Finite Group Databasebeta

← #24985439

Subgroups — #24985439

Order 11008.

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

normal subgroups only

This group has 424 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#19142580C211yesmaximal, characteristic
2#19135925C211yesmaximal, characteristic
3#19135695C211yesmaximal, characteristic
4#19132420C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132418C211yesmaximal, characteristic
7C43×#2058C211yesmaximal, characteristic
8C22×#10621885—21no—
9C2×#13063256—21no—
10C2×#13063249—21no—
11#14582841—21no—
12#14582830—21no—
13#14582829—21no—
14#14582805C2211yescharacteristic
15#14582803—21no—
16#14582797C2211yescharacteristic
17#14582785—21no—
18#14582780—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×#106×C43—21no—
24C43×#389C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621885—42no—
29C2×#10621885—42no—
30C2×#10621885—42no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×C4⋊Dic43D411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—21no—
39C2×C4×Dic43—21no—
40#13063256—42no—
41#13063249—42no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C22×Q8×C43—21no—
51C22×C8×C43—21no—
52C4⋊Q8×C43—42no—
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#106×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×Dic86—21no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86SD1612yes—
81C2×C8×C43—22no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C4⋊C4×C43—41no—
93C42×C43—41no—
94#10621885—48no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99Dic43⋊C4—41no—
100Dic43⋊C4—41no—
101Dic43⋊C4—81no—
102Dic43⋊C4—81no—
103C4×Dic43—81no—
104C2×C43⋊C8—22no—
105C2×C43⋊C8—22no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109C2×C43⋊C8—41no—
110C23×C43#12011yescharacteristic
111Q8×C43—42no—
112Q8×C43—42no—
113Q8×C43—81no—
114Q8×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—42no—
128C2×C4×C43—81no—
129C2×C4×C43—81no—
130C2×C4×C43C2×SD1611yescharacteristic
131C2×C4×C43#13511yescharacteristic
132C2×C4×C43#13511yescharacteristic
133C2×C4×C43#13711yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×C4×C43#13711yescharacteristic
136C2×Dic43—22no—
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—
147C2×Dic43—41no—
148Dic86—42no—
149Dic86—81no—
150C8×C43—42no—
151C43⋊C8—42no—
152C43⋊C8—42no—
153#7760—431nomaximal, Sylow
154C22×C43#44811yescharacteristic
155C22×C43#45211yescharacteristic
156C22×C43#45211yescharacteristic
157C22×C43#45311yescharacteristic
158C22×C43#45611yescharacteristic
159C22×C43#45611yescharacteristic
160C22×C43B(4,𝔽2)11yescharacteristic
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—21no—
167C4×C43—82no—
168C4×C43—81no—
169C4×C43—81no—
170Dic43—42no—
171Dic43—81no—
172Dic43—81no—
173Dic43—81no—
174#2809—431no—
175#2058—431no—
176#2058D4311yescharacteristic
177#2016—431no—
178#1272—431no—
179#1271—431no—
180#1271—431no—
181C2×C43#159611yescharacteristic
182C2×C43#160311yescharacteristic
183C2×C43#160311yescharacteristic
184C2×C43#163411yescharacteristic
185C2×C43#165311yescharacteristic
186C2×C43#165311yescharacteristic
187C2×C43#166011yescharacteristic
188C22×Q16—861no—
189C2×C4⋊Q8C2×D4311yescharacteristic
190C2×#106—21no—
191C2×#106—861no—
192C2×#103—861no—
193#400—861no—
194#398—861no—
195#398—861no—
196#391—431no—
197#391—861no—
198#389—431no—
199#389C2×D4311yescharacteristic
200#387—861no—
201#387—861no—
202#340—21no—
203#340—861no—
204#336—431no—
205#336—431no—
206#336C2×D4311yescharacteristic
207C43#776011yescharacteristic, complemented, Sylow
208C22×Q8—21no—
209C22×Q8—431no—
210C2×Q16—1722no—
211C2×Q16—1722no—
212C2×Q16—1722no—
213C22×C8—21no—
214C22×C8—861no—
215C22×C8—861no—
216C4⋊Q8—42no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—861no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4C22⋊D4311yescharacteristic
227C2×C4⋊C4C22⋊D4311yescharacteristic
228C2×C42—861no—
229C2×C42C22×D4311yescharacteristic
230#106—42no—
231#106—1722no—
232#103—1722no—
233#95—21no—
234#95—861no—
235#95—861no—
236#95—861no—
237#95—861no—
238#95—861no—
239#95—861no—
240#95—861no—
241#95—861no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—432no—
249C2×Q8—861no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—41no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—861no—
259C22×C4D4×D4311yescharacteristic
260C22×C4D4×D4311yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262Q16—1728no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—41no—
266C2×C8—862no—
267C2×C8—862no—
268C2×C8—1721no—
269C2×C8—1721no—
270C2×C8—1721no—
271C2×C8—1721no—
272C4⋊C4—22no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—3441no—
284C4⋊C4—3441no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C42—41no—
290C42—3441no—
291C23#1306329311yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296Q8—3441no—
297Q8—1722no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—862no—
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×C4—1721no—
324C2×C4—1721no—
325C2×C4SD16×D4311yescharacteristic
326C2×C4#1306334511yescharacteristic
327C2×C4#1306334611yescharacteristic
328C2×C4#1306335411yescharacteristic
329C2×C4#1306335411yescharacteristic
330C2×C4#1306335611yescharacteristic
331C8—42no—
332C8—1722no—
333C8—1722no—
334C22#1458303611yescharacteristic
335C22#1458305811yescharacteristic
336C22#1458305911yescharacteristic
337C22#1458306511yescharacteristic
338C22#1458308011yescharacteristic
339C22#1458308111yescharacteristic
340C22#1458308511yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—82no—
349C4—81no—
350C4—3441no—
351C4—3441no—
352C4—3441no—
353C4—1722no—
354C2#1913351611yescharacteristic
355C2#1913355511yescharacteristic
356C2#1913355611yescharacteristic
357C2#1913373911yescharacteristic
358C2#1913386911yescharacteristic
359C2#1913387111yescharacteristic
360C2#1913390511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2058C2
socle, prime radicalC23×C43#120
hypercenter#2058D43
hypocenterC43#7760
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
207. C43#7760semidirect

Maximal subgroups

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

subgroupindex
#191425802
#191359252
#191356952
#191324202
#191324192
#191324182
C43×#20582
#776043