Finite Group Databasebeta

← #24994791

Subgroups — #24994791

Order 11008.

408 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#19135531C211yesmaximal, characteristic
2C4×#13063248C211yesmaximal, characteristic
3C2×#14582651C211yesmaximal, characteristic
4C2×#14582629C211yesmaximal, characteristic
5#19132436C211yesmaximal, characteristic
6C43⋊#1273C211yesmaximal, characteristic
7C8×C4⋊C4×C43C211yesmaximal, characteristic
8C2×C4×Dic86C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×#13063248C411yescharacteristic
11C2×#13063248C411yescharacteristic
12C2×C4×C43⋊C8C2211yescharacteristic
13C2×C4×C43⋊C8C2211yescharacteristic
14#14582661C411yescharacteristic
15#14582661C411yescharacteristic
16#14582653—21no—
17#14582653—21no—
18#14582651—22no—
19#14582629—22no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C2×C4×C8×C43—21no—
22C2×C4×C8×C43C2211yescharacteristic
23C4×C4⋊C4×C43C2211yescharacteristic
24C43×#336—21no—
25C22×Dic86C2×C411yescharacteristic
26C22×C43⋊C8—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8C2×C411yescharacteristic
29C22×C43⋊C8C2×C411yescharacteristic
30C4×Dic86—21no—
31C4×Dic86—21no—
32C4×Dic86—21no—
33C4×Dic86—21no—
34C2×C4⋊Dic43C2×C411yescharacteristic
35C2×Dic43⋊C4—21no—
36C2×C4×Dic43—21no—
37C4⋊(C43⋊C8)—21no—
38C4⋊(C43⋊C8)—21no—
39#13063248—22no—
40#13063248C814yescomplemented
41C4×C43⋊C8—21no—
42C4×C43⋊C8—21no—
43C4×C43⋊C8—21no—
44C4×C43⋊C8—21no—
45C22×C8×C43—21no—
46C22×C8×C43D411yescharacteristic
47C22×C8×C43D411yescharacteristic
48C2×C4⋊C4×C43C2×C411yescharacteristic
49C2×C4⋊C4×C43C2×C411yescharacteristic
50C2×C42×C43—21no—
51C2×C42×C43C2311yescharacteristic
52C4⋊C8×C43—21no—
53C4⋊C8×C43D412yes—
54C4×C8×C43—21no—
55C4×C8×C43—21no—
56C4×C8×C43—42no—
57#95×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—21no—
60C22×C4×C43C22×C411yescharacteristic
61C22×C4×C43C2×D411yescharacteristic
62C22×C4×C43#4111yescharacteristic
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—22no—
74C2×C8×C43—21no—
75C2×C8×C43—21no—
76C2×C8×C43—21no—
77C2×C8×C43—41no—
78C2×C8×C43—41no—
79C2×C8×C43Q1612yes—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2×C812yes—
83C4⋊C4×C43M1612yes—
84C42×C43—41no—
85C42×C43—41no—
86C42×C43C2×D411yescharacteristic
87C42×C43#4111yescharacteristic
88C42×C43#4111yescharacteristic
89C42×C43#4111yescharacteristic
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94C4×Dic43—41no—
95C4×Dic43—41no—
96C2×C43⋊C8—21no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—22no—
99C2×C43⋊C8—21no—
100C2×C43⋊C8—21no—
101C2×C43⋊C8—21no—
102C2×C43⋊C8—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8—41no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2×C812yes—
108C23×C43C4×D411yescharacteristic
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—22no—
112C2×C4×C43—22no—
113C2×C4×C43—41no—
114C2×C4×C43—41no—
115C2×C4×C43—41no—
116C2×C4×C43—41no—
117C2×C4×C43#11711yescharacteristic
118C2×C4×C43C4×D411yescharacteristic
119C2×C4×C43#12111yescharacteristic
120C2×C4×C43#12311yescharacteristic
121C2×C4×C43#12411yescharacteristic
122C2×C4×C43#12611yescharacteristic
123C2×C4×C43C22×C811yescharacteristic
124C2×C4×C43C2×M1611yescharacteristic
125C2×C4×C43#13111yescharacteristic
126C2×C4×C43#13111yescharacteristic
127C2×C4×C43C2×Q1611yescharacteristic
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C43#13711yescharacteristic
131C2×Dic43—22no—
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—42no—
143C8×C43—41no—
144C43⋊C8—22no—
145C43⋊C8—42no—
146C43⋊C8—41no—
147C43⋊C8—81no—
148#9544—431nomaximal, Sylow
149C22×C43#38811yescharacteristic
150C22×C43C8×D411yescharacteristic
151C22×C43#43511yescharacteristic
152C22×C43C4×Q1611yescharacteristic
153C22×C43#44011yescharacteristic
154C22×C43#44311yescharacteristic
155C22×C43#44411yescharacteristic
156C4×C43—21no—
157C4×C43—21no—
158C4×C43—42no—
159C4×C43—42no—
160C4×C43#43111yescharacteristic
161C4×C43#43311yescharacteristic
162C4×C43C8×D411yescharacteristic
163C4×C43#43611yescharacteristic
164C4×C43#46211yescharacteristic
165C4×C43#46311yescharacteristic
166C4×C43#48411yescharacteristic
167C4×C43#48511yescharacteristic
168Dic43—42no—
169Dic43—81no—
170#1984—431no—
171C8×C4⋊C4D4311yescharacteristic
172C4×#103—431no—
173C2×#335—431no—
174C2×Q8⋊C8—431no—
175#1279—431no—
176#1273—431no—
177C2×C43C8×Q1611yescharacteristic
178C2×C43SD16⋊C811yescharacteristic
