Finite Group Databasebeta

← #14909346

Subgroups — #14909346

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#13079195C211yesmaximal, characteristic, complemented
2#13079186C211yesmaximal, characteristic, complemented
3#13070902C211yesmaximal, characteristic, complemented
4#13070882C211yesmaximal, characteristic, complemented
5#13070858C211yesmaximal, characteristic, complemented
6#13070853C211yesmaximal, characteristic, complemented
7#13070729C212yesmaximal, complemented
8#13070719C212yesmaximal, complemented
9C4×#66864C212yesmaximal, complemented
10C4×D176C212yesmaximal, complemented
11C4×C11×M32C211yesmaximal, characteristic, complemented
12#10623010—21no—
13#10623008—21no—
14C2×C11×M32C2212yes—
15C2×C4×C8×C11C2211yescharacteristic
16#10622729C2211yescharacteristic
17#10622728—21no—
18#10622728C2211yescharacteristic
19#10622728C2212yes—
20#10622727—21no—
21C2×#66864C2212yes—
22C2×D176C2212yes—
23C4×Dic44C2211yescharacteristic
24#10622310—21no—
25#10622309C2211yescharacteristic
26#10622308C2211yescharacteristic
27#10622307—21no—
28C4×D88—21no—
29C4×D88C2211yescharacteristic
30C4×D88C2212yes—
31C4×#4314—21no—
32#10622296C2211yescharacteristic
33#10622295C2211yescharacteristic
34C11×#346C2211yescharacteristic
35C11×#346C2211yescharacteristic
36C4×C11×C16C2212yes—
37#10622147C2212yes—
38#10622147C2212yes—
39#10622147C2212yes—
40#10622143C2212yes—
41#10622142C2212yes—
42#10622141C2212yes—
43C2×#4339—41no—
44C22×C8×C11D411yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C42×C11D411yescharacteristic
47#66983—21no—
48#66983—22no—
49#66983—41no—
50#66982—41no—
51C4×C22⋊D11—41no—
52#66977—21no—
53C2×Dic44C2311yescharacteristic
54C2×D88—21no—
55C2×D88C2311yescharacteristic
56C2×D88C2312yes—
57C2×#4314—21no—
58#66929—41no—
59#66928—21no—
60#66928—41no—
61#66927—21no—
62C4×D44—22no—
63C4×D44—21no—
64C4×D44—41no—
65#66925—41no—
66#66923—21no—
67#66922—21no—
68C4×Dic22—21no—
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—22no—
78#66885—21no—
79#66885—22no—
80#66882—21no—
81#66882C2312yes—
82#66882C2311yescharacteristic
83#66882C2311yescharacteristic
84#66881—21no—
85#66880—21no—
86#66880—21no—
87#66864—24no—
88D176—24no—
89#33737—111nomaximal, Sylow
90C22×C4×C11D811yescharacteristic
91C22×C4×C11D811yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—41no—
94C2×C22⋊D11—42no—
95#4339—84no—
96C2×D44—22no—
97C2×D44—21no—
98C2×D44—41no—
99C2×D44—41no—
100C2×C4×D11—41no—
101C2×C4×D11—42no—
102C2×Dic22—21no—
103C2×Dic22—41no—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2×D411yescharacteristic
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2411yescharacteristic
110C42×C11D811yescharacteristic
111C42×C11D811yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C22⋊Dic11—41no—
115(C2×D11)⋊C4—41no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—42no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—41no—
121C4⋊Dic11—21no—
122C4⋊Dic11—21no—
123C4⋊Dic11—22no—
124C4⋊Dic11—41no—
125Dic11⋊C4—41no—
126Dic11⋊C4—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C4×Dic11—41no—
130Dic44—22no—
131D88—22no—
132D88—22no—
133D88—22no—
134D88—42no—
135#4314—42no—
136C11×C16—22no—
137C11×C16#4114yescomplemented
138#3169—111no—
139#3168—111no—
140#2255—111no—
141#2250—111no—
142#2244—111no—
143#2243—111no—
144#2220—112no—
145#2218—112no—
146C4×SD32—112no—
147C4×D16—112no—
148C4×M32D1111yescharacteristic, complemented
149C23×C11C2×D811yescharacteristic
150C22×D11—41no—
151C22×D11—42no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11C2×D811yescharacteristic
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C2×D811yescharacteristic
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C22×D411yescharacteristic
162C22⋊D11—84no—
163C22⋊D11—82no—
164C2×Dic11—41no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167C2×Dic11—42no—
168D44—41no—
169D44—42no—
170D44—41no—
171D44—42no—
172D44—82no—
173D44—82no—
174C4×D11—82no—
175C4×D11—84no—
176Dic22—41no—
177Dic22—41no—
178Dic22—82no—
179C8×C11—21no—
180C8×C11—21no—
181C8×C11#13512yes—
182C8×C11C2×#4112yes—
183#532—221no—
184#529—221no—
185C2×SD32—112no—
186C2×D16—112no—
187C2×M32C2×D1112yes—
188#500—111no—
