Finite Group Databasebeta

← #25065042

Subgroups — #25065042

Order 11008.

1308 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143706C211yesmaximal, characteristic, complemented
2#19143163C211yesmaximal, characteristic, complemented
3#19133272C213yesmaximal, complemented
4#19133263C213yesmaximal, complemented
5#19133244C213yesmaximal, complemented
6C2×#14582643C213yesmaximal, complemented
7C43×#3498C211yesmaximal, characteristic
8C2×#13063332—21no—
9Q8×C43⋊C8—21no—
10D4×C43⋊C8—23no—
11#14582952C2213yescomplemented
12#14582926—23no—
13#14582923C2213yescomplemented
14C2×C4⋊(C43⋊C8)C2213yescomplemented
15C2×C4⋊(C43⋊C8)C2213yescomplemented
16#14582645C2211yescharacteristic, complemented
17#14582645C2213yescomplemented
18#14582643C2213yescomplemented
19#14582643C2216yescomplemented
20#14582643C2213yescomplemented
21C2×H(5,𝔽2)×C43—21no—
22C43×#550—21no—
23C43×#550C412yes—
24D42×C43—23no—
25D42×C43C416yes—
26C43×#535—23no—
27C43×#532C2213yes—
28C2×#127×C43C2213yes—
29C4×#41×C43C2211yescharacteristic
30#13063332—44no—
31C2×#10621877—23no—
32C22×C43⋊C8—23no—
33C22×C43⋊C8—23no—
34C4⋊(C43⋊C8)—23no—
35C4⋊(C43⋊C8)—23no—
36C4⋊(C43⋊C8)—23no—
37C4⋊(C43⋊C8)C2311yescharacteristic
38C4⋊(C43⋊C8)C2313yes—
39C4⋊(C43⋊C8)C2313yes—
40C4⋊(C43⋊C8)C2311yescharacteristic
41C22⋊(C43⋊C8)—23no—
42C4×C43⋊C8—23no—
43H(5,𝔽2)×C43—44no—
44H(5,𝔽2)×C43—44no—
45C2×#41×C43—22no—
46C2×#41×C43—23no—
47C2×#41×C43D411yescharacteristic
48C22×D4×C43—26no—
49C22×D4×C43—23no—
50C22×D4×C43—23no—
51C22×D4×C43C2×C416yes—
52C4⋊Q8×C43C2311yescharacteristic
53#127×C43—23no—
54#127×C43—23no—
55#127×C43C2×C416yes—
56#127×C43C2313yes—
57#124×C43—23no—
58#121×C43—23no—
59#121×C43—26no—
60#121×C43—26no—
61#121×C43C2×C416yes—
62#120×C43—212no—
63C4×Q8×C43C2×C411yescharacteristic
64C4×Q8×C43D411yescharacteristic
65C4×D4×C43—23no—
66C4×D4×C43C2×C416yes—
67C4×D4×C43C2×C413yes—
68C4×D4×C43D413yes—
69#117×C43D413yes—
70C2×C42×C43C2313yes—
71C24×C43—26no—
72#41×C43—48no—
73#41×C43—46no—
74#41×C43—46no—
75#41×C43D814yes—
76#41×C43SD1614yes—
77C2×Q8×C43—21no—
78C2×Q8×C43C22⋊C411yescharacteristic
79C2×D4×C43—26no—
80C2×D4×C43—26no—
81C2×D4×C43—26no—
82C2×D4×C43—23no—
83C2×D4×C43—23no—
84C2×D4×C43—26no—
85C2×D4×C43—424no—
86C2×D4×C43—46no—
87C2×D4×C43—46no—
88C2×D4×C43—83no—
89C2×D4×C43—83no—
90C2×D4×C43—86no—
91C2×D4×C43C22⋊C413yes—
92C2×D4×C43C22×C416yes—
93C22×C4×C43—26no—
94C22×C4×C43C22×C413yes—
95C22×C4×C43C2×D413yes—
96C22×C4×C43C2×D413yes—
97C4⋊C4×C43—21no—
98C4⋊C4×C43C22⋊C413yes—
99C4⋊C4×C43C22⋊C413yes—
100C4⋊C4×C43C22×C412yes—
101C22⋊C4×C43—26no—
102C22⋊C4×C43—26no—
103C22⋊C4×C43C22⋊C416yes—
104C42×C43C22×C413yes—
105C42×C43C2×D413yes—
106C42×C43C2×D413yes—
107C42×C43C2411yescharacteristic
108#10621877—46no—
109C2×C43⋊C8—21no—
