Finite Group Databasebeta

← #24985442

Subgroups — #24985442

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#19135929C211yesmaximal, characteristic
3#19135928C211yesmaximal, characteristic
4#19135697C211yesmaximal, characteristic
5#19132420C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic
8C22×Dic172—21no—
9C2×#13063325C2211yescharacteristic
10C2×#13063257—21no—
11C2×#13063256—21no—
12C2×#13063250—21no—
13#14582841—21no—
14#14582830—21no—
15#14582829—21no—
16#14582805C2211yescharacteristic
17#14582803—21no—
18#14582797C2211yescharacteristic
19#14582785—21no—
20#14582780—21no—
21#14582662—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86—21no—
28C22×Dic86D411yescharacteristic
29C2×Dic172—42no—
30C2×Dic172—42no—
31C2×Dic172—42no—
32C22×C43⋊C8—21no—
33#13063325—42no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×C4⋊Dic43D411yescharacteristic
38C2×C4⋊Dic43D411yescharacteristic
39C2×Dic43⋊C4—21no—
40C2×Dic43⋊C4—21no—
41C2×Dic43⋊C4—21no—
42C2×C4×Dic43—21no—
43#13063257—42no—
44#13063256—42no—
45#13063250—42no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C22×C8×C43—21no—
55C22×C8×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43D411yescharacteristic
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C42×C43C2311yescharacteristic
60#95×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43C2×D411yescharacteristic
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×Dic43—21no—
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—41no—
71C2×Dic86—22no—
72C2×Dic86—21no—
73C2×Dic86—41no—
74C2×Dic86—41no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86SD1612yes—
81C2×C8×C43—22no—
82C2×C8×C43—22no—
83C2×C8×C43—41no—
84C2×C8×C43—41no—
85C2×C8×C43—41no—
86C2×C8×C43—41no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—41no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C42×C43—41no—
93C4⋊Dic43—22no—
94C4⋊Dic43—22no—
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100C4⋊Dic43—41no—
101Dic43⋊C4—41no—
102Dic43⋊C4—41no—
103Dic43⋊C4—81no—
104Dic43⋊C4—81no—
105C4×Dic43—81no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—41no—
108C2×C43⋊C8—41no—
109Dic172—48no—
110C23×C43#12011yescharacteristic
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43C2×SD1611yescharacteristic
124C2×C4×C43#13511yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43#13711yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×Dic43—22no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—41no—
140C2×Dic43—41no—
141C2×Dic43—42no—
142C2×Dic43—81no—
143C2×Dic43—81no—
144Dic86—42no—
145Dic86—42no—
146Dic86—42no—
147Dic86—81no—
148Dic86—81no—
149Dic86—81no—
150C8×C43—42no—
151C8×C43—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—81no—
168C4×C43—81no—
169Dic43—42no—
170Dic43—82no—
171Dic43—81no—
172Dic43—81no—
173Dic43—81no—
174#2809—431no—
175#2058—431no—
176#2058—431no—
177#2016—431no—
178#1272—431no—
179#1271—431no—
180#1271D4311yescharacteristic
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⋊Q8—431no—
190C2×#106—861no—
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—861no—
203#340—861no—
204#336—431no—
205#336C2×D4311yescharacteristic
206#336C2×D4311yescharacteristic
207C43#776011yescharacteristic, complemented, Sylow
208C22×Q8—431no—
209C22×Q8—861no—
210C2×Q16—1722no—
211C2×Q16—1722no—
212C2×Q16—1722no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—861no—
216C4⋊Q8—1722no—
217C2×C4⋊C4—21no—
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⋊C4D17211yescharacteristic
227C2×C4⋊C4D17211yescharacteristic
228C2×C42—861no—
229C2×C42C22×D4311yescharacteristic
230#106—1722no—
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—432no—
243C2×Q8—862no—
244C2×Q8—861no—
245C2×Q8—1721no—
246C2×Q8—1721no—
247C2×Q8—1721no—
248C2×Q8—1721no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—1721no—
259C22×C4C2×D17211yescharacteristic
260C22×C4D4×D4311yescharacteristic
261C22×C4D4×D4311yescharacteristic
262Q16—1728no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—862no—
270C2×C8—1721no—
271C2×C8—1721no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—862no—
278C4⋊C4—862no—
279C4⋊C4—861no—
280C4⋊C4—861no—
281C4⋊C4—3441no—
282C4⋊C4—3441no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C42—41no—
290C42—3441no—
291C23#1306329511yescharacteristic
292Q8—3441no—
293Q8—3441no—
294Q8—3441no—
295Q8—1722no—
296Q8—1722no—
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—862no—
311C2×C4—3441no—
312C2×C4—3441no—
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—1722no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4SD16×D4311yescharacteristic
326C2×C4#1306334411yescharacteristic
327C2×C4#1306334711yescharacteristic
328C2×C4#1306335411yescharacteristic
329C2×C4#1306335711yescharacteristic
330C2×C4#1306335811yescharacteristic
331C8—42no—
332C8—42no—
333C8—1722no—
334C22#1458303911yescharacteristic
335C22#1458306211yescharacteristic
336C22#1458306311yescharacteristic
337C22#1458306811yescharacteristic
338C22#1458308311yescharacteristic
339C22#1458308411yescharacteristic
340C22#1458308711yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—3441no—
350C4—3442no—
351C4—3441no—
352C4—3441no—
353C4—1722no—
354C2#1913351911yescharacteristic
355C2#1913355911yescharacteristic
356C2#1913356011yescharacteristic
357C2#1913374211yescharacteristic
358C2#1913387311yescharacteristic
359C2#1913387511yescharacteristic
360C2#1913390811yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socle, prime radicalC23×C43#120
hypercenter#1271D43
hypocenterC43#7760
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

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
#191359292
#191359282
#191356972
#191324202
#191324172
C43×#12712
#776043