Finite Group Databasebeta

← #24995153

Subgroups — #24995153

Order 11008.

378 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135314C211yesmaximal, characteristic
2#19135311C211yesmaximal, characteristic
3C4×#13063256C211yesmaximal, characteristic
4C2×#14582649C211yesmaximal, characteristic
5C2×#14582621C211yesmaximal, characteristic
6#19132435C211yesmaximal, characteristic
7C43×#1279C211yesmaximal, characteristic
8C2×#13063256C411yescharacteristic
9C2×#13063256C411yescharacteristic
10C2×C4⋊(C43⋊C8)—21no—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×Dic43⋊C8—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14C2×C4×C43⋊C8C2211yescharacteristic
15C4×C4⋊Dic43C2211yescharacteristic
16#14582661C411yescharacteristic
17#14582661C411yescharacteristic
18#14582654—21no—
19#14582653—21no—
20#14582649—22no—
21#14582621—22no—
22C2×C4⋊C8×C43C2211yescharacteristic
23C2×C4×C8×C43C2211yescharacteristic
24C4×C4⋊C4×C43C2211yescharacteristic
25C22×C43⋊C8—21no—
26C22×C43⋊C8C2×C411yescharacteristic
27C22×C43⋊C8C2×C411yescharacteristic
28C22×C43⋊C8D411yescharacteristic
29C22×C43⋊C8D411yescharacteristic
30C2×C4⋊Dic43C2×C411yescharacteristic
31C2×C4⋊Dic43C2×C411yescharacteristic
32C2×C4×Dic43—21no—
33#13063256—22no—
34#13063256—22no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—42no—
38Dic43⋊C8—42no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8—21no—
41C4×C43⋊C8D412yes—
42C4×C43⋊C8Q812yes—
43C43⋊#95—21no—
44C22×C8×C43—21no—
45C22×C8×C43—21no—
46C2×C4⋊C4×C43C2×C411yescharacteristic
47C2×C4⋊C4×C43C2×C411yescharacteristic
48C2×C42×C43—21no—
49C2×C42×C43C2311yescharacteristic
50C4⋊C8×C43—21no—
51C4⋊C8×C43—21no—
52C4×C8×C43—21no—
53C4×C8×C43Q812yes—
54#95×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43—21no—
57C22×C4×C43C22×C411yescharacteristic
58C22×C4×C43C2×D411yescharacteristic
59C22×C4×C43#4111yescharacteristic
60C22×Dic43—21no—
61C22×Dic43—21no—
62C2×C8×C43—22no—
63C2×C8×C43—41no—
64C2×C8×C43—41no—
65C2×C8×C43—41no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C4⋊C4×C43—21no—
69C4⋊C4×C43—21no—
70C4⋊C4×C43—21no—
71C4⋊C4×C43M1612yes—
72C42×C43—41no—
73C42×C43—41no—
74C42×C43C2×D411yescharacteristic
75C42×C43C2×Q811yescharacteristic
76C42×C43C2×Q811yescharacteristic
77C42×C43#4111yescharacteristic
78C4⋊Dic43—21no—
79C4⋊Dic43—21no—
80C4⋊Dic43—21no—
81C4⋊Dic43M1612yes—
82C4×Dic43—41no—
83C4×Dic43—41no—
84C2×C43⋊C8—21no—
85C2×C43⋊C8—21no—
86C2×C43⋊C8—21no—
87C2×C43⋊C8—21no—
88C2×C43⋊C8—21no—
89C2×C43⋊C8—21no—
90C2×C43⋊C8—21no—
91C2×C43⋊C8—21no—
92C2×C43⋊C8—41no—
93C2×C43⋊C8—41no—
94C2×C43⋊C8—41no—
95C2×C43⋊C8C4⋊C412yes—
96C2×C43⋊C8C4⋊C412yes—
97C2×C43⋊C8SD1612yes—
98C2×C43⋊C8SD1612yes—
99C23×C43C4×D411yescharacteristic
100C2×C4×C43—21no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43—41no—
107C2×C4×C43—41no—
108C2×C4×C43C2×C4⋊C411yescharacteristic
109C2×C4×C43C4×Q811yescharacteristic
110C2×C4×C43#12111yescharacteristic
111C2×C4×C43C22⋊Q811yescharacteristic
112C2×C4×C43#12511yescharacteristic
113C2×C4×C43C4⋊Q811yescharacteristic
114C2×C4×C43C2×M1611yescharacteristic
115C2×C4×C43C2×M1611yescharacteristic
116C2×C4×C43#13111yescharacteristic
117C2×C4×C43#13111yescharacteristic
118C2×C4×C43C2×SD1611yescharacteristic
119C2×C4×C43C2×SD1611yescharacteristic
120C2×C4×C43#13511yescharacteristic
121C2×C4×C43#13511yescharacteristic
122C2×Dic43—22no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C2×Dic43—41no—
127C2×Dic43—41no—
128C8×C43—42no—
129C8×C43—81no—
130C43⋊C8—22no—
131C43⋊C8—22no—
132C43⋊C8—22no—
133C43⋊C8—22no—
134C43⋊C8—81no—
135#9597—431nomaximal, Sylow
136C22×C43#38911yescharacteristic
137C22×C43#43511yescharacteristic
138C22×C43#43511yescharacteristic
139C22×C43C4×SD1611yescharacteristic
140C22×C43C4×SD1611yescharacteristic
141C22×C43#44411yescharacteristic
142C22×C43#44411yescharacteristic
143C4×C43—21no—
144C4×C43—21no—
145C4×C43—42no—
146C4×C43—81no—
147C4×C43#42311yescharacteristic
148C4×C43#42411yescharacteristic
149C4×C43#44611yescharacteristic
150C4×C43#44611yescharacteristic
151C4×C43#46511yescharacteristic
152C4×C43#46511yescharacteristic
153C4×C43#49811yescharacteristic
154C4×C43#49911yescharacteristic
