Finite Group Databasebeta

← #24994752

Subgroups — #24994752

Order 11008.

356 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135314C211yesmaximal, characteristic
2C4×#13063256C211yesmaximal, characteristic
3#19134465C211yesmaximal, characteristic
4#19132435C211yesmaximal, characteristic
5#19132429C211yesmaximal, characteristic
6C43⋊#1273C211yesmaximal, characteristic
7C43×#1279C211yesmaximal, characteristic
8C2×#13063256C411yescharacteristic
9C2×#13063256C411yescharacteristic
10C2×C4⋊(C43⋊C8)—21no—
11C2×C4⋊(C43⋊C8)C2211yescharacteristic
12C2×#13063235—21no—
13C2×C4×C43⋊C8C2211yescharacteristic
14C2×C4×C43⋊C8C2211yescharacteristic
15C4×C4⋊Dic43C2211yescharacteristic
16#14582661C411yescharacteristic
17#14582661C411yescharacteristic
18#14582654—21no—
19#14582653—21no—
20C2×C4⋊C8×C43C2211yescharacteristic
21C2×C4×C8×C43C2211yescharacteristic
22C4×C4⋊C4×C43C2211yescharacteristic
23C22×C43⋊C8—21no—
24C22×C43⋊C8C2×C411yescharacteristic
25C22×C43⋊C8C2×C411yescharacteristic
26C22×C43⋊C8D411yescharacteristic
27C22×C43⋊C8D411yescharacteristic
28C2×C4⋊Dic43C2×C411yescharacteristic
29C2×C4⋊Dic43C2×C411yescharacteristic
30C2×C4×Dic43—21no—
31#13063256—22no—
32#13063256—22no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—42no—
36#13063235—42no—
37C4×C43⋊C8—21no—
38C4×C43⋊C8—21no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8—21no—
41C43⋊#95—21no—
42C22×C8×C43—21no—
43C22×C8×C43—21no—
44C2×C4⋊C4×C43C2×C411yescharacteristic
45C2×C4⋊C4×C43C2×C411yescharacteristic
46C2×C42×C43—21no—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—21no—
49C4⋊C8×C43Q812yes—
50C4×C8×C43—21no—
51C4×C8×C43—21no—
52#95×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—21no—
55C22×C4×C43C22×C411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43#4111yescharacteristic
58C22×Dic43—21no—
59C22×Dic43—21no—
60C2×C8×C43—22no—
61C2×C8×C43—22no—
62C2×C8×C43—41no—
63C2×C8×C43—41no—
64C2×C8×C43—41no—
65C2×C8×C43—41no—
66C4⋊C4×C43—21no—
67C4⋊C4×C43—21no—
68C4⋊C4×C43—21no—
69C4⋊C4×C43M1612yes—
70C42×C43—41no—
71C42×C43—41no—
72C42×C43C2×Q811yescharacteristic
73C42×C43#4111yescharacteristic
74C42×C43#4111yescharacteristic
75C42×C43#4111yescharacteristic
76C4⋊Dic43—21no—
77C4⋊Dic43—21no—
78C4⋊Dic43—21no—
79C4⋊Dic43—21no—
80C4×Dic43—41no—
81C4×Dic43—41no—
82C2×C43⋊C8—21no—
83C2×C43⋊C8—21no—
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⋊C8M1612yes—
96C2×C43⋊C8SD1612yes—
97C23×C43C4×D411yescharacteristic
98C2×C4×C43—21no—
99C2×C4×C43—21no—
100C2×C4×C43—22no—
101C2×C4×C43—41no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—41no—
105C2×C4×C43—41no—
106C2×C4×C43#11711yescharacteristic
107C2×C4×C43C4×Q811yescharacteristic
108C2×C4×C43C22⋊Q811yescharacteristic
109C2×C4×C43#12311yescharacteristic
110C2×C4×C43#12511yescharacteristic
111C2×C4×C43#12611yescharacteristic
112C2×C4×C43C2×M1611yescharacteristic
113C2×C4×C43C2×M1611yescharacteristic
114C2×C4×C43#13111yescharacteristic
115C2×C4×C43#13111yescharacteristic
116C2×C4×C43C2×SD1611yescharacteristic
117C2×C4×C43#13511yescharacteristic
118C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C43#13711yescharacteristic
120C2×Dic43—41no—
121C2×Dic43—41no—
122C2×Dic43—41no—
123C2×Dic43—41no—
124C2×Dic43—41no—
125C2×Dic43—41no—
126C8×C43—42no—
127C8×C43—42no—
128C43⋊C8—22no—
129C43⋊C8—22no—
130C43⋊C8—41no—
131C43⋊C8—41no—
132C43⋊C8—81no—
133#9538—431nomaximal, Sylow
134C22×C43#38711yescharacteristic
135C22×C43#43511yescharacteristic
136C22×C43#43611yescharacteristic
137C22×C43C4×SD1611yescharacteristic
138C22×C43#44011yescharacteristic
139C22×C43#44311yescharacteristic
140C22×C43#44411yescharacteristic
141C4×C43—21no—
142C4×C43—21no—
143C4×C43—42no—
144C4×C43—81no—
145C4×C43#43211yescharacteristic
146C4×C43#43311yescharacteristic
147C4×C43#44611yescharacteristic
148C4×C43#44611yescharacteristic
149C4×C43#47511yescharacteristic
150C4×C43#47811yescharacteristic
151C4×C43#48111yescharacteristic
152C4×C43#48511yescharacteristic
153Dic43—81no—
154Dic43—81no—
155#1939—431no—