110C2×C43⋊C8—23no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8—23no—
113C2×C43⋊C8—46no—
114C2×C43⋊C8—83no—
115C23×C43—26no—
116C23×C43—412no—
117C23×C43—86no—
118C23×C43—86no—
119C23×C43C2×C22⋊C413yes—
120Q8×C43—41no—
121Q8×C43—41no—
122Q8×C43#10214yes—
123D4×C43—46no—
124D4×C43—412no—
125D4×C43—43no—
126D4×C43—43no—
127D4×C43—43no—
128D4×C43—43no—
129D4×C43—412no—
130D4×C43—86no—
131D4×C43—86no—
132D4×C43#102112yes—
133C2×C4×C43—23no—
134C2×C4×C43—23no—
135C2×C4×C43—22no—
136C2×C4×C43—43no—
137C2×C4×C43—412no—
138C2×C4×C43C2×C22⋊C413yes—
139C2×C4×C43C2×C22⋊C413yes—
140C2×C4×C43C2×C22⋊C413yes—
141C2×C4×C43C2×D816yes—
142C2×C4×C43C2×SD1616yes—
143C2×C4×C43C23×C411yescharacteristic
144C2×C4×C43C22×D411yescharacteristic
145C2×C4×C43C22×D411yescharacteristic
146C43⋊C8—41no—
147C43⋊C8—43no—
148C43⋊C8—43no—
149C43⋊C8—41no—
150#17720—431nomaximal, Sylow
151C22×C43—23no—
152C22×C43—23no—
153C22×C43—46no—
154C22×C43—46no—
155C22×C43—46no—
156C22×C43—1612no—
157C22×C43C2×#10216yes—
158C22×C43C22×C22⋊C411yescharacteristic
159C4×C43—21no—
160C4×C43—23no—
161C4×C43—23no—
162C4×C43—42no—
163C4×C43C2×#10216yes—
164C4×C43C22×D811yescharacteristic
165C4×C43C22×SD1611yescharacteristic
166C4×C43#57611yescharacteristic
167C4×C43#57711yescharacteristic
168#3498D4311yescharacteristic
169#2988—431no—
170#2906—431no—
171#1547—433no—
172#1545—433no—
173#1540—433no—
174C2×#331—433no—
175C2×C43—26no—
176C2×C43—86no—
177C2×C43#288811yescharacteristic
178C2×C43C22×#10211yescharacteristic
179C2×C43#289711yescharacteristic
180C2×H(5,𝔽2)—21no—
181C2×#131—861no—
182#550—21no—
183#550Dic4312yes—
184D42—23no—
185D42Dic4316yes—
186#535—23no—
187#532C2×D4313yes—
188C2×#127C2×D4313yes—
189C4×#41C2×D4311yescharacteristic
190C8×Q8—861no—
191C8×D4—863no—
192#431—433no—
193#424—863no—
194#423—433no—
195C2×C4⋊C8—433no—
196C2×C4⋊C8—433no—
197#332—431no—
198#332—433no—
199#331—433no—
200#331—436no—
201#331—433no—
202C43#1772011yescharacteristic, complemented, Sylow
203H(5,𝔽2)—44no—
204H(5,𝔽2)—44no—
205C2×#41—22no—
206C2×#41—23no—
207C2×#41C22⋊D4311yescharacteristic
208C22×D4—26no—
209C22×D4—23no—
210C22×D4—23no—
211C22×D4C2×Dic4316yes—
212#131—1724no—
213C2×M16—863no—
214C22×C8—863no—
215C22×C8—863no—
216C4⋊Q8C22×D4311yescharacteristic
217#127—23no—
218#127—23no—
219#127C2×Dic4316yes—
220#127C22×D4313yes—
221#124—23no—
222#121—23no—
223#121—26no—
224#121—26no—
225#121C2×Dic4316yes—
226#120—212no—
227C4×Q8C2×Dic4311yescharacteristic
228C4×Q8C22⋊D4311yescharacteristic
229C4×D4—23no—
230C4×D4C2×Dic4316yes—
231C4×D4C2×Dic4313yes—
232C4×D4C22⋊D4313yes—
233#117C22⋊D4313yes—
234C2×C42C22×D4313yes—
235C4⋊C8—431no—
236C4⋊C8—433no—
237C4⋊C8—433no—
238C4⋊C8—431no—
239C4⋊C8—863no—
240C4⋊C8—863no—
241C4⋊C8—863no—
242C22⋊C8—863no—
243C4×C8—863no—
244C24—26no—
245#41—48no—
