Finite Group Databasebeta

← #24993390

Subgroups — #24993390

Order 11008.

416 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 105 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#19144396C211yesmaximal, characteristic
2#19143678C211yesmaximal, characteristic
3#19134611C211yesmaximal, characteristic
4#19133159C211yesmaximal, characteristic
5#19132492C211yesmaximal, characteristic
6#19132454C211yesmaximal, characteristic
7C43×#1481C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583203—22no—
10#14583191C412yescomplemented
11#14583181C412yescomplemented
12#14583029—22no—
13#14583026—22no—
14#14582953—22no—
15#14582952C2211yescharacteristic
16#14582942—21no—
17#14582923C2211yescharacteristic
18#14582907—21no—
19C2×#13063250—21no—
20#14582765C2211yescharacteristic
21#14582662—21no—
22#14582636—22no—
23C43×#533C2211yescharacteristic
24C43×#431C2211yescharacteristic
25C2×C4⋊C8×C43C2211yescharacteristic
26C43×Q8⋊C8—22no—
27C22×Dic86D411yescharacteristic
28C2×#10621877—21no—
29C4×Dic86—21no—
30C4×Dic86—21no—
31C4×Dic86C2×C412yes—
32C4×Dic86D412yes—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43D411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×C4×Dic43—21no—
37#13063258—22no—
38#13063256—22no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)C2×C412yes—
42Dic43⋊C8—24no—
43#13063250—42no—
44#13063248—22no—
45#13063248—22no—
46C22⋊(C43⋊C8)D412yes—
47#13063235—24no—
48C4×C43⋊C8—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C22×C8×C43—21no—
52C4⋊Q8×C43C2×C411yescharacteristic
53C4⋊Q8×C43C2×C411yescharacteristic
54#125×C43—21no—
55C22⋊Q8×C43—21no—
56C22⋊Q8×C43—21no—
57C4×Q8×C43—21no—
58C4×Q8×C43—21no—
59#117×C43—21no—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C4⋊C8×C43—21no—
64C22⋊C8×C43—21no—
65C4×C8×C43D412yes—
66C2×Q8×C43—21no—
67C2×Q8×C43—21no—
68C22×C4×C43C2×D411yescharacteristic
69C22×C4×C43C2×D411yescharacteristic
70C22×C4×C43#4111yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73C22×Dic43—41no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—21no—
77C2×Dic86—21no—
78C2×Dic86—21no—
79C2×Dic86C22⋊C412yes—
80C2×C8×C43—22no—
81C2×C8×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43—41no—
84C4⋊C4×C43—21no—
85C4⋊C4×C43—21no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—41no—
89C4⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C42×C43—41no—
92C42×C43C22×C411yescharacteristic
93C42×C43C2×D411yescharacteristic
94C42×C43C2×D411yescharacteristic
95C42×C43#4111yescharacteristic
96C4⋊Dic43—21no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43C22⋊C412yes—
100Dic43⋊C4—22no—
101Dic43⋊C4—22no—
102C4×Dic43—22no—
103C4×Dic43—22no—
104#10621877—41no—
105#10621877—41no—
106C2×C43⋊C8—22no—
107C2×C43⋊C8—22no—
108C23×C43#12111yescharacteristic
109Q8×C43—42no—
110Q8×C43—81no—
111C2×C4×C43—41no—
112C2×C4×C43—41no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43C2×C22⋊C411yescharacteristic
116C2×C4×C43C4×D411yescharacteristic
117C2×C4×C43C4×D411yescharacteristic
118C2×C4×C43#12011yescharacteristic
119C2×C4×C43#12111yescharacteristic
120C2×C4×C43#12311yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133Dic86—22no—
134Dic86—22no—
135Dic86—41no—
136Dic86—41no—
137C8×C43—42no—
138C8×C43—81no—
139C43⋊C8—42no—
140C43⋊C8—42no—
141#9308—431nomaximal, Sylow
142C22×C43—21no—
143C22×C43—21no—
144C22×C43#38611yescharacteristic
145C22×C43#46811yescharacteristic
146C22×C43#47011yescharacteristic
147C4×C43—21no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—81no—
152C4×C43—81no—
153C4×C43#41711yescharacteristic
154C4×C43#41911yescharacteristic
155C4×C43#46811yescharacteristic
156C4×C43#47011yescharacteristic
157Dic43—42no—
158Dic43—42no—
159Dic43—161no—
160#3078—431no—
161#2983—431no—
162#1805—431no—
