Finite Group Databasebeta

← #14907113

Subgroups — #14907113

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
1C2×#10622521C211yesmaximal, characteristic
2#13077490C211yesmaximal, characteristic, complemented
3#13077467C211yesmaximal, characteristic, complemented
4#13070491C212yesmaximal, complemented
5#13070479C212yesmaximal, complemented
6#13070467C212yesmaximal, complemented
7#13070462C212yesmaximal, complemented
8#13070321C211yesmaximal, characteristic, complemented
9C2×#10622129C211yesmaximal, characteristic, complemented
10#13070215C211yesmaximal, characteristic, complemented
11C11×#2159C211yesmaximal, characteristic, complemented
12C2×#66957C2211yescharacteristic
13C22×D88C2211yescharacteristic
14#10623052—21no—
15#10623035—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19#10622714C2211yescharacteristic
20C22×C11⋊C16C2211yescharacteristic
21#10622614—21no—
22#10622579—21no—
23#10622521C418yescomplemented
24C2×#66864C2212yes—
25C2×D176C2212yes—
26#10622502—22no—
27#10622486C2212yescomplemented
28#10622485C2212yes—
29#10622485C2212yes—
30#10622485C2212yescomplemented
31#10622482—22no—
32C11×#367C2212yescomplemented
33C11×#366C2212yescomplemented
34#10622140C2212yescomplemented
35C16×Dic11C2212yescomplemented
36#10622130C2211yescharacteristic, complemented
37#10622130C2211yescharacteristic, complemented
38#10622129C2212yes—
39#10622129C2212yes—
40#10622129C2211yescharacteristic, complemented
41#10622129C2211yescharacteristic, complemented
42C2×#4339—21no—
43C22×D44—21no—
44C22×C8×C11C2311yescharacteristic
45C11×#117—21no—
46C2×C11×C4⋊C4—21no—
47C4×C22⋊D11—42no—
48#66979D411yescharacteristic
49C2×#4318D411yescharacteristic
50C2×Dic44C2311yescharacteristic
51#66957—22no—
52#66957C2×C414yescomplemented
53C2×D88—21no—
54C2×D88—22no—
55C2×D88C2×C414yescomplemented
56C2×D88C2312yes—
57C2×D88C2311yescharacteristic
58C2×#4314—21no—
59#66946—22no—
60#66946—22no—
61#66946—22no—
62#66945—41no—
63C4⋊C4×D11—41no—
64#66940—22no—
65C22⋊C4×D11—42no—
66C4×D44—41no—
67C4×D44—41no—
68C11×M32C2×C414yescomplemented
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2311yescharacteristic
72C11×#107C2311yescharacteristic
73C11×#107C2312yes—
74C11×#106—21no—
75#66879D412yes—
76C8×Dic11C2312yes—
77C2×C11⋊C16—22no—
78C2×C11⋊C16C2311yescharacteristic
79C2×C11⋊C16C2311yescharacteristic
80#66874—22no—
81#66873—22no—
82#66873—22no—
83#66873—22no—
84#66864C2×C418yescomplemented
85D176C2×C418yescomplemented
86#33454—111nomaximal, Sylow
87C23×D11—41no—
88C22×C4×C11—41no—
89C22×C4×C11C2×D411yescharacteristic
90C2×C22⋊D11—41no—
91#4339—24no—
92#4339—42no—
93C2×D44—24no—
94C2×D44—21no—
95C2×D44—22no—
96C2×D44—41no—
97C2×D44—42no—
98C2×C4×D11—42no—
99C2×C4×D11—42no—
100C2×C4×D11—42no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×C8×C11C22×C412yes—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11#4112yes—
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—21no—
108C11×C4⋊C4—21no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—41no—
111C11×C22⋊C4—41no—
112C42×C11—41no—
