Finite Group Databasebeta

← #24992886

Subgroups — #24992886

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144630C211yesmaximal, characteristic
2#19137072C211yesmaximal, characteristic
3#19133094C211yesmaximal, characteristic
4#19133023C211yesmaximal, characteristic
5#19132496C211yesmaximal, characteristic
6#19132428C211yesmaximal, characteristic
7C43×#1994C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9#14583232—21no—
10#14583191C412yescomplemented
11#14583106C412yescomplemented
12#14583054—21no—
13C4×#10621885—22no—
14#14582952C2211yescharacteristic
15#14582952C2211yescharacteristic
16#14582805—21no—
17#14582797—21no—
18#14582783—22no—
19C4×Dic43⋊C4—21no—
20C4×C4⋊Dic43C2211yescharacteristic
21#14582745—21no—
22#14582636—22no—
23#14582629—22no—
24C43×#533C2211yescharacteristic
25C43×#423C2211yescharacteristic
26C43×C43C2211yescharacteristic
27C43×#339—21no—
28C43×#339—21no—
29C22×Dic86D411yescharacteristic
30C2×#10621885—22no—
31C4×Dic86—21no—
32C4×Dic86—21no—
33C4×Dic86C2×C412yes—
34C4×Dic86D412yes—
35C2×C4⋊Dic43—21no—
36C2×C4⋊Dic43D411yescharacteristic
37C2×Dic43⋊C4—21no—
38C2×Dic43⋊C4—22no—
39C2×C4×Dic43—21no—
40C2×C4×Dic43—21no—
41#13063258—22no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)C2×C412yes—
44#13063249—22no—
45#13063248—22no—
46C22⋊(C43⋊C8)—21no—
47C22⋊(C43⋊C8)—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C43⋊#95—22no—
51C43⋊#95—22no—
52C43⋊#95—22no—
53C43⋊#95D412yes—
54C2×M16×C43—21no—
55C4⋊Q8×C43C2×C411yescharacteristic
56C4⋊Q8×C43C2×C411yescharacteristic
57#125×C43—21no—
58C22⋊Q8×C43—21no—
59C22⋊Q8×C43—21no—
60C4×Q8×C43—21no—
61C4×Q8×C43—21no—
62#117×C43—21no—
63C2×C42×C43—21no—
64C2×C42×C43—21no—
65C2×C42×C43D411yescharacteristic
66C2×C42×C43D411yescharacteristic
67C2×C42×C43C2311yescharacteristic
68C4⋊C8×C43—21no—
69C4⋊C8×C43—21no—
70C2×Q8×C43—21no—
71C2×Q8×C43—21no—
72C22×C4×C43—21no—
73C22×C4×C43—21no—
74C22×C4×C43C2×D411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C22×C4×C43C2×D411yescharacteristic
77C22×Dic43—21no—
78C22×Dic43—21no—
79C22×Dic43—22no—
80C2×Dic86—21no—
81C2×Dic86—42no—
82C2×Dic86C22⋊C412yes—
83M16×C43—41no—
84M16×C43—41no—
85C2×C8×C43—41no—
86C4⋊C4×C43—21no—
87C4⋊C4×C43—21no—
88C4⋊C4×C43—21no—
89C4⋊C4×C43—21no—
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C42×C43—21no—
94C42×C43—21no—
95C42×C43—21no—
96C42×C43—42no—
97C42×C43—42no—
98C42×C43—41no—
99C42×C43Q1612yescomplemented
100C42×C43C22×C411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43#4111yescharacteristic
103C42×C43#4111yescharacteristic
104#10621885—44no—
105C4⋊Dic43—21no—
106C4⋊Dic43—42no—
107C4⋊Dic43C22⋊C412yes—
108Dic43⋊C4—22no—
109Dic43⋊C4—22no—
110Dic43⋊C4—44no—
111C4×Dic43—22no—
112C4×Dic43—22no—
113C4×Dic43—41no—
114C4×Dic43—41no—
115C2×C43⋊C8—22no—
116C2×C43⋊C8—41no—
117C23×C43#12011yescharacteristic
118Q8×C43—42no—
119Q8×C43—81no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43—41no—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—41no—
127C2×C4×C43—41no—
128C2×C4×C43—41no—
129C2×C4×C43—41no—
130C2×C4×C43C2×C22⋊C411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×D411yescharacteristic
133C2×C4×C43#12111yescharacteristic
134C2×C4×C43#12111yescharacteristic
135C2×C4×C43#12311yescharacteristic
136C2×C4×C43C2×Q1611yescharacteristic
137C2×C4×C43#13511yescharacteristic
138C2×C4×C43#13711yescharacteristic
139C2×C4×C43#13711yescharacteristic
140C2×Dic43—22no—
141C2×Dic43—22no—
142C2×Dic43—42no—
143C2×Dic43—42no—
144C2×Dic43—42no—
145C2×Dic43—42no—
146C2×Dic43—42no—
147Dic86—22no—
148Dic86—22no—
149Dic86—42no—
150C8×C43—81no—
151C43⋊C8—42no—
152C43⋊C8—81no—
153#9236—431nomaximal, Sylow
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#38611yescharacteristic
157C22×C43#45111yescharacteristic
158C22×C43#45211yescharacteristic
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—42no—
163C4×C43—42no—
164C4×C43—81no—
165C4×C43—81no—
166C4×C43#42112yes—
167C4×C43C4×Q1611yescharacteristic
168C4×C43#44111yescharacteristic
169C4×C43#46211yescharacteristic
170C4×C43#46411yescharacteristic
