Finite Group Databasebeta

← #14908835

Subgroups — #14908835

Order 2816.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079186C211yesmaximal, characteristic, complemented
2#13070813C211yesmaximal, characteristic, complemented
3#13070796C211yesmaximal, characteristic, complemented
4#13070773C212yesmaximal, complemented
5#13070671C212yesmaximal, complemented
6#13070545C211yesmaximal, characteristic, complemented
7#13070528C211yesmaximal, characteristic
8#13070490C212yesmaximal, complemented
9#13070480C212yesmaximal, complemented
10#13070419C211yesmaximal, characteristic, complemented
11C2×C4×C11×D8C211yesmaximal, characteristic, complemented
12C22×C11×D8C2211yescharacteristic
13C2×C4×D4×C11—21no—
14#10623010—21no—
15C4×C11×D8—21no—
16C4×C11×D8—21no—
17C4×C11×D8C2212yes—
18C4×C11×D8C2212yes—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#102—21no—
21C2×C4×C8×C11C2211yescharacteristic
22C2×#66891C2212yes—
23C2×#66890C2212yes—
24#10622729C2211yescharacteristic
25#10622728C2211yescharacteristic
26#10622727—21no—
27C4×Dic44C2211yescharacteristic, complemented
28#10622310—21no—
29#10622309C2211yescharacteristic, complemented
30C4×D88C2211yescharacteristic, complemented
31C4×#4314—21no—
32#10622296C2211yescharacteristic, complemented
33#10622200C2212yes—
34#10622200C2212yes—
35C22⋊(C11⋊C16)C2211yescharacteristic
36C22⋊(C11⋊C16)C2211yescharacteristic
37#10622130C2212yescomplemented
38#10622129C2212yescomplemented
39#10622128C2212yescomplemented
40#10622127C2212yescomplemented
41C4⋊(C11⋊C16)C2212yescomplemented
42#10622099C2212yescomplemented
43C22×D4×C11—21no—
44C23×C4×C11—41no—
45C2×C11×D8—24no—
46C2×C11×D8—21no—
47C2×C11×D8C2312yes—
48C22×C8×C11D411yescharacteristic
49C22×C8×C11C2311yescharacteristic
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C4×D4×C11—41no—
53C4×D4×C11—41no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C22⋊C4—41no—
56C2×C42×C11D411yescharacteristic
57#66983—21no—
58#66982—41no—
59C4×C22⋊D11—41no—
60#66977—21no—
61C2×Dic44C2311yescharacteristic
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64#66929—41no—
65#66928—21no—
66C4×D44—21no—
67#66925—41no—
68#66923—21no—
69C4×Dic22—21no—
70C11×#107—21no—
71C11×#107C2312yes—
72C11×#102—22no—
73C11×#102—22no—
74C4×C8×C11D411yescharacteristic
75C4×C8×C11D411yescharacteristic
76C4×C8×C11C2311yescharacteristic
77C4×C8×C11C2311yescharacteristic
78#66891—24no—
79#66890—24no—
80#66885—21no—
81#66885—21no—
82#66882C2311yescharacteristic
83#66882C2311yescharacteristic
84#66881—21no—
85#66880—21no—
86#66880—21no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33674—111nomaximal, Sylow
90C24×C11—41no—
91C2×D4×C11—24no—
92C2×D4×C11—22no—
93C2×D4×C11—42no—
94C2×D4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—84no—
99C22×C4×C11D811yescharacteristic
100C22×C4×C11D811yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C2×C22⋊D11—41no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C11×D8—24no—
107C11×D8—22no—
108C11×D8#4114yes—
109C2×C8×C11—22no—
110C2×C8×C11—41no—
111C2×C8×C11C2×D411yescharacteristic
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11C2×D411yescharacteristic
114C2×C8×C11C2411yescharacteristic