163#1518—431no—
164#1481D4311yescharacteristic
165#1301—431no—
166#1286—431no—
167C2×C43—21no—
168C2×C43—21no—
169C2×C43#188111yescharacteristic
170C2×C43#189411yescharacteristic
171C2×C43#190511yescharacteristic
172#533C2×D4311yescharacteristic
173C2×C4×Q8—431no—
174#479—862no—
175#477—432no—
176#475—432no—
177#446—862no—
178#446—862no—
179#432—862no—
180#431—431no—
181#431C2×D4311yescharacteristic
182#428—861no—
183#423—431no—
184C2×C4⋊C8C2×D4311yescharacteristic
185#419—861no—
186C2×#103—861no—
187#382—431no—
188#340—861no—
189#328—862no—
190Q8⋊C8—22no—
191C43#930811yescharacteristic, complemented, Sylow
192C22×Q8—431no—
193C2×M16—861no—
194C22×C8—21no—
195C4⋊Q8C4×D4311yescharacteristic
196C4⋊Q8C4×D4311yescharacteristic
197#125—21no—
198C22⋊Q8—21no—
199C22⋊Q8—21no—
200C4×Q8—21no—
201C4×Q8—21no—
202C4×Q8—432no—
203C4×Q8—432no—
204C4×Q8—861no—
205C4×Q8—861no—
206#117—21no—
207C2×C4⋊C4—431no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—861no—
210C2×C42—861no—
211C2×C42C22×D4311yescharacteristic
212#107—862no—
213#106—862no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—432no—
218C4⋊C8—864no—
219C4⋊C8—861no—
220C4⋊C8—861no—
221#103—862no—
222#103—862no—
223#103—1722no—
224C22⋊C8—21no—
225C22⋊C8—432no—
226#97—864no—
227C4×C8—861no—
228C4×C8C22⋊D4312yes—
229#95—861no—
230#95—861no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—432no—
234C2×Q8—861no—
235C2×Q8—861no—
236C2×Q8—861no—
237C2×Q8—861no—
238C2×Q8—861no—
239C22×C4—861no—
240C22×C4—861no—
241C22×C4—1721no—
242C22×C4#1062189811yescharacteristic
243C22×C4D4×D4311yescharacteristic
244C22×C4D4×D4311yescharacteristic
245M16—1721no—
246M16—1721no—
247C2×C8—22no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—862no—
252C2×C8—862no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—432no—
260C4⋊C4—862no—
261C4⋊C4—861no—
262C4⋊C4—862no—
263C4⋊C4—1721no—
264C4⋊C4—1721no—
265C22⋊C4—41no—
266C42—41no—
267C42—862no—
268C42—862no—
269C42C2×C4×D4311yescharacteristic
270C42D4×D4311yescharacteristic
271C42#1062190011yescharacteristic
272C42C2×C22⋊D4311yescharacteristic
273C23#1306329811yescharacteristic
274Q8—42no—
275Q8—81no—
276Q8—862no—
277Q8—862no—
278Q8—1721no—
279Q8—1721no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—862no—
285C2×C4—862no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—3441no—
289C2×C4—3441no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4C22⋊C4×D4311yescharacteristic
293C2×C4(C22⋊D43)⋊C411yescharacteristic
294C2×C4C4×C22⋊D4311yescharacteristic
295C2×C4#1306329311yescharacteristic
296C2×C4#1306329611yescharacteristic
297C2×C4#1306330711yescharacteristic
298C2×C4#1306335211yescharacteristic
299C2×C4#1306335411yescharacteristic
300C2×C4#1306335711yescharacteristic
301C2×C4#1306335711yescharacteristic
302C8—42no—
303C8—81no—
304C8—1722no—
305C8—1722no—
306C22—21no—
307C22—21no—
308C22#1458277511yescharacteristic
309C22#1458314811yescharacteristic
310C22#1458315611yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—1722no—
318C4—1722no—
319C4—6881no—
320C4#1458289911yescharacteristic
321C4#1458290611yescharacteristic
322C4#1458314211yescharacteristic
323C4#1458315411yescharacteristic
324C2—21no—
325C2—21no—
326C2#1913496011yescharacteristic
327C2#1913502511yescharacteristic
328C2#1913508611yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1481C2
socleC22×C43#386
prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1481D43
hypocenterC43#9308
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
10. #14583191C4semidirect
11. #14583181C4semidirect
191. C43#9308semidirect

Maximal subgroups

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

subgroupindex
#191443962
#191436782
#191346112
#191331592
#191324922
#191324542
C43×#14812
#930843