Finite Group Databasebeta

← #25014399

Subgroups — #25014399

Order 11008.

390 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582726C211yesmaximal, characteristic, complemented
2C2×#14582701C211yesmaximal, characteristic
3C2×#14582699C211yesmaximal, characteristic
4#19135459C211yesmaximal, characteristic
5#107×Dic43C211yesmaximal, characteristic, complemented
6#19132672C211yesmaximal, characteristic, complemented
7C43×#1380C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C22×C43⋊C16C2211yescharacteristic
10C2×#13063259C2211yescharacteristic
11C2×#13063245—21no—
12C2×C8×Dic43C2211yescharacteristic
13#14582800—21no—
14C4⋊C4×Dic43—21no—
15#14582726—22no—
16#14582701—22no—
17#14582699C414yescomplemented
18#14582661—21no—
19C22×C16×C43C2211yescharacteristic
20C2×#107×C43C2211yescharacteristic
21C2×#107×C43C2211yescharacteristic
22C22×D172—21no—
23C2×D344—21no—
24C2×D344—21no—
25C2×D344—21no—
26C2×D344—21no—
27C2×D344—21no—
28C2×D344C2×C412yes—
29C22×C43⋊C8D411yescharacteristic
30C2×C4⋊Dic43—21no—
31C2×(C2×D43)⋊C4—41no—
32C2×(C2×D43)⋊C4—41no—
33C2×C4×Dic43—41no—
34C2×C4×Dic43D411yescharacteristic
35C2×C43⋊C16—21no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16C2×C412yes—
38#13063259—21no—
39#13063259D412yes—
40#13063245—42no—
41C8×Dic43—21no—
42C8×Dic43—21no—
43C43⋊#95—41no—
44C22×C8×C43C2311yescharacteristic
45C2×C4⋊C4×C43—21no—
46C2×C4⋊C4×C43—21no—
47C2×C16×C43—21no—
48C2×C16×C43—21no—
49C2×C16×C43—21no—
50#107×C43—21no—
51#107×C43—21no—
52#107×C43—21no—
53#107×C43C2×C412yes—
54C23×D43—41no—
55C22×C4×C43—41no—
56C22×C4×C43—41no—
57C22×C4×C43C2×D411yescharacteristic
58C22×Dic43—41no—
59C22×Dic43D811yescharacteristic
60C22×Dic43D811yescharacteristic
61C2×D172—22no—
62C2×D172—41no—
63C2×D172—41no—
64C2×D172—41no—
65C2×D172—41no—
66C2×D172—41no—
67C2×C8×C43C22×C411yescharacteristic
68C2×C8×C43C2×D411yescharacteristic
69C2×C8×C43#4111yescharacteristic
70C2×C8×C43#4111yescharacteristic
71C2×C8×C43#4111yescharacteristic
72C2×C8×C43#4111yescharacteristic
73C4⋊C4×C43—22no—
74C4⋊C4×C43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77(C2×D43)⋊C4—82no—
78(C2×D43)⋊C4—82no—
79C4⋊Dic43—22no—
80C4⋊Dic43—41no—
81C4×Dic43—21no—
82C4×Dic43—21no—
83C4×Dic43—82no—
84C2×C43⋊C8—21no—
85C2×C43⋊C8—21no—
86C2×C43⋊C8—21no—
87D344—22no—
88D344—22no—
89D344—41no—
90D344—41no—
91C16×C43—41no—
92C43⋊C16—22no—
93C23×C43C2×D811yescharacteristic
94C22×D43—42no—
95C22×D43—81no—
96C22×D43—81no—
97C22×D43—81no—
98C22×D43—81no—
99C22×D43—81no—
100C22×D43—81no—
101C2×C4×C43—42no—
102C2×C4×C43—81no—
103C2×C4×C43—81no—
104C2×C4×C43—81no—
105C2×C4×C43—81no—
106C2×C4×C43—81no—
107C2×C4×C43C4×D411yescharacteristic
108C2×C4×C43#12111yescharacteristic
109C2×C4×C43#12311yescharacteristic
110C2×C4×C43#13511yescharacteristic
111C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C43#13711yescharacteristic
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43—42no—
119C2×Dic43—81no—
120C2×Dic43—81no—
121C2×Dic43SD3212yes—
122D172—42no—
123D172—42no—
124D172—81no—
125D172—81no—
126C8×C43#11711yescharacteristic
127C8×C43C4×D411yescharacteristic
128C8×C43#12411yescharacteristic
129C8×C43#12611yescharacteristic
130C43⋊C8—41no—
131#13131—431nomaximal, Sylow
132C22×C43C4×D811yescharacteristic
133C22×C43#45911yescharacteristic
134C22×C43#48011yescharacteristic
135C22×C43C2×SD3211yescharacteristic
136C22×C43#50811yescharacteristic
137C22×C43#50911yescharacteristic
138C22×C43#50911yescharacteristic
139C2×D43—82no—
140C2×D43—82no—
141C2×D43—82no—
142C2×D43—161no—
143C2×D43—161no—
144C2×D43—161no—
145C2×D43—161no—
146C4×C43—82no—
147C4×C43—161no—
148C4×C43#38811yescharacteristic
149C4×C43#44011yescharacteristic
150C4×C43#46411yescharacteristic
151C4×C43#48211yescharacteristic
152Dic43—22no—
153Dic43—41no—
154Dic43—82no—
155C2×#367—431no—
156C2×#357—431no—
157C2×#357—431no—
158#1970—431no—
159C4×#107—431no—
160#1380D4311yescharacteristic, complemented
161#1374—431no—
162C2×C43#192511yescharacteristic
163C2×C43C4×SD3211yescharacteristic
