Finite Group Databasebeta

← #25009593

Subgroups — #25009593

Order 11008.

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

normal subgroups only

This group has 394 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#19139964C211yesmaximal, characteristic
2#19135937C211yesmaximal, characteristic
3#19133603C211yesmaximal, characteristic
4#19132602C211yesmaximal, characteristic
5#19132601C211yesmaximal, characteristic
6#19132540C211yesmaximal, characteristic
7C43×#1611C211yesmaximal, characteristic
8C2×#13063290—21no—
9#14583227—21no—
10#14582942—21no—
11#14582832—21no—
12#14582829C2211yescharacteristic
13#14582803—21no—
14#14582803—21no—
15#14582796—21no—
16#14582794—21no—
17#14582768C2211yescharacteristic
18#14582668C2211yescharacteristic
19#14582658—21no—
20#14582636—21no—
21#14582625C2211yescharacteristic
22C43×#544C2211yescharacteristic
23C43×#483—21no—
24C43×#398C2211yescharacteristic
25C43×#328—21no—
26C43×#324C2211yescharacteristic
27C22×Dic86—21no—
28C2×#10621877—21no—
29#13063290—42no—
30#13063290—42no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×Dic43⋊C4—21no—
34C2×Dic43⋊C4—21no—
35C2×Dic43⋊C4—21no—
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—21no—
38C2×C4×Dic43—21no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43D411yescharacteristic
41#13063258—41no—
42#13063256—41no—
43#13063256—41no—
44#13063249—41no—
45C22⋊(C43⋊C8)—21no—
46C43⋊#95—21no—
47C43⋊#95—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95D411yescharacteristic
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×C43D411yescharacteristic
58C2×C4⋊C4×C43C2311yescharacteristic
59#106×C43—41no—
60#103×C43—41no—
61C22⋊C8×C43—21no—
62#95×C43—21no—
63#95×C43D411yescharacteristic
64C2×Q8×C43—21no—
65C2×Q8×C43—21no—
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—24no—
76C2×Dic86—42no—
77C2×Dic86—42no—
78C2×C8×C43—41no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43—41no—
84C4⋊C4×C43—41no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C42×C43—41no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93Dic43⋊C4—42no—
94Dic43⋊C4—42no—
95Dic43⋊C4—42no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98Dic43⋊C4—81no—
99C4×Dic43—21no—
100C4×Dic43—42no—
101C4×Dic43—42no—
102C4×Dic43SD1612yes—
103#10621877—22no—
104#10621877—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C23×C43#12011yescharacteristic
108Q8×C43—81no—
109Q8×C43—81no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43—41no—
118C2×C4×C43—41no—
119C2×C4×C43—41no—
120C2×C4×C43—41no—
121C2×C4×C43—41no—
122C2×C4×C43—41no—
123C2×C4×C43—41no—
124C2×C4×C43C2×SD1611yescharacteristic
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×Dic43—22no—
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137C2×Dic43—41no—
138Dic86—48no—
139C8×C43—81no—
140C43⋊C8—42no—
141C43⋊C8—81no—
142#12247—431nomaximal, Sylow
143C22×C43—21no—
144C22×C43—21no—
145C22×C43#45011yescharacteristic
146C22×C43#45611yescharacteristic
147C22×C43B(4,𝔽2)11yescharacteristic
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—42no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—81no—
154C4×C43—81no—
155C4×C43—81no—
156Dic43—24no—
157Dic43—42no—
158Dic43—81no—
159Dic43—81no—
160#2582—431no—
161#2060—431no—
162#1611—431no—
163#1611D4311yescharacteristic
164#1346—431no—
165#1346—431no—
166#1325—431no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43#160411yescharacteristic
170C2×C43#219811yescharacteristic
171C2×C43#220511yescharacteristic
172#544C2×D4311yescharacteristic
173C2×C4×Q8—861no—
174#483—21no—
175#483—861no—
176#428—861no—
177#398—431no—
178#398—861no—
179#398C2×D4311yescharacteristic
180#391—861no—
181#391—861no—
182#389—861no—
183#389—861no—
184#384—431no—
185#343—431no—
186#339—861no—
187#328—21no—
188#328—861no—
189#324—431no—
190#324C2×D4311yescharacteristic
191C43#1224711yescharacteristic, complemented, Sylow
192C22×Q8—861no—
193C2×M16—861no—
194C4⋊Q8—41no—
195#125—41no—
196C22⋊Q8—21no—
197C22⋊Q8—21no—
198C4×Q8—1722no—
199C4×Q8—1722no—
200#117—21no—
201C2×C4⋊C4—21no—
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⋊C4C22⋊D4311yescharacteristic
210C2×C4⋊C4C22×D4311yescharacteristic
211C2×C42—431no—
212C2×C42—861no—
213C2×C42—861no—
214#107—1721no—
215#106—41no—
216#106—1721no—
217#106—1721no—
218#103—41no—
219#103—1721no—
220C22⋊C8—21no—
221C22⋊C8—861no—
222#95—21no—
223#95—431no—
224#95—861no—
225#95—861no—
226#95—861no—
227#95—861no—
228#95C22⋊D4311yescharacteristic
229C2×Q8—21no—
230C2×Q8—21no—
231C2×Q8—864no—
232C2×Q8—1722no—
233C2×Q8—1722no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4D4×D4311yescharacteristic
241C22×C4D4×D4311yescharacteristic
242C22×C4C2×C22⋊D4311yescharacteristic
243M16—862no—
244M16—1721no—
245C2×C8—41no—
246C2×C8—1721no—
247C2×C8—1721no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—3441no—
259C4⋊C4—1721no—
260C4⋊C4—1721no—
261C4⋊C4—1722no—
262C4⋊C4—1722no—
263C4⋊C4—1722no—
264C4⋊C4—1721no—
265C4⋊C4—1721no—
266C22⋊C4—41no—
267C42—41no—
268C42—432no—
269C42—861no—
270C42—1722no—
271C42—1722no—
272C23#1306329311yescharacteristic
273Q8—81no—
274Q8—81no—
275Q8—1728no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—862no—
291C2×C4—862no—
292C2×C4—862no—
293C2×C4—862no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4SD16×D4311yescharacteristic
303C2×C4#1306335211yescharacteristic
304C8—81no—
305C8—3441no—
306C8—1722no—
307C22—21no—
308C22—21no—
309C22#1458304811yescharacteristic
310C22#1458308011yescharacteristic
311C22#1458308511yescharacteristic
312C4—21no—
313C4—21no—
314C4—42no—
315C4—41no—
316C4—41no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—864no—
321C4—3441no—
322C4—3441no—
323C4—1722no—
324C2—21no—
325C2—21no—
326C2#1913356211yescharacteristic
327C2#1913658911yescharacteristic
328C2#1913662411yescharacteristic
subgroupG/H
centerC22#14583085
commutator, cosocleC2×C4⋊C4×C43C23
FrattiniC2×C4⋊C4C22×D43
FittingC43×#1611C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1611D43
hypocenterC43#12247
LCSG ▷ C2×C4⋊C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1611

Complements

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

NH ≅ G/Ntype
191. C43#12247semidirect

Maximal subgroups

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

subgroupindex
#191399642
#191359372
#191336032
#191326022
#191326012
#191325402
C43×#16112
#1224743