Finite Group Databasebeta

← #14907116

Subgroups — #14907116

Order 2816.

696 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077492C211yesmaximal, characteristic, complemented
2#13077468C211yesmaximal, characteristic, complemented
3#13070492C212yesmaximal, complemented
4#13070481C212yesmaximal, complemented
5SD32×Dic11C212yesmaximal, complemented
6D16×Dic11C212yesmaximal, complemented
7#13070404C211yesmaximal, characteristic, complemented
8#13070323C211yesmaximal, characteristic, complemented
9C2×#10622200C211yesmaximal, characteristic, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C2×C11×#509C211yesmaximal, characteristic
12C2×C11×#135C2211yescharacteristic
13C22×C11×D8C2211yescharacteristic
14#10623358—21no—
15#10623329—21no—
16C11×#509C418yescomplemented
17C2×C11×SD32C2212yes—
18C2×C11×D16C2212yes—
19C2×C11×M32C2211yescharacteristic
20#10622845—21no—
21#10622828—21no—
22Q16×Dic11C2212yescomplemented
23#10622777—22no—
24#10622765—22no—
25D8×Dic11C2212yes—
26D8×Dic11C2212yes—
27D8×Dic11C2212yescomplemented
28#10622719C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30#10622714C2211yescharacteristic
31C22×C11⋊C16C2211yescharacteristic
32#10622202C2211yescharacteristic, complemented
33#10622202C2211yescharacteristic, complemented
34#10622200C2212yes—
35#10622200C2212yes—
36#10622200C2211yescharacteristic, complemented
37#10622200C2211yescharacteristic, complemented
38#10622143C2212yescomplemented
39#10622142C2212yescomplemented
40#10622140C2212yescomplemented
41C16×Dic11C2212yescomplemented
42C2×C11×#41—21no—
43C22×D4×C11—21no—
44C11×#135—22no—
45C11×#135C2×C414yescomplemented
46C2×C11×Q16C2311yescharacteristic
47C2×C11×SD16—21no—
48C2×C11×D8—21no—
49C2×C11×D8—22no—
50C2×C11×D8C2×C414yescomplemented
51C2×C11×D8C2311yescharacteristic
52C2×C11×D8C2312yes—
53C22×C8×C11C2311yescharacteristic
54C2×C22⋊Dic11—42no—
55Q8×Dic11—22no—
56D4×Dic11—22no—
57D4×Dic11—22no—
58D4×Dic11—22no—
59D4×Dic11—42no—
60D4×Dic11—41no—
61D4×Dic11—41no—
62#66979—21no—
63#66979—41no—
64#66979D411yescharacteristic
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—41no—
67C2×#4318D411yescharacteristic
68C11×SD32C2×C418yescomplemented
69C11×D16C2×C418yescomplemented
70C11×M32C2×C414yescomplemented
71C2×C11×C16C2312yes—
72#66899—22no—
73#66896—22no—
74#66896—22no—
75#66896—22no—
76#66882—21no—
77#66882C2311yescharacteristic
78#66882C2311yescharacteristic
79#66882C2312yes—
80#66881—21no—
81#66879D412yes—
82C8×Dic11C2312yes—
83C2×C11⋊C16—22no—
84C2×C11⋊C16C2311yescharacteristic
85C2×C11⋊C16C2311yescharacteristic
86#33454—111nomaximal, Sylow
87C24×C11—41no—
88C11×#41—24no—
89C11×#41—42no—
90C2×Q8×C11—21no—
91C2×D4×C11—24no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—42no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×Dic11—42no—
100C22×Dic11—42no—
101C22×Dic11—42no—
102C22×Dic11—41no—
103C11×Q16—21no—
104C11×Q16C22×C412yes—
105C11×SD16—24no—
106C11×D8—24no—
107C11×D8—22no—
108C11×D8—21no—
109C11×D8C22×C412yes—
110C11×D8C22×C414yes—
111C2×C8×C11C22×C412yes—
112C2×C8×C11C2×D411yescharacteristic
113C2×C8×C11#4112yes—
114C2×C8×C11C2411yescharacteristic
115C22⋊Dic11—42no—
116C22⋊Dic11—42no—
117C22⋊Dic11—42no—
118C22⋊Dic11—41no—
