Finite Group Databasebeta

← #14909343

Subgroups — #14909343

Order 2816.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079193C211yesmaximal, characteristic, complemented
2#13079183C211yesmaximal, characteristic, complemented
3#13070902C211yesmaximal, characteristic, complemented
4#13070857C211yesmaximal, characteristic, complemented
5#13070852C211yesmaximal, characteristic, complemented
6#13070726C212yesmaximal, complemented
7#13070716C212yesmaximal, complemented
8SD32×Dic11C212yesmaximal, complemented
9D16×Dic11C212yesmaximal, complemented
10#13070209C211yesmaximal, characteristic, complemented
11C11×#2250C211yesmaximal, characteristic, complemented
12#10623247—21no—
13#10623211—21no—
14C2×C11×SD32C2212yes—
15C2×C11×D16C2212yes—
16C11×#495C2211yescharacteristic
17C11×#493C2211yescharacteristic
18#10622801C2211yescharacteristic
19Q16×Dic11C2211yescharacteristic
20#10622784—21no—
21SD16×Dic11—21no—
22#10622770—21no—
23#10622770C2211yescharacteristic
24#10622770C2212yes—
25D8×Dic11—21no—
26D8×Dic11C2211yescharacteristic
27D8×Dic11C2212yes—
28#10622683—21no—
29#10622669—21no—
30C2×#66862C2212yes—
31C4×C8×D11C2211yescharacteristic
32#10622296C2211yescharacteristic
33#10622295C2211yescharacteristic
34C11×#346C2211yescharacteristic
35#10622202C2212yes—
36#10622200C2212yes—
37#10622200C2212yes—
38#10622200C2212yes—
39#10622143C2212yes—
40#10622142C2212yes—
41C16×Dic11C2212yes—
42#10622099C2211yescharacteristic
43C2×#4341—41no—
44C2×C11×Q16C2311yescharacteristic
45C2×C11×SD16—21no—
46C2×C11×D8—21no—
47C2×C11×D8C2312yes—
48C2×C11×D8C2311yescharacteristic
49C11×#127—21no—
50C11×#124—21no—
51#66999—21no—
52Q8×Dic11—21no—
53#66991—22no—
54#66991—21no—
55#66991—41no—
56#66989—41no—
57D4×Dic11—22no—
58D4×Dic11—21no—
59D4×Dic11—41no—
60C2×C8×D11D411yescharacteristic
61C2×C8×D11C2311yescharacteristic
62#66936—41no—
63(C22⋊D11)⋊C4—41no—
64#66932—41no—
65#66930—41no—
66C42×D11D411yescharacteristic
67#66923—21no—
68#66922—21no—
69C11×SD32—24no—
70C11×D16—24no—
71C2×C11×C16C2312yes—
72C4×C8×C11C2311yescharacteristic
73#66899—21no—
74#66899—21no—
75#66896—22no—
76#66896—22no—
77#66896—21no—
78#66896—21no—
79#66882—21no—
80#66882C2312yes—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66881—21no—
84C8×Dic11D411yescharacteristic
85C8×Dic11C2311yescharacteristic
86C2×C11⋊C16C2312yes—
87C4×C11⋊C8D411yescharacteristic
88#66862—24no—
89#33737—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—22no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×C22⋊D11—41no—
96C2×C22⋊D11—42no—
97C22×Dic11—41no—
98C22×Dic11—42no—
99#4341—84no—
100C2×C4×D11D811yescharacteristic
101C2×C4×D11D811yescharacteristic
102C2×C4×D11C2×D411yescharacteristic
103C2×Dic22—41no—
104C11×Q16—22no—
105C11×SD16—42no—
106C11×D8—22no—
107C11×D8—22no—
108C11×D8—22no—
109C11×D8—42no—
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117C22⋊Dic11—42no—
