Finite Group Databasebeta

← #25013107

Subgroups — #25013107

Order 11008.

442 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582726C211yesmaximal, characteristic, complemented
2C2×#14582724C211yesmaximal, characteristic, complemented
3C2×C22⋊(C43⋊C16)C211yesmaximal, characteristic
4#19134624C211yesmaximal, characteristic
5#19132686C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C2×C43×#427C211yesmaximal, characteristic
8C22×C43⋊C16C2211yescharacteristic
9C22×C43⋊C16C2211yescharacteristic
10C2×#13063259C2211yescharacteristic
11C2×#13063259C2211yescharacteristic
12#14582759—21no—
13#14582726—22no—
14#14582724—22no—
15C22⋊(C43⋊C16)C414yescomplemented
16#14582662—21no—
17C23×C8×C43C2211yescharacteristic
18C2×#117×C43—21no—
19C43×#427—22no—
20C43×#427—22no—
21C2×#107×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#106×C43—21no—
24C2×C4⋊Dic43—21no—
25C2×C4⋊Dic43—21no—
26C2×C22⋊Dic43—41no—
27C2×C43⋊C16—21no—
28C2×C43⋊C16—21no—
29C2×C43⋊C16—21no—
30C2×C43⋊C16—21no—
31C2×C43⋊C16C2×C412yes—
32C2×C43⋊C16C2×C412yes—
33#13063259—21no—
34#13063259—21no—
35#13063259—21no—
36#13063259—21no—
37C43⋊#95—41no—
38C23×C4×C43D411yescharacteristic
39C22×C8×C43—21no—
40C22×C8×C43—21no—
41C22×C8×C43—21no—
42C22×C8×C43—21no—
43C22×C8×C43C2×C412yes—
44C22×C8×C43D411yescharacteristic
45C22×C8×C43Q812yes—
46C22×C8×C43C2311yescharacteristic
47#117×C43—24no—
48#117×C43—42no—
49C2×C4⋊C4×C43—21no—
50C2×C4⋊C4×C43—21no—
51C2×C22⋊C4×C43—41no—
52C2×C42×C43—41no—
53#107×C43—21no—
54#107×C43—21no—
55#107×C43D412yes—
56#107×C43D412yes—
57#106×C43—24no—
58C24×C43D811yescharacteristic
59C22×C4×C43—21no—
60C22×C4×C43—21no—
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C22×C4×C43—41no—
64C22×C4×C43—41no—
65C22×C4×C43C4⋊C412yes—
66C22×C4×C43D811yescharacteristic
67C22×C4×C43Q1612yes—
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—41no—
70C22×Dic43—41no—
71C2×C8×C43—21no—
72C2×C8×C43—21no—
73C2×C8×C43—22no—
74C2×C8×C43—22no—
75C2×C8×C43—22no—
76C2×C8×C43—22no—
77C2×C8×C43C4⋊C412yes—
78C2×C8×C43C22×C411yescharacteristic
79C2×C8×C43C2×D411yescharacteristic
80C2×C8×C43C2×D411yescharacteristic
81C2×C8×C43C2×Q811yescharacteristic
82C2×C8×C43#4111yescharacteristic
83C2×C8×C43#4111yescharacteristic
84C4⋊C4×C43—22no—
85C4⋊C4×C43—22no—
86C4⋊C4×C43—41no—
87C4⋊C4×C43—41no—
88C22⋊C4×C43—44no—
89C42×C43—44no—
90C22⋊Dic43—82no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C43⋊C16—22no—
96C43⋊C16—22no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43#10712yes—
104C23×C43C2×D811yescharacteristic
105C2×C4×C43—21no—
106C2×C4×C43—21no—
107C2×C4×C43—22no—
108C2×C4×C43—22no—
109C2×C4×C43—22no—
110C2×C4×C43—22no—
111C2×C4×C43—42no—
112C2×C4×C43—42no—
113C2×C4×C43—81no—
114C2×C4×C43—81no—
115C2×C4×C43—81no—
116C2×C4×C43—81no—
117C2×C4×C43#10712yes—
118C2×C4×C43C2×C4⋊C411yescharacteristic
119C2×C4×C43#12011yescharacteristic
120C2×C4×C43#12311yescharacteristic
121C2×C4×C43C2×Q1611yescharacteristic
122C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×Dic43—81no—
125C2×Dic43—81no—
126C2×Dic43—81no—
127C2×Dic43—81no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C8×C43—22no—
131C8×C43C4×D411yescharacteristic
132C8×C43C4×D411yescharacteristic
133C8×C43C22⋊Q811yescharacteristic
134C8×C43C22⋊Q811yescharacteristic
135#12921—431nomaximal, Sylow
136C22×C43—22no—
137C22×C43—22no—
138C22×C43—22no—
139C22×C43—41no—
140C22×C43—41no—
141C22×C43—41no—
142C22×C43—41no—
143C22×C43C2×#10711yescharacteristic
144C22×C43#44711yescharacteristic
145C22×C43#48011yescharacteristic
146C22×C43#50811yescharacteristic
147C22×C43#50811yescharacteristic
148C22×C43#50911yescharacteristic
149C22×C43#51011yescharacteristic
150C4×C43—22no—
151C4×C43—82no—
152C4×C43—82no—
153C4×C43#38511yescharacteristic
154C4×C43#42811yescharacteristic
155C4×C43#45111yescharacteristic
156C4×C43#48411yescharacteristic
157Dic43—161no—
158Dic43—161no—
159C2×#427D4311yescharacteristic
160C2×#367—431no—
161C2×#366—431no—
162C2×C22⋊C16—431no—
163#1808—431no—
164#1380—431no—
