Finite Group Databasebeta

← #14908361

Subgroups — #14908361

Order 2816.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622806C211yesmaximal, characteristic, complemented
2#13081719C211yesmaximal, characteristic, complemented
3C2×#10622755C211yesmaximal, characteristic, complemented
4#13070748C214yesmaximal, complemented
5#13070734C214yesmaximal, complemented
6#13070410C211yesmaximal, characteristic, complemented
7#13070365C211yesmaximal, characteristic, complemented
8C2×#10622133C211yesmaximal, characteristic, complemented
9C11×#3067C211yesmaximal, characteristic, complemented
10C11×#575—21no—
11C2×C11×#135C2211yescharacteristic
12C2×C11×#131C2211yescharacteristic
13C2×#67002—21no—
14C22×D88C2211yescharacteristic
15C11×#473C2212yescomplemented
16C11×#472C2212yescomplemented
17C11×#471—22no—
18C2×C11×#108C2211yescharacteristic
19C11×#413—21no—
20#10622806—22no—
21#10622806—22no—
22C2×#66892C2212yescomplemented
23C2×#66890C2212yescomplemented
24#10622755—22no—
25#10622755C2214yes—
26#10622753—22no—
27#10622753C2214yescomplemented
28C2×#66887—21no—
29C2×#66883C2211yescharacteristic
30C2×#66876—22no—
31C2×#66876C2211yescharacteristic
32C2×#66876C2211yescharacteristic
33#10622203C2212yescomplemented
34#10622201C2212yescomplemented
35#10622133C2214yescomplemented
36#10622131C2214yescomplemented
37C2×C11×#41—21no—
38C2×C11×#41D411yescharacteristic
39C22×D44—21no—
40C11×#137—22no—
41C11×#137—41no—
42C11×AGL(1,ℤ/8)—22no—
43C11×AGL(1,ℤ/8)—41no—
44C11×#135—21no—
45C11×#135—21no—
46C11×#135—21no—
47C11×#135—21no—
48C11×#135—42no—
49C2×C11×Q16C2311yescharacteristic
50C2×C11×SD16—21no—
51C2×C11×D8C2311yescharacteristic
52C11×#131—21no—
53C11×#131—21no—
54C11×#131D412yes—
55C11×#131C2312yes—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16D411yescharacteristic
59C22×C8×C11—21no—
60C22×C8×C11C2311yescharacteristic
61#67002—24no—
62#67002—42no—
63C2×#4325—41no—
64C2×#4323—41no—
65C2×#4318—21no—
66C2×D88—21no—
67C2×D88—21no—
68C2×D88—21no—
69C2×D88—21no—
70C2×D88—21no—
71C2×D88C2312yes—
72C11×#108—21no—
73C11×#108C2312yes—
74C11×#101—22no—
75C11×#100—22no—
76#66892—24no—
77#66890—24no—
78#66887—24no—
79#66883—21no—
80#66883C2312yes—
81#66876—21no—
82#66876—24no—
83#66876D412yes—
84#66876D412yes—
85#66876C2312yes—
86C2×C11⋊C16—21no—
87C2×C11⋊C16—24no—
88C2×C11⋊C16C2312yes—
89#33618—111nomaximal, Sylow
90C23×D11—41no—
91C11×#41—21no—
92C11×#41—21no—
93C11×#41—41no—
94C11×#41—41no—
95C11×#41—41no—
96C11×#41—41no—
97C11×#41D812yes—
98C11×#41C2×D412yes—
99C2×Q8×C11—21no—
100C2×Q8×C11D811yescharacteristic
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—41no—
104C2×D4×C11D811yescharacteristic
105C22×C4×C11—21no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C2×D44—22no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—41no—
114C11×Q16—21no—
115C11×Q16—21no—
116C11×Q16—42no—
117C11×SD16—41no—
118C11×SD16—41no—
119C11×SD16—42no—
120C11×SD16—42no—
121C11×D8—21no—
122C11×D8—21no—
123C11×D8—42no—
124C11×M16—22no—
125C11×M16—22no—
126C11×M16—21no—
127C11×M16—22no—
128C11×M16—41no—
129C11×M16C2×D412yes—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—21no—
133C2×C8×C11—41no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2×D411yescharacteristic
136C2×C8×C11C2×D411yescharacteristic
137C2×C8×C11#4111yescharacteristic
138C2×C8×C11#4111yescharacteristic
