Finite Group Databasebeta

← #24985761

Subgroups — #24985761

Order 11008.

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

normal subgroups only

This group has 366 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#19136072C211yesmaximal, characteristic
3#19136067C211yesmaximal, characteristic
4#19132421C211yesmaximal, characteristic
5#19132419C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#2096C211yesmaximal, characteristic
8C2×#13063258—21no—
9C2×#13063256—21no—
10#14582841—21no—
11#14582839—21no—
12#14582818—21no—
13#14582797C2211yescharacteristic
14#14582797C2211yescharacteristic
15#14582796—21no—
16#14582782—21no—
17#14582780—21no—
18#14582661—21no—
19#14582661—21no—
20#14582654C2211yescharacteristic
21#14582654C2211yescharacteristic
22C2×#106×C43—21no—
23C2×#103×C43—21no—
24C43×#391C2211yescharacteristic
25C43×#384C2211yescharacteristic
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#13063258—42no—
39#13063256—42no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C22×Q8×C43D411yescharacteristic
48C22×C8×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C4⋊C4×C43—21no—
52C2×C4⋊C4×C43D411yescharacteristic
53C2×C42×C43C2311yescharacteristic
54#106×C43—42no—
55#103×C43—42no—
56#95×C43—21no—
57#95×C43—21no—
58C2×Q8×C43—21no—
59C2×Q8×C43—21no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—41no—
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×Dic43—21no—
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C2×C8×C43—22no—
73C2×C8×C43—41no—
74C2×C8×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C42×C43—41no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43SD1612yes—
89Dic43⋊C4—41no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—81no—
94Dic43⋊C4—81no—
95C4×Dic43—81no—
96C2×C43⋊C8—22no—
97C2×C43⋊C8—22no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C23×C43#12011yescharacteristic
103Q8×C43—42no—
104Q8×C43—81no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43C2×SD1611yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×C4×C43#13511yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×C4×C43#13711yescharacteristic
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138C8×C43—42no—
139C43⋊C8—42no—
140C43⋊C8—42no—
141#7807—431nomaximal, Sylow
142C22×C43#44811yescharacteristic
143C22×C43#44911yescharacteristic
144C22×C43#45211yescharacteristic
145C22×C43#45311yescharacteristic
146C22×C43#45611yescharacteristic
147C22×C43#45611yescharacteristic
148C22×C43#45811yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—81no—
156C4×C43—81no—
157C4×C43—161no—
158Dic43—42no—
159Dic43—81no—
160Dic43—81no—
161Dic43—81no—
162#2805—431no—
163#2096D4311yescharacteristic
164#2084—431no—
165#2083—431no—
166#1272—431no—
167#1271—431no—
168#1271—431no—
169C2×C43#160911yescharacteristic
170C2×C43#161111yescharacteristic
171C2×C43#161811yescharacteristic
172C2×C43#162211yescharacteristic
173C2×C43#165011yescharacteristic
174C2×C43#165311yescharacteristic
175C2×C43#166011yescharacteristic
176C2×#107—861no—
177C2×#106—21no—
178C2×#106—861no—
179C2×#103—21no—
180#400—861no—
181#400—861no—
182#395—861no—
183#391C2×D4311yescharacteristic
184#389—431no—
185#389—431no—
186#389—861no—
187#387—861no—
188#387—861no—
189#384C2×D4311yescharacteristic
190#340—861no—
191#340—861no—
192#336—431no—
193#336—431no—
194#336C2×D4311yescharacteristic
195C43#780711yescharacteristic, complemented, Sylow
196C22×Q8C22⋊D4311yescharacteristic
197C22×C8—21no—
198C22×C8—861no—
199C22×C8—861no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—431no—
204C2×C4⋊C4—431no—
205C2×C4⋊C4—431no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4—861no—
211C2×C4⋊C4C22⋊D4311yescharacteristic
212C2×C42—861no—
213C2×C42C22×D4311yescharacteristic
214#107—1722no—
215#106—42no—
216#106—1722no—
217#103—42no—
218#95—21no—
219#95—21no—
220#95—861no—
221#95—861no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227C2×Q8—21no—
228C2×Q8—21no—
229C2×Q8—41no—
230C2×Q8—41no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4D4×D4311yescharacteristic
239C22×C4D4×D4311yescharacteristic
240C22×C4C2×C22⋊D4311yescharacteristic
241C2×C8—22no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—862no—
245C2×C8—862no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—432no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—3441no—
262C4⋊C4—3441no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C42—41no—
270C42—3441no—
271C23#1306329311yescharacteristic
272Q8—42no—
273Q8—81no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—862no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4SD16×D4311yescharacteristic
302C2×C4#1306334511yescharacteristic
303C2×C4#1306334611yescharacteristic
304C2×C4#1306335211yescharacteristic
305C2×C4#1306335411yescharacteristic
306C2×C4#1306335611yescharacteristic
307C8—42no—
308C8—1722no—
309C8—1722no—
310C22#1458303611yescharacteristic
311C22#1458304311yescharacteristic
312C22#1458305911yescharacteristic
313C22#1458306611yescharacteristic
314C22#1458308011yescharacteristic
315C22#1458308011yescharacteristic
316C22#1458308811yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—161no—
326C4—3441no—
327C4—3441no—
328C4—3441no—
329C4—1722no—
330C2#1913359111yescharacteristic
331C2#1913360111yescharacteristic
332C2#1913364111yescharacteristic
333C2#1913366411yescharacteristic
334C2#1913385011yescharacteristic
335C2#1913387111yescharacteristic
336C2#1913390411yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2096C2
socle, prime radicalC23×C43#120
hypercenter#2096D43
hypocenterC43#7807
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
195. C43#7807semidirect

Maximal subgroups

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

subgroupindex
#191425502
#191360722
#191360672
#191324212
#191324192
#191324172
C43×#20962
#780743