118C22⋊Dic11—42no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—41no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128C4×Dic11—41no—
129C4×Dic11D811yescharacteristic
130C4×Dic11D811yescharacteristic
131C4×Dic11C2×D411yescharacteristic
132C2×C11⋊C8C2×D411yescharacteristic
133C2×C11⋊C8C2×D411yescharacteristic
134C8×D11—22no—
135C8×D11—22no—
136C11×C16#4114yescomplemented
137C11⋊C16—22no—
138#3169—111no—
139#3168—111no—
140#2255—111no—
141#2250D1111yescharacteristic, complemented
142#2244—111no—
143#2243—111no—
144#2220—112no—
145#2218—112no—
146C4×SD32—112no—
147C4×D16—112no—
148C4×M32—111no—
149C23×C11—41no—
150C23×C11—42no—
151C22×D11C2×D811yescharacteristic
152Q8×C11—41no—
153Q8×C11—41no—
154D4×C11—41no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—41no—
158D4×C11—82no—
159D4×C11—82no—
160C2×C4×C11—41no—
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C22×D411yescharacteristic
164C22⋊D11—84no—
165C22⋊D11—82no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11—42no—
169C2×Dic11—84no—
170C2×Dic11—82no—
171C2×Dic11C2×D811yescharacteristic
172C2×Dic11C2×D811yescharacteristic
173C2×Dic11C2×D811yescharacteristic
174C4×D11—21no—
175C4×D11—21no—
176C4×D11—22no—
177C4×D11—41no—
178Dic22—82no—
179C8×C11#13512yes—
180C8×C11C2×#4112yes—
181C11⋊C8—21no—
182C11⋊C8—21no—
183#532—221no—
184#529—221no—
185C2×SD32C2×D1112yes—
186C2×D16C2×D1112yes—
187C2×M32—112no—
188#500—111no—
189#499—111no—
190#495C2×D1111yescharacteristic
191#493C2×D1111yescharacteristic
192#488—221no—
193#486—221no—
194#467—111no—
195#466—111no—
196#466—112no—
197#466—221no—
198#465—221no—
199C4×Q16—111no—
200C4×SD16—221no—
201C4×D8—111no—
202C4×D8—112no—
203C4×D8—221no—
204C2×C4×C8—111no—
205#367—112no—
206#366—112no—
207#358—112no—
208#357—112no—
209#357—112no—
210#357—112no—
211#346—111no—
212#346C2×D1111yescharacteristic
213C4×C16—112no—
214C22×C11—82no—
215C22×C11—81no—
216C22×C11—82no—
217C22×C11—81no—
218C22×C11—82no—
219C22×C11—81no—
220C22×C11C22×D811yescharacteristic
221C2×D11—21no—
222C2×D11—21no—
223C2×D11—21no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—81no—
227C4×C11#53211yescharacteristic
228C4×C11C2×#13511yescharacteristic
229Dic11—21no—
230Dic11—21no—
231Dic11—82no—
232Dic11—81no—
233Dic11—81no—
234Dic11#50912yes—
235C2×#41—441no—
236C2×Q16C22×D1111yescharacteristic
237C2×SD16—21no—
238C2×D8—21no—
239C2×D8C22×D1112yes—
240C2×D8C22×D1111yescharacteristic
241C22×C8—111no—
242C22×C8—111no—
243C4⋊Q8—221no—
244#127—21no—
245#126—441no—
246#125—221no—
247#124—21no—
248#124—441no—
249#123—441no—
250C22⋊Q8—221no—
251#121—221no—
252#121—222no—
253#121—441no—
254C4×Q8—221no—
255C4×D4—221no—
256C4×D4—222no—
257C4×D4—441no—
258C4×D4—441no—
259#117—441no—
260C2×C42—111no—
261SD32—24no—
262D16—24no—
263M32—224no—
264C2×C16—112no—
265C2×C16C22×D1112yes—
266#107—111no—
267#107—111no—
268#107—112no—
269#107—221no—
270#106—221no—
271#103—221no—
272#103—221no—
273#102—221no—
274#102—222no—
275#102—222no—
276#102—221no—