139C2×C8×C11C2411yescharacteristic
140#4325—44no—
141#4323—44no—
142#4318—22no—
143#4318—41no—
144C2×C11⋊C8—41no—
145D88—22no—
146D88—22no—
147D88—41no—
148D88—41no—
149C11⋊C16—22no—
150C11⋊C16C2×D414yes—
151C2×#509—111no—
152#3407—111no—
153#3067D1111yescharacteristic, complemented
154C2×#472—111no—
155#2223—114no—
156#2221—114no—
157#2161—111no—
158#2148—111no—
159C2×#361—111no—
160C23×C11—21no—
161C23×C11—41no—
162C23×C11#13511yescharacteristic
163C22×D11—42no—
164C22×D11—81no—
165C22×D11—81no—
166C22×D11—162no—
167Q8×C11—21no—
168Q8×C11—41no—
169Q8×C11—41no—
170Q8×C11C2×D812yes—
171D4×C11—22no—
172D4×C11—22no—
173D4×C11—21no—
174D4×C11—41no—
175D4×C11—41no—
176D4×C11—81no—
177D4×C11—81no—
178D4×C11C2×D812yes—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11—81no—
184C2×C4×C11—81no—
185C2×C4×C11#12111yescharacteristic
186C2×C4×C11#12111yescharacteristic
187C2×C4×C11C2×D811yescharacteristic
188C2×C4×C11C2×D811yescharacteristic
189C2×C4×C11#13511yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191D44—42no—
192D44—42no—
193D44—81no—
194D44—81no—
195C8×C11—22no—
196C8×C11—42no—
197C8×C11#12111yescharacteristic
198C8×C11#12111yescharacteristic
199C8×C11C22×D411yescharacteristic
200C8×C11C2×#4111yescharacteristic
201C11⋊C8—42no—
202#575—21no—
203C2×AGL(1,ℤ/8)—221no—
204C2×#135C2×D1111yescharacteristic
205C22×D8—111no—
206C2×#131C2×D1111yescharacteristic
207#509—222no—
208#509—222no—
209C2×SD32—112no—
210C2×D16—112no—
211#504—114no—
212#504—222no—
213C2×M32—111no—
214C2×M32—111no—
215C2×M32—222no—
216#473C2×D1112yescomplemented
217#472—114no—
218#472—222no—
219#472C2×D1112yescomplemented
220#471—22no—
221C2×#108—111no—
222C2×#108C2×D1111yescharacteristic
223#413—21no—
224C2×#100—221no—
225#368—114no—
226#362—112no—
227#361—112no—
228#361—114no—
229C22×C11—22no—
230C22×C11—41no—
231C22×C11—81no—
232C22×C11—81no—
233C22×C11—161no—
234C22×C11#46611yescharacteristic
235C22×C11#46611yescharacteristic
236C22×C11C2×#13511yescharacteristic
237C2×D11—82no—
238C2×D11—162no—
239C2×D11—162no—
240C2×D11—162no—
241C4×C11—22no—
242C4×C11—81no—
243C4×C11#46611yescharacteristic
244C4×C11#46611yescharacteristic
245C4×C11C2×#12111yescharacteristic
246C4×C11C22×D811yescharacteristic
247C2×#41—21no—
248C2×#41C22⋊D1111yescharacteristic
249C22×D4—221no—
250#137—22no—
251#137—41no—
252AGL(1,ℤ/8)—22no—
253AGL(1,ℤ/8)—41no—
254AGL(1,ℤ/8)—224no—
255AGL(1,ℤ/8)—442no—
256#135—21no—
257#135—21no—
258#135—21no—
259#135—21no—
260#135—42no—
261C2×Q16C22×D1111yescharacteristic
262C2×SD16—21no—
263C2×SD16—441no—
264C2×D8—112no—
265C2×D8—221no—
266C2×D8—221no—
267C2×D8—221no—
268C2×D8—221no—
269C2×D8—221no—
270C2×D8—441no—
271C2×D8C22×D1111yescharacteristic
272#131—21no—
273#131—21no—
274#131C22⋊D1112yes—
275#131C22×D1112yes—
276C2×M16—21no—
277C2×M16—21no—
278C2×M16—221no—
279C2×M16C22⋊D1111yescharacteristic
280C22×C8—21no—
281C22×C8C22×D1111yescharacteristic
282SD32—224no—
283D16—224no—
284M32—112no—
285M32—112no—
286M32—112no—
287M32—224no—
288M32—221no—
289C2×C16—112no—
290C2×C16—224no—
291C2×C16—221no—
292#108—21no—
293#108—112no—
294#108—221no—
295#108C22×D1112yes—
296#101—22no—
297#100—22no—
298#100—224no—
299C2×C11—21no—
300C2×C11—21no—
301C2×C11—21no—
302C2×C11—42no—
303C2×C11—161no—
304C2×C11C2×#46611yescharacteristic
305D11—162no—
306C24—441no—
307#41—21no—
308#41—21no—
309#41—41no—
