Finite Group Databasebeta

← #24994963

Subgroups — #24994963

Order 11008.

386 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135548C211yesmaximal, characteristic
2#19135351C211yesmaximal, characteristic
3#19134462C211yesmaximal, characteristic
4C2×#14582645C211yesmaximal, characteristic
5#19132478C211yesmaximal, characteristic
6#19132430C211yesmaximal, characteristic
7C43×#1956C211yesmaximal, characteristic
8C2×#13063258—21no—
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063235—21no—
13C4×C4⋊Dic43C2211yescharacteristic
14#14582661—21no—
15#14582661—21no—
16#14582661—21no—
17#14582653—21no—
18#14582645C414yescomplemented
19C2×C4⋊Q8×C43C2211yescharacteristic
20C2×#103×C43—21no—
21C2×#103×C43—21no—
22C2×C4×C8×C43C2211yescharacteristic
23C43×#384C2211yescharacteristic
24C22×C43⋊C8—21no—
25C22×C43⋊C8—21no—
26C22×C43⋊C8—21no—
27C2×C4⋊Dic43D411yescharacteristic
28C2×C4⋊Dic43D411yescharacteristic
29C2×C4×Dic43—21no—
30#13063258—42no—
31C4⋊(C43⋊C8)—21no—
32C4⋊(C43⋊C8)—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)C2×C412yes—
36C4⋊(C43⋊C8)C2×C412yes—
37#13063235—42no—
38C43⋊#95—21no—
39C22×Q8×C43—21no—
40C22×C8×C43D411yescharacteristic
41C22×C8×C43D411yescharacteristic
42C4⋊Q8×C43—21no—
43C4⋊Q8×C43—21no—
44C4⋊Q8×C43—21no—
45C4⋊Q8×C43C2×C412yes—
46C2×C4⋊C4×C43—21no—
47C2×C4⋊C4×C43—21no—
48C2×C4⋊C4×C43—21no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C42×C43C2311yescharacteristic
52#103×C43—42no—
53#103×C43—42no—
54C4×C8×C43—21no—
55C4×C8×C43—21no—
56C2×Q8×C43—22no—
57C2×Q8×C43—41no—
58C2×Q8×C43—41no—
59C2×Q8×C43—41no—
60C2×Q8×C43—41no—
61C2×Q8×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43—41no—
64C22×C4×C43C2×D411yescharacteristic
65C22×C4×C43C2×D411yescharacteristic
66C22×C4×C43#4111yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C2×C8×C43—21no—
70C2×C8×C43—21no—
71C2×C8×C43—21no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43D812yes—
75C4⋊C4×C43—22no—
76C4⋊C4×C43—22no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C4⋊C4×C43—41no—
80C4⋊C4×C43—41no—
81C4⋊C4×C43—41no—
82C4⋊C4×C43—41no—
83C4⋊C4×C43—81no—
84C42×C43C22×C411yescharacteristic
85C42×C43#4111yescharacteristic
86C42×C43#4111yescharacteristic
87C42×C43#4111yescharacteristic
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4×Dic43—41no—
93C4×Dic43—41no—
94C2×C43⋊C8—22no—
95C2×C43⋊C8—22no—
96C2×C43⋊C8—41no—
97C2×C43⋊C8—41no—
98C2×C43⋊C8—41no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8—41no—
101C2×C43⋊C8—41no—
102C2×C43⋊C8—41no—
103C23×C43#12111yescharacteristic
104Q8×C43—42no—
105Q8×C43—42no—
106Q8×C43—81no—
107Q8×C43—81no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—42no—
111C2×C4×C43—81no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43—81no—
116C2×C4×C43#11711yescharacteristic
117C2×C4×C43C4×D411yescharacteristic
118C2×C4×C43C4×D411yescharacteristic
119C2×C4×C43#12311yescharacteristic
120C2×C4×C43#12411yescharacteristic
121C2×C4×C43#12611yescharacteristic
122C2×C4×C43C2×D811yescharacteristic
123C2×C4×C43#13511yescharacteristic
124C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C43#13711yescharacteristic
127C2×C4×C43#13711yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×C4×C43#13711yescharacteristic
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C8×C43—22no—
137C8×C43—41no—
138C43⋊C8—42no—
139C43⋊C8—42no—
140C43⋊C8—81no—
141#9569—431nomaximal, Sylow
142C22×C43#38811yescharacteristic
143C22×C43#45911yescharacteristic
144C22×C43#46411yescharacteristic
145C22×C43#46811yescharacteristic
146C22×C43#47011yescharacteristic
147C22×C43#47111yescharacteristic
148C22×C43#47311yescharacteristic
149C4×C43—21no—
150C4×C43—21no—
151C4×C43—82no—
152C4×C43—161no—
153C4×C43C4×D811yescharacteristic
154C4×C43#44011yescharacteristic
155C4×C43#44011yescharacteristic
156C4×C43#44111yescharacteristic
157C4×C43#48011yescharacteristic
158C4×C43#48211yescharacteristic
159C4×C43#48911yescharacteristic
160C4×C43#49111yescharacteristic
161Dic43—81no—
162Dic43—81no—
163#1988—431no—