246#41—46no—
247#41—46no—
248#41#1062188214yes—
249#41#1062188314yes—
250C2×Q8—21no—
251C2×Q8C22⋊Dic4311yescharacteristic
252C2×D4—26no—
253C2×D4—26no—
254C2×D4—26no—
255C2×D4—26no—
256C2×D4—23no—
257C2×D4—23no—
258C2×D4—424no—
259C2×D4—46no—
260C2×D4—46no—
261C2×D4—83no—
262C2×D4—83no—
263C2×D4—86no—
264C2×D4C22⋊Dic4313yes—
265C2×D4C22×Dic4316yes—
266C22×C4—26no—
267C22×C4C22×Dic4313yes—
268C22×C4C2×C22⋊D4313yes—
269C22×C4C2×C22⋊D4313yes—
270M16—1726no—
271C2×C8—861no—
272C2×C8—863no—
273C2×C8—861no—
274C2×C8—863no—
275C2×C8—3443no—
276C2×C8—1726no—
277C4⋊C4—21no—
278C4⋊C4C22⋊Dic4313yes—
279C4⋊C4C22⋊Dic4313yes—
280C4⋊C4C22×Dic4312yes—
281C22⋊C4—26no—
282C22⋊C4—26no—
283C22⋊C4C22⋊Dic4316yes—
284C42C22×Dic4313yes—
285C42C2×C22⋊D4313yes—
286C42C2×C22⋊D4313yes—
287C42C23×D4311yescharacteristic
288C23—26no—
289C23—412no—
290C23—86no—
291C23—86no—
292C23C2×C22⋊Dic4313yes—
293Q8—41no—
294Q8—41no—
295Q8#1306324614yes—
296D4—46no—
297D4—412no—
298D4—412no—
299D4—43no—
300D4—43no—
301D4—43no—
302D4—43no—
303D4—86no—
304D4—86no—
305D4#13063246112yes—
306C2×C4—23no—
307C2×C4—23no—
308C2×C4—22no—
309C2×C4—43no—
310C2×C4—412no—
311C2×C4C2×C22⋊Dic4313yes—
312C2×C4C2×C22⋊Dic4313yes—
313C2×C4C2×C22⋊Dic4313yes—
314C2×C4C2×#1062188216yes—
315C2×C4C2×#1062188316yes—
316C2×C4C23×Dic4311yescharacteristic
317C2×C4C22×C22⋊D4311yescharacteristic
318C2×C4C22×C22⋊D4311yescharacteristic
319C8—1721no—
320C8—1723no—
321C8—1723no—
322C8—1721no—
323C22—23no—
324C22—23no—
325C22—46no—
326C22—46no—
327C22—46no—
328C22—1612no—
329C22C2×#1306324616yes—
330C22C22×C22⋊Dic4311yescharacteristic
331C4—21no—
332C4—23no—
333C4—23no—
334C4—42no—
335C4C2×#1306324616yes—
336C4C22×#1062188211yescharacteristic
337C4C22×#1062188311yescharacteristic
338C4#1458370211yescharacteristic
339C4#1458371011yescharacteristic
340C2—26no—
341C2—86no—
342C2#1914307411yescharacteristic
343C2C22×#1306324611yescharacteristic
344C2#1914312111yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
Fitting, prime radicalC43×#3498C2
socleC22×C43C22×C22⋊C4
cosocleC42×C43C24
hypercenter#3498D43
hypocenterC43#17720
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #19143706C2semidirect
2. #19143163C2semidirect
3. #19133272C2semidirect
4. #19133263C2semidirect
5. #19133244C2semidirect
6. C2×#14582643C2semidirect
11. #14582952C22semidirect
13. #14582923C22semidirect
14. C2×C4⋊(C43⋊C8)C22semidirect
15. C2×C4⋊(C43⋊C8)C22semidirect
16. #14582645C22semidirect
17. #14582645C22semidirect
18. #14582643C22semidirect
19. #14582643C22semidirect
20. #14582643C22semidirect
202. C43#17720semidirect

Maximal subgroups

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

subgroupindex
#191437062
#191431632
#191332722
#191332632
#191332442
C2×#145826432
C43×#34982
#1772043