171Dic43—42no—
172Dic43—42no—
173Dic43—82no—
174#3104—431no—
175#2295—431no—
176#1994D4311yescharacteristic
177#1503—431no—
178#1487—431no—
179#1303—431no—
180#1276—431no—
181C2×C43—21no—
182C2×C43—21no—
183C2×C43#187811yescharacteristic
184C2×C43#189711yescharacteristic
185C2×C43#190611yescharacteristic
186#533C2×D4311yescharacteristic
187C2×C4×Q8—431no—
188#484—861no—
189#477—432no—
190#462—432no—
191#451—861no—
192C4×Q16—862no—
193#431—431no—
194#431—431no—
195#423C2×D4311yescharacteristic
196#391—861no—
197#389—861no—
198#387—862no—
199C4×C4⋊C4—431no—
200C4×C4⋊C4—861no—
201#376—861no—
202C43C2×D4311yescharacteristic
203#339—21no—
204#339—21no—
205#328—862no—
206Q8⋊C8—862no—
207C43#923611yescharacteristic, complemented, Sylow
208C22×Q8—431no—
209C2×Q16—862no—
210C2×M16—21no—
211C4⋊Q8C4×D4311yescharacteristic
212C4⋊Q8C4×D4311yescharacteristic
213#125—21no—
214C22⋊Q8—21no—
215C22⋊Q8—21no—
216C4×Q8—21no—
217C4×Q8—21no—
218C4×Q8—432no—
219C4×Q8—432no—
220C4×Q8—861no—
221C4×Q8—861no—
222#117—21no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—861no—
225C2×C4⋊C4—862no—
226C2×C4⋊C4—861no—
227C2×C42—21no—
228C2×C42—21no—
229C2×C42—861no—
230C2×C42—861no—
231C2×C42C22⋊D4311yescharacteristic
232C2×C42C22⋊D4311yescharacteristic
233C2×C42C22×D4311yescharacteristic
234#107—862no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—432no—
238C4⋊C8—861no—
239#103—862no—
240#103—862no—
241C22⋊C8—861no—
242C22⋊C8—861no—
243C4×C8—861no—
244C4×C8—861no—
245#95—432no—
246#95—862no—
247#95—862no—
248#95—862no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—432no—
252C2×Q8—861no—
253C2×Q8—1722no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4—862no—
259C22×C4D4×D4311yescharacteristic
260C22×C4D4×D4311yescharacteristic
261C22×C4C2×C22⋊D4311yescharacteristic
262Q16—1724no—
263M16—41no—
264M16—41no—
265C2×C8—41no—
266C2×C8—862no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—432no—
275C4⋊C4—862no—
276C4⋊C4—862no—
277C4⋊C4—861no—
278C4⋊C4—1724no—
279C4⋊C4—1722no—
280C22⋊C4—41no—
281C42—21no—
282C42—21no—
283C42—21no—
284C42—42no—
285C42—42no—
286C42—41no—
287C42—862no—
288C42—862no—
289C42—1721no—
290C42—1721no—
291C42#1062188512yescomplemented
292C42C2×C4×D4311yescharacteristic
293C42#1062189811yescharacteristic
294C42D4×D4311yescharacteristic
295C42#1062190011yescharacteristic
296C23#1306329311yescharacteristic
297Q8—42no—
298Q8—81no—
299Q8—862no—
300Q8—862no—
301Q8—1722no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—862no—
313C2×C4—862no—
314C2×C4—1722no—
315C2×C4—1722no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4—1722no—
319C2×C4C22⋊C4×D4311yescharacteristic
320C2×C4(C22⋊D43)⋊C411yescharacteristic
321C2×C4C4×C22⋊D4311yescharacteristic
322C2×C4#1306329611yescharacteristic
323C2×C4#1306329811yescharacteristic
324C2×C4#1306330711yescharacteristic
325C2×C4C2×#1062188511yescharacteristic
326C2×C4#1306334511yescharacteristic
327C2×C4#1306335511yescharacteristic
328C2×C4#1306335611yescharacteristic
329C8—81no—
330C8—3441no—
331C8—1722no—
332C22—21no—
333C22—21no—
334C22#1458277511yescharacteristic
335C22#1458305411yescharacteristic
336C22#1458305911yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—81no—
343C4—81no—
344C4—3442no—
345C4—1722no—
346C4—1722no—
347C4#1458291412yes—
348C4C4×#1062188511yescharacteristic
349C4#1458300411yescharacteristic
350C4#1458310611yescharacteristic
351C4#1458311811yescharacteristic
352C2—21no—
353C2—21no—
354C2#1913493911yescharacteristic
355C2#1913504011yescharacteristic
356C2#1913509911yescharacteristic
subgroupG/H
centerC2×C4#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1994C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1994D43
hypocenterC43#9236
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
10. #14583191C4semidirect
11. #14583106C4semidirect
99. C42×C43Q16semidirect
207. C43#9236semidirect
291. C42#10621885semidirect

Maximal subgroups

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

subgroupindex
#191446302
#191370722
#191330942
#191330232
#191324962
#191324282
C43×#19942
#923643