Finite Group Databasebeta

← #25013116

Subgroups — #25013116

Order 11008.

424 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143183C211yesmaximal, characteristic
2#19136381C211yesmaximal, characteristic, complemented
3C2×#14582680C211yesmaximal, characteristic
4#19134629C211yesmaximal, characteristic
5#19132701C211yesmaximal, characteristic, complemented
6#19132700C211yesmaximal, characteristic, complemented
7C43×#2159C211yesmaximal, characteristic, complemented
8C22×#10621872C2211yescharacteristic
9#117×D43—21no—
10C2×#13063265C2211yescharacteristic
11#14582940—21no—
12#14582940—21no—
13#14582938—21no—
14#14582938—21no—
15#14582937C2211yescharacteristic
16#14582935—21no—
17C2×#13063257C2211yescharacteristic
18#14582756—21no—
19#14582726—21no—
20#14582724—21no—
21#14582680C414yescomplemented
22#14582661—21no—
23C2×M32×C43C2211yescharacteristic
24C43×#427C2211yescharacteristic
25C2×#107×C43C2211yescharacteristic
26C43×#367—21no—
27C43×#366—21no—
28C22×C4×D43D411yescharacteristic
29C2×#10621872—21no—
30C2×#10621872—21no—
31C2×#10621872—21no—
32C2×#10621872—21no—
33C2×#10621872C2×C412yes—
34C2×#10621872Q812yes—
35C22×C43⋊C8D411yescharacteristic
36#13063284—21no—
37#13063283—21no—
38#13063283—21no—
39#13063282—41no—
40#13063281—41no—
41C2×C4⋊Dic43—21no—
42C4⋊C4×D43—21no—
43C4⋊C4×D43—21no—
44C2×(C2×D43)⋊C4—41no—
45C22⋊C4×D43—41no—
46C42×D43—41no—
47#13063265—21no—
48#13063265C2×C412yescomplemented
49C2×C43⋊C16—21no—
50#13063259D411yescharacteristic
51#13063259D411yescharacteristic
52#13063258—21no—
53#13063258—21no—
54#13063257—21no—
55#13063257—21no—
56#13063257—21no—
57#13063256—21no—
58#13063256—21no—
59C43⋊#95—41no—
60C22×C8×C43C2311yescharacteristic
61#117×C43—21no—
62C2×C4⋊C4×C43—21no—
63M32×C43—21no—
64M32×C43C2×C412yescomplemented
65C2×C16×C43—21no—
66#107×C43—21no—
67#107×C43—21no—
68#107×C43D411yescharacteristic
69#107×C43D411yescharacteristic
70#106×C43—21no—
71C23×D43D811yescharacteristic
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—41no—
75C22×Dic43D811yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43—41no—
81C2×C4×D43—41no—
82C2×C4×D43C4⋊C412yes—
83C2×C4×D43Q1612yes—
84C2×C8×C43C22×C411yescharacteristic
85C2×C8×C43C2×D411yescharacteristic
86C2×C8×C43C2×D411yescharacteristic
87C2×C8×C43C2×Q811yescharacteristic
88C2×C8×C43#4111yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C4⋊C4×C43—21no—
91C4⋊C4×C43—21no—
92C4⋊C4×C43—41no—
93C4⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C42×C43—41no—
96C22⋊Dic43—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—82no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43—41no—
103C4⋊Dic43—41no—
104Dic43⋊C4—41no—
105Dic43⋊C4—41no—
106C4×Dic43—41no—
107C4×Dic43—41no—
108C4×Dic43—41no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—21no—
111C2×C43⋊C8C4⋊C412yes—
112#10621872—22no—
113#10621872—22no—
114#10621872—22no—
115#10621872—22no—
116C16×C43—22no—
117C43⋊C16—22no—
118C23×C43C2×D811yescharacteristic
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—41no—
122C22×D43—41no—
123C22×D43#10712yes—
124C2×C4×C43—41no—
125C2×C4×C43—41no—
126C2×C4×C43—81no—
127C2×C4×C43—81no—
128C2×C4×C43—81no—
129C2×C4×C43C2×C4⋊C411yescharacteristic
130C2×C4×C43#12011yescharacteristic
131C2×C4×C43#12311yescharacteristic
132C2×C4×C43C2×Q1611yescharacteristic
133C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C43#13711yescharacteristic
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—41no—
138C2×Dic43—41no—
139C2×Dic43—81no—
140C2×Dic43—81no—
141C2×Dic43—81no—
142C2×Dic43#10712yes—
143C4×D43—22no—
144C4×D43—22no—
145C4×D43—22no—
146C4×D43—22no—
147C4×D43—82no—
148C4×D43—82no—
149C8×C43C4×D411yescharacteristic
150C8×C43C4×D411yescharacteristic
151C8×C43C22⋊Q811yescharacteristic
152C8×C43C22⋊Q811yescharacteristic
153C43⋊C8—22no—
154#12923—431nomaximal, Sylow
155C22×C43—21no—
156C22×C43—21no—
157C22×C43C2×#10711yescharacteristic
158C22×C43#44711yescharacteristic
159C22×C43#48011yescharacteristic
160C2×D43—22no—
161C2×D43—41no—
162C2×D43—41no—
163C2×D43—42no—
164C2×D43—81no—
165C4×C43—81no—
166C4×C43—81no—
167C4×C43—161no—
168C4×C43#38511yescharacteristic
169C4×C43#42811yescharacteristic
170C4×C43#45111yescharacteristic
171C4×C43#48411yescharacteristic
172Dic43—22no—
173Dic43—81no—
174Dic43—81no—