179C2×C43#158411yescharacteristic
180C2×C43#158511yescharacteristic
181C2×C43#192311yescharacteristic
182C2×C43#192811yescharacteristic
183C2×C43#192911yescharacteristic
184C2×C4×Q8—431no—
185C2×C4⋊C8—431no—
186C2×C4⋊C8C2×D4311yescharacteristic
187C2×#103—431no—
188C2×#103—431no—
189C2×C4×C8—21no—
190C2×C4×C8—431no—
191C2×C4×C8—431no—
192C2×C4×C8C2×D4311yescharacteristic
193C4×C4⋊C4C2×D4311yescharacteristic
194#340—431no—
195#340—431no—
196#336—21no—
197#336—861no—
198#336—861no—
199#335—862no—
200Q8⋊C8—862no—
201C43#954411yescharacteristic, complemented, Sylow
202C22×Q8—431no—
203C22×C8—21no—
204C22×C8—431no—
205C22×C8—431no—
206C22×C8—861no—
207C22×C8—861no—
208C22×C8C22⋊D4311yescharacteristic
209C22×C8C22⋊D4311yescharacteristic
210C4×Q8—861no—
211C4×Q8—861no—
212C4×Q8—861no—
213C4×Q8—861no—
214C2×C4⋊C4—431no—
215C2×C4⋊C4—861no—
216C2×C4⋊C4C4×D4311yescharacteristic
217C2×C4⋊C4C4×D4311yescharacteristic
218C2×C42—21no—
219C2×C42—861no—
220C2×C42C22×D4311yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—861no—
223C4⋊C8—861no—
224C4⋊C8D17212yes—
225#103—434no—
226#103—862no—
227C4×C8—21no—
228C4×C8—21no—
229C4×C8—42no—
230C4×C8—861no—
231C4×C8—861no—
232C4×C8—861no—
233C4×C8—861no—
234#95—21no—
235C2×Q8—432no—
236C2×Q8—861no—
237C2×Q8—861no—
238C2×Q8—861no—
239C2×Q8—861no—
240C2×Q8—861no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4C2×C4×D4311yescharacteristic
246C22×C4#1062189811yescharacteristic
247C22×C4C2×C22⋊D4311yescharacteristic
248C2×C8—21no—
249C2×C8—21no—
250C2×C8—22no—
251C2×C8—21no—
252C2×C8—21no—
253C2×C8—21no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—432no—
257C2×C8—861no—
258C2×C8—861no—
259C2×C8—862no—
260C2×C8—861no—
261C2×C8—861no—
262C2×C8—861no—
263C2×C8—1721no—
264C2×C8—1721no—
265C2×C8—1721no—
266C2×C8—1721no—
267C2×C8—1721no—
268C2×C8#1062188512yes—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C4⋊C4C8×D4312yes—
276C4⋊C4#1062187212yes—
277C42—41no—
278C42—41no—
279C42—1721no—
280C42—1721no—
281C42C2×D17211yescharacteristic
282C42#1062189811yescharacteristic
283C42#1062189811yescharacteristic
284C42#1062189811yescharacteristic
285C23C4×C22⋊D4311yescharacteristic
286Q8—862no—
287Q8—862no—
288Q8—1721no—
289Q8—1721no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—862no—
299C2×C4—1721no—
300C2×C4—1721no—
301C2×C4—1721no—
302C2×C4—1721no—
303C2×C4—1721no—
304C2×C4#1306328211yescharacteristic
305C2×C4C4×D17211yescharacteristic
306C2×C4#1306329911yescharacteristic
307C2×C4#1306330811yescharacteristic
308C2×C4#1306331311yescharacteristic
309C2×C4#1306331911yescharacteristic
310C2×C4C2×C8×D4311yescharacteristic
311C2×C4C2×#1062187211yescharacteristic
312C2×C4#1306333111yescharacteristic
313C2×C4#1306333111yescharacteristic
314C2×C4C2×#1062188511yescharacteristic
315C2×C4#1306334511yescharacteristic
316C2×C4#1306335111yescharacteristic
317C2×C4#1306335511yescharacteristic
318C8—22no—
319C8—42no—
320C8—41no—
321C8—862no—
322C8—3441no—
323C8—1722no—
324C8—1721no—
325C22#1458279011yescharacteristic
326C22C8×C22⋊D4311yescharacteristic
327C22#1458297011yescharacteristic
328C22C4×#1062188511yescharacteristic
329C22#1458299911yescharacteristic
330C22#1458301411yescharacteristic
331C22#1458301911yescharacteristic
332C4—21no—
333C4—21no—
334C4—42no—
335C4—42no—
336C4—3441no—
337C4—1722no—
338C4#1458295011yescharacteristic
339C4#1458295811yescharacteristic
340C4C8×D17211yescharacteristic
341C4#1458297811yescharacteristic
342C4#1458310911yescharacteristic
343C4#1458311411yescharacteristic
344C4#1458323411yescharacteristic
345C4#1458324011yescharacteristic
346C2C8×#1062188511yescharacteristic
347C2#1913340711yescharacteristic
348C2#1913344511yescharacteristic
349C2#1913345211yescharacteristic
350C2#1913520111yescharacteristic
351C2#1913523611yescharacteristic
352C2#1913524311yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC2×C4×C43C22×C8
FrattiniC2×C42C22×D43
FittingC8×C4⋊C4×C43C2
socle, prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenterC8×C4⋊C4D43
hypocenterC43#9544
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ C8×C4⋊C4

Complements

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

NH ≅ G/Ntype
40. #13063248C8semidirect
201. C43#9544semidirect

Maximal subgroups

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

subgroupindex
#191355312
C4×#130632482
C2×#145826512
C2×#145826292
#191324362
C43⋊#12732
C8×C4⋊C4×C432
#954443