113C22⋊Dic11D812yes—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117C4⋊Dic11D811yescharacteristic
118C4⋊Dic11D811yescharacteristic
119Dic11⋊C4—42no—
120C4×Dic11—42no—
121C4×Dic11C2×D412yes—
122#4318—22no—
123C2×C11⋊C8C2×D412yes—
124Dic44—21no—
125Dic44C22×C412yes—
126D88—24no—
127D88—22no—
128D88—21no—
129D88C22×C412yes—
130D88C22×C414yes—
131#4314—24no—
132C11×C16C22×C414yes—
133C11⋊C16—21no—
134C11⋊C16—21no—
135C2×#509—111no—
136#2951—111no—
137#2948—111no—
138#2177—112no—
139#2175—112no—
140C4×SD32—112no—
141C4×D16—112no—
142#2159D1111yescharacteristic, complemented
143#2138—111no—
144C2×#357—111no—
145#2108—111no—
146C23×C11C2×D811yescharacteristic
147C22×D11—41no—
148C22×D11—42no—
149C22×D11—44no—
150C22×D11—161no—
151C22×D11—161no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—161no—
156C2×C4×C11C4×D412yes—
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11#13512yes—
159C2×C4×C11C22×D411yescharacteristic
160C22⋊D11—44no—
161C2×Dic11—41no—
162C2×Dic11C2×D812yes—
163C2×Dic11C2×D812yes—
164D44—22no—
165D44—24no—
166D44—42no—
167D44—41no—
168D44—44no—
169C4×D11—44no—
170C4×D11—162no—
171C4×D11—162no—
172C4×D11—162no—
173Dic22—22no—
174Dic22—41no—
175C8×C11C4×D412yes—
176C8×C11C23×C411yescharacteristic
177C8×C11C2×#4111yescharacteristic
178C11⋊C8—22no—
179C2×#135—111no—
180C22×D8—111no—
181#520—221no—
182#518—221no—
183#509—118no—
184C2×SD32—112no—
185C2×D16—112no—
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#427C2×D1111yescharacteristic
195C2×#107C2×D1111yescharacteristic
196#418—221no—
197#417—221no—
198#405—111no—
199#367C2×D1112yescomplemented
200#366C2×D1112yescomplemented
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×C11C4×D812yes—
212C22×C11C22×D811yescharacteristic
213C2×D11—44no—
214C2×D11—42no—
215C2×D11—82no—
216C2×D11—81no—
217C2×D11—81no—
218C2×D11—82no—
219C2×D11—164no—
220C4×C11—82no—
221C4×C11—81no—
222C4×C11—81no—
223C4×C11C4×D812yes—
224C4×C11C2×C4×D411yescharacteristic
225C4×C11C2×#13511yescharacteristic
226Dic11—22no—
227Dic11—22no—
228Dic11—42no—
229C2×#41—221no—
230C22×D4—221no—
231#135—114no—
232#135—222no—
233C2×Q16—111no—
234C2×SD16—221no—
235C2×D8—114no—
236C2×D8—112no—
237C2×D8—111no—
238C2×D8—221no—
239C2×D8—222no—
240C2×M16—111no—
241C22×C8C22×D1111yescharacteristic
242C4×Q8—222no—
243C4×D4—222no—
244C4×D4—222no—
245C4×D4—222no—
246C4×D4—441no—
247C4×D4—441no—
248C4×D4—442no—
249#117—21no—
250#117—111no—
251#117—441no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—441no—
254C2×C22⋊C4—442no—
255SD32—118no—
256D16—118no—
257M32C4×D1114yescomplemented
258C2×C16—111no—
259C2×C16—111no—
260C2×C16—222no—
261C2×C16C22×D1112yes—
262#107—21no—
263#107C22×D1112yes—
264#107C22×D1111yescharacteristic
265#107C22×D1111yescharacteristic
266#106—21no—
267#103—222no—
268#102—222no—
269#102—222no—
270#102—222no—
271#97—112no—
272C4×C8—112no—
273C2×C11—22no—
274C2×C11C2×C4×D811yescharacteristic
275C2×C11#341511yescharacteristic
276C2×C11#341611yescharacteristic
277D11—82no—
278D11—84no—
279C24—441no—
280#41—224no—
281#41—442no—
282C2×Q8—221no—
283C2×D4—224no—
284C2×D4—222no—
285C2×D4—221no—
286C2×D4—441no—
287C2×D4—441no—
