Finite Group Databasebeta

← #25071502

Subgroups — #25071502

Order 11008.

870 conjugacy classes of subgroups; only the 191 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 191 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#19148405C211yesmaximal, characteristic
2#19145746C212yesmaximal
3#19133636C218yesmaximal
4#19133093C212yesmaximal
5#19132919C211yesmaximal, characteristic
6C43×#2568C211yesmaximal, characteristic
7Q8×Dic86—22no—
8#14583628—22no—
9#14583625—24no—
10#14583530—21no—
11#14583530C2214yes—
12#14583456—22no—
13#14583456C2212yes—
14#14583377—21no—
15#14583302—22no—
16#14583251—22no—
17#14583234C2218yes—
18#14583191—24no—
19#14582952C2212yes—
20#14582635C2218yes—
21#14582625C2214yes—
22C2×C4⋊Q8×C43C2211yescharacteristic
23C2×C4×Q8×C43C2211yescharacteristic
24C43×#400C2214yes—
25C43×#391—21no—
26C43×#391—22no—
27C43×#382—21no—
28C4×C4⋊C4×C43C2211yescharacteristic
29#13063325—22no—
30#13063325—22no—
31#13063325D412yes—
32#13063325D412yes—
33#13063324—24no—
34#13063324—28no—
35#13063317—24no—
36#13063317—22no—
37#13063316—24no—
38#13063316—28no—
39#13063304—22no—
40#13063304—24no—
41#13063304C2314yes—
42Q8×Dic43—24no—
43Q8×Dic43—24no—
44C4×Dic86—24no—
45C4×Dic86—24no—
46C4×Dic86—22no—
47C4×Dic86D414yes—
48#13063284—24no—
49#13063284—22no—
50#13063258—28no—
51C4⋊(C43⋊C8)—22no—
52#13063248—28no—
53C22⋊(C43⋊C8)C2314yes—
54C4×C43⋊C8—22no—
55C22×Q8×C43—21no—
56C22×Q8×C43D411yescharacteristic
57C4⋊Q8×C43—22no—
58C4⋊Q8×C43—22no—
59C4×Q8×C43—22no—
60C4×Q8×C43—22no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43D411yescharacteristic
64C2×C4⋊C4×C43C2312yes—
65C2×C4⋊C4×C43C2312yes—
66C2×C42×C43—21no—
67C2×C42×C43D412yes—
68C2×C42×C43C2311yescharacteristic
69#95×C43—24no—
70#95×C43—24no—
71#95×C43C2312yes—
72C2×Q8×C43—22no—
73C2×Q8×C43—22no—
74C2×Q8×C43—44no—
75C2×Q8×C43—41no—
76C2×Q8×C43—41no—
77C2×Q8×C43Q1614yes—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43C2×D412yes—
82C22×C4×C43C2×D412yes—
83C22×C4×C43C2×D411yescharacteristic
84C22×C4×C43C2411yescharacteristic
85C2×Dic86—22no—
86C2×Dic86—24no—
87C2×Dic86C2×D414yes—
88C4⋊C4×C43—22no—
89C4⋊C4×C43—24no—
90C4⋊C4×C43—24no—
91C4⋊C4×C43—42no—
92C4⋊C4×C43—42no—
93C42×C43—22no—
94C42×C43—22no—
95C42×C43—42no—
96C42×C43C2×D412yes—
97C42×C43C2×D412yes—
98C22⋊Dic43—24no—
99C4⋊Dic43—24no—
100C4⋊Dic43—24no—
101C4⋊Dic43—24no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104C4⋊Dic43—22no—
105C4⋊Dic43C2×D414yes—
106Dic43⋊C4—28no—
107Dic43⋊C4—24no—
108Dic43⋊C4—24no—
109C4×Dic43—28no—
110C4×Dic43—24no—
111C2×C43⋊C8—24no—
112C23×C43C22×D411yescharacteristic
113Q8×C43—28no—
114Q8×C43—82no—
115Q8×C43—82no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—22no—
120C2×C4×C43—41no—
121C2×C4×C43—42no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—44no—
125C2×C4×C43—42no—
126C2×C4×C43—42no—
127C2×C4×C43#12011yescharacteristic
128C2×C4×C43#12012yes—
129C2×C4×C43#12011yescharacteristic
130C2×C4×C43C2×Q1614yes—
131C2×C4×C43C2×Q1612yes—
132C2×C4×C43#13712yes—
133C2×C4×C43C22×D412yes—
134C2×Dic43—24no—
135C2×Dic43—24no—
136Dic86—44no—
137Dic86—44no—
138Dic86—84no—
139C43⋊C8—44no—
140#18411—431nomaximal, Sylow
141C22×C43—21no—
142C22×C43—21no—
143C22×C43C2×#12011yescharacteristic
144C22×C43C22×Q1611yescharacteristic
145C22×C43C2×#13711yescharacteristic
146C4×C43—24no—
147C4×C43—21no—
148C4×C43—22no—
149C4×C43—42no—
150C4×C43—82no—
151C4×C43—82no—
152C4×C43#45114yes—
153C4×C43#45412yes—
154Dic43—44no—
155Dic43—44no—
156#3502—431no—
157#3230—432no—
