Finite Group Databasebeta

← #25063476

Subgroups — #25063476

Order 11008.

994 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic86C211yesmaximal, characteristic
2#19143163C211yesmaximal, characteristic
3#19133051C213yesmaximal, complemented
4#19133025C213yesmaximal, complemented
5#19132999C213yesmaximal, complemented
6C2×#14582631C213yesmaximal, complemented
7C8×#41×C43C211yesmaximal, characteristic
8C2×#13063332—21no—
9Q8×Dic86C411yescharacteristic
10#14583628C411yescharacteristic
11#14583625—21no—
12#14583608—23no—
13#14583606C413yes—
14D4×Dic86C413yes—
15#14583456C2213yes—
16#14583452—23no—
17#41×Dic43—21no—
18C2×C4×Dic86C2213yes—
19#14582926—23no—
20#14582923C2213yes—
21C2×C4⋊(C43⋊C8)C2213yes—
22#14582631C2211yescharacteristic
23#14582631C2213yes—
24#14582631C2213yes—
25#14582631C2213yes—
26#14582631C2216yes—
27C4×#41×C43C2211yescharacteristic
28C8×Q8×C43—21no—
29C8×D4×C43—23no—
30C43×#431C2213yes—
31C2×C4×C8×C43C2213yes—
32C22×Dic86C2×C413yes—
33#13063332—44no—
34C2×#10621877—23no—
35C22×C43⋊C8—23no—
36#13063325C2×C413yes—
37#13063325C2×C413yes—
38#13063324—23no—
39#13063324—23no—
40#13063317—23no—
41#13063316—23no—
42#13063316—23no—
43#13063304—23no—
44#13063304C2×C416yes—
45#13063302—26no—
46#13063302—26no—
47Q8×Dic43—21no—
48Q8×Dic43—21no—
49C4×Dic86—23no—
50C4×Dic86—23no—
51C4×Dic86—23no—
52C4×Dic86C2×C413yes—
53C4×Dic86C2×C413yes—
54C4×Dic86C2311yescharacteristic
55C4×Dic86C2313yes—
56D4×Dic43—23no—
57D4×Dic43—23no—
58#13063284—23no—
59C2×C4⋊Dic43C2×C413yes—
60C2×Dic43⋊C4—23no—
61C2×C4×Dic43—23no—
62C4⋊(C43⋊C8)—23no—
63C4⋊(C43⋊C8)—23no—
64C4⋊(C43⋊C8)C2311yescharacteristic
65C4⋊(C43⋊C8)C2313yes—
66C2×#41×C43D411yescharacteristic
67C22×C8×C43—23no—
68C4×Q8×C43C2×C411yescharacteristic
69C4×Q8×C43D411yescharacteristic
70C4×D4×C43C2×C413yes—
71C4×D4×C43D413yes—
72#117×C43D413yes—
73C2×C42×C43C2313yes—
74C4⋊C8×C43—23no—
75C22⋊C8×C43—23no—
76C4×C8×C43—23no—
77C4×C8×C43C2311yescharacteristic
78C4×C8×C43C2313yes—
79#41×C43SD1614yes—
80#41×C43Q1614yes—
81C2×Q8×C43C22⋊C411yescharacteristic
82C2×D4×C43C22⋊C413yes—
83C22×C4×C43C22×C413yes—
84C22×C4×C43C2×D413yes—
85C22×C4×C43C2×D413yes—
86C22×Dic43—23no—
87C22×Dic43—23no—
88C2×Dic86—26no—
89C2×Dic86—23no—
90C2×Dic86—23no—
91C2×Dic86—43no—
92C2×Dic86C22×C413yes—
93C2×Dic86C22×C411yescharacteristic
94C2×C8×C43—21no—
95C2×C8×C43—23no—
96C2×C8×C43—46no—
97C4⋊C4×C43C22⋊C413yes—
98C4⋊C4×C43C22⋊C413yes—
99C22⋊C4×C43C22⋊C416yes—
100C42×C43C22×C413yes—
101C42×C43C2×D413yes—
102C42×C43C2×D413yes—
103C42×C43C2411yescharacteristic
104C22⋊Dic43—26no—
105C4⋊Dic43—23no—
106C4⋊Dic43—23no—
107C4⋊Dic43—23no—
108C4⋊Dic43—23no—
109C4⋊Dic43C22×C411yescharacteristic
110C4⋊Dic43C22×C413yes—
111Dic43⋊C4—23no—
