Finite Group Databasebeta

← #24985729

Subgroups — #24985729

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#19142580C211yesmaximal, characteristic
2#19136137C211yesmaximal, characteristic
3#19136068C211yesmaximal, characteristic
4#19136066C211yesmaximal, characteristic
5#19132420C211yesmaximal, characteristic
6#19132417C211yesmaximal, characteristic
7C43×#1271C211yesmaximal, characteristic
8C2×#13063259—21no—
9C2×#13063258—21no—
10C2×#13063257—21no—
11C2×#13063250—21no—
12#14582841—21no—
13#14582830—21no—
14#14582829—21no—
15#14582805C2211yescharacteristic
16#14582803—21no—
17#14582797C2211yescharacteristic
18#14582785—21no—
19#14582780—21no—
20#14582769C2211yescharacteristic
21#14582662—21no—
22#14582661—21no—
23#14582654C2211yescharacteristic
24C43×#389C2211yescharacteristic
25C43×#336C2211yescharacteristic
26C43×#336C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C22×C43⋊C8—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43D411yescharacteristic
33C2×C4⋊Dic43D411yescharacteristic
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×C4×Dic43—21no—
39#13063259—42no—
40#13063258—42no—
41#13063257—42no—
42#13063250—42no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C22×C8×C43—21no—
52C22×C8×C43—21no—
53C2×C4⋊C4×C43—21no—
54C2×C4⋊C4×C43D411yescharacteristic
55C2×C4⋊C4×C43D411yescharacteristic
56C2×C42×C43C2311yescharacteristic
57#95×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43C2×D411yescharacteristic
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—21no—
66C22×Dic43—21no—
67C22×Dic43—41no—
68C2×Dic86—21no—
69C2×Dic86—41no—
70C2×Dic86—41no—
71C2×Dic86Q1612yes—
72C2×C8×C43—22no—
73C2×C8×C43—22no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C42×C43—41no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—41no—
87C4⋊Dic43—41no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—81no—
97Dic43⋊C4—81no—
98C4×Dic43—81no—
99C2×C43⋊C8—22no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C23×C43#12011yescharacteristic
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—41no—
110C2×C4×C43—41no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
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—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136Dic86—42no—
137Dic86—81no—
138C8×C43—42no—
139C8×C43—42no—
140C43⋊C8—42no—
141#7802—431nomaximal, Sylow
142C22×C43#44911yescharacteristic
143C22×C43#44911yescharacteristic
144C22×C43#45111yescharacteristic
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—
157Dic43—42no—
158Dic43—81no—
159Dic43—81no—
160Dic43—81no—
161Dic43—161no—
162#2809—431no—
163#2096—431no—
164#2083—431no—
165#2083—431no—
166#1272—431no—
167#1271—431no—
168#1271D4311yescharacteristic
169C2×C43#160911yescharacteristic
170C2×C43#160911yescharacteristic
171C2×C43#161411yescharacteristic
172C2×C43#162411yescharacteristic
173C2×C43#164811yescharacteristic
174C2×C43#164811yescharacteristic
175C2×C43#166011yescharacteristic
176C2×#107—861no—
177C2×#107—861no—
178C2×#106—861no—
179C2×#103—861no—
180#400—861no—
181#398—861no—
182#398—861no—
183#391—431no—
184#391—861no—
185#389—431no—
186#389C2×D4311yescharacteristic
187#387—861no—
188#387—861no—
189#384—431no—
190#340—861no—
191#340—861no—
192#336—431no—
193#336C2×D4311yescharacteristic
194#336C2×D4311yescharacteristic
195C43#780211yescharacteristic, complemented, Sylow
196C22×Q8—431no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—861no—
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⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C4⋊C4D17211yescharacteristic
211C2×C4⋊C4D17211yescharacteristic
212C2×C42—861no—
213C2×C42C22×D4311yescharacteristic
214#107—1722no—
215#107—1722no—
216#106—1722no—
217#103—1722no—
218#95—21no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95—861no—
223#95—861no—
224#95—861no—
225#95—861no—
226#95—861no—
227C2×Q8—432no—
228C2×Q8—861no—
229C2×Q8—1721no—
230C2×Q8—1721no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—861no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4—861no—
237C22×C4—1721no—
238C22×C4C2×D17211yescharacteristic
239C22×C4D4×D4311yescharacteristic
240C22×C4D4×D4311yescharacteristic
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—862no—
248C2×C8—1721no—
249C2×C8—1721no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—3441no—
258C4⋊C4—3441no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C4⋊C4—1721no—
268C4⋊C4—1721no—
269C42—41no—
270C42—3441no—
271C23#1306329511yescharacteristic
272Q8—3441no—
273Q8—1722no—
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—862no—
287C2×C4—3441no—
288C2×C4—3441no—
289C2×C4—3441no—
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×C4Q16×D4311yescharacteristic
302C2×C4#1306334611yescharacteristic
303C2×C4#1306334711yescharacteristic
304C2×C4#1306334911yescharacteristic
305C2×C4#1306335311yescharacteristic
306C2×C4#1306335411yescharacteristic
307C8—42no—
308C8—42no—
309C8—1722no—
310C22#1458304511yescharacteristic
311C22#1458304611yescharacteristic
312C22#1458305611yescharacteristic
313C22#1458306811yescharacteristic
314C22#1458308311yescharacteristic
315C22#1458308411yescharacteristic
316C22#1458309011yescharacteristic
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—81no—
324C4—81no—
325C4—3441no—
326C4—3441no—
327C4—3441no—
328C4—1722no—
329C4—6881no—
330C2#1913359311yescharacteristic
331C2#1913359411yescharacteristic
332C2#1913362111yescharacteristic
333C2#1913368011yescharacteristic
334C2#1913383811yescharacteristic
335C2#1913383911yescharacteristic
336C2#1913390811yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1271C2
socle, prime radicalC23×C43#120
hypercenter#1271D43
hypocenterC43#7802
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
195. C43#7802semidirect

Maximal subgroups

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

subgroupindex
#191425802
#191361372
#191360682
#191360662
#191324202
#191324172
C43×#12712
#780243