Finite Group Databasebeta

← #25013536

Subgroups — #25013536

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063259C211yesmaximal, characteristic, complemented
2C2×#14582700C212yesmaximal, complemented
3C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic, complemented
4#19132686C212yesmaximal, complemented
5C2×C43×#466C211yesmaximal, characteristic
6C22×C4⋊Dic43—21no—
7C22×C43⋊C16C2212yes—
8C2×#13063259—24no—
9C2×#13063259—21no—
10C2×#13063259C2212yes—
11#14582700—24no—
12C22⋊(C43⋊C16)—22no—
13C22×D8×C43C2211yescharacteristic
14C23×C8×C43C2211yescharacteristic
15C2×#121×C43—21no—
16C43×#466—22no—
17C43×#466C414yescomplemented
18C2×#107×C43C2211yescharacteristic
19C2×#102×C43—21no—
20C23×Dic43—41no—
21C2×C4⋊Dic43—24no—
22C2×C4⋊Dic43—22no—
23C2×C4⋊Dic43—42no—
24C2×C4⋊Dic43—41no—
25C2×C43⋊C16—22no—
26C2×C43⋊C16—22no—
27C2×C43⋊C16—22no—
28#13063259—24no—
29#13063259—22no—
30#13063259D414yescomplemented
31C22×D4×C43—21no—
32C22×D4×C43—41no—
33C23×C4×C43D411yescharacteristic
34C2×D8×C43—22no—
35C2×D8×C43—21no—
36C2×D8×C43—22no—
37C2×D8×C43C2×C412yescomplemented
38C22×C8×C43—22no—
39C22×C8×C43—22no—
40C22×C8×C43C2×C412yes—
41C22×C8×C43D411yescharacteristic
42C22×C8×C43D412yes—
43C22×C8×C43C2311yescharacteristic
44#121×C43—24no—
45#121×C43—42no—
46C2×C4⋊C4×C43—21no—
47C2×C22⋊C4×C43—41no—
48#107×C43—21no—
49#107×C43C2×C412yescomplemented
50#102×C43—24no—
51C24×C43—41no—
52C24×C43D811yescharacteristic
53C2×D4×C43—22no—
54C2×D4×C43—41no—
55C2×D4×C43—44no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×D4×C43—82no—
61C2×D4×C43—82no—
62C22×C4×C43—21no—
63C22×C4×C43—21no—
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43—41no—
67C22×C4×C43C22⋊C412yes—
68C22×C4×C43D811yescharacteristic
69C22×C4×C43SD1612yes—
70C22×C4×C43C2×D411yescharacteristic
71C22×Dic43—44no—
72C22×Dic43—42no—
73C22×Dic43—82no—
74C22×Dic43—82no—
75D8×C43—24no—
76D8×C43—42no—
77C2×C8×C43—21no—
78C2×C8×C43—21no—
79C2×C8×C43—24no—
80C2×C8×C43—24no—
81C2×C8×C43C22⋊C412yes—
82C2×C8×C43C22×C411yescharacteristic
83C2×C8×C43C2×D412yes—
84C2×C8×C43C2×D411yescharacteristic
85C2×C8×C43#4112yes—
86C4⋊C4×C43—22no—
87C4⋊C4×C43—41no—
88C22⋊C4×C43—44no—
89C4⋊Dic43—24no—
90C4⋊Dic43—44no—
91C4⋊Dic43—42no—
92C43⋊C16—42no—
93C23×C43—21no—
94C23×C43—21no—
95C23×C43—21no—
96C23×C43—21no—
97C23×C43—42no—
98C23×C43—81no—
99C23×C43—81no—
100C23×C43—81no—
101C23×C43—81no—
102C23×C43—81no—
103C23×C43—81no—
104C23×C43#10212yes—
105C23×C43D1612yes—
106C23×C43SD3212yes—
107C23×C43C2×D811yescharacteristic
108D4×C43—42no—
109D4×C43—42no—
110D4×C43—88no—
111D4×C43—81no—
112D4×C43—81no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—22no—
116C2×C4×C43—22no—
117C2×C4×C43—22no—
118C2×C4×C43—22no—
119C2×C4×C43—42no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43#10212yes—
123C2×C4×C43C2×C22⋊C411yescharacteristic
124C2×C4×C43#12011yescharacteristic
125C2×C4×C43#12311yescharacteristic
126C2×C4×C43C2×SD1611yescharacteristic
127C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C43#13711yescharacteristic
129C2×Dic43—44no—
130C2×Dic43—88no—
131C2×Dic43—82no—
132C2×Dic43—82no—
133C8×C43—22no—
134C8×C43C4×D412yes—
135C8×C43#12112yes—
136#12991—431nomaximal, Sylow
137C22×C43—22no—
138C22×C43—22no—
139C22×C43—22no—
140C22×C43—22no—
141C22×C43—22no—
142C22×C43—22no—
143C22×C43—82no—
144C22×C43—82no—
145C22×C43—82no—
146C22×C43—161no—
147C22×C43—161no—
148C22×C43—161no—
149C22×C43—161no—
150C22×C43#35714yescomplemented
151C22×C43C2×#10211yescharacteristic
152C22×C43#44711yescharacteristic
153C22×C43#48011yescharacteristic
154C22×C43C2×D1611yescharacteristic
155C22×C43C2×SD3211yescharacteristic
156C22×C43#50911yescharacteristic
157C22×C43#51011yescharacteristic
158C4×C43—22no—
159C4×C43—82no—
160C4×C43#38611yescharacteristic
161C4×C43#41711yescharacteristic
162C4×C43#44811yescharacteristic
163C4×C43#48111yescharacteristic
164Dic43—84no—
165C2×#466D4311yescharacteristic
166C22×#107—431no—
167C2×#357—432no—
168C2×C22⋊C16—431no—
169#1380—432no—
170C2×C43—24no—
171C2×C43—162no—
172C2×C43#187411yescharacteristic
173C2×C43C2×#35711yescharacteristic
174C2×C43#213911yescharacteristic
175C2×C43#218411yescharacteristic
176C2×C43#218511yescharacteristic