112Dic43⋊C4—23no—
113Dic43⋊C4—26no—
114Dic43⋊C4—21no—
115Dic43⋊C4—23no—
116C4×Dic43—23no—
117C4×Dic43—23no—
118C4×Dic43—21no—
119C4×Dic43—23no—
120#10621877—46no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—23no—
123C2×C43⋊C8—46no—
124C23×C43C2×C22⋊C413yes—
125Q8×C43#10314yes—
126D4×C43#103112yes—
127C2×C4×C43—23no—
128C2×C4×C43—23no—
129C2×C4×C43—43no—
130C2×C4×C43C2×C22⋊C413yes—
131C2×C4×C43C2×C22⋊C413yes—
132C2×C4×C43C2×C22⋊C413yes—
133C2×C4×C43C2×SD1616yes—
134C2×C4×C43C2×Q1616yes—
135C2×C4×C43C23×C411yescharacteristic
136C2×C4×C43C22×D411yescharacteristic
137C2×C4×C43C22×D411yescharacteristic
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—23no—
141C2×Dic43—23no—
142C2×Dic43—46no—
143C2×Dic43—83no—
144Dic86—21no—
145Dic86—23no—
146Dic86—23no—
147Dic86—46no—
148Dic86—83no—
149Dic86#13112yescomplemented
150C8×C43—22no—
151C8×C43—43no—
152C43⋊C8—41no—
153C43⋊C8—43no—
154#17509—431nomaximal, Sylow
155C22×C43—23no—
156C22×C43—23no—
157C22×C43C2×#10316yes—
158C22×C43C22×C22⋊C411yescharacteristic
159C4×C43—23no—
160C4×C43—21no—
161C4×C43—23no—
162C4×C43C2×#10316yes—
163C4×C43C2×#13111yescharacteristic
164C4×C43#56811yescharacteristic
165C4×C43C22×SD1611yescharacteristic
166C4×C43C22×Q1611yescharacteristic
167Dic43—22no—
168Dic43—43no—
169Dic43—43no—
170Dic43—41no—
171Q8×#41—431no—
172C8×#41D4311yescharacteristic
173#2906—431no—
174#1493—433no—
175#1487—433no—
176#1481—433no—
177C2×Q8⋊C8—433no—
178C2×C43—26no—
179C2×C43#288011yescharacteristic
180C2×C43C22×#10311yescharacteristic
181C2×C43#290111yescharacteristic
182C2×#131—861no—
183Q82—431no—
184#557—431no—
185#557—861no—
186#554—433no—
187#554—863no—
188D4×Q8—433no—
189#533—433no—
190#533—863no—
191C4×#41—861no—
192C4×#41C2×D4311yescharacteristic
193C2×C4×Q8—433no—
194C8×Q8—21no—
195C8×D4—23no—
196#431C2×D4313yes—
197#424—863no—
198#423—433no—
199C2×C4⋊C8—433no—
200C2×C4×C8C2×D4313yes—
201Q8⋊C8—431no—
202Q8⋊C8—433no—
203Q8⋊C8—433no—
204Q8⋊C8—433no—
205Q8⋊C8—436no—
206C43#1750911yescharacteristic, complemented, Sylow
207C2×#41D17211yescharacteristic
208C22×Q8—433no—
209#131—1724no—
210C2×M16—863no—
211C22×C8—23no—
212C22×C8—863no—
213C4⋊Q8—433no—
214C4⋊Q8—433no—
215C4⋊Q8—863no—
216C4⋊Q8—863no—
217#125—863no—
218#125—863no—
219#125—863no—
220C22⋊Q8—436no—
221C22⋊Q8—863no—
222C22⋊Q8—866no—
223C22⋊Q8—866no—
224C4×Q8—433no—
225C4×Q8—433no—
226C4×Q8—431no—
227C4×Q8—433no—
228C4×Q8—861no—
229C4×Q8—861no—
230C4×Q8—863no—
231C4×Q8—863no—
232C4×Q8—863no—
233C4×Q8C4×D4311yescharacteristic
234C4×Q8C22⋊D4311yescharacteristic
235C4×D4—863no—
236C4×D4—863no—
237C4×D4C4×D4313yes—
238C4×D4C22⋊D4313yes—
239#117—863no—
240#117D17213yes—
241C2×C4⋊C4—433no—
242C2×C4⋊C4—863no—
243C2×C42—863no—
244C2×C42C22×D4313yes—