158#2568D4311yescharacteristic
159#1617—438no—
160#1503—432no—
161#1461—431no—
162C2×C43—21no—
163C2×C43—21no—
164C2×C43C2×#45111yescharacteristic
165C2×C43C2×#45411yescharacteristic
166C2×C43#302811yescharacteristic
167Q82—862no—
168#557—864no—
169#557—862no—
170#544—434no—
171#544—861no—
172#533—432no—
173#533—862no—
174C2×C4⋊Q8C2×D4311yescharacteristic
175#519—861no—
176C2×C4×Q8C2×D4311yescharacteristic
177#500—862no—
178#487—862no—
179#484—438no—
180#477—864no—
181#431—432no—
182#400C2×D4314yes—
183#391—21no—
184#391—22no—
185#382—21no—
186C4×C4⋊C4C2×D4311yescharacteristic
187#328—438no—
188#324—434no—
189C43#1841111yescharacteristic, complemented, Sylow
190C22×Q8—21no—
191C22×Q8C22⋊D4311yescharacteristic
192C4⋊Q8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—432no—
195C4⋊Q8—432no—
196C4⋊Q8—862no—
197C4⋊Q8—862no—
198C4⋊Q8—868no—
199C4⋊Q8—864no—
200#125—864no—
201#125—868no—
202#125—864no—
203#125—862no—
204C22⋊Q8—434no—
205C22⋊Q8—862no—
206C22⋊Q8—864no—
207C4×Q8—22no—
208C4×Q8—22no—
209C4×Q8—434no—
210C4×Q8—864no—
211C4×Q8—864no—
212C4×Q8—864no—
213C4×Q8—864no—
214C4×Q8—862no—
215#117—862no—
216#117—864no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4C22⋊D4311yescharacteristic
220C2×C4⋊C4C22×D4312yes—
221C2×C4⋊C4C22×D4312yes—
222C2×C42—21no—
223C2×C42C22⋊D4312yes—
224C2×C42C22×D4311yescharacteristic
225#107—868no—
226C4⋊C8—862no—
227#103—868no—
228C22⋊C8—434no—
229C4×C8—862no—
230#95—24no—
231#95—24no—
232#95C22×D4312yes—
233C2×Q8—22no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—434no—
239C2×Q8—864no—
240C2×Q8—862no—
241C2×Q8#1062188514yes—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4C2×C22⋊D4311yescharacteristic
245C22×C4C2×C22⋊D4312yes—
246C22×C4C2×C22⋊D4312yes—
247C22×C4C2×C22⋊D4311yescharacteristic
248C22×C4C23×D4311yescharacteristic
249C2×C8—864no—
250C4⋊C4—22no—
251C4⋊C4—24no—
252C4⋊C4—24no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—434no—
256C4⋊C4—864no—
257C4⋊C4—864no—
258C4⋊C4—864no—
259C4⋊C4—868no—
260C4⋊C4—862no—
261C4⋊C4—862no—
262C4⋊C4—864no—
263C4⋊C4—862no—
264C4⋊C4—864no—
265C22⋊C4—864no—
266C42—22no—
267C42—22no—
268C42—42no—
269C42—868no—
270C42—864no—
271C42D4×D4312yes—
272C42D4×D4312yes—
273C23C22×C22⋊D4311yescharacteristic
274Q8—28no—
275Q8—82no—
276Q8—82no—
277Q8—3444no—
278Q8—1724no—
279Q8—1724no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—864no—
292C2×C4—864no—
293C2×C4#1306329311yescharacteristic
294C2×C4#1306329312yes—
295C2×C4#1306329311yescharacteristic
296C2×C4C2×#1062188514yes—
297C2×C4C2×#1062188512yes—
298C2×C4#1306335512yes—
299C2×C4C2×D4×D4312yes—
300C8—1724no—
301C22—21no—
302C22—21no—
303C22C2×#1306329311yescharacteristic
304C22C22×#1062188511yescharacteristic
305C22C2×#1306335511yescharacteristic
306C4—22no—
307C4—24no—
308C4—21no—
309C4—42no—
310C4—82no—
311C4—82no—
312C4—1724no—
313C4—1724no—
314C4#1458305414yes—
315C4#1458307112yes—
316C2—21no—
317C2—21no—
318C2C2×#1458305411yescharacteristic
319C2C2×#1458307111yescharacteristic
320C2#1914400011yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2568C2
socleC22×C43C2×#120
prime radicalC23×C43C22×D4
hypercenter#2568D43
hypocenterC43#18411
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2568

Complements

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

NH ≅ G/Ntype
189. C43#18411semidirect

Maximal subgroups

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

subgroupindex
#191484052
#191457462
#191336362
#191330932
#191329192
C43×#25682
#1841143