Finite Group Databasebeta

← #14909357

Subgroups — #14909357

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2#13079186C211yesmaximal, characteristic
3#13070902C211yesmaximal, characteristic, complemented
4#13070887C211yesmaximal, characteristic, complemented
5#13070862C211yesmaximal, characteristic, complemented
6#13070853C211yesmaximal, characteristic, complemented
7#13070729C212yesmaximal
8#13070724C212yesmaximal, complemented
9C4×Dic88C212yesmaximal, complemented
10C4×#66864C212yesmaximal, complemented
11C4×C11×M32C211yesmaximal, characteristic, complemented
12#10623010—21no—
13#10623001—21no—
14C2×C11×M32C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16#10622729—21no—
17#10622729C2211yescharacteristic
18#10622729C2212yes—
19#10622728C2211yescharacteristic
20#10622727—21no—
21C2×Dic88C2212yes—
22C2×#66864C2212yes—
23#10622312C2211yescharacteristic
24C4×Dic44—21no—
25C4×Dic44C2212yes—
26C4×Dic44C2211yescharacteristic
27#10622310—21no—
28#10622309C2211yescharacteristic
29C4×D88C2211yescharacteristic
30C4×#4314—21no—
31#10622296C2211yescharacteristic
32#10622295C2211yescharacteristic
33#10622294—21no—
34C11×#346C2211yescharacteristic
35C11×#346C2211yescharacteristic
36C4×C11×C16C2212yes—
37#10622147C2212yes—
38#10622143C2212yes—
39#10622142C2212yes—
40#10622141C2212yes—
41#10622141C2212yes—
42#10622141C2212yes—
43C22×C8×C11D411yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C2×C42×C11D411yescharacteristic
46#66983—21no—
47#66982—41no—
48C4×C22⋊D11—41no—
49#66979—41no—
50#66977—21no—
51#66977—22no—
52#66977—41no—
53C2×Dic44—21no—
54C2×Dic44C2312yes—
55C2×Dic44C2311yescharacteristic
56C2×D88C2311yescharacteristic
57C2×#4314—21no—
58#66929—41no—
59#66928—21no—
60C4×D44—21no—
61#66925—41no—
62#66923—21no—
63#66923—41no—
64#66922—21no—
65#66922—21no—
66C4×Dic22—22no—
67C4×Dic22—21no—
68C4×Dic22—41no—
69C11×M32—24no—
70C2×C11×C16C2312yes—
71C2×C11×C16C2312yes—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66885—21no—
77#66885—21no—
78#66882—21no—
79#66882C2311yescharacteristic
80#66882C2312yes—
81#66882C2311yescharacteristic
82#66881—21no—
83#66880—21no—
84#66880—22no—
85#66880—22no—
86#66880—21no—
87Dic88—24no—
88#66864—24no—
89#33738—111nomaximal, Sylow
90C22×C4×C11D811yescharacteristic
91C22×C4×C11D811yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C2×D44—21no—
95C2×C4×D11—41no—
96C2×Dic22—22no—
97C2×Dic22—21no—
98C2×Dic22—41no—
99C2×C8×C11—22no—
100C2×C8×C11—22no—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2411yescharacteristic
105C42×C11D811yescharacteristic
106C42×C11D811yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11C2×D411yescharacteristic
109C22⋊Dic11—42no—
110C22⋊Dic11—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—41no—
113(C2×D11)⋊C4—41no—
114(C2×D11)⋊C4—41no—
115C4⋊Dic11—22no—
116C4⋊Dic11—21no—
117C4⋊Dic11—21no—
118C4⋊Dic11—41no—
119C4⋊Dic11—41no—
120C4⋊Dic11—41no—
121Dic11⋊C4—42no—
122Dic11⋊C4—41no—
123Dic11⋊C4—42no—
124Dic11⋊C4—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127C4×Dic11—42no—
128C4×Dic11—41no—
129Dic44—22no—
130Dic44—22no—
131Dic44—22no—
132Dic44—42no—
133D88—22no—
134#4314—42no—
135C11×C16—22no—
136C11×C16#4114yes—
137#3170—111no—
138#3168—111no—
139#2255—111no—
140#2251—111no—
141#2245—111no—
142#2243—111no—
143#2220—112no—
144#2219—112no—
145C4×Q32—112no—
146C4×SD32—112no—
147C4×M32D1111yescharacteristic, complemented
148C23×C11C2×D811yescharacteristic
149C22×D11—41no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11C2×D811yescharacteristic
155C2×C4×C11C2×D811yescharacteristic
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C22⋊D11—82no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—42no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166D44—41no—
167D44—41no—
168C4×D11—82no—
169Dic22—42no—
170Dic22—41no—
171Dic22—41no—
172Dic22—42no—
173Dic22—82no—
174C8×C11—21no—
175C8×C11—21no—
176C8×C11#13512yes—
177C8×C11C2×#4112yes—
178#533—221no—
179#529—221no—
180C2×Q32—112no—
181C2×SD32—112no—
182C2×M32C2×D1112yes—
183#500—111no—
184#499—111no—
185#495—111no—
186#494—111no—
187#488—221no—
188#487—221no—
189#467—111no—
190#467—112no—
191#467—221no—
192#466—111no—
193#465—221no—
194C4×Q16—111no—
195C4×Q16—112no—
196C4×Q16—221no—
