Finite Group Databasebeta

← #24985487

Subgroups — #24985487

Order 11008.

392 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 81 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#19142550C211yesmaximal, characteristic
2#19135925C211yesmaximal, characteristic
3#19135838C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#2024C211yesmaximal, characteristic
8C2×#13063256—21no—
9C2×#13063249—21no—
10C2×#13063249—21no—
11#14582841—21no—
12#14582839—21no—
13#14582818—21no—
14#14582797C2211yescharacteristic
15#14582797C2211yescharacteristic
16#14582796—21no—
17#14582782—21no—
18#14582780—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#103×C43—21no—
24C43×#391C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43D411yescharacteristic
30C2×C4⋊Dic43D411yescharacteristic
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38#13063256—42no—
39#13063249—42no—
40#13063249—42no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C22×Q8×C43—21no—
49C22×Q8×C43D411yescharacteristic
50C22×C8×C43—21no—
51C4⋊Q8×C43—42no—
52C2×C4⋊C4×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C42×C43C2311yescharacteristic
56#103×C43—42no—
57#95×C43—21no—
58#95×C43—21no—
59C2×Q8×C43—22no—
60C2×Q8×C43—21no—
61C2×Q8×C43—21no—
62C2×Q8×C43—41no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43—41no—
72C22×C4×C43C2×D411yescharacteristic
73C22×C4×C43C2×D411yescharacteristic
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—21no—
76C22×Dic43—21no—
77C22×Dic43—21no—
78C22×Dic43—21no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43—41no—
82C4⋊C4×C43—22no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C42×C43—41no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43SD1612yes—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99Dic43⋊C4—81no—
100C4×Dic43—81no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43#12011yescharacteristic
108Q8×C43—42no—
109Q8×C43—42no—
110Q8×C43—42no—
111Q8×C43—81no—
112Q8×C43—81no—
113Q8×C43—81no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—42no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43C2×SD1611yescharacteristic
130C2×C4×C43#13511yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43#13711yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×Dic43—22no—
136C2×Dic43—41no—
137C2×Dic43—41no—
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—
147C8×C43—81no—
148C43⋊C8—42no—
149C43⋊C8—81no—
150#7767—431nomaximal, Sylow
151C22×C43#44811yescharacteristic
152C22×C43#45211yescharacteristic
153C22×C43#45211yescharacteristic
154C22×C43#45411yescharacteristic
155C22×C43#45511yescharacteristic
156C22×C43#45611yescharacteristic
157C22×C43B(4,𝔽2)11yescharacteristic
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—82no—
165C4×C43—81no—
166C4×C43—81no—
167Dic43—42no—
168Dic43—81no—
169Dic43—81no—
170Dic43—81no—
171#2805—431no—
172#2058—431no—
173#2043—431no—
174#2024D4311yescharacteristic
175#1272—431no—
176#1271—431no—
177#1271—431no—
178C2×C43#159911yescharacteristic
179C2×C43#160311yescharacteristic
180C2×C43#160611yescharacteristic
181C2×C43#163811yescharacteristic
182C2×C43#164311yescharacteristic
183C2×C43#165311yescharacteristic
184C2×C43#166411yescharacteristic
185C2×C4⋊Q8C2×D4311yescharacteristic
186C2×#106—861no—
187C2×#103—21no—
188C2×#103—861no—
189C2×#103—861no—
190#400—861no—
191#400—861no—
192#395—861no—
193#391C2×D4311yescharacteristic
194#389—431no—
195#389—431no—
196#389—861no—
197#387—861no—
198#387—861no—
199#340—21no—
200#340—861no—
201#336—431no—
202#336—431no—
203#336C2×D4311yescharacteristic
204C43#776711yescharacteristic, complemented, Sylow
205C22×Q8—21no—
206C22×Q8C22⋊D4311yescharacteristic
207C22×C8—21no—
208C22×C8—861no—
209C22×C8—861no—
210C4⋊Q8—42no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—861no—
218C2×C4⋊C4—861no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C22⋊D4311yescharacteristic
222C2×C42—861no—
223C2×C42C22×D4311yescharacteristic
224#106—1722no—
225#103—42no—
226#103—1722no—
227#103—1722no—
228#95—21no—
229#95—21no—
230#95—861no—
231#95—861no—
232#95—861no—
233#95—861no—
234#95—861no—
235#95—861no—
236#95—861no—
237C2×Q8—22no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—41no—
241C2×Q8—41no—
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—1721no—
262C2×C8—1721no—
263C2×C8—1721no—
264C2×C8—1721no—
265C2×C8—1721no—
266C4⋊C4—22no—
267C4⋊C4—22no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—432no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—3441no—
276C4⋊C4—3441no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C42—41no—
284C42—3441no—
285C23#1306329311yescharacteristic
286Q8—42no—
287Q8—42no—
288Q8—42no—
289Q8—81no—
290Q8—81no—
291Q8—81no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—862no—
308C2×C4—1721no—
309C2×C4—1721no—
310C2×C4—1721no—
311C2×C4—1721no—
312C2×C4—1721no—
313C2×C4—1721no—
314C2×C4—1721no—
315C2×C4—1721no—
316C2×C4—1721no—
317C2×C4—1721no—
318C2×C4—1721no—
319C2×C4SD16×D4311yescharacteristic
320C2×C4#1306334511yescharacteristic
321C2×C4#1306334811yescharacteristic
322C2×C4#1306335411yescharacteristic
323C2×C4#1306335611yescharacteristic
324C2×C4#1306335711yescharacteristic
325C8—81no—
326C8—3441no—
327C8—1722no—
328C22#1458303611yescharacteristic
329C22#1458305911yescharacteristic
330C22#1458306011yescharacteristic
331C22#1458307011yescharacteristic
332C22#1458307611yescharacteristic
333C22#1458308011yescharacteristic
334C22#1458308511yescharacteristic
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—82no—
342C4—81no—
343C4—81no—
344C4—3441no—
345C4—3441no—
346C4—3441no—
347C4—1722no—
348C2#1913353311yescharacteristic
349C2#1913355711yescharacteristic
350C2#1913357311yescharacteristic
351C2#1913376611yescharacteristic
352C2#1913379911yescharacteristic
353C2#1913387111yescharacteristic
354C2#1913392811yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2024C2
socle, prime radicalC23×C43#120
hypercenter#2024D43
hypocenterC43#7767
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
204. C43#7767semidirect

Maximal subgroups

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

subgroupindex
#191425502
#191359252
#191358382
#191324212
#191324192
#191324172
C43×#20242
#776743