175Dic43—161no—
176#2911—431no—
177#2159—431no—
178#2159D4311yescharacteristic, complemented
179C2×#349—431no—
180#1809—431no—
181#1386—431no—
182#1386—431no—
183C2×C43—21no—
184C2×C43—21no—
185C2×C43#185211yescharacteristic
186C2×C43#219011yescharacteristic
187C2×C43#219111yescharacteristic
188D43—42no—
189C22×M16—431no—
190C2×#117—861no—
191C2×M32—431no—
192C2×M32C2×D4311yescharacteristic
193#428—861no—
194#428—861no—
195#428—861no—
196#428—861no—
197#427—431no—
198#427—861no—
199#427C2×D4311yescharacteristic
200C2×#107C2×D4311yescharacteristic
201C2×#106—431no—
202#380—861no—
203#367—21no—
204#367—861no—
205#366—21no—
206#366—861no—
207#349—434no—
208#340—861no—
209C43#1292311yescharacteristic, complemented, Sylow
210C23×C4—431no—
211C2×M16—432no—
212C2×M16—432no—
213C2×M16—861no—
214C2×M16—861no—
215C2×M16—861no—
216C2×M16—861no—
217C22×C8—431no—
218C22×C8C22×D4311yescharacteristic
219#117—21no—
220#117—861no—
221#117—861no—
222#117—861no—
223#117—1721no—
224#117—1721no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—861no—
227C2×C4⋊C4—861no—
228C2×C4⋊C4—861no—
229C2×C22⋊C4—1721no—
230C2×C22⋊C4—1721no—
231C2×C42—1721no—
232M32—21no—
233M32—432no—
234M32—861no—
235M32C4×D4312yescomplemented
236C2×C16—21no—
237C2×C16—861no—
238#107—21no—
239#107—21no—
240#107—431no—
241#107—431no—
242#107—861no—
243#107—861no—
244#107C22⋊D4311yescharacteristic
245#107C22⋊D4311yescharacteristic
246#106—21no—
247#106—861no—
248#106—861no—
249#106—861no—
250#106—861no—
251#106—861no—
252#95—1721no—
253C24—431no—
254C22×C4—41no—
255C22×C4—431no—
256C22×C4—432no—
257C22×C4—432no—
258C22×C4—861no—
259C22×C4—861no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—1721no—
263C22×C4—1721no—
264C22×C4—1721no—
265C22×C4D4×D4311yescharacteristic
266M16—862no—
267M16—862no—
268M16—862no—
269M16—862no—
270C2×C8—432no—
271C2×C8—861no—
272C2×C8—861no—
273C2×C8C2×C4×D4311yescharacteristic
274C2×C8#1062189811yescharacteristic
275C2×C8D4×D4311yescharacteristic
276C2×C8Q8×D4311yescharacteristic
277C2×C8#1062190211yescharacteristic
278C2×C8C2×C22⋊D4311yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C4⋊C4—1721no—
289C22⋊C4—41no—
290C22⋊C4—3442no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C42—41no—
295C42—1721no—
296C42—1721no—
297C42—1721no—
298C16—22no—
299C16—862no—
300C23—432no—
301C23—861no—
302C23—861no—
303C23—1721no—
304C23—1721no—
305C23D8×D4311yescharacteristic
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—432no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—862no—
315C2×C4—862no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—3442no—
319C2×C4—3442no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4—1721no—
324C2×C4—1721no—
325C2×C4C4⋊C4×D4311yescharacteristic
326C2×C4#1306329311yescharacteristic
327C2×C4#1306331011yescharacteristic
328C2×C4Q16×D4311yescharacteristic
329C2×C4#1306334911yescharacteristic
330C2×C4#1306335711yescharacteristic
331C8—862no—
332C8C4×C22⋊D4311yescharacteristic
333C8#1306328711yescharacteristic
334C8#1306330111yescharacteristic
335C8#1306330311yescharacteristic
336C22—21no—
337C22—21no—
338C22—862no—
339C22—3441no—
340C22—1722no—
341C22—1721no—
342C22—1721no—
343C22#107×D4311yescharacteristic
344C22#1458303111yescharacteristic
345C22#1458321411yescharacteristic
346C4—81no—
347C4—81no—
348C4—161no—
349C4—862no—
350C4—3441no—
351C4—3441no—
352C4—6881no—
353C4#1458277011yescharacteristic
354C4#1458294011yescharacteristic
355C4#1458305311yescharacteristic
356C4#1458323611yescharacteristic
357C2—21no—
358C2—21no—
359C2—1722no—
360C2#1913478111yescharacteristic
361C2#1913653911yescharacteristic
362C2#1913654411yescharacteristic
subgroupG/H
centerC22#14583031
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2159C2
socleC22×C43#447
prime radicalC23×D43D8
cosocleC22×C8×C43C23
hypercenter#2159D43
hypocenterC43#12923
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
2. #19136381C2semidirect
5. #19132701C2semidirect
6. #19132700C2semidirect
7. C43×#2159C2semidirect
21. #14582680C4semidirect
48. #13063265C2×C4semidirect
64. M32×C43C2×C4semidirect
178. #2159D43semidirect
209. C43#12923semidirect
235. M32C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191431832
#191363812
C2×#145826802
#191346292
#191327012
#191327002
C43×#21592
#1292343