Finite Group Databasebeta

← #14908837

Subgroups — #14908837

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
2C2×C4×D88C211yesmaximal, characteristic, complemented
3#13070814C211yesmaximal, characteristic, complemented
4#13070797C211yesmaximal, characteristic, complemented
5#13070774C212yesmaximal, complemented
6#13070672C212yesmaximal, complemented
7#13070547C211yesmaximal, characteristic, complemented
8#13070530C211yesmaximal, characteristic
9#13070493C212yesmaximal, complemented
10#13070482C212yesmaximal, complemented
11C11×#2163C211yesmaximal, characteristic, complemented
12C22×D88C2211yescharacteristic
13#10623010—21no—
14C2×C4×D44—21no—
15C2×C4×C8×C11C2211yescharacteristic
16#10622729C2211yescharacteristic
17#10622728C2211yescharacteristic
18#10622727—21no—
19C2×#66885—21no—
20C2×#66882C2211yescharacteristic
21C2×#66864C2212yes—
22C2×D176C2212yes—
23C4×Dic44C2211yescharacteristic, complemented
24#10622310—21no—
25#10622309C2211yescharacteristic, complemented
26C4×D88—21no—
27C4×D88—21no—
28C4×D88C2212yes—
29C4×D88C2212yes—
30C4×D88C2211yescharacteristic, complemented
31C4×#4314—21no—
32#10622296C2211yescharacteristic, complemented
33C11×C4⋊C16C2212yescomplemented
34C11×C22⋊C16C2211yescharacteristic
35C11×C22⋊C16C2211yescharacteristic
36C11×#346C2212yescomplemented
37#10622147C2212yes—
38#10622147C2212yes—
39#10622147C2212yescomplemented
40#10622143C2212yescomplemented
41#10622142C2212yescomplemented
42#10622141C2212yescomplemented
43C22×D44—21no—
44C22×C4×D11—41no—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C2×C42×C11D411yescharacteristic
48#66983—21no—
49#66982—41no—
50C4×C22⋊D11—41no—
51C2×(C2×D11)⋊C4—41no—
52C2×C4⋊Dic11—21no—
53#66977—21no—
54C2×Dic44C2311yescharacteristic
55C2×D88—21no—
56C2×D88—24no—
57C2×D88C2311yescharacteristic
58C2×D88C2312yes—
59C2×#4314—21no—
60#66929—41no—
61#66928—21no—
62C4×D44—22no—
63C4×D44—22no—
64C4×D44—21no—
65C4×D44—41no—
66C4×D44—41no—
67#66925—41no—
68#66923—21no—
69C4×Dic22—21no—
70C2×C11×C16C2312yes—
71C2×C11×C16C2312yes—
72C4×C8×C11D411yescharacteristic
73C4×C8×C11D411yescharacteristic
74C4×C8×C11C2311yescharacteristic
75C4×C8×C11C2311yescharacteristic
76#66885—22no—
77#66885—22no—
78#66885—21no—
79#66885—21no—
80#66882—21no—
81#66882C2311yescharacteristic
82#66882C2311yescharacteristic
83#66882C2312yes—
84#66881—21no—
85#66880—21no—
86#66880—21no—
87#66864—24no—
88D176—24no—
89#33674—111nomaximal, Sylow
90C23×D11—41no—
91C22×C4×C11D811yescharacteristic
92C22×C4×C11D811yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96C2×D44—24no—
97C2×D44—22no—
98C2×D44—21no—
99C2×D44—42no—
100C2×D44—41no—
101C2×C4×D11—41no—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C2×C4×D11—84no—
105C2×Dic22—21no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11C2×D411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11C2×D411yescharacteristic
111C2×C8×C11C2411yescharacteristic
112C42×C11D811yescharacteristic
113C42×C11D811yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C22⋊Dic11—41no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—42no—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—41no—
