Finite Group Databasebeta

← #25064600

Subgroups — #25064600

Order 11008.

960 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
1#19143615C211yesmaximal, characteristic, complemented
2#19143023C211yesmaximal, characteristic, complemented
3#19133210C213yesmaximal, complemented
4#19133202C213yesmaximal, complemented
5#19133190C213yesmaximal, complemented
6#19133183C213yesmaximal, complemented
7C43×#3518C211yesmaximal, characteristic
8C2×#13063332—21no—
9Q8×C43⋊C8—21no—
10#14582977—23no—
11#14582956C2213yes—
12#14582855—23no—
13C4×#10621877C2213yes—
14C4×#10621877C2213yes—
15C2×#13063236C2213yes—
16#14582641C2213yes—
17#14582641C2216yes—
18#14582641C2213yes—
19#14582639C2213yes—
20#14582639C2211yescharacteristic
21Q82×C43C411yescharacteristic
22C43×#556—23no—
23C43×#556C413yes—
24C43×#555C413yes—
25D4×Q8×C43C411yescharacteristic
26C43×#548—21no—
27C43×#542—23no—
28C43×#533C2213yes—
29C43×#529C2213yes—
30C43×#519—21no—
31C4×#41×C43C2211yescharacteristic
32#13063332—28no—
33C2×#10621877—23no—
34C2×#10621877—23no—
35C22×C43⋊C8—23no—
36C4⋊(C43⋊C8)—23no—
37C22⋊(C43⋊C8)—23no—
38#13063236—23no—
39#13063236C2311yescharacteristic
40#13063236C2313yes—
41#13063236C2311yescharacteristic
42#13063236C2313yes—
43C4×C43⋊C8—23no—
44C4×C43⋊C8—23no—
45C2×#41×C43D411yescharacteristic
46C22×Q8×C43—21no—
47C4⋊Q8×C43—23no—
48C4⋊Q8×C43C2×C413yes—
49C4⋊Q8×C43C2×C413yes—
50#126×C43—26no—
51#126×C43—23no—
52#125×C43C2313yes—
53#124×C43—23no—
54#124×C43—26no—
55#124×C43C2311yescharacteristic
56#123×C43—23no—
57C22⋊Q8×C43—23no—
58C22⋊Q8×C43—23no—
59C22⋊Q8×C43—23no—
60C22⋊Q8×C43C2×C413yes—
61#121×C43—23no—
62#121×C43C2×C413yes—
63C4×Q8×C43—21no—
64C4×Q8×C43—23no—
65C4×Q8×C43—23no—
66C4×Q8×C43—23no—
67C4×Q8×C43C2×C413yes—
68C4×Q8×C43C2×C411yescharacteristic
69C4×Q8×C43D411yescharacteristic
70C4×D4×C43—23no—
71C4×D4×C43C2×C413yes—
72C4×D4×C43C2×C413yes—
73C4×D4×C43D413yes—
74#117×C43—23no—
75#117×C43—23no—
76#117×C43C2×C416yes—
77#117×C43D413yes—
78C2×C42×C43C2313yes—
79#41×C43—24no—
80C2×Q8×C43—23no—
81C2×Q8×C43—23no—
82C2×Q8×C43—44no—
83C2×Q8×C43C22⋊C411yescharacteristic
84C2×Q8×C43C22×C411yescharacteristic
85C2×D4×C43—23no—
86C2×D4×C43C22⋊C413yes—
87C2×D4×C43C22×C411yescharacteristic
88C22×C4×C43—23no—
89C22×C4×C43C22×C413yes—
90C22×C4×C43C2×D413yes—
91C22×C4×C43C2×D413yes—
92C4⋊C4×C43—23no—
93C4⋊C4×C43—23no—
94C4⋊C4×C43—23no—
95C4⋊C4×C43—23no—
96C4⋊C4×C43—23no—
97C4⋊C4×C43—23no—
98C4⋊C4×C43C22⋊C413yes—
99C4⋊C4×C43C22⋊C413yes—
100C4⋊C4×C43C22×C413yes—
101C4⋊C4×C43C22×C413yes—
102C22⋊C4×C43—23no—
103C22⋊C4×C43—23no—
104C22⋊C4×C43—21no—
105C22⋊C4×C43—21no—
106C22⋊C4×C43—26no—