115C11×C4⋊C4—22no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—42no—
118C11×C22⋊C4—42no—
119C42×C11D811yescharacteristic
120C42×C11D811yescharacteristic
121C42×C11C2×D411yescharacteristic
122C42×C11C2×D411yescharacteristic
123C22⋊Dic11—41no—
124(C2×D11)⋊C4—41no—
125(C2×D11)⋊C4—41no—
126(C2×D11)⋊C4—41no—
127(C2×D11)⋊C4—41no—
128C4⋊Dic11—21no—
129C4⋊Dic11—21no—
130Dic11⋊C4—41no—
131Dic11⋊C4—41no—
132Dic11⋊C4—41no—
133Dic11⋊C4—41no—
134C4×Dic11—41no—
135Dic44—22no—
136D88—22no—
137#4314—42no—
138C11⋊C16—22no—
139C11⋊C16—22no—
140#3168—111no—
141C2×C4×D8D1111yescharacteristic, complemented
142#2235—111no—
143#2232—111no—
144#2228—112no—
145#2210—112no—
146#2187—111no—
147#2184—111no—
148#2177—112no—
149#2175—112no—
150#2163—111no—
151C23×C11—44no—
152C23×C11—42no—
153C23×C11—82no—
154C23×C11—82no—
155C23×C11C2×D811yescharacteristic
156C22×D11—41no—
157D4×C11—24no—
158D4×C11—44no—
159D4×C11—42no—
160C2×C4×C11—22no—
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—84no—
166C2×C4×C11—84no—
167C2×C4×C11—82no—
168C2×C4×C11C2×D811yescharacteristic
169C2×C4×C11C2×D811yescharacteristic
170C2×C4×C11C2×D811yescharacteristic
171C2×C4×C11C2×D811yescharacteristic
172C2×C4×C11C2×D811yescharacteristic
173C2×C4×C11C22×D411yescharacteristic
174C22⋊D11—82no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178D44—41no—
179D44—41no—
180C4×D11—82no—
181Dic22—41no—
182Dic22—41no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11C2×#4112yes—
187C22×D8C2×D1111yescharacteristic
188#529—221no—
189C2×C4×D4—21no—
190C2×SD32—112no—
191C2×D16—112no—
192#499—111no—
193#495—111no—
194#488—221no—
195#467—111no—
196#466—111no—
197#465—221no—
198C4×Q16—111no—
199C4×SD16—221no—
200C4×D8—21no—
201C4×D8—21no—
202C4×D8—111no—
203C4×D8C2×D1112yes—
204C4×D8C2×D1112yes—
205C2×#107C2×D1111yescharacteristic
206C2×#102—21no—
207C2×C4×C8C2×D1111yescharacteristic
208#367—112no—
209#366—112no—
210C4⋊C16—112no—
211#358—112no—
212#357—112no—
213#357—112no—
214#357—112no—
215C22⋊C16—111no—
216C22⋊C16—111no—
217#346—112no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—44no—
221C22×C11—88no—
222C22×C11—82no—
223C22×C11—82no—
224C22×C11#50912yes—
225C22×C11C22×D811yescharacteristic
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C4×C11—21no—
230C4×C11—21no—
231C4×C11—21no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—82no—
235C4×C11#52511yescharacteristic
236C4×C11#57511yescharacteristic
237Dic11—81no—
238Dic11—81no—
239Dic11—81no—
240C22×D4—21no—
241C23×C4—41no—
242C2×Q16—111no—
243C2×SD16—221no—
244C2×D8—24no—
245C2×D8—21no—
246C2×D8—111no—
247C2×D8C22×D1112yes—
248C22×C8C22⋊D1111yescharacteristic
249C22×C8C22×D1111yescharacteristic
250#126—441no—
251#125—221no—
252#124—221no—
253#123—441no—
254C22⋊Q8—221no—
255#121—221no—
256C4×Q8—221no—
257C4×D4—22no—
258C4×D4—22no—
259C4×D4—41no—
260C4×D4—41no—
261C4×D4—221no—
262C4×D4—441no—
263#117—441no—
264C2×C4⋊C4—21no—
265C2×C22⋊C4—41no—
266C2×C42C22⋊D1111yescharacteristic
267SD32—224no—
268D16—224no—
269C2×C16—112no—
270C2×C16—112no—
271#107—21no—
272#107—111no—
273#107—111no—
274#107C22×D1112yes—
275#106—221no—
276#103—221no—
277#103—221no—
278#102—22no—
279#102—22no—
280#102—221no—
281#102—221no—
