteristic
138C2×C4×C43C2×SD1611yescharacteristic
139C2×C4×C43C2×Q1611yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43#13711yescharacteristic
143C2×Dic43—22no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C2×Dic43—41no—
150C2×Dic43—41no—
151C2×Dic43—41no—
152D172—42no—
153D172—81no—
154C4×D43—84no—
155Dic86—84no—
156C8×C43—81no—
157C43⋊C8—42no—
158C43⋊C8—81no—
159#7826—431nomaximal, Sylow
160C22×C43#45011yescharacteristic
161C22×C43#45011yescharacteristic
162C22×C43#45111yescharacteristic
163C22×C43#45311yescharacteristic
164C22×C43#45411yescharacteristic
165C22×C43#45411yescharacteristic
166C22×C43#45811yescharacteristic
167C2×D43—42no—
168C2×D43—42no—
169C2×D43—42no—
170C2×D43—81no—
171C2×D43—81no—
172C2×D43—81no—
173C2×D43—81no—
174C4×C43—21no—
175C4×C43—21no—
176C4×C43—21no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—42no—
181C4×C43—81no—
182C4×C43—161no—
183Dic43—42no—
184Dic43—81no—
185Dic43—81no—
186#2683—431no—
187#2100—431no—
188#2100D4311yescharacteristic, complemented
189#2094—431no—
190#1271—431no—
191#1271—431no—
192#1270—431no—
193C2×C43#161411yescharacteristic
194C2×C43#161611yescharacteristic
195C2×C43#161611yescharacteristic
196C2×C43#162911yescharacteristic
197C2×C43#163711yescharacteristic
198C2×C43#163711yescharacteristic
199C2×C43#165711yescharacteristic
200D43—82no—
201C2×C22⋊Q8—861no—
202C2×C22⋊Q8—861no—
203C2×#106—861no—
204C2×#102—861no—
205#396—861no—
206#396—861no—
207#395—861no—
208#390—431no—
209#389—431no—
210#389C2×D4311yescharacteristic
211#386—861no—
212#384C2×D4311yescharacteristic
213#340—21no—
214#340—21no—
215#340—861no—
216#340—861no—
217#336—431no—
218#336—431no—
219#336C2×D4311yescharacteristic
220C43#782611yescharacteristic, complemented, Sylow
221C22×Q8—861no—
222C22×D4—431no—
223C23×C4—861no—
224C22×C8—21no—
225C22×C8—861no—
226C22×C8—861no—
227C22⋊Q8—1722no—
228C22⋊Q8—1722no—
229C22⋊Q8—1722no—
230C22⋊Q8—1722no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—861no—
239C2×C4⋊C4—861no—
240C2×C4⋊C4—861no—
241C2×C4⋊C4C22⋊D4311yescharacteristic
242C2×C4⋊C4C22⋊D4311yescharacteristic
243C2×C22⋊C4—861no—
244C2×C22⋊C4—861no—
245C2×C22⋊C4—861no—
246C2×C22⋊C4—861no—
247C2×C22⋊C4—861no—
248C2×C42C22×D4311yescharacteristic
249#106—1722no—
250#102—1722no—
251#95—21no—
252#95—861no—
253#95—861no—
254C24—861no—
255C2×Q8—3441no—
256C2×Q8—1722no—
257C2×Q8—1722no—
258C2×D4—432no—
259C2×D4—861no—
260C2×D4—1721no—
261C2×D4—1721no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—41no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—3441no—
269C22×C4—1722no—
270C22×C4—1722no—
271C22×C4D4×D4311yescharacteristic
272C22×C4D4×D4311yescharacteristic
273C22×C4C2×C22⋊D4311yescharacteristic
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—862no—
278C2×C8—1721no—
279C2×C8—1721no—
280C2×C8—1721no—
281C2×C8—1721no—
282C2×C8—1721no—
283C4⋊C4—21no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—42no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—432no—
292C4⋊C4—861no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C4⋊C4—1722no—
296C4⋊C4—1722no—
297C4⋊C4—1721no—
298C4⋊C4—1721no—
299C4⋊C4#1062188412yes—
300C22⋊C4—3441no—
301C22⋊C4—1722no—
302C22⋊C4—1722no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C42—41no—
308C23—862no—
309C23—1721no—
310C23—1721no—
311C23—1721no—
312C23—1721no—
313C23—1721no—
314C23—1721no—
315C23#1306329311yescharacteristic
316Q8—3444no—
317D4—3441no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—862no—
335C2×C4—3444no—
336C2×C4—1721no—
337C2×C4—1721no—
338C2×C4—1721no—
339C2×C4—1721no—
340C2×C4—1721no—
341C2×C4—1721no—
342C2×C4—1721no—
343C2×C4—1721no—
344C2×C4SD16×D4311yescharacteristic
345C2×C4C2×#1062188411yescharacteristic
346C2×C4Q16×D4311yescharacteristic
347C2×C4#1306335011yescharacteristic
348C2×C4#1306335211yescharacteristic
349C2×C4#1306335711yescharacteristic
350C8—81no—
351C8—3441no—
352C8—1722no—
353C22—3441no—
354C22—3441no—
355C22—3441no—
356C22—3441no—
357C22—1722no—
358C22—1722no—
359C22—1722no—
360C22#1458304811yescharacteristic
361C22#1458304911yescharacteristic
362C22#1458305311yescharacteristic
363C22#1458306511yescharacteristic
364C22#1458307011yescharacteristic
365C22#1458307111yescharacteristic
366C22#1458308811yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—42no—
374C4—81no—
375C4—161no—
376C4—3441no—
377C4—3441no—
378C4—1722no—
379C2—3442no—
380C2#1913361811yescharacteristic
381C2#1913363011yescharacteristic
382C2#1913363111yescharacteristic
383C2#1913371011yescharacteristic
384C2#1913375711yescharacteristic
385C2#1913375811yescharacteristic
386C2#1913389211yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2100C2
socleC23×C43#120
prime radicalC22×D172D4
hypercenter#2100D43
hypocenterC43#7826
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
2. #19136157C2semidirect
4. #19132419C2semidirect
5. #19132418C2semidirect
7. C43×#2100C2semidirect
188. #2100D43semidirect
220. C43#7826semidirect

Maximal subgroups

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

subgroupindex
#191409662
#191361572
#191361292
#191324192
#191324182
#191324152
C43×#21002
#782643