164C2×C43#217711yescharacteristic
165C2×C43#220711yescharacteristic
166C2×C43#221011yescharacteristic
167C2×C43#223311yescharacteristic
168C2×C43#223411yescharacteristic
169D43—162no—
170C22×D8—431no—
171C22×C16—431no—
172C22×C16C2×D4311yescharacteristic
173C2×#107—431no—
174C2×#107C2×D4311yescharacteristic
175C2×#107C2×D4311yescharacteristic
176C2×#102—861no—
177C2×C4×C8—431no—
178#390—861no—
179C4×C4⋊C4—861no—
180#367—862no—
181#357—434no—
182#357—862no—
183#340—861no—
184C43#1313111yescharacteristic, complemented, Sylow
185C22×D4—861no—
186C2×D8—432no—
187C2×D8—861no—
188C2×D8—861no—
189C2×D8—861no—
190C2×D8—861no—
191C2×D8—861no—
192C22×C8—431no—
193C22×C8C22×D4311yescharacteristic
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—861no—
197C2×C22⋊C4—1721no—
198C2×C22⋊C4—1721no—
199C2×C42—431no—
200C2×C42—1721no—
201C2×C16—21no—
202C2×C16—21no—
203C2×C16—21no—
204C2×C16—432no—
205C2×C16—861no—
206C2×C16—861no—
207#107—21no—
208#107—21no—
209#107—21no—
210#107—432no—
211#107—861no—
212#107C4×D4312yes—
213#102—1722no—
214C4×C8—861no—
215C4×C8—861no—
216#95—1721no—
217C24—1721no—
218C2×D4—862no—
219C2×D4—1721no—
220C2×D4—1721no—
221C2×D4—1721no—
222C2×D4—1721no—
223C2×D4—1721no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—431no—
227C22×C4—431no—
228C22×C4—1721no—
229C22×C4D4×D4311yescharacteristic
230D8—862no—
231D8—862no—
232D8—1721no—
233D8—1721no—
234C2×C8—861no—
235C2×C8—861no—
236C2×C8—861no—
237C2×C8C2×C4×D4311yescharacteristic
238C2×C8#1062189811yescharacteristic
239C2×C8#1062189811yescharacteristic
240C2×C8D4×D4311yescharacteristic
241C2×C8#1062190011yescharacteristic
242C2×C8#1062190211yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—862no—
248C4⋊C4—1721no—
249C22⋊C4—3442no—
250C22⋊C4—3442no—
251C42—861no—
252C42—861no—
253C42—3442no—
254C16—41no—
255C16—862no—
256C23—3441no—
257C23—3441no—
258C23—3441no—
259C23—3441no—
260C23—3441no—
261C23—3441no—
262C23—1722no—
263C23D8×D4311yescharacteristic
264D4—3441no—
265D4—3441no—
266D4—1722no—
267D4—1722no—
268C2×C4—42no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—432no—
275C2×C4—861no—
276C2×C4—861no—
277C2×C4—861no—
278C2×C4—861no—
279C2×C4—861no—
280C2×C4—3441no—
281C2×C4—3441no—
282C2×C4—1722no—
283C2×C4(C22⋊D43)⋊C411yescharacteristic
284C2×C4#1306329811yescharacteristic
285C2×C4#1306331011yescharacteristic
286C2×C4#1306334611yescharacteristic
287C2×C4#1306335211yescharacteristic
288C2×C4#1306335711yescharacteristic
289C8—1721no—
290C8#1306328211yescharacteristic
291C8#1306328711yescharacteristic
292C8#1306331111yescharacteristic
293C8#1306332011yescharacteristic
294C22—3442no—
295C22—3442no—
296C22—3442no—
297C22—6881no—
298C22—6881no—
299C22—6881no—
300C22—6881no—
301C22#1458297911yescharacteristic
302C22#1458309311yescharacteristic
303C22#1458321411yescharacteristic
304C22SD32×D4311yescharacteristic
305C22#1458333211yescharacteristic
306C22#1458333311yescharacteristic
307C22#1458333611yescharacteristic
308C4—82no—
309C4—161no—
310C4—862no—
311C4—3442no—
312C4—1721no—
313C4#1458278811yescharacteristic
314C4#1458300211yescharacteristic
315C4#1458312411yescharacteristic
316C4#1458322511yescharacteristic
317C2—6882no—
318C2#1913521311yescharacteristic
319C2#1913644411yescharacteristic
320C2#1913646811yescharacteristic
321C2#1913663411yescharacteristic
322C2#1913665311yescharacteristic
323C2#1913678211yescharacteristic
324C2#1913678911yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1380C2
socleC23×C43C2×D8
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenter#1380D43
hypocenterC43#13131
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
1. C2×#14582726C2semidirect
5. #107×Dic43C2semidirect
6. #19132672C2semidirect
7. C43×#1380C2semidirect
17. #14582699C4semidirect
160. #1380D43semidirect
184. C43#13131semidirect

Maximal subgroups

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

subgroupindex
C2×#145827262
C2×#145827012
C2×#145826992
#191354592
#107×Dic432
#191326722
C43×#13802
#1313143