155Dic43—42no—
156Dic43—81no—
157#1939—431no—
158#1939—431no—
159C4×#106—431no—
160C2×#334—431no—
161C2×#322—431no—
162#1279—431no—
163#1279D4311yescharacteristic
164C2×C43#158211yescharacteristic
165C2×C43#158211yescharacteristic
166C2×C43#158311yescharacteristic
167C2×C43#158311yescharacteristic
168C2×C43#194011yescharacteristic
169C2×C43#194111yescharacteristic
170C2×C43#194611yescharacteristic
171C2×#106—431no—
172C2×#106—431no—
173C2×C4⋊C8—431no—
174C2×C4⋊C8—861no—
175C2×C4⋊C8—861no—
176C2×C4⋊C8C2×D4311yescharacteristic
177C2×C4×C8—431no—
178C2×C4×C8—431no—
179C2×C4×C8C2×D4311yescharacteristic
180C4×C4⋊C4—431no—
181C4×C4⋊C4C2×D4311yescharacteristic
182#340—431no—
183#340—431no—
184#336—861no—
185#336—861no—
186#334—862no—
187#322—862no—
188C43#959711yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—431no—
192C22×C8—431no—
193C22×C8—431no—
194C22×C8—431no—
195C22×C8—861no—
196C2×C4⋊C4—431no—
197C2×C4⋊C4—431no—
198C2×C4⋊C4C4×D4311yescharacteristic
199C2×C4⋊C4C4×D4311yescharacteristic
200C2×C42—21no—
201C2×C42—861no—
202C2×C42C22×D4311yescharacteristic
203#106—862no—
204#106—862no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—861no—
208C4⋊C8—861no—
209C4⋊C8—1722no—
210C4⋊C8—1722no—
211C4×C8—21no—
212C4×C8—432no—
213C4×C8—432no—
214C4×C8—861no—
215C4×C8—861no—
216C4×C8Dic8612yes—
217#95—21no—
218#95—861no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—861no—
222C22×C4—861no—
223C22×C4C2×C4×D4311yescharacteristic
224C22×C4D4×D4311yescharacteristic
225C22×C4#1062190011yescharacteristic
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—432no—
233C2×C8—432no—
234C2×C8—432no—
235C2×C8—432no—
236C2×C8—861no—
237C2×C8—861no—
238C2×C8—861no—
239C2×C8—861no—
240C2×C8—861no—
241C2×C8—861no—
242C2×C8—861no—
243C2×C8—861no—
244C2×C8—1721no—
245C2×C8—1721no—
246C2×C8—1721no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—432no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4#1062187212yes—
255C42—41no—
256C42—41no—
257C42—1721no—
258C42—1721no—
259C42C2×Dic8611yescharacteristic
260C42#1062189811yescharacteristic
261C42D4×D4311yescharacteristic
262C42Q8×D4311yescharacteristic
263C23(C22⋊D43)⋊C411yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—862no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4C4⋊C4×D4311yescharacteristic
279C2×C4C4×Dic8611yescharacteristic
280C2×C4#1306329811yescharacteristic
281C2×C4#1306330211yescharacteristic
282C2×C4#1306331511yescharacteristic
283C2×C4#1306332411yescharacteristic
284C2×C4M16×D4311yescharacteristic
285C2×C4C2×#1062187211yescharacteristic
286C2×C4#1306333111yescharacteristic
287C2×C4#1306333311yescharacteristic
288C2×C4SD16×D4311yescharacteristic
289C2×C4SD16×D4311yescharacteristic
290C2×C4#1306334411yescharacteristic
291C2×C4#1306334811yescharacteristic
292C8—42no—
293C8—81no—
294C8—862no—
295C8—862no—
296C8—862no—
297C8—862no—
298C8—3441no—
299C22#1458279611yescharacteristic
300C22#1458296711yescharacteristic
301C22#1458297311yescharacteristic
302C22#1458298411yescharacteristic
303C22#1458299011yescharacteristic
304C22#1458301811yescharacteristic
305C22#1458301811yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—3441no—
311C4—1722no—
312C4#1458292111yescharacteristic
313C4#1458292411yescharacteristic
314C4#1458302711yescharacteristic
315C4#1458302911yescharacteristic
316C4#1458312711yescharacteristic
317C4#1458313111yescharacteristic
318C4#1458329611yescharacteristic
319C4#1458330011yescharacteristic
320C2#1913342811yescharacteristic
321C2#1913343411yescharacteristic
322C2#1913343511yescharacteristic
323C2#1913344111yescharacteristic
324C2#1913531711yescharacteristic
325C2#1913532211yescharacteristic
326C2#1913534711yescharacteristic
subgroupG/H
centerC22×C4D4×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1279C2
socle, prime radicalC23×C43C4×D4
cosocleC2×C42×C43C23
hypercenter#1279D43
hypocenterC43#9597
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
188. C43#9597semidirect

Maximal subgroups

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

subgroupindex
#191353142
#191353112
C4×#130632562
C2×#145826492
C2×#145826212
#191324352
C43×#12792
#959743