Finite Group Databasebeta

← #25015066

Subgroups — #25015066

Order 11008.

494 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
1C2×#14583277C211yesmaximal, characteristic
2C2×Dic43⋊C16C211yesmaximal, characteristic
3C2×#14582704C211yesmaximal, characteristic
4C2×#14582703C211yesmaximal, characteristic
5C2×#14582702C211yesmaximal, characteristic
6#107×Dic43C211yesmaximal, characteristic
7C2×C43×#358C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9C22×#10621885—21no—
10C2×#13063323—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583277—22no—
13#14583277C414yescomplemented
14C2×#13063259C2211yescharacteristic
15C2×C8×Dic43C2211yescharacteristic
16C4⋊C4×Dic43—21no—
17Dic43⋊C16—22no—
18#14582704—22no—
19#14582703—22no—
20#14582702—22no—
21#14582661—21no—
22C22×Q16×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#358—22no—
26C22×Dic86—21no—
27C2×Dic172—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172C2×C412yes—
33C2×#10621885—24no—
34C2×#10621885—42no—
35C2×#10621885—42no—
36C22×C43⋊C8D411yescharacteristic
37#13063323—24no—
38#13063323—42no—
39C2×C4⋊Dic43—21no—
40C2×Dic43⋊C4—41no—
41C2×Dic43⋊C4—41no—
42C2×C4×Dic43—41no—
43C2×C4×Dic43D411yescharacteristic
44C2×C43⋊C16—21no—
45C2×C43⋊C16—21no—
46C2×C43⋊C16—21no—
47#13063259—21no—
48#13063259D412yes—
49C8×Dic43C2×C412yes—
50C8×Dic43D412yes—
51C43⋊#95—41no—
52C22×Q8×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43—21no—
55C2×Q16×C43—21no—
56C2×Q16×C43—21no—
57C2×Q16×C43—21no—
58C2×Q16×C43C2×C412yes—
59C22×C8×C43C2311yescharacteristic
60C2×C4⋊C4×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43—21no—
63C2×C16×C43—21no—
64#107×C43—21no—
65#107×C43D412yes—
66C2×Q8×C43—22no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C2×Q8×C43—41no—
70C2×Q8×C43—41no—
71C2×Q8×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43—41no—
74C22×C4×C43C2×D411yescharacteristic
75C22×Dic43—41no—
76C22×Dic43—41no—
77C22×Dic43D811yescharacteristic
78C22×Dic43D811yescharacteristic
79C2×Dic86—22no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C2×Dic86—41no—
85Q16×C43—22no—
86Q16×C43—22no—
87Q16×C43—41no—
88Q16×C43—41no—
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43C2×D411yescharacteristic
92C2×C8×C43C2×D411yescharacteristic
93C2×C8×C43#4111yescharacteristic
94C2×C8×C43#4111yescharacteristic
95C4⋊C4×C43—22no—
96C4⋊C4×C43—41no—
97#10621885—48no—
98C4⋊Dic43—22no—
99C4⋊Dic43—41no—
100Dic43⋊C4—44no—
101Dic43⋊C4—44no—
102C4×Dic43—82no—
103C4×Dic43C22⋊C412yes—
104C4×Dic43SD1612yes—
105C2×C43⋊C8—21no—
106C2×C43⋊C8—21no—
107C2×C43⋊C8C22⋊C412yes—
108Dic172—22no—
109Dic172—22no—
110Dic172—41no—
111Dic172—41no—
112C16×C43—41no—
113C43⋊C16—41no—
114C23×C43C2×D811yescharacteristic
115Q8×C43—42no—
116Q8×C43—42no—
117Q8×C43—81no—
118Q8×C43—81no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43—81no—
122C2×C4×C43—81no—
123C2×C4×C43—81no—
124C2×C4×C43—81no—
125C2×C4×C43C2×C22⋊C411yescharacteristic
126C2×C4×C43#12111yescharacteristic
127C2×C4×C43#12111yescharacteristic
128C2×C4×C43C2×SD1611yescharacteristic
129C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—42no—
134C2×Dic43—42no—
135C2×Dic43—81no—
136C2×Dic43—81no—
137C2×Dic43—81no—
138C2×Dic43—81no—
139C2×Dic43#10212yes—
140C2×Dic43#10212yes—
141C2×Dic43SD3212yes—
142C2×Dic43Q3212yes—
143Dic86—42no—
144Dic86—42no—
145Dic86—81no—
146Dic86—81no—
147C8×C43C4×D411yescharacteristic
148C8×C43C4×D411yescharacteristic
149C8×C43#12411yescharacteristic
150C8×C43#12711yescharacteristic
151C43⋊C8—22no—
152#13253—431nomaximal, Sylow
153C22×C43C2×#10211yescharacteristic
154C22×C43#45911yescharacteristic
155C22×C43#45911yescharacteristic
156C22×C43C2×SD3211yescharacteristic
157C22×C43C2×Q3211yescharacteristic
158C22×C43#51011yescharacteristic
159C22×C43#51011yescharacteristic
160C4×C43—82no—
161C4×C43—82no—
162C4×C43#39011yescharacteristic
163C4×C43#41811yescharacteristic
164C4×C43#46011yescharacteristic
165C4×C43#46011yescharacteristic
166Dic43—22no—
167Dic43—82no—
168Dic43—82no—
169Dic43#35814yescomplemented
170C2×#494—431no—
171C2×C4⋊C16—431no—
172C2×#358—431no—
173C2×#358—431no—
174C2×#358—431no—
175C2×#358D4311yescharacteristic
176C4×#107—431no—
