Finite Group Databasebeta

← #14907231

Subgroups — #14907231

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081752C211yesmaximal, characteristic
2#13077532C211yesmaximal, characteristic, complemented
3#13077499C211yesmaximal, characteristic, complemented
4#13070513C214yesmaximal, complemented
5#13070506C214yesmaximal, complemented
6#13070363C211yesmaximal, characteristic, complemented
7C2×#10622126C211yesmaximal, characteristic, complemented
8#13070220C211yesmaximal, characteristic, complemented
9C2×C11×#365C211yesmaximal, characteristic, complemented
10#10623276—21no—
11C2×#66957C2211yescharacteristic
12C2×#66957C2211yescharacteristic
13#10623035—21no—
14C2×C11×M32C2211yescharacteristic
15C2×C11×#108C2211yescharacteristic
16C2×C11×#106C2211yescharacteristic
17#10622752—21no—
18#10622714C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622579—21no—
21#10622522C412yescomplemented
22#10622522C2212yes—
23#10622521C412yescomplemented
24#10622521C2212yes—
25#10622517C414yescomplemented
26#10622508—22no—
27#10622507C2214yes—
28#10622482C2212yescomplemented
29#10622466C2212yescomplemented
30#10622465—22no—
31C11×#365C2214yescomplemented
32#10622150C2214yescomplemented
33#10622134C2212yescomplemented
34#10622133C2212yescomplemented
35#10622126C2214yes—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×C11×M16—21no—
39C22×C8×C11C2311yescharacteristic
40C2×C11×C4⋊C4—21no—
41C4×C22⋊D11—42no—
42#66979D411yescharacteristic
43C2×#4318D411yescharacteristic
44#66960—24no—
45M16×D11—42no—
46C2×Dic44C2×C411yescharacteristic, complemented
47C2×Dic44C2311yescharacteristic
48#66957—21no—
49#66957—21no—
50#66957—21no—
51#66957—21no—
52#66957C2×C412yes—
53#66957C2×C412yes—
54#66957C2×C412yescomplemented
55#66957C2312yes—
56C2×D88C2×C411yescharacteristic, complemented
57C2×D88C2311yescharacteristic
58C2×#4314—21no—
59C2×#4314—21no—
60#66954—42no—
61#66946—22no—
62#66945—41no—
63C4⋊C4×D11—41no—
64#66940—22no—
65C11×M32C2×C412yescomplemented
66C11×M32C2312yes—
67C2×C11×C16C2×C412yescomplemented
68C11×#108—21no—
69C11×#108C2312yes—
70C11×#106—21no—
71C11×#106C2312yes—
72#66889—24no—
73#66879C2312yes—
74C8×Dic11D412yes—
75#66876—21no—
76#66876C2312yes—
77C2×C11⋊C16—21no—
78#66874—22no—
79#66873—22no—
80Dic88C2×C414yescomplemented
81#66864C2×C414yescomplemented
82#66864C2×C414yescomplemented
83D176C2×C414yescomplemented
84#33469—111nomaximal, Sylow
85C22×C4×C11—41no—
86C22×C4×C11C2×D411yescharacteristic
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89#4339—22no—
90#4339—22no—
91#4339—22no—
92#4339—22no—
93#4339—41no—
94#4339—41no—
95#4339—41no—
96#4339—41no—
97C2×D44—21no—
98C2×D44—21no—
99C2×C4×D11—42no—
100C2×C4×D11—41no—
101C2×C4×D11—41no—
102C2×Dic22—21no—
103C2×Dic22—21no—
104C11×M16—22no—
105C11×M16—41no—
106C2×C8×C11—41no—
107C2×C8×C11C22×C411yescharacteristic
108C2×C8×C11C22×C411yescharacteristic
109C2×C8×C11C2×D411yescharacteristic
110C2×C8×C11#4111yescharacteristic
111C2×C8×C11#4111yescharacteristic
112C2×C8×C11C2411yescharacteristic
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C22⋊Dic11—21no—
116(C2×D11)⋊C4—42no—
117C4⋊Dic11—21no—
118Dic11⋊C4—42no—
119C4×Dic11—42no—
120C4×Dic11C2×D412yes—
121#4318—21no—
122#4318—21no—
123C2×C11⋊C8C2×D412yes—
124Dic44—21no—
