Finite Group Databasebeta

← #25013203

Subgroups — #25013203

Order 11008.

490 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
1C2×#14582726C211yesmaximal, characteristic, complemented
2C2×#14582700C211yesmaximal, characteristic
3C2×#14582700C211yesmaximal, characteristic
4#19135328C211yesmaximal, characteristic, complemented
5#19132686C211yesmaximal, characteristic, complemented
6#19132673C211yesmaximal, characteristic, complemented
7C2×C4×D8×C43C211yesmaximal, characteristic
8C22×C43⋊C16C2211yescharacteristic
9C22×C43⋊C16C2211yescharacteristic
10C2×#13063259C2211yescharacteristic
11C2×#13063259C2211yescharacteristic
12#14582797—21no—
13#14582726—22no—
14#14582700—22no—
15#14582700C414yescomplemented
16#14582662—21no—
17C22×D8×C43C2211yescharacteristic
18C2×C4×D4×C43—21no—
19C4×D8×C43—22no—
20C4×D8×C43—22no—
21C2×#107×C43C2211yescharacteristic
22C2×#102×C43—21no—
23C2×C4×C8×C43C2211yescharacteristic
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×Dic43⋊C4—41no—
27C2×C43⋊C16—21no—
28C2×C43⋊C16—21no—
29C2×C43⋊C16—21no—
30C2×C43⋊C16—21no—
31C2×C43⋊C16—21no—
32C2×C43⋊C16C2×C412yescomplemented
33#13063259—21no—
34#13063259—21no—
35#13063259—21no—
36#13063259C2×C412yescomplemented
37C43⋊#95—41no—
38C22×D4×C43—21no—
39C23×C4×C43—41no—
40C2×D8×C43—21no—
41C2×D8×C43—21no—
42C2×D8×C43—21no—
43C2×D8×C43C2×C412yes—
44C2×D8×C43D412yes—
45C2×D8×C43Q812yes—
46C22×C8×C43D411yescharacteristic
47C22×C8×C43C2311yescharacteristic
48C4×D4×C43—24no—
49C4×D4×C43—42no—
50C2×C4⋊C4×C43—21no—
51C2×C22⋊C4×C43—41no—
52C2×C42×C43D411yescharacteristic
53#107×C43—21no—
54#107×C43D412yes—
55#102×C43—24no—
56C4×C8×C43—21no—
57C4×C8×C43—21no—
58C24×C43—41no—
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C22×C4×C43—44no—
66C22×C4×C43—41no—
67C22×C4×C43—82no—
68C22×C4×C43—82no—
69C22×C4×C43D811yescharacteristic
70C22×C4×C43D811yescharacteristic
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—41no—
73C22×Dic43—41no—
74D8×C43—22no—
75D8×C43—22no—
76D8×C43—22no—
77D8×C43C4⋊C414yescomplemented
78C2×C8×C43—21no—
79C2×C8×C43—21no—
80C2×C8×C43—21no—
81C2×C8×C43C22×C411yescharacteristic
82C2×C8×C43C2×D411yescharacteristic
83C2×C8×C43C2×D411yescharacteristic
84C2×C8×C43C2×Q811yescharacteristic
85C2×C8×C43#4111yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C4⋊C4×C43—22no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—44no—
90C42×C43—21no—
91C42×C43—21no—
92C4⋊Dic43—22no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4⋊Dic43—41no—
96Dic43⋊C4—82no—
97C43⋊C16—22no—
98C43⋊C16—41no—
99C23×C43—42no—
100C23×C43—42no—
101C23×C43—42no—
102C23×C43—81no—
103C23×C43—81no—
104C23×C43—81no—
105C23×C43—81no—
106C23×C43C2×D811yescharacteristic
107D4×C43—24no—
108D4×C43—42no—
109D4×C43—42no—
110D4×C43—42no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—42no—
117C2×C4×C43—88no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43SD3212yes—
121C2×C4×C43C4×D411yescharacteristic
122C2×C4×C43#12011yescharacteristic
123C2×C4×C43C22⋊Q811yescharacteristic
124C2×C4×C43#13511yescharacteristic
125C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C43#13711yescharacteristic
127C2×Dic43—42no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C8×C43—41no—
134C8×C43C2×C4⋊C411yescharacteristic
135C8×C43C4×D411yescharacteristic
136C8×C43C22⋊Q811yescharacteristic
137C8×C43#12311yescharacteristic
138#12937—431nomaximal, Sylow
139C22×C43—44no—
140C22×C43—82no—
141C22×C43—82no—
142C22×C43—82no—
143C22×C43—82no—
144C22×C43—82no—
145C22×C43—82no—
146C22×C43C4×D811yescharacteristic
147C22×C43#44711yescharacteristic
148C22×C43#47411yescharacteristic
149C22×C43C2×SD3211yescharacteristic
150C22×C43#50811yescharacteristic
151C22×C43#50911yescharacteristic
152C22×C43#50911yescharacteristic
153C4×C43—22no—
154C4×C43—41no—
155C4×C43—82no—
156C4×C43#38511yescharacteristic
157C4×C43#44011yescharacteristic
158C4×C43#45211yescharacteristic
159C4×C43#47811yescharacteristic
160Dic43—82no—
161Dic43—161no—
162C2×C4×D8D4311yescharacteristic
163C2×#367—431no—
164C2×#357—431no—
165C2×#357—431no—
166#1942—431no—
167#1380—431no—
168#1374—431no—
