Finite Group Databasebeta

← #24985492

Subgroups — #24985492

Order 11008.

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

normal subgroups only

This group has 416 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#19141546C211yesmaximal, characteristic
2#19135925C211yesmaximal, characteristic
3#19135925C211yesmaximal, characteristic
4#19132418C211yesmaximal, characteristic
5#19132417C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#2043C211yesmaximal, characteristic
8C2×#13063316—21no—
9C2×#13063256—21no—
10C2×#13063256—21no—
11#14582832—21no—
12#14582832—21no—
13#14582831—21no—
14#14582797C2211yescharacteristic
15#14582797C2211yescharacteristic
16#14582796—21no—
17#14582785—21no—
18#14582661—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#103×C43—21no—
24C2×#103×C43—21no—
25C43×#389C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29#13063316—42no—
30#13063316—42no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×C4×Dic43—21no—
42#13063256—42no—
43#13063256—42no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C22×Q8×C43—21no—
50C22×C8×C43—21no—
51C4⋊Q8×C43—42no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43—21no—
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C4⋊C4×C43D411yescharacteristic
57C2×C42×C43C2311yescharacteristic
58#103×C43—42no—
59#103×C43—42no—
60#95×C43—21no—
61C2×Q8×C43—22no—
62C2×Q8×C43—41no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C22×C4×C43—21no—
68C22×C4×C43—21no—
69C22×C4×C43—41no—
70C22×C4×C43C2×D411yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—21no—
74C22×Dic43—21no—
75C22×Dic43—21no—
76C22×Dic43—21no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—22no—
82C4⋊C4×C43—22no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43SD1612yes—
89C42×C43—41no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43—42no—
94C4⋊Dic43—42no—
95C4⋊Dic43—41no—
96C4⋊Dic43—41no—
97C4⋊Dic43SD1612yes—
98Dic43⋊C4—42no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—81no—
104C4×Dic43—42no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C2×C43⋊C8—41no—
111C23×C43#12011yescharacteristic
112Q8×C43—42no—
113Q8×C43—42no—
114Q8×C43—81no—
115Q8×C43—81no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—42no—
129C2×C4×C43—81no—
130C2×C4×C43—81no—
131C2×C4×C43C2×SD1611yescharacteristic
132C2×C4×C43C2×SD1611yescharacteristic
133C2×C4×C43#13511yescharacteristic
134C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C2×C4×C43#13711yescharacteristic
137C2×Dic43—22no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—41no—
142C2×Dic43—41no—
143C2×Dic43—41no—
144C2×Dic43—41no—
145C2×Dic43—41no—
146C2×Dic43—41no—
147C2×Dic43—41no—
148C2×Dic43—41no—
149C8×C43—81no—
150C43⋊C8—42no—
151C43⋊C8—42no—
152#7768—431nomaximal, Sylow
153C22×C43#44811yescharacteristic
154C22×C43#45011yescharacteristic
155C22×C43#45211yescharacteristic
156C22×C43#45411yescharacteristic
157C22×C43#45611yescharacteristic
158C22×C43#45611yescharacteristic
159C22×C43B(4,𝔽2)11yescharacteristic
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—42no—
167C4×C43—82no—
168C4×C43—81no—
169Dic43—42no—
170Dic43—81no—
171Dic43—81no—
172Dic43—81no—
173#2726—431no—
174#2058—431no—
175#2058—431no—
176#2043D4311yescharacteristic
177#1271—431no—
178#1271—431no—
179#1271—431no—
180C2×C43#159911yescharacteristic
181C2×C43#160311yescharacteristic
182C2×C43#160411yescharacteristic
183C2×C43#163511yescharacteristic
184C2×C43#165111yescharacteristic
185C2×C43#165311yescharacteristic
186C2×C43#166311yescharacteristic
187C2×C4⋊Q8C2×D4311yescharacteristic
188C2×#125—861no—
189C2×#106—861no—
190C2×#106—861no—
191C2×#103—21no—
192C2×#103—21no—
193#398—861no—
194#398—861no—
195#398—861no—
196#389—431no—
197#389—431no—
198#389—861no—
199#389C2×D4311yescharacteristic
200#387—861no—
201#340—861no—
202#340—861no—
203#336—431no—
204#336—431no—
205#336C2×D4311yescharacteristic
206C43#776811yescharacteristic, complemented, Sylow
207C22×Q8—21no—
208C22×C8—21no—
209C22×C8—861no—
210C22×C8—861no—
211C4⋊Q8—42no—
212#125—1722no—
213#125—1722no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—861no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4C22⋊D4311yescharacteristic
228C2×C4⋊C4C22⋊D4311yescharacteristic
229C2×C42—861no—
230C2×C42C22×D4311yescharacteristic
231#106—1722no—
232#106—1722no—
233#103—42no—
234#103—42no—
235#95—21no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240#95—861no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4D4×D4311yescharacteristic
255C22×C4D4×D4311yescharacteristic
256C22×C4C2×C22⋊D4311yescharacteristic
257C2×C8—41no—
258C2×C8—41no—
259C2×C8—41no—
260C2×C8—862no—
261C2×C8—862no—
262C2×C8—1721no—
263C2×C8—1721no—
264C2×C8—1721no—
265C2×C8—1721no—
266C4⋊C4—21no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—432no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—3441no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1722no—
282C4⋊C4—1722no—
283C4⋊C4—1722no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4#1062188312yes—
289C42—41no—
290C42—1722no—
291C23#1306329311yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—862no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4—1721no—
320C2×C4—1721no—
321C2×C4—1721no—
322C2×C4—1721no—
323C2×C4SD16×D4311yescharacteristic
324C2×C4C2×#1062188311yescharacteristic
325C2×C4#1306334811yescharacteristic
326C2×C4#1306335211yescharacteristic
327C2×C4#1306335511yescharacteristic
328C2×C4#1306335711yescharacteristic
329C8—81no—
330C8—1722no—
331C8—1722no—
332C22#1458303711yescharacteristic
333C22#1458304811yescharacteristic
334C22#1458306011yescharacteristic
335C22#1458307111yescharacteristic
336C22#1458308011yescharacteristic
337C22#1458308011yescharacteristic
338C22#1458308511yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—82no—
347C4—81no—
348C4—3441no—
349C4—3441no—
350C4—3441no—
351C4—1722no—
352C2#1913353411yescharacteristic
353C2#1913355711yescharacteristic
354C2#1913356211yescharacteristic
355C2#1913374311yescharacteristic
356C2#1913385611yescharacteristic
357C2#1913387011yescharacteristic
358C2#1913392111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2043C2
socle, prime radicalC23×C43#120
hypercenter#2043D43
hypocenterC43#7768
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
206. C43#7768semidirect

Maximal subgroups

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

subgroupindex
#191415462
#191359252
#191324182
#191324172
C43×#20432
#776843