310#41—41no—
311#41—41no—
312#41—41no—
313#41#432312yes—
314#41C2×C22⋊D1112yes—
315C2×Q8—21no—
316C2×Q8#432311yescharacteristic
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—41no—
320C2×D4—222no—
321C2×D4—441no—
322C2×D4—441no—
323C2×D4—441no—
324C2×D4—441no—
325C2×D4—441no—
326C2×D4#432311yescharacteristic
327C22×C4—21no—
328C22×C4—41no—
329C22×C4C2×C22⋊D1111yescharacteristic
330Q16—21no—
331Q16—21no—
332Q16—42no—
333SD16—42no—
334SD16—42no—
335SD16—41no—
336SD16—41no—
337SD16—444no—
338D8—21no—
339D8—21no—
340D8—42no—
341D8—222no—
342D8—222no—
343D8—444no—
344D8—441no—
345D8—441no—
346M16—21no—
347M16—22no—
348M16—22no—
349M16—22no—
350M16—41no—
351M16—222no—
352M16—441no—
353M16C2×C22⋊D1112yes—
354C2×C8—21no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—41no—
358C2×C8—441no—
359C2×C8D4×D1111yescharacteristic
360C2×C8D4×D1111yescharacteristic
361C2×C8#434111yescharacteristic
362C2×C8#434111yescharacteristic
363C2×C8C2×C22⋊D1111yescharacteristic
364C2×C8C23×D1111yescharacteristic
365C16—114no—
366C16—222no—
367C11#3361811yescharacteristic, complemented, Sylow
368C23—21no—
369C23—41no—
370C23—442no—
371C23—881no—
372C23—881no—
373C23—1762no—
374C23#6700311yescharacteristic
375Q8—21no—
376Q8—41no—
377Q8—41no—
378Q8C2×#432312yes—
379D4—22no—
380D4—22no—
381D4—21no—
382D4—41no—
383D4—41no—
384D4—81no—
385D4—81no—
386D4—442no—
387D4—442no—
388D4—881no—
389D4—881no—
390D4C2×#432312yes—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4C2×#432311yescharacteristic
398C2×C4C2×#432311yescharacteristic
399C2×C4#6699211yescharacteristic
400C2×C4#6699211yescharacteristic
401C2×C4#6700311yescharacteristic
402C2×C4C22×C22⋊D1111yescharacteristic
403C8—22no—
404C8—42no—
405C8—442no—
406C8#6699211yescharacteristic
407C8#6699211yescharacteristic
408C8C2×D4×D1111yescharacteristic
409C8C2×#434111yescharacteristic
410C22—22no—
411C22—41no—
412C22—81no—
413C22—81no—
414C22—161no—
415C22—882no—
416C22—1762no—
417C22—1762no—
418C22—1762no—
419C22#1062265111yescharacteristic
420C22#1062265111yescharacteristic
421C22C2×#6700311yescharacteristic
422C4—22no—
423C4—81no—
424C4#1062265111yescharacteristic
425C4#1062265111yescharacteristic
426C4C22×#432311yescharacteristic
427C4C2×#6699211yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—42no—
432C2—161no—
433C2—1762no—
434C2C2×#1062265111yescharacteristic
subgroupG/H
centerC2C2×#10622651
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3067C2
socleC2×C11C2×#466
hypercenter#3067D11
hypocenterC11#33618
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. C2×#10622806C2semidirect
2. #13081719C2semidirect
3. C2×#10622755C2semidirect
4. #13070748C2semidirect
5. #13070734C2semidirect
6. #13070410C2semidirect
7. #13070365C2semidirect
8. C2×#10622133C2semidirect
9. C11×#3067C2semidirect
15. C11×#473C22semidirect
16. C11×#472C22semidirect
22. C2×#66892C22semidirect
23. C2×#66890C22semidirect
27. #10622753C22semidirect
33. #10622203C22semidirect
34. #10622201C22semidirect
35. #10622133C22semidirect
36. #10622131C22semidirect
153. #3067D11semidirect
216. #473C2×D11semidirect
219. #472C2×D11semidirect
367. C11#33618semidirect

Maximal subgroups

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

subgroupindex
C2×#106228062
#130817192
C2×#106227552
#130707482
#130707342
#130704102
#130703652
C2×#106221332
C11×#30672
#3361811