245C4⋊C8—23no—
246C4⋊C8—431no—
247C4⋊C8—433no—
248C4⋊C8—863no—
249C4⋊C8—863no—
250C22⋊C8—23no—
251C4×C8—23no—
252C4×C8C22×D4311yescharacteristic
253C4×C8C22×D4313yes—
254#41#1062187314yes—
255#41Dic17214yes—
256C2×Q8—431no—
257C2×Q8—433no—
258C2×Q8—866no—
259C2×Q8—863no—
260C2×Q8—863no—
261C2×Q8—1723no—
262C2×Q8(C2×D43)⋊C411yescharacteristic
263C2×D4(C2×D43)⋊C413yes—
264C22×C4—863no—
265C22×C4—863no—
266C22×C4C2×C4×D4313yes—
267C22×C4C2×D17213yes—
268C22×C4C2×C22⋊D4313yes—
269M16—1726no—
270C2×C8—21no—
271C2×C8—23no—
272C2×C8—46no—
273C2×C8—861no—
274C2×C8—863no—
275C2×C8—1726no—
276C4⋊C4—431no—
277C4⋊C4—433no—
278C4⋊C4—863no—
279C4⋊C4—863no—
280C4⋊C4—863no—
281C4⋊C4—863no—
282C4⋊C4—863no—
283C4⋊C4—866no—
284C4⋊C4—863no—
285C4⋊C4—861no—
286C4⋊C4—863no—
287C4⋊C4(C2×D43)⋊C413yes—
288C4⋊C4(C2×D43)⋊C413yes—
289C22⋊C4—866no—
290C22⋊C4(C2×D43)⋊C416yes—
291C42—863no—
292C42—863no—
293C42—861no—
294C42—863no—
295C42C2×C4×D4313yes—
296C42C2×D17213yes—
297C42C2×C22⋊D4313yes—
298C42C23×D4311yescharacteristic
299C23C2×(C2×D43)⋊C413yes—
300Q8—432no—
301Q8—861no—
302Q8—863no—
303Q8—863no—
304Q8—3443no—
305Q8—1726no—
306Q8#1306325014yes—
307D4#13063250112yes—
308C2×C4—23no—
309C2×C4—23no—
310C2×C4—43no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—863no—
314C2×C4—863no—
315C2×C4—3443no—
316C2×C4—1726no—
317C2×C4C2×(C2×D43)⋊C413yes—
318C2×C4C2×(C2×D43)⋊C413yes—
319C2×C4C2×(C2×D43)⋊C413yes—
320C2×C4C2×#1062187316yes—
321C2×C4C2×Dic17216yes—
322C2×C4C22×C4×D4311yescharacteristic
323C2×C4C22×C22⋊D4311yescharacteristic
324C2×C4C22×D17211yescharacteristic
325C8—22no—
326C8—43no—
327C8—1721no—
328C8—1723no—
329C22—23no—
330C22—23no—
331C22C2×#1306325016yes—
332C22C22×(C2×D43)⋊C411yescharacteristic
333C4—23no—
334C4—21no—
335C4—23no—
336C4—862no—
337C4—1723no—
338C4—1721no—
339C4—1723no—
340C4C2×#1306325016yes—
341C4#131×D4311yescharacteristic
342C4#1458366411yescharacteristic
343C4C22×#1062187311yescharacteristic
344C4C22×Dic17211yescharacteristic
345C2—26no—
346C2#1914304211yescharacteristic
347C2C22×#1306325011yescharacteristic
348C2#1914314311yescharacteristic
subgroupG/H
centerC2×C4C22×D172
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC8×#41×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#41×C43D4
cosocleC42×C43C24
hypercenterC8×#41D43
hypocenterC43#17509
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
3. #19133051C2semidirect
4. #19133025C2semidirect
5. #19132999C2semidirect
6. C2×#14582631C2semidirect
149. Dic86#131semidirect
206. C43#17509semidirect

Maximal subgroups

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

subgroupindex
#41×Dic862
#191431632
#191330512
#191330252
#191329992
C2×#145826312
C8×#41×C432
#1750943