Finite Group Databasebeta

← #25014817

Subgroups — #25014817

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583282C211yesmaximal, characteristic
2C2×#14582704C211yesmaximal, characteristic, complemented
3C2×#14582702C211yesmaximal, characteristic, complemented
4C2×#14582700C211yesmaximal, characteristic
5C2×C16×Dic43C211yesmaximal, characteristic, complemented
6#19134758C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic
8C22×Dic172C2211yescharacteristic
9C22×#10621883—21no—
10C2×#13063312—21no—
11C22×C43⋊C16C2211yescharacteristic
12#14583282—22no—
13#14583282C414yescomplemented
14C2×#13063259C2211yescharacteristic
15C2×#13063256—21no—
16C2×C8×Dic43C2211yescharacteristic
17#14582764—21no—
18#14582704—22no—
19#14582702—22no—
20#14582700—22no—
21C16×Dic43—22no—
22C22×D8×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#357—22no—
26C22×Dic86—21no—
27C2×Dic172—21no—
28C2×Dic172—21no—
29C2×Dic172—21no—
30C2×Dic172—21no—
31C2×Dic172—21no—
32C2×Dic172C2×C412yes—
33C2×#10621883—24no—
34C2×#10621883—42no—
35C2×#10621883—42no—
36C22×C43⋊C8D411yescharacteristic
37#13063312—24no—
38#13063312—42no—
39C2×C4⋊Dic43—21no—
40C2×C22⋊Dic43—42no—
41C2×C4×Dic43D411yescharacteristic
42C2×C43⋊C16—21no—
43C2×C43⋊C16—21no—
44C2×C43⋊C16D412yes—
45#13063259—21no—
46#13063259—21no—
47#13063256—42no—
48C8×Dic43C2×C412yes—
49C8×Dic43D412yes—
50C43⋊#95—42no—
51C22×D4×C43—21no—
52C2×D8×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—21no—
56C2×D8×C43—21no—
57C2×D8×C43C2×C412yes—
58C22×C8×C43C2311yescharacteristic
59C2×C4⋊C4×C43—21no—
60C2×C16×C43—21no—
61C2×C16×C43—21no—
62C2×C16×C43D412yes—
63#107×C43—21no—
64#107×C43—21no—
65C24×C43—41no—
66C2×D4×C43—22no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C22×C4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—41no—
75C22×Dic43—41no—
76C22×Dic43D812yes—
77C2×Dic86—22no—
78C2×Dic86—41no—
79C2×Dic86—41no—
80C2×Dic86—41no—
81C2×Dic86—41no—
82C2×Dic86—41no—
83D8×C43—22no—
84D8×C43—22no—
85D8×C43—41no—
86D8×C43—41no—
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C22⋊Dic43—48no—
96#10621883—48no—
97C4⋊Dic43—41no—
98C4⋊Dic43—41no—
99C4×Dic43C22⋊C412yes—
100C4×Dic43SD1612yes—
101C2×C43⋊C8C22⋊C412yes—
102C2×C43⋊C8D812yes—
103C2×C43⋊C8SD1612yes—
104Dic172—22no—
105Dic172—22no—
106Dic172—41no—
107Dic172—41no—
108C16×C43—22no—
109C43⋊C16—22no—
110C23×C43—42no—
111C23×C43—81no—
112C23×C43—81no—
113C23×C43—82no—
114C23×C43—82no—
115C23×C43C2×D811yescharacteristic
116D4×C43—42no—
117D4×C43—42no—
118D4×C43—81no—
119D4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—82no—
122C2×C4×C43C2×C22⋊C411yescharacteristic
123C2×C4×C43#12411yescharacteristic
124C2×C4×C43#12711yescharacteristic
125C2×C4×C43C2×D811yescharacteristic
126C2×C4×C43C2×SD1611yescharacteristic
127C2×C4×C43C2×SD1611yescharacteristic
128C2×Dic43—22no—
129C2×Dic43—22no—
130C2×Dic43—42no—
131C2×Dic43—81no—
132C2×Dic43—81no—
133C2×Dic43—81no—
134C2×Dic43—82no—
135C2×Dic43#10214yes—
136Dic86—42no—
137Dic86—42no—
138Dic86—81no—
139Dic86—81no—
140C8×C43C4×D411yescharacteristic
141C8×C43C4×D411yescharacteristic
142C8×C43#12111yescharacteristic
143C8×C43#12111yescharacteristic
144C43⋊C8#10214yes—
145#13204—431nomaximal, Sylow
146C22×C43—84no—
147C22×C43—82no—
148C22×C43—162no—
149C22×C43—161no—
150C22×C43—161no—
151C22×C43C2×#10211yescharacteristic
152C22×C43#48611yescharacteristic
153C22×C43#49311yescharacteristic
154C22×C43#50812yes—
155C22×C43#50812yes—
156C4×C43—161no—
157C4×C43#39011yescharacteristic
158C4×C43C2×#10211yescharacteristic
159C4×C43#48611yescharacteristic
160C4×C43#49211yescharacteristic
161Dic43—24no—
162Dic43—82no—
163Dic43—161no—
164C2×#495—431no—
165C2×#358—431no—
166C2×#358—431no—
167C2×#357—431no—
168C2×#357D4311yescharacteristic
169C2×C4×C16—431no—
170#1846—431no—
171C2×C43—162no—
172C2×C43#195711yescharacteristic