107C22⋊C4×C43—23no—
108C22⋊C4×C43C22⋊C416yes—
109C42×C43—26no—
110C42×C43—23no—
111C42×C43C22×C413yes—
112C42×C43C2×D413yes—
113C42×C43C2×D413yes—
114C42×C43C2411yescharacteristic
115#10621877—212no—
116#10621877—46no—
117C2×C43⋊C8—212no—
118C2×C43⋊C8—21no—
119C2×C43⋊C8—23no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—23no—
122C23×C43—21no—
123C23×C43C2×C22⋊C413yes—
124Q8×C43—41no—
125Q8×C43—46no—
126Q8×C43—83no—
127Q8×C43#10414yes—
128D4×C43—26no—
129D4×C43—41no—
130D4×C43—83no—
131C2×C4×C43—26no—
132C2×C4×C43—21no—
133C2×C4×C43—23no—
134C2×C4×C43—23no—
135C2×C4×C43—43no—
136C2×C4×C43—43no—
137C2×C4×C43—46no—
138C2×C4×C43C2×C22⋊C413yes—
139C2×C4×C43C2×C22⋊C413yes—
140C2×C4×C43C2×C22⋊C413yes—
141C2×C4×C43C23×C411yescharacteristic
142C2×C4×C43C22×D411yescharacteristic
143C2×C4×C43C22×D411yescharacteristic
144C43⋊C8—22no—
145C43⋊C8—26no—
146C43⋊C8—22no—
147C43⋊C8—43no—
148#17654—431nomaximal, Sylow
149C22×C43—23no—
150C22×C43—23no—
151C22×C43—23no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×C22⋊C411yescharacteristic
156C4×C43—21no—
157C4×C43—23no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—23no—
161C4×C43—41no—
162C4×C43—43no—
163C4×C43—43no—
164C4×C43C2×#10416yes—
165#3518D4311yescharacteristic
166#2971—431no—
167#2875—431no—
168#1531—433no—
169#1529—433no—
170#1526—433no—
171#1524—433no—
172C2×C43—43no—
173C2×C43—81no—
174C2×C43#288911yescharacteristic
175C2×C43C22×#10411yescharacteristic
176C2×C43#290111yescharacteristic
177C2×#131—861no—
178Q82Dic4311yescharacteristic
179#556—23no—
180#556Dic4313yes—
181#555Dic4313yes—
182D4×Q8Dic4311yescharacteristic
183#548—21no—
184#542—23no—
185#533C2×D4313yes—
186#529C2×D4313yes—
187#519—21no—
188C4×#41C2×D4311yescharacteristic
189C8×Q8—861no—
190#436—863no—
191#432—433no—
192#405—863no—
193C4×M16—433no—
194C4×M16—433no—
195C2×#97—433no—
196#330—433no—
197#330—433no—
198#330—436no—
199#329—431no—
200#329—433no—
201C43#1765411yescharacteristic, complemented, Sylow
202C2×#41C22⋊D4311yescharacteristic
203C22×Q8—21no—
204#131—868no—
205C2×M16—863no—
206C2×M16—863no—
207C22×C8—863no—
208C4⋊Q8—23no—
209C4⋊Q8C2×Dic4313yes—
210C4⋊Q8C2×Dic4313yes—
211#126—26no—
212#126—23no—
213#125C22×D4313yes—
214#124—23no—
215#124—26no—
216#124C22×D4311yescharacteristic
217#123—23no—
218C22⋊Q8—23no—
219C22⋊Q8—23no—
220C22⋊Q8—23no—
221C22⋊Q8C2×Dic4313yes—
222#121—23no—
223#121C2×Dic4313yes—
224C4×Q8—21no—
225C4×Q8—23no—
226C4×Q8—23no—
227C4×Q8—23no—
228C4×Q8C2×Dic4313yes—
229C4×Q8C2×Dic4311yescharacteristic
230C4×Q8C22⋊D4311yescharacteristic
231C4×D4—23no—
232C4×D4C2×Dic4313yes—
233C4×D4C2×Dic4313yes—
