Finite Group Databasebeta

← #14736889

Subgroups — #14736889

Order 2816.

650 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079746C211yesmaximal, characteristic
2#13079744C211yesmaximal, characteristic
3C2×#10622691C211yesmaximal, characteristic, complemented
4#13077327C211yesmaximal, characteristic
5#13068138C214yesmaximal, complemented
6#13068014C214yesmaximal, complemented
7#13067362C211yesmaximal, characteristic, complemented
8#13067298C211yesmaximal, characteristic, complemented
9C11×#1548C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66960—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622742—21no—
17#10622701—21no—
18#10622697C2214yes—
19#10622692—21no—
20#10622691—21no—
21#10622691—21no—
22#10622691C2212yes—
23#10622691C2212yes—
24#10622581—22no—
25C2×#66871—21no—
26C2×#66871—21no—
27#10622538C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29#10622455C2214yes—
30#10622451—21no—
31#10622451C2212yes—
32#10622447—21no—
33#10622447C2212yes—
34#10622348—22no—
35#10622307—21no—
36#10622293—21no—
37C11×#333C2214yes—
38#10622119C2214yes—
39#10622118C2212yes—
40#10622117C2212yes—
41C22×Q8×C11—21no—
42C2×#4339—21no—
43C22×Dic22—21no—
44C2×C11×M16—21no—
45C11×C4⋊Q8—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8C2312yes—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C42×C11C2311yescharacteristic
52#66983—21no—
53#66983D412yes—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C22×C11⋊C8D411yescharacteristic
57C22×C11⋊C8D411yescharacteristic
58#66960—44no—
59C2×#4313—22no—
60C2×C8×D11—22no—
61#66928—21no—
62#66927D411yescharacteristic
63C4×D44—21no—
64C4×D44C2312yes—
65#66922—21no—
66#66922—21no—
67#66922—21no—
68#66922D411yescharacteristic
69#66922C2312yes—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C22⋊C8—21no—
74C4×C8×C11—21no—
75C22⋊(C11⋊C8)—21no—
76#66885—24no—
77(C2×D11)⋊C8—22no—
78(C2×D11)⋊C8—22no—
79#66881—24no—
80#66873—24no—
81#66872—24no—
82#66871—22no—
83#66871—22no—
84#66871—22no—
85#66871—22no—
86C4⋊(C11⋊C8)C2312yes—
87C4×C11⋊C8—21no—
88C4×C11⋊C8D411yescharacteristic
89C4×C11⋊C8D411yescharacteristic
90C4×C11⋊C8C2311yescharacteristic
91C4×C11⋊C8C2311yescharacteristic
92#19193—111nomaximal, Sylow
93C2×Q8×C11—22no—
94C2×Q8×C11—41no—
95C2×Q8×C11—82no—
96C22×C4×C11—41no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×C22⋊D11—22no—
101C22×Dic11—41no—
102#4339—42no—
103#4339—42no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44C2×D412yes—
107C2×C4×D11—22no—
108C2×Dic22—21no—
109C2×Dic22—22no—
110C2×Dic22—41no—
111C2×Dic22—82no—
112C11×M16—42no—
113C2×C8×C11—22no—
114C2×C8×C11—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123(C2×D11)⋊C4—22no—
124(C2×D11)⋊C4—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130C4⋊Dic11C2×D412yes—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8SD1614yes—
134C2×C11⋊C8C2×D411yescharacteristic
135C2×C11⋊C8C2×D411yescharacteristic
136C2×C11⋊C8C2×D411yescharacteristic
137C2×C11⋊C8C2×D411yescharacteristic
138#4313—44no—
139C8×D11—44no—
140#3227—111no—
141#3227—111no—
142C2×#500—111no—
143#2931—111no—
144#1695—114no—
145#1675—114no—
146#1564—111no—
147#1548—111no—
148#1548D1111yescharacteristic, complemented
149C23×C11#12111yescharacteristic
150C22×D11—22no—
151Q8×C11—82no—
152Q8×C11—82no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—42no—
156C2×C4×C11—82no—
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11C2×SD1612yes—
161C2×C4×C11#13712yes—
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C2×#4111yescharacteristic
165C22⋊D11—44no—
166C2×Dic11—22no—
167C2×Dic11—42no—
168C2×Dic11—82no—
169D44—24no—
170D44—42no—
171D44—42no—
172C4×D11—42no—
173C4×D11—42no—
174Dic22—42no—
175Dic22—82no—
176Dic22—82no—
177C8×C11—42no—
178C8×C11—42no—
179C11⋊C8—21no—
180C11⋊C8—21no—
181C11⋊C8—42no—
182C11⋊C8C2×SD1612yes—
183C11⋊C8C2×SD1612yes—
184C2×#131—221no—
185#532—111no—
186C2×C4⋊Q8—111no—
187C2×C4⋊Q8C2×D1111yescharacteristic
188#500—112no—
189#500—112no—
190#500—221no—
191#500—221no—
192#498—221no—
193#498—221no—
194#486—221no—
195#486—221no—
196#481—222no—
197#481—222no—
198#476—114no—
199#476—114no—
200#436—112no—
201#436—221no—
202C8×D4—112no—
203C8×D4—221no—