164#1956D4311yescharacteristic
165#1947—431no—
166#1770—431no—
167C2×#332—431no—
168#1296—431no—
169#1277—431no—
170C2×C43#168511yescharacteristic
171C2×C43#168911yescharacteristic
172C2×C43#170011yescharacteristic
173C2×C43#170411yescharacteristic
174C2×C43#192511yescharacteristic
175C2×C43#193011yescharacteristic
176C2×C43#193511yescharacteristic
177C2×C4⋊Q8C2×D4311yescharacteristic
178C2×#107—861no—
179C2×C4⋊C8—431no—
180C2×C4⋊C8—431no—
181C2×C4⋊C8—431no—
182C2×#103—21no—
183C2×#103—21no—
184C2×#97—861no—
185C2×C4×C8C2×D4311yescharacteristic
186#384C2×D4311yescharacteristic
187C4×C4⋊C4—431no—
188#340—861no—
189#340—861no—
190#340—861no—
191#336—861no—
192#332—434no—
193C43#956911yescharacteristic, complemented, Sylow
194C22×Q8—21no—
195C22×C8—861no—
196C22×C8—861no—
197C22×C8—861no—
198C22×C8C22⋊D4311yescharacteristic
199C22×C8C22⋊D4311yescharacteristic
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8C4×D4312yes—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—431no—
210C2×C4⋊C4—431no—
211C2×C42—861no—
212C2×C42C22×D4311yescharacteristic
213#107—1722no—
214C4⋊C8—432no—
215C4⋊C8—432no—
216C4⋊C8—861no—
217C4⋊C8—861no—
218C4⋊C8—861no—
219C4⋊C8—861no—
220#103—42no—
221#103—42no—
222#97—1722no—
223C4×C8—21no—
224C4×C8—21no—
225#95—861no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4D4×D4311yescharacteristic
237C22×C4#1062190011yescharacteristic
238C22×C4C2×C22⋊D4311yescharacteristic
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—862no—
245C2×C8—862no—
246C2×C8—1721no—
247C2×C8—1721no—
248C2×C8—1721no—
249C2×C8—1721no—
250C2×C8—1721no—
251C2×C8—1721no—
252C2×C8—1721no—
253C2×C8#1062188212yes—
254C4⋊C4—22no—
255C4⋊C4—22no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C42—1721no—
268C42—1721no—
269C42C2×C4×D4311yescharacteristic
270C42#1062189811yescharacteristic
271C42#1062190011yescharacteristic
272C42#1062190011yescharacteristic
273C23#1306329611yescharacteristic
274Q8—42no—
275Q8—42no—
276Q8—81no—
277Q8—81no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—1721no—
287C2×C4—1721no—
288C2×C4—1721no—
289C2×C4—1721no—
290C2×C4—1721no—
291C2×C4—1721no—
292C2×C4#1306328111yescharacteristic
293C2×C4(C22⋊D43)⋊C411yescharacteristic
294C2×C4C4×C22⋊D4311yescharacteristic
295C2×C4#1306330611yescharacteristic
296C2×C4#1306331111yescharacteristic
297C2×C4#1306331811yescharacteristic
298C2×C4C2×#1062188211yescharacteristic
299C2×C4#1306334511yescharacteristic
300C2×C4#1306335111yescharacteristic
301C2×C4#1306335211yescharacteristic
302C2×C4#1306335411yescharacteristic
303C2×C4#1306335511yescharacteristic
304C2×C4#1306335711yescharacteristic
305C2×C4#1306335711yescharacteristic
306C8—22no—
307C8—41no—
308C8—3441no—
309C8—1722no—
310C8—1722no—
311C22#1458278711yescharacteristic
312C22#1458309111yescharacteristic
313C22#1458311811yescharacteristic
314C22#1458314211yescharacteristic
315C22#1458315411yescharacteristic
316C22#1458315911yescharacteristic
317C22#1458317111yescharacteristic
318C4—21no—
319C4—21no—
320C4—82no—
321C4—161no—
322C4—3441no—
323C4—3441no—
324C4C4×#1062188211yescharacteristic
325C4#1458299911yescharacteristic
326C4#1458300211yescharacteristic
327C4#1458300311yescharacteristic
328C4#1458321011yescharacteristic
329C4#1458322011yescharacteristic
330C4#1458326011yescharacteristic
331C4#1458326611yescharacteristic
332C2#1913405711yescharacteristic
333C2#1913408111yescharacteristic
334C2#1913414611yescharacteristic
335C2#1913417411yescharacteristic
336C2#1913521211yescharacteristic
337C2#1913524711yescharacteristic
338C2#1913528211yescharacteristic
subgroupG/H
centerC23#13063296
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1956C2
socle, prime radicalC23×C43#121
cosocleC2×C42×C43C23
hypercenter#1956D43
hypocenterC43#9569
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
18. #14582645C4semidirect
193. C43#9569semidirect

Maximal subgroups

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

subgroupindex
#191355482
#191353512
#191344622
C2×#145826452
#191324782
#191324302
C43×#19562
#956943