234C4×D4C22⋊D4313yes—
235#117—23no—
236#117—23no—
237#117C2×Dic4316yes—
238#117C22⋊D4313yes—
239C2×C42C22×D4313yes—
240C4⋊C8—863no—
241C22⋊C8—863no—
242#97—431no—
243#97—433no—
244#97—431no—
245#97—433no—
246#97—863no—
247C4×C8—863no—
248C4×C8—863no—
249#41—24no—
250C2×Q8—23no—
251C2×Q8—23no—
252C2×Q8—44no—
253C2×Q8C22⋊Dic4311yescharacteristic
254C2×Q8C22×Dic4311yescharacteristic
255C2×D4—23no—
256C2×D4C22⋊Dic4313yes—
257C2×D4C22×Dic4311yescharacteristic
258C22×C4—23no—
259C22×C4C22×Dic4313yes—
260C22×C4C2×C22⋊D4313yes—
261C22×C4C2×C22⋊D4313yes—
262M16—8612no—
263M16—1726no—
264C2×C8—8612no—
265C2×C8—861no—
266C2×C8—863no—
267C2×C8—861no—
268C2×C8—863no—
269C4⋊C4—23no—
270C4⋊C4—23no—
271C4⋊C4—23no—
272C4⋊C4—23no—
273C4⋊C4—23no—
274C4⋊C4—23no—
275C4⋊C4C22⋊Dic4313yes—
276C4⋊C4C22⋊Dic4313yes—
277C4⋊C4C22×Dic4313yes—
278C4⋊C4C22×Dic4313yes—
279C22⋊C4—26no—
280C22⋊C4—23no—
281C22⋊C4—23no—
282C22⋊C4—23no—
283C22⋊C4—21no—
284C22⋊C4—21no—
285C22⋊C4C22⋊Dic4316yes—
286C42—26no—
287C42—23no—
288C42C22×Dic4313yes—
289C42C2×C22⋊D4313yes—
290C42C2×C22⋊D4313yes—
291C42C23×D4311yescharacteristic
292C23—21no—
293C23C2×C22⋊Dic4313yes—
294Q8—41no—
295Q8—46no—
296Q8—83no—
297Q8#1306325214yes—
298D4—26no—
299D4—41no—
300D4—83no—
301C2×C4—26no—
302C2×C4—21no—
303C2×C4—23no—
304C2×C4—23no—
305C2×C4—43no—
306C2×C4—43no—
307C2×C4—46no—
308C2×C4C2×C22⋊Dic4313yes—
309C2×C4C2×C22⋊Dic4313yes—
310C2×C4C2×C22⋊Dic4313yes—
311C2×C4C23×Dic4311yescharacteristic
312C2×C4C22×C22⋊D4311yescharacteristic
313C2×C4C22×C22⋊D4311yescharacteristic
314C8—862no—
315C8—866no—
316C8—862no—
317C8—1723no—
318C22—23no—
319C22—23no—
320C22—23no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22C22×C22⋊Dic4311yescharacteristic
325C4—21no—
326C4—23no—
327C4—21no—
328C4—21no—
329C4—23no—
330C4—41no—
331C4—43no—
332C4—43no—
333C4C2×#1306325216yes—
334C2—43no—
335C2—81no—
336C2#1914307811yescharacteristic
337C2C22×#1306325211yescharacteristic
338C2#1914314211yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
Fitting, prime radicalC43×#3518C2
socleC22×C43C22×C22⋊C4
cosocleC42×C43C24
hypercenter#3518D43
hypocenterC43#17654
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3518

Complements

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

NH ≅ G/Ntype
1. #19143615C2semidirect
2. #19143023C2semidirect
3. #19133210C2semidirect
4. #19133202C2semidirect
5. #19133190C2semidirect
6. #19133183C2semidirect
201. C43#17654semidirect

Maximal subgroups

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

subgroupindex
#191436152
#191430232
#191332102
#191332022
#191331902
#191331832
C43×#35182
#1765443