169C2×C43—84no—
170C2×C43#186211yescharacteristic
171C2×C43C4×SD3211yescharacteristic
172C2×C43#217711yescharacteristic
173C2×C43#218611yescharacteristic
174C2×C43#218711yescharacteristic
175C2×C43#222611yescharacteristic
176C2×C43#222811yescharacteristic
177C22×D8C2×D4311yescharacteristic
178C2×C4×D4—21no—
179C22×C16—431no—
180C22×C16—431no—
181C4×D8—22no—
182C4×D8—22no—
183C2×#107—431no—
184C2×#107—431no—
185C2×#107C2×D4311yescharacteristic
186C2×#102—21no—
187C2×C4×C8C2×D4311yescharacteristic
188#389—861no—
189#367—862no—
190#357—434no—
191#357—862no—
192#340—861no—
193C43#1293711yescharacteristic, complemented, Sylow
194C22×D4—21no—
195C23×C4—41no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8Dic8612yes—
200C2×D8C4×D4312yes—
201C2×D8C22⋊D4312yes—
202C22×C8C22⋊D4311yescharacteristic
203C22×C8C22×D4311yescharacteristic
204C4×D4—24no—
205C4×D4—42no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C4⋊C4—1721no—
210C2×C22⋊C4—41no—
211C2×C42C22⋊D4311yescharacteristic
212C2×C16—432no—
213C2×C16—861no—
214C2×C16—861no—
215C2×C16—861no—
216C2×C16—861no—
217C2×C16—861no—
218#107—21no—
219#107—432no—
220#107—861no—
221#107—861no—
222#107—861no—
223#107C22⋊D4312yes—
224#102—24no—
225C4×C8—21no—
226C4×C8—21no—
227#95—1721no—
228C24—41no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—44no—
236C22×C4—41no—
237C22×C4—82no—
238C22×C4—82no—
239C22×C4—1721no—
240C22×C4—1721no—
241C22×C4#1062188211yescharacteristic
242C22×C4#1062188211yescharacteristic
243C22×C4C2×C22⋊D4311yescharacteristic
244D8—22no—
245D8—22no—
246D8—22no—
247D8Dic43⋊C414yescomplemented
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8C2×Dic8611yescharacteristic
252C2×C8C2×C4×D4311yescharacteristic
253C2×C8#1062189811yescharacteristic
254C2×C8#1062189811yescharacteristic
255C2×C8C2×C22⋊D4311yescharacteristic
256C2×C8C2×C22⋊D4311yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—862no—
260C4⋊C4—3442no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C4⋊C4—1721no—
264C22⋊C4—44no—
265C42—21no—
266C42—21no—
267C16—862no—
268C16—1721no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23C2×#1062188211yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—42no—
287C2×C4—88no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—3441no—
291C2×C4—3441no—
292C2×C4—3441no—
293C2×C4—3441no—
294C2×C4—3441no—
295C2×C4—1722no—
296C2×C4#1306326912yes—
297C2×C4C4×C22⋊D4311yescharacteristic
298C2×C4#1306329411yescharacteristic
299C2×C4#1306330411yescharacteristic
300C2×C4#1306334511yescharacteristic
301C2×C4#1306335111yescharacteristic
302C2×C4#1306335511yescharacteristic
303C8—41no—
304C8C2×Dic43⋊C411yescharacteristic
305C8C4×C22⋊D4311yescharacteristic
306C8#1306330411yescharacteristic
307C8#1306330811yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22C4×#1062188211yescharacteristic
316C22#1458303311yescharacteristic
317C22#1458317911yescharacteristic
318C22C2×#1306326911yescharacteristic
319C22#1458332911yescharacteristic
320C22#1458333411yescharacteristic
321C22#1458333511yescharacteristic
322C4—22no—
323C4—41no—
324C4—82no—
325C4—3442no—
326C4—6881no—
327C4#1458277211yescharacteristic
328C4#1458299911yescharacteristic
329C4#1458306111yescharacteristic
330C4#1458319911yescharacteristic
331C2—84no—
332C2#1913484211yescharacteristic
333C2C4×#1306326911yescharacteristic
334C2#1913646911yescharacteristic
335C2#1913651811yescharacteristic
336C2#1913652411yescharacteristic
337C2#1913674211yescharacteristic
338C2#1913675211yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C4×D8×C43C2
socleC23×C43C2×D8
prime radicalC22×D8×C43C22
cosocleC22×C8×C43C23
hypercenterC2×C4×D8D43
hypocenterC43#12937
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#14582726C2semidirect
4. #19135328C2semidirect
5. #19132686C2semidirect
6. #19132673C2semidirect
15. #14582700C4semidirect
32. C2×C43⋊C16C2×C4semidirect
36. #13063259C2×C4semidirect
77. D8×C43C4⋊C4semidirect
193. C43#12937semidirect
247. D8Dic43⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145827262
C2×#145827002
#191353282
#191326862
#191326732
C2×C4×D8×C432
#1293743