282C4×C8C22⋊D1111yescharacteristic
283C4×C8C22⋊D1111yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C4×C8C22×D1111yescharacteristic
286C2×C11—22no—
287C2×C11—84no—
288C2×C11#310011yescharacteristic
289C2×C11C2×#50911yescharacteristic
290C2×C11#341411yescharacteristic
291D11—161no—
292C24—41no—
293C2×Q8—221no—
294C2×D4—24no—
295C2×D4—22no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—221no—
299C2×D4—441no—
300C22×C4—41no—
301C22×C4—42no—
302C22×C4—42no—
303C22×C4—84no—
304C22×C4—441no—
305C22×C4#432311yescharacteristic
306C22×C4#432311yescharacteristic
307C22×C4C2×C22⋊D1111yescharacteristic
308Q16—222no—
309SD16—442no—
310D8—24no—
311D8—22no—
312D8—222no—
313D8#433914yes—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8C2×C22⋊D1111yescharacteristic
317C2×C8C2×C22⋊D1111yescharacteristic
318C2×C8C2×C22⋊D1111yescharacteristic
319C2×C8C23×D1111yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—42no—
329C22⋊C4—42no—
330C22⋊C4—441no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42—441no—
336C42#432311yescharacteristic
337C42#432311yescharacteristic
338C42C2×C22⋊D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C16—222no—
341C16—222no—
342C11#3367411yescharacteristic, complemented, Sylow
343C23—44no—
344C23—42no—
345C23—82no—
346C23—82no—
347C23—441no—
348C23C2×#432311yescharacteristic
349Q8—441no—
350Q8—441no—
351D4—24no—
352D4—44no—
353D4—42no—
354D4—441no—
355D4—441no—
356D4—882no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—84no—
363C2×C4—84no—
364C2×C4—82no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4—441no—
368C2×C4—882no—
369C2×C4C2×#432311yescharacteristic
370C2×C4C2×#432311yescharacteristic
371C2×C4C2×#432311yescharacteristic
372C2×C4C2×#432311yescharacteristic
373C2×C4C2×#432311yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8C2×#433912yes—
379C22—21no—
380C22—21no—
381C22—44no—
382C22—88no—
383C22—82no—
384C22—82no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22#1062276012yes—
389C22C22×#432311yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—82no—
396C4—881no—
397C4—881no—
398C4—881no—
399C4#1062332211yescharacteristic
400C4#1062335311yescharacteristic
401C2—22no—
402C2—84no—
403C2—1761no—
404C2#1307861611yescharacteristic
405C2C2×#1062276011yescharacteristic
406C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C4×C11×D8C2
socleC22×C11C22×D8
prime radical#13070528C2
hypercenterC2×C4×D8D11
hypocenterC11#33674
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. #13070813C2semidirect
3. #13070796C2semidirect
4. #13070773C2semidirect
5. #13070671C2semidirect
6. #13070545C2semidirect
8. #13070490C2semidirect
9. #13070480C2semidirect
10. #13070419C2semidirect
11. C2×C4×C11×D8C2semidirect
27. C4×Dic44C22semidirect
29. #10622309C22semidirect
30. C4×D88C22semidirect
32. #10622296C22semidirect
37. #10622130C22semidirect
38. #10622129C22semidirect
39. #10622128C22semidirect
40. #10622127C22semidirect
41. C4⋊(C11⋊C16)C22semidirect
42. #10622099C22semidirect
141. C2×C4×D8D11semidirect
342. C11#33674semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130708132
#130707962
#130707732
#130706712
#130705452
#130705282
#130704902
#130704802
#130704192
C2×C4×C11×D82
#3367411