125Dic44—21no—
126Dic44C22×C412yes—
127Dic44C22×C412yes—
128D88—21no—
129D88—21no—
130D88C22×C412yes—
131D88C22×C412yes—
132#4314—22no—
133#4314—22no—
134#4314—22no—
135#4314—22no—
136#4313—44no—
137C8×D11—44no—
138C11×C16C22×C414yes—
139C11⋊C16—22no—
140#3414—111no—
141#2957—111no—
142#2952—111no—
143AGL(1,ℤ/16)—114no—
144#2180—114no—
145C2×#365D1111yescharacteristic, complemented
146#2148—111no—
147C2×#360—111no—
148#2110—111no—
149C23×C11AGL(1,ℤ/8)11yescharacteristic
150C22×D11—41no—
151C22×D11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—161no—
154C2×C4×C11C4×D411yescharacteristic
155C2×C4×C11C4×D411yescharacteristic
156C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C22⋊D11—42no—
161C22⋊D11—42no—
162C22⋊D11—42no—
163C22⋊D11—42no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—41no—
167D44—22no—
168D44—22no—
169D44—41no—
170D44—41no—
171C4×D11—42no—
172C4×D11—42no—
173C4×D11—42no—
174C4×D11—42no—
175C4×D11—162no—
176Dic22—22no—
177Dic22—22no—
178Dic22—41no—
179Dic22—41no—
180C8×C11—42no—
181C8×C11C4×D411yescharacteristic
182C8×C11C4×D411yescharacteristic
183C8×C11C23×C411yescharacteristic
184C8×C11C2×#4111yescharacteristic
185C11⋊C8—22no—
186C2×#135—111no—
187C2×#135—111no—
188#568—221no—
189#520—221no—
190#510—112no—
191#510—112no—
192#509—112no—
193#509—112no—
194#508—114no—
195C2×M32—111no—
196C2×M32C2×D1111yescharacteristic
197#444—114no—
198#443—222no—
199#442—112no—
200#441—112no—
201C4×SD16—222no—
202C2×#108C2×D1111yescharacteristic
203C2×#106C2×D1111yescharacteristic
204#421—221no—
205#417—221no—
206#405—111no—
207#365C2×D1114yescomplemented
208#362—112no—
209#361—112no—
210#360—114no—
211#347—114no—
212C22×C11—41no—
213C22×C11#44211yescharacteristic
214C22×C11#44211yescharacteristic
215C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—81no—
219C2×D11—81no—
220C2×D11—161no—
221C4×C11—82no—
222C4×C11#44211yescharacteristic
223C4×C11#44211yescharacteristic
224C4×C11C2×C4×D411yescharacteristic
225C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
226Dic11—42no—
227Dic11—42no—
228Dic11—42no—
229C2×#41—221no—
230C2×#41—221no—
231#135—112no—
232#135—112no—
233#135—112no—
234#135—112no—
235#135—221no—
236#135—221no—
237#135—221no—
238#135—221no—
239C2×Q16—111no—
240C2×Q16—111no—
241C2×SD16—221no—
242C2×SD16—221no—
243C2×D8—111no—
244C2×D8—111no—
245#131—224no—
246#131—442no—
247C2×M16—21no—
248C2×M16—111no—
249C2×M16—442no—
250C22×C8C22×D1111yescharacteristic
251C4×Q8—222no—
252C4×D4—222no—
253C4×D4—442no—
254#117—111no—
255#117—441no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—441no—
258Q32—114no—
259SD32—114no—
260SD32—114no—
261D16—114no—
262M32—112no—
263M32—221no—
264M32C4×D1112yescomplemented
265M32C22×D1112yes—
266C2×C16—221no—
267C2×C16C4×D1112yescomplemented
268#108—21no—
269#108C22×D1112yes—
270#106—21no—
271#106C22×D1112yes—
272#104—224no—
273#103—222no—
274#102—222no—
275#97—112no—
276C4×C8—112no—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11C2×#44211yescharacteristic
281D11—82no—
282D11—82no—
283#41—222no—
284#41—222no—
285#41—222no—
286#41—222no—
287#41—441no—
288#41—441no—
289#41—441no—
290#41—441no—
291C2×Q8—221no—
292C2×Q8—221no—
293C2×D4—221no—
294C2×D4—221no—
295C2×D4—441no—
296C2×D4—441no—
