Finite Group Databasebeta

← #24994866

Subgroups — #24994866

Order 11008.

398 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135530C211yesmaximal, characteristic
2#19135311C211yesmaximal, characteristic
3C4×#13063250C211yesmaximal, characteristic
4C2×#14582629C211yesmaximal, characteristic
5C2×#14582620C211yesmaximal, characteristic
6#19132434C211yesmaximal, characteristic
7C43×#1277C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9C2×Dic43⋊C8—21no—
10C2×#13063250C411yescharacteristic
11C2×#13063250C411yescharacteristic
12C2×C4×C43⋊C8C2211yescharacteristic
13C2×C4×C43⋊C8C2211yescharacteristic
14C4×C4⋊Dic43C2211yescharacteristic
15#14582662C411yescharacteristic
16#14582662C411yescharacteristic
17#14582653—21no—
18#14582653—21no—
19#14582653—21no—
20#14582629—22no—
21#14582620—22no—
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×C4×C8×C43C2211yescharacteristic
25C22×Dic86C2×C411yescharacteristic
26C22×C43⋊C8—21no—
27C22×C43⋊C8D411yescharacteristic
28C22×C43⋊C8D411yescharacteristic
29C4×Dic86—21no—
30C4×Dic86—21no—
31C4×Dic86—21no—
32C4×Dic86—21no—
33C2×C4⋊Dic43C2×C411yescharacteristic
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×C4×Dic43—21no—
38C2×C4×Dic43—21no—
39Dic43⋊C8—42no—
40#13063250—22no—
41#13063250C814yescomplemented
42C4×C43⋊C8—21no—
43C4×C43⋊C8—21no—
44C4×C43⋊C8—21no—
45C4×C43⋊C8D412yes—
46C43⋊#95—21no—
47C22×C8×C43—21no—
48C22×C8×C43—21no—
49C22×C8×C43C2×C411yescharacteristic
50C22×C8×C43C2×C411yescharacteristic
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—21no—
53C4⋊C8×C43—21no—
54C4⋊C8×C43—21no—
55C4⋊C8×C43—21no—
56C4×C8×C43—21no—
57C4×C8×C43—21no—
58C22×C4×C43C22×C411yescharacteristic
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43#4111yescharacteristic
61C22×Dic43—21no—
62C22×Dic43—21no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C2×Dic86—21no—
66C2×Dic86—21no—
67C2×Dic86—21no—
68C2×Dic86—21no—
69C2×Dic86—21no—
70C2×Dic86C2×C812yes—
71C2×C8×C43—21no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43—21no—
75C2×C8×C43—41no—
76C2×C8×C43—41no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43—41no—
80C2×C8×C43—41no—
81C2×C8×C43C2×C812yes—
82C2×C8×C43M1612yes—
83C42×C43C2×D411yescharacteristic
84C42×C43#4111yescharacteristic
85C42×C43#4111yescharacteristic
86C42×C43#4111yescharacteristic
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43C2×C812yes—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95C4×Dic43—41no—
96C4×Dic43—41no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8—21no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8—41no—
108C23×C43C4×D411yescharacteristic
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43#11711yescharacteristic
112C2×C4×C43C4×D411yescharacteristic
113C2×C4×C43#12111yescharacteristic
114C2×C4×C43#12311yescharacteristic
115C2×C4×C43#12411yescharacteristic
116C2×C4×C43#12611yescharacteristic
117C2×C4×C43C22×C811yescharacteristic
118C2×C4×C43C2×M1611yescharacteristic
119C2×C4×C43#13111yescharacteristic
120C2×C4×C43#13111yescharacteristic
121C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
122C2×C4×C43#13711yescharacteristic
123C2×C4×C43#13711yescharacteristic
124C2×C4×C43#13711yescharacteristic
125C2×Dic43—22no—
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—41no—
129C2×Dic43—41no—
130C2×Dic43—41no—
131C2×Dic43—41no—
132C2×Dic43—41no—
133C2×Dic43—41no—
134C2×Dic43—41no—
135C2×Dic43—41no—
136C2×Dic43—41no—
137Dic86—22no—
138Dic86—22no—
139Dic86—41no—
140Dic86—41no—
141C8×C43—22no—
142C8×C43—22no—
143C8×C43—81no—
144C8×C43—81no—
145C43⋊C8—42no—
146C43⋊C8—41no—
147C43⋊C8—41no—
148#9555—431nomaximal, Sylow
149C22×C43#38811yescharacteristic
150C22×C43C8×D411yescharacteristic
151C22×C43#43611yescharacteristic
152C22×C43#44011yescharacteristic
153C22×C43#44111yescharacteristic
154C22×C43#44411yescharacteristic
155C22×C43#44411yescharacteristic
156C4×C43—21no—
157C4×C43—21no—
158C4×C43#43111yescharacteristic
159C4×C43#43311yescharacteristic
160C4×C43C8×D411yescharacteristic
161C4×C43#43511yescharacteristic
162C4×C43#46811yescharacteristic
163C4×C43#47011yescharacteristic
164C4×C43#48911yescharacteristic
165C4×C43#49111yescharacteristic
166Dic43—42no—
167Dic43—42no—
168Dic43—81no—
169Dic43—81no—
170#1984—431no—
171#1939—431no—
172C4×#103—431no—
173C2×Q8⋊C8—431no—
174C2×#322—431no—