156C4×#106—431no—
157#1770—431no—
158#1279—431no—
159#1279D4311yescharacteristic
160#1277—431no—
161#1273—431no—
162C2×C43#158211yescharacteristic
163C2×C43#158811yescharacteristic
164C2×C43#159011yescharacteristic
165C2×C43#159211yescharacteristic
166C2×C43#191711yescharacteristic
167C2×C43#191911yescharacteristic
168C2×C43#192211yescharacteristic
169C2×#106—431no—
170C2×#106—431no—
171C2×C4⋊C8—431no—
172C2×C4⋊C8—861no—
173C2×C4⋊C8C2×D4311yescharacteristic
174C2×#97—861no—
175C2×C4×C8—431no—
176C2×C4×C8—431no—
177C2×C4×C8C2×D4311yescharacteristic
178C4×C4⋊C4—431no—
179C4×C4⋊C4C2×D4311yescharacteristic
180#340—431no—
181#340—431no—
182#336—861no—
183#336—861no—
184C43#953811yescharacteristic, complemented, Sylow
185C22×C8—21no—
186C22×C8—21no—
187C22×C8—431no—
188C22×C8—431no—
189C22×C8—431no—
190C22×C8—431no—
191C22×C8—861no—
192C2×C4⋊C4—431no—
193C2×C4⋊C4—431no—
194C2×C4⋊C4C4×D4311yescharacteristic
195C2×C4⋊C4C4×D4311yescharacteristic
196C2×C42—21no—
197C2×C42—861no—
198C2×C42C22×D4311yescharacteristic
199#106—862no—
200#106—862no—
201C4⋊C8—21no—
202C4⋊C8—861no—
203C4⋊C8—861no—
204C4⋊C8—1722no—
205C4⋊C8Dic8612yes—
206#97—1722no—
207C4×C8—21no—
208C4×C8—21no—
209C4×C8—861no—
210C4×C8—861no—
211C4×C8—861no—
212C4×C8—861no—
213#95—21no—
214#95—861no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—861no—
218C22×C4—861no—
219C22×C4C2×C4×D4311yescharacteristic
220C22×C4D4×D4311yescharacteristic
221C22×C4#1062190011yescharacteristic
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—432no—
229C2×C8—432no—
230C2×C8—861no—
231C2×C8—861no—
232C2×C8—861no—
233C2×C8—861no—
234C2×C8—861no—
235C2×C8—861no—
236C2×C8—861no—
237C2×C8—861no—
238C2×C8—861no—
239C2×C8—861no—
240C2×C8—1721no—
241C2×C8—1721no—
242C2×C8—1721no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—861no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4#1062187212yes—
251C42—41no—
252C42—41no—
253C42—1721no—
254C42—1721no—
255C42C2×Dic8611yescharacteristic
256C42#1062189811yescharacteristic
257C42#1062190011yescharacteristic
258C42#1062190211yescharacteristic
259C23(C22⋊D43)⋊C411yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—1721no—
269C2×C4—1721no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4#1306328311yescharacteristic
275C2×C4C4×Dic8611yescharacteristic
276C2×C4#1306330211yescharacteristic
277C2×C4#1306331011yescharacteristic
278C2×C4#1306331611yescharacteristic
279C2×C4#1306331811yescharacteristic
280C2×C4M16×D4311yescharacteristic
281C2×C4C2×#1062187211yescharacteristic
282C2×C4#1306333111yescharacteristic
283C2×C4#1306333311yescharacteristic
284C2×C4SD16×D4311yescharacteristic
285C2×C4#1306334411yescharacteristic
286C2×C4#1306335211yescharacteristic
287C2×C4#1306335711yescharacteristic
288C8—42no—
289C8—42no—
290C8—862no—
291C8—862no—
292C8—3441no—
293C8—1721no—
294C8—1721no—
295C22#1458278611yescharacteristic
296C22#1458296711yescharacteristic
297C22#1458297411yescharacteristic
298C22#1458299011yescharacteristic
299C22#1458300211yescharacteristic
300C22#1458301311yescharacteristic
301C22#1458301811yescharacteristic
302C4—21no—
303C4—21no—
304C4—42no—
305C4—81no—
306C4—3441no—
307C4—3441no—
308C4#1458295511yescharacteristic
309C4#1458295911yescharacteristic
310C4#1458302711yescharacteristic
311C4#1458302911yescharacteristic
312C4#1458318211yescharacteristic
313C4#1458319711yescharacteristic
314C4#1458321911yescharacteristic
315C4#1458324211yescharacteristic
316C2#1913342811yescharacteristic
317C2#1913347011yescharacteristic
318C2#1913348811yescharacteristic
319C2#1913350011yescharacteristic
320C2#1913516211yescharacteristic
321C2#1913517611yescharacteristic
322C2#1913519711yescharacteristic
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#9538
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
184. C43#9538semidirect

Maximal subgroups

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

subgroupindex
#191353142
C4×#130632562
#191344652
#191324352
#191324292
C43⋊#12732
C43×#12792
#953843