277C4×C8—111no—
278C4×C8—111no—
279C4×C8—111no—
280C4×C8C22×D1111yescharacteristic
281C2×C11—162no—
282C2×C11—161no—
283C2×C11#316911yescharacteristic
284C2×C11C2×#50911yescharacteristic
285C2×C11#341411yescharacteristic
286D11—41no—
287#41—884no—
288C2×Q8—21no—
289C2×Q8—441no—
290C2×D4—21no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—441no—
295C2×D4—442no—
296C22×C4—111no—
297C22×C4—111no—
298C22×C4—111no—
299C22×C4—441no—
300C22×C4—442no—
301Q16—22no—
302SD16—42no—
303D8—22no—
304D8—22no—
305D8—22no—
306D8—42no—
307C2×C8—111no—
308C2×C8—111no—
309C2×C8—222no—
310C2×C8—222no—
311C2×C8D4×D1111yescharacteristic
312C2×C8C23×D1111yescharacteristic
313C4⋊C4—222no—
314C4⋊C4—221no—
315C4⋊C4—221no—
316C4⋊C4—441no—
317C4⋊C4—441no—
318C4⋊C4—441no—
319C4⋊C4—441no—
320C4⋊C4—441no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—441no—
324C22⋊C4—441no—
325C22⋊C4—442no—
326C22⋊C4—441no—
327C22⋊C4—442no—
328C42—111no—
329C42—111no—
330C42—111no—
331C42—441no—
332C42D4×D1111yescharacteristic
333C16—222no—
334C16#434114yescomplemented
335C11#3373711yescharacteristic, complemented, Sylow
336C23—41no—
337C23—42no—
338C23—111no—
339Q8—41no—
340Q8—41no—
341Q8—882no—
342D4—41no—
343D4—42no—
344D4—42no—
345D4—41no—
346D4—82no—
347D4—82no—
348D4—884no—
349D4—882no—
350C2×C4—41no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—222no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—442no—
361C2×C4—884no—
362C2×C4—882no—
363C2×C4D8×D1111yescharacteristic
364C2×C4D8×D1111yescharacteristic
365C2×C4C2×D4×D1111yescharacteristic
366C8—221no—
367C8—221no—
368C8#6696512yes—
369C8C2×#434112yes—
370C22—82no—
371C22—81no—
372C22—82no—
373C22—81no—
374C22—82no—
375C22—81no—
376C22—221no—
377C22—221no—
378C22—221no—
379C22C2×D8×D1111yescharacteristic
380C4—21no—
381C4—21no—
382C4—81no—
383C4—112no—
384C4—221no—
385C4—221no—
386C4—882no—
387C4—881no—
388C4—881no—
389C4#1062324711yescharacteristic
390C4C2×#6696511yescharacteristic
391C2—162no—
392C2—161no—
393C2—441no—
394C2#1307919311yescharacteristic
395C2D11×#50911yescharacteristic
396C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2250C2
socleC22×C11C22×D8
hypercenter#2250D11
hypocenterC11#33737
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2250

Complements

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

NH ≅ G/Ntype
1. #13079193C2semidirect
2. #13079183C2semidirect
3. #13070902C2semidirect
4. #13070857C2semidirect
5. #13070852C2semidirect
6. #13070726C2semidirect
7. #13070716C2semidirect
8. SD32×Dic11C2semidirect
9. D16×Dic11C2semidirect
10. #13070209C2semidirect
11. C11×#2250C2semidirect
136. C11×C16#41semidirect
141. #2250D11semidirect
334. C16#4341semidirect
335. C11#33737semidirect

Maximal subgroups

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

subgroupindex
#130791932
#130791832
#130709022
#130708572
#130708522
#130707262
#130707162
SD32×Dic112
D16×Dic112
#130702092
C11×#22502
#3373711