197C4×SD16—221no—
198C4×D8—111no—
199C2×C4×C8C2×D1111yescharacteristic
200#367—112no—
201#366—112no—
202#358—112no—
203#358—112no—
204#358—112no—
205#357—112no—
206#346C2×D1111yescharacteristic
207#346C2×D1111yescharacteristic
208C4×C16C2×D1112yes—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11C22×D811yescharacteristic
213C2×D11—81no—
214C2×D11—81no—
215C2×D11—81no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11#51012yes—
221C4×C11#53211yescharacteristic
222C4×C11C2×#13511yescharacteristic
223Dic11—81no—
224Dic11—82no—
225Dic11—81no—
226Dic11—81no—
227Dic11—82no—
228C2×Q16—112no—
229C2×Q16—111no—
230C2×Q16—221no—
231C2×SD16—221no—
232C2×D8—111no—
233C22×C8D4411yescharacteristic
234C22×C8C22×D1111yescharacteristic
235C4⋊Q8—221no—
236C4⋊Q8—221no—
237#126—441no—
238#125—221no—
239#125—441no—
240#124—221no—
241#123—441no—
242C22⋊Q8—221no—
243C22⋊Q8—222no—
244C22⋊Q8—441no—
245#121—221no—
246C4×Q8—221no—
247C4×Q8—222no—
248C4×Q8—441no—
249C4×D4—221no—
250C4×D4—441no—
251#117—441no—
252#117—441no—
253C2×C42D4411yescharacteristic
254Q32—224no—
255SD32—224no—
256M32—24no—
257C2×C16C22×D1112yes—
258C2×C16C22×D1112yes—
259#107—112no—
260#107—111no—
261#107—111no—
262#107—221no—
263#106—221no—
264#103—221no—
265#103—221no—
266#103—222no—
267#103—222no—
268#102—221no—
269#102—221no—
270C4×C8D4411yescharacteristic
271C4×C8D4411yescharacteristic
272C4×C8C22×D1111yescharacteristic
273C4×C8C22×D1111yescharacteristic
274C2×C11—41no—
275C2×C11#316911yescharacteristic
276C2×C11C2×#51011yescharacteristic
277C2×C11#341411yescharacteristic
278D11—161no—
279C2×Q8—221no—
280C2×Q8—222no—
281C2×Q8—441no—
282C2×D4—221no—
283C2×D4—441no—
284C22×C4—441no—
285C22×C4D8811yescharacteristic
286C22×C4D8811yescharacteristic
287C22×C4C2×D4411yescharacteristic
288Q16—222no—
289Q16—222no—
290Q16—222no—
291Q16—442no—
292SD16—442no—
293D8—222no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×D4411yescharacteristic
297C2×C8C2×D4411yescharacteristic
298C2×C8C2×D4411yescharacteristic
299C2×C8C23×D1111yescharacteristic
300C4⋊C4—221no—
301C4⋊C4—221no—
302C4⋊C4—222no—
303C4⋊C4—441no—
304C4⋊C4—441no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4—441no—
308C4⋊C4—442no—
309C4⋊C4—441no—
310C4⋊C4—442no—
311C4⋊C4—441no—
312C22⋊C4—442no—
313C22⋊C4—441no—
314C22⋊C4—441no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42—441no—
319C42—442no—
320C42D8811yescharacteristic
321C42D8811yescharacteristic
322C42C2×D4411yescharacteristic
323C42C2×D4411yescharacteristic
324C16—22no—
325C16#433914yes—
326C11#3373811yescharacteristic, complemented, Sylow
327C23—441no—
328C23C2×D8811yescharacteristic
329Q8—442no—
330Q8—441no—
331Q8—441no—
332Q8—442no—
333Q8—882no—
334D4—441no—
335D4—441no—
336D4—882no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—41no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—442no—
344C2×C4—442no—
345C2×C4—441no—
346C2×C4—882no—
347C2×C4C2×D8811yescharacteristic
348C2×C4C2×D8811yescharacteristic
349C2×C4C2×D8811yescharacteristic
350C2×C4C2×D8811yescharacteristic
351C2×C4C2×D8811yescharacteristic
352C2×C4C22×D4411yescharacteristic
353C8—21no—
354C8—21no—
355C8#6695712yes—
356C8C2×#433912yes—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—881no—
361C22—881no—
362C22—881no—
363C22C22×D8811yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—881no—
369C4—881no—
370C4—882no—
371C4—881no—
372C4—882no—
373C4#1062252212yes—
374C4#1062300811yescharacteristic
375C4C2×#6695711yescharacteristic
376C2—41no—
377C2—1761no—
378C2#1307919511yescharacteristic
379C2C2×#1062252211yescharacteristic
380C2#1308175211yescharacteristic
subgroupG/H
centerC2×C4C2×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×M32C2
socleC22×C11C22×D8
prime radical#10622728C22
hypercenterC4×M32D11
hypocenterC11#33738
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
3. #13070902C2semidirect
4. #13070887C2semidirect
5. #13070862C2semidirect
6. #13070853C2semidirect
8. #13070724C2semidirect
9. C4×Dic88C2semidirect
10. C4×#66864C2semidirect
11. C4×C11×M32C2semidirect
147. C4×M32D11semidirect
326. C11#33738semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130791862
#130709022
#130708872
#130708622
#130708532
#130707292
#130707242
C4×Dic882
C4×#668642
C4×C11×M322
#3373811