288C2×D4—442no—
289C22×C4—41no—
290C22×C4—442no—
291C22×C4—442no—
292C22×C4—442no—
293C22×C4—441no—
294C22×C4D4×D1111yescharacteristic
295Q16—112no—
296Q16—221no—
297SD16—224no—
298D8—112no—
299D8—114no—
300D8—224no—
301D8—222no—
302D8—221no—
303M16—222no—
304C2×C8—112no—
305C2×C8C2×C4×D1112yes—
306C2×C8D4×D1111yescharacteristic
307C2×C8#434312yes—
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—22no—
312C4⋊C4—41no—
313C4⋊C4—111no—
314C4⋊C4—111no—
315C4⋊C4—442no—
316C22⋊C4—41no—
317C22⋊C4—112no—
318C22⋊C4—442no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C42—41no—
322C42—112no—
323C42—442no—
324C16—221no—
325C16—221no—
326C16C2×C4×D1114yes—
327C11#3345411yescharacteristic, complemented, Sylow
328C23—441no—
329C23—442no—
330C23—444no—
331C23—1761no—
332C23—1761no—
333C23D8×D1111yescharacteristic
334Q8—222no—
335Q8—441no—
336D4—224no—
337D4—222no—
338D4—444no—
339D4—444no—
340D4—442no—
341D4—441no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—42no—
345C2×C4—112no—
346C2×C4—112no—
347C2×C4—161no—
348C2×C4—441no—
349C2×C4—444no—
350C2×C4—1762no—
351C2×C4—1762no—
352C2×C4—1762no—
353C2×C4#6694612yes—
354C2×C4D8×D1111yescharacteristic
355C2×C4#6697212yes—
356C2×C4C2×D4×D1111yescharacteristic
357C8—222no—
358C8#6694612yes—
359C8C22×C4×D1111yescharacteristic
360C8C2×#434311yescharacteristic
361C22—21no—
362C22—21no—
363C22—442no—
364C22—444no—
365C22—881no—
366C22—882no—
367C22—882no—
368C22—881no—
369C22—1764no—
370C22#1062248512yes—
371C22C2×D8×D1111yescharacteristic
372C4—82no—
373C4—81no—
374C4—81no—
375C4—222no—
376C4—222no—
377C4—442no—
378C4#1062248512yes—
379C4C2×#6694611yescharacteristic
380C4C2×#6697211yescharacteristic
381C2—22no—
382C2—884no—
383C2—882no—
384C2C2×#1062248511yescharacteristic
385C2#1308175611yescharacteristic
386C2#1308176111yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2159C2
socleC22×C11C22×D8
prime radicalC2×#10622521C2
cosocleC2×C8×C11C24
hypercenter#2159D11
hypocenterC11#33454
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2159

Complements

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

NH ≅ G/Ntype
2. #13077490C2semidirect
3. #13077467C2semidirect
4. #13070491C2semidirect
5. #13070479C2semidirect
6. #13070467C2semidirect
7. #13070462C2semidirect
8. #13070321C2semidirect
9. C2×#10622129C2semidirect
10. #13070215C2semidirect
11. C11×#2159C2semidirect
23. #10622521C4semidirect
27. #10622486C22semidirect
30. #10622485C22semidirect
32. C11×#367C22semidirect
33. C11×#366C22semidirect
34. #10622140C22semidirect
35. C16×Dic11C22semidirect
36. #10622130C22semidirect
37. #10622130C22semidirect
40. #10622129C22semidirect
41. #10622129C22semidirect
52. #66957C2×C4semidirect
55. C2×D88C2×C4semidirect
68. C11×M32C2×C4semidirect
84. #66864C2×C4semidirect
85. D176C2×C4semidirect
142. #2159D11semidirect
199. #367C2×D11semidirect
200. #366C2×D11semidirect
257. M32C4×D11semidirect
327. C11#33454semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
#130774902
#130774672
#130704912
#130704792
#130704672
#130704622
#130703212
C2×#106221292
#130702152
C11×#21592
#3345411