297C22×C4—41no—
298C22×C4—442no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4D4×D1111yescharacteristic
302Q16—112no—
303Q16—112no—
304Q16—221no—
305Q16—221no—
306SD16—222no—
307SD16—222no—
308SD16—222no—
309SD16—222no—
310D8—112no—
311D8—112no—
312D8—221no—
313D8—221no—
314M16—22no—
315M16—41no—
316M16—221no—
317M16—221no—
318M16—444no—
319C2×C8—41no—
320C2×C8—112no—
321C2×C8—444no—
322C2×C8C2×C4×D1111yescharacteristic
323C2×C8C2×C4×D1111yescharacteristic
324C2×C8D4×D1111yescharacteristic
325C2×C8#434311yescharacteristic
326C2×C8#434311yescharacteristic
327C2×C8C23×D1111yescharacteristic
328C4⋊C4—22no—
329C4⋊C4—41no—
330C4⋊C4—221no—
331C4⋊C4—442no—
332C22⋊C4—221no—
333C22⋊C4—442no—
334C42—112no—
335C42—442no—
336C16—222no—
337C16C2×C4×D1114yes—
338C11#3346911yescharacteristic, complemented, Sylow
339C23—441no—
340C23—441no—
341C23#6696711yescharacteristic
342Q8—222no—
343Q8—222no—
344Q8—441no—
345Q8—441no—
346D4—222no—
347D4—222no—
348D4—442no—
349D4—442no—
350D4—442no—
351D4—442no—
352D4—441no—
353D4—441no—
354C2×C4—42no—
355C2×C4—161no—
356C2×C4—222no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—1762no—
364C2×C4#6694611yescharacteristic
365C2×C4#6694611yescharacteristic
366C2×C4#6696711yescharacteristic
367C2×C4#6696711yescharacteristic
368C2×C4#6696711yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C8—42no—
371C8—222no—
372C8#6694611yescharacteristic
373C8#6694611yescharacteristic
374C8C22×C4×D1111yescharacteristic
375C8C2×#434311yescharacteristic
376C22—41no—
377C22—442no—
378C22—442no—
379C22—881no—
380C22—881no—
381C22—1761no—
382C22#1062248211yescharacteristic
383C22#1062248211yescharacteristic
384C22C2×#6696711yescharacteristic
385C4—82no—
386C4—442no—
387C4—442no—
388C4—442no—
389C4#1062248211yescharacteristic
390C4#1062248211yescharacteristic
391C4C2×#6694611yescharacteristic
392C4C2×#6696711yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—882no—
397C2—882no—
398C2C2×#1062248211yescharacteristic
subgroupG/H
centerC2C2×#10622482
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#365C2
socleC2×C11C2×#442
prime radical#13081752C2
cosocleC2×C8×C11C24
hypercenterC2×#365D11
hypocenterC11#33469
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
2. #13077532C2semidirect
3. #13077499C2semidirect
4. #13070513C2semidirect
5. #13070506C2semidirect
6. #13070363C2semidirect
7. C2×#10622126C2semidirect
8. #13070220C2semidirect
9. C2×C11×#365C2semidirect
21. #10622522C4semidirect
23. #10622521C4semidirect
25. #10622517C4semidirect
28. #10622482C22semidirect
29. #10622466C22semidirect
31. C11×#365C22semidirect
32. #10622150C22semidirect
33. #10622134C22semidirect
34. #10622133C22semidirect
46. C2×Dic44C2×C4semidirect
54. #66957C2×C4semidirect
56. C2×D88C2×C4semidirect
65. C11×M32C2×C4semidirect
67. C2×C11×C16C2×C4semidirect
80. Dic88C2×C4semidirect
81. #66864C2×C4semidirect
82. #66864C2×C4semidirect
83. D176C2×C4semidirect
145. C2×#365D11semidirect
207. #365C2×D11semidirect
264. M32C4×D11semidirect
267. C2×C16C4×D11semidirect
338. C11#33469semidirect

Maximal subgroups

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

subgroupindex
#130817522
#130775322
#130774992
#130705132
#130705062
#130703632
C2×#106221262
#130702202
C2×C11×#3652
#3346911