173C2×C43#213812yes—
174C2×C43#224212yes—
175C2×C43#224911yescharacteristic
176C2×C43#224911yescharacteristic
177C22×Q16—431no—
178C22×SD16—861no—
179C22×D8C2×D4311yescharacteristic
180C2×#124—861no—
181C22×C16—431no—
182C22×C16C2×D4311yescharacteristic
183#495—434no—
184#495—862no—
185C2×#107—431no—
186C2×#107C2×D4311yescharacteristic
187C2×#106—861no—
188C2×C4×C8—431no—
189#382—861no—
190#358—862no—
191#358—862no—
192#357—22no—
193#357—862no—
194C4×C16—862no—
195C43#1320411yescharacteristic, complemented, Sylow
196C22×Q8—861no—
197C22×D4—21no—
198C2×Q16—432no—
199C2×Q16—861no—
200C2×Q16—861no—
201C2×Q16—861no—
202C2×Q16—861no—
203C2×Q16—861no—
204C2×SD16—864no—
205C2×SD16—1722no—
206C2×SD16—1722no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8C4×D4312yes—
213C22×C8—431no—
214C22×C8C22×D4311yescharacteristic
215#124—864no—
216#124—1722no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—861no—
219C2×C22⋊C4—1722no—
220C2×C42—431no—
221C2×C16—21no—
222C2×C16—21no—
223C2×C16—432no—
224C2×C16—861no—
225C2×C16—861no—
226C2×C16C22⋊D4312yes—
227#107—21no—
228#107—21no—
229#107—861no—
230#107—861no—
231#106—1722no—
232C4×C8—432no—
233C4×C8—432no—
234#95—1722no—
235C24—41no—
236C2×Q8—862no—
237C2×Q8—1721no—
238C2×Q8—1721no—
239C2×Q8—1721no—
240C2×Q8—1721no—
241C2×Q8—1721no—
242C2×D4—22no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C22×C4—41no—
249C22×C4—432no—
250C22×C4—1721no—
251C22×C4—1721no—
252C22×C4D4×D4311yescharacteristic
253Q16—862no—
254Q16—862no—
255Q16—1721no—
256Q16—1721no—
257SD16—1728no—
258D8—22no—
259D8—22no—
260D8—41no—
261D8—41no—
262C2×C8—432no—
263C2×C8—432no—
264C2×C8—432no—
265C2×C8C2×C4×D4311yescharacteristic
266C2×C8#1062189811yescharacteristic
267C2×C8D4×D4311yescharacteristic
268C2×C8D4×D4311yescharacteristic
269C2×C8#1062190011yescharacteristic
270C2×C8C2×C22⋊D4311yescharacteristic
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—1721no—
274C4⋊C4—1721no—
275C22⋊C4—1728no—
276C42—432no—
277C42—432no—
278C16—22no—
279C16—862no—
280C23—42no—
281C23—82no—
282C23—82no—
283C23—81no—
284C23—81no—
285C23D8×D4311yescharacteristic
286Q8—3441no—
287Q8—3441no—
288Q8—1722no—
289Q8—1722no—
290D4—42no—
291D4—42no—
292D4—81no—
293D4—81no—
294C2×C4—82no—
295C2×C4—81no—
296C2×C4—434no—
297C2×C4—862no—
298C2×C4—862no—
299C2×C4—3441no—
300C2×C4—3441no—
301C2×C4—3442no—
302C2×C4—3441no—
303C2×C4—1722no—
304C2×C4C22⋊C4×D4311yescharacteristic
305C2×C4#1306331111yescharacteristic
306C2×C4#1306332111yescharacteristic
307C2×C4D8×D4311yescharacteristic
308C2×C4SD16×D4311yescharacteristic
309C2×C4SD16×D4311yescharacteristic
310C8—434no—
311C8(C22⋊D43)⋊C411yescharacteristic
312C8C4×C22⋊D4311yescharacteristic
313C8#1306329711yescharacteristic
314C8#1306329811yescharacteristic
315C22—84no—
316C22—82no—
317C22—162no—
318C22—161no—
319C22—161no—
320C22#102×D4311yescharacteristic
321C22#1458324411yescharacteristic
322C22#1458327411yescharacteristic
323C22#1458332812yes—
324C22#1458333012yes—
325C4—161no—
326C4—864no—
327C4—3442no—
328C4—6881no—
329C4#1458279911yescharacteristic
330C4#102×D4311yescharacteristic
331C4#1458324411yescharacteristic
332C4#1458327011yescharacteristic
333C2—162no—
334C2#1913539911yescharacteristic
335C2#1913629912yes—
336C2#1913682512yes—
337C2#1913685311yescharacteristic
338C2#1913685511yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC22×D8×C43C22
cosocleC22×C8×C43C23
hypercenterC2×#357D43
hypocenterC43#13204
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
2. C2×#14582704C2semidirect
3. C2×#14582702C2semidirect
5. C2×C16×Dic43C2semidirect
6. #19134758C2semidirect
13. #14583282C4semidirect
195. C43#13204semidirect

Maximal subgroups

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

subgroupindex
C2×#145832822
C2×#145827042
C2×#145827022
C2×#145827002
C2×C16×Dic432
#191347582
C2×C43×#3572
#1320443