122(C2×D11)⋊C4—41no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—22no—
126C4⋊Dic11—41no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130Dic11⋊C4—41no—
131C4×Dic11—41no—
132Dic44—22no—
133D88—24no—
134D88—22no—
135D88—22no—
136D88#4114yes—
137#4314—42no—
138C11×C16—22no—
139C11×C16—22no—
140#3168—111no—
141C2×C4×D8—111no—
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#2163D1111yescharacteristic, complemented
151C23×C11C2×D811yescharacteristic
152C22×D11—44no—
153C22×D11—42no—
154C22×D11—41no—
155C22×D11—82no—
156C22×D11—82no—
157C2×C4×C11—22no—
158C2×C4×C11—21no—
159C2×C4×C11—21no—
160C2×C4×C11—41no—
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11C2×D811yescharacteristic
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C22⋊D11—82no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—82no—
173D44—24no—
174D44—44no—
175D44—41no—
176D44—42no—
177D44—41no—
178C4×D11—82no—
179C4×D11—84no—
180C4×D11—84no—
181Dic22—41no—
182Dic22—41no—
183C8×C11—21no—
184C8×C11—21no—
185C8×C11—21no—
186C8×C11C2×#4112yes—
187C22×D8—111no—
188#529—221no—
189C2×C4×D4—221no—
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—111no—
201C4×D8—112no—
202C4×D8—112no—
203C4×D8—221no—
204C4×D8—221no—
205C2×#107—111no—
206C2×#102—221no—
207C2×C4×C8C2×D1111yescharacteristic
208#367—112no—
209#366—112no—
210C4⋊C16C2×D1112yescomplemented
211#358—112no—
212#357—112no—
213#357—112no—
214#357—112no—
215C22⋊C16C2×D1111yescharacteristic
216C22⋊C16C2×D1111yescharacteristic
217#346C2×D1112yescomplemented
218C22×C11—21no—
219C22×C11—21no—
220C22×C11#50912yes—
221C22×C11C22×D811yescharacteristic
222C2×D11—44no—
223C2×D11—88no—
224C2×D11—82no—
225C2×D11—82no—
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#52511yescharacteristic
235C4×C11#57511yescharacteristic
236Dic11—81no—
237Dic11—82no—
238Dic11—81no—
239Dic11—81no—
240C22×D4—221no—
241C23×C4—441no—
242C2×Q16—111no—
243C2×SD16—221no—
244C2×D8—112no—
245C2×D8—111no—
246C2×D8—224no—
247C2×D8—221no—
248C22×C8D4411yescharacteristic
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—222no—
258C4×D4—222no—
259C4×D4—221no—
260C4×D4—441no—
261C4×D4—441no—
262C4×D4—441no—
263#117—441no—
264C2×C4⋊C4—221no—
265C2×C22⋊C4—441no—
266C2×C42D4411yescharacteristic
267SD32—224no—
268D16—224no—
269C2×C16C22×D1112yes—
270C2×C16C22×D1112yes—
271#107—111no—
272#107—111no—
273#107—112no—
274#107—221no—
275#106—221no—
276#103—221no—
277#103—221no—
278#102—222no—
279#102—222no—
280#102—221no—
281#102—221no—
282C4×C8D4411yescharacteristic
283C4×C8D4411yescharacteristic
284C4×C8C22×D1111yescharacteristic
285C4×C8C22×D1111yescharacteristic
286C2×C11—22no—
287C2×C11#310011yescharacteristic
288C2×C11C2×#50911yescharacteristic
289C2×C11#341411yescharacteristic
290D11—84no—
291D11—161no—
292C24—441no—
293C2×Q8—221no—
294C2×D4—224no—
295C2×D4—222no—
296C2×D4—221no—
297C2×D4—442no—
298C2×D4—441no—
299C2×D4—441no—
300C22×C4—441no—
301C22×C4—441no—
302C22×C4—442no—
303C22×C4—442no—
304C22×C4—884no—
305C22×C4D8811yescharacteristic
