Finite Group Databasebeta

← #25013674

Subgroups — #25013674

Order 11008.

490 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
1C22×Dic344C211yesmaximal, characteristic
2C2×C4×Dic172C211yesmaximal, characteristic
3C2×#14582704C211yesmaximal, characteristic
4C2×#14582704C211yesmaximal, characteristic
5#19135456C211yesmaximal, characteristic
6#19132687C211yesmaximal, characteristic
7C43×#1374C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9C22×Dic172C2211yescharacteristic
10C2×C4×Dic86—21no—
11C2×Dic344—22no—
12C2×Dic344—22no—
13C2×Dic344C414yescomplemented
14C4×Dic172—22no—
15C4×Dic172—22no—
16C2×#13063259C2211yescharacteristic
17C2×#13063259C2211yescharacteristic
18C2×#13063250—21no—
19C2×#13063250—21no—
20#14582805—21no—
21#14582704—22no—
22#14582704—22no—
23C22×C16×C43C2211yescharacteristic
24C22×C16×C43C2211yescharacteristic
25C2×C4×C8×C43C2211yescharacteristic
26C22×Dic86—21no—
27C22×Dic86—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172—21no—
33C2×Dic172—21no—
34C2×Dic172—21no—
35C2×Dic172—21no—
36C2×Dic172C2×C412yes—
37C2×Dic172C2×C412yes—
38C2×Dic172D412yes—
39C2×Dic172D412yes—
40C4×Dic86—24no—
41C4×Dic86—42no—
42C2×C4⋊Dic43—21no—
43C2×C4⋊Dic43—21no—
44C2×Dic43⋊C4—41no—
45C2×C4×Dic43—41no—
46Dic344—28no—
47#13063259—21no—
48#13063259—21no—
49#13063259—21no—
50#13063259D412yes—
51#13063250—24no—
52#13063250—42no—
53C43⋊#95—41no—
54C43⋊#95—41no—
55C22×C8×C43D411yescharacteristic
56C22×C8×C43C2311yescharacteristic
57C2×C42×C43D411yescharacteristic
58C2×C16×C43—21no—
59C2×C16×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63C2×C16×C43C2×C412yes—
64C4×C8×C43—21no—
65C4×C8×C43—21no—
66C22×C4×C43D811yescharacteristic
67C22×C4×C43D811yescharacteristic
68C22×C4×C43C2×D411yescharacteristic
69C22×Dic43—41no—
70C22×Dic43—41no—
71C22×Dic43—41no—
72C22×Dic43—41no—
73C2×Dic86—22no—
74C2×Dic86—22no—
75C2×Dic86—22no—
76C2×Dic86—22no—
77C2×Dic86—41no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85C2×C8×C43—21no—
86C2×C8×C43—21no—
87C2×C8×C43—21no—
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C42×C43—21no—
95C42×C43—21no—
96C4⋊Dic43—22no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100Dic43⋊C4—44no—
101C4×Dic43—44no—
102Dic172—22no—
103Dic172—22no—
104Dic172—22no—
105Dic172—22no—
106Dic172—22no—
107Dic172—41no—
108Dic172—41no—
109Dic172C22⋊C414yes—
110C16×C43—22no—
111C16×C43—41no—
112C23×C43C2×D811yescharacteristic
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43Q3212yescomplemented
119C2×C4×C43C4×D411yescharacteristic
120C2×C4×C43#12011yescharacteristic
121C2×C4×C43#12111yescharacteristic
122C2×C4×C43#13511yescharacteristic
123C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
125C2×Dic43—42no—
126C2×Dic43—42no—
127C2×Dic43—42no—
128C2×Dic43—42no—
129C2×Dic43—42no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—81no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137Dic86—24no—
138Dic86—42no—
139Dic86—42no—
140Dic86—42no—
141Dic86—42no—
142Dic86—42no—
143Dic86—81no—
144Dic86—81no—
145C8×C43—41no—
146C8×C43C2×C22⋊C411yescharacteristic
147C8×C43C4×D411yescharacteristic
148C8×C43#12111yescharacteristic
149C8×C43#12311yescharacteristic
150#13015—431nomaximal, Sylow
151C22×C43C4×D811yescharacteristic
152C22×C43#44711yescharacteristic
153C22×C43#45911yescharacteristic
154C22×C43C2×Q3211yescharacteristic
155C22×C43#50811yescharacteristic
156C22×C43#51011yescharacteristic
157C22×C43#51011yescharacteristic
158C4×C43—22no—
159C4×C43—41no—
160C4×C43#38611yescharacteristic
161C4×C43#44211yescharacteristic
162C4×C43#44911yescharacteristic
163C4×C43#46311yescharacteristic
164Dic43—44no—
165Dic43—82no—
166Dic43—82no—
167Dic43—161no—
168C22×Q32—431no—
169C2×C4×Q16—431no—
170C2×#358—431no—
171C2×#358—431no—
172#1969—431no—
173#1380—431no—
174#1374D4311yescharacteristic
175C2×C43#187911yescharacteristic
176C2×C43C4×Q3211yescharacteristic
177C2×C43#217611yescharacteristic
178C2×C43#218811yescharacteristic
179C2×C43#218911yescharacteristic
180C2×C43#220911yescharacteristic
181C2×C43#221111yescharacteristic
182C22×Q16—431no—
183C22×Q16—431no—
184C2×C4×Q8—861no—
185C2×Q32—434no—