119C22⋊Dic11D812yes—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C4⋊Dic11—22no—
123C4⋊Dic11—42no—
124C4⋊Dic11—41no—
125C4⋊Dic11D811yescharacteristic
126C4⋊Dic11D811yescharacteristic
127C4×Dic11—42no—
128C4×Dic11—41no—
129C4×Dic11C2×D412yes—
130#4318—22no—
131C2×C11⋊C8C2×D412yes—
132C11×C16C22×C414yes—
133C11⋊C16—21no—
134C11⋊C16—21no—
135C2×#509D1111yescharacteristic
136#2951—111no—
137#2948—111no—
138#2177—112no—
139#2175—112no—
140C4×SD32—112no—
141C4×D16—112no—
142#2159—111no—
143#2138—111no—
144C2×#357—111no—
145#2108—111no—
146C23×C11—41no—
147C23×C11—42no—
148C23×C11—44no—
149C23×C11—161no—
150C23×C11—161no—
151C23×C11C2×D811yescharacteristic
152Q8×C11—22no—
153Q8×C11—41no—
154D4×C11—24no—
155D4×C11—22no—
156D4×C11—44no—
157D4×C11—42no—
158D4×C11—41no—
159D4×C11—44no—
160C2×C4×C11—41no—
161C2×C4×C11—44no—
162C2×C4×C11C4×D412yes—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11#13512yes—
165C2×C4×C11C22×D411yescharacteristic
166C2×Dic11—42no—
167C2×Dic11—41no—
168C2×Dic11—41no—
169C2×Dic11—162no—
170C2×Dic11—162no—
171C2×Dic11—162no—
172C2×Dic11—161no—
173C2×Dic11C2×D812yes—
174C2×Dic11C2×D812yes—
175C8×C11C4×D412yes—
176C8×C11C23×C411yescharacteristic
177C8×C11C2×#4111yescharacteristic
178C11⋊C8—22no—
179C2×#135C2×D1111yescharacteristic
180C22×D8C2×D1111yescharacteristic
181#520—221no—
182#518—221no—
183#509Dic1118yescomplemented
184C2×SD32C2×D1112yes—
185C2×D16C2×D1112yes—
186C2×M32C2×D1111yescharacteristic
187C22×C16—111no—
188#442—222no—
189#440—222no—
190C4×Q16—112no—
191C4×D8—112no—
192C4×D8—112no—
193C4×D8—112no—
194#427—111no—
195C2×#107—111no—
196#418—221no—
197#417—221no—
198#405—111no—
199#367—112no—
200#366—112no—
201#358—111no—
202#358—111no—
203#357—112no—
204#357—112no—
205#357—111no—
206#357—111no—
207#346—112no—
208C4×C16—112no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—42no—
212C22×C11—44no—
213C22×C11—82no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11—82no—
217C22×C11—164no—
218C22×C11C4×D812yes—
219C22×C11C22×D811yescharacteristic
220C4×C11—42no—
221C4×C11C4×D812yes—
222C4×C11C2×C4×D411yescharacteristic
223C4×C11C2×#13511yescharacteristic
224Dic11—22no—
225Dic11—22no—
226Dic11—82no—
227Dic11—81no—
228Dic11—81no—
229C2×#41—21no—
230C22×D4—21no—
231#135—22no—
232#135C2×Dic1114yescomplemented
233C2×Q16C22×D1111yescharacteristic
234C2×SD16—21no—
235C2×D8—21no—
236C2×D8—22no—
237C2×D8C2×Dic1114yescomplemented
238C2×D8C22×D1112yes—
239C2×D8C22×D1111yescharacteristic
240C2×M16—111no—
241C22×C8C22×D1111yescharacteristic
242C4×Q8—222no—
243C4×D4—222no—
244C4×D4—222no—
245C4×D4—222no—
246C4×D4—442no—
247C4×D4—441no—
248C4×D4—441no—
249#117—111no—
250#117—221no—
251#117—441no—
252C2×C4⋊C4—221no—
253C2×C4⋊C4—441no—
254C2×C22⋊C4—442no—
255SD32C2×Dic1118yescomplemented
256D16C2×Dic1118yescomplemented
257M32C2×Dic1114yescomplemented
258C2×C16—111no—
259C2×C16—111no—
260C2×C16—222no—
261C2×C16C22×D1112yes—
262#107—112no—
263#107—111no—
264#107—111no—
265#107—221no—
266#106—221no—
267#103—222no—
268#102—222no—
269#102—222no—
270#102—222no—
271#97—112no—
272C4×C8—112no—
273C2×C11—22no—
274C2×C11—82no—
275C2×C11—84no—
276C2×C11C2×C4×D811yescharacteristic
277C2×C11#341511yescharacteristic
278C2×C11#341611yescharacteristic
279C24—41no—
280#41—24no—
281#41—42no—
282C2×Q8—21no—