306C22×C4D8811yescharacteristic
307C22×C4C2×D4411yescharacteristic
308Q16—222no—
309SD16—442no—
310D8—114no—
311D8—224no—
312D8—222no—
313D8—222no—
314C2×C8—22no—
315C2×C8—41no—
316C2×C8C2×D4411yescharacteristic
317C2×C8C2×D4411yescharacteristic
318C2×C8C2×D4411yescharacteristic
319C2×C8C23×D1111yescharacteristic
320C4⋊C4—222no—
321C4⋊C4—221no—
322C4⋊C4—221no—
323C4⋊C4—441no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C22⋊C4—441no—
329C22⋊C4—442no—
330C22⋊C4—442no—
331C22⋊C4—441no—
332C22⋊C4—441no—
333C22⋊C4—441no—
334C22⋊C4—441no—
335C42—441no—
336C42D8811yescharacteristic
337C42D8811yescharacteristic
338C42C2×D4411yescharacteristic
339C42C2×D4411yescharacteristic
340C16—22no—
341C16—22no—
342C11#3367411yescharacteristic, complemented, Sylow
343C23—444no—
344C23—442no—
345C23—441no—
346C23—882no—
347C23—882no—
348C23C2×D8811yescharacteristic
349Q8—441no—
350Q8—441no—
351D4—224no—
352D4—444no—
353D4—442no—
354D4—441no—
355D4—441no—
356D4—882no—
357C2×C4—22no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—441no—
362C2×C4—441no—
363C2×C4—441no—
364C2×C4—442no—
365C2×C4—884no—
366C2×C4—884no—
367C2×C4—882no—
368C2×C4—882no—
369C2×C4C2×D8811yescharacteristic
370C2×C4C2×D8811yescharacteristic
371C2×C4C2×D8811yescharacteristic
372C2×C4C2×D8811yescharacteristic
373C2×C4C2×D8811yescharacteristic
374C2×C4C22×D4411yescharacteristic
375C8—21no—
376C8—21no—
377C8—21no—
378C8#41×D1112yes—
379C22—21no—
380C22—21no—
381C22—444no—
382C22—888no—
383C22—882no—
384C22—882no—
385C22—881no—
386C22—881no—
387C22—881no—
388C22#1062252112yes—
389C22C22×D8811yescharacteristic
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—21no—
395C4—881no—
396C4—882no—
397C4—881no—
398C4—881no—
399C4#1062305511yescharacteristic
400C4#1062327911yescharacteristic
401C2—22no—
402C2—884no—
403C2—1761no—
404C2#1307861711yescharacteristic
405C2C2×#1062252111yescharacteristic
406C2#1308175211yescharacteristic
subgroupG/H
centerC22C22×D88
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2163C2
socleC22×C11C22×D8
prime radical#13070530C2
hypercenter#2163D11
hypocenterC11#33674
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ #2163

Complements

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

NH ≅ G/Ntype
1. #13079186C2semidirect
2. C2×C4×D88C2semidirect
3. #13070814C2semidirect
4. #13070797C2semidirect
5. #13070774C2semidirect
6. #13070672C2semidirect
7. #13070547C2semidirect
9. #13070493C2semidirect
10. #13070482C2semidirect
11. C11×#2163C2semidirect
23. C4×Dic44C22semidirect
25. #10622309C22semidirect
30. C4×D88C22semidirect
32. #10622296C22semidirect
33. C11×C4⋊C16C22semidirect
36. C11×#346C22semidirect
39. #10622147C22semidirect
40. #10622143C22semidirect
41. #10622142C22semidirect
42. #10622141C22semidirect
150. #2163D11semidirect
210. C4⋊C16C2×D11semidirect
217. #346C2×D11semidirect
342. C11#33674semidirect

Maximal subgroups

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

subgroupindex
#130791862
C2×C4×D882
#130708142
#130707972
#130707742
#130706722
#130705472
#130705302
#130704932
#130704822
C11×#21632
#3367411