Finite Group Databasebeta

← #25009424

Subgroups — #25009424

Order 11008.

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

normal subgroups only

This group has 346 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#19142482C211yesmaximal, characteristic
2#19135753C211yesmaximal, characteristic
3#19133637C211yesmaximal, characteristic
4#19132625C211yesmaximal, characteristic
5#19132623C211yesmaximal, characteristic
6#19132528C211yesmaximal, characteristic
7C43×#1605C211yesmaximal, characteristic
8#14583232—21no—
9#14582907—21no—
10#14582840—21no—
11#14582838C2211yescharacteristic
12#14582829—21no—
13#14582806—21no—
14#14582804C2211yescharacteristic
15#14582803—21no—
16#14582785—21no—
17#14582782—21no—
18#14582668C2211yescharacteristic
19#14582658—21no—
20#14582636—21no—
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#451—21no—
24C43×#395C2211yescharacteristic
25C43×#328—21no—
26C43×#324C2211yescharacteristic
27C22×Dic86D411yescharacteristic
28C2×#10621877—21no—
29C2×C4⋊Dic43—21no—
30C2×C4⋊Dic43D411yescharacteristic
31C2×Dic43⋊C4—21no—
32C2×Dic43⋊C4—21no—
33C2×C4×Dic43—21no—
34C2×C4×Dic43D411yescharacteristic
35#13063258—41no—
36#13063249—41no—
37#13063248—41no—
38#13063248—41no—
39C22⋊(C43⋊C8)—21no—
40C43⋊#95—21no—
41C43⋊#95—21no—
42C43⋊#95—21no—
43C43⋊#95—21no—
44C43⋊#95—21no—
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95D411yescharacteristic
49C22×Q8×C43D411yescharacteristic
50C2×Q16×C43—41no—
51C4⋊Q8×C43—41no—
52#125×C43—41no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43—21no—
55#117×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43C2311yescharacteristic
58#103×C43—41no—
59C22⋊C8×C43—21no—
60#95×C43—21no—
61#95×C43D411yescharacteristic
62C2×Q8×C43—21no—
63C2×Q8×C43—21no—
64C2×Q8×C43—42no—
65C2×Q8×C43—41no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—21no—
74C22×Dic43—21no—
75C2×Dic86—21no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C2×Dic86Q1612yescomplemented
79Q16×C43—82no—
80C2×C8×C43—41no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—21no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—42no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C42×C43—41no—
91C4⋊Dic43—42no—
92C4⋊Dic43—41no—
93Dic43⋊C4—81no—
94Dic43⋊C4—81no—
95C4×Dic43—41no—
96C4×Dic43—81no—
97#10621877—41no—
98#10621877—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C23×C43#12011yescharacteristic
102Q8×C43—42no—
103Q8×C43—81no—
104Q8×C43—81no—
105Q8×C43—81no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—22no—
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—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43C2×Q1611yescharacteristic
121C2×C4×C43#13711yescharacteristic
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—42no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133Dic86—42no—
134Dic86—81no—
135C8×C43—81no—
136C43⋊C8—81no—
137C43⋊C8—81no—
138#12222—431nomaximal, Sylow
139C22×C43—21no—
140C22×C43—21no—
141C22×C43#45111yescharacteristic
142C22×C43#45511yescharacteristic
143C22×C43B(4,𝔽2)11yescharacteristic
144C4×C43—21no—
145C4×C43—21no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43—42no—
149C4×C43—81no—
150C4×C43—81no—
151C4×C43—81no—
152Dic43—42no—
153Dic43—81no—
154Dic43—81no—
155Dic43—81no—
156#2799—431no—
157#2028—431no—
158#1617—431no—
159#1605D4311yescharacteristic
160#1354—431no—
161#1353—431no—
162#1319—431no—
163C2×C43—21no—
164C2×C43—21no—
165C2×C43#160211yescharacteristic
166C2×C43#219711yescharacteristic
167C2×C43#220311yescharacteristic
168#544C2×D4311yescharacteristic
169#484—861no—
170#451—21no—
171#419—861no—
172#400—431no—
173#400—861no—
174#398—861no—
175#395C2×D4311yescharacteristic
176#391—431no—
177#391—861no—
178#391—861no—
179#387—861no—
180#387—861no—
181#343—431no—
182#339—861no—
183#328—21no—
184#328—861no—
185#324—431no—
186#324C2×D4311yescharacteristic
187C43#1222211yescharacteristic, complemented, Sylow
188C22×Q8—431no—
189C22×Q8C22⋊D4311yescharacteristic
190C2×Q16—41no—
191C2×M16—861no—
192C4⋊Q8—41no—
193#125—41no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196#117—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—431no—
199C2×C4⋊C4—861no—
200C2×C4⋊C4—861no—
201C2×C4⋊C4—861no—
202C2×C4⋊C4C22×D4311yescharacteristic
203C2×C42—431no—
204C2×C42—861no—
205#107—1721no—
206#103—41no—
207#103—1721no—
208#103—1721no—
209#103—1721no—
210C22⋊C8—21no—
211C22⋊C8—861no—
212#95—21no—
213#95—431no—
214#95—861no—
215#95—861no—
216#95—861no—
217#95—861no—
218#95—861no—
219#95—861no—
220#95—861no—
221#95—861no—
222#95C22⋊D4311yescharacteristic
223C2×Q8—21no—
224C2×Q8—21no—
225C2×Q8—42no—
226C2×Q8—41no—
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×C4D4×D4311yescharacteristic
238C22×C4D4×D4311yescharacteristic
239C22×C4C2×C22⋊D4311yescharacteristic
240Q16—82no—
241M16—1721no—
242M16—1721no—
243C2×C8—41no—
244C2×C8—1721no—
245C2×C8—1721no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—3441no—
255C4⋊C4—3441no—
256C4⋊C4—1721no—
257C4⋊C4—1722no—
258C22⋊C4—41no—
259C42—41no—
260C42—3441no—
261C42—1721no—
262C23#1306329311yescharacteristic
263Q8—42no—
264Q8—81no—
265Q8—81no—
266Q8—81no—
267Q8—3441no—
268Q8—1722no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
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—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—862no—
284C2×C4—1721no—
285C2×C4—1721no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1722no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4—1721no—
293C2×C4—1721no—
294C2×C4Q16×D4311yescharacteristic
295C2×C4#1306335711yescharacteristic
296C8—81no—
297C8—3441no—
298C8—3441no—
299C22—21no—
300C22—21no—
301C22#1458305311yescharacteristic
302C22#1458307511yescharacteristic
303C22#1458308511yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—42no—
309C4—81no—
310C4—81no—
311C4—81no—
312C4—3441no—
313C4—3441no—
314C4—3441no—
315C4—1722no—
316C2—21no—
317C2—21no—
318C2#1913355011yescharacteristic
319C2#1913658311yescharacteristic
320C2#1913661411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1605C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1605D43
hypocenterC43#12222
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1605

Complements

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

NH ≅ G/Ntype
78. C2×Dic86Q16semidirect
187. C43#12222semidirect

Maximal subgroups

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

subgroupindex
#191424822
#191357532
#191336372
#191326252
#191326232
#191325282
C43×#16052
#1222243