165#1380—431no—
166C2×C43—42no—
167C2×C43#185211yescharacteristic
168C2×C43#215811yescharacteristic
169C2×C43#215911yescharacteristic
170C2×C43#218611yescharacteristic
171C2×C43#218911yescharacteristic
172C2×C43#223411yescharacteristic
173C2×C43#223711yescharacteristic
174C23×C8C2×D4311yescharacteristic
175C2×#117—21no—
176C22×C16—431no—
177C22×C16—431no—
178#427—22no—
179#427—22no—
180C2×#107—431no—
181C2×#107—431no—
182C2×#107C2×D4311yescharacteristic
183C2×#107C2×D4311yescharacteristic
184C2×#106—21no—
185#380—861no—
186#367—862no—
187#366—862no—
188C22⋊C16—434no—
189#340—861no—
190C43#1292111yescharacteristic, complemented, Sylow
191C23×C4C22⋊D4311yescharacteristic
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8Dic8612yes—
197C22×C8C4×D4312yes—
198C22×C8C22⋊D4311yescharacteristic
199C22×C8C22×D4311yescharacteristic
200#117—24no—
201#117—42no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—861no—
205C2×C4⋊C4—861no—
206C2×C22⋊C4—41no—
207C2×C22⋊C4—1721no—
208C2×C42—41no—
209C2×C16—432no—
210C2×C16—432no—
211C2×C16—861no—
212C2×C16—861no—
213C2×C16—861no—
214C2×C16—861no—
215#107—21no—
216#107—21no—
217#107—861no—
218#107—861no—
219#107—861no—
220#107—861no—
221#107C22⋊D4312yes—
222#107C22⋊D4312yes—
223#106—24no—
224#95—1721no—
225C24#1062188211yescharacteristic
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—1721no—
233C22×C4—1721no—
234C22×C4Dic43⋊C412yes—
235C22×C4#1062188211yescharacteristic
236C22×C4#1062188512yes—
237C22×C4C2×C22⋊D4311yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—22no—
242C2×C8—22no—
243C2×C8—22no—
244C2×C8Dic43⋊C412yes—
245C2×C8C2×Dic8611yescharacteristic
246C2×C8C2×C4×D4311yescharacteristic
247C2×C8#1062189811yescharacteristic
248C2×C8#1062189811yescharacteristic
249C2×C8C2×C22⋊D4311yescharacteristic
250C2×C8C2×C22⋊D4311yescharacteristic
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—1721no—
256C4⋊C4—1721no—
257C4⋊C4—1721no—
258C4⋊C4—1721no—
259C22⋊C4—44no—
260C22⋊C4—3442no—
261C42—44no—
262C16—862no—
263C16—862no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23#1306325812yes—
271C23C2×#1062188211yescharacteristic
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—3441no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—3441no—
289C2×C4—3441no—
290C2×C4#1306325812yes—
291C2×C4C2×Dic43⋊C411yescharacteristic
292C2×C4#1306329411yescharacteristic
293C2×C4#1306330811yescharacteristic
294C2×C4C2×#1062188511yescharacteristic
295C2×C4#1306335111yescharacteristic
296C2×C4#1306335611yescharacteristic
297C8—22no—
298C8C4×C22⋊D4311yescharacteristic
299C8C4×C22⋊D4311yescharacteristic
300C8#1306330411yescharacteristic
301C8#1306330411yescharacteristic
302C22—22no—
303C22—22no—
304C22—22no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C2×#1306325811yescharacteristic
310C22#1458303311yescharacteristic
311C22#1458321211yescharacteristic
312C22#1458332911yescharacteristic
313C22#1458332911yescharacteristic
314C22#1458333411yescharacteristic
315C22#1458333911yescharacteristic
316C4—22no—
317C4—82no—
318C4—82no—
319C4—6881no—
320C4—6881no—
321C4#1458277211yescharacteristic
322C4#1458293911yescharacteristic
323C4#1458305511yescharacteristic
324C4#1458323411yescharacteristic
325C2—42no—
326C2#1913478311yescharacteristic
327C2#1913637711yescharacteristic
328C2#1913638411yescharacteristic
329C2#1913651811yescharacteristic
330C2#1913653511yescharacteristic
331C2#1913678611yescharacteristic
332C2#1913680311yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#427C2
socleC23×C43C2×D8
prime radicalC24×C43D8
cosocleC22×C8×C43C23
hypercenterC2×#427D43
hypocenterC43#12921
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
1. C2×#14582726C2semidirect
2. C2×#14582724C2semidirect
5. #19132686C2semidirect
6. #19132686C2semidirect
15. C22⋊(C43⋊C16)C4semidirect
190. C43#12921semidirect

Maximal subgroups

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

subgroupindex
C2×#145827262
C2×#145827242
C2×C22⋊(C43⋊C16)2
#191346242
#191326862
C2×C43×#4272
#1292143