Finite Group Databasebeta

← #25012905

Subgroups — #25012905

Order 11008.

442 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#107×D43C211yesmaximal, characteristic
2#19136205C211yesmaximal, characteristic
3#19134630C211yesmaximal, characteristic
4#19132705C211yesmaximal, characteristic, complemented
5#19132704C211yesmaximal, characteristic, complemented
6#19132703C211yesmaximal, characteristic, complemented
7C43×#1387C211yesmaximal, characteristic, complemented
8C22×C8×D43C2211yescharacteristic
9C2×C4⋊C4×D43—21no—
10C2×#13063265C2211yescharacteristic
11C2×#13063261C2211yescharacteristic
12C2×#13063259C2211yescharacteristic
13C2×#13063258—21no—
14#107×D43—21no—
15#107×D43—21no—
16#107×D43C412yes—
17#107×D43C412yes—
18#14582862—21no—
19(C2×D43)⋊C16—21no—
20(C2×D43)⋊C16—21no—
21#14582663—21no—
22C2×M32×C43C2211yescharacteristic
23C2×#108×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C22×C4×D43—41no—
26C22×C4×D43D411yescharacteristic
27C2×#10621877—21no—
28C22×C43⋊C8D411yescharacteristic
29C2×C8×D43—21no—
30C2×C8×D43—21no—
31C2×C8×D43—21no—
32C2×C8×D43—21no—
33C2×C8×D43C2×C411yescharacteristic
34C2×C8×D43C2×C411yescharacteristic
35C2×C8×D43D411yescharacteristic
36C2×C8×D43D411yescharacteristic
37C2×C4⋊Dic43—21no—
38C2×Dic43⋊C4—41no—
39C4⋊C4×D43—22no—
40C4⋊C4×D43—22no—
41C4⋊C4×D43—41no—
42C4⋊C4×D43—41no—
43#13063265—21no—
44#13063265—21no—
45C2×C43⋊C16—21no—
46#13063261—21no—
47#13063261—21no—
48#13063259—21no—
49#13063259C2×C412yes—
50#13063258—22no—
51#13063258—22no—
52(C2×D43)⋊C8—41no—
53(C2×D43)⋊C8—41no—
54C2×M16×C43—21no—
55C22×C8×C43C2311yescharacteristic
56C2×C4⋊C4×C43—21no—
57M32×C43—21no—
58M32×C43—21no—
59C2×C16×C43—21no—
60#108×C43—21no—
61#108×C43—21no—
62#107×C43—21no—
63#107×C43C2×C412yes—
64C23×D43SD1611yescharacteristic
65C22×C4×C43—41no—
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—41no—
68C22×Dic43SD1611yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43—42no—
74C2×C4×D43—42no—
75C2×C4×D43—84no—
76C2×C4×D43C22⋊C411yescharacteristic
77C2×C4×D43C22⋊C411yescharacteristic
78C2×C4×D43D811yescharacteristic
79C2×C4×D43D811yescharacteristic
80M16×C43—41no—
81M16×C43—41no—
82C2×C8×C43—41no—
83C2×C8×C43C22×C411yescharacteristic
84C2×C8×C43C2×D411yescharacteristic
85C2×C8×C43#4111yescharacteristic
86C2×C8×C43#4111yescharacteristic
87C2×C8×C43#4111yescharacteristic
88C2×C8×C43#4111yescharacteristic
89C4⋊C4×C43—22no—
90C4⋊C4×C43—41no—
91C4⋊Dic43—22no—
92C4⋊Dic43—41no—
93Dic43⋊C4—42no—
94Dic43⋊C4—42no—
95#10621877—41no—
96#10621877—41no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8—41no—
100C2×C43⋊C8C22⋊C411yescharacteristic
101C2×C43⋊C8C22⋊C411yescharacteristic
102C8×D43—21no—
103C8×D43—21no—
104C8×D43—21no—
105C8×D43—21no—
106C8×D43—21no—
107C8×D43—21no—
108C8×D43—21no—
109C8×D43—21no—
110C16×C43—41no—
111C43⋊C16—41no—
112C23×C43C2×SD1611yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—22no—
116C22×D43—22no—
117C22×D43#10211yescharacteristic
118C22×D43#10211yescharacteristic
119C2×C4×C43—42no—
120C2×C4×C43—82no—
121C2×C4×C43C2×C22⋊C411yescharacteristic
122C2×C4×C43#12311yescharacteristic
123C2×C4×C43#12311yescharacteristic
124C2×C4×C43C2×D811yescharacteristic
125C2×C4×C43#13711yescharacteristic
126C2×C4×C43#13711yescharacteristic
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—42no—
130C2×Dic43—82no—
131C2×Dic43#10211yescharacteristic
132C2×Dic43#10211yescharacteristic
133C4×D43—21no—
134C4×D43—21no—
135C4×D43—21no—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—21no—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—84no—
142C4×D43—84no—
143C8×C43—81no—
144C8×C43#11711yescharacteristic
145C8×C43#11711yescharacteristic
146C8×C43#12311yescharacteristic
147C8×C43#12311yescharacteristic
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—81no—
151#12871—431nomaximal, Sylow
152C22×C43—21no—
153C22×C43—21no—
154C22×C43C2×#10211yescharacteristic
155C22×C43#48311yescharacteristic
156C22×C43#48311yescharacteristic
157C2×D43—24no—
158C2×D43—24no—
159C2×D43—21no—
160C2×D43—21no—
161C2×D43—21no—
162C2×D43—21no—
163C2×D43#36112yes—
164C2×D43#36212yes—
165C4×C43—82no—
166C4×C43#38111yescharacteristic
167C4×C43#41911yescharacteristic
168C4×C43#48011yescharacteristic
169C4×C43#48011yescharacteristic