177C2×C43#223211yescharacteristic
178C2×C43#223311yescharacteristic
179C22×D8C2×D4311yescharacteristic
180C23×C8C2×D4311yescharacteristic
181C2×#121—21no—
182C22×C4⋊C4—861no—
183C22×C16—432no—
184#466—22no—
185#466Dic4314yescomplemented
186C2×#107—432no—
187C2×#107—864no—
188C2×#107—861no—
189C2×#107C2×D4311yescharacteristic
190C2×#102—21no—
191#357—864no—
192C22⋊C16—862no—
193C43#1299111yescharacteristic, complemented, Sylow
194C22×D4—21no—
195C22×D4—41no—
196C23×C4—1721no—
197C23×C4C22⋊D4311yescharacteristic
198C2×D8—22no—
199C2×D8—22no—
200C2×D8—21no—
201C2×D8C2×Dic4312yescomplemented
202C22×C8—22no—
203C22×C8—22no—
204C22×C8C2×Dic4312yes—
205C22×C8C22⋊D4311yescharacteristic
206C22×C8C22⋊D4312yes—
207C22×C8C22×D4311yescharacteristic
208#121—24no—
209#121—42no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—864no—
212C2×C4⋊C4—862no—
213C2×C4⋊C4—1722no—
214C2×C4⋊C4—1721no—
215C2×C22⋊C4—41no—
216C2×C16—862no—
217C2×C16—862no—
218C2×C16—862no—
219#107—21no—
220#107—434no—
221#107—864no—
222#107—862no—
223#107C2×Dic4312yescomplemented
224#102—24no—
225C24—41no—
226C24#1062188211yescharacteristic
227C2×D4—22no—
228C2×D4—44no—
229C2×D4—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—82no—
235C2×D4—82no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—41no—
241C22×C4—3442no—
242C22×C4—3442no—
243C22×C4—1724no—
244C22×C4—1722no—
245C22×C4#1062188211yescharacteristic
246C22×C4#1062188312yes—
247C22×C4C22⋊Dic4312yes—
248C22×C4C2×C22⋊D4311yescharacteristic
249D8—24no—
250D8—42no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—24no—
254C2×C8—24no—
255C2×C8C22⋊Dic4312yes—
256C2×C8D4×D4312yes—
257C2×C8#1062190012yes—
258C2×C8C22×Dic4311yescharacteristic
259C2×C8C2×C22⋊D4311yescharacteristic
260C4⋊C4—22no—
261C4⋊C4—41no—
262C4⋊C4—864no—
263C4⋊C4—1724no—
264C4⋊C4—1722no—
265C22⋊C4—44no—
266C16—1722no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—21no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23—81no—
277C23—81no—
278C23#1306324612yes—
279C23#1306326612yes—
280C23#1306326912yes—
281C23C2×#1062188211yescharacteristic
282D4—42no—
283D4—42no—
284D4—88no—
285D4—81no—
286D4—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—3448no—
297C2×C4—3442no—
298C2×C4—3442no—
299C2×C4—1724no—
300C2×C4#1306324612yes—
301C2×C4C2×C22⋊Dic4311yescharacteristic
302C2×C4#1306329311yescharacteristic
303C2×C4#1306330611yescharacteristic
304C2×C4C2×#1062188311yescharacteristic
305C2×C4#1306335011yescharacteristic
306C2×C4#1306335511yescharacteristic
307C8—22no—
308C8D4×Dic4312yes—
309C8#1306329712yes—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—82no—
317C22—82no—
318C22—82no—
319C22—161no—
320C22—161no—
321C22—161no—
322C22—161no—
323C22#1458270014yescomplemented
324C22C2×#1306324611yescharacteristic
325C22#1458303211yescharacteristic
326C22#1458321011yescharacteristic
327C22C2×#1306326611yescharacteristic
328C22C2×#1306326911yescharacteristic
329C22#1458333411yescharacteristic
330C22#1458333911yescharacteristic
331C4—22no—
332C4—82no—
333C4—3444no—
334C4#1458277911yescharacteristic
335C4#1458290011yescharacteristic
336C4#1458303711yescharacteristic
337C4#1458321511yescharacteristic
338C2—24no—
339C2—162no—
340C2#1913491311yescharacteristic
341C2C2×#1458270011yescharacteristic
342C2#1913630711yescharacteristic
343C2#1913650611yescharacteristic
344C2#1913651111yescharacteristic
345C2#1913677311yescharacteristic
346C2#1913677811yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
Fitting, prime radicalC2×C43×#466C2
socleC23×C43C2×D8
cosocleC22×C8×C43C23
hypercenterC2×#466D43
hypocenterC43#12991
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C22×#13063259C2semidirect
2. C2×#14582700C2semidirect
3. C2×C22⋊(C43⋊C16)C2semidirect
4. #19132686C2semidirect
17. C43×#466C4semidirect
30. #13063259D4semidirect
37. C2×D8×C43C2×C4semidirect
49. #107×C43C2×C4semidirect
150. C22×C43#357semidirect
185. #466Dic43semidirect
193. C43#12991semidirect
201. C2×D8C2×Dic43semidirect
223. #107C2×Dic43semidirect
323. C22#14582700semidirect

Maximal subgroups

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

subgroupindex
C22×#130632592
C2×#145827002
C2×C22⋊(C43⋊C16)2
#191326862
C2×C43×#4662
#1299143