186C2×Q32—862no—
187C2×Q32—862no—
188C22×C16C2×D4311yescharacteristic
189C22×C16C2×D4311yescharacteristic
190C4×Q16—862no—
191C4×Q16—862no—
192C2×#107—431no—
193C2×#107—431no—
194C2×#103—861no—
195C2×#103—861no—
196C2×C4×C8C2×D4311yescharacteristic
197#391—861no—
198#358—862no—
199#358—862no—
200C43#1301511yescharacteristic, complemented, Sylow
201C22×Q8—861no—
202C22×Q8—861no—
203C2×Q16—432no—
204C2×Q16—432no—
205C2×Q16—432no—
206C2×Q16—432no—
207C2×Q16—861no—
208C2×Q16—861no—
209C2×Q16—861no—
210C2×Q16—861no—
211C2×Q16—861no—
212C2×Q16—861no—
213C2×Q16—861no—
214C2×Q16—861no—
215C22×C8D17211yescharacteristic
216C22×C8C22×D4311yescharacteristic
217C4×Q8—864no—
218C4×Q8—1722no—
219C2×C4⋊C4—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4—1721no—
222C2×C42—1721no—
223C2×C42D17211yescharacteristic
224Q32—868no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—21no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16C4×D4312yes—
231#107—432no—
232#107—861no—
233#107—861no—
234#107—861no—
235#103—864no—
236#103—1722no—
237C4×C8—21no—
238C4×C8—21no—
239#95—1721no—
240#95—1721no—
241C2×Q8—862no—
242C2×Q8—862no—
243C2×Q8—862no—
244C2×Q8—862no—
245C2×Q8—1721no—
246C2×Q8—1721no—
247C2×Q8—1721no—
248C2×Q8—1721no—
249C2×Q8—1721no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C22×C4—1721no—
254C22×C4—1721no—
255C22×C4—1721no—
256C22×C4—1721no—
257C22×C4D34411yescharacteristic
258C22×C4D34411yescharacteristic
259C22×C4C2×D17211yescharacteristic
260Q16—434no—
261Q16—862no—
262Q16—862no—
263Q16—862no—
264Q16—862no—
265Q16—862no—
266Q16—1721no—
267Q16—1721no—
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8C2×C4×D4311yescharacteristic
272C2×C8#1062189811yescharacteristic
273C2×C8D4×D4311yescharacteristic
274C2×C8D4×D4311yescharacteristic
275C2×C8D4×D4311yescharacteristic
276C2×C8#1062190211yescharacteristic
277C4⋊C4—862no—
278C4⋊C4—1724no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C42—21no—
283C42—21no—
284C42—1724no—
285C16—22no—
286C16—41no—
287C23C2×D34411yescharacteristic
288Q8—864no—
289Q8—3441no—
290Q8—3441no—
291Q8—1722no—
292Q8—1722no—
293Q8—1722no—
294Q8—1722no—
295Q8—1722no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—3441no—
302C2×C4—3441no—
303C2×C4—3441no—
304C2×C4—3441no—
305C2×C4—3441no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—1722no—
309C2×C4—1722no—
310C2×C4—1722no—
311C2×C4—1722no—
312C2×C4—1722no—
313C2×C4Dic34412yescomplemented
314C2×C4C4×D17211yescharacteristic
315C2×C4#1306329511yescharacteristic
316C2×C4#1306330011yescharacteristic
317C2×C4#1306334711yescharacteristic
318C2×C4#1306335311yescharacteristic
319C2×C4#1306335311yescharacteristic
320C8—41no—
321C8C22⋊C4×D4311yescharacteristic
322C8#1306328711yescharacteristic
323C8#1306329811yescharacteristic
324C8#1306331011yescharacteristic
325C22C4×D34411yescharacteristic
326C22#1458303511yescharacteristic
327C22#1458309511yescharacteristic
328C22C2×Dic34411yescharacteristic
329C22#1458333111yescharacteristic
330C22#1458334211yescharacteristic
331C22#1458334211yescharacteristic
332C4—22no—
333C4—41no—
334C4—3442no—
335C4—3442no—
336C4—1724no—
337C4—6881no—
338C4#1458277711yescharacteristic
339C4#1458301211yescharacteristic
340C4#1458304611yescharacteristic
341C4#1458311511yescharacteristic
342C2#1913494211yescharacteristic
343C2C4×Dic34411yescharacteristic
344C2#1913646711yescharacteristic
345C2#1913653111yescharacteristic
346C2#1913653711yescharacteristic
347C2#1913664611yescharacteristic
348C2#1913665811yescharacteristic
subgroupG/H
centerC23C2×D344
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1374C2
socle, prime radicalC23×C43C2×D8
cosocleC22×C8×C43C23
hypercenter#1374D43
hypocenterC43#13015
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1374

Complements

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

NH ≅ G/Ntype
13. C2×Dic344C4semidirect
118. C2×C4×C43Q32semidirect
200. C43#13015semidirect
313. C2×C4Dic344semidirect

Maximal subgroups

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

subgroupindex
C22×Dic3442
C2×C4×Dic1722
C2×#145827042
#191354562
#191326872
C43×#13742
#1301543