170Dic43—21no—
171Dic43—21no—
172Dic43—82no—
173C22×#107—431no—
174#2112—431no—
175#1810—431no—
176#1387—431no—
177#1387—431no—
178#1387—431no—
179#1387D4311yescharacteristic, complemented
180C2×C43—21no—
181C2×C43—21no—
182C2×C43#182311yescharacteristic
183C2×C43C2×#36111yescharacteristic
184C2×C43C2×#36211yescharacteristic
185D43—22no—
186D43—22no—
187C23×C8—431no—
188C22×C4⋊C4—861no—
189C2×M32—431no—
190C2×M32C2×D4311yescharacteristic
191C2×#108—431no—
192C2×#108C2×D4311yescharacteristic
193C2×#107—431no—
194C2×#107—432no—
195C2×#107—432no—
196C2×#107—861no—
197C2×#107—861no—
198C2×#107—861no—
199C2×#107C2×D4311yescharacteristic
200#407—861no—
201C22⋊C16—861no—
202C22⋊C16—861no—
203#341—861no—
204C43#1287111yescharacteristic, complemented, Sylow
205C23×C4—431no—
206C23×C4—1721no—
207C2×M16—21no—
208C2×M16—861no—
209C22×C8—431no—
210C22×C8—431no—
211C22×C8—431no—
212C22×C8—431no—
213C22×C8—431no—
214C22×C8—861no—
215C22×C8—861no—
216C22×C8—861no—
217C22×C8—861no—
218C22×C8C22×D4311yescharacteristic
219C2×C4⋊C4—21no—
220C2×C4⋊C4—862no—
221C2×C4⋊C4—862no—
222C2×C4⋊C4—861no—
223C2×C4⋊C4—1721no—
224C2×C4⋊C4—1721no—
225C2×C4⋊C4—1721no—
226M32—21no—
227M32—21no—
228M32—861no—
229M32—861no—
230C2×C16—21no—
231C2×C16—861no—
232#108—21no—
233#108—21no—
234#108—861no—
235#108—861no—
236#107—21no—
237#107—432no—
238#107—862no—
239#107—862no—
240#107—861no—
241#107C4×D4312yes—
242C22⋊C8—1721no—
243C22⋊C8—1721no—
244C24—431no—
245C22×C4—41no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—431no—
250C22×C4—431no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—3444no—
256C22×C4—1722no—
257C22×C4—1722no—
258C22×C4—1721no—
259C22×C4D4×D4311yescharacteristic
260M16—41no—
261M16—41no—
262M16—1721no—
263M16—1721no—
264C2×C8—41no—
265C2×C8—431no—
266C2×C8—431no—
267C2×C8—861no—
268C2×C8—861no—
269C2×C8—861no—
270C2×C8—861no—
271C2×C8—861no—
272C2×C8—861no—
273C2×C8—861no—
274C2×C8—861no—
275C2×C8—861no—
276C2×C8—861no—
277C2×C8—1721no—
278C2×C8C2×C4×D4311yescharacteristic
279C2×C8#1062189811yescharacteristic
280C2×C8#1062189811yescharacteristic
281C2×C8D4×D4311yescharacteristic
282C2×C8#1062190011yescharacteristic
283C2×C8#1062190211yescharacteristic
284C4⋊C4—22no—
285C4⋊C4—41no—
286C4⋊C4—862no—
287C4⋊C4—1722no—
288C4⋊C4—1722no—
289C4⋊C4—1721no—
290C16—41no—
291C16—1721no—
292C23—431no—
293C23—431no—
294C23—862no—
295C23—862no—
296C23—861no—
297C23—861no—
298C23SD16×D4311yescharacteristic
299C2×C4—42no—
300C2×C4—82no—
301C2×C4—431no—
302C2×C4—431no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—3444no—
314C2×C4—3444no—
315C2×C4—3442no—
316C2×C4—1722no—
317C2×C4C22⋊C4×D4311yescharacteristic
318C2×C4#1306330711yescharacteristic
319C2×C4#1306331011yescharacteristic
320C2×C4D8×D4311yescharacteristic
321C2×C4#1306335411yescharacteristic
322C2×C4#1306335711yescharacteristic
323C8—81no—
324C8—861no—
325C8—861no—
326C8—3441no—
327C8#1306328211yescharacteristic
328C8#1306328311yescharacteristic
329C8#1306330711yescharacteristic
330C8#1306331011yescharacteristic
331C22—21no—
332C22—21no—
333C22—432no—
334C22—432no—
335C22—864no—
336C22—864no—
337C22—861no—
338C22—861no—
339C22—861no—
340C22—861no—
341C22#102×D4311yescharacteristic
342C22#1458322811yescharacteristic
343C22#1458323111yescharacteristic
344C4—82no—
345C4—861no—
346C4—861no—
347C4—3442no—
348C4#1458276111yescharacteristic
349C4#1458290611yescharacteristic
350C4#1458321111yescharacteristic
351C4#1458321411yescharacteristic
352C2—21no—
353C2—21no—
354C2—862no—
355C2—862no—
356C2#1913468011yescharacteristic
357C2#361×D4311yescharacteristic
358C2#362×D4311yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1387C2
socleC22×C43C2×#102
prime radicalC23×D43SD16
cosocleC22×C8×C43C23
hypercenter#1387D43
hypocenterC43#12871
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1387

Complements

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

NH ≅ G/Ntype
4. #19132705C2semidirect
5. #19132704C2semidirect
6. #19132703C2semidirect
7. C43×#1387C2semidirect
179. #1387D43semidirect
204. C43#12871semidirect

Maximal subgroups

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

subgroupindex
C2×#107×D432
#191362052
#191346302
#191327052
#191327042
#191327032
C43×#13872
#1287143