177C2×C43#198211yescharacteristic
178C2×C43C2×#35811yescharacteristic
179C2×C43#214111yescharacteristic
180C2×C43#220811yescharacteristic
181C2×C43#220811yescharacteristic
182C2×C43#220911yescharacteristic
183C2×C43#220911yescharacteristic
184C22×Q16—431no—
185C22×Q16—861no—
186C22×Q16C2×D4311yescharacteristic
187C2×C4⋊Q8—861no—
188C22×C16—431no—
189C22×C16C2×D4311yescharacteristic
190#494—434no—
191#494—862no—
192C2×#107—431no—
193C2×#107C2×D4311yescharacteristic
194C2×C4×C8—431no—
195C4×C4⋊C4—861no—
196C4⋊C16—862no—
197#358—22no—
198#358—862no—
199#358—862no—
200#358—862no—
201#340—861no—
202C43#1325311yescharacteristic, complemented, Sylow
203C22×Q8—21no—
204C22×Q8—861no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16—432no—
211C2×Q16—864no—
212C2×Q16—861no—
213C2×Q16—861no—
214C2×Q16—861no—
215C2×Q16—861no—
216C2×Q16—861no—
217C2×Q16—1722no—
218C2×Q16—1722no—
219C2×Q16C4×D4312yes—
220C22×C8—431no—
221C22×C8C22×D4311yescharacteristic
222C4⋊Q8—864no—
223C4⋊Q8—1722no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—861no—
226C2×C4⋊C4—1721no—
227C2×C4⋊C4—1721no—
228C2×C42—431no—
229C2×C42—1721no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—861no—
234C2×C16—861no—
235C2×C16—861no—
236#107—21no—
237#107—432no—
238#107—861no—
239#107C22⋊D4312yes—
240C4×C8—432no—
241C4×C8—432no—
242#95—1721no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—862no—
250C2×Q8—1721no—
251C2×Q8—1721no—
252C2×Q8—1721no—
253C2×Q8—1721no—
254C2×Q8—1721no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—1721no—
260C22×C4—1721no—
261C22×C4D4×D4311yescharacteristic
262Q16—22no—
263Q16—22no—
264Q16—41no—
265Q16—41no—
266Q16—862no—
267Q16—862no—
268Q16—1728no—
269Q16—1721no—
270Q16—1721no—
271C2×C8—432no—
272C2×C8—861no—
273C2×C8—861no—
274C2×C8C2×C4×D4311yescharacteristic
275C2×C8#1062189811yescharacteristic
276C2×C8D4×D4311yescharacteristic
277C2×C8D4×D4311yescharacteristic
278C2×C8#1062190011yescharacteristic
279C2×C8C2×C22⋊D4311yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—41no—
282C4⋊C4—862no—
283C4⋊C4—1724no—
284C4⋊C4—1724no—
285C4⋊C4—1721no—
286C42—432no—
287C42—432no—
288C42—3442no—
289C16—41no—
290C16—1721no—
291C23D8×D4311yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296Q8—3441no—
297Q8—3441no—
298Q8—1722no—
299Q8—1722no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—81no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—432no—
307C2×C4—432no—
308C2×C4—432no—
309C2×C4—432no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—3441no—
313C2×C4—3441no—
314C2×C4—3441no—
315C2×C4—3441no—
316C2×C4—1722no—
317C2×C4—1722no—
318C2×C4C22⋊C4×D4311yescharacteristic
319C2×C4#1306329711yescharacteristic
320C2×C4#1306329811yescharacteristic
321C2×C4SD16×D4311yescharacteristic
322C2×C4#1306334911yescharacteristic
323C2×C4#1306335211yescharacteristic
324C8—862no—
325C8(C22⋊D43)⋊C411yescharacteristic
326C8C4×C22⋊D4311yescharacteristic
327C8#1306331111yescharacteristic
328C8#1306332111yescharacteristic
329C22#102×D4311yescharacteristic
330C22#1458309211yescharacteristic
331C22#1458309311yescharacteristic
332C22SD32×D4311yescharacteristic
333C22Q32×D4311yescharacteristic
334C22#1458333811yescharacteristic
335C22#1458334111yescharacteristic
336C4—82no—
337C4—82no—
338C4—434no—
339C4—862no—
340C4—3442no—
341C4—3442no—
342C4#1458279911yescharacteristic
343C4#1458290211yescharacteristic
344C4#1458309711yescharacteristic
345C4#1458309811yescharacteristic
346C2#1913552011yescharacteristic
347C2#358×D4311yescharacteristic
348C2#1913631311yescharacteristic
349C2#1913663811yescharacteristic
350C2#1913663911yescharacteristic
351C2#1913664311yescharacteristic
352C2#1913664411yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#358C2
socle, prime radicalC23×C43C2×D8
cosocleC22×C8×C43C23
hypercenterC2×#358D43
hypocenterC43#13253
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
13. #14583277C4semidirect
169. Dic43#358semidirect
202. C43#13253semidirect

Maximal subgroups

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

subgroupindex
C2×#145832772
C2×Dic43⋊C162
C2×#145827042
C2×#145827032
C2×#145827022
#107×Dic432
C2×C43×#3582
#1325343