189#499—111no—
190#495—111no—
191#493—111no—
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×C8C2×D1111yescharacteristic
205#367—112no—
206#366—112no—
207#358—112no—
208#357—112no—
209#357—112no—
210#357—112no—
211#346C2×D1111yescharacteristic
212#346C2×D1111yescharacteristic
213C4×C16C2×D1112yes—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11C22×D811yescharacteristic
218C2×D11—81no—
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—81no—
222C2×D11—81no—
223C2×D11—82no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—21no—
228C4×C11#50912yes—
229C4×C11#53211yescharacteristic
230C4×C11C2×#13511yescharacteristic
231Dic11—82no—
232Dic11—81no—
233Dic11—81no—
234Dic11—81no—
235C2×#41—441no—
236C2×Q16—111no—
237C2×SD16—221no—
238C2×D8—112no—
239C2×D8—111no—
240C2×D8—221no—
241C22×C8D4411yescharacteristic
242C22×C8C22×D1111yescharacteristic
243C4⋊Q8—221no—
244#127—221no—
245#126—441no—
246#125—221no—
247#124—221no—
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×C42D4411yescharacteristic
261SD32—224no—
262D16—224no—
263M32—24no—
264C2×C16C22×D1112yes—
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×C8D4411yescharacteristic
278C4×C8D4411yescharacteristic
279C4×C8C22×D1111yescharacteristic
280C4×C8C22×D1111yescharacteristic
281C2×C11—41no—
282C2×C11#316911yescharacteristic
283C2×C11C2×#50911yescharacteristic
284C2×C11#341411yescharacteristic
285D11—161no—
286D11—162no—
287#41—884no—
288C2×Q8—221no—
289C2×Q8—441no—
290C2×D4—221no—
291C2×D4—222no—
292C2×D4—441no—
293C2×D4—442no—
294C2×D4—441no—
295C2×D4—441no—
296C22×C4—441no—
297C22×C4—442no—
298C22×C4D8811yescharacteristic
299C22×C4D8811yescharacteristic
300C22×C4C2×D4411yescharacteristic
301Q16—222no—
302SD16—442no—
303D8—222no—
304D8—222no—
305D8—222no—
306D8—442no—
307C2×C8—22no—
308C2×C8—22no—
309C2×C8C2×D4411yescharacteristic
310C2×C8C2×D4411yescharacteristic
311C2×C8C2×D4411yescharacteristic
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—441no—
322C22⋊C4—441no—
323C22⋊C4—441no—
324C22⋊C4—442no—
325C22⋊C4—441no—
326C22⋊C4—442no—
327C22⋊C4—441no—
328C42—441no—
329C42D8811yescharacteristic
330C42D8811yescharacteristic
331C42C2×D4411yescharacteristic
332C42C2×D4411yescharacteristic
333C16—22no—
334C16#433914yescomplemented
335C11#3373711yescharacteristic, complemented, Sylow
336C23—441no—
337C23—442no—
338C23C2×D8811yescharacteristic
339Q8—441no—
340Q8—441no—
341Q8—882no—
342D4—441no—
343D4—442no—
344D4—442no—
345D4—441no—
346D4—882no—
347D4—882no—
348D4—884no—
349D4—882no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—41no—
354C2×C4—441no—
355C2×C4—441no—
356C2×C4—441no—
357C2×C4—442no—
358C2×C4—884no—
359C2×C4—882no—
360C2×C4C2×D8811yescharacteristic
361C2×C4C2×D8811yescharacteristic
362C2×C4C2×D8811yescharacteristic
363C2×C4C2×D8811yescharacteristic
364C2×C4C2×D8811yescharacteristic
365C2×C4C22×D4411yescharacteristic
366C8—21no—
367C8—21no—
368C8#6695712yes—
369C8C2×#433912yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—882no—
374C22—881no—
375C22—882no—
376C22—881no—
377C22—882no—
378C22—881no—
379C22C22×D8811yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—882no—
385C4—881no—
386C4—881no—
387C4—881no—
388C4#1062252112yes—
389C4#1062300811yescharacteristic
390C4C2×#6695711yescharacteristic
391C2—41no—
392C2—1762no—
393C2—1761no—
394C2#1307919511yescharacteristic
395C2C2×#1062252111yescharacteristic
396C2#1308175211yescharacteristic
subgroupG/H
centerC2×C4C2×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC4×C11×M32C2
socleC22×C11C22×D8
hypercenterC4×M32D11
hypocenterC11#33737
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. #13079195C2semidirect
2. #13079186C2semidirect
3. #13070902C2semidirect
4. #13070882C2semidirect
5. #13070858C2semidirect
6. #13070853C2semidirect
7. #13070729C2semidirect
8. #13070719C2semidirect
9. C4×#66864C2semidirect
10. C4×D176C2semidirect
11. C4×C11×M32C2semidirect
137. C11×C16#41semidirect
148. C4×M32D11semidirect
334. C16#4339semidirect
335. C11#33737semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130791862
#130709022
#130708822
#130708582
#130708532
#130707292
#130707192
C4×#668642
C4×D1762
C4×C11×M322
#3373711