204#431—111no—
205#431C2×D1111yescharacteristic
206C2×#107—221no—
207C2×#107—221no—
208#423C2×D1111yescharacteristic
209#408—221no—
210C2×C4×C8—111no—
211#335—112no—
212#334—112no—
213#333—114no—
214#333C2×D1114yes—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11#46112yes—
218C22×C11C2×#12111yescharacteristic
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—42no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—82no—
225C4×C11#46112yes—
226C4×C11#47212yes—
227C4×C11C22×SD1611yescharacteristic
228C4×C11C2×#13711yescharacteristic
229C4×C11#57812yes—
230Dic11—42no—
231Dic11—82no—
232C2×#41—221no—
233C22×Q8—21no—
234C22×Q8—221no—
235#131—444no—
236C2×M16—21no—
237C2×M16—222no—
238C22×C8—111no—
239C22×C8—111no—
240C22×C8—222no—
241C4⋊Q8—21no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—111no—
245C4⋊Q8—112no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248C4⋊Q8—221no—
249C4⋊Q8C22×D1112yes—
250#127—111no—
251#124—221no—
252#121—112no—
253#121—221no—
254C4×D4—112no—
255C4×D4—221no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C42C22×D1111yescharacteristic
261#107—222no—
262#107—222no—
263#107—222no—
264#107—222no—
265#106—224no—
266#106—224no—
267C4⋊C8—21no—
268C4⋊C8—112no—
269C4⋊C8C22×D1112yes—
270C4⋊C8C22×D1112yes—
271#102—224no—
272#102—224no—
273C22⋊C8—21no—
274C22⋊C8—222no—
275C22⋊C8—222no—
276C22⋊C8—221no—
277C4×C8—21no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8—111no—
281C4×C8—111no—
282C4×C8—221no—
283C2×C11—22no—
284C2×C11C2×#46111yescharacteristic
285C2×C11#305911yescharacteristic
286C2×C11C2×#47211yescharacteristic
287D11—82no—
288#41—442no—
289#41—442no—
290C2×Q8—22no—
291C2×Q8—41no—
292C2×Q8—82no—
293C2×Q8—221no—
294C2×Q8—222no—
295C2×Q8—441no—
296C2×Q8—882no—
297C2×D4—112no—
298C2×D4—222no—
299C2×D4—221no—
300C2×D4—221no—
301C22×C4—41no—
302C22×C4—222no—
303C22×C4—441no—
304C22×C4#433911yescharacteristic
305C22×C4D4×D1111yescharacteristic
306C22×C4D4×D1111yescharacteristic
307M16—42no—
308M16—444no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—114no—
312C2×C8—111no—
313C2×C8—111no—
314C2×C8—111no—
315C2×C8—111no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—444no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—112no—
324C4⋊C4—221no—
325C4⋊C4—222no—
326C4⋊C4—222no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C42#433911yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1919311yescharacteristic, complemented, Sylow
336C23—222no—
337C23#6693711yescharacteristic
338Q8—82no—
339Q8—82no—
340Q8—442no—
341Q8—882no—
342Q8—882no—
343D4—224no—
344D4—444no—
345D4—442no—
346D4—442no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—42no—
350C2×C4—82no—
351C2×C4—222no—
352C2×C4—442no—
353C2×C4—442no—
354C2×C4—442no—
355C2×C4—882no—
356C2×C4#6693711yescharacteristic
357C2×C4#6693711yescharacteristic
358C2×C4#6693711yescharacteristic
359C2×C4SD16×D1112yes—
360C2×C4#6697112yes—
361C2×C4C2×#433911yescharacteristic
362C2×C4C2×D4×D1111yescharacteristic
363C2×C4C2×D4×D1111yescharacteristic
364C8—42no—
365C8—42no—
366C8—112no—
367C8—112no—
368C8—221no—
369C8—221no—
370C8—442no—
371C22—21no—
372C22—21no—
373C22—442no—
374C22—442no—
375C22—442no—
376C22#1062243112yes—
377C22C2×#6693711yescharacteristic
378C4—21no—
379C4—21no—
380C4—82no—
381C4—442no—
382C4—882no—
383C4#1062236212yes—
384C4#1062243112yes—
385C4C2×SD16×D1111yescharacteristic
386C4C2×#6697111yescharacteristic
387C4#1062331012yes—
388C2—22no—
389C2—882no—
390C2C2×#1062243111yescharacteristic
391C2#1307827011yescharacteristic
392C2C2×#1062236211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1548C2
socleC22×C11C2×#121
prime radical#10623008C22
hypercenter#1548D11
hypocenterC11#19193
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
3. C2×#10622691C2semidirect
5. #13068138C2semidirect
6. #13068014C2semidirect
7. #13067362C2semidirect
8. #13067298C2semidirect
9. C11×#1548C2semidirect
148. #1548D11semidirect
335. C11#19193semidirect

Maximal subgroups

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

subgroupindex
#130797462
#130797442
C2×#106226912
#130773272
#130681382
#130680142
#130673622
#130672982
C11×#15482
#1919311