Finite Group Databasebeta

← #25009664

Subgroups — #25009664

Order 11008.

352 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 57 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#19140297C211yesmaximal, characteristic
2#19135946C211yesmaximal, characteristic
3#19133639C211yesmaximal, characteristic
4#19133568C211yesmaximal, characteristic
5#19132621C211yesmaximal, characteristic
6#19132538C211yesmaximal, characteristic
7C43×#1354C211yesmaximal, characteristic
8#14583530C2211yescharacteristic
9#14583235—21no—
10#14583055—21no—
11#14582941—21no—
12#14582838C2211yescharacteristic
13#14582831—21no—
14#14582806—21no—
15#14582798—21no—
16#14582784—21no—
17#14582780—21no—
18#14582764C2211yescharacteristic
19#14582744—21no—
20#14582660—21no—
21#14582637—21no—
22#14582635—21no—
23#14582625C2211yescharacteristic
24C43×#395C2211yescharacteristic
25C43×#343C2211yescharacteristic
26C43×#324C2211yescharacteristic
27C2×#10621885—41no—
28#13063324—41no—
29#13063316—41no—
30#13063304—21no—
31#13063304—21no—
32#13063284—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43D411yescharacteristic
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43D411yescharacteristic
41#13063259—41no—
42#13063259—41no—
43#13063257—41no—
44#13063250—41no—
45#13063249—41no—
46C22⋊(C43⋊C8)—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95D411yescharacteristic
55C22×Q8×C43D411yescharacteristic
56C2×M16×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2311yescharacteristic
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C2×Q8×C43—42no—
63C2×Q8×C43—41no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2×D411yescharacteristic
67C22×C4×C43C2×D411yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—21no—
70C22×Dic43—21no—
71C22×Dic43—21no—
72C22×Dic43—21no—
73C2×Dic86—21no—
74C2×Dic86—21no—
75M16×C43—22no—
76M16×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—42no—
81C22⋊Dic43—41no—
82#10621885—82no—
83C4⋊Dic43—21no—
84C4⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—42no—
88C4⋊Dic43—41no—
89C4⋊Dic43—41no—
90C4⋊Dic43—81no—
91Dic43⋊C4—42no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C4×Dic43—21no—
95C4×Dic43—42no—
96C4×Dic43—42no—
97C4×Dic43—41no—
98C4×Dic43Q1612yescomplemented
99C2×C43⋊C8—41no—
100C23×C43#12011yescharacteristic
101Q8×C43—42no—
102Q8×C43—81no—
103C2×C4×C43—21no—
104C2×C4×C43—21no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
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#13711yescharacteristic
117C2×Dic43—22no—
118C2×Dic43—41no—
119C2×Dic43—41no—
120C2×Dic43—41no—
121C2×Dic43—41no—
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—
131Dic86—81no—
132Dic86—81no—
133C8×C43—42no—
134C8×C43—81no—
135C43⋊C8—81no—
136#12258—431nomaximal, Sylow
137C22×C43—21no—
138C22×C43—21no—
139C22×C43#45111yescharacteristic
140C22×C43#45611yescharacteristic
141C22×C43B(4,𝔽2)11yescharacteristic
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—42no—
145C4×C43—41no—
146C4×C43—41no—
147C4×C43—42no—
148Dic43—42no—
149Dic43—81no—
150Dic43—81no—
151Dic43—81no—
152Dic43—81no—
153Dic43—81no—
154#2612—431no—
155#2061—431no—
156#1617—431no—
157#1605—431no—
158#1354D4311yescharacteristic
159#1353—431no—
160#1324—431no—
161C2×C43—21no—
162C2×C43—21no—
163C2×C43#160511yescharacteristic
164C2×C43#219711yescharacteristic
165C2×C43#220411yescharacteristic
166#544—431no—
167#484—861no—
168#451—861no—
169#428—861no—
170#400—431no—
171#398—861no—
172#395C2×D4311yescharacteristic
173#391—861no—
174#389—861no—
175#387—861no—
176#387—861no—
177#382—431no—
178#376—861no—
179#343C2×D4311yescharacteristic
180#339—861no—
181#328—861no—
182#328—861no—
183#324—431no—
184#324C2×D4311yescharacteristic
185C43#1225811yescharacteristic, complemented, Sylow
186C22×Q8D17211yescharacteristic
187C2×Q16—1721no—
188C2×M16—21no—
189C4⋊Q8—1721no—
190#125—1721no—
191C22⋊Q8—861no—
192C22⋊Q8—861no—
193#117—861no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—431no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—861no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4C22×D4311yescharacteristic
201C2×C42—431no—
202C2×C42—861no—
203C2×C42—861no—
204#107—1721no—
205#107—1721no—
206#106—1721no—
207#103—1721no—
208#103—1721no—
209C22⋊C8—21no—
210C22⋊C8—861no—
211#95—21no—
212#95—431no—
213#95—861no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95—861no—
219#95—861no—
220#95D17211yescharacteristic
221C2×Q8—42no—
222C2×Q8—41no—
223C2×Q8—861no—
224C2×Q8—861no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4C2×D17211yescharacteristic
232C22×C4D4×D4311yescharacteristic
233C22×C4D4×D4311yescharacteristic
234Q16—3442no—
235M16—22no—
236M16—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—1721no—
240C4⋊C4—41no—
241C4⋊C4—42no—
242C4⋊C4—861no—
243C4⋊C4—861no—
244C4⋊C4—861no—
245C4⋊C4—861no—
246C4⋊C4—3441no—
247C4⋊C4—1721no—
248C4⋊C4—1721no—
249C4⋊C4—1722no—
250C4⋊C4—1722no—
251C4⋊C4—1721no—
252C4⋊C4—1721no—
253C22⋊C4—1721no—
254C42—432no—
255C42—861no—
256C42—1722no—
257C42—1722no—
258C42—1721no—
259C23#1306329511yescharacteristic
260Q8—42no—
261Q8—81no—
262Q8—3441no—
263Q8—3441no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—862no—
277C2×C4—1721no—
278C2×C4—1721no—
279C2×C4—1721no—
280C2×C4—1721no—
281C2×C4—1721no—
282C2×C4—1721no—
283C2×C4—1721no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4Q16×D4311yescharacteristic
291C2×C4#1306335411yescharacteristic
292C8—42no—
293C8—81no—
294C8—3441no—
295C22—21no—
296C22—21no—
297C22#1458305611yescharacteristic
298C22#1458308311yescharacteristic
299C22#1458308711yescharacteristic
300C4—21no—
301C4—21no—
302C4—42no—
303C4—41no—
304C4—41no—
305C4—42no—
306C4—3441no—
307C4—3441no—
308C4—3441no—
309C4—3441no—
310C4—3441no—
311C4—1722no—
312C2—21no—
313C2—21no—
314C2#1913357011yescharacteristic
315C2#1913658711yescharacteristic
316C2#1913662311yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1354C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1354D43
hypocenterC43#12258
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1354

Complements

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

NH ≅ G/Ntype
98. C4×Dic43Q16semidirect
185. C43#12258semidirect

Maximal subgroups

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

subgroupindex
#191402972
#191359462
#191336392
#191335682
#191326212
#191325382
C43×#13542
#1225843