175#1279—431no—
176#1277D4311yescharacteristic
177C2×C43SD16⋊C811yescharacteristic
178C2×C43#157911yescharacteristic
179C2×C43#159211yescharacteristic
180C2×C43#159311yescharacteristic
181C2×C43#192311yescharacteristic
182C2×C43#193511yescharacteristic
183C2×C43#193811yescharacteristic
184C2×C4×Q8—431no—
185C2×C4⋊C8—861no—
186C2×C4⋊C8C2×D4311yescharacteristic
187C2×C4⋊C8C2×D4311yescharacteristic
188C2×#103—431no—
189C2×#103—431no—
190C2×C4×C8—431no—
191C2×C4×C8—431no—
192C2×C4×C8C2×D4311yescharacteristic
193C4×C4⋊C4—431no—
194#340—431no—
195#340—431no—
196#336—861no—
197#336—861no—
198#336—861no—
199Q8⋊C8—862no—
200#322—862no—
201C43#955511yescharacteristic, complemented, Sylow
202C22×Q8—431no—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—431no—
206C22×C8—431no—
207C22×C8—861no—
208C22×C8C4×D4311yescharacteristic
209C22×C8C4×D4311yescharacteristic
210C4×Q8—861no—
211C4×Q8—861no—
212C4×Q8—861no—
213C4×Q8—861no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—431no—
216C2×C4⋊C4—431no—
217C2×C4⋊C4—861no—
218C2×C42—861no—
219C2×C42—861no—
220C2×C42C22×D4311yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—1722no—
226#103—434no—
227#103—862no—
228C4×C8—21no—
229C4×C8—21no—
230C4×C8—432no—
231C4×C8—861no—
232C4×C8—861no—
233C4×C8—861no—
234#95—861no—
235C2×Q8—432no—
236C2×Q8—861no—
237C2×Q8—861no—
238C2×Q8—861no—
239C2×Q8—861no—
240C2×Q8—861no—
241C22×C4—861no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4D4×D4311yescharacteristic
247C22×C4#1062190211yescharacteristic
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—21no—
251C2×C8—21no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C2×C8—41no—
258C2×C8—861no—
259C2×C8—861no—
260C2×C8—862no—
261C2×C8—861no—
262C2×C8—861no—
263C2×C8—861no—
264C2×C8—861no—
265C2×C8—1721no—
266C2×C8—1721no—
267C2×C8C8×D4312yes—
268C2×C8#1062187212yes—
269C4⋊C4—432no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—1721no—
276C4⋊C4—1721no—
277C42—1721no—
278C42—1721no—
279C42—1721no—
280C42—1721no—
281C42#1062189811yescharacteristic
282C42#1062189811yescharacteristic
283C42D4×D4311yescharacteristic
284C42#1062190011yescharacteristic
285C23#1306328711yescharacteristic
286Q8—862no—
287Q8—862no—
288Q8—1721no—
289Q8—1721no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—862no—
293C2×C4—862no—
294C2×C4—1721no—
295C2×C4—1721no—
296C2×C4—1721no—
297C2×C4—1721no—
298C2×C4—1721no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4#1306328211yescharacteristic
305C2×C4(C22⋊D43)⋊C411yescharacteristic
306C2×C4#1306329811yescharacteristic
307C2×C4#1306331011yescharacteristic
308C2×C4#1306331111yescharacteristic
309C2×C4#1306332011yescharacteristic
310C2×C4C2×C8×D4311yescharacteristic
311C2×C4C2×#1062187211yescharacteristic
312C2×C4#1306333311yescharacteristic
313C2×C4#1306333311yescharacteristic
314C2×C4#1306334911yescharacteristic
315C2×C4#1306335411yescharacteristic
316C2×C4#1306335411yescharacteristic
317C2×C4#1306335711yescharacteristic
318C8—22no—
319C8—22no—
320C8—81no—
321C8—81no—
322C8—1722no—
323C8—1721no—
324C8—1721no—
325C22#1458278811yescharacteristic
326C22#1458296411yescharacteristic
327C22#1458297611yescharacteristic
328C22#1458299811yescharacteristic
329C22#1458300511yescharacteristic
330C22#1458302011yescharacteristic
331C22#1458302011yescharacteristic
332C4—21no—
333C4—21no—
334C4—3441no—
335C4—3441no—
336C4—1722no—
337C4—1722no—
338C4#1458295011yescharacteristic
339C4#1458296111yescharacteristic
340C4(C22⋊D43)⋊C811yescharacteristic
341C4#1458296711yescharacteristic
342C4#1458314411yescharacteristic
343C4#1458315611yescharacteristic
344C4#1458325711yescharacteristic
345C4#1458326611yescharacteristic
346C2#1913340611yescharacteristic
347C2#1913341311yescharacteristic
348C2#1913349611yescharacteristic
349C2#1913350311yescharacteristic
350C2#1913519911yescharacteristic
351C2#1913528311yescharacteristic
352C2#1913530411yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC43×#1277C2
socle, prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenter#1277D43
hypocenterC43#9555
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
41. #13063250C8semidirect
201. C43#9555semidirect

Maximal subgroups

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

subgroupindex
#191355302
#191353112
C4×#130632502
C2×#145826292
C2×#145826202
#191324342
C43×#12772
#955543