Finite Group Databasebeta

← #24985753

Subgroups — #24985753

Order 11008.

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

normal subgroups only

This group has 350 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#19142545C211yesmaximal, characteristic
2#19136152C211yesmaximal, characteristic
3#19136004C211yesmaximal, characteristic
4#19132420C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132418C211yesmaximal, characteristic
7C43×#2083C211yesmaximal, characteristic
8C2×#13063248—21no—
9#14582841—21no—
10#14582837—21no—
11#14582819—21no—
12#14582805C2211yescharacteristic
13#14582797C2211yescharacteristic
14#14582794—21no—
15#14582785—21no—
16#14582784—21no—
17#14582661—21no—
18#14582661—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×#107×C43—21no—
23C43×#389C2211yescharacteristic
24C43×#384C2211yescharacteristic
25C43×#340—21no—
26C43×#336C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×C4×Dic43—21no—
37#13063248—42no—
38C43⋊#95—21no—
39C43⋊#95—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C22×C8×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43D411yescharacteristic
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C42×C43C2311yescharacteristic
54#107×C43—42no—
55#95×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—21no—
66C2×Dic86—21no—
67C2×Dic86—21no—
68C2×Dic86—41no—
69C2×Dic86—41no—
70C2×C8×C43—22no—
71C2×C8×C43—41no—
72C2×C8×C43—41no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—42no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C42×C43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—41no—
86C4⋊Dic43—41no—
87C4⋊Dic43Q1612yes—
88Dic43⋊C4—41no—
89Dic43⋊C4—41no—
90Dic43⋊C4—81no—
91Dic43⋊C4—81no—
92C4×Dic43—81no—
93C2×C43⋊C8—41no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8—41no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C23×C43#12011yescharacteristic
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—21no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43—41no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43C2×Q1611yescharacteristic
116C2×C4×C43#13511yescharacteristic
117C2×C4×C43#13511yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C43#13711yescharacteristic
121C2×Dic43—22no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133Dic86—42no—
134Dic86—81no—
135C8×C43—42no—
136C43⋊C8—81no—
137C43⋊C8—81no—
138#7806—431nomaximal, Sylow
139C22×C43#44911yescharacteristic
140C22×C43#44911yescharacteristic
141C22×C43#45111yescharacteristic
142C22×C43#45411yescharacteristic
143C22×C43#45511yescharacteristic
144C22×C43#45611yescharacteristic
145C22×C43#45811yescharacteristic
146C4×C43—21no—
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—81no—
153C4×C43—81no—
154C4×C43—161no—
155Dic43—42no—
156Dic43—81no—
157Dic43—81no—
158Dic43—81no—
159#2805—431no—
160#2099—431no—
161#2083D4311yescharacteristic
162#2072—431no—
163#1272—431no—
164#1271—431no—
165#1271—431no—
166C2×C43#160911yescharacteristic
167C2×C43#161211yescharacteristic
168C2×C43#161711yescharacteristic
169C2×C43#162811yescharacteristic
170C2×C43#164411yescharacteristic
171C2×C43#164811yescharacteristic
172C2×C43#166411yescharacteristic
173C2×#107—21no—
174C2×#103—861no—
175#400—861no—
176#400—861no—
177#395—861no—
178#391—431no—
179#389—431no—
180#389—861no—
181#389C2×D4311yescharacteristic
182#387—861no—
183#387—861no—
184#384C2×D4311yescharacteristic
185#340—21no—
186#340—861no—
187#340—861no—
188#340—861no—
189#336—431no—
190#336—431no—
191#336C2×D4311yescharacteristic
192C43#780611yescharacteristic, complemented, Sylow
193C22×Q8—431no—
194C22×C8—21no—
195C22×C8—861no—
196C22×C8—861no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—431no—
202C2×C4⋊C4—431no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C4⋊C4—861no—
207C2×C4⋊C4C22⋊D4311yescharacteristic
208C2×C4⋊C4C22⋊D4311yescharacteristic
209C2×C42—861no—
210C2×C42C22×D4311yescharacteristic
211#107—42no—
212#103—1722no—
213#95—21no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222C2×Q8—861no—
223C2×Q8—861no—
224C2×Q8—1721no—
225C2×Q8—1721no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—41no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232C22×C4—861no—
233C22×C4D4×D4311yescharacteristic
234C22×C4D4×D4311yescharacteristic
235C22×C4C2×C22⋊D4311yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—1721no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8—1721no—
243C2×C8—1721no—
244C2×C8—1721no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—42no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—432no—
256C4⋊C4—861no—
257C4⋊C4—3441no—
258C4⋊C4—3441no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C42—41no—
264C42—3441no—
265C23#1306329311yescharacteristic
266Q8—3441no—
267Q8—1722no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—862no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4Q16×D4311yescharacteristic
296C2×C4#1306334411yescharacteristic
297C2×C4#1306334511yescharacteristic
298C2×C4#1306334911yescharacteristic
299C2×C4#1306335111yescharacteristic
300C2×C4#1306335711yescharacteristic
301C8—42no—
302C8—3441no—
303C8—3441no—
304C22#1458304111yescharacteristic
305C22#1458304211yescharacteristic
306C22#1458305311yescharacteristic
307C22#1458307011yescharacteristic
308C22#1458307511yescharacteristic
309C22#1458308111yescharacteristic
310C22#1458308811yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—81no—
319C4—161no—
320C4—3441no—
321C4—3441no—
322C4—3441no—
323C4—1722no—
324C2#1913359011yescharacteristic
325C2#1913360611yescharacteristic
326C2#1913363511yescharacteristic
327C2#1913370311yescharacteristic
328C2#1913380711yescharacteristic
329C2#1913383411yescharacteristic
330C2#1913392711yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2083C2
socle, prime radicalC23×C43#120
hypercenter#2083D43
hypocenterC43#7806
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
192. C43#7806semidirect

Maximal subgroups

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

subgroupindex
#191425452
#191361522
#191360042
#191324202
#191324192
#191324182
C43×#20832
#780643