283C2×D4—24no—
284C2×D4—22no—
285C2×D4—21no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—42no—
289C22×C4—41no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4—441no—
294C22×C4D4×D1111yescharacteristic
295Q16—21no—
296Q16C22×Dic1112yes—
297SD16—24no—
298D8—24no—
299D8—22no—
300D8—21no—
301D8C22×Dic1112yes—
302D8C22×Dic1114yes—
303M16—222no—
304C2×C8—112no—
305C2×C8D4×D1111yescharacteristic
306C2×C8#434112yes—
307C2×C8C22×Dic1112yes—
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—111no—
310C4⋊C4—111no—
311C4⋊C4—221no—
312C4⋊C4—221no—
313C4⋊C4—222no—
314C4⋊C4—442no—
315C4⋊C4—441no—
316C22⋊C4—112no—
317C22⋊C4—442no—
318C22⋊C4—442no—
319C22⋊C4—442no—
320C22⋊C4—441no—
321C42—112no—
322C42—442no—
323C42—441no—
324C16—221no—
325C16—221no—
326C16C22×Dic1114yes—
327C11#3345411yescharacteristic, complemented, Sylow
328C23—41no—
329C23—42no—
330C23—44no—
331C23—161no—
332C23—161no—
333C23D8×D1111yescharacteristic
334Q8—22no—
335Q8—41no—
336D4—24no—
337D4—22no—
338D4—44no—
339D4—44no—
340D4—42no—
341D4—41no—
342C2×C4—41no—
343C2×C4—44no—
344C2×C4—112no—
345C2×C4—112no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4—442no—
349C2×C4—1762no—
350C2×C4—1762no—
351C2×C4—1762no—
352C2×C4—1761no—
353C2×C4D8×D1111yescharacteristic
354C2×C4#6696512yes—
355C2×C4D4×Dic1112yes—
356C2×C4C2×D4×D1111yescharacteristic
357C8—222no—
358C8D4×Dic1112yes—
359C8C2×#434111yescharacteristic
360C8C23×Dic1111yescharacteristic
361C22—21no—
362C22—21no—
363C22—42no—
364C22—44no—
365C22—81no—
366C22—82no—
367C22—82no—
368C22—81no—
369C22—164no—
370C22D8×Dic1112yes—
371C22C2×D8×D1111yescharacteristic
372C4—42no—
373C4—222no—
374C4—222no—
375C4—881no—
376C4—882no—
377C4—881no—
378C4D8×Dic1112yes—
379C4C2×#6696511yescharacteristic
380C4C2×D4×Dic1111yescharacteristic
381C2—22no—
382C2—84no—
383C2—82no—
384C2C2×D8×Dic1111yescharacteristic
385C2#1308175611yescharacteristic
386C2#1308176211yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
Fitting, prime radicalC2×C11×#509C2
socleC22×C11C22×D8
cosocleC2×C8×C11C24
hypercenterC2×#509D11
hypocenterC11#33454
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #13077492C2semidirect
2. #13077468C2semidirect
3. #13070492C2semidirect
4. #13070481C2semidirect
5. SD32×Dic11C2semidirect
6. D16×Dic11C2semidirect
7. #13070404C2semidirect
8. #13070323C2semidirect
9. C2×#10622200C2semidirect
10. #13070215C2semidirect
16. C11×#509C4semidirect
22. Q16×Dic11C22semidirect
27. D8×Dic11C22semidirect
32. #10622202C22semidirect
33. #10622202C22semidirect
36. #10622200C22semidirect
37. #10622200C22semidirect
38. #10622143C22semidirect
39. #10622142C22semidirect
40. #10622140C22semidirect
41. C16×Dic11C22semidirect
45. C11×#135C2×C4semidirect
50. C2×C11×D8C2×C4semidirect
68. C11×SD32C2×C4semidirect
69. C11×D16C2×C4semidirect
70. C11×M32C2×C4semidirect
183. #509Dic11semidirect
232. #135C2×Dic11semidirect
237. C2×D8C2×Dic11semidirect
255. SD32C2×Dic11semidirect
256. D16C2×Dic11semidirect
257. M32C2×Dic11semidirect
327. C11#33454semidirect

Maximal subgroups

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

subgroupindex
#130774922
#130774682
#130704922
#130704812
SD32×Dic112
D16×Dic112
#130704042
#130703232
C2×#106222002
#130702152
C2×C11×#5092
#3345411